Capturing the Red Queen using Adaptive Dynamics in a predator-prey coevolution
Chauke, Hlpheka Evans
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In this paper we describe the coevolution of phenotypes in a community of predators and of prey using adaptive dynamics. Evolutionary cycling can be one of the outcome of the process. The Models on which the description is based are formed from microscopic stochastic birth and death events, together with a process of random mutation. Births and deaths, can occur as a results of phenotype-dependent interactions between predator and prey individuals and therefore natural selection can be generated. We demonstrate three outcomes of evolution in this paper. A community may evolve to a state at which the predator becomes extinct, or to one at which the species coexist with constant phenotypic values, or the species may coexist with cyclic changes in phenotypic values. The last outcome corresponds to a Red Queen dynamic, in which the selection pressures arising from the predator-prey interaction cause the species to evolve without ever reaching an equilibrium phenotypic state. The Red Queen dynamic will require an intermediate harvesting effciency of the prey by the predator and suffciently high evolutionary rate constant of the prey, and is complex when the model is made stochastic and phenotypically polymorphic. A cyclic outcome lies outside the contemporary focus on evolutionary equilibria, and argues for an extension to a dynamical framework for describing the asymptotic states of evolution.