Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Moreover, heritability estimates are often influenced not only by genetic background, but also by gene-environment interactions (Purcell, 2002; Thapar, Cooper, Eyre, & Langley, 2013).”

“This sample was adequately powered to detect both linear and non-linear G×E (see simulation studies in Purcell, 2002).”

“There was no indication of the presence of moderation on the covariance between depressive symptoms and career-goal appraisals when the full bivariate model as suggested by Purcell (2002) was fitted.”

“…parent gender would be said to moderate the association between X and Y. Gene–environment interactions (G × E) are defined as genetic sensitivity to the environment (Purcell, 2002); they help explain why people who share the same environmental experience have different consequences to events.”

“Gene‐environment correlations exist when there is genetic control of exposure to the environment, or environmental control of genetic expression (Purcell, 2002).”

“A general sex-limitation model incorporating age as a moderator was applied to the raw data (Purcell, 2002).”

“The importance of gene-environment correlations and interactions, and the need to separate the two, has led to the development of improved statistical models for use in twin studies (Purcell, 2002; Purcell & Sham, 2002).”

“By contrast, G×E often refers to a gene effect that differs as a linear function of the environment (Purcell, 2002).”

“Not accounting for G–E correlation while investigating G–E interaction can lead to biased variance component estimates (Purcell, 2002), and have been shown to inflate the significance of interaction results (Ni et al.”

“Nevertheless, it may be possible to model (and test for the existence of) some varieties of gene × age interaction by e.g. including age as a moderator variable in the model (Purcell 2002).”

“, GxE) occur when environmental influences activate genetic risk (Moffitt, Caspi, & Rutter, 2005; Purcell, 2002).”

“Because it is generally recommended that unstandardized or absolute parameter estimates be presented in etiologic moderation models (Purcell, 2002), we then standardized our log-transformed child RB scores to have a mean of 0 and a standard deviation of 1 (to facilitate interpretation of the unstandardized value).”

“(2013) have examined statistical aspects of Purcell’s approach and found in preliminary studies that, under some plausible conditions, identification of GxM interaction in Purcell’s model is not fully convincing because models not including such interactions may explain the data as well as Purcell’s interaction model.…”

“Future studies including quanti fi able measures of the environment and their interaction with genetic factors (Purcell, 2002) are thus required to investigate how these circumstances impact NTFM-based estimates.”

“…the standardized components (A, C, E) were considered, such moderation effects would not necessarily be apparent because, first, the total variance may differ between the groups considered; and, second, the standardized components may vary as a function of each other (Mönkediek 2022; Purcell 2002).”

“…and neurochemical aspects, but also with genetic and environmental designs (e.g., longitudinal twin and family studies, for more details please see Purcell, 2002), neuroimaging methods (focusing on the reward’s circuitry activation, and dynamic patterns of brain activity in health and disease due…”

“Thus, the extended univariate moderation model was applied as a solution to avoid false positives that arise under a standard univariate moderation model [77, 78].”

“The moderated ACE model [45] offers a formal way of assessing gene–environment interactions by allowing parameters (including the intercept) to be linear functions of one or more moderators.”

“2012), we directly adopted the univariate moderation model (Purcell 2002) to examine potential G × E involving parenting behaviors.”

“Beginning with advances in twin modeling almost two decades ago (Purcell, 2002), researchers were able to estimate genetic (and environmental) influences on a phenotype at different levels of a “moderator” variable that was putatively environmental (but often had some genetic influence as well).”

“For example, geneticenvironment interactions (Purcell, 2002; Caspi andMoffitt, 2006) are not being modeled here.”

“Additionally, because education differed within pair, we used the bivariate approach in which each twins’ level of education was formally included in the model (Purcell, 2002; van der Sluis et al.”

“Furthermore, the classical twin model cannot reflect gene–environment interaction with a possible result of an overestimation of environmental contribution to variance (Purcell, 2002).”

“Further, to examine heritability as a function of age, the gene-environment interaction model (Purcell 2002) was fitted.”

“Different from the approach we take, however, Eaves (2017) used the nonidentifiable solution introduced by Purcell (2002).”

“This approach is a similar to that proposed by Purcell (2002), treating the covariate as a fixed effect in a manner comparable to those used in the analysis of G × E in other species (see, e.g., Bucio-Alanis & Hill, 1966; Perkins & Jinks, 1973; and references).”

“The statistical consequences of this type of A C interaction have been described before (Purcell 2002) but are briefly reproduced here for comparison.”

“However, since the introduction of the GxE twin model in a seminal paper by Purcell [8], this situation has changed and many twin studies including those for CVD risk factors have explored GxE interaction.”

“As we recognize that LDSC-based heritability estimates tend to be downwardly biased [86,101,112,113], in contrast to twin studies that can capture gene-environment interactions, along with other factors, that potentially inflate heritability estimates [105,114,115].”

“Second, interactions between additive genetics and shared environments are encompassed within the additive genetic variance in these types of designs 55 .”

“In modern genetics and genomics, the model is often written directly for the marginal distribution of Y : where K = ZZ T ; see for example Purcell (2002); Kang et al. (2010); Zhang et al. (2010); Lippert et al. (2011); Yang et al. (2011); Zhou and Stephens (2012); Zhou et al. (2013); Loh et al.…”

“The ACE-moderation model including a continuous moderator assumes linear moderating effects on the ACE components, while there may be threshold effects (Purcell 2002).”

“1) (Purcell 2002) to test whether parent-and youth-reported family cultural values at age 11–12 moderated the additive genetic, shared, and nonshared environmental influences on youth psychopa - thology symptoms at age 12–13, accounting for psychopathology symptoms at age 11–12.”

“Moreover, the classical twin design disregards the possibility of gene-environment interaction, which could have in fl ated estimates of both additive genetic and non-shared environmental contributions to the variance (Briley et al., 2018; Purcell, 2002).”

“…the PReF as to variance in the resistance phenotypes, we will extend the analyses to bivariate modeling, allowing moderation of the parameters accounting for covariation between resistance phenotypes and PReF as well as moderation of parameters specific to the resistance phenotypes (Purcell, 2002).”

“Adding environment-environment interactions is necessary to avoid potential bias in the estimation of geneenvironment interaction (Purcell, 2002).”

“As recommended in prior work (van der Sluis et al., 2012), we also fitted bivariate G × E models as an important clarification of our uni-variate G × E results (Purcell, 2002).”

“In other words, such models might erroneously conclude that heritability increases when it does not (Purcell, 2002).”

“Assigning polygenic scores the role of moderator in the twin moderation model (Purcell, 2002) will facilitate the study of AxE and AxC interaction, allowing for the developmentally important distinction of AxC and AxE.”

“on the twins_ leisure time physical activity in young adulthood was assessed with gene–environment interaction models (33).”

“Entering the moderator in the means model as a main effect, as is done here, will effectively remove from 21 the covariance model any genetic effects that are shared between trait and moderator [8].”

“while further modification of these equations is possible, previous studies have noted the difficulty of modeling G × Es within a DeFries–Fulker (DF) framework (Purcell, 2002).”

“Biometric moderation models were run to determine if genetic and environmental components of variance on externalizing varied by level of parental marital discord (Purcell, 2002).”

“To study GxE, we used twin models incorporating moderation effects (Purcell, 2002).”

“Note however that these shortcomings are not unique to the item level approach used here, as they are also problematic in, for instance, the popular genotype by measured environment approach (Purcell 2002).”

“If gene-by-environment interactions did occur for identical twins, in particular, they would be of the shared environment, functioning to make the twins more similar, rather than different (Purcell, 2002).”

“The difference depends on which source of environmental variation interacts with genetic variation; if A and C interact, G×E effects appear as A; if A and E interact, G×E effects appear as E (Purcell, 2002).”

“Active or evocative rGE (i.e., seeking out environments or receiving reactions from environments that fi t heritable characteristics) and AxC interaction effects would be confounded with estimates of A effects in ACE models (Briley et al., 2018; Purcell, 2002).”

“Given that estimates of C in TEDS were very small at baseline, this sign reversal may reflect parameter instability introduced by estimating C moderation (Purcell, 2002; van der Sluis et al., 2012; Verhulst, Prom-Wormley, Keller, Medland, & Neale, 2019).”

“…more robust forms of disease resistance, host-by-pathogen interactions may be included in prediction models in the same way that environmental data are included to predict genotype-by-environment (G × E) interactions (Crossa et al., 2017; Jarquín et al., 2014; Purcell, 2002; Tang et al., 2022).”

“Following previous recommendations (Purcell, 2002), tables and figures report unstandardized path coefficients and moderator estimates that reflect absolute differences in genetic/environmental influences across the moderators.”

“A bivariate Cholesky decomposition (Purcell 2002) was fitted with practice as a moderator.”

“However, it is also plausible that these contrasting directions of effect are artifactual, 38,39 and replication in another sample would improve confidence in this pattern of results.”

“…prior simula - tions suggest that we should have been sufficiently powered to detect non-shared environmental moderation (Burt et al. 2020a , b ; Purcell 2002 ), the rather large E moderation effect size observed in the academic resilience moderation models diathesis-stress model of GxE (termed…”

“2) can vary as a function of each other, it is generally recommended to report the unstandardized variance components (a 2 , c 2 , e 2 ) when studying moderation effects (Purcell 2002).”

“…models, the standard A, C, and E paths that indicate the magnitude of additive genetic, shared environmental, and non-shared environmental effects are specified to include a β term, which indicates the significance of a potential moderator on each influence (Dick et al., 2007; Purcell, 2002).”

“To investigate the second objective, we specified a bivariate moderation model in which FC was modeled as a moderator (Figure 1; Purcell, 2002).”

“Specific twin models where genetic influences on the phenotypic variance are expressed as a linear function of the environment [40], have been applied before to explore gene-environment interactions in phenotypes other than ASD [41, 42].”

“As Purcell (2002) noted, gene–environment interplay could impact parameter estimates when not explicitly modeled.”

“In Model 3, the “residual variances” model, we estimated the extent to which these variances vary as a function of the Singh index (Purcell, 2002).”

“…done by relaxing the assumption that genetic and environmental influences operate independently, and, in particular, estimates extents to which genetic and environmental influences interact so that variance components in one variable vary with the phenotypic magnitude of the other (Purcell 2002).”

“Recent evidence suggests the important role of examining dynamic components of variance; however, the existing twin models for this problem assuming a linear or quadratic form of the moderator effects (Purcell 2002) are often too restricted in reality.”

“These include everything from Fisher’s test of mixture distributions in MZ pairs from 1925, to moderation models as in Purcell (2002), item-level data methodology, evaluation of candidate genes, variations including an instrumental variables framework and genetic risk scores, gene-region based…”

“…genetics has only recently been made feasible by the development of both biometric approaches, which provide overall tests for the existence of GxE (Purcell, 2002), and measured genotype approaches, which test hypotheses about the interaction of specific functional genetic polymorphisms with…”

“It is now possible to examine G × E within quantitative genetic designs using normative samples (Purcell, 2002; Purcell & Koenen, 2005).”

“Its use has been fundamental in gene-by-environment moderation, where the most used method leverages a definition variable to estimate the moderating effect (Purcell, 2002).”

“Models were fi tted with moderation effects 41,42 of birth year on the variance of genetic component (model 2), environmental component (model 3), orboth(model1), withadjustment for sex and birthyearfor the liability threshold (Supplementary Method 4; Supplementary Fig.”

“…is significant, as the genetic correlation indicates whether the genes influencing GA also affect exposure to CFG. Toinvestigate gene-environment interaction (G × E) effects, bivariate G × E model-fitting analyses were performed based on methods by Purcell (2002) and van Sluis et al. (2012).”

“With respect to prevention, gene-environment interaction models (Purcell 2002 ) can be used to identify modifiable environmental influences which increase genetic influ - ences on psychopathology and can be targeted for preven - tive interventions (e.g., Oginni & Hur, 2022 ).”