Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Two main varieties are common: those with measured genotypes (Caspi, Harrington, Moffitt, Milne, & Poulton, 2006) and those with unmeasured variance components (Purcell, 2002).”

“If so, the genetic variance components of personality traits should increase in magnitude with age (Kandler & Zapko-Willmes, 2017; Purcell, 2002), although it is important to stress that this would reflect the accumulation of genetically influenced environmental experiences rather than direct…”

“As advocated by (Purcell, 2002), therefore we also report and focus on the unstandardized results.”

“The squares of the paths from the ACE components to the phenotypes quantify the variance in the phenotype that is due to genetic and environmental differences, as a function of the moderator values (Purcell, 2002).”

“Gene–environment interaction means that different genotypes respond differently to same environmental factors or that genetic variance differs dependent on some environmental factors (28).”

“The bivariate models used in this study (Purcell, 2002) examine the association between P300 amplitude and AAU (see Figure 2).”

“These models used Mx script from Purcell (2002) that allowed the estimation of the moderating effects of age on variance components and on the overall mean of each stressor variable.”

“We relax this assumption by fitting models that assume interactions between each included variance component and the socioeconomic characteristics of the parents (Guo and Wang, 2002; Purcell, 2002).”

“1B) (Neale and Schmitt, 2005; Purcell, 2002).”

“It is important to account for potential rGE because it may erroneously be reflected as G×E (Purcell, 2002).”

“A further limitation is that gene–environment interaction effects and genetic correlation were not modeled simultaneously using the moderated Cholesky approach (Purcell 2002).”

“…the moderating effects of intelligence on environmental and genetic influences on attained education is an extension of the standard Cholesky decomposition used to estimate the extent to which environmental and genetic influences are correlated across two variables (Johnson, 2007; Purcell, 2002).”

“1985; Heath and Eaves 1985; Posthuma and Boomsma 2000), to sibpair and family linkage and association designs, either in- or excluding gene by environment interaction (Abecasis et al. 2000a, b; Boomsma and Dolan 1998; Dolan et al. 1999; Fulker and Cherny 1996; Purcell 2002; Purcell and Sham 2002; Sham et al. 2000; Sha…”

“Fourth, the CTD does not model gene–environment (GE) correlation, whose presence may impact heritability estimates and shared environmental influences (Kandler & Zapko-Willmes, 2017; Purcell, 2002).”

“Second, the data set was relatively small, a fact that reduced the opportunity for a combined analytic consideration of gene–environment interaction and correlation (Purcell, 2002).”

“, whether offspring were twins, full-siblings, or half-siblings), Rodgers et al. (1994) developed a linking algorithm that assigns children from the CNLSY a sibling status and genetic relatedness score.”

“Instead, these ‘AxC’ effects will be included in the genetic component of variance (along with genetic main effects), since family wide events that interact with the child’s genes would increase the similarity of genetically identical siblings relative to other sibling types (Purcell, 2002).”

“These models allowed us to calculate accurate parameters in the presence of both G E interaction and rGE (Purcell, 2002).”

“This is particularly troublesome in the context of GxE, as rGE can “masquerade” as GxE (Moffitt et al., 2006; Purcell, 2002).”

“The multiformity models may be viewed as restricted forms of a bivariate moderator model (Martin et al. 1987; Dick et al. 2001; Purcell, 2002), where the A, C and E influencing cannabis and OID experimentation are uncorrelated and the variance in OID experimentation is estimated freely in individuals who are experimen…”

“In the classical twin model, the proportion of phenotypic variance explained by gene-environment interaction is, unless specifically modelled, automatically included in the genetic variance component, and this would tend to inflate the estimate of genetic variance [Purcell, 2002].”

“For our primary analyses, we evaluated whether parent–child conflict moderated the etiology of CP using the ‘extended univariate G×E’ model (Purcell, 2002; van der Sluis et al. 2012).”

“Model specifics, algebra and simulations are specified in detail by Purcell (2002).”

“[27] to allow for gene– environment correlation, we still did not observe gene– BMI interactions for total cholesterol and HDL-cholesterol (data not shown).”

“For example, a heritability estimate of 50% may reflect a scenario where a trait is entirely due to the environment in half the population and entirely due to genetics in the other half of the population (Purcell, 2002).”

“Next, we used an extension of the bivariate model (i.e., gene-environment interaction [GxE] in presence of gene-environment correlation [rGE] model; Purcell, 2002) to investigate the influence of ED-specific moderators on genetic and environmental associations between negative urgency and binge…”

“In Step 3, the bivariate Cholesky models were modified to include gene-environment interactions and environment-environment interactions (Purcell, 2002; dashed paths ac′, ec′, au′, and eu′ in Figure 1).”

“Current statistical modeling, which allows testing of gene–environment interactions [38], tests whether the magnitude of additive genetic variance, common environmental variance and unique environmental variance change as a function of a measured environmental factor [39].”

“All of these diagnostics are available in the R package ‘coda’ (Plummer et al. 2005).”

“…characteristics (e.g. Boomsma et al., 1999), gene–environment covariation which models selection into environments based on one’s genotype (e.g. Purcell, 2002), and multivariate models that simultaneously decompose variance of multiple items (e.g. Hatemi et al., 2007) are all extensions of…”

“The second caveat is that the coefficient for nonshared environ mental effects indexes not only the direct effects of nonshared experiences but also the effects of interactions between nonshared em"ironments and genes (Purcell, 2002; Rutter & Silberg, 2(02).”

“In addition to traditional bivariate Cholesky models, the current study also estimated a series of modified models that includes interaction terms to more directly examine G × Es (Brendgen et al., 2009; Purcell, 2002; Turkheimer, Beam, Sundet, & Tambs, 2017).”

“Following previous recommendations (Purcell, 2002), we present standardized parameter estimates in tables and unstandardized estimates in figures.”

“To address our three remaining research questions, we made use of a model developed by Purcell (2002) that allows for the explicit quantification of genetic and environmental influences on a particular trait in the context of correlation with and moderation by genetic and environmental influences…”

“To investigate these hypotheses, we made use of a model that was developed by Purcell (2002) to quantify the genetic and environmental influences on a particular trait explicitly in the context of correlation with and moderation by genetic and environmental influences on an associated trait.”

“However, these lower genetic correlations of BMI can also be affected by environmental factors if they interact with genetic factors affecting weight and thus modifying the genetic components [29].”

“…and no interaction between genetic and environmental effects (Eaves et al., 1999).1 Further, the models we use do not explicitly consider nonindependence of genetic and environmental influences, but these developmental processes exert predictable influences on model parameters (see Purcell, 2002).”

“Although less versatile than the continuous moderator model outlined by Martin et al. (1987), which was comprehensively elaborated by Purcell (2002), the approach used was considered to be a reasonable approximation at this stage of the study prior to future planned multi-variate analyses.”

“To test whether the A, C or E components of the correlation between Ncomp and the cognitive variables change as a function of the level of Ncomp, one can use the same approach as described above using continuous moderator values (Purcell, 2002).”

“The moderating effect of age on the RT variables was estimated using a modified version of the gene by environment interaction model described by Purcell ( 2002 ).”

“To quantify interplay, we have applied biometric moderation models (Purcell, 2002; van der Sluis et al., 2008).”

“Next, we tested for Gene Environment interaction in the presence of gene–environment correlation (Purcell, 2002).”

“Advances in twin research have provided powerful new analytical techniques to detect gene by environment (G E) interactions (Purcell, 2002; van der Sluis et al., 2012), where the proportions of variance attributable to genetic and environmental sources are themselves moderated by environmental variables.”

“We fitted the basic gene-environment interaction models as described by Purcell [24], using age as a continuous moderator incorporating all the available (complete) twin pairs.”

“Although the Jinks and Fulker test (henceforth JFT) is particularly easy to conduct, its application is hampered by low power, and sensitivity to nonnormality in the data (e.g., Boomsma & Martin, 2002; Martin, 1999; Purcell, 2002).”

“Models for continuous G × E interaction (Neale, 1998; Neale & Cardon, 1992; Purcell, 2002) that involve an ordinal or continuous environmental measure would be similarly affected when the observed sum scores to be analyzed fail to meet the assumption of measurement invariance.”

“To test the effect of the level of urbanization of the home district on the genetic and environmental influences of nature orientation and nature experiences, we built full bivariate moderation models to examine the gene–environment and environment– environment interactions in the presence of gene–environment and envi…”

“…of (i) unfolding of individuals’ genetic endowments via genetic maturation (Kandler, 2012a), (ii) increasingly active person–environment transactions (Scarr & McCartney, 1983) or (iii) cumulative interactions between the genotype and environmental circumstances shared by twins (Purcell, 2002).”

“These parametric moderation models (Purcell, 2002) allow for the paths from ACE factors to p and g and their correlations to be specified as consisting of a main effect and”

“Over time, youths’ selfselected situations may deepen the personality characteristics that led to them in the first place, a phenomenon referred to as the corresponsive principle of personality development (Caspi, Roberts, & Shiner, 2005; Roberts et al., 2003).”

“The bivariate G×Emodel is an extension of the bivariate Cholesky decomposition model (Neale & Cardon, 1992).”

“Assuming a perfectly homogeneous and common environmental influence is probably not reasonable, so it will be important to verify our conclusions with a larger-scale gene-association study (Purcell, 2002; Tan et al., 2010).”

“Yet, it is highly probable that gene–environment interactions, which are difficult to disentangle from unique environmental effects (Purcell, 2002; Purcell & Sham, 2002), also contribute.”

“The specific biometric moderation model used is depicted in Figure 1 (Purcell, 2002).”

“In most twin models that rely on the assumption that sources of influence are independent, variance involved in correlations between shared environmental and genetic influences falls into the estimate of shared environmental influences, causing it to be overstated (Purcell, 2002).”

“Finally, Purcell (2002) reports that quadratic moderator models are prone to local minima, and should therefore be run at least five times using multiple start values to ensure that the obtained estimates do in fact minimize minus twice the log-likelihood (–2lnL).”

“The power of a number of gene–environment interaction models using the general approach employed in this study has recently been examined (Purcell, 2002).”

“Follow-up studies can disentangle these processes by moderating the genetic architecture of BPD traits by self- and parent-reports of parenting (Purcell, 2002).”

“significance of the moderator effect of parental education (21).”

“By modeling the common (correlated) variance between attained SES and cognition, moderation effects observed on variance unique to cognitive performance provide evidence for a causal role of attained SES (Purcell, 2002).”

“that childhood environment has effects on the development of many psychological traits, including SOC, but because such effects interact with genetic predispositions of children, they cannot be disentangled from genetic factors without direct measures of childhood environment rarely available in twin studies [17].”

“This concurs with previous research (e.g., Pike et al. 1996a, b) and is consistent with the operation of gene-environment correlation, a process representing genetic control of exposure to environments (Purcell 2002).”

“Interaction of genetic and unique environmental influences will inflate the contribution of the unique environment and underestimate genetic influences, whereas interaction of genetic and shared environmental factors will inflate the contribution of genetic influences (36,37).”

“Since these analyses were conducted, models have been developed that attempt to test for G E in the presence of genotype by environment correlation (Purcell, 2002), and these models may be informative for studying additional environmental variables in the future.”

“Violations of these assumptions can lead to either upward or downward bias in the estimated variance components and have consequently sparked an extensive debate in the literature (Felson, 2014; Lerner, 2006; Purcell, 2002; Visscher et al., 2008; Zuk et al., 2012).”

“Possible age-related modification of genetic and environmental effects on the EQ scales was also tested by interaction models (Purcell, 2002) that incorporated age as a continuous moderator to avoid arbitrary categorizations.”

“The majority of these previous GxE studies used the univariate and bivariate models to study moderation as delineated in Purcell (2002). The univariate model allows for”

“We used a twin moderation model (Klump et al. 2007; Purcell 2002) to test whether the estimates for genetic and environmental influences on the CBCL measures varied linearly with age of midpuberty in both sexes or with age at menarche in girls (our sample size prevented testing for nonlinear…”

“Since the publication of Purcell’s article, researchers have relied on his model to test gene-by-environment interactions for a wide range of phenotypes, including perceived control and physical health (Johnson & Krueger, 2005), family income and intelligence scores (Turkheimer, Haley, Waldron, D’Onofrio, & Gottesman,…”

“By including the mean effects in the genetic models, gene–environment correlations were controlled for [31].”

“Finally, we tested whether the correlation between neuroticism and cortisol changed as a function of the level of neuroticism (Purcell, 2002).”

“When such information is not available, studies of gene–environment interactions rely on statistical approaches such as those that provide evidence that putative environmental factors modulate heritability (49,50).”

“Figure 1 illustrates the basic model used to simultaneously estimate the degree to which the relationship between frequency of exposure and PTSS is attributable to shared etiology and to interplay effects described by Purcell (2002).”