  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.
