gene-environment interaction models karri silventoinen
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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
Tra
it V
alue
/Ris
k of
Dis
orde
r
Aa
AA
aa
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
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
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
M
A
T
C E
c+βYM e+βZMa+βXM
μ+βMM
G-E interaction model
M
A
T
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
T
A2
a1+βY1M
P
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
Aa
AA
aa
A C E
T
a + βXM +βX2M2
c + βyM +βY2M2
e + βZM +βZ2M2
+ βMM
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.