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The influence of small population size (N) on the genetic variance within and between randomly bred unselected lines, with selfing permitted, is investigated for a model of a quantitative trait determined by linked genes that show dominance within loci but are additive over loci. Formulae for within-line variance include terms in linkage disequilibrum, which occurs by chance in the lines and these are evaluated in terms of N, map length and gene number. —The expected variance within lines is increased by this disequilibrium, quite substantially if there are many loci, with most of the increase being between or within full-sib families and almost no change expected between half-sib families or in the covariance of offspring and parent. If all loci are unlinked, there is no increase in variance within full-sib families. The variance between lines is little affected by disequilibrum generated by chance.— Expressions for the variance between individuals in heterozygosity over the whole genome are special cases of those for the variance due to linked dominated genes, and formulae are given and evaluated. The coefficient of variation of heterozygosity is at least 1/√3N and can be much higher for species with few chromosomes.

VARIANCE IN QUANTITATIVE TRAITS DUE TO LINKED DOMINANT GENES AND VARIANCE IN HETEROZYGOSITY IN SMALL POPULATIONS