title: Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.
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.
authors: Evolution Paris-Seine (UMR 7138) and Atelier de Bio-Informatique, UPMC, Paris, France; SMILE, CIRB (UMR 7241), Collège de France, Paris, France; The Pirbright Institute, Woking, United Kingdom. Electronic address: luca.ferretti@gmail.com.
authors: Luca
authors: L
authors: Ferretti
authors: Institute for Theoretical Physics, University of Cologne, Germany.
authors: Benjamin
authors: B
authors: Schmiegelt
authors: Ecology and Evolutionary Biology, Brown University, Providence, USA.
authors: Daniel
authors: D
authors: Weinreich
authors: Center for Ecological Research, Kyoto University, Japan.
authors: Atsushi
authors: A
authors: Yamauchi
authors: Kochi University of Technology, Japan.
authors: Yutaka
authors: Y
authors: Kobayashi
authors: Department of Biological Sciences, University of Tokyo, Japan.
authors: Fumio
authors: F
authors: Tajima
authors: Evolution Paris-Seine (UMR 7138) and Atelier de Bio-Informatique, UPMC, Paris, France; SMILE, CIRB (UMR 7241), Collège de France, Paris, France. Electronic address: guillaume.achaz@upmc.fr.
authors: Guillaume
authors: G
authors: Achaz
mesh_terms: D004843:Epistasis, Genetic; D005838:Genotype; D008957:Models, Genetic; D009154:Mutation
keywords: Epistasis; Fitness; Mutations; Ruggedness