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Loss of genetic variation in the two-locus multiallelic haploid model

View ORCID ProfileMartin Pontz, View ORCID ProfileMarcus W. Feldman
doi: https://doi.org/10.1101/2020.03.07.981852
Martin Pontz
aDepartment of Mathematics, University of Vienna, Austria
bVienna Graduate School of Population Genetics
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  • For correspondence: martin.pontz@univie.ac.at
Marcus W. Feldman
cDepartment of Biology, Stanford University, Stanford, CA
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Abstract

In the evolutionary biology literature, it is generally assumed that in deterministic haploid selection models, in the absence of variation-generating mechanisms such as mutation, no polymorphic equilibrium can be stable. However, results corroborating this claim are scarce and almost always depend upon additional assumptions. Using ideas from game theory, we establish a condition on the fitness parameters of haplotypes formed by two loci such that a monomorphism is a global attractor. Further, we show that no isolated equilibrium exists, at which an unequal number of alleles from two loci is present. Under the assumption of convergence of trajectories to equilirium points, we settle the two-locus three-allele case for a fitness scheme formally equivalent to the classical symmetric viability model.

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Posted March 08, 2020.
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Loss of genetic variation in the two-locus multiallelic haploid model
Martin Pontz, Marcus W. Feldman
bioRxiv 2020.03.07.981852; doi: https://doi.org/10.1101/2020.03.07.981852
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Loss of genetic variation in the two-locus multiallelic haploid model
Martin Pontz, Marcus W. Feldman
bioRxiv 2020.03.07.981852; doi: https://doi.org/10.1101/2020.03.07.981852

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