Relation Between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions

Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Her...

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Published in:Bulletin of mathematical biology Vol. 84; no. 8; p. 74
Main Authors: Saona, Raimundo, Kondrashov, Fyodor A., Khudiakova, Ksenia A.
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2022
Springer Nature B.V
Subjects:
Cell Biology
Epistasis
Epistasis, Genetic
Fitness
Genetic Fitness
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
Models, Genetic
Mutation
Original
Original Article
Morse theory
Fitness landscapes
Reciprocal sign epistasis
Multiple peaks
ISSN:0092-8240, 1522-9602, 1522-9602
Online Access:Get full text
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Summary:Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-022-01029-z