Nonequilibrium population dynamics of "ideal and free" prey and predators

Aggregated spatial distributions of prey and predators promote stability of the otherwise unstable Nicholson-Bailey model. Nevertheless, when both pre dators and prey choose patches in an ideal free way, sufficiently aggregate d distributions will only arise if patch quality (e.g., reflected in prey f ecundity) is very heterogeneous. This requirement profoundly limits the pos sibilities for simultaneous population dynamical and evolutionary stability . However, stability is not necessary for coexistence. Under cyclic or chao tic dynamics, the rate at which species change their distributions becomes important. Here we consider two endpoints of a continuum of rates. The firs t is "rigid" selection of patch types based on the expected longterm distri bution of conditions. The second is "flexible" selection based on current c onditions. We carried out systematic surveys of the population-level conseq uences of coevolutionarily stable patch-selection strategies for different combinations of rigid and flexible strategies of predator and prey First, i f both prey and predators have rigid strategies, the evolutionary end resul t is either a stable population dynamical equilibrium or diverging cycles e ventually leading to extinction. Second, for the case with rigid prey and f lexible predators, the persistence boundary in parameter space is shifted f rom the boundaries obtained for rigid predators. The mechanism underlying p ersistence is different in that the flexible strategies of the predators de stabilize the equilibrium, while the evolutionary response of the rigid pre y leads to reduced cycles. Third, if both prey and predators are flexible, simulations lead either to chaotic fluctuations or to extinction (but not t o stable equilibria, nor to limit cycles), and the conditions for coexisten ce 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 di scuss how these predictions can be tested by field observations on expansio ns and contractions in dietary range (or habitat range) in relation to popu lation fluctuations.