Foraging as an evidence accumulation process
Fig 2
Patch-leaving decision strategies.
Different strategies are represented with different choices of the drift rate (α) and the threshold (η) (Eq 10). (A) The optimal threshold from Eq 9 plotted as a function of the drift, showing the general classes of increment-decrement and decremental strategies. The solid line shows the optimal threshold in the region of parameter space where both α and η have the same sign, and the dotted line indicates the region where they have the opposite sign. Parameters used are A = 5, E* = 2 (or equivalently, ρ0 = 9.439), and s = 2; these parameters are also used in (B-E), which illustrate each strategy using discrete rewards and zero noise on the decision variable. (B) The choice α = ρ0 is optimal for uncertainty in patch food density; this represents an “increment-decrement” mechanism for patch decisions. (C) A threshold of zero is optimal for uncertainty in patch size. Since η = 0 is sensitive to noise, we choose a small value η > 0 to illustrate. (D) The counting strategy uses zero drift, so that the forager leaves after a set amount of food rewards (E) The robust counting strategy uses α < 0 so that there is still drift towards the threshold. Each plot shows the patch decision variable along with the time-dependent patch decision threshold that changes with receipt of food reward due to updates of energy estimate.