Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations

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Abstract
Summary: Models of variability in quantitative traits maintained by a balance between mutation and stabilizing selection are investigated. The effects of mutant alleles are assumed to be additive and to be randomly sampled from a stationary distribution. With a two-allele model the equilibrium genetic variance in an infinite population is independent of the distribution of mutant effects, and dependent only on the total number of mutants appearing per generation. In a finite population, however, both the shape and standard deviation of the distribution of mutant effects are important. The equilibrium variance is lower when most of the mutational variance is contributed by few genes of large effect. Genes of small effect can eventually contribute substantially to the variance with increasing population size (N.) The equilibrium variance can be higher in a finite than an infinite population since near-neutral alleles can drift to intermediate frequencies where selection is weakest. Linkage leads to a reduction in the maintained variance which is small unless linkage is very tight and selection is strong, but the reduction becomes greater with increasingNsince more mutants segregate. A multi-allele model is simulated and it is concluded that the two-allele model gives a good approximation of its behaviour. It is argued that the total number of loci capable of influencing most quantitative traits is large, and that the distribution of mutant effects is highly leptokurtic with the effects of most mutants very small, and such mutants are important in contributing to the maintained variance since selection against them is slight. The weakness of the simple optimum model is discussed in relation to the likely consequences of pleiotropy.