Environment determines epistatic patterns for a ssDNA virus

Abstract

Despite the accumulation of substantial quantities of information about epistatic interactions among both deleterious and beneficial mutations in a wide array of experimental systems, neither consistent patterns nor causal explanations for these interactions have yet emerged. Furthermore, the effects of mutations depend on the environment in which they are characterized, implying that the environment may also influence epistatic interactions. Recent work with beneficial mutations for the single-stranded DNA bacteriophage ID11 demonstrated that interactions between pairs of mutations could be understood by means of a simple model that assumes that mutations have additive phenotypic effects and that epistasis arises through a nonlinear phenotype-fitness map with a single intermediate optimum. To determine whether such a model could also explain changes in epistatic patterns associated with changes in environment, we measured epistatic interactions for these same mutations under conditions for which we expected to find the wild-type ID11 at different distances from its phenotypic optimum by assaying fitnesses at three different temperatures: 33°, 37°, and 41°. Epistasis was present and negative under all conditions, but became more pronounced as temperature increased. We found that the additive-phenotypes model explained these patterns as changes in the parameters of the phenotype-fitness map, but that a model that additionally allows the phenotypes to vary across temperatures performed significantly better. Our results show that ostensibly complex patterns of fitness effects and epistasis across environments can be explained by assuming a simple structure for the genotype-phenotype relationship.

Keywords: bacteriophage; beneficial mutation; epistasis.

Figure 1

Fitness effects increased with temperature. The dashed lines designate the mean fitness effects at each temperature. The fitness of the wild-type genotype, ID11, declined with increasing temperature (Table 2, Table 3, and Table 4), while the average benefit of the mutations increased. Note that the rank order of the genotypes changes across temperatures. Values are given in units of population doublings per hour. Error bars designate plus or minus one standard error. The letters correspond to the mutational identities described in Table 1.

Figure 2

As fitness-effect sizes increased with temperature, epistasis became more negative. (A) Fitness effects changed from predominantly negative to entirely positive as the temperature increased from 33° to 41°. The dashed line distinguishes deleterious from beneficial fitness effects. Fitnesses were measured as population doublings per hour. (B) Epistasis became more negative as temperature increased from 33° to 41°. The dashed line indicates additivity of mutational effects. Deviations from additivity were calculated according to Equation 2 and are given in units of doublings per hour. Values for the same mutant are connected by solid lines.

Figure 3

Epistasis was predominantly negative and antagonistic. Negative epistasis dominated at all temperatures, and the average magnitude of the deviation from additivity increased with increasing temperature. Most pairs of mutations showed antagonistic epistasis at 37° and 41° but showed synergistic epistasis at 33°.

Figure 4

Fitness landscapes show that sign epistasis was most common in the original environment (37°). The plots show the two possible mutational pathways linking the wild-type ID11 to each double mutant. Single mutations are listed below each plot with the higher-fitness mutant above the lower-fitness mutant. Paths shown as dashed lines indicate the presence of sign epistasis. Fitness values are shown in units of doublings per hour.

Figure 5

The phenotype–fitness maps for three temperatures with constant phenotypes across temperatures. The G1 model assumes a single phenotype for each genotype with a gamma phenotype–fitness map that changes with temperature. The overall fit of the model was R² = 0.51, and we were able to reject a null model, assuming that fitnesses are normally distributed with different means for each temperature by means of a randomization test (P < 0.01). Note that at 33°, all of the singles were to the right of the peak and at 41°, they were all to the left of the peak.

Figure 6

The phenotype–fitness maps for three temperatures with independent phenotypes for each temperature. The G3 model assumes that each temperature has its own gamma phenotype–fitness map and phenotypes. The overall fit of the model was R² = 0.81, and we were able to reject the G1 model in favor of the G3 model with P = 0.05 by means of parametric bootstrapping.