Abstract
We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let V(g) be the genic variance of the trait and C(L) be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (V(g), C(L)) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.
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Selected References
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- Bodmer W. F., Felsenstein J. Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics. 1967 Oct;57(2):237–265. doi: 10.1093/genetics/57.2.237. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bulmer M. G. Linkage disequilibrium and genetic variability. Genet Res. 1974 Jun;23(3):281–289. doi: 10.1017/s0016672300014920. [DOI] [PubMed] [Google Scholar]
- Bürger R. Predictions of the dynamics of a polygenic character under directional selection. J Theor Biol. 1993 Jun 21;162(4):487–513. doi: 10.1006/jtbi.1993.1101. [DOI] [PubMed] [Google Scholar]
- GIBSON J. B., THODAY J. M. EFFECTS OF DISRUPTIVE SELECTION. VIII. IMPOSED QUASI-RANDOM MATING. Heredity (Edinb) 1963 Nov;18:513–524. doi: 10.1038/hdy.1963.56. [DOI] [PubMed] [Google Scholar]
- Gavrilets S., Hastings A. Maintenance of genetic variability under strong stabilizing selection: a two-locus model. Genetics. 1993 May;134(1):377–386. doi: 10.1093/genetics/134.1.377. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Gibson J. B., Bradley B. P. Stabilising selection in constant and fluctuating environments. Heredity (Edinb) 1974 Dec;33(3):293–302. doi: 10.1038/hdy.1974.95. [DOI] [PubMed] [Google Scholar]
- Hastings A. Monotonic change of the mean phenotype in two-locus models. Genetics. 1987 Nov;117(3):583–585. doi: 10.1093/genetics/117.3.583. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Karlin S., Feldman M. W. Linkage and selection: two locus symmetric viability model. Theor Popul Biol. 1970 May;1(1):39–71. doi: 10.1016/0040-5809(70)90041-9. [DOI] [PubMed] [Google Scholar]
- Lande R. Isolation by distance in a quantitative trait. Genetics. 1991 Jun;128(2):443–452. doi: 10.1093/genetics/128.2.443. [DOI] [PMC free article] [PubMed] [Google Scholar]
- SCHARLOO W. THE EFFECT OF DISRUPTIVE AND STABILIZING SELECTION ON THE EXPRESSION OF A CUBITUS INTERRUPTUS MUTANT IN DROSOPHILA. Genetics. 1964 Oct;50:553–562. doi: 10.1093/genetics/50.4.553. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Scharloo W., Hoogmoed M. S., Kuile A. T. Stabilizing and disruptive selection on a mutant character in Drosophila. I. The phenotypic variance and its components. Genetics. 1967 Aug;56(4):709–726. doi: 10.1093/genetics/56.4.709. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Turelli M. Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theor Popul Biol. 1984 Apr;25(2):138–193. doi: 10.1016/0040-5809(84)90017-0. [DOI] [PubMed] [Google Scholar]
- Wagner G. P. Coevolution of functionally constrained characters: prerequisites for adaptive versatility. Biosystems. 1984;17(1):51–55. doi: 10.1016/0303-2647(84)90015-7. [DOI] [PubMed] [Google Scholar]