Turelli, Michael; Barton, Nick HISTA
Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations.
Theoretical Population Biology
We thank R. Burger, J. A. Coyne, W. G. Hill, A. A. Hoffmann, J. H. Gillespie, M. Slatkin, T. Nagylaki and Z.-B. Zeng for helpful discussions and comments on earlier drafts. Our research is supported by grants from the National Science Foundation (BSR-8866548), the Science and Engineering Research Council, and the Institute of Theoretical Dynamics at UCD.
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Turelli M, Barton NH. Dynamics of polygenic characters under selection. Theoretical Population Biology. 1990;38(1):1-57. doi:10.1016/0040-5809(90)90002-D
Turelli, M., & Barton, N. H. (1990). Dynamics of polygenic characters under selection. Theoretical Population Biology. Academic Press. https://doi.org/10.1016/0040-5809(90)90002-D
Turelli, Michael, and Nicholas H Barton. “Dynamics of Polygenic Characters under Selection.” Theoretical Population Biology. Academic Press, 1990. https://doi.org/10.1016/0040-5809(90)90002-D.
M. Turelli and N. H. Barton, “Dynamics of polygenic characters under selection,” Theoretical Population Biology, vol. 38, no. 1. Academic Press, pp. 1–57, 1990.
Turelli M, Barton NH. 1990. Dynamics of polygenic characters under selection. Theoretical Population Biology. 38(1), 1–57.
Turelli, Michael, and Nicholas H. Barton. “Dynamics of Polygenic Characters under Selection.” Theoretical Population Biology, vol. 38, no. 1, Academic Press, 1990, pp. 1–57, doi:10.1016/0040-5809(90)90002-D.
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