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J Theor Biol. 2016 May 7;396:132-43. doi: 10.1016/j.jtbi.2016.01.037. Epub 2016 Feb 20.

Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.

Author information

1
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.
2
Institute for Theoretical Physics, University of Cologne, Germany.
3
Ecology and Evolutionary Biology, Brown University, Providence, USA.
4
Center for Ecological Research, Kyoto University, Japan.
5
Kochi University of Technology, Japan.
6
Department of Biological Sciences, University of Tokyo, Japan.
7
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.

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.

KEYWORDS:

Epistasis; Fitness; Mutations; Ruggedness

PMID:
26854875
DOI:
10.1016/j.jtbi.2016.01.037
[Indexed for MEDLINE]

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