Foraging Under Uncertainty Follows the Marginal Value Theorem with Bayesian Updating of Environment Representations

Foraging theory has been a remarkably successful approach to understanding the behavior of animals in many contexts. In patch-based foraging contexts, the marginal value theorem (MVT) shows that the optimal strategy is to leave a patch when the marginal rate of return declines to the average for the environment. However, the MVT is only valid in deterministic environments whose statistics are known to the forager; naturalistic environments seldom meet these strict requirements. As a result, the strategies used by foragers in naturalistic environments must be empirically investigated. We developed a novel behavioral task and a corresponding computational framework for studying patch-leaving decisions in head-fixed and freely moving mice. We varied between-patch travel time, as well as within-patch reward depletion rate, both deterministically and stochastically. We found that mice adopt patch residence times in a manner consistent with the MVT and not explainable by simple ethologically motivated heuristic strategies. Critically, behavior was best accounted for by a modified form of the MVT wherein environment representations were updated based on local variations in reward timing, captured by a Bayesian estimator and dynamic prior. Thus, we show that mice can strategically attend to, learn from, and exploit task structure on multiple timescales simultaneously, thereby efficiently foraging in volatile environments. The results provide a foundation for applying the systems neuroscience toolkit in freely moving and head-fixed mice to understand the neural basis of foraging under uncertainty.