Phenotype-environment correlations in longitudinal twin models

Abstract

Gene-environment correlation (rGE) exists both within and between families. Between families, accumulating rGE has been used to explain dramatic changes in phenotypic means over time. The Dickens and Flynn model of increases in cognitive ability over generational time, for example, suggests that small changes in phenotype can lead to subsequent reallocation of environmental resources. This process sets up a reciprocal feedback loop between phenotype and environment, producing accumulating rGE that can cause large changes in the mean of ability, even though ability remains highly heritable in cross-sectional data. We report simulations suggesting that similar processes may operate within twin and sibling pairs. Especially in dizygotic twins and siblings, small differences in phenotype can become associated with reallocations of environmental resources within families. We show that phenotype-environment effects can account for age-related increases in rGE, rapid differentiation of siblings raised together, and widely reported increases in the heritability of behavior during childhood and adolescence.

Figure 1

Simulated within-family phenotype–environment effect model. X, simulated phenotypic twin score; A^b, between-family genetic effect; E^b, between-family environmental effect; $A_i^{\mathrm{w}}$, within-family genetic effect; $E_i^{\mathrm{w}}$, within-family environmental effect; b_PE, phenotype–environmental effect of low (0.10) or moderate (0.40) value. A^b and $A_i^{\mathrm{w}}$ variances on the left-hand side of the slash (/) specify MZ twin variances and DZ variances are on the right-hand side.

Figure 2

Misspecified correlated classical genetic (A), shared environmental (C), and nonshared environmental (E) values (ACE) factor model fit to the simulated five occasion data sets. X_i, simulated phenotypic twin score across five measurement occasions; A^b, between-family genetic effect; E^b, between-family environmental effect; $A_i^{\mathrm{w}}$, within-family genetic effect; $E_i^{\mathrm{w}}$, within-family environmental effect. Although not shown, A^b and A^w variance estimates in the dizygotic (DZ) twins equal one-half the A^b variance of the monozygotic (MZ) twins. E^b and $E_i^{\mathrm{w}}$ variance estimates were equal between MZ and DZ twins. The covariance matrix for the A^b components and the $A_i^{\mathrm{w}}$ components are equivalent. $A_i^{\mathrm{w}}$ is estimated only in the DZ twins (no within-family genetic variation in the MZ twins).

Figure 3

Phenotypic monozygotic (MZ) and dizygotic (DZ) mean twin pair score differences over the five simulated occasions for low (0.10) and moderate (0.40) phenotype–environment effects.

Figure 4

Monozygotic (MZ) and dizygotic (DZ) interclass correlation coefficients across the five simulated occasions for low (0.10) and moderate (0.40) phenotype–environment effects.