To investigate whether C. elegans make accept–reject decisions upon encounter with bacterial patches, we observed the behavior of animals foraging on an agar surface containing an isometric grid of small, low-density bacterial patches (Figure 1A, Videos 1 and 2). Animals were confined to an arena where their behavior was recorded and tracked for 60 min (Figure 1A, Figure 1—figure supplement 1, Video 3). During this time, animals were observed to move about the arena (Figure 1A–C, Figure 1—figure supplement 2, Video 4) with each animal encountering, on average, ~8.4 total patches and ~5.3 unique patches during the 1-hr recording (Figure 1D). These patch encounters ranged in duration from seconds to tens of minutes and could be classified as either short or long (2+ min) using a Gaussian mixture model (GMM) (Figure 1E, Figure 1—figure supplement 3). Notably, animals were significantly more likely to stay on patch for longer durations at later time points (Figure 1F), which corresponded to an overall increase in their probability of residing on patch (Figure 1G, Figure 1—figure supplement 4). Specifically, we found that while animals initially resided on bacterial patches at levels close to those predicted by chance, an animal’s probability of residing on a bacterial patch increased significantly after ~10 min. These findings, that patch duration and residence increased over time, suggest that animals are more likely to exploit an encountered patch as time goes on.

Given that the bacterial density of the experimental patches was approximately 20 times more dilute than that of conditions animals experienced during development and immediately preceding the assay, it was possible that the initial delay in exploitation could be due to animals’ inability to detect the presence of bacteria in these more dilute patches. We therefore sought to determine if animals detected patches at all time points. Previous studies have shown that C. elegans display an immediate and marked slowdown upon encounter with the edge of a food patch and sustain these slower speeds on food (Iwanir et al., 2016; Fujiwara et al., 2002). Therefore, velocity can be used as a proxy for an animal’s ability to sense a bacterial patch. Following this precedent, we quantified the instantaneous velocity of individuals in our assay (Figure 1H). We observed significant deceleration of an animal’s instantaneous velocity upon encounter with the patch edge (Figure 1I), with no obvious difference between short-duration, early time point (Figure 1J) and long-duration, late time point (Figure 1K) encounters. Animals consistently displayed marked slowdown when approaching the patch edge (Figure 1L), achieving an average deceleration of –19.5 μm/s² upon encounter with the bacterial patch (Figure 1M, Figure 1—figure supplement 5). This slowdown was statistically significant for both long- and short-duration encounters (Figure 1M). Further, consistent with C. elegans behavior on larger and more densely seeded patches in other studies (Sawin et al., 2000), animals in our assay maintained significantly lower average velocities on patch (~52 μm/s) compared to off patch (~198 μm/s) (Figure 1N, O). These results suggest that, despite detecting the availability of food during early patch encounters, C. elegans opt to initially prioritize exploration of the environment before switching to a more exploitatory foraging strategy during subsequent patch encounters.

To determine whether this explore-then-exploit foraging strategy is dependent upon food-related characteristics of the environment, we varied the density of the bacterial patches. By diluting bacterial stocks and controlling growth time, we created 12 bacterial density conditions with relative density ranging from 0 to ~200 (Figure 2A, Figure 2—figure supplements 1–3). At the low end of this range (densities less than ~0.5), animals do not appear to detect bacterial patches as indicated by on-patch velocities matching those of animals foraging on bacteria-free (density 0) patches (Figure 2B, C). At the high end of the range (density ~200), bacterial density is comparable to the environments animals experienced during development and immediately prior to the assay (Figure 2—figure supplements 2 and 3).

Previous studies have shown that in diet choice assays where animals are given the option between patches of varying quality or density, animals spend more time on preferred patches (Scheer and Bargmann, 2023; Shtonda and Avery, 2006; Madirolas et al., 2023). We hypothesized that even when all patches in the environment are of equal density, an efficient forager should still modulate the amount of time spent on the bacterial patches in a density-dependent manner. To test this, behavior was recorded and tracked for 1 hr as animals foraged in patchy environments matching one of the bacterial density conditions (Figure 2D, Figure 2—figure supplement 4). Consistent with our hypothesis, we found that the total time animals spent on bacterial patches increased monotonically with increasing bacterial density following a sigmoidal trend (Figure 2E). Further, the probability of an animal residing on patch as a function of time was highly dependent on the bacterial density (Figure 2F, Figure 2—figure supplement 5). At the highest densities (50 and 200), animals spent nearly 100% of time in the assay on bacterial patches, while at the lowest densities (0–0.3), animals spent chance levels of time on patch for the duration of the experiment. At intermediate densities (0.5–10) animals initially resided on patches at rates predicted by chance, later transitioning to more time spent on patch. Notably, this delayed increase in patch residence is density dependent with animals switching earlier in environments with patches of greater density.

Consistent with our previous observation that animals reside on patches for either short or long durations (Figure 1E), we observed two distinct patch encounter types: (1) short (less than 2 minute) patch visits and (2) long (often tens of minutes) patch visits (Figure 2G). We validated the existence of two patch types using Silverman’s test (Ahmed and Walther, 2012; Silverman, 1981) for bimodality Figure 2—figure supplement 6 and then, using a two-component GMM, classified all encounters based on the duration of these patch visits and animals’ average velocity during the encounter (Figure 2H, Figure 2—figure supplement 6). We identified two behaviorally distinct clusters: (1) short-duration and fast velocity (explore) and (2) long-duration and slow velocity (exploit) encounters. The explore encounters suggest that an animal has rejected a patch, opting to continue exploration of the environment. In contrast, the exploit encounters suggest that an animal has accepted a patch and is consuming the bacteria within.

While we previously found that animals consistently slowed down upon encounter with the patch edge when foraging in relative density ~10 (Figure 1J–M), we observed that a large portion of short-duration, exploratory encounters were not accompanied by this slow down (Figure 2—figure supplement 7A, B), especially for the lowest bacterial densities tested. Therefore, to determine which exploratory encounters displayed evidence that the patch was detected by the animal, we further classified encounters by an animal’s minimum velocity on patch, deceleration upon patch entry, and maximum change in the animal’s velocity upon encounter (i.e., the difference between the peak velocity immediately before the patch encounter and the minimum velocity achieved during the patch encounter) (Figure 2I, Figure 2—figure supplement 7). We again observed two behaviorally distinct clusters: (1) large slowdown and slow on-patch velocity and (2) small slowdown and fast on-patch velocity. We validated the existence of these two clusters using Silverman’s test (Ahmed and Walther, 2012; Silverman, 1981) for bimodality (Figure 2—figure supplement 7) and then classified these encounters as sensing or non-responding, respectively, using a semi-supervised quadratic discriminant analysis (QDA) approach (Figure 2—figure supplement 8, Video 5). The presence of a slowdown and the subsequent continuation of slower on-patch velocity suggest that an animal sensed the bacteria, while the absence of a slowdown response suggests that the animal either did not perceive the encounter or chose to ignore it. For simplicity, we define: (1) non-responding encounters as searching (i.e., on-patch behavior that matches off-patch behavior where an animal appears to be searching for food); (2) sensing, short-duration encounters as sampling (i.e., evaluating a patch’s suitability as a food source, but ultimately rejecting the patch and continuing to explore the environment); and (3) sensing, long-duration encounters as exploiting (i.e., accepting a patch and consuming its bacteria) (Figure 2J). Consistent with our interpretation of searching encounters, the average velocities that animals achieved during search on (~200 μm/s) and off (~207 μm/s) patch were similar, especially when compared to markedly slower on-patch velocities during sample (~114 μm/s) and exploit (~57 μm/s) encounters (Figure 2K). In summary, we have identified three distinct patch encounter types: encounters lacking a slowdown that were either not detected or ignored (search) and encounters that were detected with the animal subsequently deciding to reject (sample) or accept (exploit) the patch.

We next characterized how the frequency of encounter types varied as a function of time and patch density. The behavior of 443 animals (20–50 worms per condition) was tracked and classified at each time point (Figure 2L, Video 6). In low-density conditions (0–0.3), animals spent nearly all of their time searching on or off patch. With increasing bacterial patch density, animals spent less time searching and more time sampling and exploiting. Animals foraging in medium-density patches (0.5–10) initially spent most of their time sampling patches upon encounter. However, animals eventually switched to mostly exploiting patches. Animals foraging on high-density patches (50 and 200) almost exclusively exploited. Classification of on-patch behavior across all densities tested revealed a consistent switch from exploratory behaviors (searching and sampling) to exploitation (Figure 2M) with the timing of the switch occurring earlier for animals foraging in environments with higher bacterial patch density (Figure 2N). The delay in exploitation corresponded to a comparatively large number of initial exploratory encounters with animals on medium density conditions (0.5–10) exploiting after an average of 4.8–18.7 exploratory encounters (Figure 2O). To summarize, for densities similar to those experienced immediately preceding the experiment (50 and 200), animals immediately exploit available bacteria. On the other hand, for bacterial densities that appear to be below an animal’s sensory threshold (0–0.3), animals never exploit patches and spend the entire 60-min assay searching for food. When foraging in medium-density patches (0.5–10), animals initially explore the environment via a combination of searching and sampling encounters and eventually switch to exploiting. Notably, the timing of this switch is density dependent with animals switching earlier when foraging on higher-density patches.

Given that bacterial patches within an environment were relatively invariable and that bacterial growth during the experiment was negligible (Figure 2—figure supplement 3), it was surprising that animals were often willing to reject 10+ patches before exploiting a patch of the same density as those previously rejected (Figure 2O). This sampling behavior may be beneficial when food is patchily distributed in the environment, as exploiting a dilute patch may result in a lost opportunity for future encounter with a higher quality patch. Thus, we hypothesized that an animal’s willingness to accept a patch whose density matched that of a previously rejected patch could be a specific feature of a patchily distributed environment where numerous observations of individual patches could contribute to learning the features of a changing environment. To investigate this, we observed whether animals were willing to reject a patch numerous times before accepting it even when only one patch is available in the environment. We created environments with single large (~8.3 mm) or small (~1.8 mm) diameter patches with relative density ranging from 0 to ~400 (Figure 3A–C). Behavior was tracked for 60 min as animals foraged in these environments (Figure 3D, E, Figure 3—figure supplements 1 and 2). We found that even in these single patch environments, animals initially explore (search and sample) before exploiting (Figure 3F, G) in a density-dependent manner. Just as when foraging in a patchily distributed environment (Figure 2N), animals explored (search and sample) the small and large single patches numerous times prior to exploiting, with the timing of this switch occurring significantly earlier with increasing bacterial density (Figure 3H, I). These results suggest that the explore-then-exploit strategy employed by C. elegans is not specific to a patchily distributed environment. Rather, animals may sample the same patch numerous times before deciding to exploit, especially when foraging on dilute patches. The decision of when to stop exploring and start exploiting is highly dependent upon the density of bacteria within a patch, with the switch occurring earlier when animals encounter patches of higher density.

While our behavioral analysis demonstrated that C. elegans modulate their decision to explore or exploit in a density-dependent manner, it remains unclear whether these animals use more complex cognitive processes such as learning and memory to guide their foraging decision. It is plausible that animals are making decisions using simple heuristics given only available sensory information about the current patch. However, previous studies have shown that food-related behaviors in C. elegans can be driven by internal states (Scheer and Bargmann, 2023) as well as memories of the environment (Calhoun et al., 2015; Shtonda and Avery, 2006; Pradhan et al., 2019). Thus, to better understand the factors driving the exploitation decision, we implemented a generalized linear model (GLM) to test how foraging decisions are influenced by the density of the current patch as well as additional food-related factors such as an animal’s level of satiety and prior experience (Figure 4A).

We considered that the probability of exploiting a patch upon any given encounter can be described by a logistic function:p(yk=1|β⋅xk) = 11+e−β⋅xk,\begin{document}$$\displaystyle p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\ =\ \frac{1}{1 + e^{-\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}}},$$\end{document}

where pyk=1β⋅xk\begin{document}$p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)$\end{document} represents the conditional probability that an animal exploited during patch encounter k\begin{document}$k$\end{document}; xk∈Rn\begin{document}$\boldsymbol{x}_{k}\in R^{n}$\end{document} is a vector of covariates; and β∈Rn\begin{document}$\boldsymbol{\beta }\in R^{n}$\end{document} is a vector of weights that describes how much each covariate influences the animal’s choice. In models compared here, xk\begin{document}$\boldsymbol{x}_{k}$\end{document} includes a combination of a constant element and covariates that may empirically influence the decision to exploit. We considered the simplest model where every encounter is independent with fixed probability of exploiting (i.e., pyk=1β0\begin{document}$p\left (y_{k}=1|\beta _{0}\right)$\end{document}) where β0\begin{document}$\beta _{0}$\end{document} represents the average animal’s propensity to exploit. We compared this null model against a set of nested models containing covariates that vary from encounter to encounter and relate to: (1) the relative density of the encountered patch k\begin{document}$k$\end{document} (ρk\begin{document}$\rho _{k}$\end{document}), (2) the duration of time spent off food since departing the last exploited patch (τs\begin{document}$\tau _{s}$\end{document}), (3) the relative density of the patch encountered immediately before encounter k\begin{document}$k$\end{document} (ρh\begin{document}$\rho _{h}$\end{document}), and (4) the relative density of the last exploited patch (ρe\begin{document}$\rho _{e}$\end{document}). Using this model design (i.e., β⋅xk=β0+βkρk+βsτs+βhρh+βeρe\begin{document}$\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}=\beta _{0}+\beta _{k}\mathrm{\rho }_{k}+\beta _{s}\mathrm{\tau }_{s}+\beta _{h}\rho _{h}+\beta _{e}\rho _{e}$\end{document}), we assessed how each of these covariates influences the probability of exploitation at each patch encounter k\begin{document}$k$\end{document} (Figure 4A).

Given that our aim is to understand what factors influence an animal’s decision to explore or exploit, we rationalized that encounters where the animal did not detect the presence of bacteria were unlikely to contribute to decision-making. Therefore, we excluded searching encounters from our analysis where animals did not respond to the bacterial patch. To account for the uncertainty in our classification of sensing, we probabilistically included patch encounters with frequency equal to the probability that the bacterial patch was sensed (Figure 4B) as previously estimated by semi-supervised QDA (Figure 2I, Figure 2—figure supplement 8). In doing so, we simulated sets of observations of sensed (sample and exploit) encounters. Further, to account for the uncertainty in our classification of patch encounters as exploration or exploitation, we fit our GLM to the probability of exploiting p(yk=1|zk)\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} as previously estimated by GMM (Figure 2H, Figure 2—figure supplement 6) rather than fitting to direct observations of exploitation yk\begin{document}$y_{k}$\end{document} (see Models of exploitation probability).

When selecting covariates for our model, we calculated the Bayesian information criterion – a model selection test to avoid overfitting by penalizing increases in the number of parameters – and observed the best model performance when all covariates were included (Figure 4—figure supplement 1A–B). Further, we found that all covariates (i.e., ρk\begin{document}$\rho _{k}$\end{document}, τs\begin{document}$\tau _{s}$\end{document}, ρh\begin{document}$\rho _{h}$\end{document}, and ρe\begin{document}$\rho _{e}$\end{document}) significantly contribute to the decision to exploit p(yk=1|β⋅xk)\begin{document}$p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)$\end{document} as indicated by coefficient values significantly greater than or less than zero (Figure 4C, Figure 4—figure supplement 1). Specifically, we found that βk\begin{document}$\beta _{k}$\end{document} and βs\begin{document}$\beta _{s}$\end{document} are significantly greater than zero, which suggests that animals are more likely to exploit patches with increasing patch density ρk\begin{document}$\rho _{k}$\end{document} and duration of food deprivation τs\begin{document}$\tau _{s}$\end{document}. On the other hand, βh\begin{document}$\beta _{h}$\end{document} and βe\begin{document}$\beta _{e}$\end{document} are significantly negative, which suggests that the greater the density of a recently encountered or exploited patch, ρh\begin{document}$\rho _{h}$\end{document} and ρe\begin{document}$\rho _{e}$\end{document}, the less likely an animal should be willing to exploit the current patch.

In order to better understand how each of the covariates in our model affects the exploitation decision, we examined the probability of observing exploitation for the first time as a function of the cumulative number of patches an animal encountered. Exploitation events were simulated from a Bernoulli distribution with probability estimated by the model (i.e., yk|xk∼Bern(p(yk=1|β⋅xk))\begin{document}$y_{k}|\boldsymbol{x}_{k} \sim \mathrm{B}\mathrm{e}\mathrm{r}\mathrm{n}\left (p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\right)$\end{document}) or observed from our classification of exploitation (i.e., yk|zk∼Bern(p(yk=1|zk))\begin{document}$y_{k}|\boldsymbol{z}_{k}\sim \mathrm{B}\mathrm{e}\mathrm{r}\mathrm{n}\left (p\left (y_{k}=1|\boldsymbol{z}_{k}\right)\right)$\end{document}). Although the probability of exploiting for the first time was not expressly fit by our model, this derived metric highlights the model’s ability to predict the delay in exploitation observed for animals foraging on low to medium density bacterial patches in our experiments (Figure 4D, Figure 4—figure supplement 2). For the simplest model where every encounter is independent with fixed probability of exploiting pyk=1β0\begin{document}$p\left (y_{k}=1|\beta _{0}\right)$\end{document}, we find that the probability of exploiting for the first time is greatest for the first encounter and decreases for every subsequent encounter (Figure 4D, Figure 4—figure supplement 2), fitting a geometric distribution.

We next considered whether the observed delay in exploitation could be explained by a simple density-dependent model (i.e., pyk=1β0+βkρk\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}\right)$\end{document}). This model predicts that animals are more likely to exploit bacterial patches of greater density with probability proportional to the relative density of the current patch ρk\begin{document}$\rho _{k}$\end{document}. While this density-dependent model accurately predicted that the first exploitation occurs earlier on average for higher density patches, it also predicted that, regardless of patch density, the first exploitation is most frequently observed on the first encounter, which did not match the observed distribution (Figure 4D, Figure 4—figure supplement 2). We subsequently considered that the onset of food deprivation during exploration of these low-density environments could drive the observed time-dependent delay in exploitation. We assume that animals become satiated during exploitation and use the duration of time an animal spent searching off-food since the last exploitation event (i.e., τs\begin{document}$\tau _{s}$\end{document}) as a proxy for the animal’s likely decrease in satiety. With the addition of this satiety-related signal (i.e., pyk=1β0+βkρk+βsτs\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}+\beta _{s}\tau _{s}\right)$\end{document}), we observed a slight delay in when animals are predicted to first exploit for the lowest density conditions tested (Figure 4D, Figure 4—figure supplement 2). To validate our finding that animals use a satiety-related signal to inform decision-making, we applied our model to observations of animals foraging in patchily distributed environments following 3 hr of food deprivation (Figure 4—figure supplement 3A–B). We found that only with the inclusion of a satiety-related covariate in our model were we able to reliably predict the immediate exploitation that food-deprived animals exhibit (Figure 4—figure supplement 3C).

We next considered the alternative possibility that this time-dependent signal could actually be related to the physical stress induced by the process of moving animals into the experimental arena rather than the onset of food deprivation. While we used an agar plug method to mitigate the stress of moving (see Nematode cultures), we sought to examine the impact of satiety as compared to transfer-induced stress on the exploitation decision. We quantified both τs\begin{document}$\tau _{s}$\end{document}, the duration of time an animal spent searching off-food since the last exploitation event, and τt\begin{document}$\tau _{t}$\end{document}, the duration of time since transfer (i.e., the time elapsed in the experiment). However, as our initial experiments were only 1 hr, we typically observed only one exploitation event. Resultantly, τs\begin{document}$\tau _{s}$\end{document} and τt\begin{document}$\tau _{t}$\end{document} were highly correlated, and their individual contributions to the model could not be easily parsed. Therefore, we ran additional experiments with animals foraging in environments with multiple patch densities over 2 hr (Figure 4E, Figure 4—figure supplement 4A–C), which led to observations containing multiple exploitation events and a resultant decorrelation of τs\begin{document}$\tau _{s}$\end{document} and τt\begin{document}$\tau _{t}$\end{document}. When the model was re-fit to this 2-hr data set using both τs\begin{document}$\tau _{s}$\end{document} and τt\begin{document}$\tau _{t}$\end{document} covariates (i.e., p(yk=1|β0+βkρk+βsτs+βtτt+βhρh+βeρe)\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}+\beta _{s}\tau _{s}+\beta _{t}\tau _{t}+\beta _{h}\rho _{h}+\beta _{e}\rho _{e}\right)$\end{document}), only the satiety-related covariate τs\begin{document}$\tau _{s}$\end{document} was statistically significant (Figure 4—figure supplement 4D). This result suggests that the time-dependent change in exploitation is likely due to a satiety-related signal rather than a stress-related signal. Altogether, these results suggest that animals use available external and internal sensory information to guide the decision to exploit.

Although the current patch density and satiety covariates significantly influence the decision to exploit, this model (i.e., pyk=1β0+βkρk+βsτs\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}+\beta _{s}\tau _{s}\right)$\end{document}) does not accurately predict the extent that exploitation was delayed. We hypothesized that because animals had experienced very densely seeded bacterial patches immediately prior to the assay, animals may have built an expectation that high-density bacterial patches are available in the new environment. We would therefore expect an initial suppression in the probability of exploiting while animals updated their expectation using information learned from sampling patches in the current environment. To test whether the decision to exploit could be influenced by prior experience, we added a history-dependent covariate to our model (i.e., pyk=1β0+βkρk+βsτs+βhρh\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}+\beta _{s}\tau _{s}+\beta _{h}\rho _{h}\right)$\end{document} where ρh\begin{document}$\rho _{h}$\end{document} is the relative density of the patch encountered immediately before encounter k\begin{document}$k$\end{document}). We find that inclusion of the density of the most recently encountered patch significantly improves our prediction of exploitation (Figure 4D, Figure 4—figure supplement 2). We then considered whether the animal’s expectation of bacterial density in the environment might be a longer lasting memory. Specifically, we considered if the relative density of the most recently exploited patch ρe\begin{document}$\rho _{e}$\end{document} could have influenced the animal’s decision to exploit. The addition of this second history-dependent term to our model (i.e., pyk=1β0+βkρk+βsτs+βhρh+βeρe\begin{document}$p\left (y_{k}=1|\beta _{0}+\beta _{k}\rho _{k}+\beta _{s}\tau _{s}+\beta _{h}\rho _{h}+\beta _{e}\rho _{e}\right)$\end{document}) further improved the fit of our model (Figure 4D, Figure 4—figure supplement 2), suggesting that C. elegans use recent experiences of encountered and exploited patches to guide their decision to exploit. Animals may use this learned information to create and update an expectation for the relative density of bacterial patches available in their environment and compare that estimate against the density of a subsequently encountered patch. Altogether, these results suggest that animals use recent experiences to estimate available resources and modulate their decision to explore or exploit, a strategy that is highly beneficial for behavioral adaptation in a changing environment.

To validate the role of prior experience in guiding foraging decisions, we observed animals foraging in environments with multiple patch densities (Figure 4E, Figure 4—figure supplement 4A–C). Our model predicts that the lower the density of recently encountered and/or exploited patches, the more likely an animal should be to exploit a subsequent patch. Without the history-dependent terms ρh\begin{document}$\rho _{h}$\end{document} and ρe\begin{document}$\rho _{e}$\end{document}, our model predicts that no relationship should exist between prior experience and the probability of exploiting the current patch. To test which model best fit the animals’ behavior, we calculated the conditional probabilities of exploiting pyk=1β⋅xk\begin{document}$p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)$\end{document} using the coefficients β learned previously (Figure 4C) for this new multi-density, multi-patch data set containing more nuanced combinations of current (ρk\begin{document}$\rho _{k}$\end{document}) and recent patch (ρh\begin{document}$\rho _{h}$\end{document} and ρe\begin{document}$\rho _{e}$\end{document}) density. We observed significantly improved predictions of exploitation probability for the model including prior experience as compared to the model without the terms ρh\begin{document}$\rho _{h}$\end{document} and ρe\begin{document}$\rho _{e}$\end{document} (Figure 4F, Figure 4—figure supplement 4E) as confirmed by a likelihood-ratio test. We observed an augmentation in exploitation when animals move from low to high density (e.g., 1–4 or 1–7) as predicted by the model with history dependence, but not the model without. It is important to note that this improvement in prediction was achieved without re-fitting the model to this new multi-density data set. In summary, our modeling results suggest that animals evaluate bacterial density, monitor internal signals of satiety, and leverage recent experiences to drive their decision to exploit a bacterial patch upon encounter.

The quantitative modeling applied in this study provides a useful framework for testing the influence of behaviorally relevant features on decision-making. To validate this approach and further elucidate how animals evaluate current and recent patch density, we assessed the foraging behavior of mutants with sensory deficiencies (Figure 4—figure supplement 5). We found that animals with reduced function of non-ciliated mechanoreceptor neurons due to a null mutation in the mec-4 gene behave similarly to wild-type N2 animals, displaying increasingly delayed exploitation as patch density decreases (Figure 4G, Figure 4—figure supplement 5). Contrastingly, animals with reduced function of ciliated chemoreceptor and mechanoreceptor neurons due to a null mutation in the osm-6 gene displayed immediate exploitation even while foraging on low-density patches (Figure 4G, Figure 4—figure supplement 5). These results indicate altered decision-making in the osm-6 mutants. Specifically, it appears that the influence of patch density on the exploitation decision is reduced in osm-6 mutants and that these animals are more likely to accept a patch by default.

To further elaborate on these findings, we fit our GLM to each of the three data sets (i.e., N2, mec-4, and osm-6) and assessed the difference in the estimated distributions of coefficients β\begin{document}$\boldsymbol{\beta }$\end{document} between mutant and wild-type models (Figure 4H). We hypothesized that the density-related covariates (ρk\begin{document}$\rho _{k}$\end{document}, ρh\begin{document}$\rho _{h}$\end{document}, and ρe\begin{document}$\rho _{e}$\end{document}) would have smaller magnitude (i.e., less influence on decision-making) for animals with reduced sensation of bacterial density. Consistent with this hypothesis, we found a significant reduction in the magnitude of the influence of current patch density (i.e., βk\begin{document}$\beta _{k}$\end{document}) on the decision to exploit in osm-6 mutants. Further, we found a significant increase in the intercept β0\begin{document}$\beta _{0}$\end{document} in osm-6 mutants which corresponds to the overall increase in exploitation observed in these animals (Figure 4G, Figure 4—figure supplement 5). These results suggest that the ciliated sensory neurons play an important role in evaluating the density of the current patch and that when sensation is impaired, animals modify their default behavioral strategy to prioritize exploitation. We also observed a marginal increase in our estimate of the influence of recently exploited patches (i.e., βe\begin{document}$\beta _{e}$\end{document}) in osm-6 mutants, which suggests that reduced efficacy in the evaluation of current patch density also affects learning and memory of patch density. No significant changes were detected in the mec-4 mutants. Although we cannot rule out a role for non-ciliated mechanoreceptor neurons in contributing to the assessment of patch density, this modality likely provides less salient information. Altogether, these results suggest that ciliated sensory neurons are necessary for the evaluation of patch density and that when the function of these neurons is impaired, animals prioritize exploitation. Further, these results demonstrate that this quantitative modeling approach can be used to probe mechanisms underlying decision-making.

While C. elegans have been shown to alter food preferences in a diet choice assay, this behavior has only been described by a set of stay–switch decisions (Scheer and Bargmann, 2023; Shtonda and Avery, 2006; Madirolas et al., 2023). Specifically, C. elegans were found to modulate their patch-leaving frequency to stay on high-quality bacterial patches and switch with declining food quality and quantity (Bendesky et al., 2011; Shtonda and Avery, 2006; Milward et al., 2011; Olofsson, 2014). The overall effect of leaving low-quality patches more frequently is that animals are more likely to reside on high-quality patches. Thus, stay–switch decision-making enables C. elegans to allocate time spent between exploring or exploiting in a manner consistent with optimal foraging theory (Stephens, 2008; Schoener, 1971; Pyke et al., 1977; Stephens and Krebs, 1986; Stephens et al., 2007; Nonacs, 2001). However, optimal foraging theory also predicts that an animal should never exploit (i.e., always reject) a low-density patch if higher-density patches are sufficiently abundant, as inclusion of the low-density patch type in the animals’ diet decreases the overall rate of energy gained (Stephens, 2008; Stephens and Krebs, 1986). Thus, while leaving low-density patches more frequently drives an overall increase in the rate of energy gained, it can still result in sub-optimal foraging behavior.

Here, we demonstrate that C. elegans are capable of making accept–reject decisions upon encounter with bacterial patches. We employed quantitative methods – GMM and semi-supervised QDA – to estimate whether animals sensed a patch and, if they did, whether they accepted or rejected it. We found that when transferred from high- to low-density bacterial patches, animals initially rejected several patches, opting to continue exploration of the environment, and that this reject decision did not reflect an animal’s inability to detect the presence of bacteria in these dilute patches. Further, we found that the decision to explore or exploit is density-dependent and robust across a range of bacterial densities, distributions, and sizes. The initial preference for exploration during foraging on low-density patches suggests that animals may be searching for denser bacterial patches such as those experienced immediately preceding the assay and throughout development. This explore-then-exploit strategy is advantageous for animals when bacterial patch density is low or variable. On the other hand, we observed immediate exploitation of high-density patches. In these environments, an explore-then-exploit strategy is disadvantageous, as delaying exploitation when patch density is already high results in spending more energy on food search with no expected increase in energy gained during exploitation of a subsequently encountered patch. Thus, consistent with an energy-maximizing optimal forager, C. elegans initially explores when bacterial patch density is low but immediately exploits when bacterial patch density is sufficiently high. Altogether, our results demonstrate that C. elegans make a distinct decision to either explore or exploit a patch upon encounter and that the density dependence of this decision is consistent with predictions from optimal foraging theory.

The concepts of accept–reject and stay–switch decision-making are well described in foraging theory literature (see Pyke et al., 1977 for a review on the subject) and represent the questions ‘Do you want to eat it?’ and, if so, ‘How long do you want to eat it for?’. These concepts are easily distinguishable for animals that forage using the following framework: (1) search for prey, (2) encounter prey from a distance, (3) identify prey type, (4) decide to pursue (accept–reject decision), (5) pursue and capture the prey, (6) exploit prey, and (7) decide to stop exploiting and start searching again (stay–switch decision). However, in some scenarios, animals must physically encounter prey prior to identification. In these cases where pursuit and capture are not visualized, it is harder to distinguish between accept–reject and stay–switch decisions. In our experiments, C. elegans do not appear to detect the presence of bacterial patches prior to encounter as slowdown only occurs within one body length of the patch edge (Figure 2B). Further, we find significant bimodality in encounter duration (Figure 2H) where short-duration (exploratory) encounters appear to represent a lower bound where animals spend the minimum amount of time possible on a patch (less than 2 min), which we interpret as a rejection of the patch. On the other hand, exploitatory encounters span a large range of durations from 2 to 60+ min which we interpret as an initial acceptance of the patch followed by a series of stay–switch decisions which determine the overall duration of the encounter. While we could certainly model our data using only stay–switch decision-making, we ascertain that an encounter of minimal duration is better interpreted ethologically as a rejection rather than as an immediate switch decision. In accordance with this interpretation, we hypothesize that if C. elegans were able to detect the presence of a bacterial patch prior to encountering it, it is possible that animals may be observed to navigate toward (accept) or away from (reject) a patch. However, it could be the case that, for C. elegans, sampling the patch is prerequisite to an accept-reject decision which would suggest that gustation, mechanosensation, and/or post-ingestive feedback may guide C. elegans foraging decisions.

Our finding that C. elegans are willing to reject numerous encountered patches is somewhat surprising, especially given that C. elegans likely possess limited spatial memory (Calhoun et al., 2015) and are likely unaware of how many patches are in the environment as evidenced by their willingness to reject a patch even when only one patch is available (Figure 3). Taken together, this suggests that animals are ‘knowingly’ passing up an opportunity to exploit an immediately available food source for the potential opportunity to exploit preferred food later. This type of behavior has been described in humans and other animals in the context of delayed gratification (Fawcett et al., 2012; Susini et al., 2021), intertemporal choice (Fawcett et al., 2012; Constantino and Daw, 2015; Carter et al., 2015), self-control (Hayden, 2019; Stephens and Anderson, 2001), and optimal stopping (Ferguson, 1967; Robbins, 1970). Notably, few animals display the capacity for delayed gratification when given the option between eating an immediately available but less preferred food item and waiting for a preferred food item (Mischel and Ebbesen, 1970; Rosati et al., 2007; Schnell et al., 2021; Range et al., 2020). Even fewer animals are willing to wait if the delayed reward is not visible or increases in quantity rather than quality (Hillemann et al., 2014; Miller et al., 2020). Our observation that C. elegans can exhibit delayed gratification suggests that this and similar processes require less complex cognition than previously considered or that we may have underestimated the cognitive capacity of C. elegans.

Stay–switch decisions in C. elegans are strongly modulated by a variety of internal and external sensory cues over a range of behavioral timescales. For example, patch-leaving frequency can be modulated by an animal’s prior experience (Calhoun et al., 2015; Pradhan et al., 2019), metabolic status, arousal state (Scheer and Bargmann, 2023), as well as the presence of pathogens (Pujol et al., 2001; Melo and Ruvkun, 2012), chemorepellents (Pradel et al., 2007), predators (Quach and Chalasani, 2022; Pribadi et al., 2023), and varying levels of environmental O₂ and CO₂ (Milward et al., 2011; Busch and Olofsson, 2012).

Here, we used a quantitative framework to show that recent experiences (i.e., the density of current and recently encountered and exploited bacterial patches) guide accept–reject decision-making. In our study and others (Madirolas et al., 2023; Sawin et al., 2000), C. elegans appear to be able to detect the presence of and assess the relative density of bacterial patches. When foraging in environments with low-density bacterial patches, we initially observed many searching encounters where animals did not appear to slow down; however, over time, the proportion of searching encounters decreased (Figure 2L, M). This increased responsiveness to dilute patches over time could have resulted from small changes in bacterial growth or a modulation of patch detection sensitivity. Contrastingly, animals with reduced function of ciliated chemoreceptor and mechanoreceptor neurons due to a null mutation in the osm-6 gene almost never searched. Rather, they displayed immediate exploitation even while foraging on low-density patches. This suggests that osm-6 mutants display an augmented ability to detect bacterial patches but a diminished ability to assess the bacterial density of those patches. While this may seem contradictory, it suggests that bacterial detection and density assessment are mediated by distinct sensory mechanisms. Specifically, post-ingestive feedback or other non-ciliary sensory cues may drive the initial detection of bacteria, while ciliated sensory neurons appear to be crucial for the nuanced evaluation of bacterial patch density. This interplay allows for a flexible foraging strategy where initial detection by one modality can trigger exploitation, which can then be modulated or overridden by more detailed chemosensory and mechanosensory information. This framework may explain why osm-6 mutants, lacking the ability to finely assess bacterial density, prioritize exploitation; if all patches appear effectively equivalent, further exploration is inefficient. Collectively, these results suggest an important role for sensory modalities in the detection and assessment of bacterial patch density and highlight a need to investigate the mechanisms behind these effects in future studies.

The difficulty in assessing bacterial patch density is more than just a sensory challenge. Within-patch spatial inhomogeneity resulting from areas of active proliferation of bacteria (Gloria-Soria and Azevedo, 2008; Hallatschek et al., 2007) complicates an animal’s ability to accurately assess the quantity of bacteria within a patch and, consequently, our ability to accurately compute a metric related to our assumptions of what the animal is sensing. In our study, we used the relative density of the patch edge where bacterial density is highest as a proxy for an animal’s assessment of bacterial patch density (Figure 2—figure supplement 1). This decision was based on a previous finding that the time spent on the edge of a bacterial patch affected the dynamics of subsequent area-restricted search (Calhoun et al., 2015). While within-patch spatial inhomogeneity likely affects an animal’s ability to assess patch density, we do not believe that this qualitatively affects the results of our study. Both the patch densities tested (Figure 2—figure supplement 3A) as well as our observations of time-dependent changes in exploitation (Figure 2E, N, O and Figure 3H, I) maintained a monotonic relationship. Therefore, alternative methods of patch density estimation should yield similar results.

According to early models in optimal foraging theory, foragers behave as if they have complete information about the environment (e.g., animals are assumed to know the average density of bacterial patches) (Stephens and Krebs, 1986). Later theoretical and empirical work expanded models of patch choice to accommodate situations where animals have incomplete information (e.g., environments with fluctuating resources) and, therefore, must both acquire information and forage (Pyke et al., 1977; Stephens et al., 2007; Krebs and Inman, 1992). This work suggests that animals may continuously sample areas in their environment to keep track of resource availability. Here, we found that animals initially choose to sample patches and that the duration of this period of sampling is correlated with the degree of mismatch between current and recently experienced and exploited patches (i.e., animals spend more time sampling as the magnitude of difference between the patch density experienced immediately before and during the experiment increases). When there is no difference between current and prior experience (i.e., animals foraging on patches of relative density 200), animals rarely sample. These results suggest that C. elegans use sampling as a way of re-evaluating the overall quality of patches available in the environment when a change is detected. Further, the results of our model suggest that animals likely use the information learned during sampling encounters to guide their decision to explore or exploit on subsequent patch encounters. We behaviorally validated this hypothesis by applying our model predictions to animals foraging in environments with multiple patch densities. Consistent with our predictions, we observed that the lower the density of recently encountered or exploited patches and the higher the density of the current patch, the more likely an animal would be to exploit (Figure 4F). These results suggest that C. elegans can learn and remember features of recent experiences and use that learned information to guide efficient decision-making. Incorporating prior experience into the decision to explore or exploit currently available food is highly beneficial when foraging in a fluctuating environment. C. elegans thus may have evolved this ability to maximize foraging in the wild where animals experience a boom-and-bust environment (Frézal and Félix, 2015). Future studies investigating the effects of varying patch density during animal development could provide additional insights into the effects of more distant experiences on the explore–exploit decision. However, testing this is non-trivial as maintaining stable bacterial density conditions over long timescales requires matching the rate of bacterial growth with the rate of bacterial consumption.

In addition to external sensory information, internal state signals serve a critical role in modifying decision-making in C. elegans (Scheer and Bargmann, 2023; Matty et al., 2022). For example, food-deprived animals are more likely to cross an aversive barrier in search of food as compared to well-fed controls (Matty et al., 2022; Ezcurra et al., 2011). Here, we find that a satiety-related signal likely drives the decision to exploit. Specifically, our model suggests that as animals’ satiety decreases, their willingness to accept a lower quality patch increases. We confirmed this prediction by analyzing the behavior of food-deprived animals, which immediately exploit even when bacterial patches are very dilute (Figure 4—figure supplement 3). Further, we showed that this temporal signal was not likely to have been caused by transfer-induced stress (Figure 4—figure supplement 4D). Combined with the effect of prior experience, these results suggest that the decision to explore or exploit likely requires integration of food-related internal and external cues. Future studies should probe if additional factors related to the animal’s biotic and abiotic environment (Guisnet et al., 2021; Anderson et al., 2011; Petersen et al., 2014; Fraune and Bosch, 2010; Dirksen P et al., 2020) as well as alternative motivations (e.g., reproduction and predatory avoidance) (Ding et al., 2020; Lipton et al., 2004; Barrios et al., 2008; Matsuura et al., 2005) further modify these foraging decisions.

Naturalistic observations of C. elegans behavior are necessary to achieve a more complete cellular, molecular, and genetic understanding of how the nervous system has evolved to drive animal behavior. For example, large patches of densely seeded bacteria have primarily been used in experiments assessing C. elegans foraging (White et al., 1986; de Bono and Maricq, 2005; Gray and Lissmann, 1964; Croll, 1975a; Croll, 1975b). However, wild nematodes experience a boom-and-bust environment (Frézal and Félix, 2015) that may be more consistent with sparse, patchily distributed bacteria (Iwanir et al., 2016). Thus, just as quiescence is only observed on high-quality bacterial patches (You et al., 2008), additional behavioral states may be discovered when assessing foraging in dilute patchy environments. By conducting detailed analyses of ecologically inspired foraging behaviors in individual animals, we discovered that C. elegans make accept–reject decisions upon encounter with bacterial patches. By studying foraging in these environments containing small, dilute bacterial patches, we increased the frequency of opportunities for accept–reject decision-making (i.e., patch encounters and patch-leaving events are more frequent) and decreased the condition-specific bias toward accept decisions (i.e., animals are less likely to accept patches when moved between environments of differing bacterial density). We expect that further investigation into naturalistic behaviors could reveal additional insights into more complex behaviors and decision-making in C. elegans and other animals.

In this study, we developed an assay that enables observation of ecologically relevant decision-making in freely moving animals. We posit that future studies can leverage this assay to investigate the neuronal mechanisms underlying decision-making. The frequency of decision-making opportunities (i.e., numerous accept–reject decisions could be observed in the span of minutes) and consistency of patch choice decisions across hundreds of animals and a range of environmental conditions tested supports this claim. Further, we anticipate that the accept–reject decision occurs during a narrow time window – possibly at the time of encounter with the patch edge or shortly thereafter. Therefore, we expect that this assay could be adapted for experiments utilizing calcium imaging in freely moving animals (Faumont and Lockery, 2006; Ji et al., 2021; Prevedel et al., 2014; Nguyen et al., 2016; Venkatachalam et al., 2016; Voleti et al., 2019; Hallinen et al., 2021) to monitor neuronal activity as animals make these decisions. Additionally, the foraging task used here could be leveraged as an accumulation of evidence paradigm, which has been predominantly studied using mammalian animal models (Davidson and El Hady, 2019).

Finally, we used simple quantitative models to dissect and validate the components underlying decision-making. Specifically, we employed a logistic regression GLM which we adapted to accommodate our uncertainty in classification of sensing and exploitation for each encounter. While alternative models may provide more mechanistic predictions, the GLM enabled us to conduct a sequence of hypothesis tests probing the influence of food-related signals on the decision to exploit. Indeed, we conducted a great number of analyses involving model selection and optimization. Ultimately, we focused our study on asking whether a set of simple covariates could be used to predict foraging decisions. The GLM enabled us to identify the simplest model that could explain the observed delay in exploitation. While even the null model predicted that, on average, numerous exploratory encounters were likely to occur before the first exploitation, models including satiety and prior experience significantly better predicted the extent of this delay. Further, we demonstrated that we could validate these model predictions in food-deprived animals, animals exploring multiple patch densities, and animals with sensory deficiencies. We regard our study as an initial foray into demonstrating accept–reject decision-making in nematodes and, while our model is a useful tool for testing the effects of past experiences, our results do not imply that C. elegans discretize their experiences into the parameters used in our model. The exact mechanisms and, consequently, the best model design require further investigation. For example, it is possible that the density of recently exploited patches is predictive of subsequent exploitation because post-ingestive feedback is required for the memory and/or because more distant experiences are remembered (i.e., long-term memory is involved). Future studies should seek to differentiate between these possibilities and characterize the time window of the memory. Altogether, we suggest that this quantitative and ecologically inspired approach to investigating behavior and decision-making is incredibly powerful for refining hypotheses and enables subsequent investigation into the underlying cellular, molecular, and circuit pathways in C. elegans, a strategy that could be adopted across species.

Stock liquid cultures of the OP50 strain of E. coli were prepared via inoculation of a single colony in sterile lysogeny broth (LB) grown overnight at room temperature. Stock liquid cultures were subsequently stored at 4°C for up to 6 weeks.

Solutions of OP50 for each experiment were prepared via a series of dilutions in LB (Figure 1—figure supplement 1A). 50 ml of OP50 stock solution was centrifuged at 3000 rpm for 5 min. After removal of the supernatant, approximately 500–1000 µl of saturated liquid culture remained. The bacterial density of this saturated solution was estimated by measuring the optical density at 600 nm (OD₆₀₀) of a 1:50 dilution of the homogenized solution on a spectrophotometer (Molecular Devices SpectraMax Plus 384). The saturated solution was subsequently diluted to achieve an OD₆₀₀ of ~10 (μ = 10.22, σ = 0.31). Measurements of the number of colony-forming units in the ‘10’ solution estimated 13.1 × 10⁹ cells per ml on average. Additional densities (OD₆₀₀ = {0.05, 0.1, 0.5, 1, 2, 3, 4, 5}) were prepared via dilution of the ‘10’ solution with LB and kept on ice to prevent bacterial growth. A ‘0’ density solution was prepared with just LB.

For all experiments, these density solutions were seeded onto cold, low-moisture nematode growth medium (NGM) plates (3% agar) to facilitate pipetting of small, circular, quick-drying patches. Unless otherwise noted, seeded plates were immediately returned to 4°C after patches dried to prevent bacterial growth. Plates were stored at 4°C for an average of 6 days before experimentation.

For experiments using an OP50 strain expressing green fluorescent protein (OP50-GFP) (Labrousse et al., 2000), cultures were prepared as above, but with the addition of 100 µg/ml of carbenicillin to the liquid LB. All bacterial strains used in this study are listed in the Key Resources table.

C. elegans strains were maintained under standard conditions at 20°C on NGM plates (1.7% agar) seeded with stock liquid culture of OP50 (Brenner, 1974). All experiments were performed on young adult hermaphrodites, picked as L4 larvae the day before the experiment (μ = 24.6 hr, σ = 3.4). Unless otherwise indicated, well-fed animals of the standard C. elegans strain N2 Bristol were used for experiments. Transgenic strains were always compared to matched controls tested in parallel on the same days. All C. elegans strains used in this study are listed in the Key Resources table.

Most bacterial densities tested in these experiments were too dilute to be visible under normal imaging conditions. Therefore, several strategies were employed to accurately detect the location of bacterial patches. First, a small reference dot was cut into the arena and pipetting templates enabling consistent and traceable patch placement. Further, prior to each behavior recording, a ‘contrast’ video was acquired wherein a piece of dark cardstock was passed between the light source and the condition plate (Figure 1—figure supplement 1B–D, Video 2). This produced an effect where diffraction of light through the patches provided enough contrast to view the patches. Binary masks of the circular arena and patches were extracted from these videos in MATLAB using the Image Processing Toolbox and further refined manually in Photoshop (Adobe, 2024). Arena masks were used to calculate the scale (pixels/mm) of each image. In early experiments, the ‘contrast’ video was acquired prior to worms being added to the condition plate, which resulted in displacement of the arena within the camera’s field of view. Image registration using MATLAB’s Computer Vision Toolbox was performed to accurately map the patches detected in the ‘contrast’ video onto the behavioral recording.

As described above (see Assay preparation and recording), we varied the relative density of bacterial solutions by diluting OP50 in LB and growing patches for different lengths of time. As a result of these procedures, the relative bacterial density throughout the assay was not known and needed to be estimated. To determine the relative density of these bacterial patches, we seeded plates with fluorescently labeled OP50-GFP under identical conditions as in our assays (Figure 2—figure supplement 1A). We imaged these bacterial patches for several hours using a Zeiss Axio Zoom.V16. Images were analyzed using the Image Processing Toolbox in MATLAB. After correcting for inconsistent illumination across the field of view and normalizing images using matched controls (Figure 2—figure supplement 1B, C), we detected the location of each bacterial patch and extracted a fluorescence intensity profile along each patch’s radius (Figure 2—figure supplement 1D). Consistent with previous studies, we found that even in extremely dilute conditions, bacterial density was greater at the patch edge where actively proliferating bacteria are concentrated (Gloria-Soria and Azevedo, 2008; Hallatschek et al., 2007). Therefore, we detected the patch edge and computed the peak amplitude of each bacterial patch at all time points assayed (Figure 2—figure supplement 1E). We then performed linear regression on the values for each condition to create models of peak amplitude as a function of time. For low-density conditions (i.e., OD₆₀₀ = {0.05, 0.1}) of small patches, fluorescent signals could not be detected. We therefore estimated these functions from a multinomial regression of values taken from OD₆₀₀ = {0.5, 1, 2}. Through this process, we used the total time that bacteria were allowed to grow at room temperature for each condition plate to estimate the peak amplitude at each time point (Figure 2—figure supplement 3). Finally, to minimize confusion about density conditions between experiments, we computed values for relative density by linearly scaling estimated peak amplitude values so that 0.5 µl patches seeded with OD₆₀₀ = 10 and grown for 1 hr at room temperature would have relative density equal to 10. We labeled each condition using the relative density rounded to one significant digit.

WormLab (MBF Bioscience) was used for tracking animal behavior (Figure 1—figure supplement 1E–G, Video 3). For each video, we adjusted thresholds for pixel intensity and worm dimensions to enable automatic tracking. WormLab then fit the worm’s body at every frame and stitched together a track of each worm across frames. Subsequent manual corrections were required for instances where the software created new worm tracks. This occurred most frequently when animals: (1) encountered the arena border, (2) collided with each other, or (3) overlapped with bubbles or dust particles embedded in the agar. To correct for these discontinuities, we manually ‘stitched’ worm tracks together enabling us to keep track of each animal’s location throughout the duration of the experiment. We exported the location of each animal’s midpoint for further analysis in MATLAB (Mathworks, 2024a). For small, single-patch assays where higher spatial resolution enabled reliable distinction between the head and tail of the animal, we manually confirmed the head–tail and exported 25 points along the animal’s midline (Figure 1—figure supplement 2A–C).

Animals were excluded from analyses when (1) the animal’s location could only be tracked for less than 75% of the video due to the animal escaping the arena and when (2) the location of bacterial patches could not be reliably assessed due to missing or low-quality ‘contrast’ videos (see Bacterial patch location detection).

As the head position of animals in our experiments was difficult to track due to low spatial resolution and limited automated detection of head position using WormLab, we instead tracked the midpoint position of the worm’s body and estimated patch encounters using a set of measured criteria. To do this, we tracked the behavior of worms in higher resolution (~105 pixels/mm compared to ~33 pixels/mm and 8 fps compared to 3 fps), single patch assays (Figure 1—figure supplement 2A–C). We found that when the head of the animal was in contact (i.e., within 1 pixel) with the patch edge (see Bacterial patch location detection), the animal’s midpoint was on average 0.46024 mm away (Figure 1—figure supplement 2D). We therefore defined a patch encounter as the time when an animal’s midpoint came within 0.46024 mm of the patch edge. However, this definition led to two types of errors: (1) putative entry events where the animal merely passed by the patch and (2) putative leaving events where the animal did not fully leave the patch.

To remove putative entry events where the animal nearly passed by the patch, we defined an additional distance threshold based on the distance between the animal’s midpoint and the patch edge for all time points when the head was within the patch (Figure 1—figure supplement 2E). The midpoint was almost always (99% of the time) within 0.28758 mm of the patch edge. Therefore, we removed patch encounters where the midpoint never got closer than 0.28758 mm from the patch edge. Although this criterion removes most ‘near-miss’ events, some events remain where the animal approached the patch, but its head never entered. Further decreasing this threshold (e.g., midpoint must be on patch) would result in real events being excluded due to the animal taking on specific postures where the midpoint remains outside the patch while feeding within the patch. Therefore, we chose to be more liberal (i.e., more false positive patch encounters than false negatives) in our detection of patch encounters. Subsequent analysis of these putative patch encounters removed the majority of remaining false positives (see Patch encounter classification as sensing or non-responding).

To address putative leaving events and avoid splitting a single patch encounter into multiple encounters, we considered that a lawn leaving event is most frequently defined as an event where all body parts have left the patch (Scheer and Bargmann, 2023). When tracking only the midpoint, it is not possible to ensure that the worm’s entire body has exited the patch. Using the criterion that an animal exits a patch when its midpoint exceeds 0.46024 mm from the patch edge accurately predicts exit events most of the time, but under certain scenarios (e.g., animals maintain an outstretched feeding posture Quach and Chalasani, 2022) false leaving events were detected. To exclude these leaving events, we analyzed the variability in the distance from the midpoint to the patch edge during on- and off-patch events (Figure 1—figure supplement 2F). We found that on-patch events had low distance variability while off-patch events displayed a bimodal distribution, with some events having high variability as expected, and some events having low variability. We fit a two-component GMM to the off-patch distance variability and found that low variability leaving events could be reliably excluded when the standard deviation of off-patch distances was less than 0.22221. We subsequently combined putative patch encounters where variability was below this threshold, resulting in fewer overall encounters.

To classify patch encounters as exploration or exploitation events, patch encounters were detected (see Patch encounter detection) and two features were computed: (1) duration of patch encounter and (2) average on-patch velocity. Both the duration and velocity features displayed a bimodal distribution with two visible clusters: one with short-duration encounters and high on-patch velocity and one with long-duration encounters and low on-patch velocity (Figure 2—figure supplement 6A). To confirm the existence of two clusters, we conducted a modified version of Silverman’s test for bimodality (Ahmed and Walther, 2012; Silverman, 1981). Broadly, Silverman’s test uses kernel density estimation (KDE) to investigate the number of modes in a distribution. By solving for a critical bandwidth at which the KDE switches modality from j\begin{document}$j$\end{document} to j+1\begin{document}$j+1$\end{document} modes, one is able to test the null hypothesis that a distribution has j\begin{document}$j$\end{document} modes, versus the alternative that it has more than j\begin{document}$j$\end{document} modes. Following a previously described protocol (Ahmed and Walther, 2012; Silverman, 1981), we tested the null hypothesis that our data set was unimodal (i.e., j=1\begin{document}$j=1$\end{document}). We first mean-centered the matrix zk\begin{document}$\boldsymbol{z}_{k}$\end{document} containing the log transforms of the duration and average velocity of each patch encounter k\begin{document}$k$\end{document}. We then calculated the projection of each data point onto the first principal component (PC1) of the data to get a one-dimensional distribution representing the data in zk\begin{document}$\boldsymbol{z}_{k}$\end{document} (Figure 2—figure supplement 6B). The use of principal components instead of principle curves as described previously was justified as both methods are indistinguishable when j=1\begin{document}$j=1$\end{document} (Ahmed and Walther, 2012). Two modes are visible in both the histogram and KDE of the distribution of PC1 projected data when the KDE is computed using a Gaussian kernel and Silverman’s Rule of Thumb for bandwidth (Silverman, 1986) defined as h^=σ(4(d+2) n)1d+4\begin{document}$\hat {h}=\sigma \left (\frac{4}{\left (d+2\right)\ n}\right)^{\frac{1}{d+4}}$\end{document} where, for this data set, σ\begin{document}$\sigma $\end{document} is the standard deviation, d=1\begin{document}$d=1$\end{document} is the dimensionality, and n=6560\begin{document}$n=6560$\end{document} is the number of observations. To test the significance of this distribution being bimodal rather than unimodal, we computed the critical bandwidth h*\begin{document}$h^{*}$\end{document} defined as the minimum bandwidth for which the KDE has only one mode. Following Silverman’s test procedure, we computed a smoothed bootstrap across 2000 replicates by sampling the data with replacement and adding noise such that for any data point zi\begin{document}$z_{i}$\end{document} and bootstrap resample b\begin{document}$b$\end{document}, we make noisy z~i,b=zi+h*ϵi,b1+h*σ2\begin{document}$\overset{\sim }{z}_{i,b}=\frac{z_{i}+h^{*}\epsilon _{i,b}}{\sqrt{1+\left (\frac{h^{*}}{\sigma }\right)^{2}}}$\end{document} where ϵi,b\begin{document}$\epsilon _{i,b}$\end{document} is a standard normal random variable independently drawn for each i\begin{document}$i$\end{document} and b\begin{document}$b$\end{document}. We found that the critical bandwidth h*\begin{document}$h^{*}$\end{document} of our data set was significantly (p < 0.001) greater than that of the bootstrapped data sets, which allows us to reject the null hypothesis that the distribution of zk\begin{document}$\boldsymbol{z}_{k}$\end{document} is unimodal and justifies the use of a two-cluster model in classifying these data (Figure 2—figure supplement 6C).

After confirming the bimodality of the data set, we classified patch encounters using a two-component GMM to estimate pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} where for each encounter k\begin{document}$k$\end{document}, zk\begin{document}$\boldsymbol{z}_{k}$\end{document} are the log transforms of the duration and average velocity of the patch encounter, yk=1\begin{document}$y_{k}=1$\end{document} indicates an exploitation, and yk=0\begin{document}$y_{k}=0$\end{document} indicates an exploration (Figure 2—figure supplement 6D). We optimized the GMM across cross-validated replicates with respect to the regularization value α\begin{document}$\alpha $\end{document} to minimize the posterior variance given by∑kp(yk=1|zk)p(yk=0|zk).\begin{document}$$\displaystyle \sum _{k}p\left (y_{k}=1|\boldsymbol{z}_{k}\right) p\left (y_{k}=0|\,\boldsymbol{z}_{k}\right).$$\end{document}

We found that α=0.025\begin{document}$\alpha =0.025$\end{document} best separated the exploration and exploitation clusters (Figure 2—figure supplement 6E). The posterior probability of exploitation pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} was subsequently estimated for all encounters (Figure 2—figure supplement 6F, G).

To classify patch encounters as sensing or non-responding events, we computed animals’ (1) deceleration upon encounter with the patch edge, (2) minimum velocity during the patch encounter, and (3) maximum change in velocity between the peak velocity immediately prior to the start of the patch encounter and the minimum velocity during the encounter (Figure 2—figure supplement 7A, B). Deceleration was defined as the slope of the line fit on an animal’s velocity between –1.5 s before and 6.5 s after the start of an encounter. Minimum velocity was defined as the absolute minimum velocity observed during the duration of the patch encounter. The maximum change in velocity was computed by subtracting the minimum velocity from the peak velocity within 10 s of the patch encounter. The combination of these three metrics reveals two non-Gaussian clusters confirmed by Silverman’s test (p = 0.003) as described in the previous section (Figure 2—figure supplement 7C–F). These clusters represent encounters where animals sensed the patch (i.e., slow minimum velocity, large changes in velocity) or did not respond to it (i.e., maintained fast minimum velocity, with little to no change).

We estimated the probability of sensing pvk=1wk\begin{document}$p\left (v_{k}=1|\boldsymbol{w}_{k}\right)$\end{document} where for each encounter k\begin{document}$k$\end{document}, wk=(sk,tk,uk)\begin{document}$\boldsymbol{w}_{k} =\left (s_{k},t_{k},u_{k}\right)$\end{document} are the three velocity-related features, vk=1\begin{document}$v_{k}=1$\end{document} indicates an encounter that was sensed, and vk=0\begin{document}$v_{k}=0$\end{document} indicates an encounter where no response was detected. Using a semi-supervised approach to QDA, we labeled a subset of all encounters and iteratively estimated labels on the remaining unlabeled data (Figure 2—figure supplement 8A–C, Video 5). To label the data, we made two simple assumptions: (1) animals must have sensed the patch if they exploited it and (2) animals must not have sensed the patch if there was no bacteria to sense. Therefore, all encounters with bacteria-free patches (i.e., LB only, relative density 0) were labeled as true negatives vk=0\begin{document}$v_{k}=0$\end{document} and, across 1000 replicates, we probabilistically included exploitation encounters yk=1\begin{document}$y_{k}=1$\end{document} estimated from the distribution yk|zk∼ Bern(p(yk=1|zk))\begin{document}$y_{k}|\boldsymbol{z}_{k}\sim \text{Bern}\left (p\left (y_{k}=1|\boldsymbol{z}_{k}\right)\right)$\end{document} as true positives vk=1\begin{document}$v_{k}=1$\end{document}. The semi-supervised QDA method then used these initial labels to iteratively fit a paraboloid that best separated the labeled data, by minimizing the posterior variance of classification. Using this approach, the conditional probability of sensing pvk=1wk\begin{document}$p\left (v_{k}=1|\boldsymbol{w}_{k}\right)$\end{document} was estimated for all encounters using QDA and averaged across replicates (Figure 2—figure supplement 8D–E).

Although we found that the two clusters were successfully discriminated by this semi-supervised QDA approach, a small subset of encounters (252 of 20109 encounters) could not be reliably classified in this manner as the onset of the patch encounter was not observed. This type of data censoring occurred when the behavioral recording was started after the animal had already entered the patch. Although we could compute deceleration-related metrics for these encounters with the assumption that the animal entered the patch at the first frame, these measurements are censored with a bias toward lower magnitudes of deceleration. Therefore, to better predict the conditional probabilities of sensing for these 252 encounters, we assumed that the minimum velocity on-patch sk\begin{document}$s_{k}$\end{document} was a reliable metric and marginalized the conditional probabilities over the other two metrics (tk\begin{document}$t_{k}$\end{document} and uk\begin{document}$u_{k}$\end{document}) as defined byp(vk=1|sk)=∫−∞∞∫−∞∞p(vk=1|sk,tk,uk) p(tk,uk |sk)dt du.\begin{document}$$\displaystyle p\left (v_{k}=1|s_{k}\right)={\int_{-\mathrm{\infty }}^{\mathrm{\infty }}}{\int _{-\mathrm{\infty }}^{\mathrm{\infty }}}p\left (v_{k}=1 | s_{k},t_{k},u_{k}\right)\ p\left (t_{k},u_{k}\ |s_{k}\right) dt\ du.$$\end{document}

We numerically integrated using an adaptive quadrature method over the product of the QDA estimated conditional probability distribution and the KDE of the joint probability distribution. This procedure resulted in a slight increase (μ = +0.0615, σ = 0.1832) in our estimation of the probability of sensing (Figure 2—figure supplement 8F).

Altogether, this classification approach resulted in low false positive and false negative rates. Specifically, 3.35% of the time encounters with bacteria-free patches were incorrectly identified as sensing, while 2.92% of the time exploitatory encounters were incorrectly identified as non-responding. Further, this classification removed many of the remaining near-miss patch encounters in which animals came close to but did not truly enter the patch (see Patch encounter detection). For all analyses, we excluded near-miss encounters where the animal’s midpoint never entered the patch and the probability of sensing was less than 5% (i.e., p(vk=1|wk)<0.05\begin{document}$p\left (v_{k}=1|\boldsymbol{w}_{k}\right) \lt 0.05$\end{document}).

We consider that the probability of exploiting a patch upon any given encounter can be described by a logistic function:p(yk=1|β⋅xk)=11+e−β⋅xk,\begin{document}$$\displaystyle p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right) = \frac{1}{1 + e^{-\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}}},$$\end{document}

where pyk=1β⋅xk\begin{document}$p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)$\end{document} represents the conditional probability that an animal exploited during patch encounter k\begin{document}$k$\end{document}; xk∈Rn\begin{document}$\boldsymbol{x}_{k}\in R^{n}$\end{document} is a vector of covariates; and β∈Rn\begin{document}$\boldsymbol{\beta }\in R^{n}$\end{document} is a vector of weights that describes how much each covariate influences the animal’s choice. In models compared here, xk\begin{document}$\boldsymbol{x}_{k}$\end{document} includes a combination of a constant element as well as covariates that may empirically influence the decision to exploit: (1) the log-transformed relative density of the encountered patch k\begin{document}$k$\end{document} (ρk\begin{document}$\rho _{k}$\end{document}), (2) the duration of time spent off food since departing the last exploited patch (τs\begin{document}$\tau _{s}$\end{document}), (3) the log-transformed relative density of the patch encountered immediately before encounter k\begin{document}$k$\end{document} (ρh\begin{document}$\rho _{h}$\end{document}), and (4) the log-transformed relative density of the last exploited patch (ρe\begin{document}$\rho _{e}$\end{document}).

The observations of exploitation and sensation for our data are derived predictions from classification models rather than direct measurements (see Patch encounter classification as exploration or exploitation and Patch encounter classification as sensing or non-responding). As such, the labels for both whether a patch encounter was sensed by the animal pvk=1wk\begin{document}$p\left (v_{k}=1|\boldsymbol{w}_{k}\right)$\end{document} and whether the animal exploited the patch pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document}, are both reported as probabilities rather than binary, deterministic variables.

To account for uncertainty in sensation, we produced 100 sets of ‘encounter sampled’ observations wherein we probabilistically included sensed encounters vk=1\begin{document}$v_{k}=1$\end{document} estimated from the distribution vk|wk∼ Bern(p(vk=1|wk))\begin{document}$v_{k}|\boldsymbol{w}_{k}\sim \text{Bern}\left (p\left (v_{k}=1|\boldsymbol{w}_{k}\right)\right)$\end{document}. In doing so, we assume that only patch encounters recognized by the animal guide the decision to exploit (Figure 4B). After removing non-responding encounters where vk=0\begin{document}$v_{k}=0$\end{document}, we defined observations of all covariates (i.e., ρk\begin{document}$\rho _{k}$\end{document}, τs\begin{document}$\tau _{s}$\end{document}, ρh\begin{document}$\rho _{h}$\end{document}, and ρe\begin{document}$\rho _{e}$\end{document}) using only sensed encounters.

To account for uncertainty in exploitation, we modified the standard maximum likelihood. To understand our approach, consider that standard logistic regression models binary observations as realizations of the Bernoulli distribution yk|xk∼ Bern(p(yk=1|β⋅xk))\begin{document}$y_{k}|\boldsymbol{x}_{k}\sim \text{Bern}\left (p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\right)$\end{document} and that the likelihood for this model is given by∏kp(yk=1|β⋅xk)yk(1−p(yk=1|β⋅xk))1−yk.\begin{document}$$\displaystyle \prod _{k}p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)^{y_{k}} \left (1-p\left (y_{k}=1|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\right)^{1-y_{k}}.$$\end{document}

However, we do not have direct observations of yk\begin{document}$y_{k}$\end{document} and cannot evaluate the logistic likelihood directly. Rather, we have posterior probabilities of exploitation determined by a classifier, denoted by pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document}, where zk\begin{document}$\boldsymbol{z}_{k}$\end{document} are a set of velocity-related features that are distinct from xk\begin{document}$\boldsymbol{x}_{k}$\end{document} (see Patch encounter classification as exploration or exploitation). Thus, rather than maximizing the Bernoulli likelihood, we accommodate our uncertainty about yk\begin{document}$y_{k}$\end{document} by learning the regression parameters that minimize the Kullback–Leibler (KL) divergence between pykβ⋅xk\begin{document}$p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)$\end{document} and the reference probability distribution pykzk\begin{document}$p\left (y_{k}|\boldsymbol{z}_{k}\right)$\end{document} as given byDKL[p(yk|zk)||p(yk|β⋅xk)]≡∑ykp(yk|zk)log⁡[p(yk|zk)p(yk|β⋅xk)]=Cβ−∑ykp(yk|zk)log⁡[p(yk|β⋅xk)]=Cβ−∑ykp(yk|zk)log⁡[p(yk|β⋅xk)yk (1−p(yk|β⋅xk))1−yk]=Cβ−p(yk=1|zk)log⁡[p(yk|β⋅xk)]  −(1−p(yk=1|zk))log⁡[1−p(yk|β⋅xk)]=Cβ−log⁡[p(yk|β⋅xk)p(yk=1|zk)(1−p(yk|β⋅xk))1−p(yk=1|zk)],\begin{document}$$\displaystyle \begin {aligned} \mathrm{D}_{KL}\left [p\left (y_{k}|\boldsymbol{z}_{k}\right )||p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )\right ] \equiv &\, \sum _{y_{k}}p\left (y_{k}|\boldsymbol{z}_{k}\right )\log \left [\frac{p\left (y_{k}|\boldsymbol{z}_{k}\right )}{p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )}\right ]\\ = &\, C_{\boldsymbol{\beta }}-\sum _{y_{k}}p\left (y_{k}|\boldsymbol{z}_{k}\right )\log \left [p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )\right ]\\ = &\, C_{\boldsymbol{\beta }}-\sum _{y_{k}}p\left (y_{k}|\boldsymbol{z}_{k}\right )\log \left [p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )^{y_{k}}\ \left (1-p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )\right )^{1-y_{k}}\right ]\\ =&\, C_{\boldsymbol{\beta }}-p\left (y_{k}=1|\boldsymbol{z}_{k}\right )\log \left [p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )\right ]\\ & \mathrm{\ }\mathrm{\ }-\left (1-p\left (y_{k}=1|\boldsymbol{z}_{k}\right )\right )\log \left [1-p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right )\right ]\\ = &\, C_{\boldsymbol{\beta }}\\ & -\log \left [p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)^{p\left (y_{k}=1|\boldsymbol{z}_{k}\right)}\left (1-p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\right)^{1-p\left (y_{k}=1|\boldsymbol{z}_{k}\right)}\right ], \end {aligned}$$\end{document}

where Cβ\begin{document}$C_{\beta }$\end{document} is a term that is constant with respect to β\begin{document}$\boldsymbol{\beta }$\end{document}, and the second term is equivalent to the logarithm of the logistic likelihood with pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} replacing yk\begin{document}$y_{k}$\end{document}. Put plainly, minimizing the sum of the KL divergence between our classifier probabilities and logistic regression probabilities over all encounters k\begin{document}$k$\end{document} is equivalent to maximizing the logistic likelihood with our classifier-based exploitation probabilities pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} as observations instead of direct measurements of exploitation yk\begin{document}$y_{k}$\end{document} as given by∑klog⁡[p(yk|β⋅xk)p(yk=1|zk)(1−p(yk|β⋅xk))1−p(yk=1|zk)].\begin{document}$$\displaystyle \sum _{k}\log \left [p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)^{p\left (y_{k}=1|\boldsymbol{z}_{k}\right)}\left (1-p\left (y_{k}|\boldsymbol{\beta }\cdot \boldsymbol{x}_{k}\right)\right)^{1-p\left (y_{k}=1|\boldsymbol{z}_{k}\right)}\right].$$\end{document}

Notably, when there is no observation uncertainty, pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} collapses to a delta function on yk=1\begin{document}$y_{k}=1$\end{document} and we recover the standard likelihood function. Thus, our method is a generalization of maximum likelihood. To train our model, we therefore fit a standard logistic regression GLM where we provided sets of observations of covariates xk\begin{document}$\boldsymbol{x}_{k}$\end{document} and response variables pyk=1zk\begin{document}$p\left (y_{k}=1|\boldsymbol{z}_{k}\right)$\end{document} for sensed encounters.

The covariates xk\begin{document}$\boldsymbol{x}_{k}$\end{document} included the relative density of the encountered patch k\begin{document}$k$\end{document} (ρk\begin{document}$\rho _{k}$\end{document}), the duration of time spent off food since departing the last exploited patch (τs\begin{document}$\tau _{s}$\end{document}), the relative density of the patch encountered immediately before encounter k\begin{document}$k$\end{document} (ρh\begin{document}$\rho _{h}$\end{document}), and the relative density of the last exploited patch (ρe\begin{document}$\rho _{e}$\end{document}). For every encounter k\begin{document}$k$\end{document}, ρk\begin{document}$\rho _{k}$\end{document} is the log-transformed relative density of the encounter patch as estimated from experiments using a fluorescent bacterial strain, OP50-GFP (as described in Bacterial patch density estimation). τs\begin{document}$\tau _{s}$\end{document} is the duration of time spent off food since the beginning of the recorded experiment (i.e., total time elapsed minus duration of time on patch). For the first patch encounter (i.e., k=1\begin{document}$k=1$\end{document}), this is equivalent to the total time elapsed. ρh\begin{document}$\rho _{h}$\end{document} is the log-transformed relative density of the patch encountered immediately before encounter k\begin{document}$k$\end{document}. For the first patch encounter, we initialized this parameter using the approximated relative density of the bacterial patch on the acclimation plates (see Assay preparation and recording in Methods). Acclimation plates contained one large 200 µl patch seeded with OD₆₀₀ = 1 and grown for a total of ~48 hr. The relative density of these acclimation plates was estimated using the same procedure used to estimate values of ρk\begin{document}$\rho _{k}$\end{document} (see Bacterial patch density estimation). ρe\begin{document}$\rho _{e}$\end{document} is the log-transformed relative density of the most recently exploited patch. For the first patch encounter as well as every encounter prior to the first observed exploitation, we assume that animals must have exploited within the last 24 hr while on the acclimation plates and thus initialized ρe\begin{document}$\rho _{e}$\end{document} using the approximated relative density of the bacterial patch on the acclimation plates.