Expansion of error thresholds for the Moran model

Maxime Berger (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We propose new definitions 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/ is computed, it depends on the chosen criterion.

Mots clés: Markov chain; phase transition; genetics Mathematics Subject Classification: 60J10; 92D10

Domaines: Probabilités [math.PR]; Génétique des populations [q-bio.PE]

Maxime Berger. Expansion of error thresholds for the Moran model. 2020. ⟨hal-02981523⟩