Bayesian foraging model reveals depletion speeds rate learning, not composition

Researchers Zachary P. Kilpatrick and Ahmed El Hady have released a new theoretical paper on arXiv titled "Resource depletion accelerates rate learning but not composition learning in patch foraging" (arXiv:2607.29476, q-bio.NC). The work builds a normative Bayesian account of an agent that must simultaneously learn the structure of a patchy environment and exploit it—a hierarchical inference problem. Their central finding is that resource depletion affects the two levels of this hierarchy differently. Within a patch, depletion actually accelerates rate learning: each successive encounter occurs at a falling rate, and the spacing between encounters pins down the initial rate more quickly. Across patches, however, composition learning—inferring what fraction of patches are high-yield—remains slow, governed by the number of patches sampled rather than time spent in each, and is unaffected by depletion once rates are known.

The model reveals a sharp divergence between reward-maximizing and information-seeking strategies. A reward-maximizing forager underharvests rich patches because solving composition requires departures from those patches, especially early in exposure. When a fixed set of patches replenishes between visits, the optimal policy collapses onto a stable orbit over high-yield patches, and the replenishment rate determines whether the forager maps the whole environment or locks onto a rich subset. Intriguingly, the best departure rule itself depends on patch variability: agents switch from counting prey to timing the gaps between them once richness varies by more than about a quarter. Overall, learning the environment buys significant intake over learning a rule from reward alone—provided its assumptions about depletion leave room for the truth. The paper spans 35 pages with 10 figures, offering both mathematical proofs and behavioral predictions for experimentalists.