Normative theory of patch foraging decisions

Abstract

Foraging is a fundamental behavior as animals' search for food is crucial for their survival. Patch leaving is a canonical foraging behavior, but classic theoretical conceptions of patch leaving decisions lack some key naturalistic details. Optimal foraging theory provides general rules for when an animal should leave a patch, but does not provide mechanistic insights about how those rules change with the structure of the environment. Such a mechanistic framework would aid in designing quantitative experiments to unravel behavioral and neural underpinnings of foraging. To address these shortcomings, we develop a normative theory of patch foraging decisions. Using a Bayesian approach, we treat patch leaving behavior as a statistical inference problem. We derive the animals' optimal decision strategies in both non-depleting and depleting environments. A majority of these cases can be analyzed explicitly using methods from stochastic processes. Our behavioral predictions are expressed in terms of the optimal patch residence time and the decision rule by which an animal departs a patch. We also extend our theory to a hierarchical model in which the forager learns the environmental food resource distribution. The quantitative framework we develop will therefore help experimenters move from analyzing trial based behavior to continuous behavior without the loss of quantitative rigor. Our theoretical framework both extends optimal foraging theory and motivates a variety of behavioral and neuroscientific experiments investigating patch foraging behavior. CONTENTS

Timescales of Evidence Evaluation for Decision Making and Associated Confidence Judgments Are Adapted to Task Demands

“…Failure to respond within that time resulted in trial termination. This is similar to many natural situations where failure to respond quickly to an environmental change can have immediate negative consequences, such as predator avoidance, optimal foraging behavior (Kilpatrick et al, 2020), or specifically for humans, driving a vehicle. Previous work has shown the timescales of evidence evaluation can be adapted to expected signal durations when humans perform a visual change detection task (Ossmy et al, 2013).…”

Control over patch encounters changes foraging behaviour

“…The present experiment has three main limitations. First, the experiment did not provide a normative account for optimal patch leaving in environments where three patches can be revisited and agents have control over patch encounters (see Kilpatrick et al, 2020; Possingham & Houston, 1990 for two-patch revisiting solutions). While foraging patterns showed striking differences between choice conditions with respect to the patches visited, rewards on arrival, rewards prior to leaving and net reward rates, we have not assessed whether these would be the same differences shown under an optimal solution.…”

Evolution of innate behavioral strategies through competitive population dynamics

“…In this work we investigated the evolution of innate foraging behaviors using evolutionary population dynamics [4], in contrast to the more common normative approaches in which evolution is assumed to act like an optimization process that extremizes some objective function subject to constraints [6,26,27]. One of our motivations for doing so was to better understand conditions under which we might expect such normative approaches to be mimicked naturally by the population dynamics, either through the population dynamics being interpretable as gradient-descent dynamics or by deriving an effective "fitness function" that predicts the dominant phenotype, or conditions under which typical normative approaches might need to consider "multi-agent" interactions to properly predict emergent phenotypes, a growing trend in deep reinforcement learning [28].…”

“…Beyond master-equation based models, there are many other studies that take normative approaches to understanding the behaviors and structures of organisms performing similar foraging tasks. Work in this vein may take several forms of abstraction, ranging from models in which the quantities to be optimized are directly relevant quantitiessuch as expected numbers of offspring [5] or the expected time it takes organisms to find a stockpile of food [6,7]-to more abstract "rewards" such as the information an organism has extracted from its environment [11,17,27,53,54]. In some cases these normative models consider just a single representative agent and its associated parameters that determine its dynamics, and hence phenotype.…”

“…This idea has given rise to modeling evolution as an optimization process that maximizes an organism's fitness [4], i.e., selects for the phenotype parameters that maximize the fitness function. Fitness functions can range from relatively straightforward and concrete quantities, such as an organism's rate of producing offspring or the time it takes to find shelter or food [5][6][7][8], or they can be relatively abstract, such as the amount of information an organism's sensory organs convey to its nervous system [9][10][11][12]-the idea being that the more efficiently an organism's nervous system can process information it acquires about its environment, the more successful it will be at finding food, shelter, mates, etc.…”