Expectations of means and genetic variances in backcross populations

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Abstract
The genetic variance among F2-derived lines of backcrosses (BCgF2-derived lines) depends on the backcross generation (g), the number of F1 plants crossed and selfed in generations 1 through g, and the number of BCgF2-derived lines evaluated. Additive genetic variance decreases linearly with backcrossing when one BCF1 plant per generation is crossed and selfed. The relationship is curvilinear if more than one BCF1 plant is used; as the number of BCF1 plants increases, additive genetic variance among BC1F2-derived lines approaches that among BC0F2-derived lines. The effect of population size on genetic variance is due both to fixation of alleles in previous generations and to sampling of genotypes in the population being evaluated. Dominance and repulsion linkage can cause small increases in genetic variance from BC0 to BC1.