To model heterogeneity, we evaluated models in which separate variance components were fitted for males, σg,male 2 and σe,male 2, and females, σg,female 2 and σe,female 2. The variances for each trait measurement and the covariances for trait-measurements between individuals of the same sex follow naturally from the formulae given in the section describing the Base Polygenic Model (above). When individuals i and j were of opposite sexes, we set the covariance to Cov(Yi, Yj) = 2 ϕij . When there was evidence for heterogeneity, we proceeded to consider a series of intermediate models in which heterogeneity was allowed only for environmental effects (i.e., where σg,male 2 = σg,female 2), only for genetic effects (i.e., where σe,male 2 = σe,female 2) or where variability increased uniformly for both genetic and environmental factors (σg,male 2 = k σg,female 2 and σe,male 2 = k σe,female 2, with k ≠ 1).
