Home environments and socioeconomic status (SES) correlate moderately with offspring educational attainment (EA) (r ~ 0.3; Duncan et al., Reference Duncan, Morris and Rodrigues2011). However, as parents both transmit genes and create environments for offspring, these correlations are confounded. Measured environments, such as exposure to books or language in the home that are correlated with attainment (Martin et al., Reference Martin, Hansell, Wainwright, Shekar, Medland, Bates and Wright2009) may, therefore, not be causal (cultural transmission), and instead reflect passive gene-environment correlation (Puglisi et al., Reference Puglisi, Hulme, Hamilton and Snowling2017). This confounding can take on complex, evocative forms such that environments too are heritable, either due to passive parental creation of the environment, or active evocation of the environment by offspring (Plomin, Reference Plomin1994). Here, we utilize recent advances in genetics in the form of polygenic risk scores (PRS) for EA, combined with the well-known process of meiosis in which each parent passes a random 50% of their genome to an offspring (with 50% un-transmitted). This allowed use of the pseudo-control method (Cordell et al., Reference Cordell, Barratt and Clayton2004) to create polygenic scores for parents consisting only of EA-associated alleles they did not transmit to their offspring (Howey, Reference Howey2014), a parental control EA2 risk score: PC_EA PRS. This PC_EA PRS was used in a sample 2,333 genotyped twins and their parents to test for evidence of parenting effects by testing the effect of non-transmitted parental alleles on a high-quality measure of offspring EA, un-confounded by offspring genetics.

Below, we briefly describe the causal ambiguity of observational data, the development of PRS, and the pseudo-control method utilized here to create independent genetic scores for parents and offspring. Following this, we test hypotheses regarding how parenting competence, SES niche-construction, and children's genetic potentials impact on EA.

Background Correlations between parenting and outcomes such as offspring EA are ubiquitous. However, as parents transmit genes and create environments for offspring (Neale & Cardon, Reference Neale and Cardon1992), these correlations are confounded. Even factors often favored on intuitive grounds as causes of cognitive development — such as complexity and number of words spoken in the home environment — may not be causal. For instance, Puglisi et al. (Reference Puglisi, Hulme, Hamilton and Snowling2017) conducted a longitudinal study of children at risk for reading disorder and found that while variation in the home literacy environment was a significant predictor of children's reading and language skills, controlling for maternal language ability removed this effect. While mothers with better language and phonological skills had children with higher reading and language skills, and did predict such factors as storybook exposure, factors such as storybook exposure were not significant predictors of offspring reading ability. By contrast, the study found that direct literacy training (such as phonics) did independently predict acquired reading skill, but was unrelated to maternal language ability. This example exemplifies both the possibility of intervention and the risks of confounding leading to incorrect research conclusions. It also indicates that effects on child outcomes may reach beyond genetic transmission from parents to include factors such as literacy training. These are not direct consequences of parental ability, but are instead factors under at least partial parental control and involve constructing niches for children that include such effective interventions. In this way, they reflect effective parenting competence. This competence may both play an important causal role and itself be heritable. In such cases, not only are genetics transmitted to the child, but their relevant environment, too, is heritable.

Disentangling Causal Effects of Offspring Genetics From Parent Genetics The need to disentangle different forms of transmission and methods to enable such disentanglement has been central to the work of behavior geneticists seeking to understand family and cultural effects (Eaves et al., Reference Eaves, Pourcain, Smith, York and Evans2014). This seminal work proposed statistical controls to disentangle transmission via parent behavior and parent genetics. These designs require the ability to randomize parent genetics with respect to offspring, the classic example being an adoption design. In the conventional adoption design; however, factors such as large sample sizes, random entrance to the study and, most importantly, random allocation of children to adopting homes (Loehlin, Reference Loehlin and Sternberg2000) are seldom possible (Plomin & Loehlin, Reference Plomin and Loehlin1989). Instead, our study uses polygenic scores associated with education attainment, along with the basic biological mechanism of meiosis in which parental gametes (egg and sperm) each contain only a haploid copy of the parental genome to their offspring, with these halves being combined to form the offspring zygote to create a ‘virtual parent’ design.

Independent Assortment and Independence of Transmitted and Non-Transmitted PRS Mendel's second law, the ‘law of independent assortment’, reflects the fact that gamete formation results in a halving of the chromosomal complement, with alleles having a 50% chance of being transmitted to the gamete. Researchers in genetic epidemiology capitalized on this independent assortment to create the concept of a ‘pseudo-control’, consisting of non-transmitted parental alleles. Pseudo controls have been widely used in the study of gene-environment interactions and parent-of-origin effects among factors (Cordell et al., Reference Cordell, Barratt and Clayton2004), and software such as PseudoCons (Howey, Reference Howey2014) exists to readily generate these pseudo-control genomes. Importantly, whereas offspring and parent genotypes share 50% of their DNA, the offspring genotype and pseudo-con or non-transmitted genotype are uncorrelated. Moreover, this pseudo-control genotype, consisting of the non-transmitted parental alleles, can itself be scored using PRS, leading to the creation of uncorrelated offspring- and non-transmitted parental risk scores. In the present method, two PRS are formed: one for the offspring, consisting of the EA-associated alleles they have inherited (EA PRS) and a second parental-control risk score (PC_EA PRS) consisting of the EA-associated alleles in the parental genomes that were not passed on to their offspring. Here, we use these two independent scores to address the following question: To what extent do non-transmitted genetic variants in parents create environments influencing the attainment of their offspring? To implement this design, we used a high-quality measure of attainment and the well-validated PRS for EA (Okbay et al., Reference Okbay, Beauchamp, Fontana, Lee, Pers, Rietveld and Benjamin2016), assessed in 2,335 offspring and their 2,145 parents where both offspring and both parents had been genotyped, and SES recorded for parents, along with a measure of highest educational outcome and a comprehensive seven-hour assessment of EA (terminal high-school core-skills scores) undertaken by the offspring. This allowed computing both the conventional PRS for EA, parental pseudo-control PC_EA PRS, with measured SES and educational outcomes. These data allowed us to test the following four hypotheses: 1. That children's EA PRS is significantly associated with their attainment. 2. That parents’ EA PRS is associated with the SES they attain. 3. That parent SES is associated with offspring EA. 4. That offspring EA is associated with non-transmitted parental EA PRS, reflecting cultural transmission via creation of EA-linked environments.

Methods Subjects The sample consisted of all 2,335 children and their genotyped parents available within the Brisbane Adolescent Twin Study (Wright & Martin, Reference Wright and Martin2004) for whom EA data and genotype data were available, along with genotype and SES data for their parents: 1,333 mothers (mean age at testing of twins, 17.15 years, SD = 0.39) and 1,002 fathers (mean age at test 17.2 years, SD = 0.41). Exclusion criteria for entry to the cohort were significant head injury, neurological, or psychiatric illness, substance dependence, or chronic use of medications with central nervous system effects. Subjects were genotyped on the 610K Illumina genome-wide SNP platform (Medland et al., Reference Medland, Nyholt, Painter, McEvoy, McRae, Zhu and Martin2009). The study was approved by the Human Research Ethics Committee at QIMR Berghofer Medical Research Institute. Phenotypic Measures The Queensland Core Skills Test (QCST; Queensland Studies Authority, 2003) is a seven-hour comprehensive assessment of EA taken over two consecutive days and sat by most (~85%) Queensland school-leavers in their final year of schooling, typically aged 17. It is used in high-stakes outcomes, such as selection for entry into tertiary education. As such, it was designed specifically to assess general scholastically acquired higher-order skills and provides a global index of academic achievement across a very diverse range of skills, including mathematical problem solving, comprehension and explanation, interpretation (e.g., cartoons, photographs, and flow charts), grasp of scientific methodology, reading graphs, spelling and basic calculations, understanding spatial and mechanical relationships, and producing written prose, as well as creative ability and presentational skills (Queensland Studies Authority, 2003). The QCST exam differs from year to year, and to allow analysis, scores were standardized using the means and standard deviation of the entire Queensland sample within each year. In previous work using this sample, and taking advantage of the twin design, we have shown QCST scores to have a heritability of 0.76 (from bivariate twin modeling) and with genetic correlations with measures of cognitive ability ranging from 0.64 to 0.91 depending on the specific cognitive test (Wainwright et al., Reference Wainwright, Wright, Geffen, Luciano and Martin2005). SES was assessed using the Australian Socioeconomic Index 2006 (AUSEI06) occupational status scale (McMillan et al., Reference McMillan, Beavis and Jones2009). Where an individual's occupation was outside the current definitions of the labor force (e.g., housewife, unemployed), their partner's occupation was used to determine their SES. In the case where occupation information could not be ascertained, then an occupational score, based on years of education completed, was imputed. Forming Polygenic Risk Scores for Educational Attainment in Offspring and Parents For parents, the PseudoCons application (Howey, Reference Howey2014) was used to create non-transmitted parental genomes. This program creates a control parent genome consisting only of those genetic variants that are not present in the offspring, a pseudo-control (Cordell et al., Reference Cordell, Barratt and Clayton2004). PRS for EA2 were calculated in the conventional manner using the LDpred application (Vilhjalmsson et al., Reference Vilhjalmsson, Yang, Finucane, Gusev, Lindstrom, Ripke and Price2015) using SNP effect sizes from 100% of SNPs in the second EA GWAS (Okbay et al., Reference Okbay, Beauchamp, Fontana, Lee, Pers, Rietveld and Benjamin2016), recomputed leaving out the BATS sample (which formed part of the original EA2 project), and using European population LD information from the 1,000 Genomes reference set. Polygenic scores were standardized to have mean of zero and a standard deviation of 1. EA2 PRS were computed for the offspring and parental pseudo-control genomes in the same way.

Results As an initial validity check, the independence of the non-transmitted and transmitted EA polygenic scores was verified using a linear model. The association did not differ significantly from zero, β = 0.01 (95% CI [-0.04, 0.05]), t = 0.31, p = .755 (see Figure 1). EA is, of course, highly heritable creating a large non-independence in attainment nested within families, χ²(1) = 242.69, p < .0001, ICC = 0.57, so family ID and zygosity were entered as random variables in all models. Thus, models that fail to account for these covariances among the subjects will not be able to distinguish genuine parental-gene effects from confounding due to assortative mating and other factors. Two modeling approaches were used to control for this nesting and patterns of gene and environment sharing. In our initial analyses, we used a multilevel framework, using the linear mixed-effects (lme) function from the nlme package (Pinheiro et al., Reference Pinheiro, Bates, DebRoy and Sarkar2017). In addition, we tested the core hypothesis in a structural equation model, where we were able to model the full nesting within families via a multigroup approach, and also include genetic associations among twins and siblings. For instance, the non-transmitted EA2 PRS of one DZ twin, while uncorrelated with their own transmitted EA2 PRS, has expected correlations of 0.5 with the transmitted EA2 PRS of their co-twin and other siblings. Multilevel model results with nesting in family and zygosity are presented first. 1. Are children's EA polygenic scores associated with their EA? We first tested the prediction that in this family-control design, children with higher EA PRS would score higher on the QCST. This was confirmed in a multilevel model with QCST scores as the dependent variable and offspring EA PRS score as the predictor, controlling for age at which the QCST was taken, sex, and parental SES. Offspring EA PRS was a highly significant predictor of offspring QCST, β = 0.15 (95% CI [0.09, 0.21]), χ²(1) = 17.8, p = < .001: AIC = 1,736.797 (see Figure 2, panel A). This confirmed that EA PRS was associated with EA and that this association was not due to stratification or other artifacts of gene frequency, which are controlled in this within-family design. 2. Are parents’ EA PRS associated with the SES they attain and provide to offspring? We next tested whether parents’ own EA PR scores were positively associated with their own SES. In a linear model, mean parental EA PRS was a highly significant predictor of parental SES, F(1, 1,245) = 52.55, p = 7.32*10−13, with a standardized β = 0.20 (95% CI [0.15, 0.26]). This association indicates a significant effect of parents’ EA PRS on their own SES. 3. Are parental SES and offspring EA associated? As shown in Figure 3, in the same model, SES was also a highly significant predictor of QCST, β = 0.33 [0.27, 0.4], t(647) = 10.21, p < .001. Because G × SES interactions have been reported in which SES moderates the impact of genetic differences on attained cognitive ability (Tucker-Drob & Bates, Reference Tucker-Drob and Bates2016), we next tested whether offspring genetic potential (EA PRS) interacted with SES in predicting QCST scores. This was tested by adding an EA PRS × SES interaction term to the model. This term was not significant and was estimated at zero, β = -0.001 (95% CI [-0.004, 0.002]), t(594) = -0.754, p = .451, suggesting that in this sample there was no evidence for SES moderating the impact of EA2 PRS on EA (see Figure 4). 4. Are parents’ EA PRS alleles associated with higher offspring EA, even when not transmitted to their children? Finally, we moved to our core hypothesis in the present paper: testing for evidence that EA2 PRS has its effects on EA, at least in part, via a parenting phenotype. Evidence for such a trait would be found if alleles contributing to the EA PRS and present in the parents, but not transmitted to their offspring are associated with higher offspring EA, despite not being transmitted across the generations. This would constitute support for a parental-competence phenotype impacting offspring EA, un-confounded by parent–offspring genetic relatedness. This hypothesis was tested using a multilevel model with QCST as the dependent variable, with sex, age-at-test, children's own EA PRS and, finally, parental scores for their non-transmitted alleles (PC_EA PRS) as predictors. As shown in Figure 2, panel B, non-transmitted parental EA-alleles had a significant effect, F(1, 606) = 4.245, p = .0397, β = 0.058 (95% CI [0.003, 0.114]): approximately 38% of the effect size of children's own EA PRS. To test the idea that effects of parental competence are expressed via SES formation, we next tested the hypothesis that the PC_EA PRS effect would be removed by controlling for parental SES. This hypothesis was confirmed: the effect size of non-transmitted alleles dropped to zero, β = 0.01 (95% CI [-0.04, 0.07]), and was no longer significant, F(1, 594) = 0.011, p = .917. Flynn (Reference Flynn2016) recently formulated a G × SES model in which home environments superior to a child's own genetic tendency tend to raise attainment, while for children with higher genetic potential, home environments are typically lower than their potential, and in most cases therefore retard their development relative to their potential. We examined evidence for this effect in the present sample by testing the significance of an interaction between EA PRS and PC_EA PRS as an index of disparity between parent and child potential. No support was found, however, for this predicted interaction, F(1, 605) = 0.339, p = .561, which was estimated at near zero, β = 0.003 (95% CI [-0.052, 0.057]). Structural Equation Model-Based Testing The results of the multilevel models suggested that while no predicted G × E effects emerged, there was support for effects of non-transmitted parental polygenic scores on offspring EA. These models controlled for nesting in family and zygosity in the data and, empirically, the non-transmitted and transmitted scores were shown to be independent (see Figure 1). These models do not, however, capture the full, complex familial structure of genetic relatedness for the transmitted and non-transmitted scores among the different classes of twins and their sibs. To do this, we next reproduced the final results in a structural model capturing these sources of covariance including the expectation of a 0.5 correlation of parents’ non-transmitted PRS for a child with the transmitted PRS for their sibs. We also included the known complete sharing of transmitted and non-transmitted scores for MZ twin members. Finally, the residual QCST covariance was included in the model (see Figure 5). This model yielded a similar estimate of the transmitted EA PRS effect (0.167) and a similarly ratio of non-transmitted effects (0.062, or approximately 1/3 the size). The latter effect was, however, non-significant in this model, with its many more degrees of freedom expended in modeling the covariance of family structure. This work was begun in August of 2016 (with ethics permission) completed in June of 2017. Given the value of increased power, we decided to await the imminent release of EA3 and publish the results of the identical analyses with an enhanced genetic predictor. However, delays in the publication and release of EA3 and the publication of a test of the same idea by independent researchers (Kong et al., Reference Kong, Thorleifsson, Frigge, Vilhjalmsson, Young, Thorgeirsson and Stefansson2018) leads us to publish this version now, with analyses to be rerun when EA3 results are available.