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

International audienceBeneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane’sapplication of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arisingbeneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations andmight further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as amultitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linkeddeleterious mutations, which we call lineage contamination. We first study the lineage-contamination phenomenon in isolation,deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survivalprobability is zero when $U\gtrsim s_b$, where $U$ is deleterious mutation rate and $s_b$ is the selective advantage of the beneficial mutation inquestion, and is otherwise depressed below classical predictions by a factor bounded from below by $\sim 1-U/s_b$. We then put thelineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection.We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is neverzero but is depressed below classical predictions by a factor bounded from below by $e^{-\varepsilon U/ \overline{s}_b}$, where $\overline{s}_b$ is mean selective advantage of beneficial mutations, and $\varepsilon=1-e^{-1}\approx 0.63$. This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or(2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely