A maximum principle for the mutation-selection equilibrium of nucleotide sequences |
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Authors: | Email author" target="_blank">Tini?GarskeEmail author Uwe?Grimm |
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Institution: | (1) Applied Mathematics Department, Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK |
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Abstract: | We study the equilibriumbehaviour of a deterministic four-statemutation-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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Keywords: | |
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