We use the theory of adaptive dynamics to construct and analyse a generic example of cycling evolution with alternating levels of polymorphism. A monomorphic population evolves towards larger trait values until it reaches a so-called evolutionary branching point. Disruptive selection at the branching point splits the population into two strategies. In the dimorphic population the strategies undergo parallel coevolution towards smaller trait values. Finally one of the two strategies goes extinct, and the remaining single strategy evolves upwards again to the branching point. The reversal of the direction of evolution is brought about by the changing level of polymorphism. Extinction is deterministic, i.e., it occurs inevitably and always at the same trait values; which of the two strategies goes extinct is, however, random. The present model is discussed in relation to other mechanisms for evolutionary cycles involving branching and extinction.
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Paper provided by International Institute for Applied Systems Analysis in its series Working Papers with number
ir00030.
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