Modifiers of mutation rate: a general reduction principle |
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| Authors: | U Liberman M W Feldman |
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| Affiliation: | 1. Columbia University, New York, NY, USA;2. Fourier Genetics, Austin, TX, USA;1. School of Environment and Science, Griffith University, Gold Coast, Qld 4215, Australia;2. Centre for Applications in Natural Resource Mathematics, School of Mathematics and Physics, The University of Queensland, St Lucia, Qld 4072, Australia;3. Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Woodstock Road, Oxford OX2 6GG, UK;1. Department of Political Economy and Moral Science, University of Arizona, United States;2. Department of Philosophy and Religion, Northeastern University, United States;1. Department of Biomedical Engineering, Faculty of Engineering, Okayama University of Science, 1-1 Ridai-Cho Kita-Ku, Okayama 700-0005, Japan;2. Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-Naka Kita-Ku, Okayama 700-8530, Japan;3. Department of Mechanical Engineering, Faculty of Engineering, Okayama University, 3-1-1 Tsushima-Naka Kita-Ku, Okayama 700-8530, Japan |
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| Abstract: | A deterministic two-locus population genetic model with random mating is studied. The first locus, with two alleles, is subject to mutation and arbitrary viability selection. The second locus, with an arbitrary number of alleles, controls the mutation at the first locus. A class of viability-analogous Hardy-Weinberg equilibria is analyzed in which the selected gene and the modifier locus are in linkage equilibrium. It is shown that at these equilibria a reduction principle for the success of new mutation-modifying alleles is valid. A new allele at the modifier locus succeeds if its marginal average mutation rate is less than the mean mutation rate of the resident modifier allele evaluated at the equilibrium. Internal stability properties of these equilibria are also described. |
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