Table 1.

Parameters in models 0, 1, and 2

Parameter	Interpretation
Y	Phenotypic score
$ϵ$	Residual score
$\mu$	Primary phenotypic assortative mating (AM) copath coefficient; $\frac{cov(Y_p,Y_m)}{V_Y^2}$
F	Family environmental score arising from $Y_{\ast }$ $\to$ $F_o$ vertical transmission (VT)
f	VT path coefficient; the causal effect of $Y_{\ast }$ $\to$ $F_o$
$T_{\ast }$	Polygenic score (PGS) of one of the two transmitted haplotypes
$N{T}_{\ast }$	PGS of one of the two nontransmitted haplotypes
k	Variance of the haplotypic PGS in the base population (before AM or VT). It is a constant that depends on the scaling of the PGS (see Model 1)
g	Increase in the (co)variance of the haplotypic PGS’s under AM
$\delta$	effect of haplotypic PGS on Y
w	Genetic nurture between the PGS and F; $cov(T_{\ast }+N{T}_{\ast },F_{\ast })=cov([N]T_p+[N]T_m,F_o)$
$\mathrm{\Omega }$	Covariance between $Y_{\ast }$ and either of that parent’s haplotypic PGS’s; $cov(Y_{\ast },[N]T_{\ast })$
${\theta }_T$	Covariance between $Y_o$ and both of the transmitted haplotypes; $cov(Y_o,T_m+T_p)$
${\theta }_{\mathit{NT}}$	Covariance between $Y_o$ and both of the nontransmitted haplotypes; $cov(Y_o,N{T}_m+N{T}_p)$
$L{T}_{\ast }$	Latent genetic score (LGS) of one of the two transmitted haplotypes
$LN{T}_{\ast }$	LGS of one of the two nontransmitted haplotypes
j	Variance of the haplotypic LGS in the base population. It is a constant defined analogously to k (see Model 2)
h	Increase in the (co)variance of the haplotypic LGS’s under AM
i	Increase in the covariance between the haplotypic PGS’s and LGS’s under AM
a	Effect of haplotypic LGS on Y
v	Genetic nurture between the LGS and F; $cov(L{T}_{\ast }+LN{T}_{\ast },F_{\ast })=cov(L[N]T_p+L[N]T_m,F_o)$
$\mathrm{\Gamma }$	Covariance between $Y_{\ast }$ and either of that parent’s haplotypic LGS’s; $cov(Y_{\ast },L[N]T_{\ast })$
${\theta }_{\mathit{LT}}$	Covariance between $Y_o$ and the transmitted LGS; $cov(Y_o,L{T}_m+L{T}_p)$
${\theta }_{\mathit{LNT}}$	Covariance between $Y_o$ and the nontransmitted LGS; $cov(Y_o,LN{T}_m+LN{T}_p)$
$V_A$	Full variance due to direct additive genetic effects; $2a^2(j+2h)+2{\delta }^2(k+2g)+8ai\delta$
$V_{A_0}$	full variance due to direct additive genetic effects in base population; $2a^{2}j+2{\delta }^{2}k$
$v+w$	Full genetic nurture (a type of passive G-E covariance)
$V_F$	Full variance due to VT; $2f^2{V}_Y(1+\mu V_Y)$
$V_{ϵ}$	Residual variance not explained by other factors (i.e., unique environmental variance)
$V_Y$	Phenotypic variance; $V_A+V_F+2(av+\delta w)+V_{ϵ}$

Subscripts: m: maternal; p: paternal; o: offspring; $\ast$: m or p; no subscript: m, p, or o