Selection, mutation, and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically unobserved. Can we understand how the macroscopic observables evolve without following these microscopic processes? This problem has been studied previously by analogy with statistical mechanics: the allele frequency distribution at each time point is approximated by the stationary form, which maximizes entropy. We explore the limitations of this method when mutation is small (4Nμ < 1) so that populations are typically close to fixation, and we extend the theory in this regime to account for changes in mutation strength. We consider a single diallelic locus either under directional selection or with overdominance and then generalize to multiple unlinked biallelic loci with unequal effects. We find that the maximum-entropy approximation is remarkably accurate, even when mutation and selection change rapidly.
1523 - 1548
Bod’ová K, Tkacik G, Barton NH. A general approximation for the dynamics of quantitative traits. Genetics. 2016;202(4):1523-1548. doi:10.1534/genetics.115.184127
Bod’ová, K., Tkacik, G., & Barton, N. H. (2016). A general approximation for the dynamics of quantitative traits. Genetics, 202(4), 1523–1548. https://doi.org/10.1534/genetics.115.184127
Bod’ová, Katarína, Gasper Tkacik, and Nicholas H Barton. “A General Approximation for the Dynamics of Quantitative Traits.” Genetics 202, no. 4 (2016): 1523–48. https://doi.org/10.1534/genetics.115.184127.
K. Bod’ová, G. Tkacik, and N. H. Barton, “A general approximation for the dynamics of quantitative traits,” Genetics, vol. 202, no. 4, pp. 1523–1548, 2016.
Bod’ová K, Tkacik G, Barton NH. 2016. A general approximation for the dynamics of quantitative traits. Genetics. 202(4), 1523–1548.
Bod’ová, Katarína, et al. “A General Approximation for the Dynamics of Quantitative Traits.” Genetics, vol. 202, no. 4, Genetics Society of America, 2016, pp. 1523–48, doi:10.1534/genetics.115.184127.