The stability of symmetrical solutions to polygenic models

N.H. Barton, M. Shpak, Theoretical Population Biology 57 (2000) 249–263.

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Abstract
Analysis of multilocus evolution is usually intractable for more than n ~ 10 genes, because the frequencies of very large numbers of genotypes must be followed. An exact analysis of up to n ~ 100 loci is feasible for a symmetrical model, in which a set of unlinked loci segregate for two alleles (labeled '0' and '1') with interchangeable effects on fitness. All haploid genotypes with the same number of 1 alleles can then remain equally frequent. However, such a symmetrical solution may be unstable: for example, under stabilizing selection, populations tend to fix any one genotype which approaches the optimum. Here, we show how the 2' x 2' stability matrix can be decomposed into a set of matrices, each no larger than n x n. This allows the stability of symmetrical solutions to be determined. We apply the method to stabilizing and disruptive selection in a single deme and to selection against heterozygotes in a linear cline. (C) 2000 Academic Press.
Publishing Year
Date Published
2000-05-01
Journal Title
Theoretical Population Biology
Volume
57
Issue
3
Page
249 - 263
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Barton NH, Shpak M. The stability of symmetrical solutions to polygenic models. Theoretical Population Biology. 2000;57(3):249-263. doi:10.1006/tpbi.2000.1455
Barton, N. H., & Shpak, M. (2000). The stability of symmetrical solutions to polygenic models. Theoretical Population Biology, 57(3), 249–263. https://doi.org/10.1006/tpbi.2000.1455
Barton, Nicholas H, and Max Shpak. “The Stability of Symmetrical Solutions to Polygenic Models.” Theoretical Population Biology 57, no. 3 (2000): 249–63. https://doi.org/10.1006/tpbi.2000.1455.
N. H. Barton and M. Shpak, “The stability of symmetrical solutions to polygenic models,” Theoretical Population Biology, vol. 57, no. 3, pp. 249–263, 2000.
Barton NH, Shpak M. 2000. The stability of symmetrical solutions to polygenic models. Theoretical Population Biology. 57(3), 249–263.
Barton, Nicholas H., and Max Shpak. “The Stability of Symmetrical Solutions to Polygenic Models.” Theoretical Population Biology, vol. 57, no. 3, Academic Press, 2000, pp. 249–63, doi:10.1006/tpbi.2000.1455.

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