<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.2 20190208//EN"  "JATS-archivearticle1.dtd"><article article-type="research-article" dtd-version="1.2" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn pub-type="epub" publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">67336</article-id><article-id pub-id-type="doi">10.7554/eLife.67336</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research Article</subject></subj-group><subj-group subj-group-type="heading"><subject>Evolutionary Biology</subject></subj-group></article-categories><title-group><article-title>Contingency and chance erase necessity in the experimental evolution of ancestral proteins</article-title></title-group><contrib-group><contrib contrib-type="author" equal-contrib="yes" id="author-226293"><name><surname>Xie</surname><given-names>Victoria Cochran</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund5"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" equal-contrib="yes" id="author-226294"><name><surname>Pu</surname><given-names>Jinyue</given-names></name><email>pujy@uchicago.edu</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" equal-contrib="yes" id="author-110238"><name><surname>Metzger</surname><given-names>Brian PH</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-4878-2913</contrib-id><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund4"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-11193"><name><surname>Thornton</surname><given-names>Joseph W</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0001-9589-6994</contrib-id><email>joet1@uchicago.edu</email><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-96113"><name><surname>Dickinson</surname><given-names>Bryan C</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0002-9616-1911</contrib-id><email>Dickinson@uchicago.edu</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="other" rid="fund6"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf3"/></contrib><aff id="aff1"><label>1</label><institution>Department of Chemistry, University of Chicago</institution><addr-line><named-content content-type="city">Chicago</named-content></addr-line><country>United States</country></aff><aff id="aff2"><label>2</label><institution>Department of Ecology and Evolution, University of Chicago</institution><addr-line><named-content content-type="city">Chicago</named-content></addr-line><country>United States</country></aff><aff id="aff3"><label>3</label><institution>Department of Human Genetics, University of Chicago</institution><addr-line><named-content content-type="city">Chicago</named-content></addr-line><country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Courtier-Orgogozo</surname><given-names>Virginie</given-names></name><role>Reviewing Editor</role><aff><institution>Université Paris-Diderot CNRS</institution><country>France</country></aff></contrib><contrib contrib-type="senior_editor"><name><surname>Przeworski</surname><given-names>Molly</given-names></name><role>Senior Editor</role><aff><institution>Columbia University</institution><country>United States</country></aff></contrib></contrib-group><author-notes><fn fn-type="con" id="equal-contrib1"><label>†</label><p>These authors contributed equally to this work</p></fn></author-notes><pub-date date-type="publication" publication-format="electronic"><day>01</day><month>06</month><year>2021</year></pub-date><pub-date pub-type="collection"><year>2021</year></pub-date><volume>10</volume><elocation-id>e67336</elocation-id><history><date date-type="received" iso-8601-date="2021-02-08"><day>08</day><month>02</month><year>2021</year></date><date date-type="accepted" iso-8601-date="2021-05-30"><day>30</day><month>05</month><year>2021</year></date></history><permissions><copyright-statement>© 2021, Xie et al</copyright-statement><copyright-year>2021</copyright-year><copyright-holder>Xie et al</copyright-holder><ali:free_to_read/><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref>http://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife-67336-v2.pdf"/><abstract><p>The roles of chance, contingency, and necessity in evolution are unresolved because they have never been assessed in a single system or on timescales relevant to historical evolution. We combined ancestral protein reconstruction and a new continuous evolution technology to mutate and select proteins in the B-cell lymphoma-2 (BCL-2) family to acquire protein–protein interaction specificities that occurred during animal evolution. By replicating evolutionary trajectories from multiple ancestral proteins, we found that contingency generated over long historical timescales steadily erased necessity and overwhelmed chance as the primary cause of acquired sequence variation; trajectories launched from phylogenetically distant proteins yielded virtually no common mutations, even under strong and identical selection pressures. Chance arose because many sets of mutations could alter specificity at any timepoint; contingency arose because historical substitutions changed these sets. Our results suggest that patterns of variation in BCL-2 sequences – and likely other proteins, too – are idiosyncratic products of a particular and unpredictable course of historical events.</p></abstract><abstract abstract-type="executive-summary"><title>eLife digest</title><p>One of the most fundamental and unresolved questions in evolutionary biology is whether the outcomes of evolution are predictable. Is the diversity of life we see today the expected result of organisms adapting to their environment throughout history (also known as natural selection) or the product of random chance? Or did chance events early in history shape the paths that evolution could take next, determining the biological forms that emerged under natural selection much later?</p><p>These questions are hard to study because evolution happened only once, long ago. To overcome this barrier, Xie, Pu, Metzger et al. developed an experimental approach that can evolve reconstructed ancestral proteins that existed deep in the past. Using this method, it is possible to replay evolution multiple times, from various historical starting points, under conditions similar to those that existed long ago. The end products of the evolutionary trajectories can then be compared to determine how predictable evolution actually is.</p><p>Xie, Pu, Metzger et al. studied proteins belonging to the BCL-2 family, which originated some 800 million years ago. These proteins have diversified greatly over time in both their genetic sequences and their ability to bind to specific partner proteins called co-regulators. Xie, Pu, Metzger et al. synthesized BCL-2 proteins that existed at various times in the past. Each ancestral protein was then allowed to evolve repeatedly under natural selection to acquire the same co-regulator binding functions that evolved during history.</p><p>At the end of each evolutionary trajectory, the genetic sequence of the resulting BCL-2 proteins was recorded. This revealed that the outcomes of evolution were almost completely unpredictable: trajectories initiated from the same ancestral protein produced proteins with very different sequences, and proteins launched from different ancestral starting points were even more dissimilar.</p><p>Further experiments identified the mutations in each trajectory that caused changes in coregulator binding. When these mutations were introduced into other ancestral proteins, they did not yield the same change in function. This suggests that early chance events influenced each protein’s evolution in an unpredictable way by opening and closing the paths available to it in the future.</p><p>This research expands our understanding of evolution on a molecular level whilst providing a new experimental approach for studying evolutionary drivers in more detail. The results suggest that BCL-2 proteins, in all their various forms, are unique products of a particular, unpredictable course of history set in motion by ancient chance events.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>PACE</kwd><kwd>continuous directed evolution</kwd><kwd>protein-protein interactions</kwd><kwd>genetic variance</kwd><kwd>epistasis</kwd><kwd>ancestral protein reconstruction</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd><italic>E. coli</italic></kwd></kwd-group><funding-group><award-group id="fund1"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01GM131128</award-id><principal-award-recipient><name><surname>Thornton</surname><given-names>Joseph W</given-names></name></principal-award-recipient></award-group><award-group id="fund2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01GM121931</award-id><principal-award-recipient><name><surname>Thornton</surname><given-names>Joseph W</given-names></name></principal-award-recipient></award-group><award-group id="fund3"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01GM139007</award-id><principal-award-recipient><name><surname>Thornton</surname><given-names>Joseph W</given-names></name></principal-award-recipient></award-group><award-group id="fund4"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>F32GM122251</award-id><principal-award-recipient><name><surname>Metzger</surname><given-names>Brian PH</given-names></name></principal-award-recipient></award-group><award-group id="fund5"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000001</institution-id><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>DGE-1746045</award-id><principal-award-recipient><name><surname>Xie</surname><given-names>Victoria Cochran</given-names></name></principal-award-recipient></award-group><award-group id="fund6"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000001</institution-id><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>1749364</award-id><principal-award-recipient><name><surname>Dickinson</surname><given-names>Bryan C</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Replicating experimental evolution from ancestral proteins shows that historical contingency steadily overwhelms chance and necessity as the primary cause of evolutionary variation in molecular sequences on long phylogenetic timescales.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>The extent to which biological diversity is the necessary result of optimization by natural selection or the unpredictable product of random events and historical contingency is one of evolutionary biology’s most fundamental and unresolved questions (<xref ref-type="bibr" rid="bib36">Gould, 1989</xref>; <xref ref-type="bibr" rid="bib43">Jablonski, 2017</xref>; <xref ref-type="bibr" rid="bib77">Ramsey and Pence, 2016</xref>; <xref ref-type="bibr" rid="bib96">Travisano et al., 1995</xref>). The answer would have strong implications not only for our understanding of evolutionary processes but also for how we should analyze the particular forms of variation that exist today. For example, if diversity primarily reflects a predictable process of adaptation to distinct environments, then a central goal of biology would be to explain how the characteristics of living things help to execute particular functions and improve fitness (<xref ref-type="bibr" rid="bib57">Mayr, 1983</xref>). By contrast, if diversity reflects chance sampling from a set of similarly fit possibilities, then the variation itself is of little interest because it does not affect biological properties or shape future evolutionary outcomes; the goal of biology would be to identify the invariant characteristics of natural systems and explain how they contribute to function (<xref ref-type="bibr" rid="bib49">Kimura, 1983</xref>; <xref ref-type="bibr" rid="bib55">Lobkovsky and Koonin, 2012</xref>; <xref ref-type="bibr" rid="bib62">Monod, 1972</xref>; <xref ref-type="bibr" rid="bib64">Morris, 2015</xref>). Finally, if diversity reflects contingency – a strong dependence of future outcomes on initial conditions or subsequent events, also known as path-dependence – then the outcomes of evolution would be predictable only given complete knowledge of the constraints and opportunities specific to each set of conditions (<xref ref-type="bibr" rid="bib8">Beatty, 2009</xref>; <xref ref-type="bibr" rid="bib13">Blount et al., 2018</xref>; <xref ref-type="bibr" rid="bib26">Desjardins, 2011</xref>; <xref ref-type="bibr" rid="bib37">Gould and Lewontin, 1979</xref>); the goal of biology would then be to characterize these constraints and opportunities, their mechanistic causes, and the historical events that shaped them.</p><p>Many studies have provided insight into the ways that chance, contingency, and necessity can affect the evolution of molecular sequences and functions, but the relative importance of these factors during evolutionary history remains unresolved because they have never been measured in the same system, and their effects over long evolutionary time scales have not been characterized. For example, experiments on ancestral proteins have shown that particular historical mutations have different effects when introduced into different ancestral backgrounds – suggesting contingency – but they do not reveal the extent to which context-dependence actually influenced evolutionary outcomes; further, these historical trajectories happened only once, so they cannot elucidate the effect of contingency relative to chance (<xref ref-type="bibr" rid="bib10">Bloom et al., 2010</xref>; <xref ref-type="bibr" rid="bib16">Bridgham et al., 2009</xref>; <xref ref-type="bibr" rid="bib34">Gong et al., 2013</xref>; <xref ref-type="bibr" rid="bib38">Harms and Thornton, 2014</xref>; <xref ref-type="bibr" rid="bib58">McKeown et al., 2014</xref>; <xref ref-type="bibr" rid="bib65">Natarajan et al., 2016</xref>; <xref ref-type="bibr" rid="bib68">Ortlund et al., 2007</xref>; <xref ref-type="bibr" rid="bib81">Risso et al., 2015</xref>; <xref ref-type="bibr" rid="bib91">Starr et al., 2018</xref>; <xref ref-type="bibr" rid="bib101">Wu et al., 2018</xref>). Experimental evolution studies could, in principle, characterize both chance and contingency if they had sufficient replication from multiple starting points, but to date no study has done so; furthermore, no study has imposed selection on historical proteins to acquire functions that changed during history, so their relevance to historical evolution is not clear (<xref ref-type="bibr" rid="bib6">Baier et al., 2019</xref>; <xref ref-type="bibr" rid="bib12">Blount et al., 2012</xref>; <xref ref-type="bibr" rid="bib14">Bollback and Huelsenbeck, 2009</xref>; <xref ref-type="bibr" rid="bib23">Couñago et al., 2006</xref>; <xref ref-type="bibr" rid="bib27">Dickinson et al., 2013</xref>; <xref ref-type="bibr" rid="bib45">Kacar et al., 2017</xref>; <xref ref-type="bibr" rid="bib53">Kryazhimskiy et al., 2014</xref>; <xref ref-type="bibr" rid="bib60">Meyer et al., 2012</xref>; <xref ref-type="bibr" rid="bib83">Salverda et al., 2011</xref>; <xref ref-type="bibr" rid="bib89">Spor et al., 2014</xref>; <xref ref-type="bibr" rid="bib97">van Ditmarsch et al., 2013</xref>; <xref ref-type="bibr" rid="bib100">Wichman et al., 1999</xref>; <xref ref-type="bibr" rid="bib102">Wünsche et al., 2017</xref>; <xref ref-type="bibr" rid="bib108">Zheng et al., 2019</xref>). Studies of phenotypic convergence in nature suggest some degree of repeatability at the genetic level (reviewed in <xref ref-type="bibr" rid="bib3">Arendt and Reznick, 2008</xref>; <xref ref-type="bibr" rid="bib33">Gompel and Prud'homme, 2009</xref>; <xref ref-type="bibr" rid="bib67">Orgogozo, 2015</xref>; <xref ref-type="bibr" rid="bib92">Storz, 2016</xref>), but these studies rarely involve replicate lineages from the same starting genotypes, and evolutionary conditions are seldom identical; as a result, similarities and differences among lineages cannot be attributed to chance, contingency, or necessity. Furthermore, these studies have typically involved closely related species or populations and therefore do not measure the effects of chance and contingency that might be generated during long-term evolution.</p><p>The ideal experiment to determine the relative roles of chance, contingency, and necessity in historical evolution would be to travel back in time, re-launch evolution multiple times from each of various starting points that existed during history, and allow these trajectories to play out under historical environmental conditions (<xref ref-type="bibr" rid="bib36">Gould, 1989</xref>). By comparing outcomes among replicates launched from the same starting point, we could estimate the effects of chance; by comparing those from different starting points, we could quantify the effects of contingency that was generated along historical evolutionary paths (<xref ref-type="fig" rid="fig1">Figure 1</xref>). Necessity would be apparent if the same outcome recurred in every replicate, irrespective of the point from which evolutionary trajectories were launched and changes that occurred subsequently: in that case, evolution would be both deterministic (free of chance) and insensitive to initial and intervening conditions (noncontingent). Although time travel is currently impossible, we can approximate this ideal design by reconstructing ancestral proteins as they existed in the deep past (<xref ref-type="bibr" rid="bib94">Thornton, 2004</xref>) and using them to launch replicated evolutionary trajectories in the laboratory under selection to acquire the same molecular functions that evolved during history.</p><fig id="fig1" position="float"><label>Figure 1.</label><caption><title>Assessing the effects of chance and contingency during evolution.</title><p>Each panel (A-D) shows the capacity of one experimental design to detect chance and contingency; the quadrants within each panel show evolutionary scenarios with varying degrees of chance and contingency. Chance (y-axis within each panel) is defined as random occurrence of events from a probability distribution in which multiple events have probability &gt; 0 given some defined starting point; in the absence of chance, evolution is deterministic because a single outcome always occurs from any starting genotype. Contingency (x-axis within each panel) is defined as differences in this probability distribution given different starting or subsequent conditions; in the absence of contingency, outcomes are insensitive to these conditions, and all starting points lead to the same outcome or set of outcomes. Lines connect starting genotypes (white circles) to evolutionary outcomes. Quadrants show evolution under the influence of chance (orange), contingency (blue), or both (black); outcomes are necessary (brown, with dotted line) when neither chance nor contingency is important. Potential trajectories that are not observed because of deficiencies in experimental design are shown with reduced opacity. Thick black lines between quadrants in (<bold>A</bold>–<bold>D</bold>) separate evolutionary scenarios that can be distinguished from each other given each design. (<bold>A</bold>) Assessing one evolutionary replicate from one starting point provides no information about the extent to which chance, contingency, or necessity shape the outcome. (<bold>B</bold>) Assessing multiple replicates from one starting point can detect chance but provides no information about contingency. (<bold>C</bold>) Assessing one replicate each from multiple starting points can detect necessity or its absence, but cannot not distinguish between chance and contingency. (<bold>D</bold>) Studying multiple replicates from multiple starting genotypes allows chance, contingency, and necessity to be distinguished.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig1-v2.tif"/></fig><p>Here we implement this strategy using the B-cell lymphoma-2 (BCL-2) protein family as a model system and the specificity of protein–protein interactions (PPIs) as the target of selection. BCL-2 family proteins are involved in the regulation of apoptosis (<xref ref-type="bibr" rid="bib22">Chipuk et al., 2010</xref>; <xref ref-type="bibr" rid="bib24">Danial and Korsmeyer, 2004</xref>; <xref ref-type="bibr" rid="bib46">Kale et al., 2018</xref>; <xref ref-type="bibr" rid="bib70">Petros et al., 2004</xref>) through PPIs with coregulators (<xref ref-type="bibr" rid="bib20">Chen et al., 2005</xref>; <xref ref-type="bibr" rid="bib21">Chen et al., 2013</xref>; <xref ref-type="bibr" rid="bib28">Dutta et al., 2010</xref>; <xref ref-type="bibr" rid="bib56">Lomonosova and Chinnadurai, 2008</xref>). Although there are many dimensions to BCL-2 family proteins’ cellular effects, different binding specificities for coregulator proteins are a critical determinant of their particular biological functions. Among BCL-2 family members, the myeloid cell leukemia sequence 1 protein (MCL-1) class strongly binds both the BID and NOXA coregulators, whereas the BCL-2 class (a subset of the larger BCL-2 protein family) strongly binds BID but not NOXA (<xref ref-type="fig" rid="fig2">Figure 2A</xref>; <xref ref-type="bibr" rid="bib18">Certo et al., 2006</xref>). The two classes share an ancient evolutionary origin: both are found throughout the Metazoa (<xref ref-type="bibr" rid="bib7">Banjara et al., 2020</xref>; <xref ref-type="bibr" rid="bib54">Lanave et al., 2004</xref>) and are structurally similar, using the same cleft to interact with their coregulators (<xref ref-type="fig" rid="fig2">Figure 2B</xref>, <xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>), despite having only 20% sequence identity.</p><fig-group><fig id="fig2" position="float"><label>Figure 2.</label><caption><title>BID specificity was acquired during vertebrate BCL-2 evolution.</title><p>(<bold>A</bold>) Protein binding specificities of extant BCL-2 family members. Human MCL-1 (hsMCL-1, purple) strongly binds BID (blue) and NOXA (red), while human BCL-2 (hsBCL-2, green) strongly binds BID but not NOXA. (<bold>B</bold>) Crystal structures of MCL-1 (purple) bound to NOXA (red, PDB 2nla), and BCL-xL (green, a closely related paralog of BCL-2) bound to BID (blue, PDB 4qve). (<bold>C</bold>) Reduced maximum likelihood phylogeny of BCL-2 family proteins. Purple bar, MCL-1 class; green bar, BCL-2 class. The phylogeny was rooted using as outgroups the paralogs BOX, BAK, and BAX (black bar). Heatmaps indicate BID (blue) and NOXA (red) binding measured using the luciferase assay. Each shaded box shows the normalized mean of three biological replicates. Red dotted lines, interval during which NOXA binding was lost, yielding BID specificity in the BCL-2 proteins of vertebrates (green box). Purple box, vertebrate MCL-1. Silhouettes, representative species in each terminal group. AncMB1-M and -B are alternative reconstructions using different approaches to alignment ambiguity (see Materials and methods). For complete phylogeny, see <xref ref-type="fig" rid="fig2s3">Figure 2—figure supplement 3</xref>.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig2-v2.tif"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 1.</label><caption><title>BCL-2 family proteins are structurally similar but have different binding profiles.</title><p>Crystal structures and overlays of BCL-xL (a vertebrate paralog of BCL-2, light green) bound to BID (light blue; PDB: 4qve); BCL-2 (green) bound to BAX (a protein with a BID-like binding profile, blue; PDB: 2xa0); MCL-1 (purple) bound to BAX (blue; PDB: 3pk1); and MCL-1 bound to NOXA (red; PDB: 2nla). The BCL-2 family proteins bind the coregulator proteins at the same interface.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig2-figsupp1-v2.tif"/></fig><fig id="fig2s2" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 2.</label><caption><title>Ancestral sequence reconstruction procedure in schematic form.</title><p>(1) Sequences are collected, including those of proteins conferring different functions (red v. blue)and others with unknown functions (black). These sequences may be orthologs from various species, paralogs related by gene duplication events, or both. (2) Sequences are aligned. (3) A phylogeny is inferred. (4) Using the inferred phylogeny, the aligned sequences, and a model of sequence evolution, the most likely state at each ancestral node is determined. (5) Ancestral sequences are synthesized and tested for function. (6) Functional differences among successive ancestral proteins indicate functional changes during evolutionary history (red bar).</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig2-figsupp2-v2.tif"/></fig><fig id="fig2s3" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 3.</label><caption><title>Maximum likelihood phylogeny of BCL-2 family proteins.</title><p>Light green, vertebrate BCL-2; light-medium and dark-medium green, vertebrate BCLX and BCLW, respectively; dark green, non-vertebrate sequences most closely related to vertebrate BCL-2; red, vertebrate MCL-1; maroon, vertebrate BFL1; light purple, vertebrate NRH; dark purple, non-vertebrate sequences most closely related to vertebrate MCL-1; dark blue, BAX; medium blue, BAK; light blue, BOK; black, ctenophore sequences. Parentheses, number of sequences in each clade. Black squares, ancestral sequences reconstructed and tested. Node labels, approximate likelihood ratio statistics and transfer bootstrap values. Asterisks, nodes constrained to be congruent with known taxonomic relationships.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig2-figsupp3-v2.tif"/></fig><fig id="fig2s4" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 4.</label><caption><title>Binding of BID and NOXA to extant and ancestral proteins.</title><p>(<bold>A</bold>) Schematic of the luciferase reporter assay to assess PPIs. If a BCL-2 family protein (black) binds a coregulator protein (blue), the split T7 RNAP biosensor (gray) assembles and drives luciferase expression. If a coregulator (pink) is not bound, no luciferase is expressed. (<bold>B</bold>) Interactions of human BCL-2 and MCL-1 with BID (blue bars) and NOXA (red) in the luciferase assay, compared to no-coregulator control (gray). Activity is scaled relative to no-coregulator control with no-BCL-2 protein. Columns and error bars, mean ± SD of three biological replicates (circles). Shaded boxes above show the same data in heatmap form: BID activity is normalized relative to hsBCL-2 with BID; NOXA activity is normalized to hsMCL-1 with NOXA. (<bold>C</bold>) Interactions of ancestral reconstructed proteins with BID (blue) and NOXA (red) in the luciferase assay, compared to no-coregulator control (gray). Activity is scaled relative to no-coregulator control with no-BCL-2 family protein. Columns and error bars, mean ± SD of three biological replicates. hsBCL-2 with BID (dashed blue line). hsMCL-1 with NOXA (dashed red line). (<bold>D</bold>) Same as (<bold>C</bold>), but for extant species <italic>Hydra magnapapillata</italic> (Cnidaria), <italic>Octopus bimaculoides</italic> (Lophotrochozoa), <italic>Saccoglossus kowalevskii</italic> (Hemichordata), <italic>Branchiostoma belcheri</italic> (Cephalochordata), <italic>Trichoplax adhaerens</italic> (Placozoa), and <italic>Stegodyphus mimosarum</italic> (Ecdysozoa). (<bold>E</bold>) Same as (<bold>C</bold>), but contains alternative reconstructions (Alt) for each ancestral protein, which combine all plausible alternative amino acid states (PP &gt; 0.2) in a single ‘worst-case’ alternative reconstruction. (<bold>F</bold>) Same as (<bold>C</bold>), but contains multiple alternative reconstructions for AncMB1_B. In each case, all plausible alternative amino acid states with PP greater than the listed value are included in a single ‘worst-case’ alternative reconstruction.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig2-figsupp4-v2.tif"/></fig></fig-group><p>To drive the evolution of new PPI specificities, we developed a new high-throughput phage-assisted continuous evolution (PACE) system (<xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>) that can simultaneously select for and against particular PPIs (<xref ref-type="bibr" rid="bib75">Pu et al., 2019</xref>; <xref ref-type="bibr" rid="bib74">Pu et al., 2017b</xref>). We applied this technique to a series of reconstructed ancestral BCL-2 family members, repeatedly evolving each starting genotype to acquire PPI specificities found among extant family members. By comparing sequence outcomes among PACE replicates from the same starting point, we quantified the role of chance in the evolution of historically relevant molecular functions under strong and identical selection pressures; by comparing outcomes of PACE initiated from different starting points, we quantified the effect of contingency generated by the sequence changes that accumulated during these proteins’ histories. This design also allowed us to characterize how these factors have changed over phylogenetic time and dissect the underlying genetic basis by which they emerged.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>BID specificity is derived from an ancestor that bound both BID and NOXA</title><p>We first characterized the historical evolution of PPI specificity in the BCL-2 family using ancestral protein reconstruction (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>). We inferred the maximum likelihood phylogeny of the family, which recovered the expected sister relationship between the metazoan BCL-2 and MCL-1 classes (<xref ref-type="fig" rid="fig2">Figure 2C</xref>, <xref ref-type="fig" rid="fig2s3">Figure 2—figure supplement 3</xref>). We then reconstructed the most recent common ancestor (AncMB1) of the two classes – a gene duplication that occurred before the last common ancestor (LCA) of all animals – and 11 other ancestral proteins that existed along the lineages leading from AncMB1 to human BCL-2 (hsBCL-2) and to human MCL-1 (hsMCL-1) (<xref ref-type="supplementary-material" rid="supp1">Supplementary file 1</xref>).</p><p>We synthesized genes coding for these proteins and experimentally assayed their ability to bind BID and NOXA using a proximity-dependent split RNA polymerase (RNAP) luciferase assay (<xref ref-type="fig" rid="fig2s4">Figure 2—figure supplement 4</xref>; <xref ref-type="bibr" rid="bib74">Pu et al., 2017b</xref>). AncMB1 bound both BID and NOXA, as did all ancestral proteins in the MCL-1 clade and hsMCL-1 (<xref ref-type="fig" rid="fig2">Figure 2C</xref>, <xref ref-type="supplementary-material" rid="supp1">Supplementary file 1</xref>). Ancestral proteins in the BCL-2 clade that existed before the LCA of deuterostomes also bound both BID and NOXA, whereas BCL-2 ancestors within the deuterostomes bound only BID, just as hsBCL-2 does. This reconstruction of history was robust to uncertainty in the ancestral sequences: experiments on ‘AltAll’ proteins at each ancestral node – which combine all plausible alternative amino acid states (posterior probability &gt; 0.2) in a single ‘worst-case’ alternative reconstruction – also showed that BID specificity arose within the BCL-2 clade (<xref ref-type="fig" rid="fig2s4">Figure 2—figure supplement 4</xref>, <xref ref-type="supplementary-material" rid="supp2">Supplementary file 2</xref>).</p><p>To further test this inferred history, we characterized the coregulator specificity of extant BCL-2 class proteins from taxonomic groups in particularly informative phylogenetic positions. Those from Cnidaria were activated by both BID and NOXA, whereas those from protostomes and invertebrate deuterostomes were BID-specific (<xref ref-type="fig" rid="fig2">Figure 2C</xref>, <xref ref-type="fig" rid="fig2s4">Figure 2—figure supplement 4</xref>, <xref ref-type="supplementary-material" rid="supp1">Supplementary file 1</xref>). These results corroborate the inferences made from ancestral proteins, indicating that BID specificity evolved when the ancestral ability to bind NOXA was lost between AncB2 (in the ancestral eumetazoan) and AncB4 (in the ancestral deuterostome).</p></sec><sec id="s2-2"><title>A directed continuous evolution system for rapid changes in PPI specificity</title><p>To rapidly evolve BCL-2 family proteins to acquire the same PPI specificities that existed during the family’s history, we developed a new PACE system (<xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>; <xref ref-type="fig" rid="fig3">Figure 3A–B</xref>, <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>). Previous PACE systems have evolved binding to new protein partners using a bacterial 2-hybrid approach (<xref ref-type="bibr" rid="bib4">Badran et al., 2016</xref>), but evolving PPI specificity requires simultaneous selection for a desired PPI and against an undesired PPI. For this purpose, we used two orthogonal proximity-dependent split RNAPs that recognize different promoters in the same cell and – if reconstituted by a PPI – activate transcription of positive and negative selectable markers. Specifically, the N-terminal fragment of RNAP was fused to the BCL-2 protein of interest and encoded in the phage genome, and two C-terminal RNAP fragments (RNAPc), each fused to a different BCL-2 coregulator, were encoded on host cell plasmids. One RNAPc is fused to the selected-for coregulator and drives expression of an essential viral gene (gIII) when reconstituted by binding to the BCL-2 protein; the other RNAPc, fused to the counter-selected coregulator, drives expression of a dominant-negative version of gIII (<xref ref-type="bibr" rid="bib73">Pu et al., 2017a</xref>). Phage containing BCL-2 variants that bind the positive selection protein but not the counterselection protein produce infectious phage. After optimizing this system, we used activity-dependent plaque assays and phage growth assays to confirm that it imposes strong selection for the PPI specificity profiles of extant hsBCL-2 and hsMCL1 (<xref ref-type="fig" rid="fig3">Figure 3D</xref>).</p><fig-group><fig id="fig3" position="float"><label>Figure 3.</label><caption><title>Continuous directed evolution of specificity in modern and ancestral BCL-2 family proteins.</title><p>(<bold>A</bold>) <italic>Top:</italic> Components of the PACE system for evolving PPI specificity. Solid arrows show potential binding events. Dashed arrows show potential protein expression. The protein targeted for altered specificity (black) is fused to the N-terminus of RNA polymerase (RNAP<sub>N</sub>, dark gray) and placed into the M13 phage genome (SP, selection plasmid). Upon infection of host <italic>E. coli</italic>, the target gene-RNAP<sub>N</sub> fusion is expressed. Host cells carry accessory plasmids (+AP and −AP) that contain the C-terminus of RNAP (RNAP<sub>C</sub>) fused to peptides for which specificity is desired (blue, positive selection protein; pink, counterselection protein). Binding of the target protein to either the selection protein or counterselection protein reconstitutes a functional RNAP. Binding of RNAP to the corresponding promoter results in the expression of either gIII (teal) or gIII<sub>neg</sub> (gold). gIII is necessary to produce infectious phage. gIII<sub>neg</sub> is a dominant-negative version of gIII which results in the production of non-infectious phage. An arabinose-inducible mutagenesis plasmid in the system (MP) increases the mutation rate of the evolving protein. <italic>Bottom</italic>: PACE schemes for evolving PPI specificities. To select for BCL-2 like specificity, positive selection to bind BID was imposed with counterselection to avoid binding NOXA (blue arrow and red bar). To evolve MCL-1 like activity, positive selection to bind NOXA (red arrow) was imposed after a phase of selection for BID binding, both with counterselection to avoid nonspecific binding using a control zipper peptide (ZBneg). (<bold>B</bold>) Map of the phage SP, the positive and counterselection accessory plasmids (+AP and −AP), and the MP. (<bold>C</bold>) Selection for protein variants with the desired specificity. <italic>Upper left</italic>: Infection by a phage carrying a protein variant that binds neither the positive selection nor the counterselection protein results in production of little to no progeny phage. <italic>Upper right</italic>: Infection by a phage carrying a protein variant that binds only the positive selection protein results in expression of gIII and production of infectious phage. <italic>Lower left</italic>: Infection by a phage carrying a protein variant that binds only the counterselection protein results in expression of gIII<sub>neg</sub> and production of non-infectious phage. <italic>Lower right</italic>: Infection by a phage carrying a protein variant that binds the positive selection and counterselection proteins results in expression of both gIII and gIII<sub>neg</sub>, leading to production of primarily non-infectious phage. (<bold>D</bold>) Growth assays to assess selection and counterselection. Plaque forming units (PFU) after culturing 1000 phage-containing hsBCL-2 (green) or hsMCL-1 (purple) on <italic>E. coli</italic> containing various APs. Detection limit 10<sup>3</sup> PFU/mL. Bars show mean ± SD of three replicates (circles). (<bold>E</bold>) Phylogenetic relations of starting genotypes used in PACE. Each starting genotype was selected to acquire a new specificity in four independent replicates. Green, proteins selected to gain NOXA binding; purple, proteins selected to lose NOXA binding. Red dashed line, interval during which NOXA binding was historically lost, yielding BID specificity in the BCL-2 clade. Letters, index of phylogenetic intervals between ancestral proteins referred to in <xref ref-type="fig" rid="fig5">Figure 5</xref>.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig3-v2.tif"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><label>Figure 3—figure supplement 1.</label><caption><title>Using PACE to evolve target PPI specificity of BCL-2 family proteins.</title><p>(<bold>A</bold>) Schematic of a PACE experiment. Davis Rich carboy media flows into the chemostat, which contains <italic>E. coli</italic> with the positive selection (+AP), counterselection (−AP), and mutagenesis plasmids (MP). The cells then flow into the lagoons, which contain phage with the evolving BCL-2 family protein. Arabinose is pumped into the lagoons to induce the mutagenesis plasmid in the <italic>E. coli</italic>. Both chemostats and lagoons are connected to the waste to maintain proper volume, cell density, and flow rate. (<bold>B</bold>) Picture of representative PACE experiment from this work.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig3-figsupp1-v2.tif"/></fig><fig id="fig3s2" position="float" specific-use="child-fig"><label>Figure 3—figure supplement 2.</label><caption><title>Selection schemes and phage titers for changes in PPI specificity.</title><p>(<bold>A</bold>) Timeline of PACE experiments when hsMCL-1, AncM6, and AncB1 were evolved to lose NOXA binding. ZBneg is a control zipper peptide. (<bold>B</bold>) Phage titers (PFU/mL) over time (bottom) and activity-dependent phage titers at the end of the PACE experiments (top) when hsMCL-1 was evolved to lose NOXA binding. Activity-dependent plaque assays used plasmids 28–46 and Jin 487. (<bold>C</bold>) Same as (<bold>E</bold>) for AncM6. ‘dim’ means plaques were visible but weak, and therefore not quantifiable. (<bold>D</bold>) Same as (<bold>E</bold>) for AncB1. (<bold>E</bold>) Timeline of PACE experiments when hsBCL-2, AncB5, and AncB4 were evolved to gain NOXA binding. (<bold>F</bold>) Phage titers (PFU/mL) over time (bottom) and activity-dependent phage titers at the end of the PACE experiments (top) when hsBCL-2 was evolved to gain NOXA binding. Activity-dependent plaque assays used plasmids 28–48 and 29–39. (<bold>G</bold>) Same as (<bold>H</bold>) for AncB5. (<bold>H</bold>) Same as (<bold>H</bold>) for AncB4.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig3-figsupp2-v2.tif"/></fig><fig id="fig3s3" position="float" specific-use="child-fig"><label>Figure 3—figure supplement 3.</label><caption><title>Fluorescence polarization of PACE-evolved variants.</title><p>(<bold>A</bold>) BID fluorescence polarization for hsMCL-1 variants evolved to lose NOXA binding. Bars are the mean of three replicates; error bars, SD. mFP, normalized measured fluorescent polarization. Kd estimates are shown below in the table. (<bold>B</bold>) Same as (<bold>A</bold>), but for NOXA binding. (<bold>C</bold>) BID fluorescence polarization for hsBCL-2 variants evolved to gain NOXA binding. (<bold>D</bold>) Same as (<bold>C</bold>), but for NOXA binding.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig3-figsupp3-v2.tif"/></fig></fig-group><p>The simplicity of this platform allowed us to drive extant and reconstructed ancestral proteins to recapitulate or reverse the historical evolution of the BCL-2 family’s PPI specificity in multiple replicates in just days, without severe experimental bottlenecks. Three proteins that bound both BID and NOXA – hsMCL-1, AncM6, and AncB1 – were selected to acquire the derived BCL-2 phenotype, retaining BID binding and losing NOXA binding. Conversely, hsBCL-2, AncB5, and AncB4 were evolved to gain NOXA binding, reverting to the ancestral phenotype (<xref ref-type="fig" rid="fig3">Figure 3C and E</xref>, <xref ref-type="fig" rid="fig3s2">Figure 3—figure supplement 2</xref>). For each starting genotype, we performed four replicate experimental evolution trajectories (<xref ref-type="supplementary-material" rid="supp3">Supplementary file 3</xref>). Each experiment was run for 4 days, corresponding to approximately 100 rounds of viral replication (<xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>). All trajectories yielded the target PPI specificity, which we confirmed by experimental analysis of randomly isolated phage clones using activity-dependent plaque assays and in vivo and in vitro binding assays (<xref ref-type="fig" rid="fig4">Figure 4A–B</xref>, <xref ref-type="fig" rid="fig3s2">Figure 3—figure supplement 2</xref>, <xref ref-type="fig" rid="fig3s3">Figure 3—figure supplement 3</xref>). As in prior PACE experiments, variation in the selected phenotype was observed among individual phage isolates within the final populations (<xref ref-type="bibr" rid="bib27">Dickinson et al., 2013</xref>), presumably because of large populations, high mutation rates, and/or inadequate time for fixation.</p><fig-group><fig id="fig4" position="float"><label>Figure 4.</label><caption><title>Chance and contingency shape evolutionary outcomes.</title><p>(<bold>A</bold>) Phenotypic outcome of PACE experiments when proteins with MCL-1-like specificity were selected to maintain BID and lose NOXA binding. For each starting genotype, the BID (blue) and NOXA (red) binding activity of the starting genotype and three phage variants isolated from each evolved replicate (number) are shown as heatmaps. (<bold>B</bold>) Phenotypic outcome of PACE experiments when proteins with BCL-2-like specificity were selected to gain NOXA binding. (<bold>C</bold>) Frequency of acquired states in PACE experiments when proteins with MCL-1-like specificity were selected to maintain BID and lose NOXA binding. Rows, outcomes of each replicate trajectory. Columns, sites that acquired one or more non-wild-type amino acids (letters in cells) at frequency &gt;5%; color saturation shows the frequency of the acquired state. Site numbers and wild-type amino acid (WT AA) states are listed. Gray, sites that do not exist in AncB1. (<bold>D</bold>) Frequency of acquired states when BCL-2-like proteins were selected to gain NOXA binding. (<bold>E</bold>) Repeatability of acquired states across replicates. The 100 non-WT states acquired in all experiments were categorized as occurring in 1 or &gt;1 replicate trajectory from 1 or &gt;1 unique starting genotype, with the number in each category shown. The vast majority of states evolved in just one replicate from one starting point (black). (<bold>F</bold>) Historical substitutions that contributed to the change in PPI specificity rarely occur or revert during PACE. Rows, substitutions that historically occurred between AncB1 and AncB4, the ancestral proteins that flank the loss of NOXA on the phylogeny. For each substitution, columns show whether the historical ancestral or derived state was acquired in PACE trajectories from each ancestral starting point. Purple and green boxes, PACE acquisition of ancestral or derived state, respectively, in each replicate. White boxes, neither state acquired.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-v2.tif"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 1.</label><caption><title>MiSeq library preparation.</title><p>After isolation of phage DNA, the coding region of the evolving BCL-2 family protein was amplified in three overlapping fragments, each of which was smaller than 300 bp. The DNA fragments were then amplified using sequence-specific primers. MiSeq adapters were added in a second PCR step. These fragment libraries were combined and used for MiSeq sequencing. Blue, target gene coding region. Gray, adjacent vector sequence. Green, forward adapter and barcode sequence. Orange, reverse adapter and barcode sequence. Magenta, index one sequence. Purple, index two sequence.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp1-v2.tif"/></fig><fig id="fig4s2" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 2.</label><caption><title>Frequency of insertions and deletions during PACE.</title><p>(<bold>A</bold>) Allele frequency of frameshifts in replicate PACE experiments started from hsMCL-1, AncM6, and AncB1 evolved to lose NOXA binding. Site numbers and wild-type (WT) amino acid states are listed above each sequence. Each row represents an independent replicate population. Non-wild-type insertions and deletions that reached &gt;5% in frequency are shown, with frequency proportional to color saturation. Split cells show populations with multiple non-WT states &gt; 5%. Plus (+) indicates an addition of a nucleotide. Delta (Δ) indicates a deletion of a nucleotide. (<bold>B</bold>) Same as (<bold>A</bold>), but for replicate PACE experiments of hsBCL-2, AncB5, and AncB4 evolved to gain NOXA binding.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp2-v2.tif"/></fig><fig id="fig4s3" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 3.</label><caption><title>Categories of the 100 non-WT states observed for each non-WT state.</title><p>Black box with white letters, mutant states observed in only one replicate. Teal, mutant states observed in multiple replicates from the same starting genotype. Orange, mutant states observed in a single replicate from multiple different starting genotypes. Brown, mutant states observed in multiple replicates from the same starting genotype and in at least one other replicate from a different starting genotype. Black box outline, mutant states observed in multiple replicates from the same starting genotype and from multiple replicates from a different starting genotype. Gray boxes are sites that do not exist in a particular sequence.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp3-v2.tif"/></fig><fig id="fig4s4" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 4.</label><caption><title>Effect of w271* mutation on BID and NOXA binding.</title><p>Activity is scaled relative to the control experiment with no- BCL-2 family protein and no-coregulator peptide. Bars show the mean ± SD of three biological replicates (circles). Gray bar, no-coregulator peptide. Blue bar, BID. Red bar, NOXA. Blue dotted lines mark the average signal of hsBCL-2 with BID, and red dotted lines mark the average signal of hsMCL-1 with NOXA.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp4-v2.tif"/></fig><fig id="fig4s5" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 5.</label><caption><title>Historical distribution of PACE mutations.</title><p>Historical WT states for each starting genotype are listed. Green, hsBCL-2 link function. Purple, hsMCL-1 like function. Solid vertical line, historical interval in which function changed. Dashed vertical line, location of the phylogeny root. For each PACE mutation, the genotype on which it arose is in a square. The nearest historical state that the mutation matches is in a circle. PACE mutations can either recapitulate historical substitutions, revert to historical states, or switch to a state found in a sister lineage. PACE mutations that revert historical states that changed during the interval at the same time as the change in function or outlined in red.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp5-v2.tif"/></fig><fig id="fig4s6" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 6.</label><caption><title>Phylogenetic recapitulation of PACE mutations.</title><p>Mutation state and position are given above each cladogram. Lowercase letters, WT state for PACE. Uppercase letters, mutant state for PACE. Each cladogram shows the estimated most likely state for each ancestral node and the majority state for each extant clade. Gray boxes; same WT state as the sequence in which the PACE mutation emerged. Black boxes; same WT state as the PACE mutation. Arrows point from the starting genotype for PACE (larger font) to the closest genotype with the PACE mutation. Red boxes show the two instances in which substitutions that occurred during the historical interval in which NOXA specificity was lost (red hash marks on phylogeny) also occurred during PACE.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig4-figsupp6-v2.tif"/></fig></fig-group></sec><sec id="s2-3"><title>Chance and contingency erase necessity in the evolution of PPI specificity</title><p>We used deep sequencing to compare the sequence outcomes of evolution across trajectories initiated from the same and different starting points (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>). Necessity was almost entirely absent. Across all trajectories, 100 mutant amino acid states at 75 different sites evolved to frequency &gt; 5% in at least one replicate (<xref ref-type="fig" rid="fig4">Figure 4C–D</xref>, <xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>, <xref ref-type="supplementary-material" rid="supp4">Supplementary file 4</xref>). Of these acquired states, 73 appeared in only a single trajectory, and only four arose in more than one replicate from multiple starting points (<xref ref-type="fig" rid="fig4">Figure 4E</xref>, <xref ref-type="fig" rid="fig4s3">Figure 4—figure supplement 3</xref>). When selection was imposed for binding to both BID and NOXA, no states were predictably acquired in all trajectories from all starting points. The only mutation universally acquired under any selection regime was a nonsense mutation at codon 271, which was acquired in all trajectories selected for BID specificity, but experimental analysis of this mutation shows that it has no detectable effect on coregulator binding (<xref ref-type="fig" rid="fig4s4">Figure 4—figure supplement 4</xref>).</p><p>Both chance and contingency contributed to this pervasive unpredictability. Pairs of trajectories launched from the same starting point differed, on average, at 78% of their acquired states, indicating a strong role for chance. Pairs that were launched from different starting points (but selected for the same PPI specificity) differed at an average of 92% of acquired states, indicating an additional role for contingency.</p><p>These starting points are separated by different amounts of evolutionary divergence, so to understand the extent of contingency over the timescale of metazoan evolution, we compared trajectories launched from AncB1 to those launched from hsMCL1 (the two most distant genotypes that were selected for BID specificity). Of 34 states acquired in these experiments, only three occurred in at least one trajectory from both starting points. Of 40 states acquired in trajectories launched from AncB4 and hsBCL-2 (the two most distant proteins that were selected to gain NOXA binding), only one occurred in any trajectories from both starting points. Together, contingency generated across long phylogenetic timescales and chance therefore make sequence evolution in the BCL-2 family almost entirely unpredictable.</p><p>These experiments indicate an almost complete lack of necessity in the evolution of PPI specificity in PACE. To gain insight into the extent of necessity in the historical evolution of BCL-2 PPI specificity, we asked whether substitutions that occurred during the phylogenetic interval when NOXA binding was lost (between AncB1 and AncB4) were either repeated or reversed during PACE trajectories to lose or regain NOXA binding from any starting point (<xref ref-type="fig" rid="fig4">Figure 4F</xref>, <xref ref-type="fig" rid="fig4s5">Figure 4—figure supplement 5</xref>, <xref ref-type="fig" rid="fig4s6">Figure 4—figure supplement 6</xref>). In PACE experiments to lose NOXA binding from proteins that initially bound both peptides, none of the acquired states recapitulated substitutions from the branch on which NOXA binding was historically lost. In PACE experiments to reacquire NOXA binding from proteins with BCL2-like specificity for BID, only two states reversed historical substitutions that occurred on that branch. Both of these reacquisitions occurred in PACE trajectories launched from AncB4, the immediate daughter node of this branch, suggesting that in other proteins, contingency accumulated over phylogenetic time restricted their accessibility. Furthermore, both of these states were acquired in only a subset of trajectories from AncB4, indicating a role for chance even from this starting point. Some substitutions that occurred during other historical intervals were recapitulated or reversed during PACE trajectories, indicating that these states are compatible with BCL-2 family protein functions, but these substitutions could not have contributed to historical changes in PPI specificity, which remained unchanged on these branches. Our experiments therefore suggest strong effects of chance and contingency in the historical evolution of BCL-2’s derived PPI specificity.</p></sec><sec id="s2-4"><title>Historical contingency is the major cause of sequence variation under selection for new functions</title><p>We next sought to directly quantify the relative effects of chance and historically generated contingency on sequence outcomes in our experiments. We analyzed the genetic variance – defined as the probability that two variable sites, chosen at random, are different in state – within and between trajectories from the same and different starting genotypes. To estimate the effects of chance, we compared the genetic variance between replicates initiated from the same starting genotype (V<sub>g</sub>) to the within-replicate genetic variance (V<sub>r</sub>). We found that V<sub>g</sub> was on average 30% greater than V<sub>r</sub>, indicating that chance causes evolution to produce divergent genetic outcomes between independent lineages even with strong selection for a change in function (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). We quantified contingency by comparing the pooled genetic variance among replicates from different starting genotypes (V<sub>t</sub>) to that among replicates from the same starting genotype (V<sub>g</sub>). Contingency’s effect was even larger than that of chance, increasing V<sub>t</sub> by an average of 80% across all pairs of starting points compared to V<sub>g</sub> when selecting for a new function. Together, chance and contingency had a multiplicative effect, increasing the genetic variance among trajectories from different starting genotypes (V<sub>t</sub>) by an average of 2.4-fold compared to the genetic variance within trajectories (V<sub>r</sub>). The effects of chance and contingency were not significantly different between PACE experiments in which protein interactions were gained and those in which they were lost (<xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>).</p><fig-group><fig id="fig5" position="float"><label>Figure 5.</label><caption><title>Effects of chance and contingency.</title><p>(<bold>A</bold>) Variation in evolutionary sequence outcomes caused by chance (orange), contingency (teal), and both (black). Inset: schematic for estimating the effects of chance and contingency. Chance was estimated as the average genetic variance among replicates from the same starting genotype (V<sub>g</sub>) divided by the within-replicate genetic variance (V<sub>r</sub>). Contingency was estimated as the average genetic variance among replicates from different starting genotypes (V<sub>t</sub>) divided by the average genetic variance among replicates from the same starting genotype (V<sub>g</sub>). Combined effects of chance and contingency were estimated as the average genetic variance among replicates from different starting genotypes (V<sub>t</sub>) compared to the within-replicate genetic variance (V<sub>r</sub>). Genetic variance is the probability that two randomly drawn alleles are different in state. Error bars, 95% confidence intervals on the mean by bootstrapping PACE replicates. (<bold>B</bold>) Change in the effects of chance and contingency over phylogenetic distance. Each point is for a pair of starting proteins used for PACE, comparing the phylogenetic distance (the total length of branches separating them, in substitutions per site) to the effects of chance (orange), contingency (teal), or both (black), when PACE outcomes are compared between them. Solid lines, best-fit linear regression. Letters indicate the phylogenetic branch indexed in <xref ref-type="fig" rid="fig3">Figure 3E</xref>. The combined effect of chance and contingency increased significantly with phylogenetic distance (slope = 0.19, p=2×10<sup>−5</sup>), as did the effect of contingency alone (slope = 0.11, p=0.007). The effect of chance alone did not depend on phylogenetic distance (slope = 0.02, p=0.5). The combined effect of chance and contingency increased significantly faster than the effect of contingency alone (0.08, p=0.04). Arrow, phylogenetic distance between extant hsMCL-1 and hsBCL-2 proteins, which share AncMB1 as their most recent common ancestor.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig5-v2.tif"/></fig><fig id="fig5s1" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 1.</label><caption><title>Change in chance and contingency over time.</title><p>(<bold>A</bold>) Relationship between phylogenetic distance between pairs of starting genotypes for experimental evolution (ancestral or extant proteins, as the total branch lengths separating them) and the effects of chance (orange), contingency (teal), or both (black) on the outcomes of evolution between them. Lines are best fits from linear models. Circles are observed values. Diamonds are averages of 1000 permutations of starting genotype labels. This shuffling of genotype labels results in more genetic variance among samples from the same ‘starting genotype’ than the observed data, and less genetic variance between samples from different ‘starting genotypes’ than the observed data. Letters indicate the specific branch from <xref ref-type="fig" rid="fig3">Figure 3E</xref>. (<bold>B</bold>) Change in chance over time. Green, both starting genotypes had BCL-2 like function. Purple, both starting genotypes had MCL-1 like function. Black, starting genotypes differed in function. Phylogenetically independent comparison are shown as diamonds. The effect of chance did not change with phylogenetic distance when restricting analysis to comparisons that are phylogenetically independent (slope = 0.042, p=0.71) and genotypes selected for the same function (slope = 0.029, p=0.82). (<bold>C</bold>) Change in contingency over time. Green, both starting genotypes had BCL-2 like function. Purple, both starting genotypes had MCL-1 like function. Black, starting genotypes differed in function. Phylogenetically independent comparison are shown as diamonds. The effect of contingency increased with phylogenetic distance and was marginally significant when restricting analysis to comparisons that are phylogenetically independent (slope = 0.31, p=0.07), and genotypes selected for the same function (slope = 0.42, p=0.05). (<bold>D</bold>) Change in the combined effect of chance and contingency over time. Green, both starting genotypes had BCL-2 like function. Purple, both starting genotypes had MCL-1 like function. Black, starting genotypes differed in function. Phylogenetically independent comparison are shown as diamonds. The combined effect of chance and contingency increased with phylogenetic distance when restricting analysis to comparisons that are phylogenetically independent (slope = 0.50, p=0.009) and genotypes selected for the same function (slope = 0.63, p=0.01). (<bold>E</bold>) Effects of chance and contingency do not depend on the selection regime. Each column shows the portion of genetic variance among trajectories that was caused by chance or contingency, relative to the within-population variance (see <xref ref-type="fig" rid="fig5">Figure 5A</xref>). Green, trajectories in which BCL-2 like starting genotypes were selected to gain NOXA binding. Purple, trajectories in which MCL-1 like starting genotypes were selected to lose NOXA binding but maintain BID binding (purple). Error bars, 95% confidence intervals on the mean. p-values estimated by t-test.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig5-figsupp1-v2.tif"/></fig></fig-group><p>The preceding analyses do not account for phylogenetic structure or the extent of divergence between starting points. We therefore assessed how chance and contingency changed with phylogenetic distance using linear regression (<xref ref-type="fig" rid="fig5">Figure 5B</xref>, <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>). We found that the effect of contingency on genetic variance increased significantly with phylogenetic divergence among starting points. The effect of chance did not increase with divergence, but the combined effect of contingency and chance increased even more rapidly than contingency alone because the total impact on genetic variance of these two factors is multiplicative by definition.</p><p>We next compared the impact of contingency to that of chance as phylogenetic divergence increases. On the timescale of metazoan evolution, contingency’s effect (an increase in genetic variance by about 100%) was three times greater than that of chance when evolution was launched from extant starting points whose LCA was AncMB1, near the base of Metazoa (<xref ref-type="fig" rid="fig5">Figure 5B</xref>). The combined effect of chance and contingency on this timescale was a 3.2-fold increase in variance among single trajectories launched from these starting points. Even across the shortest phylogenetic intervals we studied, contingency’s effect was larger than that of chance, although to a smaller extent. Taken together, these data indicate that contingency, magnified by chance, steadily increases the unpredictability of evolutionary outcomes as protein sequences diverge across history.</p></sec><sec id="s2-5"><title>Contingency is caused by epistasis between historical substitutions and specificity-changing mutations</title><p>Contingency is expected to arise in our experiments if historical substitutions (which separate ancestral starting points) interact epistatically with mutations that occur during PACE, causing the mutations that can confer selected PPI specificities to differ among starting points. To experimentally test this hypothesis and characterize underlying epistatic interactions, we first identified sets of candidate causal mutations that arose repeatedly during PACE replicates from each starting genotype. We then verified their causal effect on specificity by introducing only these mutations into the protein that served as the starting point for the PACE experiment in which they were observed and measuring their effects on BID and NOXA binding. We found that all sets were sufficient to confer the selected-for specificity in their ‘native’ background (<xref ref-type="fig" rid="fig6">Figure 6A, B</xref>).</p><fig id="fig6" position="float"><label>Figure 6.</label><caption><title>Sources of contingency.</title><p>(<bold>A</bold>) Epistatic incompatibility of PACE mutations in other historical proteins. Effects on activity are shown when amino acid states acquired in PACE under selection to acquire NOXA binding (red arrows) are introduced into ancestral and extant proteins. The listed mutations that occurred during PACE launched from each starting point (rows) were introduced as a group into the protein listed for each column. Observed BID (blue) and NOXA (red) activity in the luciferase assay for each mutant protein are shown as heatmaps (normalized mean of three biological replicates). Letters indicate the phylogenetic branch in <xref ref-type="fig" rid="fig3">Figure 3E</xref> that connects the PACE starting genotype to the recipient genotype. Plus and minus signs indicate whether mutations were introduced into a descendant or more ancestral sequence, respectively. (<bold>B</bold>) Effects on activity when amino acids acquired in PACE under selection to lose NOXA binding and acquire BID binding are introduced into different ancestral and extant proteins, represented as in (<bold>A</bold>). (<bold>C</bold>) Epistatic interactions between historical substitutions and PACE mutations. Restrictive historical substitutions (X) cause mutations that alter PPI specificity in an ancestor to abolish either BID (blue) or NOXA (red) activity when introduced into later historical proteins. Permissive substitutions (+) cause PACE mutations that alter PPI specificity in a descendent to abolish either BID or NOXA activity in an ancestor. Arrow, gain or maintenance of binding. Blunt bar, loss of binding. Mutations that confer selected functions in PACE are shown in the boxes at the end of solid arrows or bars. Solid lines, functional changes under PACE selection. Dashed lines, functional effects different from those selected for when PACE-derived mutations are placed on a different genetic background.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig6-v2.tif"/></fig><p>We then introduced these mutations into the other starting proteins that had been subject to the same selection regime and performed the same assay (<xref ref-type="fig" rid="fig6">Figure 6A,B</xref>). Eleven of 12 such swaps failed to confer the PPI specificity on other proteins that they conferred in their native backgrounds. These swaps compromised binding of BID, failed to confer the selected-for gain or loss of NOXA binding, or both. The only case in which the mutations that conferred the target phenotype during directed evolution had the same effect in another background was the swap into AncB4 of mutations that evolved in AncB5 – the most similar genotypes of all pairs of starting points in the analysis. Contingency therefore arose because historical substitutions that occurred during the intervals between ancestral proteins made specificity-changing mutations either deleterious or functionally inconsequential when introduced into genetic backgrounds that existed before or after those in which the mutations occurred.</p><p>To characterize the timing and effect of these epistatic substitutions during historical evolution, we mapped the observed incompatibilities onto the phylogeny (<xref ref-type="fig" rid="fig6">Figure 6C</xref>). We inferred that restrictive substitutions evolved on a branch if mutations that arose during directed evolution of an ancestral protein compromised coregulator binding when swapped into descendants of that branch. Conversely, we inferred that permissive substitutions evolved on a branch if mutations that arose during directed evolution compromised coregulator binding when swapped into more ancient ancestral proteins.</p><p>We found that both permissive and restrictive epistatic substitutions occurred on almost every branch of the phylogeny and affected both BID and NOXA binding. The only exception was the branch from AncB4 to AncB5, on which only restrictive substitutions affecting NOXA binding occurred. This is the branch immediately after NOXA function changed during history; it is also the shortest of all branches examined and the one with the smallest effect of contingency on genetic variance (<xref ref-type="fig" rid="fig5">Figure 5B</xref>). Even across this branch, however, the PACE mutations that restore the ancestral PPI specificity in AncB4 can no longer do so in AncB5. These results indicate that the paths through sequence space leading to historical PPI specificities changed repeatedly during the BCL-2 family’s history, even during intervals when the proteins’ PPI binding profiles did not evolve.</p></sec><sec id="s2-6"><title>Chance is caused by degeneracy in sequence–function relationships</title><p>For chance to strongly influence the outcomes of adaptive evolution, multiple paths to a selected phenotype must be accessible with similar probabilities of being taken. This situation could arise if several different mutations (or sets of mutations) can confer a new function or if mutations that have no effect on function accompany function-changing mutations by chance. To distinguish between these possibilities, we measured the functional effect of different sets of mutations that arose in replicates when hsMCL-1 was evolved to lose NOXA binding (<xref ref-type="fig" rid="fig7">Figure 7A</xref>, <xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>). One mutation (v189G) was found at high frequency in all four replicates, but it was always accompanied by other mutations, which varied among trajectories. We found that v189G was a major contributor to the loss of NOXA binding, but it had this effect only in the presence of the other mutations, which did not decrease NOXA binding on their own. Mutation v189G therefore required permissive mutations to occur during directed evolution, and there were multiple sets of mutations with the potential to exert that effect; precisely which permissive mutations occurred in any replicate was a matter of chance. All permissive mutations were located near the NOXA binding cleft, suggesting a common mechanistic basis (<xref ref-type="fig" rid="fig7">Figure 7B</xref>).</p><fig-group><fig id="fig7" position="float"><label>Figure 7.</label><caption><title>Sources of chance.</title><p>(<bold>A</bold>) Dissecting the effects of sets of mutations (white boxes) that caused hsMCL-1 to lose NOXA binding during four PACE trajectories. Filled boxes show the effect of introducing a subset of mutations into hsMCL-1 (normalized mean relative from three biological replicates). Solid lines show the effect of introducing v189G, which was found in all four sets. Dotted lines, effects of the other mutations in each set. (<bold>B</bold>) Structural location of mutations in (<bold>A</bold>). Alpha-carbon atom of mutated residues are shown as purple spheres on the structure of MCL-1 (light gray) bound to NOXA (red, PDB 2nla). (<bold>C</bold>) Location of repeated mutations when hsMCL-1, AncM6, and AncB1 were selected to lose NOXA binding (purple spheres), represented on the structure of MCL-1 (gray) bound to NOXA (red, PDB 2nla). (<bold>D</bold>) Location of repeated mutations when hsBCL-2, AncB5, and AncB4 were selected to gain NOXA binding (green spheres), on the structure of hsBCL-xL (gray) bound to BID (blue, PDB 4qve).</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig7-v2.tif"/></fig><fig id="fig7s1" position="float" specific-use="child-fig"><label>Figure 7—figure supplement 1.</label><caption><title>Effects on NOXA binding of hsMCL-1 PACE-derived mutations.</title><p>Each panel shows NOXA binding (y-axis) for a unique variant as additional mutations are added (x-axis). Values are the mean of three biological replicates. Heatmaps show the effects of each mutation on BID (blue) and NOXA (red) activity, and each shaded box represents the normalized mean of three biological replicates. Lines connect genotypes that differ by a single mutation. Solid lines show the effects of the v189G mutation. Dashed lines show the effects of all other mutations. Mutations come from variants L1-1 (<bold>A</bold>), L3-1 (<bold>B</bold>), L3-3 (<bold>C</bold>), and L4-3 (<bold>D</bold>).</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig7-figsupp1-v2.tif"/></fig><fig id="fig7s2" position="float" specific-use="child-fig"><label>Figure 7—figure supplement 2.</label><caption><title>Phenotypic effects of reverting frequent PACE-derived mutations.</title><p>Individual variants were isolated from PACE experiments that selected for the gain of NOXA binding in hsBCL-2 (<bold>A</bold>) and AncB4 (<bold>B</bold>) and the loss of NOXA binding in hsMCL-1 (<bold>C</bold>), AncM6 (<bold>D</bold>), and AncB1 (<bold>E</bold>). For each variant, non-WT states are colored. Sites and WT amino state are indicated at top. Heatmaps on the left show binding to BID and NOXA in the luciferase assay for each variant and their corresponding mutant without the key mutation. Each shaded box represents the normalized mean of three biological replicates.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig7-figsupp2-v2.tif"/></fig></fig-group><p>Other starting genotypes showed a similar pattern of multiple sets of mutations capable of conferring the selected function (<xref ref-type="fig" rid="fig7s2">Figure 7—figure supplement 2</xref>). In addition, when mapped onto the protein structure, all sites that were mutated in more than one replicate either directly contacted the bound peptide or were on secondary structural elements that did so (<xref ref-type="fig" rid="fig7">Figure 7C–D</xref>), suggesting a limited number of structural mechanisms by which PPIs can be altered. Taken together, these results indicate that chance arose because from each starting genotype, there were multiple mutational paths to the selected specificity; partial determinism arose because the number of accessible routes was limited by the structure-function relationships required for peptide binding in this family of proteins.</p></sec><sec id="s2-7"><title>Partial determinism is attributable to a limited number of function-changing mutations</title><p>We next analyzed the genetic basis for the limited degree of determinism that we observed in our experiments. Specifically, we sought to distinguish whether, from a given BID-specific starting point, only a few genotypes can confer NOXA binding while retaining BID binding or, alternatively, whether there are many such genotypes, but under strong selection a few are favored over others.</p><p>We performed PACE experiments in which we selected hsBCL-2 to retain its BID binding, without selection for or against NOXA binding; we then screened for variants that fortuitously gained NOXA binding using an activity-dependent plaque assay (<xref ref-type="fig" rid="fig8">Figure 8A–B</xref>). All four replicate populations produced clones that neutrally gained NOXA binding at a frequency of ~0.1% to 1% – lower than when NOXA binding was directly selected for but five orders of magnitude higher than when NOXA binding was selected against (<xref ref-type="fig" rid="fig8">Figure 8A</xref>, <xref ref-type="fig" rid="fig8s1">Figure 8—figure supplement 1</xref>). From each replicate, we then sequenced three NOXA-binding clones and found that all but one of them contained mutation r165L (<xref ref-type="fig" rid="fig8">Figure 8B</xref>), which also occurred at high frequency when the same protein was selected to gain NOXA binding (<xref ref-type="fig" rid="fig8s2">Figure 8—figure supplement 2</xref>). We introduced r165L into hsBCL-2 and found that it conferred significant NOXA binding with little effect on BID binding (<xref ref-type="fig" rid="fig8s3">Figure 8—figure supplement 3</xref>). Several other mutations appeared repeatedly in clones that fortuitously acquired NOXA binding, and these mutations were also acquired under selection for NOXA binding (<xref ref-type="fig" rid="fig8">Figure 8B</xref>, <xref ref-type="fig" rid="fig8s2">Figure 8—figure supplement 2</xref>). A similar pattern of common mutations was observed in AncB4 and AncB5 clones that fortuitously or selectively evolved NOXA binding (<xref ref-type="fig" rid="fig8s4">Figure 8—figure supplement 4</xref>). These observations indicate that the partial determinism we observed arises because from these starting points only a few mutations have the potential to confer NOXA binding while retaining BID binding.</p><fig-group><fig id="fig8" position="float"><label>Figure 8.</label><caption><title>Sources of determinism.</title><p>(<bold>A</bold>) Evolution of NOXA-binding phage under various selection regimes. Frequency was calculated as the ratio of plaque forming units (PFU) per milliliter on <italic>E. coli</italic> cells that require NOXA binding to the PFU on cells that require BID binding to form plaques. Wild-type hsBCL-2 (green) and hsMCL-1 (purple) are shown as controls. Arrow, positive selection for function. Bar, counterselection against function. Blue, BID. Red, NOXA. Bars are the mean of four trajectories for each condition (points). (<bold>B</bold>) Phenotypes and genotypes of hsBCL-2 variants that evolved NOXA binding under selection to maintain only BID binding. Sites and WT amino state are indicated at top. For each variant, non-WT states acquired are shown in green. Heatmaps show binding to BID and NOXA in the luciferase assay for each variant (normalized mean of three biological replicates).</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig8-v2.tif"/></fig><fig id="fig8s1" position="float" specific-use="child-fig"><label>Figure 8—figure supplement 1.</label><caption><title>Selection schemes and phage titers for fortuitous NOXA binding of hsBCL2.</title><p>(<bold>A</bold>) Timeline of PACE experiments when hsBCL-2 was evolved with positive selection to maintain only BID binding. Selection conditions shown as arrows and blunt bars: arrow, selection for binding to BID (blue); blunt bar, selection against binding to ZBneg (gray). (<bold>B</bold>) Phage titers (PFU/mL) over time (bottom) and activity-dependent phage titers on NOXA at the end of the PACE experiment (top) when hsBCL-2 was evolved to maintain BID binding. Activity-dependent plaque assays used plasmid 28–48. (<bold>C</bold>) Timeline of PACE experiments when hsBCL-2 was evolved with positive selection to maintain BID binding and negative selection against NOXA binding. Selection conditions shown as arrows and blunt bars: arrow, selection for binding to BID (blue); gray blunt bar, selection against binding to Zbneg; red blunt bar, selection against binding to NOXA. (<bold>D</bold>) Same as (<bold>B</bold>), but for hsBCL-2 evolved to bind BID and not NOXA. Activity-dependent plaque assays used plasmids 28–48 and Jin 487.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig8-figsupp1-v2.tif"/></fig><fig id="fig8s2" position="float" specific-use="child-fig"><label>Figure 8—figure supplement 2.</label><caption><title>Allele frequency of non-wt states during PACE.</title><p>Allele frequency of non-wild-type states when hsBCL-2 was evolved to maintain BID binding (top) or when hsBCL-2 was evolved to simultaneously maintain BID binding and lose NOXA binding (middle). For comparison, the same sites are also shown for when hsBCL-2 was evolved to gain NOXA binding (bottom). Site numbers and wild-type (WT) amino acid states are listed above each sequence. Each row represents an independent replicate population. Non-wild-type amino acids that reached &gt; 5% in frequency are shown, with frequency proportional to color saturation.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig8-figsupp2-v2.tif"/></fig><fig id="fig8s3" position="float" specific-use="child-fig"><label>Figure 8—figure supplement 3.</label><caption><title>Effect on NOXA binding of the key r165L mutation.</title><p>Bars are the mean ± SD of three biological replicates (circles). Solid lines show the effects of the r165L mutation while dotted lines show the effect of a frameshift (fs) at site 262.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig8-figsupp3-v2.tif"/></fig><fig id="fig8s4" position="float" specific-use="child-fig"><label>Figure 8—figure supplement 4.</label><caption><title>Selection and phage titers for fortuitous NOXA binding of AncB4 and AncB5.</title><p>(<bold>A</bold>) Timeline of PACE experiments when AncB4 was evolved with positive selection to maintain only BID binding. Selection conditions shown as arrows and blunt bars: arrow, selection for binding to BID (blue); blunt bar, selection against binding to ZBneg (gray). (<bold>B</bold>) Phage titers (PFU/mL) over time when AncB4 was evolved to maintain BID binding. (<bold>C</bold>) Phenotypes and genotypes of individual AncB4 variants that were isolated from PACE when selecting for BID binding and screened for the gain of NOXA binding. Site numbers and wild-type (WT) amino acid states are indicated at the top. Heatmaps on the left show binding to BID (blue) and NOXA (red) in the luciferase assay for each variant, and each shaded box represents the normalized mean of three biological replicates. (<bold>D</bold>) Non-wild-type amino acid states that reached &gt;5% in frequency are shown for PACE when AncB4 was evolved to gain NOXA binding, for comparison with (<bold>C</bold>). Frequency is proportional to color saturation. Split cells show populations with multiple non-WT states &gt; 5%. Each row represents an independent replicate lagoon. Color of WT state indicate if the mutation was seen among multiple replicates of the same starting genotype (teal), a single replicate from multiple starting genotypes (orange), or in multiple replicates and multiple starting genotypes (brown). Black box outline indicates mutant states observed in multiple replicates from the same starting genotype and from multiple replicates from a different starting genotype. (<bold>E</bold>) Same as (<bold>A</bold>) but for AncB5. (<bold>F</bold>) Same as (<bold>B</bold>) but for AncB5. (<bold>G</bold>) Same as (<bold>C</bold>) but for AncB5. (<bold>H</bold>) Same as (<bold>D</bold>) but for AncB5.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig8-figsupp4-v2.tif"/></fig></fig-group></sec><sec id="s2-8"><title>Contingency can affect accessibility of new functions</title><p>Although we found that chance and contingency strongly influenced sequence outcomes in our experiments, all trajectories acquired the historically relevant PPI specificities that were selected for, indicating strong necessity at the level of protein function. This was true whether evolution began from more ‘promiscuous’ starting points that bound both BID and NOXA or from more specific proteins that bound only BID.</p><p>To further probe the evolutionary accessibility of new functions, we used PACE to select for a PPI specificity that never arose during historical evolution – binding of NOXA but not BID. We found that trajectories launched from hsMCL-1 (which binds both coregulators) readily evolved the selected phenotype, but two PACE-evolved variants of hsBCL-2, which had acquired the same PPI profile as hsMCL-1, went extinct under the same selection conditions (<xref ref-type="fig" rid="fig9">Figure 9</xref>, <xref ref-type="fig" rid="fig9s1">Figure 9—figure supplement 1</xref>). The inability of the derived hsBCL-2 genotypes to acquire NOXA specificity was not attributable to a general lack of functional evolvability by these proteins because they successfully evolved in a separate PACE experiment to lose their NOXA binding but retain BID binding (<xref ref-type="fig" rid="fig9s2">Figure 9—figure supplement 2</xref>). These results establish that contingency can influence the accessibility of new functions and that the sequence by which a specific functional phenotype is encoded can play important roles in subsequent phenotypic evolution.</p><fig-group><fig id="fig9" position="float"><label>Figure 9.</label><caption><title>Contingency affects the evolution of novel specificity.</title><p>Starting genotypes that can bind both BID and NOXA (left) were selected to lose only BID or NOXA binding. Heatmaps show binding to BID and NOXA in the luciferase assay for each starting genotype (on the left) and for three individual variants picked at the end of one or more PACE trajectories (index numbers). Each box displays the normalized mean of three biological replicates for one variant. Trajectories initiated from starting points produced by PACE (green) and then selected for a non-historical function (loss of BID binding) went extinct .</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig9-v2.tif"/></fig><fig id="fig9s1" position="float" specific-use="child-fig"><label>Figure 9—figure supplement 1.</label><caption><title>Selection scheme and phage titers for the gain of NOXA specificity.</title><p>(<bold>A</bold>) Timeline of PACE experiments where hsMCL-1 and two previously evolved NOXA-binding hsBCL-2 variants were evolved to maintain NOXA binding and lose BID binding. Selection conditions: arrow, selection for binding NOXA (red); blunt bar, selection against binding a specific peptide (BID [blue] or ZBneg [gray]). (<bold>B</bold>) Phage titers (PFU/mL) over time (bottom) and activity-dependent phage titers at the end of the PACE experiment (top) where hsMCL-1 and NOXA-binding hsBCL-2 variants were evolved for binding NOXA and against BID. Activity-dependent plaque assays used plasmids 28–48 and Jin 518. Limit of detection = 10<sup>3</sup> PFU/mL. (<bold>C</bold>) Allele frequency of non-wild-type states after hsMCL-1 was evolved to maintain NOXA binding and lose BID binding. Site numbers and wild-type (WT) amino acid states are listed above each sequence. Each row represents an independent replicate lagoon. Non-wild-type amino acid frameshifts that reached &gt;5% in frequency are shown, with frequency proportional to color saturation.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig9-figsupp1-v2.tif"/></fig><fig id="fig9s2" position="float" specific-use="child-fig"><label>Figure 9—figure supplement 2.</label><caption><title>Selection scheme and phage titers for the regain of BID specificity.</title><p>Phage titers (PFU/mL) over time (bottom) and activity-dependent phage titers at the end of the PACE experiment (top) where NOXA-binding hsBCL-2 variants were evolved to lose NOXA binding.</p><p>Activity-dependent plaque assays used plasmids 28–46 and Jin 487.</p></caption><graphic mime-subtype="tiff" mimetype="image" xlink:href="elife-67336-fig9-figsupp2-v2.tif"/></fig></fig-group></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>The two major paradigms of 20th-century evolutionary biology – the adaptationist program (<xref ref-type="bibr" rid="bib57">Mayr, 1983</xref>) and the neutral theory of molecular evolution (<xref ref-type="bibr" rid="bib50">Kimura, 1986</xref>) – focus on either necessity or chance, respectively, as the primary mode of causation that produces natural variation in molecular sequences. Neither of these schools of thought admits much influence from contingency or history. From an adaptationist perspective, variation is caused by natural selection, which generates optimal forms under different environmental conditions. Differences in protein sequence or other properties are interpreted as the result of adaptive changes that improved a molecule’s ability to perform its function in the species’ particular environment (<xref ref-type="bibr" rid="bib35">Goodsell and Olson, 2000</xref>; <xref ref-type="bibr" rid="bib66">Nguyen et al., 2017</xref>; <xref ref-type="bibr" rid="bib88">Somero, 1995</xref>; <xref ref-type="bibr" rid="bib105">Závodszky et al., 1998</xref>). For neutralists, variation reflects the influence of chance in choosing among biologically equivalent possibilities, and conservation reflects purifying selection, both of which are viewed as largely unchanging across sequences in an alignment. For example, conserved portions of molecular sequences are interpreted as essential to structure and function, whereas differences in sequence alignments reflect a lack of constraint (<xref ref-type="bibr" rid="bib29">Echave et al., 2016</xref>; <xref ref-type="bibr" rid="bib51">Kimura and Ohta, 1974</xref>; <xref ref-type="bibr" rid="bib69">Perutz et al., 1965</xref>). In neither worldview, does the particular state of a system strongly reflect its past or shape its evolutionary future. Recent work has shown that contingency might athe sequence outcomes of evolution (<xref ref-type="bibr" rid="bib10">Bloom et al., 2010</xref>; <xref ref-type="bibr" rid="bib12">Blount et al., 2012</xref>; <xref ref-type="bibr" rid="bib11">Blount et al., 2008</xref>; <xref ref-type="bibr" rid="bib15">Breen et al., 2012</xref>; <xref ref-type="bibr" rid="bib16">Bridgham et al., 2009</xref>; <xref ref-type="bibr" rid="bib68">Ortlund et al., 2007</xref>; <xref ref-type="bibr" rid="bib71">Pollock et al., 2012</xref>; <xref ref-type="bibr" rid="bib76">Quandt et al., 2015</xref>; <xref ref-type="bibr" rid="bib82">Sailer et al., 2017</xref>; <xref ref-type="bibr" rid="bib85">Shah et al., 2015</xref>; <xref ref-type="bibr" rid="bib91">Starr et al., 2018</xref>), echoing themes raised in paleontology (<xref ref-type="bibr" rid="bib36">Gould, 1989</xref>; <xref ref-type="bibr" rid="bib43">Jablonski, 2017</xref>) and developmental biology (<xref ref-type="bibr" rid="bib32">Gompel et al., 2005</xref>; <xref ref-type="bibr" rid="bib86">Shubin et al., 2009</xref>). Despite these recent findings, the dominance of the adaptationist and neutralist worldviews – and the continuing rhetorical battle between them (<xref ref-type="bibr" rid="bib44">Jensen et al., 2019</xref>; <xref ref-type="bibr" rid="bib48">Kern and Hahn, 2018</xref>) – has obscured the possibility that contingency might join selection, drift, and mutation as a primary factor shaping the outcomes of evolution.</p><p>We found that contingency generated by sequence change over phylogenetic timescales plays a profound role in BCL-2 family protein sequence evolution under laboratory selection for new functions. The mutations that rose to high frequency during experimental evolution were almost completely different among evolutionary trajectories initiated from historical starting points separated by long phylogenetic distances. We observed a strong role for chance (because trajectories launched from the same starting point evolved extensive differences from each other) and an even greater effect of contingency (because pools of trajectories launched from different starting genotypes evolved even greater differences). When combined, chance and contingency erased virtually all traces of necessity between individual trajectories initiated from distantly related starting points. With the exception of a single truncation mutation that does not affect the selected-for function, the only predictable sequence states were those that remained unchanged from the starting point in all trajectories, presumably because they are unconditionally necessary for both PPIs tested and were therefore conserved by purifying selection.</p><p>Contingency and chance are distinct but interacting modes of causality; our experiments allowed us to disentangle their individual effects and interactions. By calculating genetic variance among replicates from the same starting point and among pooled replicates from different starting points, we quantified the effect of chance and contingency, respectively. The total effect of chance and contingency together – genetic variance among replicates from different starting points – is by definition the product of the separate effects of chance and contingency. This quantitative relationship reflects the intrinsic interaction between chance and contingency in evolutionary processes (<xref ref-type="bibr" rid="bib9">Beatty and Carrera, 2011</xref>; <xref ref-type="bibr" rid="bib26">Desjardins, 2011</xref>). At any point in history, numerous sets of mutations were accessible, and chance determined which ones occurred. These chance events then determined the steps that could be taken during future intervals, because of contingency. Without chance, contingency – dependence of the accessibility of future trajectories on the protein’s state – would never be realized or observed: all phylogenetic lineages launched from a common ancestor would always lead to the same intermediate steps and thus the same ultimate outcomes. Conversely, without contingency, chance events would have no impact on the accessibility of other mutations because every path that was ever open would remain forever so, irrespective of the random events that happen to take place. The outcomes of evolution from a common ancestral starting point are therefore unpredictable when intermediate steps shape future possibilities (contingency), and those intermediate steps cannot be predicted because multiple possibilities are accessible at any point in history (chance).</p><p>Our experimental design approximates but does not quite achieve the ideal design of multireplicate evolution from ancestral starting points under historical conditions, because the conditions we imposed during PACE differ in several ways from those that pertained during historical evolution. Many factors that give rise to chance, contingency, and necessity are likely to be similar between history and our experiments. For example, factors related to a protein’s sequence–structure–function relations – such as the number of mutations that can produce a particular function and the nature of epistasis among them – play a key role in chance and contingency and are shared between PACE and history. Other aspects of our design may underestimate the effects of chance and contingency during history. For example, the population genetic parameters in our experimental conditions favor determinism because they involve very large population sizes, strong selection pressures, and high mutation rates, all directed at a single gene. If population sizes during historical BCL-2 family evolution involved smaller populations, weaker selection, lower mutation rates, and a larger genetic ‘target size’ for adaptation, as seems likely, then chance would have played an even larger role during history than in our experiments. In addition, we used human BID and NOXA as fixed binding partners, but during real evolution these proteins would have varied in sequence as well, introducing opportunities for chance and contingency to further affect the sequence outcomes of BCL-2 evolution.</p><p>Some differences between our design and the biological setting of historical BCL-2 family evolution could have overestimated chance’s historical role. We selected for PPI interactions with two particular peptides, leaving out many potential cellular binding partners. PACE takes place in the cytosol of <italic>E. coli</italic> cells, but BCL-2 evolution occurred in animal cells, and natural BCL-2 proteins are partially membrane-bound. These additional dimensions of BCL-2 biological function could have imposed additional selective constraints on the evolution of BCL-2 family proteins historically, reducing the number of functionally equivalent genotypes available to chance. We used peptide fragments from coregulator proteins rather than full-length BID and NOXA; however, the peptide-binding cleft is cytosolic, and recent work indicates that relative affinity of BCL-2 family proteins is similar between peptides and full-length coactivators, although absolute affinity is typically higher in the latter case (<xref ref-type="bibr" rid="bib46">Kale et al., 2018</xref>). Whether these differences quantitatively affect chance and contingency in PACE versus historical evolution is unknown. Finally, because our experimental design imposed selection for new PPI specificities, it does not reveal the effects of chance and contingency under different selective regimes, such as purifying selection to maintain an existing function, which may or may not be similar.</p><p>We studied a particular protein family as a model, but we expect that qualitatively similar results may apply to many other proteins. Epistasis is a common feature of protein structure and function, so the accumulating effect of contingency across phylogenetic time in the BCL-2 family will probably be a general feature of protein evolution, although its rate and extent are likely to vary among protein families and timescales (<xref ref-type="bibr" rid="bib19">Chandler et al., 2013</xref>; <xref ref-type="bibr" rid="bib38">Harms and Thornton, 2014</xref>; <xref ref-type="bibr" rid="bib85">Shah et al., 2015</xref>; <xref ref-type="bibr" rid="bib110">Zhu et al., 2018</xref>). The influence of chance depends upon the existence of multiple mutational sets that can confer a new function; this kind of degeneracy is likely to pertain in many cases: greater determinism is expected for functions with very narrow sequence–structure–function constraints, such as catalysis (<xref ref-type="bibr" rid="bib39">Hawkins et al., 2018</xref>; <xref ref-type="bibr" rid="bib47">Karageorgi et al., 2019</xref>; <xref ref-type="bibr" rid="bib59">Menéndez-Arias, 2010</xref>; <xref ref-type="bibr" rid="bib60">Meyer et al., 2012</xref>; <xref ref-type="bibr" rid="bib83">Salverda et al., 2011</xref>; <xref ref-type="bibr" rid="bib92">Storz, 2016</xref>), than those for which sequence requirements are less strict, such as substrate binding (<xref ref-type="bibr" rid="bib12">Blount et al., 2012</xref>; <xref ref-type="bibr" rid="bib90">Starr et al., 2017</xref>; <xref ref-type="bibr" rid="bib104">Yokoyama et al., 2008</xref>; <xref ref-type="bibr" rid="bib108">Zheng et al., 2019</xref>). Consistent with this prediction, when experimental evolution regimes have imposed diffuse selection pressures on whole organisms, making loci across the entire genome potential sources of adaptive mutations, virtually no repeatability has been observed among replicates (<xref ref-type="bibr" rid="bib53">Kryazhimskiy et al., 2014</xref>; <xref ref-type="bibr" rid="bib102">Wünsche et al., 2017</xref>).</p><p>The method that we developed for rapid evolution of PPI specificity has several advantages that can be extended to other protein families. First, by using PACE, many replicates can be evolved in parallel across scores or hundreds of generations in just days, with minimal need for intervention by the experimentalist (<xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>). Second, our split RNAP design for acquiring new PPIs has fewer components than previous methods for this purpose, such as two-hybrid designs; this makes it considerably easier to tune and optimize and therefore to extend to other protein systems. Third, unlike approaches that attempt to evolve specific PPIs by alternating selection and counterselection through time, our platform simultaneously imposes selection and counterselection within the same cell, thus selecting for specificity directly. By combining these elements in a single system, our platform should allow rapid multireplicate evolution of new cytosolic PPI specificities in a variety of protein families.</p><p>Our results have implications for efforts to engineer proteins with desired properties. We found no evidence that ancestral proteins were more or less ‘evolvable’ than extant proteins: the selected-for phenotypes readily evolved from both extant and ancestral proteins with the same starting binding capabilities. Moreover, chance’s effect was virtually constant across ~1 billion years of evolution, indicating that the number of accessible mutations in the deep past that could confer a selected-for function was apparently no greater than it is now. Nevertheless, the strong effect of contingency that we observed on sequence evolution – and its partial role in the acquisition of new functions per se – suggests that efforts to produce proteins with new functions by design or directed evolution will be most effective and will lead to more diverse sets of sequence outcomes, if they use multiple different protein sequences as starting points, ideally separated by long intervals of sequence evolution. Ancestral proteins can be useful for this purpose simply because they provide routes to functions that were inaccessible from extant protein, even if those routes are not fundamentally different in number or kind.</p><p>Finally, our work has implications for understanding the processes of protein evolution and the significance of natural sequence variation. Our observations suggest that sequence–structure–function associations apparent in sequence alignments are to a significant degree the result of contingent constraints that were transiently imposed or removed by chance events during history (<xref ref-type="bibr" rid="bib34">Gong et al., 2013</xref>; <xref ref-type="bibr" rid="bib38">Harms and Thornton, 2014</xref>; <xref ref-type="bibr" rid="bib91">Starr et al., 2018</xref>; <xref ref-type="bibr" rid="bib90">Starr et al., 2017</xref>). Evolutionary explanations of sequence diversity and conservation must therefore explicitly consider the historical trajectories by which sequences evolved, in contrast to the largely history-free approaches of the dominant schools of thought in molecular evolution. Our findings suggest that present-day BCL-2 family proteins – and potentially many others, as well – are largely physical anecdotes of their particular unpredictable histories: their sequences reflect the interaction of accumulated chance events during descent from common ancestors with necessity imposed by physics, chemistry, and natural selection. Apparent ‘design principles’ in the pattern of variability and conservation in extant proteins reflect not how things must be to perform their functions, or even how they can best do so. Rather, today’s proteins reflect the legacy of opportunities and limitations that they just happen to have inherited.</p></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><table-wrap id="keyresource" position="anchor"><label>Key resources table</label><table frame="hsides" rules="groups"><thead><tr><th>Reagent type (species) or resource</th><th>Designation</th><th>Source or reference</th><th>Identifiers</th><th>Additional information</th></tr></thead><tbody><tr><td>Strain, strain background <break/>(<italic>Escherichia coli</italic>)</td><td>S1030</td><td><xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref></td><td/><td/></tr><tr><td>Strain, strain background <break/>(<italic>Escherichia coli</italic>)</td><td>1059</td><td><xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref></td><td/><td/></tr><tr><td>Strain, strain background <break/>(<italic>Escherichia coli</italic>)</td><td>NEB 10-beta</td><td>NEB</td><td>Cat# C3019I</td><td/></tr><tr><td>Strain, strain background <break/>(<italic>Escherichia coli</italic>)</td><td>BCL21 (DE3)</td><td>NEB</td><td>Cat# C2530H</td><td/></tr><tr><td>Peptide, recombinant protein</td><td>BID</td><td>GenScript</td><td>This Study</td><td>Human BID peptide used for fluorescence polarization (see Materials and methods)</td></tr><tr><td>Peptide, recombinant protein</td><td>NOXA</td><td>Genscript</td><td>This study</td><td>Human NOXA peptide used for fluorescence polarization (see Materials and methods)</td></tr><tr><td>Commercial assay or kit</td><td>DNA clean and concentrator kit</td><td>Zymo</td><td>Cat# D4013</td><td/></tr><tr><td>Commercial assay or kit</td><td>MiSeq Reagent Kit v3</td><td>Illumina</td><td>Cat# MS-102–3003</td><td/></tr><tr><td>Chemical compound, drug</td><td>Q5 DNA Polymerase</td><td>NEB</td><td>Cat# M0491</td><td/></tr><tr><td>Chemical compound, drug</td><td>Phusion DNA polymerase</td><td>ThermoFisher Scientific</td><td>Cat# F518L</td><td/></tr><tr><td>Chemical compound, drug</td><td>Isopropyl-b-D-thiogalactopyranoside (IPTG)</td><td>bioWORLD</td><td>Cat# 21530057</td><td/></tr><tr><td>Chemical compound, drug</td><td>His60 Ni Superflow Resin</td><td>Takara</td><td>Cat# 635660</td><td/></tr><tr><td>Software, algorithm</td><td>Geneious</td><td>Geneious</td><td>10.1.3</td><td/></tr><tr><td>Software, algorithm</td><td>R</td><td>CRAN</td><td>3.5.1</td><td/></tr><tr><td>Software, algorithm</td><td>RStudio</td><td>RStudio</td><td>1.1.456</td><td/></tr><tr><td>Software, algorithm</td><td>PROT Test</td><td><xref ref-type="bibr" rid="bib1">Abascal et al., 2005</xref></td><td>3.4.2</td><td/></tr><tr><td>Software, algorithm</td><td>RAXML-ng</td><td><xref ref-type="bibr" rid="bib52">Kozlov and Stamatakis, 2019</xref></td><td>0.6.0</td><td/></tr></tbody></table></table-wrap><sec id="s4-1"><title>Phylogenetics</title><p>Amino acid sequences of the human BCL-2, BCLW, BCL-xL, MCL-1, NRH, BFL1, BAK, BAX, and BOK paralogs were used as starting points for identifying BCL-2 family members in other species. For each paralog, tblastn and protein BLAST on NCBI BLAST were used to identify orthologous sequences between January and March of 2018 (<xref ref-type="bibr" rid="bib2">Altschul et al., 1997</xref>). Sequences for each paralog were aligned using MAFFT (G-INS-I) with the –allowshift option and –unalignlevel set at 0.1. For each paralog, phylogenetic structure was determined using fasttree 2.1.11 within Geneious 10.1.3. Missing clades based on known species relationships were then identified, and specific tblastn searches were used within Afrotheria (taxid:311790), Marsupials (taxid:9263), Monotremes (taxid:9255), Squamata (taxid:8509), Archosauria (taxid:8492), Testudinata (taxid:8459), Amphibia (taxid:8292), Chondrichthyes (taxid:7777), Actinopterygii (taxid:7898), Dipnomorpha (taxid:7878), Actinistia (taxid:118072), Agnatha (taxid:1476529), Cephalochordata (taxid:7735), and Tunicata (taxid:7712) as needed. Additional sequences were added by downloading genome and transcriptome data for tuatara (<xref ref-type="bibr" rid="bib61">Miller et al., 2012</xref>), sharks and rays (<xref ref-type="bibr" rid="bib103">Wyffels et al., 2014</xref>), gar (<xref ref-type="bibr" rid="bib106">Zerbino et al., 2018</xref>), ray-finned fish (<xref ref-type="bibr" rid="bib42">Hughes et al., 2018</xref>), lamprey (<xref ref-type="bibr" rid="bib87">Smith et al., 2018</xref>), hagfish (<xref ref-type="bibr" rid="bib93">Takechi et al., 2011</xref>), <italic>Ciona savignyi</italic> (<xref ref-type="bibr" rid="bib106">Zerbino et al., 2018</xref>), tunicates (<xref ref-type="bibr" rid="bib25">Delsuc et al., 2018</xref>), echinoderms (<xref ref-type="bibr" rid="bib79">Reich et al., 2015</xref>), porifera (<xref ref-type="bibr" rid="bib80">Riesgo et al., 2014</xref>), and ctenophores (<xref ref-type="bibr" rid="bib63">Moroz et al., 2014</xref>). In each case, local BLAST databases were created in Geneious and searched using tblastn. Finally, we used BCL-2DB to add missing groups as needed (<xref ref-type="bibr" rid="bib78">Rech de Laval et al., 2014</xref>).</p><p>After collection of sequences, each paralog was realigned using MAFFT (G-INS-I) with the –allowshift option and –unalignlevel set at 0.1. Based on known species relationships, lineage-specific insertions were removed and gaps manually edited. Only a single sequence was kept among pairs of sequences differing by a single amino acid and sequences with more than 25% of missing sites were removed. For difficult to align sequences, sequences were modeled on the structures of human BCL-2 family members using SWISS-Model to identify likely locations of gaps (<xref ref-type="bibr" rid="bib98">Waterhouse et al., 2018</xref>). Finally, paralogs were profile aligned to each other, and paralog-specific insertions were identified.</p><p>In total, 151 amino acid sites from 745 taxa were used to infer the phylogenetic relationships among BCL-2 family paralogs. PROT Test 3.4.2 was used to identify the best-fit model among JTT, LG, and WAG, with combinations of observed amino acid frequencies (+F), gamma distributed rate categories (+G), and an invariant category (+I) (<xref ref-type="bibr" rid="bib1">Abascal et al., 2005</xref>). From this, JTT + G + F had the highest likelihood and lowest Aikake Information Criterion score. RAXML-ng 0.6.0 was then used to identify the maximum likelihood tree using JTT+G12+F0 (12 gamma rate categories with maximum likelihood estimated amino acid frequencies) (<xref ref-type="bibr" rid="bib52">Kozlov and Stamatakis, 2019</xref>). Finally, we enforced monophyly within each paralog for the following groups: lobe-finned fish (n = 9), ray-finned fish (n = 9), jawless fish (n = 5), cartilaginous fish (n = 8), tunicates (n = 4), branchiostoma (n = 4), chordates (n = 5), ambulacraria (n = 5, hemichordata +echinodermata), deuterostomia (n = 5), protostomia (n = 5), cnidaria (n = 5), and porifera (n = 4) (values in parenthesis are number of identified paralogs in each group) and used RAXML-ng with JTT + G12 + F0 to identify the best tree given these constraints (Supplementary Data Phylogenetic.Data.zip).</p><p>Overall, we recovered three clades: a pro-apoptotic clade; a clade containing the BCL-2, BCLW, and BCLX vertebrate paralogs and BCL non-vertebrate sequences; and a clade containing the MCL-1, BFL1, and NRH vertebrate paralogs and MCL non-vertebrate sequences. We used the pro-apoptotic clade as the outgroup to the two anti-apoptotic clades. Within the BCL-2 clade, the majority of vertebrates contained all three copies. However, the exact relationship among the paralogs was unclear; only two copies were identified within jawless fish and their phylogenetic placement had weak support. Non-vertebrate clades tended to have good support and only a single copy. However, support for these groups following established species relationships was often limited. The MCL-1 clade contained the fastest evolving paralogs of the BCL-2 family. As with the BCL-2-like clade, only two copies were found within the jawless fish and the exact sister relationships among paralogs was unclear. Non-vertebrates contained only a single copy, but as with the BCL-2-like clade, support for relationships following established species relationships was often weak.</p><p>The BCL-2-like and MCL-1-like paralogs formed a clade with the BHP1 and BHP2 sequences from porifera. The sister relationships among these four clades were unresolved. In addition, we recovered a sister relationship between the BAK and BAX paralogs. While both paralogs contained copies from porifera, these clades evolved quickly and had relatively low support, and they may be artifactual. We identified only a single clade of ctenophores. Finally, the placement of BOK was unresolved; BOK may be sister to the BAK/BAX clade or an outgroup to all clades and the most ancient copy of the BCL-2 family.</p></sec><sec id="s4-2"><title>Ancestral reconstruction</title><p>Posterior probabilities of each amino acid at each site were inferred using Lazarus (<xref ref-type="bibr" rid="bib31">Finnigan et al., 2012</xref>) to run codeml within PAML. We used the same model and alignment as used to infer the phylogeny. We used the branch lengths and topology of the constrained maximum likelihood phylogeny found by raxml-ng.</p><p>We first reconstructed the LCAs of all BCL-2 and MCL-1 like sequences, AncMB1-M, using the maximum likelihood state for each alignable site. We then reconstructed a series of ancestors from AncMB1 to modern human MCL-1. These included AncM1 (LCA of MCL-1-related sequences), AncM2 (LCA of MCL-1- related deuterostomes and protostomes), AncM3 (LCA of MCL-1-related deuterostomes), AncM4 (LCA of MCL-1-related urochordates and chordates), AncM5 (LCA of MCL-1, BFL1, and NRH like copies in vertebrates), AncM6 (LCA of MCL-1 and BFL1 like copies), AncMCL-1 (LCA of MCL-1 like copies), AncMCL-1-G (LCA of MCL-1 like Gnathostomes), AncMCL-1-O (LCA of MCL-1 like Osteichthyes), and AncMCL-1-T (LCA of MCL-1 like Tetrapods), AncMCL-1-A (LCA of MCL-1 like Amniotes), and AncMCL-1-M (LCA of MCL-1 like Mammals). In each case, the sequence of each ancestor used the maximum likelihood state at each site, with gaps inserted based on parsimony. We used the modern sequences of human MCL-1 to fill in portions of the sequence that showed poor alignment and could not be reconstructed, including both the N and C terms, as well as the loop between the first and second alpha helices. Average posterior probabilities for ancestors in the MCL-1 clade ranged from 0.73 (AncM6) to 0.98 (AncMCL-1-M) with an average of 0.83 (sd 0.08) (<xref ref-type="supplementary-material" rid="supp2">Supplementary file 2</xref>).</p><p>For the BCL-2 like clade, we also reconstructed AncMB1, this time using human BCL-2 sequence to fill in the N and C terms and the loop between the first and second alpha helices (AncMB1-B). We then reconstructed sequences from AncMB1 to modern human BCL-2. These included AncB1 (LCA of BCL-2-related sequences), AncB2 (LCA of BCL-2-related Bilaterian and Cnidaria), AncB3 (LCA of BCL-2-related deuterostomes and protostomes), AncB4 (LCA of BCL-2 deuterostomes), AncB5 (LCA of BCL-2, BCLW, and BCLX like copies in vertebrates), AncBCL-2 (LCA of BCL-2 like copies), AncBCL-2-G (LCA of BCL-2 like gnathostomes), AncBCL-2-O (LCA of BCL-2 like osteichthyes), and AncBCL-2-T (LCA of BCL-2 like tetrapods), using human BCL-2 sequences for the N and C terms and the loop between the first and second alpha helices. Average posterior probabilities for ancestors in the BCL-2 clade ranged from 0.87 (AncB1) to 0.95 (AncBCL-2-T) with an average of 0.9 (sd 0.04).</p></sec><sec id="s4-3"><title>Test of robustness of ancestral inference</title><p>To determine the robustness of our conclusions on the phenotype of ancestral sequences, we synthesized and cloned alternative reconstructions for key ancestors. In each case, sequences contained the most likely alternative state with posterior probability &gt; 0.2 for all such sites where such a state existed. Alternative reconstructions contained an average of 24 alternative states and represent a conservative test of function (min: 4, max: 44, <xref ref-type="supplementary-material" rid="supp2">Supplementary file 2</xref>). In our luciferase assay, all but two alternative reconstructions retained similar BID and NOXA binding as the maximum likelihood ancestral sequences. The first alternative reconstruction that differed from the maximum likelihood reconstruction was AltAncB3, which bound both BID and NOXA, while the ML for AncB3 bound BID, but NOXA only weakly. As a result, the exact branch upon which NOXA binding was lost historically is not resolved by this data.</p><p>The second alternative reconstruction that differed from the ML reconstruction was AltAncMB1-B, which had weaker NOXA binding than the ML reconstruction. To further test the robustness of AncMB1-B to alternative reconstructions, we synthesized and tested additional reconstructions that included only alternative amino acids with posterior probabilities greater than 0.4 (n = 3), 0.35 (n = 7), 0.3 (n = 13), and 0.25 (n = 18), and compared these to AncMB1-B and the 0.2 AltAncMB1-B (n = 21) (values in parentheses are number of states that differ from the ML state). We found that the 0.4, 0.35, and 0.3 alternative reconstructions bound both BID and NOXA, while the 0.25 and 0.2 alternative reconstructions had diminished NOXA binding.</p><p>Finally, we synthesized and tested modern sequences from key groups to determine the robustness of our inference on the timing of NOXA binding loss. These included BCL-2-related sequences from groups that diverged prior to the predicted loss of NOXA binding (<italic>Trichoplax adhaerens</italic> and <italic>Hydra magnapapillata</italic>), sequences from groups that diverged around the time of predicted NOXA binding loss (<italic>Octopus bimaculoides</italic> and <italic>Stegodyphus mimosarum</italic>), or sequences from groups predicted to have diverged after NOXA binding lost (<italic>Saccoglossus kowalevskii</italic> and <italic>Branchiostoma belcheri</italic>). In each case, we used human BCL-2 sequence to replace extant N and C terms and the loop between the first and second alpha helices. The <italic>T. adhaerens</italic> and <italic>B. belcheri</italic> sequences were non-functional in our luciferase assays, binding neither BID nor NOXA. However, recent work has comprehensively characterized binding in BCL-2 family members within <italic>T. adhaerens</italic>, finding that the BCL copy can bind both BID and NOXA as predicted (<xref ref-type="bibr" rid="bib72">Popgeorgiev et al., 2020</xref>). <italic>H. magnapapillata</italic> bound both BID and NOXA in our assay and the remaining sequences bound only BID, suggesting a loss of NOXA binding prior to the divergence of protostomes and deuterostomes in the BCL-2 related clade, consistent with the conclusion drawn using reconstructed proteins.</p></sec><sec id="s4-4"><title><italic>Escherichia coli</italic> strains</title><p><italic>E. coli</italic> 10-beta cells were used for cloning and were cultured in 2xYT media. <italic>E. coli</italic> BL21 (BE3) cells were used for protein expression and were cultured in Luria-Bertain (LB) broth. <italic>E. coli</italic> S1030 cells cultured in LB broth were used for activity-dependent plaque assays, phage growth assays, and luciferase assays. S1030 cells cultured in Davis Rich media were used for PACE experiments (<xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref>). <italic>E. coli</italic> 1059 cells were used for cloning phage and assessing phage titers and were cultured in 2xYT media.</p></sec><sec id="s4-5"><title>Cloning and general methods</title><p>Plasmids were constructed by using Q5 DNA Polymerase (NEB) to amplify fragments that were then ligated via Gibson Assembly. Primers were obtained from IDT, and all plasmids were sequenced at the University of Chicago Comprehensive Cancer Center DNA Sequencing and Genotyping Facility. Vectors and gene sequences used in this study are listed in <xref ref-type="supplementary-material" rid="supp5">Supplementary file 5</xref>, with links to fully annotated vector maps on Benchling. Key vectors are deposited at Addgene, and all vectors are available upon request. The following working concentrations of antibiotics were used: 50 µg/mL carbenicillin, 50 µg/mL spectinomycin, 40 µg/mL kanamycin, and 33 µg/mL chloramphenicol. Protein structures and alignments were generated using the program PyMOL (<xref ref-type="bibr" rid="bib84">Schrödinger, 2018</xref>).</p></sec><sec id="s4-6"><title>Luciferase assay</title><p>Cloned expression vectors contained the following: (1) a previously evolved, isopropyl β-D-1-thiogalactopyranoside (IPTG)-inducible N-terminal half of T7 RNAP (<xref ref-type="bibr" rid="bib111">Zinkus-Boltz et al., 2019</xref>) fused to a BCL-2 family protein; (2) the C-terminal half of T7 RNAP fused to a peptide from a BH3-only protein; and (3) T7 promoter-driven luciferase reporter. Chemically competent S1030 <italic>E. coli</italic> cells (<xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref>) were prepared by culturing to an OD<sub>600</sub> of 0.3, washing twice with a calcium chloride/HEPES solution (60 mM CaCl<sub>2</sub>, 10 mM HEPES pH 7.0, 15% glycerol), and then resuspending in the same solution. Vectors were transformed into chemically competent S1030 cells via heat shock at 42°C for 45 s, followed by 1 hr recovery in 3× volume of 2xYT media, and then plated on agar with the appropriate antibiotics (carbenicillin, spectinomycin, and chloramphenicol) to incubate overnight at 37°C. Individual colonies (three to four biological replicates per condition) were picked and cultured in 1 mL of LB media containing the appropriate antibiotics overnight at 37°C in a shaker. The next morning, 50 µL of each culture was diluted into 450 µL of fresh LB media containing the appropriate antibiotics, as well as 1 µM of IPTG. The cells were incubated in a shaker at 37°C, and OD<sub>600</sub> and luminescence measurements were recorded between 2.5 and 4.5 hr after the start of the incubation. Measurements were taken on a Synergy Neo2 Microplate Reader (BioTek) by transferring 150 µL of the daytime cultures into Corning black, clear-bottom 96-well plates. Data were analyzed in Microsoft Excel and plotted in GraphPad Prism, as previously reported (<xref ref-type="bibr" rid="bib73">Pu et al., 2017a</xref>).</p><p>Protein expression hsBCL-2, hsMCL-1, and evolved variants were constructed as N-terminal 6xHis-GST tagged proteins. The recombinant proteins were expressed in BL21 <italic>E. coli</italic> (NEB) and purified following standard Ni-NTA resin purification protocols (ThermoFisher Scientific) (<xref ref-type="bibr" rid="bib109">Zhou et al., 2019</xref>). Briefly, BL21 <italic>E. coli</italic> containing an N-terminal 6xHis-GST tagged BCL-2 family protein were cultured in 5 mL LB with carbenicillin overnight. The following day, the culture was added to 0.5 L of LB with carbenicillin, incubated at 37°C until it reached an OD<sub>600</sub> of 0.6, induced with IPTG (final concentration: 200 µM), and cultured overnight at 16°C. The cell pellet was harvested by centrifugation followed by resuspension in 30 mL of lysis buffer (50 mM Tris 1 M NaCl, 20% glycerol, 10 mM TCEP, pH 7.5) supplemented by protease inhibitors (200 nM Aprotinin, 10 µM Bestatin, 20 µM E-64, 100 µM Leupeptin, 1 mM AEBSF, 20 µM Pepstatin A). Cells were lysed via sonication and were then centrifuged at 12,000 g for 40 min at 4°C. Solubilized proteins, located in the supernatant, were incubated with His60 Ni Superflow Resin (Takara) for 1 hr at 4°C, and the protein was eluted using a gradient of imidazole in lysis buffer (50–250 mM). Fractions with the protein, as determined by SDS-PAGE, were concentrated in Ulta-50 Centrifugal Filter Units (Amicon, EMD Millipore). Proteins were purified via a desalting column with storage buffer (50 mM Tris–HCl [pH 7.5], 300 mM NaCl, 10% glycerol, 1 mM DTT) and further concentrated. The concentration of the purified BCL-2 family proteins was determined by BCA assay (ThermoFisher Scientific), and they were flash-frozen in liquid nitrogen and stored at −80°C.</p></sec><sec id="s4-7"><title>Fluorescent polarization binding assays</title><p>Fluorescent polarization (FP) was used to measure the affinity of BCL-2 family proteins with peptide fragments of the BH3-only proteins in accordance with previously described methods (<xref ref-type="bibr" rid="bib107">Zhang et al., 2002</xref>). hsBCL-2, hsMCL-1, and evolved variants were purified as described above. The fluorescent NOXA and BID peptides (95+% purity) were synthesized by GenScript and were N-terminally labeled with 5-FAM-Ahx and C-terminally modified by amidation. These peptides were dissolved and stored in DMSO. Corning black, clear-bottom 384-well plates were used to measure FP, and three replicates were prepared for each data point. Each well contained the following 100 µL reaction: 20 nM BH3-only protein, 0.05 nM to 3 µM of BCL-2 family protein (1/3 serial dilutions), 20 mM Tris (pH 7.5), 100 mM NaCl, 1 mM EDTA, and 0.05% pluronic F-68. FP values (in milli-polarization units; mFP) of each sample were read by a Synergy Neo2 Microplate Reader (BioTek) with the FP 108 filter (485/530) at room temperature 5–15 min after mixing all the components. Data were analyzed in GraphPad Prism 8, using the following customized fitting equation, to calculate <italic>K<sub>d</sub></italic> (<xref ref-type="bibr" rid="bib109">Zhou et al., 2019</xref>):<disp-formula id="equ1"><mml:math id="m1"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mi/><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:msqrt><mml:msup><mml:mrow><mml:mfenced separators="|"><mml:mrow><mml:mi>D</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:mi/><mml:mn>4</mml:mn><mml:mi>D</mml:mi><mml:mi>x</mml:mi></mml:msqrt><mml:mo>)</mml:mo></mml:math></disp-formula>where <italic>y</italic> is normalized measured FP, <italic>x</italic> is the concentration of BCL-2 protein, <italic>D</italic> is the concentration of the BH3-only protein, <italic>B</italic> and <italic>C</italic> are parameters related to the FP value of free and bound BH3-only protein, and <italic>K<sub>d</sub></italic> is the dissociation constant.</p></sec><sec id="s4-8"><title>Phage-assisted continuous evolution</title><p>PACE was used to evolve hsBCL-2, hsMCL-1, and ancestral proteins in accord with previously reported technical methods (<xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref>; <xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>; <xref ref-type="bibr" rid="bib75">Pu et al., 2019</xref>; <xref ref-type="bibr" rid="bib74">Pu et al., 2017b</xref>) using a new vector system. Briefly, combinations of accessory plasmids and the MP6 mutagenesis plasmid (<xref ref-type="bibr" rid="bib5">Badran and Liu, 2015</xref>) were transformed into S1030 <italic>E. coli</italic>., plated on agar containing the appropriate antibiotics (carbenicillin, kanamycin, and chloramphenicol) and 10 mM glucose, and incubated overnight at 37°C. Colonies were grown overnight in 5 mL of LB containing the appropriate antibiotics and 20 mM glucose. Davis Rich media was prepared in 5–10 L carboys and autoclaved, and the PACE flasks and corresponding pump tubing were autoclaved as well. The following day, PACE was set up in a 37°C environmental chamber (Forma 3960 environmental chamber, ThermoFisher Scientific). For each replicate, an overnight culture was added to ~150 mL of Davis Rich carboy media in chemostats and grown for 2–3 hr until reaching an OD<sub>600</sub> of approximately 0.6. Lagoons containing 20 µL of phage from saturated phage stocks (10<sup>8</sup>–10<sup>9</sup> phage) were then connected to the chemostat. Magnetic stir bars were used to agitate chemostats and lagoons. The chemostat cultures were flowed into the lagoons at a rate of approximately 20 mL/h. Waste output flow rates were adjusted to maintain a constant volume of 20 mL in the lagoons, 150 mL in the chemostat, and an OD<sub>600</sub> close to 0.6 in the chemostat. A 10% w/v arabinose solution was pumped into the lagoons at a rate of 1 mL/h. If the experiment included a mixing step (two separate chemostats flowed together into one lagoon for a mixed selection pressure), a chemostat was prepared the next day (as described above) and connected to the lagoons. During this step, lagoon volumes were increased to 40 mL, and the arabinose inflow rate was increased to 2 mL/h. After disconnecting the first chemostat the next day, the lagoon volumes and arabinose inflow were both lowered to 20 mL and 1 mL/h, respectively. During the experiment, samples were collected from the lagoons every 24 hr and centrifuged at 13,000 rpm for 3 min to collect the phage-containing supernatant, as well as the cell pellet for DNA extraction. PACE experiments are listed in <xref ref-type="supplementary-material" rid="supp3">Supplementary file 3</xref>. A single replicate of AncB5 was removed because of contamination. No statistical method was used to determine the number of replicates as only four independent replicate experiments could be performed simultaneously.</p><p>During PACE, the media volume of each lagoon turned over once per hour for 4 days, or ~100 times. For a phage population to survive this amount of dilution, a similar number of generations must have occurred between the starting phage and the phage in the lagoon at the end of the experiment (<xref ref-type="bibr" rid="bib30">Esvelt et al., 2011</xref>). This is expected to be a conservative estimate; as a more fit phage rises in frequency in the population, it will undergo a greater number of generations than less-fit phage in the population. The mutagenesis plasmid MP6 induces a mutation rate of approximately 6 × 10<sup>−6</sup> per bp per generation. The BCL2 family proteins used in the PACE experiments were ~230 amino acids long, indicating that a mutation occurred on average every ~250 phage replications. Phage population sizes ranged from 10<sup>5</sup> per mL to 10<sup>10</sup> per mL over the course of a PACE experiment, indicating a rate of 400–40,000,000 new mutations every generation. Conservative estimates thus suggest that a during each individual replicate, phage populations sampled at least 40,000 mutations, and upwards of 4 × 10<sup>9</sup> mutations. While not all mutations were equally likely each generation because MP6 enriches for transitions (i.e. G→A, A→G, C→T, and T→C), the high number of mutations sampled suggests that the vast majority of possible single point mutations (approximately 230*3*4 = 2760 potential mutations) were sampled over the course of each experiment, with higher population sizes generating all potential single point mutations each generation.</p></sec><sec id="s4-9"><title>Plaque assays</title><p>Plaque assays were performed on 1059 <italic>E. coli</italic> cells (<xref ref-type="bibr" rid="bib17">Carlson et al., 2014</xref>; <xref ref-type="bibr" rid="bib41">Hubbard et al., 2015</xref>), which supply gene III (gIII) to phage in an activity-independent manner, to measure phage titers. Additionally, activity-dependent plaque assays were done on S1030 <italic>E. coli</italic> containing the desired accessory plasmids to determine the number of phage encoding a BCL-2 family protein with a given peptide-binding profile. All cells were grown to an OD<sub>600</sub> of approximately 0.6 during the day. Four serial dilutions were done in Eppendorf tubes by serially pipetting 1 μL of phage into 50 µL of cells to yield the following dilutions: 1/50, 1/2500, 1/125,000, and 1/6,250,000. 650 µL of top agar (0.7% agar with LB media) was added to each tube, which was then immediately spread onto a quad plate containing bottom agar (1.5% agar with LB media). Plates were incubated overnight at 37°C. Plaques were counted the following day, and plaque forming units (PFU) per mL was calculated using the following equation:<disp-formula id="equ2"><mml:math id="m2"><mml:mi>P</mml:mi><mml:mi>F</mml:mi><mml:mi>U</mml:mi><mml:mo>=</mml:mo><mml:mn>1000</mml:mn><mml:mi>*</mml:mi><mml:mi>A</mml:mi><mml:mi>*</mml:mi><mml:mi/><mml:msup><mml:mrow><mml:mn>50</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mo>-</mml:mo><mml:mi>B</mml:mi></mml:mrow></mml:msup></mml:math></disp-formula></p><p>Where <italic>A</italic> is the number of plaques in a given quadrant, and <italic>B</italic> is the quadrant number where the phage were counted, in which one is the least dilute quadrant and four is the most dilute quadrant.</p></sec><sec id="s4-10"><title>Phage growth assays</title><p>Phage growth assays were performed by adding the following to a culture tube and shaking at 37°C for 6 hr: 1 mL of LB with the appropriate antibiotics (carbenicillin and kanamycin), 10 µL of saturated S1030 <italic>E. coli</italic> containing the accessory plasmids of interest, and ~1000 phage. Phage were then isolated by centrifugation at 13,000 rpm for 3 min, and PFU was determined by plaque assays using 1059 <italic>E. coli</italic> and the plaque assay protocol described above.</p></sec><sec id="s4-11"><title>High-throughput sequencing library construction</title><p>PACE samples were collected from each lagoon every 24 hr. The lagoon samples were centrifuged at 13,000 rpm for 3 min on a bench top centrifuge to separate supernatant and cell pellet. The phage-containing supernatants were stored at 4°C prior to the creation of sequencing libraries. To prepare Illumina sequencing libraries, each phage sample was cultured overnight with 1059 <italic>E. coli</italic> cells, followed by phage DNA purification (Qiagen plasmid purification reagent buffer), P1 (catalog number 19051), P2 (catalog number 19052), N3 (catalog number 19064), PE (catalog number 19065), and spin column for DNA (EconoSpin, catalog number 1920–250). The resulting DNA concentration was ~50 ng/µL. Freshly generated DNA samples were then used as template for PCR amplification. For each library sample, we amplified three overlapping fragments of the BCL-2 family protein, which are 218–241 bp in length (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>). Each primer also included 6–9 ‘N’s to introduce length variation (<xref ref-type="supplementary-material" rid="supp4">Supplementary file 4</xref>). In total, 12 PCRs were used for each library. Phusion DNA polymerases and buffers (ThermoFisher Scientific, catalog number F518L) were used in the first PCR round to amplify all three fragments for all library sequencing. The 25 µL reaction contained: 0.5 µL of 50 mM MgCl<sub>2</sub>, 0.75 µL of 10 mM dNTP, 0.75 µL Phusion DNA polymerase, 20 ng library DNA, and 0.5 µL of 10 µM primer (each). The PCR were run on a C1000 Touch Thermal Cycler (Bio-Rad), with the following parameters: 98°C for 1 min, followed by 16 cycles of 98°C for 12 s, 58°C for 15 s and 72°C for 45 s, and finally 72°C for 5 min. PCR were purified using the ZYMO DNA clean and concentrator kit (catalog number D4013) and 96 well filter plate (EconoSpin, catalog number 2020–001). The DNA products were dissolved in 30 µL ddH<sub>2</sub>O. All 12 reactions for each library were combined, and 1 µL was used as the template for a second PCR round. PCR components and thermocycler parameters were the same as above, except that the annealing temperature was 56°C, and only 15 rounds of amplification were conducted. The primer and sample combinations are listed in <xref ref-type="supplementary-material" rid="supp4">Supplementary file 4</xref>. PCRs were then purified following the same procedure as previous step. Equal volumes of all 72 library samples were combined and concentration was measured using a Qubit 4 Fluorometer. The total DNA sample was 2.68 ng/µL (equivalent to 10 nM, according to the average length of PCR fragments). DNA samples were diluted to 4 nM from step 4 following the Illumina MiSeq System Denature and Dilute Libraries Guide and then diluted to 12 pM for high-throughput sequencing. The final sample contained 100 µL of 20 pM PhiX spike-in plus 500 µL of the 12 pM library sample. Sequencing was performed on the Illumina MiSeq System using MiSeq Reagent Kit v3 (600-cycle) with paired-end reads according to the manufacturer’s instructions.</p></sec><sec id="s4-12"><title>Processing of Illumina data</title><p>Illumina sequencing yielded 22 million reads, 13 million of which could be matched to a specific sample (<xref ref-type="supplementary-material" rid="supp4">Supplementary file 4</xref>). One replicate for AncB5 was found to be contaminated and removed from further analysis. To process the remaining data, we first used Trim Galore with default settings to trim reads based on quality (<ext-link ext-link-type="uri" xlink:href="https://www.bioinformatics.babraham.ac.uk/projects/trim_galore/">https://www.bioinformatics.babraham.ac.uk/projects/trim_galore/</ext-link>). Then, we used BBMerge, a script in BBTools (<ext-link ext-link-type="uri" xlink:href="https://jgi.doe.gov/data-and-tools/bbtools/">https://jgi.doe.gov/data-and-tools/bbtools/</ext-link>), to merge paired-end reads. Next, we used Clumpify to remove repeated barcode sequences. We then used Seal to identify and bin reads by sample and fragment. Finally, we used BBDuk to remove any primer or adapter sequence present. Scripts and reference sequences are available on Github (<xref ref-type="bibr" rid="bib95">Thornton, 2021</xref>).</p></sec><sec id="s4-13"><title>Illumina sequencing analysis</title><p>Reads were binned by experiment and then aligned to the appropriate WT sequence using Geneious (low sensitivity, five iterations, gaps allowed). Sequences were then processed in R to remove sequences containing ‘N’s or that were not full length. Insertions found in less than 1% of the population and sites that extended outside of the coding region were removed from all sequences. Remaining gaps were standardized among replicates and within an experiment. Finally, allele frequencies were calculated for each site and amino acid, as well as remaining insertions and deletions.</p></sec><sec id="s4-14"><title>Quantifying the effects of chance and contingency on the outcomes of evolution</title><sec id="s4-14-1"><title>Estimating the effects of chance</title><p>Allele frequency differences among replicates started from the same genotype can only be caused by chance events. Thus, to determine the effects of chance (<inline-formula><mml:math id="inf1"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>) on the outcomes of evolution, we compared allele frequencies from replicate PACE experiments started from the same genotype. We compared allele frequencies of individual replicates to the average allele frequencies among replicates started from the same genotype by estimating the probability that two randomly chosen alleles would be different, i.e. the genetic variance, for each replicate individually (<inline-formula><mml:math id="inf2"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>) and the pooled sample of all replicates from a given starting genotype (<inline-formula><mml:math id="inf3"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:math></inline-formula>:<disp-formula id="equ3"><mml:math id="m3"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mi/><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula>where <inline-formula><mml:math id="inf4"><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the probability that two randomly chosen alleles in the same replicate are identical in state and <inline-formula><mml:math id="inf5"><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the probability that two randomly chosen alleles from the pooled replicates started from the same genotype are identical in state. <inline-formula><mml:math id="inf6"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is related to Wright’s F<sub>is</sub> statistic as:<disp-formula id="equ4"><mml:math id="m4"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula><disp-formula id="equ5"><mml:math id="m5"><mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula><disp-formula id="equ6"><mml:math id="m6"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p><p>We used count data from Illumina sequencing to estimate allele frequencies and followed the approach of <xref ref-type="bibr" rid="bib40">Hivert et al., 2018</xref>, which developed a methods of moments estimator, <inline-formula><mml:math id="inf7"><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>, that is appropriate for pooled data and accounts for both the sampling of individuals within a population and the sampling of reads during sequencing. We treated each amino acid site independently and defined the following:<disp-formula id="equ7"><mml:math id="m7"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">#</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi 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mathvariant="normal">n</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext></mml:mrow><mml:mi>g</mml:mi><mml:mtext> </mml:mtext><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext></mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>Using these values, we used the estimator of <inline-formula><mml:math id="inf8"><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> defined in <xref ref-type="bibr" rid="bib40">Hivert et al., 2018</xref> to estimate <inline-formula><mml:math id="inf9"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> for a single site:<disp-formula id="equ10"><mml:math id="m10"><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup><mml:mo>≡</mml:mo><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfenced separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="script">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfenced><mml:msub><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula>where:</p><p><inline-formula><mml:math id="inf10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mstyle></mml:math></inline-formula> is the mean sum-of-squares for pooled replicates.</p><p><inline-formula><mml:math id="inf11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula> is the mean sum-of-squares within replicates.</p><p><inline-formula><mml:math id="inf12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>, is the effective number of individuals after accounting for sampling, with<disp-formula id="equ11"><mml:math id="m11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mtable columnalign="left left" columnspacing="1em" rowspacing="4pt"><mml:mtr><mml:mtd><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mstyle></mml:math></disp-formula>and<disp-formula id="equ12"><mml:math id="m12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>Here, <inline-formula><mml:math id="inf13"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the number of replicates started from genotype <inline-formula><mml:math id="inf14"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="inf15"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the number of individual phage in replicate <inline-formula><mml:math id="inf16"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula> of starting genotype <inline-formula><mml:math id="inf17"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula> in the sample used to make the sequencing library.</p><p>From the relationship between <inline-formula><mml:math id="inf18"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="inf19"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>, we approximated the site-specific effects of chance for a particular starting genotype as:<disp-formula id="equ13"><mml:math id="m13"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mtable columnalign="left left" columnspacing="1em" rowspacing="4pt"><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msubsup><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mover><mml:mi>F</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mfrac></mml:mstyle></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="2em"/><mml:mspace width="2em"/><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>When there were replicates from more than one starting genotype, we calculated <inline-formula><mml:math id="inf20"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>, <inline-formula><mml:math id="inf21"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>, and <inline-formula><mml:math id="inf22"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> separately for each starting genotype and averaged these values together, using weights proportional to the number of replicates for that genotype. Thus:<disp-formula id="equ14"><mml:math id="m14"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>where <inline-formula><mml:math id="inf23"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the number of distinct starting genotypes.</p><p>We then took the average numerator and average denominator as suggested by <xref ref-type="bibr" rid="bib40">Hivert et al., 2018</xref> and <xref ref-type="bibr" rid="bib99">Weir and Cockerham, 1984</xref> for estimating <inline-formula><mml:math id="inf24"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>:<disp-formula id="equ15"><mml:math id="m15"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>where <inline-formula><mml:math id="inf25"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the number of sites.</p></sec><sec id="s4-14-2"><title>Estimating the effects of contingency</title><p>To determine the effects of contingency (<inline-formula><mml:math id="inf26"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>) on the outcomes of evolution, we compared the average allele frequency of replicate PACE experiments between different starting genotypes. For each starting genotype, we pooled all replicates started from that genotype and treated it as a single sample. We compared allele frequencies among genotypes by estimating the probability that two randomly chosen alleles in a sample would be different if they were both drawn from the same starting genotype <inline-formula><mml:math id="inf27"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula> or drawn from different starting genotypes <inline-formula><mml:math id="inf28"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>:<disp-formula id="equ16"><mml:math id="m16"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>where <inline-formula><mml:math id="inf29"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the probability that two randomly chosen alleles from the same starting genotype are identical in state and <inline-formula><mml:math id="inf30"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the probability that two randomly chosen alleles from different starting genotypes are identical in state. To calculate <inline-formula><mml:math id="inf31"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>, we note that the probability of two randomly drawn alleles being different when chosen irrespective of starting genotype is simply the average of the probability of two randomly drawn alleles being different when they are drawn from the same and different starting genotypes, that is:<disp-formula id="equ17"><mml:math id="m17"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></disp-formula>where <inline-formula><mml:math id="inf32"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is the probability that two randomly chosen alleles irrespective of starting genotype are identical in state. From this we have:<disp-formula id="equ18"><mml:math id="m18"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>2</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ19"><mml:math id="m19"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ20"><mml:math id="m20"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>Using this and the fact that <inline-formula><mml:math id="inf33"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> is equivalent to <inline-formula><mml:math id="inf34"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> used above to calculate the effects of chance, we have:<disp-formula id="equ21"><mml:math id="m21"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>This statistic is related to Wright’s F<sub>st</sub> as:<disp-formula id="equ22"><mml:math id="m22"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ23"><mml:math id="m23"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>and<disp-formula id="equ24"><mml:math id="m24"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ25"><mml:math id="m25"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>As with the effects of chance, we used the method of moments estimator defined in <xref ref-type="bibr" rid="bib40">Hivert et al., 2018</xref> to estimate the effects of contingency:<disp-formula id="equ26"><mml:math id="m26"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>F</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>where:</p><p><inline-formula><mml:math id="inf35"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mstyle></mml:math></inline-formula> is the mean sum-of-squares for the entire pooled sample.</p><p><inline-formula><mml:math id="inf36"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula> is the mean sum-of-squares for a starting genotype.</p><p><inline-formula><mml:math id="inf37"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>, is the effective number of individuals after accounting for sampling, with</p><p><inline-formula><mml:math id="inf38"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>π</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mtext> </mml:mtext><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">q</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext></mml:mrow><mml:mtext> </mml:mtext><mml:mi>a</mml:mi><mml:mtext> </mml:mtext><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext> </mml:mtext></mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula>,<disp-formula id="equ27"><mml:math id="m27"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ28"><mml:math id="m28"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ29"><mml:math id="m29"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:mstyle></mml:math></disp-formula>and<disp-formula id="equ30"><mml:math id="m30"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>With <inline-formula><mml:math id="inf39"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> being the number of individual phage used to make the libraries for starting genotype <inline-formula><mml:math id="inf40"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula>.</p><p>From the relationship between <inline-formula><mml:math id="inf41"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="inf42"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula>, we approximated the effects of contingency as:<disp-formula id="equ31"><mml:math id="m31"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mover><mml:mi>F</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mover><mml:mi>F</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ32"><mml:math id="m32"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ33"><mml:math id="m33"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mi>s</mml:mi><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ34"><mml:math id="m34"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula><disp-formula id="equ35"><mml:math id="m35"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>Again, we treated all sites as independent and summed the numerator and denominators to estimate the effects of contingency:<disp-formula id="equ36"><mml:math id="m36"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mfrac><mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">R</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula></p></sec><sec id="s4-14-3"><title>Estimating the combined effect of chance and contingency</title><p>To determine the combined effects of chance and contingency <inline-formula><mml:math id="inf43"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula> on the outcomes of evolution, we compared allele frequencies from individual replicates to the average allele frequency among replicates from different starting genotypes. In each case, we pooled replicates started from a genotype and treated it as a single sample and compared it to the individual replicates started from different genotypes. We compared allele frequencies by estimating the probability that two randomly chosen alleles would be different if they were both drawn from the same replicate or if they were drawn from a different starting genotype:<disp-formula id="equ37"><mml:math id="m37"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>∗</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mo>≠</mml:mo><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>∗</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula></p><p>We thus used:<disp-formula id="equ38"><mml:math id="m38"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>∗</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></disp-formula>as our estimate of the combined effects of chance and contingency. This estimator indicates that the combined effects of chance and contingency are multiplicative and thus amplify each other’s effects as they get larger.</p></sec></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We thank members of the Thornton and Dickinson groups for helpful comments on the manuscript, S Ahmadiantehrani for editing, and R Ranganathan for the use of the Illumina MiSeq instrument.</p> </ack><sec id="s5" sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="COI-statement" id="conf1"><p>No competing interests declared</p></fn><fn fn-type="COI-statement" id="conf2"><p>Has a patent on the proximity-dependent split RNAP technology used in this work (US Patent App. 16/305,298, 2020).</p></fn><fn fn-type="COI-statement" id="conf3"><p>Has a patent on the proximity-dependent split RNAP technology used in this work (US Patent App. 16/305,298, 2020).</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Conceptualization, Investigation, Methodology, Writing - original draft, Writing - review and editing, Designed, engineered, optimized and implemented PACE dual-selection system. Performed PACE, biochemical assays, and sequencing experiments. Provided input on the phylogenetic, genetic, and evolutionary analyses</p></fn><fn fn-type="con" id="con2"><p>Conceptualization, Investigation, Methodology, Writing - original draft, Writing - review and editing, Designed, engineered, optimized and implemented the PACE dual-selection system. Performed PACE, biochemical assays, and sequencing experiments. Provided input on phylogenetic, genetic, and evolutionary analyses</p></fn><fn fn-type="con" id="con3"><p>Conceptualization, Data curation, Formal analysis, Funding acquisition, Methodology, Writing - original draft, Writing - review and editing, Provided input on the PACE, biochemical assays, and sequencing experiments. Developed and designed the evolutionary and genetic analyses. Led and performed the phylogenetic, genetic, and evolutionary analyses. Led writing and revision</p></fn><fn fn-type="con" id="con4"><p>Conceptualization, Supervision, Funding acquisition, Methodology, Writing - original draft, Project administration, Writing - review and editing, Developed and designed the evolutionary and genetic analyses. Led writing and revision</p></fn><fn fn-type="con" id="con5"><p>Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Writing - original draft, Project administration, Writing - review and editing, Designed the PACE dual-selection system</p></fn></fn-group></sec><sec id="s6" sec-type="supplementary-material"><title>Additional files</title><supplementary-material id="supp1"><label>Supplementary file 1.</label><caption><title>Luciferase assay data for all experiments.</title></caption><media mime-subtype="xlsx" mimetype="application" xlink:href="elife-67336-supp1-v2.xlsx"/></supplementary-material><supplementary-material id="supp2"><label>Supplementary file 2.</label><caption><title>Posterior probabilities for reconstructed ancestral sequences.</title><p>For each sequence, the site, maximum likelihood (ML) amino acid state, and posterior probability (PP) are given, along with the highest posterior probability alternative (ALT) state and posterior probability for this alternative state. Locations of paralog-specific insertions are shown as gaps. For each reconstructed sequence, the average posterior probability for the maximum likelihood states and the alternative states is given, as are the number of sites where the posterior probability of a non-maximum likelihood state is greater than 0.2. Finally, the average, maximum, minimum, and variance among reconstructed ancestors are given for the average maximum likelihood posterior probability and the number of non-maximum likelihood states greater than 0.2 posterior probability.</p></caption><media mime-subtype="xlsx" mimetype="application" xlink:href="elife-67336-supp2-v2.xlsx"/></supplementary-material><supplementary-material id="supp3"><label>Supplementary file 3.</label><caption><title>List of PACE experiments, amino acid alignments of hsBCL-2 and hsMCL-1 with their structural global alignment, and mutations found in individual variants isolated from PACE.</title><p>fs is frameshift, aa is amino acid, co is codon change.</p></caption><media mime-subtype="xlsx" mimetype="application" xlink:href="elife-67336-supp3-v2.xlsx"/></supplementary-material><supplementary-material id="supp4"><label>Supplementary file 4.</label><caption><title>PACE library and high-throughput sequencing (HTS) data.</title><p>PACE experiments are listed in the tab ‘Library-info’, which contains the name, purpose of the experiment, and HTS experiment numbers. The tab ‘Primers for HTS’ lists all the primer sequences used for HTS library constructions. The tab ‘MiSeq reads number’ include the read number of each library in this MiSeq run and the library sample information. The library samples are labeled as X*-end or X*-$$. ‘X’ indicates the specific PACE experiment, ‘*’ the experimental replicate, ‘end’ means samples were collected after 96 hr when the experiment finished, and ‘$$’ indicates the time point after removing chemostat A (e.g. ‘B2-24’ is a sample from replicate 2 of evolution B and collected 24 hr after removing chemostat A, which is 72 hr from the start of PACE). The tab ‘genotype’ includes the aligned protein sequences with corresponding residue numbers. The ‘Frequency’ tab contains the non-wild-type amino acid frequency of each sample for each site.</p></caption><media mime-subtype="xlsx" mimetype="application" xlink:href="elife-67336-supp4-v2.xlsx"/></supplementary-material><supplementary-material id="supp5"><label>Supplementary file 5.</label><caption><title>Descriptions of plasmids and sequences used.</title></caption><media mime-subtype="xlsx" mimetype="application" xlink:href="elife-67336-supp5-v2.xlsx"/></supplementary-material><supplementary-material id="transrepform"><label>Transparent reporting form</label><media mime-subtype="pdf" mimetype="application" xlink:href="elife-67336-transrepform-v2.pdf"/></supplementary-material></sec><sec id="s7" sec-type="data-availability"><title>Data availability</title><p>The high throughput sequencing data of evolved BCL-2 family protein variants were deposited in the National Center for Biotechnology Information (NCBI) Sequence Read Archive (SRA) databases. They can be accessed via BioProject: PRJNA647218. The processed sequencing data are available on Dryad (<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.5061/dryad.866t1g1ns">https://doi.org/10.5061/dryad.866t1g1ns</ext-link>). The coding scripts and reference sequences for processing the data are available on Github (<ext-link ext-link-type="uri" xlink:href="https://github.com/JoeThorntonLab/BCL2.ChanceAndContingency">https://github.com/JoeThorntonLab/BCL2.ChanceAndContingency</ext-link>).</p><p>The following datasets were generated:</p><p><element-citation id="dataset1" publication-type="data" specific-use="isSupplementedBy"><person-group person-group-type="author"><name><surname>Xie</surname><given-names>VC</given-names></name><name><surname>Pu</surname><given-names>J</given-names></name><name><surname>Metzger</surname><given-names>BPH</given-names></name><name><surname>Thornton</surname><given-names>JW</given-names></name><name><surname>Dickinson</surname><given-names>BC</given-names></name></person-group><year iso-8601-date="2020">2020</year><data-title>Experimental evolution of BCL2 family ancestral proteins</data-title><source>NCBI Bioproject</source><pub-id assigning-authority="NCBI" pub-id-type="accession" xlink:href="https://www.ncbi.nlm.nih.gov/bioproject/PRJNA647218">PRJNA647218</pub-id></element-citation></p><p><element-citation id="dataset2" publication-type="data" specific-use="isSupplementedBy"><person-group person-group-type="author"><name><surname>Xie</surname><given-names>VC</given-names></name><name><surname>Pu</surname><given-names>J</given-names></name><name><surname>Metzger</surname><given-names>BPH</given-names></name><name><surname>Thornton</surname><given-names>JW</given-names></name><name><surname>Dickinson</surname><given-names>BC</given-names></name></person-group><year iso-8601-date="2020">2020</year><data-title>BCL2-Chance and Contingency</data-title><source>Dryad Digital Repository</source><pub-id assigning-authority="Dryad" pub-id-type="doi">10.5061/dryad.866t1g1ns</pub-id></element-citation></p></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group 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contrib-type="editor"><name><surname>Courtier-Orgogozo</surname><given-names>Virginie</given-names></name><role>Reviewing Editor</role><aff><institution>Université Paris-Diderot CNRS</institution><country>France</country></aff></contrib></contrib-group><contrib-group><contrib contrib-type="reviewer"><name><surname>Courtier-Orgogozo</surname><given-names>Virginie</given-names> </name><role>Reviewer</role><aff><institution>Université Paris-Diderot CNRS</institution><country>France</country></aff></contrib><contrib contrib-type="reviewer"><name><surname>Blount</surname><given-names>Zachary David</given-names></name><role>Reviewer</role><aff><institution>Michigan State University</institution><country>United States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>Our editorial process produces two outputs: i) <ext-link ext-link-type="uri" xlink:href="https://sciety.org/articles/activity/10.1101/2020.08.29.273581">public reviews</ext-link> designed to be posted alongside <ext-link ext-link-type="uri" xlink:href="https://www.biorxiv.org/content/10.1101/2020.08.29.273581v3.full">the preprint</ext-link> for the benefit of readers; ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.</p></boxed-text><p><bold>Acceptance summary:</bold></p><p>This manuscript presents an original, clever, high throughput, and rapid experimental protein evolution method to assess the roles and contributions of contingency, chance, and necessity in the evolution of protein-protein interactions. The authors focus on the animal BCL<sup>-</sup>2 protein family and on the evolution of their binding properties to two proteins, NOXA and BID. Using several replicates and several starting points, they found little predictability between replicates of single starting points and among those from multiple starting points, indicating that there is no single pathway through sequence space to the selected function, and that historical contingency is here the primary cause of protein evolution. The original experimental set up described in this paper allows to simultaneously impose selection and counter-selection within the same cell, and shows a lot of potential for future studies of directed protein evolution in general.</p><p><bold>Decision letter after peer review:</bold></p><p>Thank you for submitting your article &quot;Contingency and chance erase necessity in the experimental evolution of ancestral proteins&quot; for consideration by <italic>eLife</italic>. Your article has been reviewed by 3 peer reviewers, including Virginie Courtier-Orgogozo as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Molly Przeworski as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Zachary David Blount (Reviewer #3).</p><p>The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.</p><p>Essential revisions:</p><p>The experiments are very nice, very well done, clearly presented and well interpreted.</p><p>1) Our main essential revision is to ask the authors to tone down their conclusions and broad claims. Indeed, the setup only allowed the authors to study the evolution of one protein family, considering only protein-protein interactions with few players, and in an artificial, bacterial environment. In living organisms, each protein is likely to exhibit particular properties such that it can bind or not bind to hundreds of different proteins, and not just two as tested here. So the constraints present in living organisms may be much larger than the ones present within this experimental evolution set up. Furthermore, the tested proteins probably encounter other constraints in their native environment besides affinity for other proteins.</p><p>2) The authors should also acknowledge the limitations of their study: BID and NOXA ancestral proteins were not used, peptides instead of full-length protein were used during interaction assays, proteins partially membrane-bound in vivo.</p><p><italic>Reviewer #1 (Recommendations for the authors):</italic></p><p>For the reversion experiment, proteins are being evolved to gain NOXA binding but the experiment after 48h does not select for proteins that retain BID binding (Figure 3-supp2, E). So how do you explain that the evolved proteins did not loose their BID binding?</p><p>Paragraph &quot;Contingency is the major cause of sequence variation on long timescales&quot; (line 268). I am not entirely convinced by this paragraph. It would be good to repeat similar measurements in conditions where plasmids are left to evolve randomly, with no selection for particular novel protein binding properties. This would give an idea of the null hypothesis. Maybe similar numbers would also be found with such a &quot;neutral&quot; evolution.</p><p>Unless I am wrong, I would suggest to remove this part.</p><p>Line 239: Figure 4: how do you explain that there is quite a lot of variability in the phenotype for replicate 3 and for replicate 4 of the evolved hsMCL<sup>-</sup>1 in terms of NOXA binding (panel A). Did you check whether the 3 individual phenotypes shown for each replicate do have the same genotype? It looks like amino acid position 202 can be N or S for replicate 3. Could it explain the difference in binding between &quot;individuals&quot;?Can you also explain variability between &quot;individual phenotypes&quot; for the few replicates of AncM6 and AncB1?</p><p><italic>Reviewer #2 (Recommendations for the authors):</italic></p><p>The amount of experimental work reported here is already quite impressive, and additional experiments, although being useful to enforce the conclusions, may not be practically feasible. This should not be an issue if the authors are ready to tone down their interpretations. Instead of discussing immediate extension of the method to other families, they could indicate the limitations of their current experimental setup in order to indicate further directions for follow-up studies.</p><p>Figure 2—figure supplement 3: the authors do not discuss the lack of binding observed between Trichoplax adhaerens BCL and human BID and NOXA, and they also do not plot them on figure 2. Actually, it would be interesting to discuss this point in the light of the recent report by Popgeorgiev et al., (Science Advances, 2020, eabc4149) that the Trichoplax BCL<sup>-</sup>2L2 actually binds the Trichoplax Bak BH3 protein (called BCL<sup>-</sup>2L3).</p><p><italic>Reviewer #3 (Recommendations for the authors):</italic></p><p>To flesh out my comment about needing to engage the conceptual work that has been done on contingency, I have two major issues I would like to see dealt with:</p><p>First, contingency and chance are discussed by the authors as being separate, but they are not. Indeed, chance is a critical component of contingency. Some more engagement with the philosophers who have specialized in this area, especially John Beatty, Eric Desjardins and Alison McConwell. They have made clear that contingency is not just causal dependence. Beatty, for instance, has articulated how contingent outcomes are not simply those that stem from earlier events, but depend on pasts with chance components so that their occurrence was not guaranteed. (See Beatty, and Carrera, When what had to happen was not bound to happen: History, chance, narrative, evolution. Journal of the Philosophy of History 5: 471-495. 2011.) Unless chance is involved in the causal paths taken over time from a given start to a given beginning, then there is not really any contingency, but merely determinism. Desjardins has elaborated this further into understanding contingency in the context of path dependence (See Desjardins, Historicity and Experimental Evolution. Biol. Philos. 26, 339-364, 2011 And Desjardins, Reflections on path dependence and irreversibility: Lessons from evolutionary biology. Philosophy of Science 78: 724 – 738, 2017.) The passage in the introduction that, &quot;…if diversity reflects contingency-a strong dependence of future events on past and current states-then the outcomes of evolution would be predictable only given complete knowledge of the constraints and opportunities specific to each starting point&quot; is therefore incorrect, because contingency involves not just dependence on starting conditions. Contingency makes for broader unpredictability because indeterminacy, such as that introduced by the randomness of mutations, is characteristic of the causal chain no matter the starting point. (This point, incidentally, is made in the Blount et al., 2018 and Beatty, 2009 papers cited to support the quoted statement.) Similarly, the conclusion, then, that &quot;Conversely, without chance, contingency in history would be inconsequential, because all phylogenetic lineages launched from a common ancestor would always lead to the same intermediate steps and thus the same ultimate outcomes&quot; is well stated, but it misses that contingency without chance is not contingency. It misses, therefore, sophisticated conceptual elaboration of what exactly what contingency really involves. I think the arguments made about what the experimental findings mean would be better if that work were taken into account. The study of contingency is rife with conceptual mix-ups and crosstalk, and it is critical to engage what the philosophers have done to clarify things and help us scientists out so that we can really all be on the same page.</p><p>My second issue is related. The work deals with chance, contingency, and necessity in the evolution of protein sequence. However, there is little grappling with how contingency actually matters if it simply means that proteins can evolve along many different paths depending on historical substitutions to the same function. If there are multiple paths to functionally equivalent end states, how do they matter? Such convergence is in line with Conway Morris's argument that contingency does not matter because, &quot;the routes are many, but the destinations are limited.&quot; Indeed, if there really are a fantastically large number of alternate paths that can be taken to the same end, then the role for contingency in the final state is actually minimal. Where it could matter would be if 1. There were end functional states reachable via different pathways that were qualitatively similar, but not actually the same, and/or 2. The end states vary in their potential for later evolution. As it stands, the manuscript leaves me unable to see how it matters if &quot;Present-day proteins are physical anecdotes of the particular unpredictable histories&quot;, but all those anecdotes have the same punchlines and meanings. Now, I will state outright that I think that history does play a role beyond simply the contingency of evolutionary paths to the same destination, but there is a functionally convergent, non-contingent elephant in the room with which the authors need to engage.</p></body></sub-article><sub-article article-type="reply" id="sa2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.67336.sa2</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><disp-quote content-type="editor-comment"><p>Essential revisions:</p><p>The experiments are very nice, very well done, clearly presented and well interpreted.</p><p>1) Our main essential revision is to ask the authors to tone down their conclusions and broad claims. Indeed, the setup only allowed the authors to study the evolution of one protein family, considering only protein-protein interactions with few players, and in an artificial, bacterial environment. In living organisms, each protein is likely to exhibit particular properties such that it can bind or not bind to hundreds of different proteins, and not just two as tested here. So the constraints present in living organisms may be much larger than the ones present within this experimental evolution set up. Furthermore, the tested proteins probably encounter other constraints in their native environment besides affinity for other proteins.</p></disp-quote><p>We agree. We have revised the manuscript in numerous places to narrow our claims appropriately and acknowledge these limitations. Specifically:</p><p>– Throughout the abstract, results, and discussion, we have made our claims particular to the BCL<sup>-</sup>2 protein family. When we suggest generality to other proteins, we make the rationale for this extension explicit and label it as speculative (e.g. lines 30, 596, 640).</p><p>– We made explicit throughout the paper that we assessed chance and contingency in evolution under selection for new functions in the PACE laboratory evolution system, rather than during the natural historical evolution of BCL<sup>-</sup>2 family proteins. Because we used ancestral starting points, the contingency we observe is generated by historical sequence substitutions, but the outcomes that are contingent are within the PACE system (e.g. text beginning at lines 263 and 535).</p><p>– We expanded the portion of the discussion in which we discuss ways in which chance and contingency during history may be different from those in our experiments (line 582). We addressed the possible effects of other protein-protein interactions, the use of bacterial cells, and other functional constraints, as suggested.</p><disp-quote content-type="editor-comment"><p>2) The authors should also acknowledge the limitations of their study: BID and NOXA ancestral proteins were not used, peptides instead of full-length protein were used during interaction assays, proteins partially membrane-bound in vivo.</p></disp-quote><p>We agree and have modified the discussion to explicitly acknowledge each of the listed differences between our PACE system and the cellular context of natural BCL<sup>-</sup>2 family function (line 582). We discussed ways in which these differences could affect the roles of chance and contingency. Also, we narrowed our claims to pertain specifically to the effects of chance and contingency during laboratory evolution using PACE, as discussed above.</p><disp-quote content-type="editor-comment"><p>3) Reviewer 1 noted that Figure 4F shows that some PACE mutations recapitulated historical substitutions, suggesting that necessity may not have been almost entirely absent.</p></disp-quote><p>We understand and have clarified the argument in the Results section (lines 263-279). and revised the figures concerning the occurrence or reversion of historical substitutions in PACE trajectories. The PACE experiments show that virtually no mutations occurred in all trajectories from all starting points under either selection regime, indicating virtually no necessity under PACE conditions. The purpose of the analysis of historical substitutions was to gain insight into the extent of chance, contingency, and necessity during historical evolutionary change in BCL<sup>-</sup>2 PPI specificity. The key question, then, is whether substitutions that occurred on the phylogenetic branch when specificity was changed also occurred (or were reverted) during PACE selection for the derived (or ancestral) function, and if so, how frequently and in what backgrounds. This did not come through clearly in the original text and figure. We revised Figure 4F so that it now shows clearly that none of the substitutions from the key phylogenetic interval occurred in PACE; moreover, there were only two reversions, and these were observed in only a subset of replicates (indicating chance) and only in trajectories from the ancestral starting point closest to the branch on which they occurred historically (indicating contingency). This therefore indicates a lack of necessity in the historical evolution of BCL<sup>-</sup>2 specificity. Some substitutions from other branches did occur in some PACE trajectories, but these could not have been historical causes of the shift in specificity and therefore do not provide information about chance and necessity during that shift; those data are now in Figure 4—figure supplement 5.</p><disp-quote content-type="editor-comment"><p>4) Reviewer 1 noted that several PACE mutations may have had no effect on NOXA or BID biding and could therefore have occurred because of mutational bias, drift or hitchhiking. R1 said this means that one cannot include such changes when calculating the fraction of acquired states that are attributable to chance. R1 said that mutations that arose repeatedly during PACE replicates from any given starting genotype, and which do contribute to the change in specificity, provide evidence for necessity.</p></disp-quote><p>We addressed this comment in two ways. First, we note that there are two ways that chance can determine sequence changes that occur under selection for a new function: (a) mutations have no effect on function (and therefore occur by chance because of drift or hitchhiking, as the reviewer notes), or (b) they may confer a new function but may be one of several mutations (or sets of mutations) that can do so, with chance determining which mutation(s) are realized. In either of these cases, differences between trajectories launched from the same starting point are attributable to chance. We clarified the text to explicitly acknowledge this (lines 418-421).</p><p>Second, we clarified in the introduction and in Figure 1 that necessity and determinism are not the same thing (line 80). Necessity requires the absence of both chance and contingency: a process must be both deterministic and insensitive to starting/intervening conditions to give rise to necessary outcomes. The observation that the reviewer refers to – some mutations that occur repeatably in trajectories from the same starting point – indicates a limited degree of chance and partial determinism. However, these mutations did not occur from trajectories launched from different starting points, indicating a large role for contingency and therefore a lack of necessity.</p><disp-quote content-type="editor-comment"><p>5) Reviewer 1 noted that there may be more mutations that can confer loss of binding to another protein than mutations that confer gain of binding to a new one. They suggested that we discuss this point in more detail.”</p></disp-quote><p>This is an interesting question, and we have performed a new analysis to test this possibility. We compared the effects of chance and contingency for starting genotypes that gained or lost NOXA binding, finding no statistically significant difference between them (line 319). This analysis is shown in Figure 5—figure supplement 1. In addition, there was no qualitative difference in the ability of gains and loss of NOXA binding to evolve; in all cases the change in NOXA binding was readily acquired during PACE.</p><disp-quote content-type="editor-comment"><p>6) Reviewer 1 noted that proteins in their natural cellular context encounter many potential binding partners, whereas we selected only for binding and specificity to just two of the biological significant binding partners for BCL<sup>-</sup>2 family proteins. As a result, the constraints during natural evolution could be more stringent than those in our experiment, leading to an underestimate of the role of determinism.</p></disp-quote><p>This comment and our response is addressed in point #1 above.</p><disp-quote content-type="editor-comment"><p>7) Reviewer 1 asked us to explain why the evolved proteins that were selected to gain NOXA binding did not lose BID binding if they were not subject to continued selection for that function.</p></disp-quote><p>BCL<sup>-</sup>2 family proteins selected to gain NOXA binding were first subject to an initial acclimation period prior to NOXA selection in which they were selected to maintain BID binding. A likely explanation for why these population did not lose BID binding during selection for NOXA binding is that the acquired mutations that enhanced NOXA binding do not diminish BID binding. Supporting this view, we also found that when proteins that had acquired dual BID/NOXA activity in PACE were subsequently subjected to PACE with selection to lose their BID activity, NOXA-specific binders failed to evolve. This suggests strong coupling of NOXA binding with BID binding in sequence space accessible from these proteins. This conclusion is somewhat speculative, however, so we have decided not to include it in the paper.</p><disp-quote content-type="editor-comment"><p>8) Reviewer 1 commented about the paragraph &quot;Contingency is the major cause of sequence variation on long timescales&quot; that a useful reference experiment would be to perform PACE under conditions where plasmids are left to evolve randomly, with no selection for particular novel protein binding properties. This would give an idea of chance, contingency, and necessity under a null hypothesis of neutral evolution.</p></disp-quote><p>We agree that our experiments reveal the effects of historical substitutions on chance and contingency during selection for a new function, not under the neutral evolutionary scenario of purifying selection for an existing function. We have made this explicit in our description of our experiments and claims. In the discussion we note that additional experiments would be required to reveal the effects of chance and contingency under the neutral evolutionary scenario and reveal any differences from their effects under selection for a new function (line 593).</p><disp-quote content-type="editor-comment"><p>9) Reviewer 2 noted as an unnatural aspect of our design that we used extant human BID and NOXA and that during history these proteins would also have evolved.</p></disp-quote><p>We agree and have added this point to the discussion (line 579). Our experiments kept BID and NOXA constant, allowing us to estimate the effects of historical substitutions on chance and contingency during PACE experiments for altered binding to human BID and NOXA. In reality, BID and NOXA would have evolved, presenting more opportunities for chance and contingency to influence the outcomes of evolution, thus making our analysis a conservative test of these factors.</p><disp-quote content-type="editor-comment"><p>10) Reviewer 2 noted that cross-species interactions among BCL2 family proteins may produce different results than using proteins that existed in the same organism at the same time and cited (Popgeorgiev et al., Science Advances 2021) as an example.</p></disp-quote><p>The referenced paper provides relevant information, and we have now cited it in the manuscript (line 763). Specifically, experiments in that paper show that the Trichoplax BCL2 family protein most closely related to vertebrate BCL2 is capable of binding both human BID and NOXA. This is the expected result based on our ancestral reconstruction, which show that BCL<sup>-</sup>2 at the time of its origin by gene duplication could bind both coactivators, and that NOXA binding was lost after placozoa diverged from the lineage leading to other animals (cnidaria, protostomes, and deuterostomes).</p><disp-quote content-type="editor-comment"><p>11) Reviewer 2 noted that binding affinity in the BCL2 family is often dependent on the length of the protein or peptide used.</p></disp-quote><p>We have added this point explicitly to the discussion as a difference between our assay conditions and natural conditions (line 588). We have also noted that the data in the cited review shows that the length of the protein or peptide affects absolute affinity but does not alter specificity (relative affinity for coactivator proteins). In addition, we altered the introduction to indicate that human BCL<sup>-</sup>2 (unlike human MCL<sup>-</sup>1) strongly prefers BID to NOXA, although that preference is not absolute (line 93).</p><disp-quote content-type="editor-comment"><p>12) Reviewer 2 commented that BCL2 family proteins are often membrane-located, while our experiments use a soluble binding assay.</p></disp-quote><p>We have added this point explicitly to the discussion as a difference between our assay conditions and natural conditions (line 584). We also pointed out that interactions with BID and NOXA naturally occur in the cytosol for BCL2 family proteins and are mediated via a cytosol-exposed hydrophobic cleft even when the BCL2 family proteins are membrane-bound. Thus, although there are critical downstream dimensions of BCL<sup>-</sup>2 family protein functions not addressed in our experiments, our particular focus – coactivator specificity – can be reasonably, albeit cautiously, studied using a cytosolic assay system.</p><disp-quote content-type="editor-comment"><p>13) Reviewer 2 suggested that “Instead of discussing immediate extension of the method to other families, they could indicate the limitations of their current experimental setup in order to indicate further directions for follow-up studies.”</p></disp-quote><p>We followed this suggestion and added an extended discussion of these and other limitations of our experimental system and the implications of those limitations for our findings, before we bring up potential extension to other proteins (text starting at line 582).</p><disp-quote content-type="editor-comment"><p>14) Reviewer 3 noted that chance and contingency interact with one another and that several philosophers of science have shown that both chance and contingency are required for history to matter in the outcomes of evolution.</p></disp-quote><p>We agree and have adjusted the introduction and discussion accordingly, adding citations to Beatty and to Desjardins as suggested (e.g. text starting at lines 44 and 553). Our goal with these changes is to make clear that chance and contingency are conceptually distinct, but they strongly interact with each other. Chance–defined as random occurrence of one event from a probability distribution of multiple possibilities– is manifest as distinct outcomes among replicates from the same starting point under identical conditions. In contrast, contingency – differences in the probability distribution of events that can ensue from different starting points – is manifest as distinct outcomes among pooled replicates from different starting points. Under some circumstances, contingency can be realized or observed only if chance is also present: for example, in an evolutionary process beginning from a common ancestor, if chance is absent, each lineage would undergo the same intermediate steps and would therefore deterministically evolve the same states. Even if different outcomes would evolve from different starting points or intermediate states – that is, contingency still exists in the underlying structure of the system itself – those differences would never be realized or observed. If multiple starting points are used initially, however, contingency will be apparent in the outcomes even in the absence of chance. Conversely, chance can exist without contingency, but it would have no further effect on future paths or outcomes, and therefore would have no meaningful evolutionary consequences. We have modified the text, legend, and Figure 1A to make this thinking clearer.</p><disp-quote content-type="editor-comment"><p>15) Reviewer 3 commented that contingency is not simply conditionality on the starting point, but is instead dependence on intermediate steps and is thus more accurately referred to as path dependence.</p></disp-quote><p>We agree and have altered the text throughout to note that contingency is defined as differences in the probability of outcomes that depend on the starting point or on intervening events in evolutionary trajectories (e.g. lines 46, 118, 559). We also explicitly used the phrase path-dependence to evoke this concept.</p><disp-quote content-type="editor-comment"><p>16) Reviewer 3 commented that our focus on chance and contingency in the evolution of molecular sequences is less consequential or interesting than those phenomena would be at the level of phenotype.</p></disp-quote><p>Our view is that both sequences and phenotypes are important biological objects, and that the evolutionary causes of variation are of great interest at both levels. Sequences and the sequence-structure-function relationship are central objects of study in biochemistry and molecular biology; and the sequence-function-phenotype relationship is the central object in molecular genetics and genomics. In these fields, mining and interpreting patterns of sequence variation is a key activity to gain insight into these relationships, so understanding how and why these patterns are produced during evolution is necessary for accurate interpretation of those patterns – e.g., are differences between orthologs or paralogs attributable to selection imposed by differences in environment/function, to a lack of constraint that yields random variation, or to differences in internal constraints that have arisen among divergent lineages? This has profound implications for how we interpret that variation. Moreover, sequences have long been a central focus of inference in molecular evolution, with interpretation of variation patterns in sequences being used to ask questions like how much of the genome – and what parts of it – are the result of different forms of selection, drift, and so on. Chance, contingency, and necessity in sequence evolution is therefore of major interest in its own right.</p><p>We modified the text in three ways to address this issue. First, we have made clear throughout that our results reveal the role of these modes of causality in molecular sequences (e.g. lines 239, 262, 305, 515). Second, we explicitly argue in the introduction and discussion why understanding how they affect sequence evolution is important (lines 104, 632). Finally, some of our results also illuminate chance, contingency, and necessity at the level of the PPI phenotype itself, with an observation of some necessity (convergence under selection) but some contingency (inaccessibility of some phenotype from some starting points under selection), and we discuss this in the last section of the results and in the discussion (lines 489, 626).</p></body></sub-article></article>