2019/09/23 by Maxime Berger, Berger, Maxime
Biochemistry, Genetics and Molecular Biology · Social Sciences · Mathematics · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1909.10422
We propose a new definition for the error threshold of a population evolving\nthrough mutation and selection. We compute the correction term due to the\nfiniteness of the population by estimating the lifetime of master sequences.\nOur technique consists in bounding from above and below the number of master\nsequences in the Moran model, by birth and death chains. The expectation of\nthis lifetime is then computed with the help of explicit formulas which are in\nturn expanded with Laplace method. The first term after \ln(\σ)/\ℓ is\ncomputed, it scales as 1/\√(\ℓ m), where \ℓ is the genome size and\nm is the number of individuals in the population.\n