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Measuring epistasis in fitness landscapes: the correlation of fitness effects of mutations

Luca Ferretti, Benjamin Schmiegelt, Daniel Weinreich, Atsushi Yamauchi, Yutaka Kobayashi, Fumio Tajima, Guillaume Achaz
doi: https://doi.org/10.1101/042010
Luca Ferretti
aEvolution Paris-Seine (UMR 7138) and Atelier de Bio-Informatique, UPMC, Paris; SMILE, CIRB (UMR 7241); Collège de France, Paris, France.
bThe Pirbright Institute, Woking, United Kingdom.
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Benjamin Schmiegelt
cInstitute for Theoretical Physics, University of Cologne, Germany.
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Daniel Weinreich
dEcology and Evolutionary Biology, Brown University, Providence, USA.
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Atsushi Yamauchi
eCenter for Ecological Research, Kyoto University, Japan.
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Yutaka Kobayashi
fKochi University of Technology, Japan.
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Fumio Tajima
gDepartment of Biological Sciences, University of Tokyo, Japan.
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Guillaume Achaz
aEvolution Paris-Seine (UMR 7138) and Atelier de Bio-Informatique, UPMC, Paris; SMILE, CIRB (UMR 7241); Collège de France, Paris, France.
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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.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted March 01, 2016.
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Measuring epistasis in fitness landscapes: the correlation of fitness effects of mutations
Luca Ferretti, Benjamin Schmiegelt, Daniel Weinreich, Atsushi Yamauchi, Yutaka Kobayashi, Fumio Tajima, Guillaume Achaz
bioRxiv 042010; doi: https://doi.org/10.1101/042010
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Measuring epistasis in fitness landscapes: the correlation of fitness effects of mutations
Luca Ferretti, Benjamin Schmiegelt, Daniel Weinreich, Atsushi Yamauchi, Yutaka Kobayashi, Fumio Tajima, Guillaume Achaz
bioRxiv 042010; doi: https://doi.org/10.1101/042010

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