Sign Epistasis and the Geometry of Interactions

Abstract: Approaches to gene interactions based on sign epistasis have been highly influential in recent time. Sign epistasis is useful for relating local and global properties of fitness landscapes, as well as for analyzing evolutionary trajectories and constraints. The geometric theory of gene interactions, on the other hand, provides complete information on interactions in terms of minimal dependence relations. We propose a new framework that combines aspects of both approaches. In particular, we provide efficient tools for identifying sign epistasis and related order perturbations in large genetic systems, with applications to the malaria-causing parasite Plasmodium vivax. We found that order perturbations beyond sign epistasis are prevalent in the drug-free environment, which agrees well with the observation that reversed evolution back to the ancestral type is difficult. As a theoretical application, we investigate how rank orders of genotypes with respect to fitness relates to additivity.