Originally published as Genetics Published Articles Ahead of Print on April 16, 2005.

Genetics, Vol. 170, 941-954, June 2005, Copyright © 2005
doi:10.1534/genetics.104.028233

Effective Size of a Fluctuating Age-Structured Population

Steinar Engen^*, Russell Lande^,1 and Bernt-Erik Saether

^* Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Department of Zoology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Department of Biology, University of California, San Diego, California 92093

¹ Corresponding author: Department of Biology, University of California, 9500 Gilman Dr., San Diego, CA 92093-0116.
E-mail: rlande{at}ucsd.edu

Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.

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