Fish and game: a game theoretic approach to habitat selection by predators and prey*

Abstract

Given a choice between habitats differing only in food availability, prey are known to select the habitat providing the highest energetic return. They do so in a frequency‐dependent manner, accounting for the reduction in food availability caused by the presence of other individuals; this results in the well‐known ‘Ideal Free Distribution’, an equilibrium solution to a spatial game. When habitats also differ in predation risk due, for example, to different predator densities, prey also appear able to take this into account. However, in most theory (and most experiments) the predation risk levels in the available habitats are assumed to be fixed. Here we ask what will happen if predators are able to adjust their distribution in response to the habitat choice decisions of their prey, i.e. we model a generalized habitat selection game between predators and prey. We first develop a basic model which captures the essence of the problem, and then expand it to include risk dilution and interference among predators. The model produces several new insights, notably that, in the absence of interference effects, the density of prey in a habitat is determined solely by the inherent‘ riskiness’of that habitat (a habitat measure independent of predator density, which might reflect cover or light levels, for example) and is unaffected by habitat productivity (a measure of the food resource available to the prey). When interference exists between predators, ptey density is also determined by habitat productivity but to a lesser extent than by riskiness. Consequently, prey may not respond significantly to changes in relative food resource availability among habitats if their predators are also free to choose the habitat which maximizes their expected fitness. We consider briefly the potential applications of game theory to diel vertical migration and other fish predator‐prey scenarios.