Mutational robustness can facilitate adaptation

Abstract

Robustness seems to be the opposite of evolvability. If phenotypes are robust against mutation, we might expect that a population will have difficulty adapting to an environmental change, as several studies have suggested. However, other studies contend that robust organisms are more adaptable. A quantitative understanding of the relationship between robustness and evolvability will help resolve these conflicting reports and will clarify outstanding problems in molecular and experimental evolution, evolutionary developmental biology and protein engineering. Here we demonstrate, using a general population genetics model, that mutational robustness can either impede or facilitate adaptation, depending on the population size, the mutation rate and the structure of the fitness landscape. In particular, neutral diversity in a robust population can accelerate adaptation as long as the number of phenotypes accessible to an individual by mutation is smaller than the total number of phenotypes in the fitness landscape. These results provide a quantitative resolution to a significant ambiguity in evolutionary theory.

FIG. 1. Illustration of Genotype-Phenotype Model

A schematic representation of the genotype-phenotype map used in our analysis. Each circle corresponds to a genotype; colors denote phenotypes. The model parameter q quantifies robustness: a proportion q of mutations are neutral (solid lines), and the remaining mutations are non-neutral (dotted lines). A non-neutral mutation changes an individual’s phenotype to one of the K accessible alternatives that form the individual’s phenotypic neighborhood. When K is smaller than the total number of alternative phenotypes in the landscape, P, then individuals may have different phenotypic neighborhoods. The central pair of adjacent genotypes shown here express the same phenotype, but they have different phenotypic neighborhoods.

FIG. 2. Robustness and Adaptation Time

The relationship between robustness, q, and the average waiting time before the arrival of a specific beneficial mutation, for three fitness landscapes. Points show the means of 10,000 replicate Monte Carlo simulations, and lines show our analytic predictions (see Box 1 and SI sec. 1). When all possible phenotypes in the landscape are directly accessible by a mutation from any genotype (i.e. when K = P), robustness always inhibits adaptation (red curve). However, when phenotypic neighborhoods are small (i.e. when K<P), neutral mutations have epistatic consequences and the resulting relationship between robustness and adaptation time is non-monotonic: adaptation is most rapid at intermediate levels of robustness. N = 10,000, μ =0.001, P = 100.

FIG. 3. Robustness and Diversity

The relationship between robustness, q, and the diversity of phenotypes produced by mutation in each generation, for two fitness landscapes. Points show the means of 100,000 replicate simulations; arrows depict slopes calculated analytically (see SI sec. 2). As these results demonstrate, an increase in robustness can increase phenotypic diversity, but only when the level of robustness, q, is small, and the number of phenotypes accessible from a single genotype, K, is less than the total number of phenotypes in the landscape, P. Parameters values: N = 10,000, μ =0.001.