Foraging animals often sample options that yield rewards with different probabilities. In such scenarios, many animals exhibit “matching”, whereby they allocate their choices such that the fraction of rewarded samples is equal across options. While matching can be optimal in environments with diminishing returns, this condition alone is not sufficient to determine optimality. Moreover, diminishing returns arise when resources deplete and replenish over time, but their form depends on the temporal structure and statistics of replenishment. Here, we investigate how these environmental properties influence whether matching is optimal. We consider an agent that samples options at fixed rates and derive the resulting reward probabilities across different types of environments. This allows us to analytically determine conditions under which the optimal policy exhibits matching. When all options share the same replenishment dynamics, matching emerges as optimal across a wide range of environments. However, when dynamics differ across options, optimal policies can deviate from matching. In such cases, the rank-ordering of observed reward probabilities depends only on the qualitative nature of the replenishment process, and not on the specific replenishment rates. As a result, the optimal policy can exhibit under- or over-matching depending on which options are more rewarding. We use this result to identify environments where performance differs substantially between matching and optimality. Finally, we show that fluctuations in replenishment rates—representing environmental stochasticity or internal uncertainty—can amplify deviations from matching. These findings deepen our understanding of the relationship between environmental variability and behavioral optimality, and provide testable predictions across diverse settings.

Maintaining physiological homeostasis requires a complex interplay among endocrine organs, peripheral tissues, and distributed neuroendocrine control circuits, all of which are coupled through feedback loops that operate over minutes to hours. Although many physiological needs are broadcast through hormones, metabolites, and other chemical compounds circulating in the bloodstream, we rarely observe more than a few of these messengers together and at high cadence during behavior. To address this, we developed a minimally disruptive workflow to measure the free fraction of hundreds of amines and small peptides at a 7.5-minute cadence for \~8 hrs in freely moving mice using chronic jugular microdialysis implants and chemical isotope labeling Liquid Chromatography-Mass Spectrometry. Single-compound profiles behave according to known physiology, such as purine turnover correlating with movement, delayed histamine/5-HIAA changes, and coordinated amino-acid dynamics. Our multiplexed measures enable high-dimensional analyses that uncover properties of the underlying dynamics. For example, systems-level analyses show that 10 dimensions explain over 70% of the variance in hormone/metabolite covariation, consistent with a low rank description of the physiological state space, with projections aligned to locomotion state transitions. Our work opens avenues for the discovery of hormonal dynamics, compound interactions, and their effects on behavior.

Animals efficiently learn to navigate their environment. In the laboratory, naive mice explore their environment via highly structured trajectories and can learn to localize new spatial targets in as few as a handful of trials. It is unclear how such efficient learning is possible, since existing computational models of spatial navigation require far more experience to achieve comparable performance and do not attempt to explain the evolving structure of animal behavior during learning. To inform a new algorithm for rapid learning of navigational goals, we took inspiration from the reliable structure of behavior as mice learned to intercept hidden spatial targets. We designed agents that generate behavioral trajectories by controlling the speed and angular velocity of smooth path segments between anchor points. To rapidly learn good anchors, we use Bayesian inference on the history of rewarded and unrewarded trajectories to infer the probability that an anchor will be successful, and active sampling to trim hypothesized anchors. Agents learn within tens of trials to generate compact trajectories that intercept a target, capturing the evolution of behavioral structure and matching the upper limits of learning efficiency observed in mice. We further show that this algorithm can explain how mice avoid obstacles and rapidly adapt to target switches. Finally, we show that this framework naturally encompasses both egocentric and allocentric strategies for navigation.

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.