2019/09/23 by Maxime Berger, Berger, Maxime
Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1909.10422
arxiv created 2019/09/23 · arxiv updated 2019/09/24
We propose a new definition for the error threshold of a population evolving through mutation and selection. We compute the correction term due to the finiteness of the population by estimating the lifetime of master sequences. Our technique consists in bounding from above and below the number of master sequences in the Moran model, by birth and death chains. The expectation of this lifetime is then computed with the help of explicit formulas which are in turn expanded with Laplace method. The first term after ln(σ)/ℓ is computed, it scales as 1/√(ℓ m), where ℓ is the genome size and m is the number of individuals in the population.