A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

Journal of Mathematical Biology
Kristan A Schneider

Abstract

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkag...Continue Reading

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Citations

Oct 19, 2007·Journal of Mathematical Biology·Michel DurinxGéza Meszéna
Aug 27, 2009·Journal of Mathematical Biology·Kristan Alexander Schneider
Feb 9, 2012·Journal of Mathematical Biology·Claus RuefflerTom J M Van Dooren
Apr 13, 2011·PloS One·Kristan A Schneider, Stephan Peischl
Oct 10, 2013·Evolution; International Journal of Organic Evolution·Benjamin C Haller, Andrew P Hendry
Mar 17, 2009·Theoretical Population Biology·Carlo Matessi, Kristan A Schneider
Aug 30, 2008·Theoretical Population Biology·Kristan A Schneider
Jan 8, 2008·Journal of Theoretical Biology·Stephan Peischl, Reinhard Bürger
Feb 6, 2007·Theoretical Population Biology·Kristan A Schneider
Dec 5, 2008·Evolution; International Journal of Organic Evolution·Michel Durinx, Tom J M Van Dooren
Apr 1, 2008·Evolution; International Journal of Organic Evolution·Peter A AbramsGary Kim
Sep 29, 2009·Evolution; International Journal of Organic Evolution·Stephan Peischl, Kristan A Schneider
Jan 24, 2007·Evolution; International Journal of Organic Evolution·Reinhard BürgerMartin Willensdorfer
Sep 30, 2019·Theoretical Population Biology·Reinhard Bürger
Nov 23, 2020·Theoretical Population Biology·Martin Pontz, Marcus W Feldman
Jun 22, 2005·Theoretical Population Biology·Kristan A Schneider

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