Epistasis between beneficial mutations and the phenotype-to-fitness Map for a ssDNA virus

Abstract

Epistatic interactions between genes and individual mutations are major determinants of the evolutionary properties of genetic systems and have therefore been well documented, but few quantitative data exist on epistatic interactions between beneficial mutations, presumably because such mutations are so much rarer than deleterious ones. We explored epistasis for beneficial mutations by constructing genotypes with pairs of mutations that had been previously identified as beneficial to the ssDNA bacteriophage ID11 and by measuring the effects of these mutations alone and in combination. We constructed 18 of the 36 possible double mutants for the nine available beneficial mutations. We found that epistatic interactions between beneficial mutations were all antagonistic-the effects of the double mutations were less than the sums of the effects of their component single mutations. We found a number of cases of decompensatory interactions, an extreme form of antagonistic epistasis in which the second mutation is actually deleterious in the presence of the first. In the vast majority of cases, recombination uniting two beneficial mutations into the same genome would not be favored by selection, as the recombinant could not outcompete its constituent single mutations. In an attempt to understand these results, we developed a simple model in which the phenotypic effects of mutations are completely additive and epistatic interactions arise as a result of the form of the phenotype-to-fitness mapping. We found that a model with an intermediate phenotypic optimum and additive phenotypic effects provided a good explanation for our data and the observed patterns of epistatic interactions.

Figure 1. Universal antagonistic epistasis for beneficial mutations.

The fitness of double mutant ID11 phage expected on the basis of addition of the effects of the two mutations is plotted against the observed effects on the doubles mutants. Additive effects would fall on the diagonal, synergistic effects would fall above the diagonal, and antagonistic effects would fall below the diagonal. Effects are given in units of doublings per hour.

Figure 2. Evidence for decompensatory epistasis.

The grid shows the fitnesses of the wild type, single mutants, and double mutants. Empty cells represent the double mutants that were not constructed. Red indicates that the average fitness of the double mutant is lower than the average fitness conferred by its two constituent single mutations. Blue indicates that its fitness is higher than that of either single mutant, and purple indicates that it is between the fitnesses of the two single mutants. A “*” in a red box indicates the double mutation confers a fitness significantly lower than that conferred by one single mutation, and a “**” indicates that the double mutation confers a fitness significantly lower than that conferred by either of its single mutations. A “*” in a blue box indicates that the double mutation confers a fitness significantly higher than that conferred by either constituent single mutation.

Figure 3. The phenotype-to-fitness map.

The plot shows the fit of our model for the phenotype-to-fitness map. The model assumes a gamma curve for the relationship between fitness and phenotype. Phenotypic effects were assumed to be additive and epistasis for fitness to arise through the shape of the curve. The variance of the normal error was estimated to be . gives the coefficient of determination. The value is based on an test comparing our model to a model assuming that single- and double-mutant fitnesses are independent of each other. For these data, . We rescaled fitness by substracting rather than the fitness of the wild type to avoid negative values.

Figure 4. Comparison between the gamma model (left) and the model of Martin et al. (right).

The plots show the predicted distributions of the deviations from additivity (; Equation 1) based on simulations under the two models. The observed values are plotted as triangles (Table 3). The gamma model fits the data better by approximately 12 log likelihoods but requires the estimation of 12 more parameters. The Akaike Information Criterion (AIC) scores of the two models are therefore similar, indicating that the two explain the data equally well.