Adaptive topography of fluctuating selection in a Mendelian population

• Published in: Journal of evolutionary biology Vol. 21; no. 4; pp. 1096 - 1105
• Main Author: LANDE, R
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01-07-2008; Blackwell Publishing Ltd
• Subjects: Adaptation, Biological; Animal reproduction; Biological Evolution; diffusion process; environmental variance; Evolutionary biology; expected relative fitness; Haldane-Jayakar model; long-run growth rate; Mathematical models; Models, Biological; Selection, Genetic; stochastic environment; Stochastic models; Theory
• ISSN: 1010-061X; 1420-9101
• DOI: 10.1111/j.1420-9101.2008.01533.x

An adaptive topography is derived for a large randomly mating diploid population under weak density-independent selection in a fluctuating environment. Assuming a stationary distribution of environmental states with no temporal autocorrelation, a diffusion approximation for population size and allele frequency, p, reveals that the expected change in p involves the gradient with respect to p of the stochastic intrinsic rate of increase (the density-independent long-run growth rate), [graphic removed] , where r is the mean Malthusian fitness in the average environment and [graphic removed] is the environmental variance in population growth rate. The expected relative fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its fitness with population growth rate. The influence of fitness correlation between genotypes is illustrated by an analysis of the Haldane-Jayakar model of fluctuating selection on a single diallelic locus, and on two loci with additive effects on a quantitative character.