A maximum principle for the mutation-selection equilibrium of nucleotide sequences

Details A maximum principle for the mutation-selection equilibrium of nucleotide sequences A maximum principle for the mutation-selection equilibrium of nucleotide sequences

2003-03-12

arxiv.org/abs/physics/0303053v2

Bulletin of Mathematical Biology 66 (2004) 397-421

Physics

Biological Physics

19 pages, 4 postscript figures, LaTeX; introduction extended and more detailed explanations added

Scientific paper

10.1016/j.bulm.2003.08.013

We study the equilibrium behaviour of a deterministic four-state mutation-selection model as a model for the evolution of a population of nucleotide sequences in sequence space. The mutation model is the Kimura 3ST mutation scheme, and the selection scheme is assumed to be invariant under permutation of sites. Considering the evolution process both forward and backward in time, we use the ancestral distribution as the stationary state of the backward process to derive an expression for the mutational loss (as the difference between ancestral and population mean fitness), and we prove a maximum principle that determines the population mean fitness in mutation-selection balance.

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