Table 1.

Detailed taxonomy of departure decision strategies. Departure strategies and observable trends depend on the environment and task: habitat selection or patch exploitation (see also figure 8). Columns describe the important aspects of the optimal decision strategy for each case, along with key model results.

environment	decision strategy and dependencies	equations	figures
habitat selection
objective: minimize time to find highest yielding habitat
known: resource yield rates of each habitat type
N-habitat types	— depart habitat when likelihood of being in highest yielding habitat falls below a threshold — optimal strategy and arrival time depend on fraction and discriminability of high-yield habitats	N = 2: equation (3.1); N ≥ 3: equation (3.5)	N = 2: figure 2; N ≥ 3: figure 3
continuum of habitat types	— categorize habitats as high or low-yielding and depart habitat if likelihood of a high-yield falls below a threshold — time to identify high-yielding habitat is non-monotonic in departure threshold, and much longer when high-yield patches are rare		figure 5
patch exploitation
objective: maximize mean resource intake rate R over a long time (several patches)
known: initial yield rates of each patch type
1-patch type	— depart when yield rate λ(t) falls to a threshold value λθ — matches MVT except when there are very few chunks per patch, in which case the forager should empty the patch	equation (4.3)	figure 6a
2-patch types: patch type known on arrival	— depart when resource yield rate λj(t) reaches a threshold — represents ‘depletion-dominated’ regime; recovers MVT	equations (4.5) and (4.6)	figure 6b
2-patch types: empty low-yield patch	— wait a time $T_{\theta }$, then depart patch if no resources found; if resources are encountered by $t<T_{\theta }$, use threshold on inferred yield rate to make leaving decision (similar to single-patch-type case) — ‘uncertainty-dominated’ regime deviates from MVT — optimal wait time and departure threshold λθ increase with prevalence of high-yielding patch		figure 6c
2-patch types: both high- and low-yield patches have resources	— decision via threshold on current estimated yield rate $\tilde{\lambda }(t)$; choose optimal threshold λθ that maximizes long-term resource intake rate — optimal return differs from known case given few resources per patch, converges to known patch case when resource density is high — forager stays in low-yield patches too long, leaves high-yield patches too soon when there are few resources per patch (uncertainty-dominated regime)	equation (4.7)	figure 7