The Rate of Molecular Evolution When Mutation May Not Be Weak

Abstract

One of the most fundamental rules of molecular evolution is that the rate of neutral evolution equals the mutation rate and is independent of effective population size. This result lies at the heart of the Neutral Theory, and is the basis for numerous analytic approaches that are widely applied to infer the action of natural selection across the genome and through time, and for dating divergence events using the molecular clock. However, this result was derived under the assumption that evolution is strongly mutation-limited, and it has not been known whether it generalizes across the range of mutation pressures or the spectrum of mutation types observed in natural populations. Validated by both simulations and exact computational analyses, we present a direct and transparent theoretical analysis of the Wright-Fisher model of population genetics, which shows that some of the most important rules of molecular evolution are fundamentally changed by considering recurrent mutation's full effect. Surprisingly, the rate of the neutral molecular clock is found to have population-size dependence and to not equal the mutation rate in general. This is because, for increasing values of the population mutation rate parameter (θ), the time spent waiting for mutations quickly becomes smaller than the cumulative time mutants spend segregating before a substitution, resulting in a net deceleration compared to classical theory that depends on the population mutation rate. Furthermore, selection exacerbates this effect such that more adaptive alleles experience a greater deceleration than less adaptive alleles, introducing systematic bias in a wide variety of methods for inferring the strength and direction of natural selection from across-species sequence comparisons. Critically, the classical weak mutation approximation performs well only when θ < 0.1, a threshold that many biological populations seem to exceed.

Substitutions are boring: some arguments about parallel mutations and repetitive DNA

“…Simply, the SSWM model breaks down in the face of high-mutation-rate genetic elements. Other recent theoretical work notes that this breakdown occurs when θ > 0.1 [47], leading to new dynamics such as population-size-dependence of the rate of evolution. Again, estimated average θ for STR mutations is approximately 100 times as large as this threshold ( Figure 1C).…”

Haldane’s Probability of Mutant Survival is Not the Probability of Allele Establishment

“…, P 0,1 , P 0,2 , …). As in de Sanctis et al (2017) and de Koning and de Sanctis (2018), the summation can be truncated at x terms for x when P 0, x falls below some small threshold ( e.g. , 10 −7 ).…”

“…Here we derive establishment properties for arbitrary discretetime Wright-Fisher models. Detailed discussion of efficient computational solutions to the discrete-time model can be found in Krukov et al (2017); de Sanctis et al (2017); de Koning and de Sanctis (2018).…”

“…We next consider some related arguments by Gillespie (2004), before moving to a diffusion approach and eventually to a direct analysis of the discrete-time Wright-Fisher model (where we are not required to assume weak mutation, weak selection, or large population size). Moving to a full Markov chain treatment is important for validation, and because the cases where establishment are most of interest occur when population mutation rates may be very large and thus could violate assumptions that diffusion approximations usually require (de Koning and de Sanctis 2018). We focus on the general case where mutants may be deleterious, neutral, or advantageous and show that a diffusion approximation to the establishment probability has a pleasing simplicity when defined appropriately.…”

Using the Mutation-Selection Framework to Characterize Selection on Protein Sequences

“…Each of the above expressions relies on the assumption that mutation is weak and selection strong. More complex dynamics arise if these assumptions are relaxed and more sophisticated methods are required for the calculation of fixation probabilities under these conditions [ 13 , 14 ].…”