1. Gene-Environment Interaction
AGES workshop, Fall 2012
Lindon Eaves – Introduction
Tim York – Lots of slides
Sarah Medland – Making it work

2. Genotype x Environment Interaction
Genetic control of sensitivity to the environment
Environmental control of gene expression

3. The Biometrical Genetic Approach: GxE = Genetic Control of “Sensitivity” to environment
See e.g. Mather and Jinks.
Like any other phenotype – individual differences in sensitivity may be genetic

4. See e.g. Purcell “a,c,e modulated by covariate”
Alternative Approach GxE = “Environmental modulation” of path from genotype to phenotype
See e.g. Purcell
“a,c,e modulated by covariate”

5. CARE!
Results depend on scale – often remove GxE (and other “interactions” – e.g. epistasis) by change in scale
Often try to choose units so model is additive/linear and simple.
“Simplicity is truth” (?)

6. “Environment”
Micro-environment (unmeasured, random) “E” and “C” in twin models
Macro-environment (measured, ?”fixed”)
SES, life events, exposure, smoking
“Independent” (of genotype)
“Correlated with genotype – of individual (“active/evocative”) or relative (“passive”)

7. Animals, Plants and Microorgansims
GxE common property of genetic systems
Ranking of lines/strains changes over environments: ?“genetic correlation across environments”
Polygenic: genes affecting response to E widely distributed across genome (Caligari and Mather)
GxE usually small relative to main effects of G and E (“power”?)
Can select separately for means and slopes (“different genes cause GxE”)
Some genes affect response to specific environmental features (Na, K, rain, diet, separation)
Some genes affect response to overall quality of environment (“stress”)
GxE adaptive – own genetic architecture (A,D etc) – genetic vulnerability, resilience, sensation-seeking, harm avoidance (rGE)
GxE scale dependent – choose units of measurement

8. Genotype x Environment Interaction

9. Where does GxE go in “ACE” model?
AxE -> “E”
AxC -> “A”
See Jinks, JL and Fulker, DW (1970) Psych. Bulletin

10. 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.

11. 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.

12. Testing for GxE and GxC
Plot absolute within MZ pair differences against pair means (CARE!!)
Plot absolute within DZ pair differences against shared measured environment

13. Basic Model (1960’s)
Yi |E = gi + biE + di Yi |E = phenotype of ith genotype in environment E gi = main effect (“intercept”) of ith genotype bi = slope (“sensitivity”) of ith genotype in response to environment (gi , bi) ~ N[m,G]

14. b=m + g1A1 + g2A2 GxE: A biometrical genetic model A2 M A1 g2 g1 b a P

15. Pi|Mk= aA1i + (m + g1A1i + g2A2i)Mk+ eEik
ith phenotype in kth level of measured environment
Pi|Mk= aA1i + (m + g1A1i + g2A2i)Mk+ eEik
aA1i + (m + g1A1i + g2A2i)Mk+ eEik
= ck+ (a + g1Mk) A1i + g2MkA2i+ eEik

16. [a2 + ag1(Mk+Ml)+ (g12+g22)MkMl]r + Cov(Ei1k,Ei2l)
Expected twin covariance
conditional on environments of first and second twins
Cov(Pi1|Mk ,Pi2|Ml ) =
[a2 + ag1(Mk+Ml)+ (g12+g22)MkMl]r
+ Cov(Ei1k,Ei2l)
r = genetic correlation (1 in MZs)

17. No GxE: Genetic covariances and correlations

18. Scalar GxE: Genetic covariances and correlations

19. Non-Scalar GxE: Genetic covariances and correlations

20. Mixed GxE: Genetic covariances and correlations

21. [c.f. Analysis of sex limited gene effects].
Note:
Can’t separate components of “mixed” GxE unless you have same or related genotypes (MZ and/or DZ pairs) in concordant and discordant environments.
[c.f. Analysis of sex limited gene effects].

22. Modulation of gene expression by measured environment
[and environmental modulation of non-genetic paths]

23. Ways to Model Gene-Environment Interaction in Twin Data
Multiple Group Models
(parallel to testing for sex effects using multiple groups)

24. Sex Effects
Females
Males

25. Sex Effects
Females
Males
aF = aM ? cF = cM ? eF = eM ?

26. GxE Effects
Urban
Rural
aU = aR ? cU = cR ? eU = eR ?

27. Problem: Many environments of interest do not fall into groups
Regional alcohol sales
Parental warmth
Parental monitoring
Socioeconomic status
Grouping these variables into high/low categories loses a lot of information

28. Standard model
Means vector
Covariance matrix

29. Model-fitting approach to GxE
Twin 1
Twin 2 M M

30. Model-fitting approach to GxE
a+XM c e
a+XM c e m m
Twin 1
Twin 1
Twin 2
Twin 2 M M

31. Individual specific moderators
a+XM1 c e
a+XM2 c e m m
Twin 1
Twin 1
Twin 2
Twin 2 M M

32. E x E interactions A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1
Twin 1
Twin 1
Twin 2
Twin 2 M M

33. ‘Definition variables’ in Mx
General definition: Definition variables are variables that may vary per subject and that are not dependent variables
In Mx: The specific value of the def var for a specific individual is read into a matrix in Mx when analyzing the data of that particular individual

34. ‘Definition variables’ in Mx
create dynamic var/cov structure
Common uses:
To model changes in variance components as function of some variable (e.g., age, SES, etc)
As covariates/effects on the means (e.g. age and sex)

35. Classic Twin Model: Var (T) = a2 + c2 + e2 Moderation Model: Var (T) =
(a + βXM)2 + (c + βYM)2 + (e + βZM)2
Purcell 2002,
Twin Research

36. Var (T) = (a + βXM)2 + (c + βYM)2 (e + βZM)2
Where M is the value of the moderator and
Significance of βX indicates genetic moderation
Significance of βY indicates common environmental moderation
Significance of βZ indicates unique environmental moderation
BM indicates a main effect of the
moderator on the mean

37. Additional Things to Consider
Unstandardized versus standardized effects

38. Additional Things to Consider
ENVIRONMENT 1
ENVIRONMENT 2
Unstandardized Variance
Standardized Variance
Genetic 60
0.60
0.30
Common environmental 35
0.35 70
Unique environmental 5
0.05
Total variance
100
200
Unstandardized versus standardized effects

39. Environment may not modulate all the genes
C.f. Biometrical genetic model – Different genes may control main effect and sensitivity/slope

40. AS AU M T aM aS + βXSM aU + βXUM βXS indicates moderation
of shared genetic effects
BXU indicates moderation
of unique genetic effects
on trait of interest M T

41. Genotype-Environment Covariance/Correlation (rGE) see e. g
Genotype-Environment Covariance/Correlation (rGE) see e.g. RB Cattell (1965)

42. Gene-environment Interaction
Genetic control of sensitivity to the environment
Environmental control of gene expression
Gene-environment Correlation
Genetic control of exposure to the environment
Different genotypes select or create different environments
Different genotypes are exposed to correlated environments (e.g. sibling effects, maternal effects)
Environments select on basis of genotype (Stratification, Mate choice)

43. This complicates interpretation of GxE effects
If there is a correlation between the moderator (environment) of interest and the outcome,
and you find a GxE effect, it’s not clear if:
The environment is moderating the effects of genes or
Trait-influencing genes are simply more likely to be present in that environment

44. Ways to deal with rGE
Limit study to moderators that aren’t correlated with outcome
Pro: easy
Con: not very satisfying
Moderator in means model will remove from the covariance genetic effects shared by trait and moderator
Pro: Any interaction detected will be moderation of the trait specific genetic effects
Con: Will fail to detect GxE interaction if the moderated genetic component is shared by the outcome and moderator
Explicitly model rGE using a bivariate framework
Pro: explicitly models rGE
Con: Power to detect BXU decreases with increasing rGE; difficulty converging

45. Getting it to work SARAH!!!!

46. Practical (1): Using Multiple Group Models to test for GxE

47. Adding Covariates to Means Model
m+MM1
m+MM2
Twin 1
Twin 2 M M

48. Matrix Letters as Specified in Mx Script
c+YM1
c+YM2
a+XM1
a+XM2
c+cM*D1
c+cM*D2
e+ZM1
e+ZM2
a +aM*D1
a+aM*D2
e+eM*D2
e+eM*D1
Mediation versus moderation
If a variable mediates an effect,
significant in the means model, M > 0
significant increase in a, c or e when M is fixed to 0
If a variable moderates an effect
X>0, Y>0, or Z > 0
irrespective of M or any reduction in a, c or e.
Twin 1
Twin 2 M M
m+MM2
m+MM1
mu+b*D2
mu+b*D1
Main effects and moderating effects

49. Practical (2): Using Definition Variables to test for GxE

50. Matrix Letters as Specified in Mx Script
c+YM1
c+YM2
a+XM1
a+XM2
c+cM*D1
c+cM*D2
e+ZM1
e+ZM2
a +aM*D1
a+aM*D2
e+eM*D2
e+eM*D1
Mediation versus moderation
If a variable mediates an effect,
significant in the means model, M > 0
significant increase in a, c or e when M is fixed to 0
If a variable moderates an effect
X>0, Y>0, or Z > 0
irrespective of M or any reduction in a, c or e.
Twin 1
Twin 2 M M m m mu mu

51. ‘Definition variables’ in Mx
create dynamic var/cov structure
Common uses:
To model changes in variance components as function of some variable (e.g., age, SES, etc)
As covariates/effects on the means (e.g. age and sex)

52. Definition variables used as covariates
General model with age and sex as covariates:
yi =  + 1(agei) + 2 (sexi) + 
Where yi is the observed score of individual i,  is the intercept or grand mean, 1 is the regression weight of age, agei is the age of individual i, 2 is the deviation of males (if sex is coded 0= female; 1=male), sexi is the sex of individual i, and  is the residual that is not explained by the covariates (and can be decomposed further into ACE etc).

53. Allowing for a main effect of X
Means vector
Covariance matrix

54. Common uses of definition variables in the means model
Incorporating covariates (sex, age, etc)
Testing the effect of SNPs (association)
In the context of GxE, controlling for rGE