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1 August 2007 EXPECTED RELATIVE FITNESS AND THE ADAPTIVE TOPOGRAPHY OF FLUCTUATING SELECTION
Russell Lande
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Abstract

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, 𝑧̄. The expected evolution of p or 𝑧̄ is a product of genetic variability and the gradient of the long-run growth rate of the population, 𝑟̃, with respect to p or 𝑧̄. This shows that the expected evolution maximizes 𝑟̃, the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, 𝑟̃ as a function of p or 𝑧̄ represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of 𝑟̃. Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.

Russell Lande "EXPECTED RELATIVE FITNESS AND THE ADAPTIVE TOPOGRAPHY OF FLUCTUATING SELECTION," Evolution 61(8), 1835-1846, (1 August 2007). https://doi.org/10.1111/j.1558-5646.2007.00170.x
Received: 29 January 2007; Accepted: 27 April 2007; Published: 1 August 2007
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KEYWORDS
diffusion
environmental variance
expected selection gradient
frequency dependence
long-run growth rate
Malthusian fitness
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