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.
Highlights
A recent paper by Novak and Barton (2017) raises one of the main questions of population genetics right in the title: ”When does frequency-independent selection maintain genetic variation?” They note that, while the answer is generally assumed to be ”never” for constant selection acting on an idealized haploid population, basically only the cases of no recombination and of no selection have been solved and corroborate this claim
We determine the conditions under which monomorphism are stable, which is in turn used to give an upper bound for the number of stable hyperbolic monomorphic equilibria
It is easy to see that each monomorphism is an equilibrium for (1)
Summary
A recent paper by Novak and Barton (2017) raises one of the main questions of population genetics right in the title: ”When does frequency-independent selection maintain genetic variation?” They note that, while the answer is generally assumed to be ”never” for constant selection acting on an idealized haploid population, basically only the cases of no recombination and of no selection have been solved and corroborate this claim. We state and prove that no isolated equilibrium exists if the numbers of alleles at the two loci are unequal. The characterization of internal equilibria given by Lemma 2 yields necessary conditions for the existence of equilibria with an equal number of alleles present.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
