When foraging for resources, animals must often sample many options that yield reward with different probabilities. In such scenarios, many animals have been shown to exhibit “matching”, an empirical behavioral observation in which the fraction of rewarded samples is the same across all options. While previous work has shown that matching can be optimal in environments with diminishing returns, this condition is not sufficient to determine optimality. Furthermore, while diminishing returns naturally arise when resources in the environment deplete and take time to be replenished, the specific form of diminishing returns depends on the temporal structure and statistics of the replenishment process. Here, we explore how these environmental properties affect whether matching is optimal. By considering an agent that samples different options with fixed sampling rates, we derive the probability of collecting a reward as a function of these sampling rates for different types of environments, and we analytically determine the conditions under which the optimal sampling-rate policy exhibits matching. When all options are governed by the same replenishment dynamics, we find that optimality gives rise to matching across a wide range of environments. However, when these dynamics differ across options, the optimal policy can deviate from matching. In such cases, the rank-ordering of observed reward probabilities depends only on the qualitative nature of the replenishment process, but not on the specific replenishment rates. As a result, the optimal policy can exhibit underor over-matching depending on how rewarding the different options are. We use this result to identify environmental settings under which performance differs substantially between matching and optimality. Finally, we show how fluctuations in these replenishment rates—which can represent either environmental stochasticity or the agent’s internal uncertainty about the environment—can accentuate deviations between optimality and matching. Together, these findings deepen our understand of the relationship between environmental variability and behavioral optimality, and they provide testable experimental predictions across a wide range of environmental settings.

To successfully forage for food, animals must balance the energetic cost of searching for food sources with the energetic benefit of exploiting those sources. While the Marginal Value Theorem provides one normative account of this balance by specifying that a forager should leave a food patch when its energetic yield falls below the average yield of other patches in the environment, it assumes the presence of other readily reachable patches. In natural settings, however, a forager does not know whether it will encounter additional food patches, and it must balance potential energetic costs and benefits accordingly. Upon first encountering a patch of food, it faces a decision of whether and when to leave the patch in search of better options, and when to return if no better options are found. Here, we explore how a forager should structure its search for new food patches when the existence of those patches is unknown, and when searching for those patches requires energy that can only be harvested from a single known food patch. We identify conditions under which it is more favorable to explore the environment in several successive trips rather than in a single long exploration, and we show how the optimal sequence of trips depends on the forager’s beliefs about the distribution and nutritional content of food patches in the environment. This optimal strategy is well approximated by a local decision that can be implemented by a simple neural circuit architecture. Together, this work highlights how energetic constraints and prior beliefs shape optimal foraging strategies, and how such strategies can be approximated by simple neural networks that implement local decision rules.

To survive, animals must be able quickly infer the state of their surroundings. For example, to successfully escape an approaching predator, prey must quickly estimate the direction of approach from incoming sensory stimuli and guide their behavior accordingly. Such rapid inferences are particularly challenging because the animal has only a brief window of time to gather sensory stimuli, and yet the accuracy of inference is critical for survival. Due to evolutionary pressures, nervous systems have likely evolved effective computational strategies that enable accurate inferences under strong time limitations. Traditionally, the relationship between the speed and accuracy of inference has been described by the “speed-accuracy tradeoff” (SAT), which quantifies how the average performance of an ideal observer improves as the observer has more time to collect incoming stimuli. While this trial-averaged description can reasonably account for individual inferences made over long timescales, it does not capture individual inferences on short timescales, when trial-to-trial variability gives rise to diverse patterns of error dynamics. We show that an ideal observer can exploit this single-trial structure by adaptively tracking the dynamics of its belief about the state of the environment, which enables it to speed its own inferences and more reliably track its own error, but also causes it to violate the SAT. We show that these features can be used to improve overall performance during rapid escape. The resulting behavior qualitatively reproduces features of escape behavior in the fruit fly Drosophila melanogaster, whose escapes have presumably been highly optimized by natural selection.

In natural environments, animals must efficiently allocate their choices across multiple concurrently available resources when foraging, a complex decision-making process not fully captured by existing models. To understand how rodents learn to navigate this challenge we developed a novel paradigm in which untrained, water-restricted mice were free to sample from six options rewarded at a range of deterministic intervals and positioned around the walls of a large ( 2m) arena. Mice exhibited rapid learning, matching their choices to integrated reward ratios across six options within the first session. A reinforcement learning model with separate states for staying or leaving an option and a dynamic, global learning rate was able to accurately reproduce mouse learning and decision-making. Fiber photometry recordings revealed that dopamine in the nucleus accumbens core (NAcC), but not dorsomedial striatum (DMS), more closely reflected the global learning rate than local error-based updating. Altogether, our results provide insight into the neural substrate of a learning algorithm that allows mice to rapidly exploit multiple options when foraging in large spatial environments.

Many animals rely on persistent internal representations of continuous variables for working memory, navigation, and motor control. Existing theories typically assume that large networks of neurons are required to maintain such representations accurately; networks with few neurons are thought to generate discrete representations. However, analysis of two-photon calcium imaging data from tethered flies walking in darkness suggests that their small head-direction system can maintain a surprisingly continuous and accurate representation. We thus ask whether it is possible for a small network to generate a continuous, rather than discrete, representation of such a variable. We show analytically that even very small networks can be tuned to maintain continuous internal representations, but this comes at the cost of sensitivity to noise and variations in tuning. This work expands the computational repertoire of small networks, and raises the possibility that larger networks could represent more and higher-dimensional variables than previously thought.

To survive, animals must be able quickly infer the state of their surroundings. For example, to successfully escape an approaching predator, prey must quickly estimate the direction of approach from incoming sensory stimuli. Such rapid inferences are particularly challenging because the animal has only a brief window of time to gather sensory stimuli, and yet the accuracy of inference is critical for survival. Due to evolutionary pressures, nervous systems have likely evolved effective computational strategies that enable accurate inferences under strong time limitations. Traditionally, the relationship between the speed and accuracy of inference has been described by the "speed-accuracy tradeoff" (SAT), which quantifies how the average performance of an ideal observer improves as the observer has more time to collect incoming stimuli. While this trial-averaged description can reasonably account for individual inferences made over long timescales, it does not capture individual inferences on short timescales, when trial-to-trial variability gives rise to diverse patterns of error dynamics. We show that an ideal observer can exploit this single-trial structure by adaptively tracking the dynamics of its belief about the state of the environment, which enables it make more rapid inferences and more reliably track its own error but also causes it to violate the SAT. We show that these features can be used to improve overall performance during rapid escape. The resulting behavior qualitatively reproduces features of escape behavior in the fruit fly Drosophila melanogaster, whose escapes have presumably been highly optimized by natural selection.

After finding food, a foraging animal must decide whether to continue feeding, or to explore the environment for potentially better options. One strategy to negotiate this tradeoff is to perform local searches around the food but repeatedly return to feed. We studied this behavior in flies and used genetic tools to uncover the underlying mechanisms. Over time, flies gradually expand their search, shifting from primarily exploiting food sources to exploring the environment, a change that is likely driven by increases in satiety. We found that flies’ search patterns preserve these dynamics even as the overall scale of the search is modulated by starvation-induced changes in metabolic state. In contrast, search induced by optogenetic activation of sugar sensing neurons does not show these dynamics. We asked what navigational strategies underlie local search. Using a generative model, we found that a change in locomotor pattern after food consumption could account for repeated returns to the food, but failed to capture relatively direct, long return trajectories. Alternative strategies, such as path integration or sensory taxis could allow flies to return from larger distances. We tested this by individually silencing the fly’s head direction system, olfaction and hygrosensation, and found that the only substantial effect was from perturbing hygrosensation, which reduced the number of long exploratory trips. Our study illustrates that local search is composed of multiple behavioral features that evolve over time based on both internal and external factors, providing a path towards uncovering the underlying neural mechanisms.

Anchoring goals to spatial representations enables flexible navigation but is challenging in novel environments when both representations must be acquired simultaneously. We propose a framework for how Drosophila uses internal representations of head direction (HD) to build goal representations upon selective thermal reinforcement. We show that flies use stochastically generated fixations and directed saccades to express heading preferences in an operant visual learning paradigm and that HD neurons are required to modify these preferences based on reinforcement. We used a symmetric visual setting to expose how flies' HD and goal representations co-evolve and how the reliability of these interacting representations impacts behavior. Finally, we describe how rapid learning of new goal headings may rest on a behavioral policy whose parameters are flexible but whose form is genetically encoded in circuit architecture. Such evolutionarily structured architectures, which enable rapidly adaptive behavior driven by internal representations, may be relevant across species.

Neurons throughout the sensory pathway adapt their responses depending on the statistical structure of the sensory environment. Contrast gain control is a form of adaptation in the auditory cortex, but it is unclear whether the dynamics of gain control reflect efficient adaptation, and whether they shape behavioral perception. Here, we trained mice to detect a target presented in background noise shortly after a change in the contrast of the background. The observed changes in cortical gain and behavioral detection followed the dynamics of a normative model of efficient contrast gain control; specifically, target detection and sensitivity improved slowly in low contrast, but degraded rapidly in high contrast. Auditory cortex was required for this task, and cortical responses were not only similarly affected by contrast but predicted variability in behavioral performance. Combined, our results demonstrate that dynamic gain adaptation supports efficient coding in auditory cortex and predicts the perception of sounds in noise.

To interpret the sensory environment, the brain combines ambiguous sensory measurements with knowledge that reflects context-specific prior experience. But environmental contexts can change abruptly and unpredictably, resulting in uncertainty about the current context. Here we address two questions: how should context-specific prior knowledge optimally guide the interpretation of sensory stimuli in changing environments, and do human decision-making strategies resemble this optimum? We probe these questions with a task in which subjects report the orientation of ambiguous visual stimuli that were drawn from three dynamically switching distributions, representing different environmental contexts. We derive predictions for an ideal Bayesian observer that leverages knowledge about the statistical structure of the task to maximize decision accuracy, including knowledge about the dynamics of the environment. We show that its decisions are biased by the dynamically changing task context. The magnitude of this decision bias depends on the observer's continually evolving belief about the current context. The model therefore not only predicts that decision bias will grow as the context is indicated more reliably, but also as the stability of the environment increases, and as the number of trials since the last context switch grows. Analysis of human choice data validates all three predictions, suggesting that the brain leverages knowledge of the statistical structure of environmental change when interpreting ambiguous sensory signals.