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

Protective Predisposing

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Conceptualizing G-E interaction in the case of a single gene

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

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2

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1928 or earlier 1929-1938 1939-1946 1947-1057

Additive genetic factors Common environmental factors

Specific environmental factors

Source: Silventoinen et al, Am J Publ Health 2000

Heritability of height in different birth cohorts in women

0

2

4

6

8

10

12

1928 or earlier 1929-1938 1939-1946 1947-1057

Additive genetic factors Common environmental factors

Specific environmental factors

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

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c+βYM e+βZMa+βXM

μ+βMM

G-E interaction model

M

A

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C E

c+βYM e+βZMa+βXM

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

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A2

a1+βY1M

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a2+βY2Ma12+βY12M

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

Moderator

Nonlinear Moderation

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a + βXM +βX2M2

c + βyM +βY2M2

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Nonlinear Moderation can be modeled with the Addition of a quadratic term

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 1 x 1 = 1

DZ Pairs/Full Sibs 1 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)

EnvironmentAdditive

Genetic Effects

Genotype x Unshared

Environment Interaction

MZ Pairs 0 1 0 x 1 = 0

DZ Pairs/Full Sibs 0 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.