Fisher's geometric model of adaptation meets the functional synthesis: data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space.

The functional synthesis uses experimental methods from molecular biology, biochemistry and structural biology to decompose evolutionarily important mutations into their more proximal mechanistic determinants. However these methods are technically challenging and expensive. Noting strong formal parallels between R.A. Fisher's geometric model of adaptation and a recent model for the phenotypic basis of protein evolution, we sought to use the former to make inferences into the latter using data on pairwise fitness epistasis between mutations. We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects. We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets. This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.