| Abstract: |
This paper describes the coevolution of phenotypes in a
community comprising a population of predators and of prey.
It is shown that evolutionary cycling is a likely outcome of
the process. The dynamical systems on which this description
is based are constructed from microscopic stochastic birth
and death events, together with a process of random
mutation. Births and deaths are caused in part by
phenotype-dependent interactions between predator and prey
individuals and therefore generate 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
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 requires an intermediate harvesting
efficiency 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 contemporary focus on
evolutionary equilibria, and argues for an extension to a
dynamical framework for describing the asymptotic states of
evolution.
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