We also considered the possibility of X-linked or mitochondrial inheritance. X-linked inheritance can produce differences in the total variance between males and females, and either of these phenomena can generate sex-dependent covariances between relatives (for example, they can lead to differences between mother–daughter correlations and father–son correlations). We compared models with heterogeneity to models with an X-linked variance component, σx 2, and to models with a mitochondrial genetic variance component, σm 2. In models with an X-linked variance component, Var(Yi) = σg 2 + σe 2 + 2 ϕii(X) σx 2 and Cov(Yi, Yj) = 2 ϕij σg 2 + 2 ϕij(X) σx 2, in which calculation of the kinship coefficient for X-linked genes is detailed at the end of the Materials and Methods section. In models with a mitochondrial variance component, Var(Yi) = σg 2 + σe 2 + σm 2 and Cov(Yi, Yj) = 2 ϕij σg 2 + M(i,j) σm 2. The indicator function M(i,j) takes a value = 1 if individuals i and j are related through their maternal lineages, and 0 otherwise.
