Effects of new mutations on fitness: insights from models and data

Abstract

The rates and properties of new mutations affecting fitness have implications for a number of outstanding questions in evolutionary biology. Obtaining estimates of mutation rates and effects has historically been challenging, and little theory has been available for predicting the distribution of fitness effects (DFE); however, there have been recent advances on both fronts. Extreme-value theory predicts the DFE of beneficial mutations in well-adapted populations, while phenotypic fitness landscape models make predictions for the DFE of all mutations as a function of the initial level of adaptation and the strength of stabilizing selection on traits underlying fitness. Direct experimental evidence confirms predictions on the DFE of beneficial mutations and favors distributions that are roughly exponential but bounded on the right. A growing number of studies infer the DFE using genomic patterns of polymorphism and divergence, recovering a wide range of DFE. Future work should be aimed at identifying factors driving the observed variation in the DFE. We emphasize the need for further theory explicitly incorporating the effects of partial pleiotropy and heterogeneity in the environment on the expected DFE.

Keywords: distribution of fitness effects; experimental evolution; mutation; mutational landscape models; population genomics.

Figure 1

Hypothetical whole distributions of fitness effects. The whole distribution of fitness effect can comprise, in principle, a continuum of fitness effects ranging from lethal to strongly or mildly deleterious to beneficial. Three distributions are pictured here that comprise different amounts of deleterious and beneficial mutations. The dotted and dashed distributions are arbitrarily chosen, while the continuous distribution (solid gray) is one of the type predicted by a Fisherian fitness landscape (a displaced and reflected Γ distribution).

Figure 2

Alternative distribution of beneficial fitness effects as predicted by extreme-value theory (EVT). All distributions displayed here are specific cases of a generalized Pareto distribution that differ by their shape. A shape of 1 corresponds to an exponential distribution (gray), a shape parameter >1 will yield a DFE with a much heavier tail (so-called Frechet domain, in blue). Alternatively, a shape parameter <1 will yield distributions that decay much more rapidly than the exponential (so-called Weibull domain), and the beneficial mutations cannot exceed a maximum beneficial effect.

Figure 3

Expected amounts of polymorphism and divergence contributed by nonsynonymous mutations as a function of the scaled selection coefficient of a mutation. The expected amount of polymorphism in a genomic region can be summarized as the total number of polymorphic sites for both nonsynonymous (P_n) and synonymous sites (P_s, lower horizontal line), and the number of rare mutations using, for example, the number of singletons (mutations seen only once) at nonsynonymous sites (S_n). Amounts of divergence are quantified using the number of divergent synonymous (D_s, upper horizontal line) and nonsynonymous sites (D_n) relative to an out-group sequence. For a given mutation rate and effective population size, sample size n of chromosomes resequenced and size of a genomic fragment population genetic theory and diffusion results on the Wright-Fisher model can be used to compute these quantities as a function of the scaled mutation effect S of a nonsynonymous mutation. Here for illustration, we assume 1000 synonymous neutral sites, 3000 nonsynonymous nucleotide sites with a scaled mutation rate θ = 4Nμ = 0.01, a scaled divergence to the out-group of λ = 0.05, and a sample comprising n = 10 chromosomes.

Figure 4

An example of site frequency spectrum (SFS) data in chimpanzee (Pan troglodytes troglodytes). Data comprising the resequencing of the exome of 12 individuals (n = 24 chromosomes) is redrawn using the data of Ref. . Circle size is proportional to counts of polymorphism. Synonymous counts are in gray (upper set of L-shaped dots) and nonsynonymous counts in black (lower set of L-shaped dots).