EVOLUTIONARY CYCLING IN PREDATOR-PREY INTERACTIONS - POPULATION-DYNAMICS AND THE RED QUEEN

This paper describes the coevolution of phenotypes in a community comp rising a population of predators and of prey. It is shown that evoluti onary cycling is a likely outcome of the process. The dynamical system s on which this description is based are constructed from microscopic stochastic birth and death events, together with a process of random m utation. Births and deaths are caused in part by phenotype-dependent i nteractions between predator and prey individuals and therefore genera te natural selection, Three outcomes of evolution are demonstrated. A community may evolve to a state at which the predator becomes extinct, or to one at which the species coexist with constant phenotypic value s, or the species may coexist with cyclic changes in phenotypic values . The last outcome corresponds to a Red Queen dynamic, in which the se lection pressures arising from the predator-prey interaction cause the species to evolve without ever reaching an equilibrium phenotypic sta te. The Red Queen dynamic requires an intermediate harvesting efficien cy of the prey by the predator and sufficiently high evolutionary rate constant of the prey, and is robust when the model is made stochastic and phenotypically polymorphic. A cyclic outcome lies outside the con temporary focus on evolutionary equilibria, and argues for an extensio n to a dynamical framework for describing the asymptotic states of evo lution. (C) 1995 Academic Press Limited