Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Negative life events and maternal punitive discipline were used as environmental risk indices, both of which involved some genetic influence, requiring appropriate modelling to take account of rGE, using an approach developed by Purcell (2002).”

“Unfortunately, the usual approach in quantitative behaviour genetic studies is additive variance decomposition, which hides both GxE interactions and GxE correlations in apparent main effects (Purcell, 2002).”

“…to shared environmental sources of variance (though, as noted, they do contain any passive rGE effects that are present).8 As ably described by Purcell (2002), nonshared environmental components of variance contain G E in which the child’s genes interact with child-specific environmental…”

“In this framework, it is also possible to model and test a variance term for G E (Eaves et al., 1977; Eaves, Silberg, & Erkanli, 2003; Heath et al., 2002; Kendler & Eaves, 1986; Purcell, 2002; Sham, 1997).”

“As Purcell (2002) noted, the influence of Gene Shared Environment interactions will be represented in the additive genetic variance component (a2) in behavioral genetic models.”

“The adapted model, described by Purcell (2002), 5 is shown in Figure 2.”

“Figure 1 presents genetic and environmental variance components as a function of SES, as implied by the meta-analytic parameter estimates for the United States.”

“To overcome this problem, we combined an extended twin design with moderator models for the examination of gene by age interaction [Purcell, 2002].”

“…Dick, Bernard, et al., 2009; Dick, Pagan, Holliday, et al., 2007; Dick, Pagan, Viken, et al., 2007; Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001; Dick, Viken, et al., 2007; Harden, Hill, Turkheimer, & Emery, 2008; Purcell, 2002; R. J. Rose, Dick, Viken, & Kaprio, 2001; South & Krueger, 2008).”

“The classical twin model for MZ twins (Purcell, 2002) postulates that the methylation values (y) at a given locus for co-twins 1 and 2 of twin pair i are defined by an overall mean (l) that may depend on age, sex, batch, CpG unit, by a random twin-pair effect (bi), the familial environment, which…”

“4 To avoid bias in polynomial and interactive regression (of which nonlinear and interactive factor analysis is a general case), it is necessary to include the main effects of all variables that were multiplied to create higher order terms (Cohen, Cohen, West, & Aiken, 2003; Purcell, 2002).”

“In other words, the effects of Gene Shared Environment interaction contribute to the estimate of genetic influence when not explicitly modeled (Purcell, 2002).”

“Our estimates of the heritability for male and female twins can be considered an average heritability estimate across all levels of a particular environmental variable (Purcell, 2002).”

“The publication of a paper the following year (Purcell 2002) that provided straightforward scripts for continuous gene-environment interaction models using the most widely used program for twin analyses, Mx (Neale 2000), led to a surge of papers studying geneenvironment interaction in the twin…”

“Increasing heritability estimates have also been observed in other traits over childhood, such as in cognitive development [48], and this is generally attributed in part to changing gene expression, but also to gene-environment interaction (G6E) [19,49] and geneenvironment correlations [50–52].”

“, differences in variance of FA, between the two moderator groups, without any genuine genetic×moderator interaction (Boomsma et al., 1999; Purcell, 2002; Turkheimer et al., 2003).”

“(1) The DRD4 Exon III VNTR (a 48 base pair repeat often referred to by the number of repeats, such as the “7 repeat” or “4-repeat” variant) generally yielded negative findings, but did show unreplicated interactions with season of birth and with maternal smoking.”

“Studying those effects necessitates models that specify measured environmental moderators (Purcell, 2002).”

“Thus, any covariance between the moderator and the outcome is incorporated into the means model (Purcell, 2002;Turkheimer, Haley, Waldron, D’Onofrio, & Gottesman, 2003); accordingly, any interactions detected will be associated with the variance components unique to the outcome (i.”

“In order to test for developmental changes and sex-differences on the genetic architecture of the four SWB measures a moderator model (Purcell 2002) was expanded to use in an extended twin-sibling design (see Fig.”

“Simulation studies of this model were provided by Purcell (2002), some recent empirical applications of the model in personality research can be seen in Johnson and Krueger (2005, 2006), and Johnson (2007) describes the broad relevance of this model for providing a richer understanding of how genes…”

“Purcell (2002) demonstrated that inclusion of the main effect of the measured environment prevents bias in estimation of G × E interactions resulting from unspecified rGE.”

“DISCUSSION Whereas ADHD carries well-established genetic influences on susceptibility (Waldman & Gizer, 2006), environmental risk factors may interact with that susceptibility in complex ways (Purcell, 2002).”

“28 Two binary MDD outcomes were analysed as dependent variables: all participants with MDD v . controls (all MDD risk) and participants with severe MDD v . controls (severe MDD risk).”

“This gene-environment interplay model (Figure 1) can be conceptualized as a bivariate extension of the univariate mode that incorporates additional moderation terms on the ACE effects.(38) This gene-environment interplay model estimates the ACE contributions to the covariance between externalizing and the environmenta…”

“Accordingly, future studies must build upon the present findings and incorporate gene-environment interaction and correlational models (Purcell, 2002) so as to delineate the mechanisms underlying stability and change in personality.”

“Furthermore, since ADHD, like ASD, carries well-established genetic influences on susceptibility (Waldman & Gizer, 2006), it will be important to determine how lead may interact with that susceptibility (Purcell, 2002).”

“This is the full model of the possible ways in which HI may be associated with HP (Purcell, 2002).”

“In our final model, the effects of A, C, and E were allowed to vary as functions of SES (Purcell, 2002).”

“If there would be G C interaction, it would be part of the genetic variance in the twin model that was employed in this paper (Purcell, 2003), i.e. it is the genotype of the individual that determines the response to the common family environment.”

“Consequently, the consideration of an overall picture of the interplay between personality and environments needs more complex interactionist perspectives (South and Krueger 2008) and research strategies that requires large sample sizes such as modeling genotype– environment correlation in the presence of genotype– en…”

“Here, we discuss a binary environment, and we refer the reader to recent work by Purcell (2002) and Rathouz, Van Hulle, Rodgers, Waldman, and Lahey (2008) for the case of continuous figure we present E Y1 Y0½ E Y1jD ¼ 1½ E Y0jD ¼ 0½ .”

“A model designed to test GE interaction of the latent genetic variable with a measured continuous moderator variable was used to test for gene-environment interaction (Fig. 1) ( Purcell, 2002 ).”

“The second caveat is that the coefficient for unique environmental effects indexes not only the direct effects of unique experiences but also the effects of interactions between unique environments and genes (Purcell, 2002; Rutter and Silberg, 2002).”

“Additionally, the correlations for DZ twins and siblings were not significantly different, indicating generalizability of twin study results to the general population.”

“Further, with the addition of individual-specific moderator variables, the standard ACE model can be expanded to account for interactions between A, C, and E with a second observed variable, such as age (Purcell, 2002).”

“Correlation between genetic and shared environmental influences acts to increase estimates of shared environmental influence; correlation between genetic and nonshared environmental influences acts to increase estimates of genetic influence (Purcell, 2002).”

“We also included the main effect of parental education in the DF regression test of the G E interaction to control for the influence of any gene-environment correlation on the G E interaction (Purcell, 2002).”

“Such effects would be expected to inflate nonshared environmental variance components and produce changes in these components across birth cohorts.(44) However, our studydid showa small increase in themean level of and variance in autistic traits, specifically among individuals born between 2004 and 2008.”

“These models have subsequently been detailed and expanded [27].”

“…test for background factors (e.g., gender, maternal age) that might moderate the genetic, shared environmental, and nonshared environmental effects on maternal sensitivity, we tested a set of nested structural models following methods developed by Purcell (2002) for continuous dependent variables.”

“A focus on standardized components, as is typical in most behavior genetic reports, can lead to misinterpretation.(42) Because this point is important and underappreciated, we digress momentarily for an illustration: Consider in a hypothetical case that there are very low levels of variance in the phenotype at one lev…”

“…have provided a productive initial platform for further research in medical, behavioral, and psychiatric genetics, including the study of gene–environment interaction (e.g., Purcell 2002 ) and the search for specific environmental factors and individual genes contributing to individual differences.”

“These mechanisms might bias parameter estimates in standard twin models and have to be taken into account when interpreting our results, as an interaction between A and E will act like E, and correlation between A and E will act like A (Purcell, 2002).”

“New twin models allow for more explicit delineation of how genetic and environmental influences act and interact (Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001; Purcell, 2002 ), and on-going analyses of the Finnish Twin data in this area clearly demonstrate the importance of gene‐environment interaction effects.”

“Independent of GE correlation, G ×E interaction involving nonshared environmental influences on personality differences would have the effect of making genetically related individuals less similar to each other (Purcell, 2002).”

“the twin model is expanded by including explicit measures of the environment or additional types of relatives, variance due to GxE can be separated from the variance due to latent genetic and environmental main effects (Purcell, 2002).”

“In the genetic models, we estimated the influence of A, D, and E on extraversion and allowed these estimates to be a function of measured moderator variables age and sex (Purcell 2002).”

“Gene-environment interactions are present when psychosocial risk factors have differential effects on disease outcome depending on the level of genetic risk.(23,24) Specifically, individuals with genetic predispositions are at increased risk for a disorder when environmental risk factors are present.”

“GXE effects detected between PRS and environmental contexts could therefore differ accordingly (78,79).”

“to unique environment, and thus decrease estimates of heritability [29,30].”

“…the sum and absolute differences of data from MZ co-twins (i.e., heteroscedasticity) (Jinks and Fulker 1970; van der Sluis et al. 2006) or by partitioning the variance components into that which is linked to variation within the environmental influence and that which is residual (see Purcell 2002).”

“000 University degree 25 (24) 19 (16) 44 (20) 486 (28) 296 (34) 782 (30) Poverty, n (%) 22 (21) 29 (25) 51 (23) 378 (22) 121 (14) 499 (19) .”

“Or as elegantly pointed out by (Purcell, 2002), “G×E is often conceptualized as genetic control of sensitivity to different environments.”

“E contributes to the additive genetic (h2, narrow-sense heritability) or nonshared environmental variance component in twin models (Purcell, 2002), so it is unclear whether—on balance—”

“Recent advances in behavioral genetic methodology offer a promising avenue for disentangling the etiological relations among these constructs by testing for both gene–environment interactions (G×E) and gene–environment correlations (rGE) within the same model (Purcell, 2002).”

“The effects of GE correlation also depend on whether E consists of unique or common environmental influences: correlation between G and C acts like C (which we did not detect); correlation between G and E acts like G (Purcell, 2002) and thus could be included in the total heritability.”

“A significant gene–environment interaction effect can be due to gene–environment correlation if this correlation is not included in the model (Purcell, 2002).”

“…a wide range of social and behavioral scientists, despite the controversy surrounding such estimates (e.g., see Breen, Plomin, and Wardle 2006; Plomin, Owen, and McGuffin 1994, 1997; Plomin and Spinath 2004; Plomin 2009; Purcell 2002; Rodgers, Rowe, and Buster 1999; Rodgers, Buster, and Rowe 2001).”

“…examine genetic and environmental contributions to antisocial behavior and disordered eating, (2) perform genetic association studies, and (3) examine gene–environment interplay, using both biometric models (Purcell, 2002) and measured-gene × measured-environment analyses (Moffitt et al., 2005).”

“Purcell SM, Wray NR, Stone JL, Visscher PM, O’Donovan MC, Sullivan PF, Sklar P (2009): Common 504 polygenic variation contributes to risk of schizophrenia and bipolar disorder.”

“Likewise, non-linear interactions between alleles—such as dominance—have been modeled in attempts to get at broad-sense heritability (H2) (see Purcell 2002 for a review of these models and simulation exercises and Purcell and Sham 2002 for an empirical example).”