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. Haldane's 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. Our approach accounts 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 dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when U * s b ; where U is deleterious mutation rate and s b is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by $ 1 2 U=s b : We then put the lineage 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 never zero but is depressed below classical predictions by a factor bounded from below by e 2eU= s b ; where s b is mean selective advantage of beneficial mutations, and e ¼ 1 2 e 21 % 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.

Interference Effects of Deleterious and Beneficial Mutations in Large Asexual Populations

“…As a result, the large population again enters the sequential fixation regime where clonal interference is absent. This effect has been recently shown by Pénisson et al (2017) when the beneficial and deleterious effects are nearly equal, and here we have provided a demonstration of the same in the limit…”

“…Thus, when µ < λ, the fixation probability is 2s b (on replacing i by its average µ) and zero otherwise. For moderately sized deleterious effect, this transition has been observed, mainly numerically, in previous work (Johnson and Barton, 2002;Pénisson et al, 2017), while here we have shown it analytically using the explicit expression (13) for the fixation probability.…”

“…However, the difference is quite small, and as discussed in Appendix C and shown in the inset of Figure 2 also shows that the upper bound (10) grossly overestimates the total fixation probability (13) for high mutation rate. As discussed ear-lier, the upper bound captures the effect of the deleterious mutations that the beneficial mutant inherits from the genetic background on which it arose (Charlesworth, 1994), but ignores the mutations accumulated by the beneficial mutant during evolution (Pénisson et al, 2017). The latter effect is taken care of by the last term on the RHS of (13) which is negative since the error function is an increasing function.…”

Imposed mutational meltdown as an antiviral strategy

“…One cluster of mutations in the polymerase subunit PA was associated with the subcellular localization of viral RdRp components, and two of these RdRp mutations conferred resistance to favipiravir in IAV-infected cells (Goldhill et al 2018). Nonetheless, under high concentrations of favipiravir, the Bank et al study observed no mutational escape, consistent with the idea that even in the presence of newly arising beneficial resistance mutations, the linked deleterious load under strong mutation pressure can be simply too great to enable significant net adaptation (Pénnison et al 2017), again emphasizing the potential advantage of such a genome-wide target size.…”

Considering mutational meltdown as a potential SARS-CoV-2 treatment strategy

“…Also working in IAV, Ormond et al (2017) examined the combined effect of favipiravir with oseltamivir, a widely-used treatment with well-studied resistance mutations. A similar mutational meltdown outcome was observed, with the selective sweeps of oseltamivir-resistant mutations appearing to actually speed population decline, owing to the resulting hitchhiking of linked deleterious variants in the viral population (and see the related work of Pénnison et al 2017).…”