, Volume 128, Issue 3, pp 781-798
Date: 22 May 2007

A New Method for the Solution of Models of Biological Evolution: Derivation of Exact Steady-State Distributions

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Abstract

We investigate well-known models of biological evolution and address the open problem of how construct a correct continuous analog of mutations in discrete sequence space. We deal with models where the fitness is a function of a Hamming distance from the reference sequence. The mutation-selection master equation in the discrete sequence space is replaced by a Hamilton-Jacobi equation for the logarithm of relative frequencies of different sequences. The steady-state distribution, mean fitness and the variance of fitness are derived. All our results are asymptotic in the large genome limit. A variety of important biological and biochemical models can be solved by this new approach.

PACS numbers: 87.10.+e, 87.15.Aa, 87.23.Kg, 02.50.-r