The statistical mechanics of a polygenic character under stabilizing selection mutation and drift Journal Article


Author(s): de Vladar, Harold P; Barton, Nicholas H
Article Title: The statistical mechanics of a polygenic character under stabilizing selection mutation and drift
Affiliation IST Austria
Abstract: By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.
Keywords: Entropy; Evolution; statistical mechanics; Epistasis; Genetic Variance; quantitative genetics
Journal Title: Journal of the Royal Society Interface
Volume: 8
Issue 58
ISSN: 1742-5662
Publisher: Royal Society of London  
Date Published: 2011-05-01
Start Page: 720
End Page: 739
Sponsor: This project was supported by the ERC-2009-AdG Grant for project 250152.
URL:
DOI: 10.1098/rsif.2010.0438
Notes: The authors would like to thank J. Polechova and F. Palero for comments and discussions.
Open access: yes (repository)