Variance Components Models for Gene–Environment Interaction in Twin Analysis

“In bivariate moderation model-fitting analysis [17, 18], this study addressed two research questions.”

“The usual approach for testing moderation of variance components in twin/family models is to estimate simultaneously the biometric structure of the dependent variable, the moderator and their covariance (Neale et al., 2006; Purcell, 2002).”

“…development, have also been observed to increase with age, which has been attributed to heterogeneity in gene-expressions (Dubois et al., 2012), gene-environment interactions (Lajunen et al., 2009; Purcell, 2002), or gene-environment correlations (Bergen et al., 2007; Jaffee & Price, 2007).”

“To investigate the effect of gene-environment correlations and interactions, future studies are needed that specify and measure specific environmental characteristics and/or specific genes (Purcell, 2002).”

“Existence of a G × E means that a single statistic is not adequate to describe a whole population because genetic effects diverge depending on environmental factors (Purcell, 2002).”

“We then standardized the log-transformed scale scores to facilitate interpretation of the unstandardized estimates derived from the model (the approach recommended by Purcell, 2002).”

“The authors point out that this negative result could be due to low power of this new method, although a recently published power analysis suggests this is unlikely (Purcell, 2002).”

“In the final chapter in this volume, Reiss (2015) discusses several contemporary approaches to increase our understanding of the function of genes (e.”

“Gene–shared environmental correlations tend to mimic shared environmental effects (C), and gene–non-shared environmental correlations tend to mimic genetic effects (A) (Purcell 2002).”

“17 This high heritability historically supported a model of ADHD as a distinct, genetically determined neurodevelopmental disorder.”

“In a biometric twin model, such forms of gene – environment interactions cannot be directly captured and would be re-fl ected by estimates of individual-speci fi c environmental sources of variance (Kandler, Bratko, et al., 2021; Purcell, 2002).”

“…and the outcome (e.g., externalizing behaviors), and G×E appear in the model as β X , where an interaction exists when β X is significantly non-zero (Purcell 2002 ). β Y and β Z represent the moderator’s effect on the shared environmental and nonshared environmental influences respectively.”

“The latent biological factor effectively aggregates genome-wide genetic associations into a single variable that does not require DNA collection, instead leveraging the differences between the variances and covariances of MZ and DZ twins (Neale and Cardon, 1992; Purcell, 2002).”

“We considered fitting double moderator, estradiol × progesterone models; however, simulation studies suggest substantially larger samples are needed for these models (Burt et al. 2020; Purcell 2002).”

“Additionally, unmodeled interactions and correlations between genetic and environmental factors impact their interpretation in standard twin and family models (Purcell 2002).”

“In addition to standard paths for A, C/D, and E components, we introduced beta ( ) terms to quantify the extent of moderation on both shared and unique paths of the self-report CES-D score (Purcell, 2002).”

“For each partner characteristic and alcohol outcome, we first specified the full bivariate moderation model proposed by Purcell (2002), which tests for G × E in the presence of gene-environment correlation.”

“As we recognize that LDSC-based heritability estimates tend to be downwardly biased [87,102,105,106], in contrast to twin studies that can capture gene-environment interactions, along with other factors, that potentially inflate heritability estimates [107–109].”

“Specifically, non-normality can give rise to spurious moderation/interaction effects (Purcell 2002; Eaves 2006; Eaves and Verhulst 2014).”

“In this framework, genotype-environment interaction can be tested by moderation models, where the environment moderates the influence of latent genetic and environmental factors on an outcome phenotype (Purcell 2002).”

“The MSCM is slightly different than the more common GxE model (Purcell 2002), in that 1 3 it models the Scarr-Rowe interaction basing on interactions between an environmental moderator and twin and sibling correlations, rather than on the genetic and environmental latent variables (ACE) that can be…”

“It is well known that positive cultural transmission is a source of additive genetic (A) and common environment (C) covariance, and that A-C covariance biases upwards the estimated C variance component in the classical twin design (Purcell, 2002).”

“Simulations have shown to be a good strategy to adopt continuous moderators whenever available, thereby increasing the power to detect a continuous moderation [27].”

“…+ eE + iAC where A, C and E are standardized latent variables due to additive genetics, the common and the unique environment and additive genetic x common environmental interaction, and a, c, e, and i are path coefficients corresponding to the magnitude of their respective effects (Purcell, 2002).”

“However, the effects of violations of these assumptions on the variance components, as estimated in the twin model, are well known (e.g., Purcell 2002).”

“Therefore, moderate-to-large estimates of A and E can signify the presence of potentially large G×E interaction effects (Purcell, 2002).”

“…these ‘‘environment-environment interaction’’ terms was important to examine whether the moderating effect of the general antisocial behavior peer group norm is truly specific to the general genetic effect Ag on aggressive antisocial behavior and non-aggressive antisocial behavior (Purcell 2002).”

“This argument can be overcome by parallel modeling of G E and rGE [53].”

“…Fiveの勤勉 性や経験への開放性，もしくは衝動性との関連性があ ることが指摘されている（Daly, Delaney, & Harmon, 2009; McLeish & Oxoby, 2007）。さらに，リスク受容 （risk tolerance），リスク回避（risk aversion）などの リスク選好に関する実験結果の個人差も，パーソナリ ティ特性の一つである刺激追求（sensation…”

“Future research should investigate possible unmodeled gene–environment interactions that could inflate the role of genetics and minimize the role of the environment (Purcell, 2002).”

“The second is based on twin G × E studies (Neale et al. 2006; Purcell 2002).”

“Positive unmodeled AC covariance results in an overestimation of C and negative AC covariance in an underestimation of C (Eaves 1976; Purcell 2002; Verhulst et al. 2017).”

“We estimated the moderating effects of age on variance in reading skill (Purcell, 2002) using full information maximum-likelihood estimation in the OpenMx package (Neale et al., 2016) in R version 4.2.1 (www.R-project.org; R Core Team, 2022).”

“The statistical validity of the ACE-M has been thoroughly studied (Purcell 2002), but it is worth showcasing four main scenarios.”

“To examine the patterns of G × E effects in the PS-ADHD relationship, bivariate G × E model-fitting analyses (Purcell, 2002; van der Sluis et al., 2012; see Figure 1) were performed.”

“…moderated the genetic and environmental variance in subsequent intelligence test scores using an extension of the standard bivariate Cho-lesky decomposition model that Purcell (2002) outlined to address the possibility of gene-environment interaction in the presence of gene-environment correlation.”

“A possible explanation is that interactions of C with additive genetic effects are counted as “A” in the classical twin design 59 .”

“As recommended (Purcell, 2002), we plotted the unstandardized moderation terms as functions of the values of the moderator (ranging between the mean ± 3SD; see supplementary material).”

“Similarly, depending on the combination of genes, environmental effects on the phenotype can differ (Purcell, 2002; Plomin et al., 2013).”

“Given that genetic and nonshared environment interactions contribute to between-individual differences on complex traits in the population (e.g., Purcell, 2002; Knopik et al., 2016), the ability to adjust for G × E represents an important and potentially substantive advancement of GAPS matching…”

“The findings of the present study contribute to the knowledge of mechanisms by which genes impact substance use behaviors (52).”

“…b3, and we can plot the effect at interesting levels of the moderator by calculating the marginal effect—taking the partial derivative of Y with respect to X: ∂Y ∂X = b1 +b3M : ð2Þ This is analogous to the gene–environment interaction model, shown in Figure 2, which we use here (Purcell, 2002).”

“A gene-by-environment interaction is indicated by a substantial difference in the magnitude of heritability when moderated by a measured environmental factor (Purcell 2002).”

“In the presence of interaction between genetic and shared environmental influences, standard estimates of genetic influence based on the independence assumption are overstated Purcell [5].”

“Biometric moderation analyses [22] are receiving increased attention in psychological science [18, 19, 23, 24, 25], and this approach allows researchers to study quantitative gene-environment interaction(s) in the context of gene-environment correlation (i.”

“With these resources, we aim to (1) identify genes for various psychiatric illnesses, personality, and cognitive abilities, (2) determine the role of puberty at the onset of psychiatric diseases, (3) examine gene–environment interactions for the development of psychiatric diseases using both biometric models (Purcell,…”

“The G × E interaction model (Purcell, 2002) allows the magnitude of influences of A, C, and E on personality to vary as a function of religiosity (REL).”

“According to Purcell (2002), in the early stages of their lives, children, depending on their genotype, can respond differently to the same type of environment provided by caregivers.”

“…variance components to adjust for a variety of other factors influencing the analysis such as assortative mating and extended families (Eaves et al., 1999; Truett et al., 1994) or gene-environment interactions (Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001; Neale & Cardon, 1992; Purcell, 2002).”

“experiences probably mostly result from transactions between genetic and environmental factors, the effects will tend to appear in the variance components reflecting the genetic and unique environmental factors (Purcell 2002).”

“…of behaviour genetics, genotype by environment interactions are investigated by either the latent continuous moderator approach (Molenaar, van der Sluis, Boomsma, & Dolan, 2012; Van der Sluis et al., 2006) or the observed continuous moderator approach (Purcell, 2002; van der Sluis et al., 2012).”

“Because rGE and GxE can co-occur (Purcell 2002), rGE was controlled in the analyses examining GxE.”

“Since then, numerous methodological studies have further discussed and provided demonstrations of dependency of appearance of presence of GxE on scaling (Eaves et al. 1977; Martin 2000; Molenaar et al. 2012; Purcell 2002; Tucker-Drob et al. 2009; van der Sluis et al. 2006).”

“…presence/absence, result in higher MZ correlations relative to DZ correlations and thus inflate estimates of heritability, while interactions between genetic and non-shared environmental factors reduce the overall twin similarity and inflate estimates of non-shared environment (Purcell 2002).”

“…examines the extent to which additive genetic (i.e. effects that add across genes), shared environmental (i.e. factors common to twins reared in the same family), and nonshared environmental (i.e. experiences unique to each co-twin) influences on ASB differ across pubertal timing (Purcell, 2002).”

“Third, we fit moderated univariate variance decomposition models (Purcell, 2002).”

“Although ADHD undoubtedly has high heritability, several researchers have reported an interaction between genetic and environmental factors [20–22] and have supported the epigenetic hypothesis of ADHD etiology [23–27].”

“After analyzing the genetic components of the variance in BMI, we performed a G × E model using feeding pattern as a moderator (Purcell, 2002).”

“…of these variance components (i.e. AE vs ACE vs ADE) to be estimated from a set of twin correlation data, but tend to rely on a number of assumptions; nonetheless, relevant limitations have previously been discussed and the yielded estimates are generally considered as good approximations [5 – 7].”