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Stochasticity in the adaptive dynamics of evolution: the bare bones
Fima C Klebaner1, Serik Sagitov, Vladimir A Vatutin
1Department of Mathematical Sciences, Monash University, Melbourne, Australia.
Abstract:
First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics.
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