Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations. (7th May 2016) - Ferretti, Luca; Schmiegelt, Benjamin; Weinreich, Daniel; Yamauchi, Atsushi; Kobayashi, Yutaka; Tajima, Fumio; Achaz, Guillaume
Abstract: Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, simple measures of their structure are used as statistics in empirical applications. Epistasis is one of the most relevant features of fitness landscapes. Here we propose a new natural measure of the amount of epistasis based on the correlation of fitness effects of mutations. This measure has a natural interpretation, captures well the interaction between mutations and can be obtained analytically for most landscape models. We discuss how this measure is related to previous measures of epistasis (number of peaks, roughness/slope, fraction of sign epistasis, Fourier–Walsh spectrum) and how it can be easily extended to landscapes with missing data or with fitness ranks only. Furthermore, the dependence of the correlation of fitness effects on mutational distance contains interesting information about the patterns of epistasis. This dependence can be used to uncover the amount and nature of epistatic interactions in a landscape or to discriminate between different landscape models. Abstract : Highlights: The correlation of fitness effects is a natural measure of local epistasis. Decay of correlations with genetic distance depends on the structure of interactions. This measure assigns more importance to epistatic interactions involving many loci. Mean correlation obtained analytically for most fitness landscape models. Correlation of fitness effects can be measured for landscapes with partial data.