Statistical mechanics and the evolution of polygenic quantitative traits

N.H. Barton, H. De Vladar, Genetics 181 (2009) 997–1011.

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Journal Article | Published | English
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Abstract
The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.
Publishing Year
Date Published
2009-03-01
Journal Title
Genetics
Acknowledgement
N.B. was supported by the Engineering and Physical Sciences Research Council (GR/T11753 and GR/T19537) and by the Royal Society. We are grateful to Ellen Baake for helping to initiate this project and for her comments on this manuscript. We also thank Michael Turelli for his comments on the manuscript and I. Pen for discussions and support in this project. This project was a result of a collaboration supported by the European Science Foundation grant “Integrating population genetics and conservation biology.”
Volume
181
Issue
3
Page
997 - 1011
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Cite this

Barton NH, De Vladar H. Statistical mechanics and the evolution of polygenic quantitative traits. Genetics. 2009;181(3):997-1011. doi:10.1534/genetics.108.099309
Barton, N. H., & De Vladar, H. (2009). Statistical mechanics and the evolution of polygenic quantitative traits. Genetics, 181(3), 997–1011. https://doi.org/10.1534/genetics.108.099309
Barton, Nicholas H, and Harold De Vladar. “Statistical Mechanics and the Evolution of Polygenic Quantitative Traits.” Genetics 181, no. 3 (2009): 997–1011. https://doi.org/10.1534/genetics.108.099309.
N. H. Barton and H. De Vladar, “Statistical mechanics and the evolution of polygenic quantitative traits,” Genetics, vol. 181, no. 3, pp. 997–1011, 2009.
Barton NH, De Vladar H. 2009. Statistical mechanics and the evolution of polygenic quantitative traits. Genetics. 181(3), 997–1011.
Barton, Nicholas H., and Harold De Vladar. “Statistical Mechanics and the Evolution of Polygenic Quantitative Traits.” Genetics, vol. 181, no. 3, Genetics Society of America, 2009, pp. 997–1011, doi:10.1534/genetics.108.099309.

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