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

Theoretical Population Biology
Martin Pontz, M W Feldman

Abstract

In the evolutionary biology literature, it is generally assumed that for deterministic frequency-independent haploid selection models, no polymorphic equilibrium can be stable in the absence of variation-generating mechanisms such as mutation. However, mathematical analyses that corroborate this claim are scarce and almost always depend upon additional assumptions. Using ideas from game theory, we show that a monomorphism is a global attractor if one of its alleles dominates all other alleles at its locus. 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 equilibrium points, we resolve the two-locus three-allele case for a fitness scheme formally equivalent to the classical symmetric viability model. We also provide an alternative proof for the two-locus two-allele case.

References

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May 27, 2017·Journal of Mathematical Biology·Martin PontzReinhard Bürger
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Nov 1, 2017·Proceedings of the National Academy of Sciences of the United States of America·Meike J WittmannDmitri A Petrov
Feb 1, 2018·Frontiers in Ecology and Evolution·Dustin Brisson

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