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Evolution with state-dependent mutations

1994-08, Bergin, James, Lipman, B. L.

Recent evolutionary models have introduced "small mutation rates" as a way of refining predictions of long-run behavior. We show that if mutation rates are allowed to vary across states, then mutations no longer narrow the set of possible preditions. 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.