ECV ~ Body Mass

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 238.1995802 122.4300308 0.1730555 1.2243573 9999.06838 220.7339537 257.0483448
prior -79.4250054 9.4717222 0.0133883 0.4989513 360.36414 -97.5722573 -62.7195212
alpha 4.4671710 7.3078805 0.0103297 0.8032901 82.76335 0.0600634 18.1867214
sigma^2 0.0225446 0.0407490 0.0000576 0.0044556 83.64089 0.0005501 0.0840875
shift number 12.5040909 2.0410771 0.0028851 0.0924041 487.90626 9.0000000 16.0000000
N theta 13.5040909 2.0410771 0.0028851 0.0924041 487.90626 10.0000000 17.0000000
root theta -0.8949691 0.2577805 0.0003644 0.0170615 228.27908 -1.2466628 -0.5250178
root beta 0.6871632 0.1181884 0.0001671 0.0066677 314.19731 0.5758711 0.8439854
all theta -0.9918978 0.5895005 NA NA NA NA NA
all beta 0.7673352 0.2330846 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 238.1166512 15.9358457 0.0225254 0.8746991 331.91957 224.3365057 253.4166558
prior -79.6167181 8.7921682 0.0124278 0.4375569 403.75960 -97.4821998 -64.9896912
alpha 3.5321504 4.4306651 0.0062628 0.7400471 35.84422 0.3916937 10.9270386
sigma^2 0.0191945 0.0298866 0.0000422 0.0046974 40.48041 0.0022675 0.0530316
shift number 12.6600546 2.1089068 0.0029810 0.1036098 414.29824 10.0000000 17.0000000
N theta 13.6600546 2.1089068 0.0029810 0.1036098 414.29824 11.0000000 18.0000000
root theta -0.7689019 0.2105803 0.0002977 0.0131899 254.89019 -0.9939623 -0.4361902
root beta 0.6729566 0.0976750 0.0001381 0.0044102 490.50384 0.5837124 0.7352264
all theta -1.0875801 0.6176098 NA NA NA NA NA
all beta 0.7952158 0.2251197 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 239.4526688 6.4815984 0.0077431 0.2247830 831.45240 225.6856029 251.7243879
prior -78.4965090 7.6618899 0.0091531 0.2985010 658.84054 -95.1556779 -66.0802773
alpha 3.1987946 4.6981872 0.0056126 0.4964562 89.55685 0.0651811 10.9043902
sigma^2 0.0156321 0.0223119 0.0000267 0.0026725 69.70143 0.0006273 0.0512932
shift number 12.4179982 1.7824208 0.0021293 0.0665229 717.92321 10.0000000 16.0000000
N theta 13.4179982 1.7824208 0.0021293 0.0665229 717.92321 11.0000000 17.0000000
root theta -0.7758925 0.2306230 0.0002755 0.0123306 349.81145 -0.9966859 -0.4650088
root beta 0.6621634 0.0898212 0.0001073 0.0038586 541.86806 0.5804227 0.7233932
all theta -1.0311697 0.5883117 NA NA NA NA NA
all beta 0.7759491 0.2254518 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 4.4671710 3.5321504 3.1987946
sigma squared 0.0225446 0.0191945 0.0156321
stationary variance 0.0025234 0.0027171 0.0024434
phylogenetic halflife 0.1551647 0.1962394 0.2166901
phylogenetic half life in units of tree height 0.0021255 0.0026881 0.0029682

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 237.9218364 19.7416313 0.0279049 0.6617010 890.107694 221.8920862 256.0552664
prior -80.3339274 8.9460986 0.0126454 0.4374058 418.309945 -98.3921206 -64.9055705
alpha 5.0679840 5.1304656 0.0072519 0.7196491 50.824373 0.1436803 15.4605445
sigma^2 0.0255562 0.0251606 0.0000356 0.0079802 9.940587 0.0010899 0.0777228
shift number 12.7274411 2.0543322 0.0029038 0.0914053 505.124724 9.0000000 16.0000000
N theta 13.7274411 2.0543322 0.0029038 0.0914053 505.124724 10.0000000 17.0000000
root theta -0.8862630 0.2704600 0.0003823 0.0232761 135.016424 -1.2755803 -0.5218193
root beta 0.6788669 0.1086343 0.0001536 0.0079276 187.780011 0.5763822 0.8559412
all theta -1.0569796 0.5850637 NA NA NA NA NA
all beta 0.7812911 0.2295259 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 223.2348819 20.1483948 0.0284799 1.2015290 281.19810 192.7599191 252.6241780
prior -107.7001588 17.4343657 0.0246436 0.6687513 679.64634 -143.4763521 -74.9549714
alpha 0.0541054 0.0487127 0.0000689 0.0070444 47.81810 0.0109892 0.1592881
sigma^2 0.0006807 0.0012414 0.0000018 0.0000449 763.39316 0.0003380 0.0010336
shift number 18.6463564 3.8560876 0.0054506 0.1349536 816.44099 11.0000000 26.0000000
N theta 19.6463564 3.8560876 0.0054506 0.1349536 816.44099 12.0000000 27.0000000
root theta -0.8922021 0.1337559 0.0001891 0.0112901 140.35559 -1.1360875 -0.6469820
root beta 0.6920913 0.0547437 0.0000774 0.0056320 94.47927 0.6027534 0.7966366
all theta -1.1677733 0.8743207 NA NA NA NA NA
all beta 0.8300406 0.4082974 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 228.4745348 14.6627923 0.0175166 1.0690629 188.11647 196.7826223 252.0807142
prior -95.2882451 21.0600772 0.0251590 1.0741921 384.37578 -134.2203000 -62.2455525
alpha 1.5826884 2.9676490 0.0035452 0.4610920 41.42380 0.0089454 8.4162423
sigma^2 0.0081899 0.0144365 0.0000172 0.0057199 6.37012 0.0002748 0.0441031
shift number 15.9444473 4.5471523 0.0054322 0.2061424 486.56884 8.0000000 24.0000000
N theta 16.9444473 4.5471523 0.0054322 0.2061424 486.56884 9.0000000 25.0000000
root theta -0.8391474 0.1453729 0.0001737 0.0108936 178.08515 -1.0759083 -0.5340917
root beta 0.6618703 0.0521507 0.0000623 0.0041416 158.55613 0.5731643 0.7628291
all theta -1.1224389 0.7885545 NA NA NA NA NA
all beta 0.8170445 0.3651531 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 5.0679840 0.0541054 1.5826884
sigma squared 0.0255562 0.0006807 0.0081899
stationary variance 0.0025213 0.0062907 0.0025873
phylogenetic halflife 0.1367698 12.8110419 0.4379556
phylogenetic half life in units of tree height 0.0018735 0.1754862 0.0059991

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 162.8501112 6.8640609 0.0097024 0.1626607 1780.7250 160.4734105 164.5401197
prior 0.2700209 0.1429087 0.0002020 0.0042257 1143.7290 -0.0015802 0.5213542
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0009615 0.0108924 0.0000154 0.0001380 6226.1991 0.0006387 0.0010156
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5479505 0.1441275 0.0002037 0.0047487 921.1743 -0.8325343 -0.2674380
root beta 0.5903931 0.0344444 0.0000487 0.0007467 2127.6723 0.5248260 0.6564211
all theta -0.5479505 0.1441275 NA NA NA NA NA
all beta 0.5903931 0.0344444 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 162.8178485 7.1347227 0.0100850 0.1754235 1654.1646 160.4389891 164.5406391
prior 0.2719569 0.1444983 0.0002042 0.0043446 1106.2020 0.0017662 0.5256841
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0009771 0.0117742 0.0000166 0.0001598 5427.6002 0.0006428 0.0010208
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5512008 0.1472396 0.0002081 0.0050064 864.9767 -0.8293682 -0.2657456
root beta 0.5904883 0.0349657 0.0000494 0.0007775 2022.5881 0.5236656 0.6566052
all theta -0.5512008 0.1472396 NA NA NA NA NA
all beta 0.5904883 0.0349657 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 162.9886803 1.2564426 0.0015010 0.0129584 9401.136 160.5252452 164.5397193
prior 0.2705965 0.1359536 0.0001624 0.0038109 1272.723 -0.0012333 0.5194633
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.000 0.0000010 0.0000010
sigma^2 0.0008240 0.0000970 0.0000001 0.0000005 33103.019 0.0006410 0.0010168
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.000 1.0000000 1.0000000
root theta -0.5480353 0.1429355 0.0001708 0.0039851 1286.453 -0.8246761 -0.2654532
root beta 0.5899000 0.0333908 0.0000399 0.0005885 3219.464 0.5248356 0.6557577
all theta -0.5480353 0.1429355 NA NA NA NA NA
all beta 0.5899000 0.0333908 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 9.615000e-04 9.771000e-04 8.240000e-04
stationary variance 4.807501e+02 4.885398e+02 4.119915e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494761e+03 9.494761e+03 9.494761e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.00000 14.65512 37.51062
OU weighted predictor -14.65512 0.00000 22.85550
BM -37.51062 -22.85550 0.00000

ECV ~ Body Mass (alternate hominin phylogeny)

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 241.0540198 20.0391281 0.0283254 0.6023059 1106.93834 227.3495954 256.1030043
prior -82.1802895 8.1332266 0.0114964 0.3561428 521.52784 -97.6786430 -69.0064584
alpha 10.2791710 11.6108181 0.0164120 1.4006483 68.71752 0.3844910 30.9124409
sigma^2 0.0504784 0.0559363 0.0000791 0.0109034 26.31837 0.0024549 0.1512941
shift number 12.7584520 1.9637988 0.0027758 0.0848774 535.31579 10.0000000 16.0000000
N theta 13.7584520 1.9637988 0.0027758 0.0848774 535.31579 11.0000000 17.0000000
root theta -0.8688541 0.2190940 0.0003097 0.0140792 242.15982 -1.2569312 -0.5352781
root beta 0.6947123 0.0990825 0.0001401 0.0051270 373.48405 0.5764297 0.8562659
all theta -0.9728190 0.5859950 NA NA NA NA NA
all beta 0.7697762 0.2195265 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 666.4546797 932.9969059 1.3187963 509.361964 3.355115 194.7579414 3186.2540644
prior -102.3526238 38.0175721 0.0537381 3.632901 109.511957 -192.2762596 -67.8976336
alpha 64.0992601 93.8180351 0.1326123 60.019601 2.443354 3.4180938 243.4524576
sigma^2 0.0561179 0.0525918 0.0000743 0.024788 4.501452 0.0000000 0.1594299
shift number 16.3551182 7.7078573 0.0108951 0.651271 140.069597 9.0000000 34.0000000
N theta 17.3551182 7.7078573 0.0108951 0.651271 140.069597 10.0000000 35.0000000
root theta -0.9353539 0.3505115 0.0004954 0.023291 226.478610 -1.6639440 -0.3997513
root beta 0.7202371 0.1426225 0.0002016 0.006797 440.287942 0.5534514 1.0253371
all theta -1.1417433 0.8053504 NA NA NA NA NA
all beta 0.8048163 0.3516405 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 545.7824104 811.1537182 0.9690270 384.6283192 4.44758 214.3624018 2823.6849728
prior -96.5382603 33.6101817 0.0401517 2.7978053 144.31343 -183.1634318 -66.3568036
alpha 49.5266984 82.9385960 0.0990808 40.9536624 4.10136 1.2302728 242.7536655
sigma^2 0.0581702 0.0577500 0.0000690 0.0133303 18.76836 0.0000000 0.1640829
shift number 15.2770870 6.8007837 0.0081244 0.4965903 187.55191 8.0000000 32.0000000
N theta 16.2770870 6.8007837 0.0081244 0.4965903 187.55191 9.0000000 33.0000000
root theta -0.8795743 0.3046272 0.0003639 0.0165234 339.89058 -1.6642355 -0.4587519
root beta 0.6956257 0.1332446 0.0001592 0.0052147 652.89661 0.5450482 0.9923559
all theta -1.0893371 0.7624987 NA NA NA NA NA
all beta 0.7957006 0.3246703 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 10.2791710 64.0992601 49.5266984
sigma squared 0.0504784 0.0561179 0.0581702
stationary variance 0.0024554 0.0004377 0.0005873
phylogenetic halflife 0.0674322 0.0108137 0.0139954
phylogenetic half life in units of tree height 0.0009221 0.0001479 0.0001914

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 205.9727727 3109.8776608 4.3958294 24.2784040 16407.64844 200.1220614 255.3505572
prior -93.7790313 16.0963880 0.0227523 0.7439134 468.17920 -124.7413254 -65.6647883
alpha 0.1793578 0.3604229 0.0005095 0.0092843 1507.05208 0.0120895 0.6594773
sigma^2 0.0011933 0.0016560 0.0000023 0.0000879 355.17360 0.0003434 0.0033960
shift number 15.8801701 3.5821213 0.0050633 0.1412347 643.27646 9.0000000 22.0000000
N theta 16.8801701 3.5821213 0.0050633 0.1412347 643.27646 10.0000000 23.0000000
root theta -0.9365646 0.1171756 0.0001656 0.0085537 187.65772 -1.1516056 -0.7076672
root beta 0.7117140 0.0495784 0.0000701 0.0052052 90.72048 0.6167695 0.8004940
all theta -1.1249988 0.8252109 NA NA NA NA NA
all beta 0.8155196 0.3259149 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 237.9578950 216.6191804 0.3061924 2.2183967 9534.883311 223.4885566 257.9912425
prior -82.3162170 9.9562004 0.0140731 0.4995316 397.247712 -101.0524954 -63.8737574
alpha 3.7915154 4.1301477 0.0058380 0.5583518 54.716133 0.1117776 12.4305982
sigma^2 0.0187940 0.0201610 0.0000285 0.0076801 6.891108 0.0006779 0.0625128
shift number 13.0956042 2.2711927 0.0032103 0.1045702 471.728476 9.0000000 17.0000000
N theta 14.0956042 2.2711927 0.0032103 0.1045702 471.728476 10.0000000 18.0000000
root theta -0.9874591 0.2634702 0.0003724 0.0169862 240.586182 -1.3015174 -0.5409743
root beta 0.7294942 0.0918124 0.0001298 0.0060437 230.775367 0.5766925 0.8602008
all theta -1.0165693 0.6576055 NA NA NA NA NA
all beta 0.7712305 0.2541231 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 238.1775393 9.5775587 0.0114416 0.4823353 394.28623 219.6433164 257.2940222
prior -85.1495045 12.9606547 0.0154832 0.5806385 498.24416 -111.9806970 -62.1644231
alpha 1.0746598 1.8739581 0.0022387 0.2582479 52.65578 0.0187830 5.8819767
sigma^2 0.0053300 0.0087385 0.0000104 0.0024885 12.33084 0.0003362 0.0285592
shift number 14.0672495 3.0108756 0.0035969 0.1262370 568.86927 9.0000000 20.0000000
N theta 15.0672495 3.0108756 0.0035969 0.1262370 568.86927 10.0000000 21.0000000
root theta -0.9511648 0.2148681 0.0002567 0.0116788 338.48919 -1.2453660 -0.5577720
root beta 0.7183411 0.0708559 0.0000846 0.0043567 264.50556 0.5958968 0.8487927
all theta -1.0263472 0.6909202 NA NA NA NA NA
all beta 0.7907559 0.2768146 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 0.1793578 3.7915154 1.0746598
sigma squared 0.0011933 0.0187940 0.0053300
stationary variance 0.0033265 0.0024784 0.0024798
phylogenetic halflife 3.8646054 0.1828153 0.6449922
phylogenetic half life in units of tree height 0.0528462 0.0024999 0.0088199

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 163.1894353 12.0707883 0.0170621 0.5242884 530.0670 161.1020518 165.1376862
prior 0.2803633 0.1566279 0.0002214 0.0050543 960.3272 0.0165250 0.5243048
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0013045 0.0240732 0.0000340 0.0004710 2612.4653 0.0006245 0.0009925
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5586863 0.1427652 0.0002018 0.0047490 903.7194 -0.8350485 -0.2824194
root beta 0.5938608 0.0336408 0.0000476 0.0007124 2229.9361 0.5289287 0.6570275
all theta -0.5586863 0.1427652 NA NA NA NA NA
all beta 0.5938608 0.0336408 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 163.2535340 11.1414943 0.0157486 0.4335143 660.5109 161.1728961 165.1364740
prior 0.2831262 0.1539420 0.0002176 0.0046095 1115.3272 0.0191449 0.5178852
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0012573 0.0240250 0.0000340 0.0004579 2753.1532 0.0006219 0.0009859
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5610413 0.1417960 0.0002004 0.0046804 917.8314 -0.8330775 -0.2849565
root beta 0.5942846 0.0330173 0.0000467 0.0006966 2246.6902 0.5304492 0.6581839
all theta -0.5610413 0.1417960 NA NA NA NA NA
all beta 0.5942846 0.0330173 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 163.5992852 1.2498141 0.0014931 0.0144825 7447.335 161.1426428 165.1362301
prior 0.2854568 0.1303117 0.0001557 0.0036554 1270.833 0.0173953 0.5205409
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.000 0.0000010 0.0000010
sigma^2 0.0007979 0.0000938 0.0000001 0.0000009 10645.040 0.0006221 0.0009855
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.000 1.0000000 1.0000000
root theta -0.5610922 0.1401196 0.0001674 0.0038897 1297.652 -0.8331344 -0.2837343
root beta 0.5943018 0.0326535 0.0000390 0.0005712 3268.229 0.5300882 0.6579688
all theta -0.5610922 0.1401196 NA NA NA NA NA
all beta 0.5943018 0.0326535 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 1.304500e-03 1.257300e-03 7.979000e-04
stationary variance 6.522382e+02 6.286470e+02 3.989616e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.478386e+03 9.478386e+03 9.478386e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.00000 -65.92240 -42.24757
OU weighted predictor 65.92240 0.00000 23.67484
BM 42.24757 -23.67484 0.00000

ECV

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 174.6214372 21.7986946 0.0308126 1.9473736 125.303279 139.1266144 211.3312720
prior -147.8590327 14.9149016 0.0210823 0.5350832 776.959223 -176.3518343 -117.9163615
alpha 3.6219062 6.6094932 0.0093426 1.3015221 25.788922 0.0389104 18.8488394
sigma^2 0.0353459 0.0631765 0.0000893 0.0256385 6.071904 0.0009980 0.1702755
shift number 28.4165966 3.5212424 0.0049773 0.1223056 828.894222 22.0000000 35.0000000
N theta 29.4165966 3.5212424 0.0049773 0.1223056 828.894222 23.0000000 36.0000000
root theta 1.3480445 0.5757473 0.0008138 0.0405189 201.905978 0.4447422 1.9137552
root beta -0.0311308 0.2131406 0.0003013 0.0129118 272.495534 -0.5124734 0.4104057
all theta 1.4944570 0.8417976 NA NA NA NA NA
all beta -0.0102943 0.3882724 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 181.4026098 27.7985558 0.0392934 3.4180908 66.141993 129.0944327 221.7753231
prior -150.1209745 15.3975558 0.0217645 0.6050480 647.625366 -181.0985482 -118.7383513
alpha 4.0728791 5.4190179 0.0076598 0.8457653 41.052670 0.0297459 16.1351651
sigma^2 0.0365275 0.0463503 0.0000655 0.0218552 4.497754 0.0012069 0.1355008
shift number 28.8274669 3.6433570 0.0051499 0.1407473 670.074766 20.0000000 35.0000000
N theta 29.8274669 3.6433570 0.0051499 0.1407473 670.074766 21.0000000 36.0000000
root theta 1.4650016 0.6003564 0.0008486 0.0394836 231.198679 0.3937086 2.5150004
root beta 0.0050696 0.2380053 0.0003364 0.0149054 254.966903 -0.5038056 0.4760795
all theta 1.4828809 0.8080249 NA NA NA NA NA
all beta 0.0274549 0.4055927 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 171.7258943 22.1196797 0.0264248 2.3800482 86.374621 131.5196106 212.2920745
prior -147.5622771 16.2029266 0.0193565 0.4724873 1175.997978 -179.1930662 -115.6217879
alpha 0.7101747 1.1182121 0.0013358 0.1828494 37.399117 0.0335257 3.1631011
sigma^2 0.0070453 0.0090573 0.0000108 0.0034185 7.019986 0.0009930 0.0279767
shift number 28.2572627 3.7563094 0.0044874 0.1055087 1267.495319 21.0000000 35.0000000
N theta 29.2572627 3.7563094 0.0044874 0.1055087 1267.495319 22.0000000 36.0000000
root theta 1.3838629 0.5783772 0.0006909 0.0354791 265.753051 0.4353998 1.9268027
root beta -0.0019358 0.1962923 0.0002345 0.0096032 417.805872 -0.4458041 0.3438042
all theta 1.4923729 0.8636315 NA NA NA NA NA
all beta 0.0121347 0.4083712 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 3.6219062 4.0728791 0.7101747
sigma squared 0.0353459 0.0365275 0.0070453
stationary variance 0.0048795 0.0044842 0.0049602
phylogenetic halflife 0.1913763 0.1701860 0.9760235
phylogenetic half life in units of tree height 0.0026215 0.0023312 0.0133696

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 77.3453046 5.0946299 0.0072013 0.0977274 2717.64263 75.4206236 78.4466005
prior 0.1350335 0.6554343 0.0009265 0.0799092 67.27672 -1.2538328 0.7055855
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0027076 0.0127084 0.0000180 0.0001405 8184.67285 0.0019890 0.0031682
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2268522 0.1783562 0.0002521 0.0073183 593.96650 0.8796723 1.5778747
root beta -0.1690987 0.4411284 0.0006235 0.0857306 26.47637 -1.0153639 0.6921253
all theta 1.2268522 0.1783562 NA NA NA NA NA
all beta -0.1690987 0.4411284 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 77.2992166 4.6730409 0.0066054 0.1053644 1967.03292 75.2779899 78.4465954
prior -0.0150455 0.7236895 0.0010229 0.0919432 61.95338 -1.5896430 0.7046351
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0026485 0.0083585 0.0000118 0.0000870 9237.90501 0.0020093 0.0031712
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2185557 0.1894400 0.0002678 0.0082231 530.73390 0.8534836 1.5921821
root beta 0.0142040 0.5432906 0.0007679 0.1292278 17.67472 -1.0551329 1.0040725
all theta 1.2185557 0.1894400 NA NA NA NA NA
all beta 0.0142040 0.5432906 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 77.4049901 1.0332654 0.0012344 0.0148397 4848.11431 75.3612431 78.4466005
prior 0.0474492 0.6836918 0.0008168 0.0753117 82.41295 -1.4653720 0.7055366
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0025608 0.0003037 0.0000004 0.0000013 57498.47407 0.0019968 0.0031664
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2293587 0.1841855 0.0002200 0.0065921 780.65078 0.8748883 1.5921417
root beta -0.0617955 0.5133787 0.0006133 0.0966758 28.19940 -1.0810888 0.9005571
all theta 1.2293587 0.1841855 NA NA NA NA NA
all beta -0.0617955 0.5133787 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 2.707600e-03 2.648500e-03 2.560800e-03
stationary variance 1.353775e+03 1.324266e+03 1.280384e+03
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494761e+03 9.494761e+03 9.494761e+03

Model Selection

Bayes Factors
OU un-weighted predictor BM
OU un-weighted predictor 0.00000 10.33027
BM -10.33027 0.00000

ECV (alternate hominin phylogeny)

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 176.9476542 21.3921933 0.0302380 1.7686473 146.29455 142.0030639 218.2957649
prior -152.6639443 16.3640578 0.0231307 0.6161128 705.44247 -184.2026613 -119.7086741
alpha 1.1211028 3.3728059 0.0047675 0.6561153 26.42545 0.0389917 8.6316867
sigma^2 0.0137244 0.0452582 0.0000640 0.0079137 32.70622 0.0008221 0.0981914
shift number 29.4152879 3.9301172 0.0055552 0.1375691 816.14807 22.0000000 37.0000000
N theta 30.4152879 3.9301172 0.0055552 0.1375691 816.14807 23.0000000 38.0000000
root theta 1.2581681 0.5319136 0.0007519 0.0336661 249.62932 0.5023069 1.9053142
root beta -0.0267969 0.1915037 0.0002707 0.0106305 324.52133 -0.4016019 0.3530201
all theta 1.5048462 0.8945219 NA NA NA NA NA
all beta 0.0029253 0.3997772 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 172.4067062 25.8575056 0.0365497 2.8417075 82.79698 122.7756336 215.0405743
prior -151.7218012 16.1925867 0.0228883 0.5479957 873.12840 -185.5566625 -121.5529627
alpha 0.5826597 1.7719813 0.0025047 0.3713733 22.76653 0.0240476 3.7040336
sigma^2 0.0061988 0.0160970 0.0000228 0.0035815 20.20068 0.0008460 0.0394493
shift number 28.9683098 3.8842489 0.0054904 0.1307877 882.02319 21.0000000 36.0000000
N theta 29.9683098 3.8842489 0.0054904 0.1307877 882.02319 22.0000000 37.0000000
root theta 1.3741725 0.5605885 0.0007924 0.0371864 227.25788 0.4623881 1.9165479
root beta 0.0014975 0.1977468 0.0002795 0.0103962 361.80022 -0.3735185 0.3913545
all theta 1.4749374 0.9179613 NA NA NA NA NA
all beta -0.0059581 0.4061569 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 170.0996299 20.3578485 0.0243201 1.9309192 111.1567 123.5051358 206.8698422
prior -152.4099065 16.7462273 0.0200055 0.4719433 1259.0829 -185.8307039 -119.0731173
alpha 0.0920603 0.0271479 0.0000324 0.0026513 104.8449 0.0391477 0.1455830
sigma^2 0.0016867 0.0003742 0.0000004 0.0000246 231.7616 0.0010345 0.0024136
shift number 29.0411871 3.9977269 0.0047758 0.1117011 1280.8895 22.0000000 37.0000000
N theta 30.0411871 3.9977269 0.0047758 0.1117011 1280.8895 23.0000000 38.0000000
root theta 1.2980816 0.5285026 0.0006314 0.0313604 284.0089 0.5057147 1.9101070
root beta -0.0061110 0.1884236 0.0002251 0.0086320 476.4789 -0.3761089 0.3411697
all theta 1.4905268 0.9460229 NA NA NA NA NA
all beta 0.0042702 0.4064725 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 1.1211028 0.5826597 0.0920603
sigma squared 0.0137244 0.0061988 0.0016867
stationary variance 0.0061209 0.0053194 0.0091606
phylogenetic halflife 0.6182726 1.1896261 7.5292716
phylogenetic half life in units of tree height 0.0084545 0.0162674 0.1029584

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 74.9738061 7.0976421 0.0100326 0.2167094 1072.68574 73.1575497 76.1321140
prior 0.0456658 0.7074042 0.0009999 0.0905378 61.04861 -1.5649174 0.7042503
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0028452 0.0156300 0.0000221 0.0002838 3033.50841 0.0020177 0.0031884
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2287395 0.1766699 0.0002497 0.0071445 611.47415 0.8791971 1.5736220
root beta -0.0537153 0.5149835 0.0007279 0.1173667 19.25293 -1.0102430 1.0547852
all theta 1.2287395 0.1766699 NA NA NA NA NA
all beta -0.0537153 0.5149835 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 74.9768890 6.2645802 0.0088550 0.1565561 1601.19357 73.1190336 76.1321137
prior 0.2572294 0.5091031 0.0007196 0.0522164 95.06006 -0.6035923 0.7054618
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0027943 0.0157252 0.0000222 0.0001990 6244.80830 0.0020047 0.0031792
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2240672 0.1831020 0.0002588 0.0076392 574.50031 0.8654063 1.5774800
root beta -0.0304771 0.3998772 0.0005652 0.0716526 31.14504 -0.8069548 0.7253226
all theta 1.2240672 0.1831020 NA NA NA NA NA
all beta -0.0304771 0.3998772 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 75.1102665 1.0059315 0.0012017 0.0139145 5226.40511 73.0838470 76.1321140
prior 0.1393694 0.6454463 0.0007711 0.0750993 73.86674 -1.3272661 0.7056844
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0025748 0.0003028 0.0000004 0.0000021 21084.01496 0.0020125 0.0031804
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 1.2290797 0.1833525 0.0002190 0.0064793 800.79983 0.8665186 1.5871384
root beta -0.0806832 0.4635894 0.0005538 0.0800483 33.53993 -1.1368225 0.7192357
all theta 1.2290797 0.1833525 NA NA NA NA NA
all beta -0.0806832 0.4635894 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 2.845200e-03 2.794300e-03 2.574800e-03
stationary variance 1.422615e+03 1.397139e+03 1.287402e+03
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.478386e+03 9.478386e+03 9.478386e+03

Model Selection

Bayes Factors
OU un-weighted predictor BM
OU un-weighted predictor 0.00000 15.13087
BM -15.13087 0.00000

Rest of Brain ~ Body Mass

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.0937340 6.0299857 0.0085234 0.0649782 8611.8647 30.1929017 40.6405504
prior -17.7202080 4.9446584 0.0069893 0.0982557 2532.5455 -26.7869443 -10.1532887
alpha 3.0112156 4.1903372 0.0059231 0.3104779 182.1531 0.0443452 8.4652205
sigma^2 0.0948241 0.1305784 0.0001846 0.0117059 124.4320 0.0021275 0.2638584
shift number 1.3026228 1.1294804 0.0015965 0.0192860 3429.8312 0.0000000 3.0000000
N theta 2.3026228 1.1294804 0.0015965 0.0192860 3429.8312 1.0000000 4.0000000
root theta 1.7827258 0.0872482 0.0001233 0.0029554 871.5519 1.6181396 1.9561358
root beta 0.6365952 0.0266114 0.0000376 0.0009060 862.7057 0.5853532 0.6872355
all theta 1.8511293 0.6545371 NA NA NA NA NA
all beta 0.6227724 0.1992435 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.0392824 4.5948791 0.0064949 0.0761639 3639.5693 30.1469878 40.5747266
prior -17.1633009 4.9348755 0.0069755 0.0988879 2490.3829 -25.9686790 -10.1514070
alpha 2.4245096 2.8645725 0.0040491 0.1765854 263.1541 0.0521792 7.4081067
sigma^2 0.0767684 0.0908343 0.0001284 0.0062350 212.2385 0.0019014 0.2338630
shift number 1.2701074 1.1438839 0.0016169 0.0194881 3445.2968 0.0000000 3.0000000
N theta 2.2701074 1.1438839 0.0016169 0.0194881 3445.2968 1.0000000 4.0000000
root theta 1.7751165 0.0885335 0.0001251 0.0030382 849.1326 1.6009166 1.9523789
root beta 0.6391139 0.0271911 0.0000384 0.0009071 898.5340 0.5869471 0.6924215
all theta 1.8313309 0.6389266 NA NA NA NA NA
all beta 0.6276917 0.1910389 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.1136970 2.5579851 0.0030558 0.0475565 2893.1841 30.1153025 40.5792956
prior -17.3707357 4.8374886 0.0057790 0.0797489 3679.5183 -26.2353334 -10.1527919
alpha 2.4883053 2.6221166 0.0031325 0.1341058 382.3042 0.0584858 7.1128795
sigma^2 0.0783042 0.0805598 0.0000962 0.0051205 247.5177 0.0019579 0.2218412
shift number 1.2927113 1.1249445 0.0013439 0.0167169 4528.4773 0.0000000 3.0000000
N theta 2.2927113 1.1249445 0.0013439 0.0167169 4528.4773 1.0000000 4.0000000
root theta 1.7789407 0.0883499 0.0001055 0.0025610 1190.0935 1.6084118 1.9534330
root beta 0.6378374 0.0265910 0.0000318 0.0007850 1147.5760 0.5850746 0.6888699
all theta 1.8429826 0.6467617 NA NA NA NA NA
all beta 0.6250019 0.1963772 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 3.0112156 2.4245096 2.4883053
sigma squared 0.0948241 0.0767684 0.0783042
stationary variance 0.0157451 0.0158317 0.0157344
phylogenetic halflife 0.2301885 0.2858917 0.2785619
phylogenetic half life in units of tree height 0.0031531 0.0039162 0.0038158

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 34.9817404 34.0805196 0.0481730 0.2102461 26275.83766 30.1645086 40.9718681
prior -17.4475603 5.0030986 0.0070719 0.0952160 2760.94615 -26.3314566 -10.1604904
alpha 2.4104040 2.5347325 0.0035829 0.2158898 137.84791 0.0996141 6.7482358
sigma^2 0.0759462 0.0787575 0.0001113 0.0145134 29.44729 0.0039144 0.2100656
shift number 1.3282651 1.1795765 0.0016673 0.0206004 3278.68844 0.0000000 3.0000000
N theta 2.3282651 1.1795765 0.0016673 0.0206004 3278.68844 1.0000000 4.0000000
root theta 1.7829262 0.0887056 0.0001254 0.0029828 884.42628 1.6125958 1.9623709
root beta 0.6363281 0.0304438 0.0000430 0.0009794 966.27086 0.5826177 0.6876583
all theta 1.8603783 0.6456922 NA NA NA NA NA
all beta 0.6196096 0.1963656 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.2581918 3.1166710 0.0044054 0.0677628 2115.43009 30.1449338 41.0102256
prior -17.7353482 4.9462905 0.0069916 0.0997299 2459.84792 -26.8515410 -10.1709847
alpha 2.6838008 2.4766979 0.0035008 0.1901318 169.68223 0.1388916 7.6123205
sigma^2 0.0840199 0.0759003 0.0001073 0.0122242 38.55211 0.0053879 0.2318710
shift number 1.3425088 1.1561857 0.0016343 0.0210889 3005.70931 0.0000000 3.0000000
N theta 2.3425088 1.1561857 0.0016343 0.0210889 3005.70931 1.0000000 4.0000000
root theta 1.7836321 0.0882633 0.0001248 0.0030532 835.67737 1.6115112 1.9562768
root beta 0.6361178 0.0270232 0.0000382 0.0009401 826.24225 0.5840623 0.6882896
all theta 1.8569272 0.6439409 NA NA NA NA NA
all beta 0.6208193 0.1904165 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.2812900 2.6589546 0.0031765 0.0515555 2659.94061 30.1616298 40.9963255
prior -17.5213760 4.9272709 0.0058863 0.0834153 3489.16662 -26.6309811 -10.1597370
alpha 2.4490592 2.6466302 0.0031617 0.1927261 188.58433 0.1026100 7.4990343
sigma^2 0.0766546 0.0816180 0.0000975 0.0123166 43.91285 0.0039715 0.2328824
shift number 1.3489990 1.1444863 0.0013672 0.0168757 4599.37818 0.0000000 3.0000000
N theta 2.3489990 1.1444863 0.0013672 0.0168757 4599.37818 1.0000000 4.0000000
root theta 1.7846413 0.0868189 0.0001037 0.0025226 1184.53069 1.6147808 1.9586763
root beta 0.6359932 0.0262720 0.0000314 0.0007701 1163.99060 0.5840369 0.6876032
all theta 1.8581881 0.6461108 NA NA NA NA NA
all beta 0.6201451 0.1929334 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 2.4104040 2.6838008 2.4490592
sigma squared 0.0759462 0.0840199 0.0766546
stationary variance 0.0157538 0.0156532 0.0156498
phylogenetic halflife 0.2875647 0.2582707 0.2830259
phylogenetic half life in units of tree height 0.0039391 0.0035378 0.0038769

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 18.2775948 7.4803682 0.0105735 0.5631936 176.4130 15.7843822 20.4164477
prior 0.6164713 0.2044164 0.0002889 0.0112881 327.9374 0.4440760 0.7061801
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0032838 0.0505091 0.0000714 0.0020181 626.3865 0.0008291 0.0019532
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 2.0113992 0.2309762 0.0003265 0.0119320 374.7224 1.5601547 2.4697285
root beta 0.5573060 0.0603019 0.0000852 0.0020121 898.1489 0.4406410 0.6764485
all theta 2.0113992 0.2309762 NA NA NA NA NA
all beta 0.5573060 0.0603019 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 18.3064079 7.3184538 0.0103447 0.5598556 170.8782 16.0688213 20.4153472
prior 0.6237749 0.1850790 0.0002616 0.0096982 364.1915 0.4663646 0.7061923
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0029100 0.0376909 0.0000533 0.0013298 803.3977 0.0008499 0.0019774
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 2.0012299 0.2160071 0.0003053 0.0104336 428.6126 1.5771577 2.4281743
root beta 0.5607403 0.0609605 0.0000862 0.0020502 884.0677 0.4467587 0.6751603
all theta 2.0012299 0.2160071 NA NA NA NA NA
all beta 0.5607403 0.0609605 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 18.7783360 1.3500690 0.0016128 0.0278327 2352.8896 16.1364436 20.4158315
prior 0.6284968 0.0834715 0.0000997 0.0032951 641.6917 0.4629641 0.7061923
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0013603 0.0002890 0.0000003 0.0000090 1035.1674 0.0008578 0.0019345
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 2.0101932 0.2202032 0.0002631 0.0091532 578.7599 1.5771642 2.4407832
root beta 0.5584174 0.0584850 0.0000699 0.0015991 1337.5705 0.4467370 0.6754541
all theta 2.0101932 0.2202032 NA NA NA NA NA
all beta 0.5584174 0.0584850 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 3.283800e-03 2.910000e-03 1.360300e-03
stationary variance 1.641894e+03 1.455002e+03 6.801678e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.0000000 0.2036888 -13.20949
OU weighted predictor -0.2036888 0.0000000 -13.41318
BM 13.2094895 13.4131783 0.00000

Neocortex ~ Body Mass

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 32.8168851 325.3523158 0.4598873 2.4571315 17532.7883 23.2103516 45.1411171
prior -24.4030877 6.2068539 0.0087734 0.1341944 2139.3137 -35.5309484 -13.6087716
alpha 0.1716046 0.8369939 0.0011831 0.0578385 209.4166 0.0000044 0.8436107
sigma^2 0.0084372 0.0391459 0.0000553 0.0028598 187.3763 0.0003062 0.0400217
shift number 3.5202887 1.5232459 0.0021531 0.0325417 2191.0895 1.0000000 6.0000000
N theta 4.5202887 1.5232459 0.0021531 0.0325417 2191.0895 2.0000000 7.0000000
root theta 1.6313836 0.1631586 0.0002306 0.0074549 479.0057 1.3181201 1.9548490
root beta 0.7629408 0.0503600 0.0000712 0.0024286 429.9871 0.6575935 0.8571897
all theta 1.3251069 0.8957646 NA NA NA NA NA
all beta 0.7960448 0.1136990 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 34.7617046 7.5023820 0.0106047 0.1727186 1886.7743 22.2552417 45.0002571
prior -24.5015083 6.3791129 0.0090169 0.1516194 1770.1548 -36.1846758 -13.6001526
alpha 0.3187654 1.1402167 0.0016117 0.0651448 306.3484 0.0000040 1.9669025
sigma^2 0.0129646 0.0430854 0.0000609 0.0026391 266.5399 0.0002867 0.0779887
shift number 3.5402487 1.5478234 0.0021879 0.0354216 1909.4418 1.0000000 6.0000000
N theta 4.5402487 1.5478234 0.0021879 0.0354216 1909.4418 2.0000000 7.0000000
root theta 1.6256985 0.1594735 0.0002254 0.0070665 509.2962 1.3082366 1.9456518
root beta 0.7663215 0.0528718 0.0000747 0.0028236 350.6163 0.6648005 0.8696241
all theta 1.4345007 0.8570816 NA NA NA NA NA
all beta 0.7966503 0.1280298 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.9948247 4.7117431 0.0056288 0.1297377 1318.9570 27.2722514 45.8533264
prior -24.5317310 6.1340891 0.0073280 0.1147180 2859.1482 -35.6316553 -13.6113687
alpha 0.0098306 0.0164825 0.0000197 0.0007413 494.4096 0.0000044 0.0264806
sigma^2 0.0009273 0.0006842 0.0000008 0.0000256 715.2035 0.0003999 0.0015633
shift number 3.5703093 1.5090296 0.0018027 0.0277791 2950.9401 1.0000000 6.0000000
N theta 4.5703093 1.5090296 0.0018027 0.0277791 2950.9401 2.0000000 7.0000000
root theta 1.6290920 0.1649816 0.0001971 0.0065984 625.1631 1.3070906 1.9535991
root beta 0.7646730 0.0490338 0.0000586 0.0025157 379.8992 0.6680403 0.8593100
all theta 1.3535442 0.9228891 NA NA NA NA NA
all beta 0.7934831 0.1016272 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 0.1716046 0.3187654 0.0098306
sigma squared 0.0084372 0.0129646 0.0009273
stationary variance 0.0245834 0.0203356 0.0471645
phylogenetic halflife 4.0392108 2.1744741 70.5089047
phylogenetic half life in units of tree height 0.0553294 0.0297861 0.9658355

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 27.7299483 7.2727090 0.0102800 0.3319691 479.95107 18.1191079 45.5480671
prior -25.5238969 7.2465200 0.0102430 0.2043728 1257.22388 -39.1606209 -13.7117725
alpha 1.9745880 1.2575676 0.0017776 0.0639144 387.13761 0.1682837 4.1813244
sigma^2 0.0791454 0.0386295 0.0000546 0.0095792 16.26233 0.0101921 0.1471391
shift number 3.5076134 1.7655332 0.0024956 0.0484508 1327.85008 1.0000000 7.0000000
N theta 4.5076134 1.7655332 0.0024956 0.0484508 1327.85008 2.0000000 8.0000000
root theta 1.5983688 0.1599716 0.0002261 0.0058570 746.00240 1.3091754 1.9102546
root beta 0.7810255 0.0784384 0.0001109 0.0027180 832.83177 0.6404256 0.9096880
all theta 1.5037504 0.6343943 NA NA NA NA NA
all beta 0.8314348 0.2018003 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 26.8093017 25.7970518 0.0364643 0.2287368 12719.44549 17.4827060 42.9254696
prior -25.0632333 6.9830689 0.0098706 0.1805274 1496.25721 -38.4131284 -14.0243474
alpha 1.9492654 1.3485050 0.0019061 0.0738196 333.70466 0.4129059 4.8562957
sigma^2 0.0813729 0.0533122 0.0000754 0.0167145 10.17336 0.0241168 0.2133917
shift number 3.3965606 1.7061457 0.0024116 0.0427553 1592.40296 1.0000000 7.0000000
N theta 4.3965606 1.7061457 0.0024116 0.0427553 1592.40296 2.0000000 8.0000000
root theta 1.5829906 0.1601966 0.0002264 0.0063977 626.99035 1.2700234 1.8832959
root beta 0.7873342 0.0779077 0.0001101 0.0028171 764.81433 0.6397492 0.9140903
all theta 1.4860431 0.6366793 NA NA NA NA NA
all beta 0.8357730 0.2032378 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 27.4931909 6.7523610 0.0080666 0.2651818 648.37136 17.8932531 44.5848315
prior -25.1563465 7.0231426 0.0083900 0.1587772 1956.53108 -38.3626798 -13.7289268
alpha 1.7700885 1.1364938 0.0013577 0.0498612 519.52864 0.1944426 3.9083460
sigma^2 0.0722819 0.0407478 0.0000487 0.0092439 19.43098 0.0101921 0.1513429
shift number 3.4719725 1.7267705 0.0020628 0.0385442 2007.01300 1.0000000 7.0000000
N theta 4.4719725 1.7267705 0.0020628 0.0385442 2007.01300 2.0000000 8.0000000
root theta 1.5883577 0.1578281 0.0001885 0.0051290 946.88858 1.2879207 1.8932525
root beta 0.7856376 0.0772600 0.0000923 0.0023906 1044.49521 0.6438340 0.9126602
all theta 1.4912459 0.6334104 NA NA NA NA NA
all beta 0.8340280 0.2015946 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 1.9745880 1.9492654 1.7700885
sigma squared 0.0791454 0.0813729 0.0722819
stationary variance 0.0200410 0.0208727 0.0204176
phylogenetic halflife 0.3510338 0.3555941 0.3915890
phylogenetic half life in units of tree height 0.0048085 0.0048709 0.0053640

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 20.8715295 5.8345207 0.0082471 0.3297257 313.1157 18.3840937 22.8589064
prior 0.5385952 0.1854439 0.0002621 0.0086007 464.8978 0.2897727 0.7061340
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0023161 0.0334421 0.0000473 0.0009781 1169.0522 0.0007949 0.0017988
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.7390091 0.2242857 0.0003170 0.0117307 365.5590 1.3267016 2.1903187
root beta 0.7418696 0.0601616 0.0000850 0.0020899 828.6437 0.6237639 0.8507326
all theta 1.7390091 0.2242857 NA NA NA NA NA
all beta 0.7418696 0.0601616 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 21.0961872 5.8271612 0.0082367 0.3416098 290.9734 18.9708934 22.8607812
prior 0.5374127 0.1708326 0.0002415 0.0076535 498.2259 0.3308981 0.7057571
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0021657 0.0289035 0.0000409 0.0009220 982.7194 0.0007761 0.0017194
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.7551085 0.1884625 0.0002664 0.0083070 514.7030 1.3846736 2.1215177
root beta 0.7354261 0.0512223 0.0000724 0.0015023 1162.4672 0.6354001 0.8339267
all theta 1.7551085 0.1884625 NA NA NA NA NA
all beta 0.7354261 0.0512223 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 21.2581897 1.3037861 0.0015575 0.0242721 2885.3370 18.6966750 22.8616275
prior 0.5448964 0.1197458 0.0001431 0.0049407 587.4213 0.3132632 0.7061011
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0012331 0.0002535 0.0000003 0.0000060 1807.7957 0.0007878 0.0017434
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.7437475 0.2079345 0.0002484 0.0086983 571.4539 1.3434474 2.1630782
root beta 0.7393104 0.0548553 0.0000655 0.0014734 1386.1299 0.6306284 0.8450501
all theta 1.7437475 0.2079345 NA NA NA NA NA
all beta 0.7393104 0.0548553 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 2.316100e-03 2.165700e-03 1.233100e-03
stationary variance 1.158037e+03 1.082865e+03 6.165456e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.000000 -3.995941 18.21388
OU weighted predictor 3.995941 0.000000 22.20983
BM -18.213884 -22.209825 0.00000

Neocortex ~ Rest of Brain

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.8484663 968.1801624 1.3685281 2.5734017 141545.86190 35.7727162 51.5812024
prior -23.2532256 4.5627496 0.0064495 0.1013316 2027.51208 -31.5383428 -13.8553269
alpha 2.1636622 1.7379749 0.0024566 0.1382129 158.12120 0.0062162 5.6566696
sigma^2 0.0472127 0.0363335 0.0000514 0.0098932 13.48773 0.0010836 0.1276905
shift number 2.9008673 1.0744340 0.0015187 0.0220908 2365.57596 1.0000000 5.0000000
N theta 3.9008673 1.0744340 0.0015187 0.0220908 2365.57596 2.0000000 6.0000000
root theta -0.6339715 0.2108443 0.0002980 0.0083834 632.53131 -1.0156088 -0.2434912
root beta 1.2418326 0.0814384 0.0001151 0.0025560 1015.15219 1.1179615 1.3615942
all theta -0.7405324 0.6921804 NA NA NA NA NA
all beta 1.2713242 0.1649926 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 43.8279981 6.5804940 0.0093016 0.1134002 3367.35852 35.5612005 51.2919730
prior -23.7055845 4.5388822 0.0064157 0.0925822 2403.49505 -32.5613466 -15.0578766
alpha 3.3374555 1.8237175 0.0025778 0.1051125 301.02788 0.4217073 6.7914446
sigma^2 0.0754616 0.0370812 0.0000524 0.0065471 32.07837 0.0096908 0.1453442
shift number 2.7738666 1.0584480 0.0014961 0.0201765 2752.00582 1.0000000 5.0000000
N theta 3.7738666 1.0584480 0.0014961 0.0201765 2752.00582 2.0000000 6.0000000
root theta -0.6552091 0.1876256 0.0002652 0.0159671 138.08124 -1.0318872 -0.2518178
root beta 1.2564397 0.0626718 0.0000886 0.0062666 100.01786 1.1307464 1.3691711
all theta -0.8135768 0.6943325 NA NA NA NA NA
all beta 1.2883986 0.1660847 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 44.2063127 3.9656266 0.0047374 0.1018626 1515.63351 35.8230725 51.3585512
prior -23.5228093 4.4778750 0.0053494 0.0810203 3054.61546 -32.4301834 -14.9626555
alpha 2.8489993 1.6936491 0.0020233 0.0919749 339.08457 0.2918139 6.1444828
sigma^2 0.0633741 0.0349860 0.0000418 0.0061284 32.59057 0.0079628 0.1317232
shift number 2.8171182 1.0398971 0.0012423 0.0172423 3637.38195 1.0000000 5.0000000
N theta 3.8171182 1.0398971 0.0012423 0.0172423 3637.38195 2.0000000 6.0000000
root theta -0.6374330 0.1974473 0.0002359 0.0085295 535.86534 -1.0119052 -0.2304020
root beta 1.2526926 0.0729528 0.0000872 0.0026681 747.60055 1.1146628 1.3610931
all theta -0.7952536 0.7046166 NA NA NA NA NA
all beta 1.2832230 0.1673607 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 2.1636622 3.3374555 2.8489993
sigma squared 0.0472127 0.0754616 0.0633741
stationary variance 0.0109104 0.0113053 0.0111222
phylogenetic halflife 0.3203583 0.2076873 0.2432950
phylogenetic half life in units of tree height 0.0043883 0.0028449 0.0033327

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 43.8979990 4.4951105 0.0063539 0.1397838 1034.11020 35.4665226 51.2292886
prior -23.8578417 4.8785533 0.0068959 0.1162950 1759.78704 -32.6891924 -13.9740455
alpha 3.5254850 3.3528039 0.0047392 0.2360772 201.70103 0.2385005 9.6435901
sigma^2 0.0797647 0.0732062 0.0001035 0.0096366 57.70999 0.0058361 0.2125637
shift number 2.8162541 1.0660587 0.0015069 0.0216442 2425.93778 1.0000000 5.0000000
N theta 3.8162541 1.0660587 0.0015069 0.0216442 2425.93778 2.0000000 6.0000000
root theta -0.6657844 0.2274737 0.0003215 0.0088728 657.26922 -1.0893730 -0.1897840
root beta 1.2472358 0.0712471 0.0001007 0.0028328 632.57222 1.0979957 1.3728979
all theta -0.7906672 0.7157514 NA NA NA NA NA
all beta 1.2814128 0.1727140 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 39.8941116 1060.6268466 1.4992020 4.2083819 63517.72602 35.5189152 51.6070603
prior -23.5907037 4.7007118 0.0066445 0.0999258 2212.95041 -32.0702708 -14.0855715
alpha 3.0880861 2.9184596 0.0041253 0.2036243 205.42261 0.1653919 8.6588482
sigma^2 0.0698243 0.0635938 0.0000899 0.0083592 57.87616 0.0037153 0.1950417
shift number 2.8634029 1.0683404 0.0015101 0.0201095 2822.37812 1.0000000 5.0000000
N theta 3.8634029 1.0683404 0.0015101 0.0201095 2822.37812 2.0000000 6.0000000
root theta -0.6804767 0.2052922 0.0002902 0.0178454 132.33971 -1.0563787 -0.2436789
root beta 1.2460685 0.0660245 0.0000933 0.0058992 125.26233 1.1226679 1.3698521
all theta -0.8217033 0.6744663 NA NA NA NA NA
all beta 1.2899395 0.1654361 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 44.1407053 4.0499875 0.0048382 0.1062974 1451.6504 35.7025606 51.4354126
prior -23.7346579 4.7996548 0.0057338 0.0949231 2556.6780 -32.4161028 -13.9690050
alpha 3.3856772 3.4595838 0.0041329 0.2157652 257.0898 0.1605903 9.9835032
sigma^2 0.0761431 0.0742844 0.0000887 0.0086867 73.1277 0.0037153 0.2226821
shift number 2.8347433 1.0601508 0.0012665 0.0179683 3481.1499 1.0000000 5.0000000
N theta 3.8347433 1.0601508 0.0012665 0.0179683 3481.1499 2.0000000 6.0000000
root theta -0.6680813 0.2048490 0.0002447 0.0091215 504.3520 -1.0502625 -0.2483801
root beta 1.2471524 0.0672071 0.0000803 0.0031225 463.2499 1.1173492 1.3699408
all theta -0.7952818 0.7000289 NA NA NA NA NA
all beta 1.2827302 0.1707245 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 3.5254850 3.0880861 3.3856772
sigma squared 0.0797647 0.0698243 0.0761431
stationary variance 0.0113126 0.0113054 0.0112449
phylogenetic halflife 0.1966104 0.2244585 0.2047293
phylogenetic half life in units of tree height 0.0026932 0.0030746 0.0028044

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 17.5150011 3.6378668 0.0051421 0.1257875 836.4088 15.0151934 19.2080224
prior 0.0165669 0.3883399 0.0005489 0.0257268 227.8525 -0.7030907 0.6884311
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0018120 0.0205364 0.0000290 0.0004406 2172.3401 0.0009041 0.0020257
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.0609930 0.3097906 0.0004379 0.0224731 190.0242 -0.6826560 0.5377753
root beta 1.0859743 0.0786945 0.0001112 0.0037377 443.2905 0.9333284 1.2395857
all theta -0.0609930 0.3097906 NA NA NA NA NA
all beta 1.0859743 0.0786945 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 17.3634726 3.4730740 0.0049092 0.1065983 1061.5174 14.3767024 19.2089078
prior 0.0313275 0.4147713 0.0005863 0.0287710 207.8292 -0.7075689 0.7059280
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0018395 0.0240165 0.0000339 0.0004343 3058.6033 0.0008981 0.0020419
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.0887087 0.3567984 0.0005043 0.0288710 152.7290 -0.8569471 0.5581567
root beta 1.0925840 0.0892841 0.0001262 0.0048934 332.9064 0.9224502 1.2750628
all theta -0.0887087 0.3567984 NA NA NA NA NA
all beta 1.0925840 0.0892841 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 17.6151197 1.3390684 0.0015997 0.0202266 4382.8985 14.9845493 19.2093645
prior 0.0204465 0.3772335 0.0004507 0.0232925 262.2946 -0.6797911 0.7018271
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0014139 0.0002979 0.0000004 0.0000032 8523.5930 0.0008871 0.0020107
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.0620764 0.3078858 0.0003678 0.0187659 269.1786 -0.6691354 0.5533120
root beta 1.0860732 0.0779255 0.0000931 0.0031770 601.6116 0.9318730 1.2387710
all theta -0.0620764 0.3078858 NA NA NA NA NA
all beta 1.0860732 0.0779255 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 1.812000e-03 1.839500e-03 1.413900e-03
stationary variance 9.059836e+02 9.197657e+02 7.069329e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.000000 9.287355 -5.080023
OU weighted predictor -9.287355 0.000000 -14.367379
BM 5.080023 14.367379 0.000000

Cerebellum ~ Body Mass

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 36.4566292 5.2871738 0.0074734 0.1968457 721.43166 26.6512833 44.8588394
prior -22.6710409 5.6442399 0.0079782 0.1343198 1765.75752 -35.4633553 -13.5989196
alpha 3.3967852 5.9438755 0.0084017 0.5952794 99.70060 0.0038035 9.9937069
sigma^2 0.1050424 0.2063346 0.0002917 0.0338398 37.17824 0.0010685 0.2946486
shift number 2.6200347 1.2740112 0.0018008 0.0261663 2370.62251 0.0000000 5.0000000
N theta 3.6200347 1.2740112 0.0018008 0.0261663 2370.62251 1.0000000 6.0000000
root theta 1.0382549 0.1167466 0.0001650 0.0061941 355.25057 0.8001524 1.2559433
root beta 0.7520156 0.0388820 0.0000550 0.0022372 302.06664 0.6811840 0.8329248
all theta 0.9931324 0.6417818 NA NA NA NA NA
all beta 0.7950026 0.2009048 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 36.4622926 5.0899284 0.0071946 0.1642591 960.20555 27.1691024 44.0587734
prior -22.9663043 5.6445773 0.0079786 0.1368128 1702.19561 -35.4640343 -13.5986330
alpha 3.9902225 5.2405207 0.0074075 0.5069369 106.86637 0.0019369 13.5508251
sigma^2 0.1188536 0.1542000 0.0002180 0.0398436 14.97788 0.0008494 0.3952444
shift number 2.5623925 1.2276378 0.0017353 0.0245591 2498.71025 1.0000000 5.0000000
N theta 3.5623925 1.2276378 0.0017353 0.0245591 2498.71025 2.0000000 6.0000000
root theta 1.0432452 0.1097785 0.0001552 0.0056271 380.59146 0.8192346 1.2560838
root beta 0.7507707 0.0363652 0.0000514 0.0019621 343.51663 0.6822760 0.8259890
all theta 1.0150288 0.6476237 NA NA NA NA NA
all beta 0.7856301 0.2000887 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 36.6716941 4.8719617 0.0058202 0.1620806 903.53652 27.0331859 44.7378321
prior -22.4925545 5.6129220 0.0067054 0.1150156 2381.57458 -35.6923940 -13.5974380
alpha 3.0593154 4.3930424 0.0052481 0.3765281 136.12444 0.0033618 8.4583884
sigma^2 0.0899002 0.1297257 0.0001550 0.0294812 19.36251 0.0008476 0.2364548
shift number 2.6073349 1.2534005 0.0014973 0.0219005 3275.45712 0.0000000 5.0000000
N theta 3.6073349 1.2534005 0.0014973 0.0219005 3275.45712 1.0000000 6.0000000
root theta 1.0458358 0.1124104 0.0001343 0.0049341 519.04028 0.8172568 1.2596879
root beta 0.7494989 0.0372117 0.0000445 0.0017705 441.74762 0.6808556 0.8273908
all theta 1.0080017 0.6410605 NA NA NA NA NA
all beta 0.7891335 0.1974405 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 3.3967852 3.9902225 3.0593154
sigma squared 0.1050424 0.1188536 0.0899002
stationary variance 0.0154620 0.0148931 0.0146929
phylogenetic halflife 0.2040598 0.1737114 0.2265694
phylogenetic half life in units of tree height 0.0027952 0.0023795 0.0031036

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 34.0371561 16.9841906 0.0240072 0.1725718 9686.12060 23.4572121 45.0021240
prior -43.0414028 17.3366744 0.0245055 0.5320266 1061.85433 -74.6248220 -13.6006896
alpha 0.0862955 0.4436760 0.0006271 0.0475792 86.95550 0.0000168 0.1818922
sigma^2 0.0031725 0.0132612 0.0000187 0.0030428 18.99399 0.0003987 0.0053736
shift number 7.7708516 4.0149894 0.0056752 0.1203739 1112.51084 1.0000000 15.0000000
N theta 8.7708516 4.0149894 0.0056752 0.1203739 1112.51084 2.0000000 16.0000000
root theta 1.0471759 0.1539052 0.0002175 0.0043775 1236.10923 0.7245957 1.3450879
root beta 0.7434921 0.0493741 0.0000698 0.0012742 1501.54666 0.6455499 0.8458869
all theta 0.9581601 0.8701998 NA NA NA NA NA
all beta 0.8192586 0.4168436 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 36.2193168 5.3442745 0.0075542 0.2045992 682.29093 26.1425057 45.0325194
prior -27.3900948 11.1956702 0.0158251 0.4123270 737.25312 -51.1514961 -10.1458263
alpha 4.2963449 6.6751439 0.0094354 0.5421482 151.59515 0.0003357 17.6570872
sigma^2 0.1248236 0.1804488 0.0002551 0.0381314 22.39451 0.0004158 0.5436612
shift number 3.6037271 2.7171061 0.0038406 0.1007678 727.05938 0.0000000 10.0000000
N theta 4.6037271 2.7171061 0.0038406 0.1007678 727.05938 1.0000000 11.0000000
root theta 1.0294418 0.1260774 0.0001782 0.0050066 634.13821 0.7858762 1.2785029
root beta 0.7534692 0.0426523 0.0000603 0.0017945 564.94620 0.6713536 0.8382244
all theta 0.9896406 0.7275289 NA NA NA NA NA
all beta 0.8054296 0.2992028 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 35.3269162 5.7027183 0.0068126 0.2043558 778.73515 24.5540173 45.3901024
prior -36.6378793 16.7264913 0.0199819 0.5212416 1029.74934 -71.0768777 -13.5984721
alpha 2.1458487 5.8823090 0.0070272 0.4698360 156.74839 0.0000168 13.8846515
sigma^2 0.0621376 0.1604863 0.0001917 0.0324137 24.51429 0.0003820 0.4285442
shift number 6.0538573 4.0295435 0.0048138 0.1279281 992.15559 1.0000000 14.0000000
N theta 7.0538573 4.0295435 0.0048138 0.1279281 992.15559 2.0000000 15.0000000
root theta 1.0395540 0.1418021 0.0001694 0.0037238 1450.07772 0.7542402 1.3213660
root beta 0.7471385 0.0462549 0.0000553 0.0011885 1514.76778 0.6541054 0.8395345
all theta 0.9645586 0.8295112 NA NA NA NA NA
all beta 0.8174347 0.3907971 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 0.0862955 4.2963449 2.1458487
sigma squared 0.0031725 0.1248236 0.0621376
stationary variance 0.0183817 0.0145267 0.0144786
phylogenetic halflife 8.0322527 0.1613342 0.3230177
phylogenetic half life in units of tree height 0.1100263 0.0022100 0.0044247

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 26.5485381 5.0509005 0.0071395 0.2360795 457.7421 24.1094743 28.3620457
prior 0.6108970 0.1417179 0.0002003 0.0051922 744.9891 0.4426606 0.7061943
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0017322 0.0289745 0.0000410 0.0006944 1741.0983 0.0006316 0.0014304
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.2015515 0.1875839 0.0002652 0.0084088 497.6499 0.8415834 1.5800614
root beta 0.6993194 0.0499740 0.0000706 0.0015356 1059.1323 0.6016079 0.8002787
all theta 1.2015515 0.1875839 NA NA NA NA NA
all beta 0.6993194 0.0499740 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 26.5629428 5.4926810 0.0077639 0.2882235 363.1700 24.2528337 28.3631810
prior 0.6183126 0.1445437 0.0002043 0.0057300 636.3396 0.4722565 0.7062234
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0018346 0.0293708 0.0000415 0.0007758 1433.3601 0.0006274 0.0014132
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.1845039 0.1806239 0.0002553 0.0076412 558.7645 0.8240929 1.5464148
root beta 0.7028933 0.0484279 0.0000685 0.0014403 1130.4657 0.6066532 0.7999328
all theta 1.1845039 0.1806239 NA NA NA NA NA
all beta 0.7028933 0.0484279 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 26.7706289 1.2912353 0.0015425 0.0201380 4111.2956 24.2360618 28.3620457
prior 0.6170407 0.0808391 0.0000966 0.0031029 678.7535 0.4545461 0.7062101
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0009983 0.0002071 0.0000002 0.0000036 3376.4739 0.0006390 0.0014160
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.1954987 0.1863705 0.0002226 0.0068648 737.0504 0.8428894 1.5792490
root beta 0.7006512 0.0495059 0.0000591 0.0012905 1471.7183 0.6033083 0.8003800
all theta 1.1954987 0.1863705 NA NA NA NA NA
all beta 0.7006512 0.0495059 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 1.732200e-03 1.834600e-03 9.983000e-04
stationary variance 8.661245e+02 9.172910e+02 4.991699e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.00000 10.83171 22.78693
OU weighted predictor -10.83171 0.00000 11.95522
BM -22.78693 -11.95522 0.00000

Cerebellum ~ Rest of Brain

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.3269425 3.9357571 0.0055632 0.1012674 1510.4870 44.7023903 54.3961533
prior -20.9461595 4.7152885 0.0066651 0.1177747 1602.9213 -29.6111772 -13.8759109
alpha 6.8740976 11.0784825 0.0156595 0.9947652 124.0279 0.2779672 25.3686391
sigma^2 0.1275789 0.2041039 0.0002885 0.0335094 37.0996 0.0070807 0.4817957
shift number 1.8596786 0.9390306 0.0013273 0.0162547 3337.3617 1.0000000 4.0000000
N theta 2.8596786 0.9390306 0.0013273 0.0162547 3337.3617 2.0000000 5.0000000
root theta -0.8119928 0.1345697 0.0001902 0.0081744 271.0109 -1.0893914 -0.5548172
root beta 1.1142681 0.0367249 0.0000519 0.0017818 424.8286 1.0456704 1.1869901
all theta -0.8537486 0.5772799 NA NA NA NA NA
all beta 1.1533021 0.1446264 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.2069385 24.8321423 0.0351004 0.2001908 15386.51547 44.7336228 54.3495102
prior -20.6981186 4.5007928 0.0063619 0.0991912 2058.88521 -28.9382894 -14.0955850
alpha 5.7780187 9.4741714 0.0133918 0.8217482 132.92448 0.4593220 14.1225901
sigma^2 0.1065654 0.1706065 0.0002412 0.0373301 20.88682 0.0107418 0.2464464
shift number 1.8447236 0.9458469 0.0013370 0.0161186 3443.38114 1.0000000 4.0000000
N theta 2.8447236 0.9458469 0.0013370 0.0161186 3443.38114 2.0000000 5.0000000
root theta -0.8175726 0.1336386 0.0001889 0.0084307 251.26502 -1.0821132 -0.5492164
root beta 1.1157420 0.0354847 0.0000502 0.0021581 270.34832 1.0438563 1.1854522
all theta -0.8297152 0.5830575 NA NA NA NA NA
all beta 1.1484814 0.1445109 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.4082883 2.3190157 0.0027704 0.0330285 4929.79499 44.8529090 54.3869963
prior -20.2735808 4.0849296 0.0048800 0.0728433 3144.77495 -27.9431388 -13.9333419
alpha 4.3403781 4.0391746 0.0048253 0.2440361 273.95365 0.3622365 11.2181190
sigma^2 0.0795458 0.0712826 0.0000852 0.0107704 43.80264 0.0077395 0.1954588
shift number 1.8437600 0.9015113 0.0010770 0.0128477 4923.73617 1.0000000 4.0000000
N theta 2.8437600 0.9015113 0.0010770 0.0128477 4923.73617 2.0000000 5.0000000
root theta -0.8121158 0.1336923 0.0001597 0.0071305 351.53857 -1.0924216 -0.5548172
root beta 1.1143510 0.0354722 0.0000424 0.0018812 355.53859 1.0457706 1.1888983
all theta -0.8479819 0.5802528 NA NA NA NA NA
all beta 1.1524684 0.1437857 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 6.8740976 5.7780187 4.3403781
sigma squared 0.1275789 0.1065654 0.0795458
stationary variance 0.0092797 0.0092216 0.0091635
phylogenetic halflife 0.1008346 0.1199628 0.1596974
phylogenetic half life in units of tree height 0.0013812 0.0016433 0.0021875

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.3481274 2.7736407 0.0039206 0.0517473 2872.9267 44.9024246 54.2997755
prior -19.6678169 4.1849779 0.0059155 0.0888331 2219.4042 -27.4896496 -13.7336059
alpha 3.7221887 5.8580373 0.0082804 0.4490953 170.1482 0.0861110 11.8009314
sigma^2 0.0686369 0.1055998 0.0001493 0.0102375 106.4000 0.0016914 0.2156493
shift number 1.8430573 0.9128674 0.0012903 0.0152115 3601.4190 1.0000000 4.0000000
N theta 2.8430573 0.9128674 0.0012903 0.0152115 3601.4190 2.0000000 5.0000000
root theta -0.8220552 0.1245090 0.0001760 0.0076035 268.1453 -1.0632893 -0.5772153
root beta 1.1169222 0.0329857 0.0000466 0.0019887 275.1177 1.0503486 1.1789120
all theta -0.8348596 0.5893023 NA NA NA NA NA
all beta 1.1494329 0.1432998 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.2633328 11.9856559 0.0169418 0.1048105 13077.1885 44.4475506 54.6753513
prior -19.5913878 4.1938216 0.0059280 0.0836046 2516.2815 -27.3412844 -13.6981301
alpha 3.0033150 3.1793302 0.0044940 0.1988068 255.7459 0.1220655 8.8839884
sigma^2 0.0554521 0.0580222 0.0000820 0.0047153 151.4141 0.0022603 0.1624690
shift number 1.8739583 0.9437113 0.0013339 0.0160975 3436.8470 1.0000000 4.0000000
N theta 2.8739583 0.9437113 0.0013339 0.0160975 3436.8470 2.0000000 5.0000000
root theta -0.8433433 0.1415927 0.0002001 0.0095398 220.2925 -1.1111085 -0.5703628
root beta 1.1226095 0.0395323 0.0000559 0.0018656 449.0013 1.0502957 1.1927854
all theta -0.8553063 0.6042763 NA NA NA NA NA
all beta 1.1545158 0.1485375 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 49.3834736 2.3793226 0.0028424 0.0377764 3967.0407 44.7301931 54.5654094
prior -19.5954467 4.1241172 0.0049268 0.0724996 3235.8677 -27.3738546 -13.7444268
alpha 3.2850853 4.4575868 0.0053252 0.2784352 256.3016 0.0949506 9.8046308
sigma^2 0.0607616 0.0831734 0.0000994 0.0066471 156.5705 0.0017156 0.1805526
shift number 1.8560947 0.9205252 0.0010997 0.0132498 4826.7162 1.0000000 4.0000000
N theta 2.8560947 0.9205252 0.0010997 0.0132498 4826.7162 2.0000000 5.0000000
root theta -0.8378266 0.1351284 0.0001614 0.0074360 330.2258 -1.0776892 -0.5727548
root beta 1.1210664 0.0361976 0.0000432 0.0020173 321.9858 1.0518719 1.1855103
all theta -0.8414627 0.5941776 NA NA NA NA NA
all beta 1.1507620 0.1444982 NA NA NA NA NA

Shifts

A shows the locations of the selection regimes on the phylogeny. B shows the optimum regression lines associated with each regime. C and D show the posterior distribution of \(\beta\) and \(\theta\) values associated with each regime.

Plot shows the median values for parameters associated with each selection regime, along with the posterior probability associeated with each regime. \(\theta\) is the intercept of the optimum regression line, and \(\beta\) is the coefficient of the predictor.

OU parameters

chain1 chain2 combined chains
alpha 3.7221887 3.0033150 3.2850853
sigma squared 0.0686369 0.0554521 0.0607616
stationary variance 0.0092200 0.0092318 0.0092481
phylogenetic halflife 0.1862203 0.2307940 0.2109982
phylogenetic half life in units of tree height 0.0025509 0.0031614 0.0028903

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 27.7751952 2.4020119 0.0033953 0.0459851 2728.4557 25.2802762 29.4104014
prior 0.3937618 0.2363242 0.0003340 0.0136611 299.2596 -0.0585239 0.7062204
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0010826 0.0120831 0.0000171 0.0001197 10198.0175 0.0006101 0.0013692
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5335550 0.2761243 0.0003903 0.0183661 226.0361 -1.0676802 0.0195057
root beta 1.0371505 0.0694229 0.0000981 0.0031915 473.1717 0.9005716 1.1748000
all theta -0.5335550 0.2761243 NA NA NA NA NA
all beta 1.0371505 0.0694229 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 27.7948634 2.2579275 0.0031916 0.0416064 2945.1048 25.2930660 29.4091996
prior 0.4024882 0.2212113 0.0003127 0.0125847 308.9778 -0.0115160 0.7062136
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0010673 0.0121688 0.0000172 0.0000996 14925.6437 0.0006119 0.0013760
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5423194 0.2701564 0.0003819 0.0170906 249.8696 -1.0794213 -0.0185238
root beta 1.0386770 0.0680850 0.0000962 0.0030871 486.4145 0.9043142 1.1715899
all theta -0.5423194 0.2701564 NA NA NA NA NA
all beta 1.0386770 0.0680850 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 27.8347888 1.2748328 0.0015230 0.0145494 7677.4573 25.3257300 29.4090188
prior 0.4060624 0.2165916 0.0002587 0.0117126 341.9621 -0.0058340 0.7061951
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0009620 0.0002027 0.0000002 0.0000010 37254.5836 0.0006154 0.0013760
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta -0.5446117 0.2660055 0.0003178 0.0144844 337.2734 -1.0719802 -0.0308299
root beta 1.0392547 0.0673263 0.0000804 0.0025535 695.1869 0.9079109 1.1714135
all theta -0.5446117 0.2660055 NA NA NA NA NA
all beta 1.0392547 0.0673263 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 1.082600e-03 1.067300e-03 9.620000e-04
stationary variance 5.412753e+02 5.336342e+02 4.809976e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.0000000 -0.1973664 -10.65050
OU weighted predictor 0.1973664 0.0000000 -10.45313
BM 10.6504986 10.4531321 0.00000

Medulla ~ Body Mass

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.5090395 3.8289470 0.0054122 0.1171954 1067.4259 35.8256584 49.7403512
prior -13.2359031 4.2147195 0.0059575 0.0975562 1866.4989 -21.1753098 -7.5672757
alpha 3.3050082 3.6660083 0.0051819 0.2550397 206.6196 0.1363300 10.3375381
sigma^2 0.0480708 0.0487685 0.0000689 0.0043616 125.0206 0.0026400 0.1485004
shift number 0.9079163 0.9474716 0.0013393 0.0188478 2527.0234 0.0000000 3.0000000
N theta 1.9079163 0.9474716 0.0013393 0.0188478 2527.0234 1.0000000 4.0000000
root theta 1.0677990 0.0784913 0.0001109 0.0023994 1070.1740 0.9133303 1.2251224
root beta 0.5870589 0.0223279 0.0000316 0.0006535 1167.5238 0.5429637 0.6312144
all theta 1.0574266 0.4913659 NA NA NA NA NA
all beta 0.5829843 0.1672830 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.3631024 266.9873493 0.3773881 0.7808967 116894.5314 36.3959447 51.5809923
prior -14.2426511 4.7314415 0.0066879 0.1238551 1459.3499 -22.8511111 -7.5456825
alpha 4.6785248 6.8827947 0.0097289 0.5139241 179.3625 0.0000963 15.8941958
sigma^2 0.0683668 0.1023175 0.0001446 0.0100184 104.3035 0.0002943 0.2297625
shift number 1.0391208 1.0308954 0.0014572 0.0225655 2087.0883 0.0000000 3.0000000
N theta 2.0391208 1.0308954 0.0014572 0.0225655 2087.0883 1.0000000 4.0000000
root theta 1.0785224 0.0819400 0.0001158 0.0026366 965.8252 0.9241345 1.2383921
root beta 0.5848160 0.0231503 0.0000327 0.0007174 1041.1920 0.5402858 0.6285270
all theta 1.0486085 0.5214857 NA NA NA NA NA
all beta 0.5846585 0.1845006 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.9231253 3.8363852 0.0045831 0.1238482 959.5443 36.1171349 51.0201071
prior -13.6856649 4.4820591 0.0053544 0.0951877 2217.1404 -22.0645257 -7.5456825
alpha 3.7860633 5.5320481 0.0066087 0.3588624 237.6381 0.0000963 12.1936336
sigma^2 0.0551960 0.0811289 0.0000969 0.0067506 144.4347 0.0002899 0.1765419
shift number 0.9848495 0.9948119 0.0011884 0.0179993 3054.7043 0.0000000 3.0000000
N theta 1.9848495 0.9948119 0.0011884 0.0179993 3054.7043 1.0000000 4.0000000
root theta 1.0745056 0.0792044 0.0000946 0.0020732 1459.4939 0.9194360 1.2309349
root beta 0.5855490 0.0225094 0.0000269 0.0005687 1566.8394 0.5411605 0.6294026
all theta 1.0552870 0.5152106 NA NA NA NA NA
all beta 0.5832427 0.1810461 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 3.3050082 4.6785248 3.7860633
sigma squared 0.0480708 0.0683668 0.0551960
stationary variance 0.0072724 0.0073064 0.0072894
phylogenetic halflife 0.2097263 0.1481551 0.1830786
phylogenetic half life in units of tree height 0.0028728 0.0020294 0.0025078

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.2835153 13.7754579 0.0194717 0.0830299 27525.98063 35.7122525 49.9597488
prior -13.6388157 4.3165686 0.0061015 0.0992767 1890.52593 -21.5471531 -7.5688246
alpha 4.2604272 4.4098640 0.0062334 0.3547219 154.55194 0.1307626 13.0623479
sigma^2 0.0632336 0.0605777 0.0000856 0.0117015 26.80038 0.0029137 0.1846570
shift number 0.8863359 0.9398395 0.0013285 0.0173897 2920.92708 0.0000000 3.0000000
N theta 1.8863359 0.9398395 0.0013285 0.0173897 2920.92708 1.0000000 4.0000000
root theta 1.0628151 0.0790345 0.0001117 0.0024745 1020.15246 0.9071124 1.2185394
root beta 0.5884737 0.0227734 0.0000322 0.0006632 1179.28354 0.5447026 0.6336061
all theta 1.0306371 0.4868995 NA NA NA NA NA
all beta 0.5931910 0.1673254 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.5112926 15.1526428 0.0214183 0.1079103 19717.46412 35.9587216 50.9632229
prior -14.8072017 4.5998722 0.0065019 0.1174755 1533.19221 -23.2159396 -7.6044929
alpha 6.5957192 7.4787290 0.0105712 0.6444929 134.65402 0.1690026 21.1131089
sigma^2 0.0982441 0.1050929 0.0001485 0.0224355 21.94206 0.0035006 0.3049199
shift number 0.9375865 0.9927251 0.0014032 0.0205929 2323.92104 0.0000000 3.0000000
N theta 1.9375865 0.9927251 0.0014032 0.0205929 2323.92104 1.0000000 4.0000000
root theta 1.0684390 0.0821825 0.0001162 0.0025050 1076.35167 0.9122302 1.2245628
root beta 0.5873688 0.0235899 0.0000333 0.0006783 1209.47255 0.5432975 0.6302896
all theta 1.0416593 0.4914309 NA NA NA NA NA
all beta 0.5890748 0.1662890 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 41.4593996 3.6096713 0.0043122 0.1089838 1097.01189 35.8481951 50.5724231
prior -14.1893126 4.5347975 0.0054174 0.0990316 2096.85432 -22.5942861 -7.5687857
alpha 5.5380599 6.3335626 0.0075663 0.4609355 188.80603 0.1310891 17.7483074
sigma^2 0.0818695 0.0862560 0.0001030 0.0148852 33.57929 0.0029077 0.2550722
shift number 0.9019543 0.9517985 0.0011370 0.0160179 3530.83604 0.0000000 3.0000000
N theta 1.9019543 0.9517985 0.0011370 0.0160179 3530.83604 1.0000000 4.0000000
root theta 1.0661482 0.0799066 0.0000955 0.0021172 1424.37666 0.9119163 1.2294966
root beta 0.5878956 0.0222287 0.0000266 0.0005490 1639.57971 0.5433200 0.6319634
all theta 1.0401616 0.4894724 NA NA NA NA NA
all beta 0.5901547 0.1660488 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 4.2604272 6.5957192 5.5380599
sigma squared 0.0632336 0.0982441 0.0818695
stationary variance 0.0074210 0.0074476 0.0073915
phylogenetic halflife 0.1626943 0.1050905 0.1251607
phylogenetic half life in units of tree height 0.0022286 0.0014395 0.0017145

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 39.2152166 5.3639924 0.0075820 0.3038042 311.7373 36.7448552 41.1466455
prior 0.6788686 0.1204073 0.0001702 0.0043025 783.1856 0.6330636 0.7062662
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0011216 0.0287079 0.0000406 0.0007992 1290.1996 0.0001907 0.0004964
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.1952786 0.1189474 0.0001681 0.0033782 1239.7808 0.9562364 1.4226816
root beta 0.5441943 0.0294542 0.0000416 0.0006725 1918.4505 0.4873376 0.6020805
all theta 1.1952786 0.1189474 NA NA NA NA NA
all beta 0.5441943 0.0294542 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 39.2401535 5.2602146 0.0074353 0.2921217 324.2496 36.7917790 41.1481149
prior 0.6801823 0.1247115 0.0001763 0.0046029 734.0918 0.6372407 0.7062661
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.0000 0.0000010 0.0000010
sigma^2 0.0011499 0.0297980 0.0000421 0.0008503 1227.9455 0.0001909 0.0005005
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.0000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.0000 1.0000000 1.0000000
root theta 1.1881919 0.1198608 0.0001694 0.0034659 1195.9835 0.9607080 1.4220706
root beta 0.5460381 0.0290105 0.0000410 0.0006493 1996.5603 0.4887957 0.6019384
all theta 1.1881919 0.1198608 NA NA NA NA NA
all beta 0.5460381 0.0290105 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 39.5398235 1.3237531 0.0015814 0.0206836 4096.012 36.9633492 41.1481359
prior 0.6843679 0.0222519 0.0000266 0.0004679 2261.199 0.6398485 0.7062674
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.000 0.0000010 0.0000010
sigma^2 0.0003298 0.0000817 0.0000001 0.0000019 1931.510 0.0001955 0.0004949
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.000 1.0000000 1.0000000
root theta 1.1910668 0.1129721 0.0001350 0.0025704 1931.692 0.9652457 1.4101063
root beta 0.5454135 0.0279189 0.0000334 0.0005067 3036.491 0.4910910 0.6011421
all theta 1.1910668 0.1129721 NA NA NA NA NA
all beta 0.5454135 0.0279189 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 1.121600e-03 1.149900e-03 3.298000e-04
stationary variance 5.608190e+02 5.749726e+02 1.648884e+02
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.000000 2.781395 10.203771
OU weighted predictor -2.781395 0.000000 7.422375
BM -10.203771 -7.422375 0.000000

Medulla ~ Brain - Medulla

OU Un-weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.7522090 3.7995359 0.0053707 0.0776254 2395.81636 -4.5470349 10.0104748
prior -22.4496164 7.5935414 0.0107335 0.1237780 3763.58437 -35.9808618 -7.5510880
alpha 1.8312202 5.4169974 0.0076570 0.3958960 187.22117 0.0018216 5.2534384
sigma^2 0.1965629 0.5648455 0.0007984 0.0604427 87.33156 0.0016171 0.5731199
shift number 3.2620115 1.8079498 0.0025555 0.0278850 4203.70457 0.0000000 6.0000000
N theta 4.2620115 1.8079498 0.0025555 0.0278850 4203.70457 1.0000000 7.0000000
root theta 0.0386984 0.1469366 0.0002077 0.0049100 895.55421 -0.2463257 0.3293682
root beta 2.0211784 0.0989513 0.0001399 0.0033985 847.73257 1.8246235 2.2197310
all theta -0.0000263 0.5695715 NA NA NA NA NA
all beta 2.0143173 0.3559705 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.6152515 4.0382400 0.0057081 0.0762111 2807.6801 -4.7612341 9.9148239
prior -22.3536421 7.3950545 0.0104530 0.1184226 3899.5440 -35.5151023 -7.5568869
alpha 1.6134493 2.4163646 0.0034155 0.1557324 240.7505 0.0077718 4.9349811
sigma^2 0.1748316 0.2657741 0.0003757 0.0228881 134.8354 0.0027762 0.5349240
shift number 3.1977419 1.7763906 0.0025109 0.0261610 4610.7304 0.0000000 6.0000000
N theta 4.1977419 1.7763906 0.0025109 0.0261610 4610.7304 1.0000000 7.0000000
root theta 0.0328168 0.1477508 0.0002088 0.0050882 843.2126 -0.2506327 0.3332717
root beta 2.0255728 0.0978225 0.0001383 0.0034046 825.5666 1.8298877 2.2177652
all theta -0.0096880 0.5575420 NA NA NA NA NA
all beta 2.0231221 0.3577688 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.7491591 3.8474998 0.0045963 0.0681550 3186.8492 -4.7366259 10.1403367
prior -22.3965279 7.5550059 0.0090254 0.1058632 5093.0693 -35.8767328 -7.5518260
alpha 1.8112893 4.8132570 0.0057501 0.3052256 248.6772 0.0016737 5.1942068
sigma^2 0.1947053 0.5049689 0.0006033 0.0434987 134.7647 0.0015708 0.5593491
shift number 3.2251050 1.8005597 0.0021510 0.0236563 5793.2264 0.0000000 6.0000000
N theta 4.2251050 1.8005597 0.0021510 0.0236563 5793.2264 1.0000000 7.0000000
root theta 0.0379746 0.1478402 0.0001766 0.0043464 1156.9536 -0.2504921 0.3326066
root beta 2.0219536 0.0985401 0.0001177 0.0029649 1104.5665 1.8254760 2.2181488
all theta -0.0018032 0.5640189 NA NA NA NA NA
all beta 2.0164429 0.3569081 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.8312202 1.6134493 1.8112893
sigma squared 0.1965629 0.1748316 0.1947053
stationary variance 0.0536699 0.0541795 0.0537477
phylogenetic halflife 0.3785166 0.4296058 0.3826816
phylogenetic half life in units of tree height 0.0051849 0.0058848 0.0052420

OU Weighted Predictor

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.6870223 6.4239754 0.0090803 0.0806102 6350.79032 -4.5209183 9.7571172
prior -22.8214888 8.0430091 0.0113688 0.1381083 3391.54429 -37.1071472 -7.5475393
alpha 0.8953529 0.7386092 0.0010440 0.0476398 240.37498 0.0050705 2.2895193
sigma^2 0.0937568 0.0717741 0.0001015 0.0233151 9.47674 0.0024696 0.2249473
shift number 3.4919511 1.9689116 0.0027831 0.0335574 3442.50539 0.0000000 7.0000000
N theta 4.4919511 1.9689116 0.0027831 0.0335574 3442.50539 1.0000000 8.0000000
root theta 0.0248345 0.1556828 0.0002201 0.0053766 838.43474 -0.2825694 0.3339287
root beta 2.0288008 0.1038741 0.0001468 0.0036624 804.42878 1.8130806 2.2263659
all theta -0.0130095 0.5930876 NA NA NA NA NA
all beta 2.0217922 0.3737887 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.8445543 15.6968246 0.0221875 0.1206296 16932.28259 -4.6937270 10.1958533
prior -22.7489227 8.3598458 0.0118167 0.1454702 3302.54166 -37.8490750 -7.5504050
alpha 0.2823932 0.2564308 0.0003625 0.0173332 218.86754 0.0029359 0.7942673
sigma^2 0.0289217 0.0233267 0.0000330 0.0080629 8.36999 0.0024580 0.0803564
shift number 3.7266799 2.0425844 0.0028872 0.0349737 3410.96417 0.0000000 7.0000000
N theta 4.7266799 2.0425844 0.0028872 0.0349737 3410.96417 1.0000000 8.0000000
root theta 0.0323440 0.1572310 0.0002222 0.0053410 866.63044 -0.2792059 0.3391053
root beta 2.0226985 0.1046363 0.0001479 0.0036066 841.73636 1.8171688 2.2287718
all theta -0.0123135 0.6117893 NA NA NA NA NA
all beta 2.0166927 0.3750270 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL 1.8177312 3.7712204 0.0045052 0.0766203 2422.56664 -4.6856370 10.0190088
prior -22.6661914 8.0869967 0.0096610 0.1176754 4722.84043 -37.1673859 -7.5519056
alpha 0.6444566 0.6271871 0.0007493 0.0382279 269.17373 0.0031093 1.9495866
sigma^2 0.0673232 0.0619972 0.0000741 0.0187136 10.97568 0.0024284 0.2001058
shift number 3.5607389 1.9872417 0.0023740 0.0286543 4809.74818 0.0000000 7.0000000
N theta 4.5607389 1.9872417 0.0023740 0.0286543 4809.74818 1.0000000 8.0000000
root theta 0.0266911 0.1558989 0.0001862 0.0045077 1196.11490 -0.2792444 0.3398225
root beta 2.0273719 0.1044117 0.0001247 0.0031082 1128.44610 1.8109234 2.2274215
all theta -0.0158730 0.5957897 NA NA NA NA NA
all beta 2.0223107 0.3721234 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 0.8953529 0.2823932 0.6444566
sigma squared 0.0937568 0.0289217 0.0673232
stationary variance 0.0523574 0.0512082 0.0522326
phylogenetic halflife 0.7741609 2.4545467 1.0755530
phylogenetic half life in units of tree height 0.0106045 0.0336225 0.0147330

BM

Convergence

Plots show Gelman’s R statistics for log likelihood, \(\alpha\), and \(\sigma^2\). Solid lines indicate values Gelman’s R, and dashed lines indicate 95% CIs.

Likelihood

Plot shows the posterior probabilities of a shift occuring on each branch for each chain prior to merging.

Summary Statistics

chain1
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL -3.1043191 4.9844194 0.0070455 0.3717504 179.77376 -5.6082686 -0.7790303
prior 0.0007215 0.5969700 0.0008438 0.0597636 99.77721 -1.0837300 0.7060184
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0046895 0.0451218 0.0000638 0.0021074 458.45575 0.0016114 0.0040762
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 0.5914128 0.3553966 0.0005024 0.0282264 158.53195 -0.1616797 1.2283366
root beta 1.6128707 0.2279454 0.0003222 0.0230127 98.11330 1.2001830 2.0837462
all theta 0.5914128 0.3553966 NA NA NA NA NA
all beta 1.6128707 0.2279454 NA NA NA NA NA
chain2
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL -3.2260003 5.0025544 0.0070711 0.3792135 174.02681 -6.1554430 -0.7650817
prior -0.1125735 0.7441400 0.0010518 0.0877217 71.96071 -1.6193891 0.7055136
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0044840 0.0399889 0.0000565 0.0015834 637.79695 0.0015618 0.0042720
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 0.6250258 0.4270128 0.0006036 0.0403877 111.78477 -0.2627850 1.4495799
root beta 1.5974439 0.2674953 0.0003781 0.0315393 71.93302 1.0813234 2.1265179
all theta 0.6250258 0.4270128 NA NA NA NA NA
all beta 1.5974439 0.2674953 NA NA NA NA NA
combined chains
Mean SD Naive SE Time-series SE Effective Size HPD95Lower HPD95Upper
lnL -2.8217676 1.4453849 0.0017267 0.0513652 791.82508 -5.6473066 -0.7748568
prior -0.0812564 0.6907863 0.0008252 0.0710773 94.45503 -1.4578125 0.7059570
alpha 0.0000010 0.0000000 0.0000000 0.0000000 0.00000 0.0000010 0.0000010
sigma^2 0.0027455 0.0006764 0.0000008 0.0000286 559.47729 0.0015901 0.0040769
shift number 0.0000000 0.0000000 0.0000000 0.0000000 0.00000 0.0000000 0.0000000
N theta 1.0000000 0.0000000 0.0000000 0.0000000 0.00000 1.0000000 1.0000000
root theta 0.6301677 0.3939463 0.0004706 0.0292737 181.10074 -0.2056259 1.3646437
root beta 1.5939555 0.2496945 0.0002983 0.0232804 115.03656 1.1096241 2.1067321
all theta 0.6301677 0.3939463 NA NA NA NA NA
all beta 1.5939555 0.2496945 NA NA NA NA NA

Shifts

No shifts were detected with a posterior probability above the cutoff.

OU parameters

chain1 chain2 combined chains
alpha 1.000000e-06 1.000000e-06 1.000000e-06
sigma squared 4.689500e-03 4.484000e-03 2.745500e-03
stationary variance 2.344731e+03 2.241980e+03 1.372757e+03
phylogenetic halflife 6.931472e+05 6.931472e+05 6.931472e+05
phylogenetic half life in units of tree height 9.494774e+03 9.494774e+03 9.494774e+03

Model Selection

Bayes Factors
OU un-weighted predictor OU weighted predictor BM
OU un-weighted predictor 0.000000 -38.11658 3.868261
OU weighted predictor 38.116580 0.00000 41.984840
BM -3.868261 -41.98484 0.000000