Counterintuitive prey strategies against predators with finite budgets: protection heterogeneity among sites matters more than their number

Combining the search and pursuit aspects of predator-prey interactions into a single game, where the payoff to the Searcher (predator) is the probability of finding and capturing the Hider (prey) within a fixed number of searches was proposed by Gal and Casas (J. R. Soc. Interface 11, 20140062 (doi:10.1098/rsif.2014.0062)). Subsequent models allowed the predator to continue its search (in another 'round') if the prey was found but escaped the chase. However, it is unrealistic to allow this pattern of prey relocation to go on forever, so here we introduce a limit of the total number of searches, in all 'rounds', that the predator can carry out. We show how habitat structural complexity affects the mean time until capture: the quality of the location with the lowest capture probability matters more than the number of hiding locations. Moreover, we observed that the parameter space defined by the capture probabilities in each location and the budget of the predator can be divided into distinct domains, defining whether the prey ought to play with pure or mixed hiding strategies.