Nonequilibrium Population Dynamics of "Ideal and Free" Prey and Predators

Abstract

Aggregated spatial distributions of prey and predators promote stability of the otherwise unstable Nicholson‐Bailey model. Nevertheless, when both predators and prey choose patches in an ideal free way, sufficiently aggregated distributions will only arise if patch quality (e.g., reflected in prey fecundity) is very heterogeneous. This requirement profoundly limits the possibilities for simultaneous population dynamical and evolutionary stability. However, stability is not necessary for coexistence. Under cyclic or chaotic dynamics, the rate at which species change their distributions becomes important. Here we consider two endpoints of a continuum of rates. The first is “rigid” selection of patch types based on the expected long‐term distribution of conditions. The second is “flexible” selection based on current conditions. We carried out systematic surveys of the population‐level consequences of coevolutionarily stable patch‐selection strategies for different combinations of rigid and flexible strategies of predator and prey. First, if both prey and predators have rigid strategies, the evolutionary end result is either a stable population dynamical equilibrium or diverging cycles eventually leading to extinction. Second, for the case with rigid prey and flexible predators, the persistence boundary in parameter space is shifted from the boundaries obtained for rigid predators. The mechanism underlying persistence is different in that the flexible strategies of the predators destabilize the equilibrium, while the evolutionary response of the rigid prey leads to reduced cycles. Third, if both prey and predators are flexible, simulations lead either to chaotic fluctuations or to extinction (but not to stable equilibria, nor to limit cycles), and the conditions for coexistence are much wider than those under rigid patch selection. These simulations suggest that information constraints on adaptive patch choice have a major impact on predator‐prey persistence under nonequilibrium conditions. We discuss how these predictions can be tested by field observations on expansions and contractions in dietary range (or habitat range) in relation to population fluctuations.