After fitting this base model, we considered refined models including additional variance components to model genetic dominance, σd 2, or the effects of shared sibling environment, σs 2. To model genetic dominance, we let Δij denote the probability that individuals i and j share two alleles identical by descent (IBD), based on their reported relationship (as usual, this quantity was calculated using generalized kinship coefficients [64]). Then we modeled the variance of each trait measurement as Var(Yi) = σg 2 + σe 2 + σd 2 and the covariance between measurements for a pair of individuals as Cov(Yi, Yj) = 2 ϕij σg 2 + Δij σd 2. To model the effects of shared sibling environment, we let Isib(i,j) be an indicator variable with value 1 when individuals i and j are full sibs, and value 0 otherwise. Then we letVar(Yi) = σg 2 + σe 2 + σs 2 and Cov(Yi, Yj) = 2 ϕij σg 2 + Isib(i,j) σs 2. In most datasets, including our own, the two models cannot be distinguished statistically [26]. In fact, because Δij
