A canonical foraging task is the patch-leaving problem, in which a forager
must decide to leave a current resource in search for another. Theoretical work
has derived optimal strategies for when to leave a patch, and experiments have
tested for conditions where animals do or do not follow an optimal strategy.
Nevertheless, models of patch-leaving decisions do not consider the imperfect
and noisy sampling process through which an animal gathers information, and how
this process is constrained by neurobiological mechanisms. In this theoretical
study, we formulate an evidence accumulation model of patch-leaving decisions
where the animal averages over noisy measurements to estimate the state of the
current patch and the overall environment. Evidence accumulation models belong
to the class of drift diffusion processes and have been used to model decision
making in different contexts. We solve the model for conditions where foraging
decisions are optimal and equivalent to the marginal value theorem, and perform
simulations to analyze deviations from optimal when these conditions are not
met. By adjusting the drift rate and decision threshold, the model can
represent different strategies, for example an increment-decrement or counting
strategy. These strategies yield identical decisions in the limiting case but
differ in how patch residence times adapt when the foraging environment is
uncertain. To account for sub-optimal decisions, we introduce an
energy-dependent utility function that predicts longer than optimal patch
residence times when food is plentiful. Our model provides a quantitative
connection between ecological models of foraging behavior and evidence
accumulation models of decision making. Moreover, it provides a theoretical
framework for potential experiments which seek to identify neural circuits
underlying patch leaving decisions