Variability in genetic parameters among small populations

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Abstract
SUMMARY: For a model in which quantitative traits are assumed to be determined solely by additive genes at many loci, formulae are developed for the variance among replicated small populations of sizeN, maintained without selection, of the additive genetic variance, heritability, genetic correlations and similar parameters. The base population is assumed to be in linkage equilibrium, but it is argued that most of the variation in the within-line additive variance (VAtat generationt) is due to linkage disequilibrium caused by sampling. Ifis the squared correlation of gene frequencies averaged over all pairs of loci at timet, the coefficient of variation (CV) ofVAtequals, with similar formulae for other parameters.The formulae are evaluated for models of loci distributed uniformly along the chromosome but much of the disequilibrium is due to loci on different chromosomes. For unlinked loci CV(VAt) reaches √4/(3(N)), and for mammalian models, this value is not greatly exceeded. The variance in successive generations has a correlation of at least one-half due to the maintenance of linkage disequilibrium. The magnitude of this variance in parameters and their autocorrelation with time shows that accurate predictions cannot be made about genetic parameters in the base population from single replicate results.