Gene-environment interaction models Karri Silventoinen

Interplay between genes and environment Genetic models usually make an assumption that the genetic and environmental effects are independent Animal and plant breeding experiments have, however, shown that G-E interactions are very common Rationality behind breeding is usually to develop plants and animals who can maximally utilize improved nutrition There is clear evidence on G-E interactions also in humans Clinical trials including MZ twins Epidemiological settings The most famous example is Pima Indians in Arizona

Conceptualizing G-E interaction in the case of a single gene AA Aa Trait Value/Risk of Disorder aa Protective Predisposing ENVIRONMENT

G-E interactions in twin modeling In many situations it is reasonable to expect G-E interactions also in twin modeling For example, the effect of place of residence (rural-urban) on the genetics of alcohol consumption in Finland (Rose et al, 2001) G-E interactions are seen as differences in the genetic (or environmental) variation at different levels of environmental exposure During this course we will use models which need measured environmental exposure However, also other types of G-E interaction models are available The most powerful design utilizes information on both measures of environmental exposures and genomic scans The problem is that usually candidate genes explain only a small proportion of the phenotypic variance

G-E correlation vs. G-E interaction It is important to make distinction between G-E interaction and G-E correlation (rGE) G-E interaction refers to situation when the expression of genes is modified by environment or, the other way round, when the effect of environment is affected by genotype For example, nutrition may modify the effect of genes affecting obesity or some genotypes may be more sensitive to increase in nutrition intake In other words, the effects of genes and environment are not independent By using the current model we cannot, however, make distinction between different causal pathways Gene-environment correlation refers to situation when allele frequencies are not independent of environment Thus, the environment people are living is partly generated by their genotype For example, moderate heritability is found for experience of negative life events

Sources of gene-environment correlations There are three possible sources of gene-environment correlation Passive gene-environment correlation Parents transmit both their genes and environment Genetically musically talented parents more often listen music and own musical instruments Active gene-environment correlation Subjects with a certain genotype actively select environments that are correlated with that genotype Genetically musically talented children like to participate musical education Reactive gene-environment correlation Subjects with a certain genotype evoke certain reactions from environment Music teachers pick up genetically musically talented children for special supervision Active and reactive gene-environment correlations may be one of the reasons why heritability of many personality traits (e.g. intelligence) seem to rather increase than decrease during aging The possibility of rGE should be taken into account in interpretations of results For example if ADHD children suffer more maltreatment at home the reason may be that their parents has also genetic predisposition to antisocial behavior

G*E interaction based on multiple group analysis A simple way to analyze G-E interactions is to stratify the data by the environmental exposure Thus, we can simply utilize multiple group comparison using univariate models Significant differences in genetic and/or environmental variance components across the categories indicate the existence of G-E interaction

Heritability of height in different birth cohorts in men Source: Silventoinen et al, Am J Publ Health 2000

Heritability of height in different birth cohorts in women Source: Silventoinen et al, Am J Publ Health 2000

Problems in multiple group comparisons Multiple group comparisons have limitations, which make them unsuitable to many situations Environmental exposure needs to be same for both co-twins Such as birth cohort or place of residence If environmental exposure is continuous, categorizing it loses a lot of information if the associations are linear However if this kind of limitations are not a problem, multiple group comparison is a good alternative to more sophisticated G-E interaction models Interpretation of the results is very straightforward Possible non-linearity is not a problem We can accept heterogeneity between the categories

G-E interaction model A C E a+βXM c+βYM e+βZM M T μ+βMM

G-E interaction model A C E a+βXM c+βYM e+βZM M T μ+βMM

Matrix algebra for G-E interactions The equation a+βXM is a linear function Why this can be used to analyze interactions? We are interested in the variance component a2 instead of the path coefficient a Thus (a+βXM)2=a2+2*a*βXM+(βXM)2 This can be easily generalized to multivariate case using matrix algebra rules

Multivariate G-E interaction model a1+βY1M a12+βY12M a2+βY2M T P

Non-linear interaction effects It is also possible that the effect of environmental exposure is not linear but curvilinear For example, genetic variation may be low both at low and high level of environmental exposure This can be modeled simply by including a new moderator term in the model Even when curvilinear effects are not difficult to model, power may be a problem Also the extreme ends of environmental exposures may be problematic Reporting errors etc. Before analyzing curvilinear associations, there should be clear theoretical justification why we expect this kind of associations Sample size should also be large and the measurement of environment high quality

Nonlinear Moderation AA Aa aa Moderator

Nonlinear Moderation can be modeled with the Addition of a quadratic term A C E a + βXM +βX2M2 c + βyM +βY2M2 e + βZM +βZ2M2  + βMM T

Effect of G-E interactions on heritability If G-E interaction is not modeled it naturally does not mean that it would not affect the results In many cases we have not measured relevant environmental exposures, but we have to speculate whether they can still explain the found results G-E interaction may well be one reason why common environmental influences are rarely seen even in the case when this in counterintuitive For example, the lack of common environmental effect in many psychological traits It may reflect rather that the effect of family related factors is modified by genetic factors than the lack of this effect

Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance Shared Environment Additive Genetic Effects Genotype x Shared Environment Interaction MZ Pairs 1 1 x 1 = 1 DZ Pairs/Full Sibs ½ 1 x ½ = ½ In other words—if gene-(shared) environment interaction is not explicitly modeled, it will be subsumed into the A term in the classic twin model.

Contributions of Genetic, Unshared Environment, Genotype x Unshared Environment Interaction Effects to Twin/Sib Resemblance Unshared (Unique) Environment Additive Genetic Effects Genotype x Unshared Environment Interaction MZ Pairs 1 0 x 1 = 0 DZ Pairs/Full Sibs ½ 0 x ½ = 0 If gene-(unshared) environment interaction is not explicitly modeled, it will be subsumed into the E term in the classic twin model.