Multivariate Genetic Analyses of Cognition and Academic Achievement from Two Population Samples of 174,000 and 166,000 School Children

Abstract

The genetic influence on the association between contemporaneously measured intelligence and academic achievement in childhood was examined in nationally representative cohorts from England and The Netherlands using a whole population indirect twin design, including singleton data. We identified 1,056 same-sex (SS) and 495 opposite-sex (OS) twin pairs among 174,098 British 11 year-olds with test scores from 2004, and, 785 SS and 327 OS twin pairs among 120,995 Dutch schoolchildren, aged 8, 10 or 12 years, with assessments from 1994 to 2002. The estimate of intelligence heritability was large in both cohorts, consistent with previous studies (h ² = 0.70 ± 0.14, England; h ² = 0.43 ± 0.28–0.67 ± 0.31, The Netherlands), as was the heritability of academic achievement variables (h ² = 0.51 ± 0.16–0.81 ± 0.16, England; h ² = 0.36 ± 0.27–0.74 ± 0.27, The Netherlands). Additive genetic covariance explained the large majority of the phenotypic correlations between intelligence and academic achievement scores in England, when standardised to a bivariate heritability (Biv h ² = 0.76 ± 0.15–0.88 ± 0.16), and less consistent but often large proportions of the phenotypic correlations in The Netherlands (Biv h ² = 0.33 ± 0.52–1.00 ± 0.43). In the British cohort both nonverbal and verbal reasoning showed very high additive genetic covariance with achievement scores (Biv h ² = 0.94–0.98; Biv h ² = 0.77–1.00 respectively). In The Netherlands, covariance estimates were consistent across age groups. The heritability of intelligence–academic achievement associations in two population cohorts of elementary schoolchildren, using a twin pair extraction method, is at the high end of estimates reported by studies of largely preselected twin samples.

Appendix 1: Univariate and multivariate parameter estimate formulae

(i) The proportions of variance attributed to additive genetic ($\hat{h}^{2}$), shared environment ($\hat{c}^{2}$) and unique environment ($\hat{e}^{2}$) effects in univariate models were estimated for intelligence and academic achievement scores, as:

$$\begin{aligned} \hat{h}^{2} & = 2(\hat{t}_{SS} - \hat{t}_{OS} )/\hat{p} \\ \hat{c}^{2} &= \left[ {\hat{t}_{OS} \left( {1 + \hat{p}} \right) - \hat{t}_{SS} } \right]/\hat{p} \\ \hat{e}^{2} &= 1 - \left( {\hat{c}^{2} + \hat{h}^{2} } \right) \end{aligned}$$

where $\hat{p}$ is the estimated proportion of MZ twins among same sex pairs (Benyamin et al. 2005), and $\hat{t}$ denotes the intra-class correlations from the between and within-pair variances for SS ($\hat{t}_{SS}$) and OS ($\hat{t}_{OS}$) twins respectively. Proportion of variance due to unique variance ($\hat{e}^{2}$) is estimated from deducting the previously estimated parameters ($\hat{h}^{2} + \hat{c}^{2}$) from unity.

(ii) Additive genetic ($\hat{r}_{G}$) and shared ($\hat{r}_{C}$) environmental correlations were estimated using:

$$\begin{aligned} \hat{r}_{G} &= 2\left( {\hat{r}_{12(SS)} - \hat{r}_{12(OS)} } \right)/( {\hat{p}\hat{h}_{1} \hat{h}_{2} })\\ \hat{r}_{C} &= \left[ {\left( {\hat{p} + 1} \right)\hat{r}_{12(OS)} - \hat{r}_{12(SS)} } \right]/( {\hat{p}\hat{c}_{1} \hat{c}_{2} } ) \end{aligned}$$

where $\hat{r}$ is the correlation coefficient between two traits for SS ($\hat{r}_{12(SS)}$) and OS ($\hat{r}_{12(OS)}$) twin pairs respectively, and where $\hat{h}_{1}$and $\hat{h}_{2}$ represent the square roots of the univariate heritability estimates for traits 1 and 2 respectively, and $\hat{c}_{1}$and $\hat{c}_{2}$represent the square roots of the shared environment parameters for traits 1 and 2.

(iii) In models to estimate bivariate heritability (Biv $\hat{h}^{2}$)—that is, the proportion of phenotypic covariance due to additive genetic factors (i.e. the ratio of additive genetic to phenotypic covariance)—and proportions of covariance due to shared (Biv $\hat{c}^{2}$) and unique environmental influence (Biv $\hat{e}^{2}$), the following formulae were used:

$$ \begin{aligned} Biv\hat{h}^{2} & = \left[ {\sqrt {\left( {\hat{h}^{2}_{1} } \right)} \sqrt {\left( {\hat{h}^{2}_{2} } \right)} \hat{r}_{G} } \right]/\hat{r}_{p} \\ Biv\hat{c}^{2} & = \left[ {\sqrt {\left( {\hat{c}^{2}_{1} } \right)} \sqrt {\left( {\hat{c}^{2}_{2} } \right)} \hat{r}_{C} } \right]/\hat{r}_{p} \\ Biv\hat{e}^{2} & = 1 - \left[ {Biv\hat{c}^{2} + Biv\hat{h}^{2} } \right] \end{aligned} $$

where $\hat{r}_{p}$ is the phenotypic correlation between two traits, $\hat{h}^{2}_{1}$ is the heritability estimate for trait 1, $\hat{h}^{2}_{2}$ is the heritability estimate for trait 2, and so on.