Fig. 1: Causes of partner similarity illustrated with path models.

Each panel includes two observed, focal phenotypes (rectangles denoted \(P\)), which belong to the two members of a partnership (\(m\) and \(p\)). \(A\), \(C\), and \(E\) refer to additive genetic (red), sibling-shared environmental (blue) and non-shared environmental influences (yellow) on the phenotype, respectively, whereas the different path coefficients (e.g., \(a\), \(c\), and \(e\)) refer to their effects. For simplicity’s sake, we assume no correlations between genetic and environmental influences, but this can be added to the models when relevant (see also Fig. 5). The copath (the arrowless path denoted \(\mu\)) denotes assortative mating on the two connected variables, which results in covariance without affecting variances. a Direct assortative mating: Here, partners are assorting directly on the focal phenotype, \({{\rm{Cov}}}\left({P}_{m},{P}_{p}\right)=\mu {\left({a}^{2}+{c}^{2}+{e}^{2}\right)}^{2}\). b Indirect assortative mating: here, the effects of \(A\), \(C\), and \(E\) on factors that are assorted upon (a sorting factor, denoted \(S\)) are allowed to differ from their respective effects on the focal phenotype, \({{\rm{Cov}}}\left({P}_{m},{P}_{p}\right)=\mu {\left(a\widetilde{a}+c\widetilde{c}+e\widetilde{e}\right)}^{2}\). c Convergence: here, partners become more similar over time, either due to mutual influence (denoted \(x\)) or exposure to similar environments (denoted \({e}_{2}\)), \({{\rm{Cov}}}\left({P}_{m2},{P}_{p2}\right)=2\left({\sigma }_{{P}_{1}}^{2}{bx}\right)+r{e}_{2}^{2}\), where \({\sigma }_{{P}_{1}}^{2}\) refers to the phenotypic variance prior to partner formation. d Inbreeding: here, the two partner’s genetic effects are correlated, \({{\rm{Cov}}}\left({P}_{m},{P}_{p}\right)=r{a}^{2}\). e Social stratification: Here, the two partner’s sibling-shared environmental effects are correlated, \({{\rm{Cov}}}\left({P}_{m},{P}_{p}\right)=r{c}^{2}\).