Sit-and-wait versus active-search hunting: A behavioral ecological model of optimal search mode

•We model the behavioral ecology of search mode for randomly moving predator and prey.•Active-search is favored at low prey movement velocity, ambush at high prey velocity.•Sit-and-wait mode is favored if predator movement is energetically costly.•Ambush is favored if faster predator velocity alerts prey or impedes their detection.•Optimal predator velocity in active-search mode balances costs against prey movement.

Drawing on Skellam׳s (1958) work on sampling animal populations using transects, we derive a behavioral ecological model of the choice between sit-and-wait and active-search hunting. Using simple, biologically based assumptions about the characteristics of predator and prey, we show how an empirically definable parameter space favoring active-search hunting expands as: (1) the average rate of movement of prey decreases, or (2) the energetic costs of hunter locomotion decline. The same parameter space narrows as: (3) prey skittishness increases as a function of a hunter׳s velocity, or (4) prey become less detectable as a function of a hunter׳s velocity. Under either search tactic, encounter rate increases as a function of increasing prey velocity and increasing detection zone radius. Additionally, we investigate the roles of habitat heterogeneity and spatial auto-correlation or grouping of prey on the optimal search mode of a hunter, finding that habitat heterogeneity has the potential to complicate application of the model to some empirical examples, while the effects of prey grouping lead to relatively similar model outcomes. As predicted by the model, the introduction of the horse to the Great Plains and the introduction of the snowmobile to Arctic foraging communities decreased the metabolic costs of active-search and led to a change in normative hunting strategies that favored active-search in place of sit-and-wait hunting.