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Evolution with state-dependent mutations. (English) Zbl 0862.90142
Summary: Recent evolutionary models have introduced “small mutation rates” as a way of refining predictions of long-run behavior. We show that this refinement effect can only be obtained by restrictions on how the magnitude of the effect of mutation on evolution varies across states of the system. In particular, given any model of the effect of mutations, any invariant distribution of the “mutationless” process is close to an invariant distribution of the process with appropriately chosen small mutation rates.

MSC:
91A20 Multistage and repeated games
92D15 Problems related to evolution
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