1. Gene-environment interaction models
Karri Silventoinen

2. 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

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

4. 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

5. 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

6. 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

7. 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

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

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

11. 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

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

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

14. 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

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

16. 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

17. Nonlinear Moderation AA Aa aa
Moderator

18. 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

21. 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

22. 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
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.

23. 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
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.