The Selection Mutation Equation

Hofbauer, J. (1985). The Selection Mutation Equation. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-85-002

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Abstract

Fisher's Fundamental Theorem of Natural Selection is extended to the selection mutation model with mutation rates epsilon_ij=epsilon_i, i.e. depending only on the target gene, by constructing a simple Lyapunov function. For other mutation rates stable limit cycles are possible. A basic tool is the description of some of the dynamical models as gradients with respect to a non-Riemann metric.

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