Monotonicity of fitness landscapes and mutation rate control

Belavkin, Roman V. and Channon, Alastair and Aston, Elizabeth and Aston, John and Krašovec, Rok and Knight, Christopher G. (2016) Monotonicity of fitness landscapes and mutation rate control. Journal of Mathematical Biology, 73 (6). pp. 1491-1524. ISSN 0303-6812

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Abstract

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.

Item Type: Article
Additional Information: Published online: 12 April 2016
Research Areas: A. > School of Science and Technology > Computer Science > Artificial Intelligence group
A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19476
Notes on copyright: © The Author(s) 2016. Open access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)
Useful Links:
Depositing User: Roman Belavkin
Date Deposited: 22 Apr 2016 09:34
Last Modified: 07 Sep 2018 20:25
URI: http://eprints.mdx.ac.uk/id/eprint/19476

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