Dynamics and fate of beneficial mutations under lineage contamination by linked deleterious mutations

Abstract

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldanes application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly-arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly-arising beneficial mutation as a multitype branching process; this approach allows us to account for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination. We first study the lineage contamination phenomenon in isolation, deriving extinction times and probabilities of beneficial lineages. We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that the survival probability of beneficial mutations is simply Haldanes classical formula multiplied by the correction factor [Formula], where U is deleterious mutation rate, [Formula] is mean selective advantage of beneficial mutations,{kappa} [isin] (1,{varepsilon} ], and{varepsilon} = 2 - e-1. We also find there exists a genomic deleterious mutation rate, [Formula], that maximizes the rate of production of surviving beneficial mutations, and that [Formula]. Both of these results, and others, are curiously independent of the fitness effects of deleterious mutations. We derive critical mutation rates above which: 1) lineage contamination alleviates competition among beneficial mutations, and 2) the adaptive substitution process all but shuts down.