Simple sign epistasis and evolutionary detours in fitness landscapes

Original Abstract

In epistatic fitness landscapes, the fitness effect of a mutation depends on the genetic background and may even switch between deleterious and beneficial depending on the presence of another mutation. Epistatic interactions may cause both mutations to change the sign of each other's fitness effects (reciprocal sign epistasis) or only one mutation to do so (simple sign epistasis). Both these forms of epistasis influence evolutionary trajectories. While reciprocal sign epistasis has been associated with multi-peaked landscapes and their ruggedness, the role and relative frequency of simple sign epistasis in fitness landscapes have not been systematically investigated. Here, we prove that the presence of simple sign epistasis is associated with evolutionary detours, i.e., indirect, longer fitness-increasing paths to fitness peaks that include back-mutations. We also show that in experimentally resolved, weakly epistatic landscapes, simple sign epistasis occurs much more frequently than reciprocal sign epistasis. This result is consistent with the theoretical predictions we derive for most landscape models, with the exception of the block model and of landscapes dominated by pairwise allelic incompatibilities, such as RNA stability landscapes. Our results suggest that detours represent a general feature of evolutionary trajectories in weakly epistatic landscapes.