Table 1.

Details of simulation models for scenarios given in Figure 1

	Simulation model
Scenario	X	Y	E
(a)	$X|G\sim N({\mu }_X+\alpha G,{\sigma }_X^2)$	$Y|G\sim N({\mu }_Y+\beta G,{\sigma }_Y^2)$
(b)	$X|G\sim N({\mu }_X+\alpha G,{\sigma }_X^2)$	$Y|X\sim N({\mu }_Y+\gamma X,{\sigma }_Y^2)$
(c)	$X|Y\sim N({\mu }_X+\gamma Y,{\sigma }_X^2)$	$Y|G\sim N({\mu }_Y+\beta G,{\sigma }_Y^2)$
(d)	$X|G\sim N({\mu }_X+\alpha G,{\sigma }_X^2)$	$Y|G,X\sim N({\mu }_Y+\beta G+\gamma X,{\sigma }_Y^2)$
(e)	$X|G,Y\sim N({\mu }_X+\alpha G+\delta Y,{\sigma }_X^2)$	$Y|G\sim N({\mu }_Y+\beta G,{\sigma }_Y^2)$
(f)	$X|G,Y\sim N({\mu }_X+\alpha G+\delta Y,{\sigma }_X^2)$	$Y\sim N({\mu }_Y,{\sigma }_Y^2)$
(g)	$X\sim N({\mu }_X,{\sigma }_X^2)$	$Y|G,X\sim N({\mu }_Y+\beta G+\gamma X,{\sigma }_Y^2)$
(h)	$X|G,E\sim N({\mu }_X+\alpha G+\zeta E,{\sigma }_X^2)$	$Y|G,E\sim N({\mu }_Y+\beta G+\zeta E,{\sigma }_Y^2)$	$E\sim N(0,{\sigma }_E^2)$
(i)	$X|G,E\sim N({\mu }_X+\alpha G+\zeta E,{\sigma }_X^2)$	$Y|X,E\sim N({\mu }_Y+\gamma X+\zeta E,{\sigma }_Y^2)$	$E\sim N(0,{\sigma }_E^2)$
(j)	$X|Y,E\sim N({\mu }_X+\delta Y+\zeta E,{\sigma }_X^2)$	$Y|G,E\sim N({\mu }_Y+\beta G+\zeta E,{\sigma }_Y^2)$	$E\sim N(0,{\sigma }_E^2)$
(k)	$X|G,E\sim N({\mu }_X+\alpha G+\zeta E,{\sigma }_X^2)$	$Y|E\sim N({\mu }_Y+\zeta E,{\sigma }_Y^2)$	$E\sim N(0,{\sigma }_E^2)$
(l)	$X|E\sim N({\mu }_X+\zeta E,{\sigma }_X^2)$	$Y|G,E\sim N({\mu }_Y+\beta G+\zeta E,{\sigma }_Y^2)$	$E\sim N(0,{\sigma }_E^2)$

The default parameter values are α= 1, β= 1, δ= 1, ${\mu }_X$= 10, ${\mu }_Y$= 10, γ= 1, ζ= 1, ${\sigma }_X$= 0.3, ${\sigma }_Y$= 0.3, ${\sigma }_E$= 0.3. G is coded as (0, 1, 2) according to the number of minor alleles present at the SNP