Fig. 3: The iAM-ACE model.

The model includes four observed individuals: a set of twins (or siblings) along with their respective partners. Differences in the observed, focal phenotype (denoted \(P\)) are thought to result from additive genetic factors (\(A\), red), sibling-shared environmental factors (\(C\), blue), twin-shared environmental factors (\(T\), purple), and non-shared environmental factors (\(E\), yellow). Their effects on the focal phenotype are denoted \(a\), \(c\), \(t\), and \(e\), respectively. Partners (i.e., Partner 1—Twin 1, and Partner 2—Twin 2) are assorting (\(\mu\)) on a sorting factor (S), which are influenced by the same factors that influence the focal phenotype, albeit with different effects (\(\widetilde{a}\), \(\widetilde{c}\), \(\widetilde{t}\), and \(\widetilde{e}\)). Only the relative importance of \(\widetilde{a}\), \(\widetilde{c}\), \(\widetilde{t}\), and \(\widetilde{e}\) can be estimated, meaning the variance of the sorting factor must be constrained. Additive genetic factors are perfectly correlated across monozygotic twin pairs (\({f}_{{{\rm{MZ}}}}=1\)), whereas for dizygotic twins and full siblings, the correlation is \({f}_{{{\rm{FS}}}}=(1+\mu {\widetilde{a}}^{2})/2\) (assuming intergenerational equilibrium). The correlation in twin-shared environmental factors depend on relation (monozygotic and dizygotic twins: \({r}_{t}=1\), ordinary full siblings: \({r}_{t}=0\)).