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Probability and time to fixation of an evolving sequence

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  • Santiago, Enrique

Abstract

The propagation of a sequence in a population is traced using a branching process model of Poisson distributions. The sequence, initially inserted in a location of the genome of a single individual, is under selective pressure and can undergo detrimental, beneficial or even neutral mutations that allow for adaptive possibilities in the future. The exact solution for the ultimate probability of fixation (u) of the sequence in this model is a Lambert W function of mutation rates and selective values:u=1+W(−γ⋅e−(γ+β))γ, where γ=1+s−μd−μb, β=2αμb, s is the intrinsic coefficient of selection of the sequence (selective advantage is set by s>0), μd and μb are the deleterious and beneficial rates of mutations that occur in the sequence and α is the effect of beneficial mutations. Predictions are adaptable to a wide range of situations, e.g., fixation of favourable mutations, local mutators or gene duplicates.

Suggested Citation

  • Santiago, Enrique, 2015. "Probability and time to fixation of an evolving sequence," Theoretical Population Biology, Elsevier, vol. 104(C), pages 78-85.
    • Handle: RePEc:eee:thpobi:v:104:y:2015:i:c:p:78-85
    DOI: 10.1016/j.tpb.2015.06.001
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    2. Weissman, Daniel B. & Desai, Michael M. & Fisher, Daniel S. & Feldman, Marcus W., 2009. "The rate at which asexual populations cross fitness valleys," Theoretical Population Biology, Elsevier, vol. 75(4), pages 286-300.
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