Genetic Variance Component Estimation in a Nested Mating Design with Positive Assortative Mating, and Application to Maize

Negative estimation of genetic variance components can arise in a nested mating design. This may be due to inaccurate estimates, experimental problems, sampling error, or failure of the assumptions of the genetic or statistical models. We examined the effect of assortative mating on male and female variance components (σ 2 M and σ 2 F , respectively) in a nested mating design. Two correlation coefficients were introduced to quantify the effect of assortative mating: the correlation coefficient between females mated to the same male ( r ) and the correlation coefficient between male and female ( r ′). Under positive assortative mating, additive variance is systematically overestimated and dominance variance is underestimated. If there is a correlation among females mated to a male but no correlation between male and female ( r ′ = 0, r ≠ 0), the additive variance is overestimated by 4 r σ 2 F and nonadditive variance is underestimated by 8 r σ 2 F . To investigate the presence of assortative mating in a nested design, expressions of correlations among parents were given as a function of the estimated components of variance and of the type of gene action. Correlations among parents were estimated utilizing experimental data for various traits in maize ( Zea mays L.) from which negative estimates of dominance had been obtained. Estimates of r were positive and high for earliness traits indicating assortative mating relative to earliness, which may in part explain negative dominance variance estimates. However, correcting variance components estimates is difficult when genetic variation of the trait is not strictly additive.