Selection limits to adaptive walks on correlated landscapes

Adaptation depends critically on the effects of new mutations and their dependency on the genetic background in which they occur. These two factors can be summarized by the fitness landscape. However, it would require testing all mutations in all backgrounds, making the definition and analysis of fitness landscapes mostly inaccessible. Instead of postulating a particular fitness landscape, we address this problem by considering general classes of landscapes and calculating an upper limit for the time it takes for a population to reach a fitness peak, circumventing the need to have full knowledge about the fitness landscape. We analyze populations in the weak-mutation regime and characterize the conditions that enable them to quickly reach the fitness peak as a function of the number of sites under selection. We show that for additive landscapes there is a critical selection strength enabling populations to reach high-fitness genotypes, regardless of the distribution of effects. This threshold scales with the number of sites under selection, effectively setting a limit to adaptation, and results from the inevitable increase in deleterious mutational pressure as the population adapts in a space of discrete genotypes. Furthermore, we show that for the class of all unimodal landscapes this condition is sufficient but not necessary for rapid adaptation, as in some highly epistatic landscapes the critical strength does not depend on the number of sites under selection; effectively removing this barrier to adaptation.