Reproductive value and fluctuating selection in an age-structured population.
Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.
Engen
Steinar
S
Centre for Conservation Biology, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway. steinaen@math.ntnu.no
Lande
Russell
R
Saether
Bernt-Erik
BE
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D019143:Evolution, Molecular; D005260:Female; D005298:Fertility / Q000235:genetics; D005787:Gene Frequency; D005828:Genetics, Population; D005838:Genotype; D006801:Humans; D008297:Male; D008957:Models, Genetic; D011156:Population Density; D012098:Reproduction / Q000235:genetics*; D012641:Selection, Genetic; D013997:Time Factors