On the application of statistical physics to evolutionary biology Journal Article

Author(s): Barton, Nicholas H; Coe, Jason B
Article Title: On the application of statistical physics to evolutionary biology
Affiliation IST Austria
Abstract: There is a close analogy between statistical thermodynamics and the evolution of allele frequencies under mutation, selection and random drift. Wright's formula for the stationary distribution of allele frequencies is analogous to the Boltzmann distribution in statistical physics. Population size, 2N, plays the role of the inverse temperature, 1/kT, and determines the magnitude of random fluctuations. Log mean fitness, View the MathML source, tends to increase under selection, and is analogous to a (negative) energy; a potential function, U, increases under mutation in a similar way. An entropy, SH, can be defined which measures the deviation from the distribution of allele frequencies expected under random drift alone; the sum View the MathML source gives a free fitness that increases as the population evolves towards its stationary distribution. Usually, we observe the distribution of a few quantitative traits that depend on the frequencies of very many alleles. The mean and variance of such traits are analogous to observable quantities in statistical thermodynamics. Thus, we can define an entropy, SΩ, which measures the volume of allele frequency space that is consistent with the observed trait distribution. The stationary distribution of the traits is View the MathML source; this applies with arbitrary epistasis and dominance. The entropies SΩ, SH are distinct, but converge when there are so many alleles that traits fluctuate close to their expectations. Populations tend to evolve towards states that can be realised in many ways (i.e., large SΩ), which may lead to a substantial drop below the adaptive peak; we illustrate this point with a simple model of genetic redundancy. This analogy with statistical thermodynamics brings together previous ideas in a general framework, and justifies a maximum entropy approximation to the dynamics of quantitative traits.
Keywords: Animals; Selection, Genetic; Models, Genetic; Gene Frequency; Models, Statistical; Entropy; Thermodynamics; Evolution
Journal Title: Journal of Theoretical Biology
Volume: 259
Issue 2
ISSN: 0022-5193
Publisher: Elsevier  
Date Published: 2009-07-21
Start Page: 317
End Page: 324
Sponsor: This work was supported by a Royal Society/Wolfson Award, and by grants EP/T11753/01, EP/C546318/01 from the EPSRC.
DOI: 10.1016/j.jtbi.2009.03.019
Notes: We are grateful to M. Cates, H.P. de Vladar and G. Sella, and to two anonymous referees, for their helpful comments.
Open access: yes (repository)
IST Austria Authors
  1. Nick Barton
    252 Barton