On the number of stable equilibria in a one-locus, multi-allelic system

It is known that in the evolution of a one-locus, multi-allelic system, the fitness increases and the system always approaches a stable equilibrium point (except for degenerate cases). However, there may be several such stable points and various results, assertions and conjectures exist in the literature concerning the number of these points. Here we present counter examples to some of these claims and give a proof of a result of some importance when new alleles are being introduced.

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