Gene-Environment Interaction & Correlation

1. Gene-Environment Interaction & Correlation Danielle Dick & Danielle Posthuma Leuven 2008

2. Interplay between genes & environment • Contribution of genes and environment is additive

3. Interplay between genes & environment • Contribution of genes and environment is additive • Genes and environment are correlated: genes alter the exposure to relevant environmental factors • Genes and environment interact: • Genes control sensitivity to the environment, • The environment controls gene expression • Eaves LJ (1984) Genetic Epidemiology, 215-228 • Kendler KS, Eaves, LJ (1986) Am J Psychiatry, 279-289

4. Gene-Environment Correlation • Passive rGE – genetically related parents provide a rearing environment that is correlated with the child’s genotype • Evocative rGE – children receive responses from others that are influenced by their genotype and interpret them differently (reactive) • Active rGE – people’s choice of environments are influenced by their genotype (niche-picking)

5. How to Model Genetic Influences on Environmental Traits?

6. How to Model Genetic Influences on Environmental Traits? • The same way we study any other phenotype!

7. A Twin Study of Life events(Kendler et al., 1993) Death/illness/crisis happened to someone close to you/natural disaster Personal – marital or financial problems, robbed/assaulted

8. 1/.5 1/.5 A1 A2 A1 A2 x11 x21 x22 x11 x21 x22 P11 P21 P12 P22 Twin 1 Twin 2 Genetic correlation Master of Neuroscience 2007/2008 - Behavior Genetics Matrix Function in Mx: O = \stnd(A)

9. Implications of active and evocative rGE • Some genetic effects are indirect, operating through effects on environmental risk • If present, heritability estimates will be misleadingly high • Some effects of adverse environments are genetically mediated • Genes are involved in individual differences in environmental risk exposure

10. Gene-Environment Interaction • Genetic control of sensitivity to the environment • Environmental control of gene expression • Bottom line: nature of genetic effects differs among environments

11. Gene-Environment Interaction • First observed by plant breeders: • Sensitive strains – did great under ideal conditions (soil type, sunlight, rainfall), but very poorly under less than ideal circumstances • Insensitive strains – did OK regardless of the condition; did worse under ideal conditions but better under poor conditions

12. Conceptualizing Gene-Environment Interaction Sensitive Strain Produce Yield Insensitive Strain Poor Ideal ENVIRONMENTAL CONDITIONS

13. G-E Interaction Animal Studies Maze “Dull” Maze “Bright” (Cooper & Zubeck, 1958)

14. G-E Interaction Animal Studies Impoverished Environment Enriched Environment Maze “Dull” Impoverished Environment Enriched Environment Maze “Bright” (Cooper & Zubeck, 1958)

15. G-E Interaction Animal Studies Impoverished Environment Enriched Environment No change Improvement Maze “Dull” Impoverished Environment Enriched Environment Poorer Performance No change Maze “Bright” (Cooper & Zubeck, 1958)

16. Standard Univariate Model P = A + C + E Var(P) = a2+c2+e2 1.0 (MZ) / .5 (DZ) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 A1 C1 E1 A2 C2 E2 c c a a e e P1 P2

17. Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance

18. Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance 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.

19. Contributions of Genetic, Unshared Environment, Genotype x Unshared Environment Interaction Effects to Twin/Sib Resemblance If gene-(unshared) environment interaction is not explicitly modeled, it will be subsumed into the E term in the classic twin model.

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

21. Sex Effects Females Males

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

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

24. Influences on Alcohol Use at Age 16:Urban/Rural Interaction a2 c2 e2 Rose et al., 2001, ACER

26. Heritability of Disinhibition estimated from Dutch twin pairs stratified by religious / non-religious upbringing

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 potentially loses a lot of information

28. 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

29. 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

30. ‘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

31. ‘Definition variables’ in Mx create dynamic var/cov structure • Common uses: 1. As covariates/effects on the means (e.g. age and sex) 2. To model changes in variance components as function of some variable (e.g., age, SES, etc)

32. 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 theintercept or grand mean, 1is the regression weight of age, ageiis the age of individual i, 2 is the deviation of males (if sex is coded 0= female; 1=male), sexiis the sex ofindividual i, and is the residual that is not explained by the covariates (and can be decomposed further into ACE etc).

33. Standard model • Means vector • Covariance matrix

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

35. Model-fitting approach to GxE A C E A C E c a e a c e m m Twin 1 Twin 2 M M

36. Adding Covariates to Means Model A C E A C E c a e a c e m+MM1 m+MM2 Twin 1 Twin 2 M M

37. ‘Definition variables’ in Mx create dynamic var/cov structure • Common uses: 1. As covariates/effects on the means (e.g. age and sex) 2. To model changes in variance components as function of some variable (e.g., age, SES, etc)

38. Model-fitting approach to GxE A C E A C E c a+XM e a+XM c e m+MM1 m+MM2 Twin 1 Twin 1 Twin 2 Twin 2 M M

39. Individual specific moderators A C E A C E c a+XM1 e a+XM2 c e m+MM1 m+MM2 Twin 1 Twin 1 Twin 2 Twin 2 M M

40. E x E interactions A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1 e+ZM2 m+MM1 m+MM2 Twin 1 Twin 1 Twin 2 Twin 2 M M

41. ACE - XYZ - M A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1 e+ZM2 m+MM1 m+MM2 Twin 1 Twin 2 M M Main effects and moderating effects

42. Interaction Equivalently…  2 1 1  1 1 -  M M Biometrical G  E model No interaction a 0 -a M AA Aa aa

43. Moderation using Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1 e+ZM2 Twin 1 Twin 2

44. Definition Variables in Mx

45. Matrix Letters as Specified in Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 C+U*R C+U*S e+ZM1 e+ZM2 A+T*R A+T*S E+V*S E+V*R Twin 1 Twin 2 M M m+MM2 m+MM1 M+B*S M+B*R

46. Practical - 1 • Fit GxE script • Is main effect of moderator significant? • Is A moderation significant? • Is C moderation significant? • Is E moderation significant?

47. Fit GxE script: Results

48. Practical • Fit GxE script • Is main effect of moderator significant? • Drop B 1 1 1 • Is A moderation significant? • Drop T 1 1 1 • Is C moderation significant? • Drop U 1 1 1 • Is E moderation significant? • Drop V 1 1 1

49. Results

50. Practical - 2 • Calculate • What is genetic variance, common environmental variance, unique environmental variance • when there is no moderation? • at different levels of the moderator (calculate for -1.5,1.5) Var (T) = (a + βXM)2 + (c + βYM)2 (e + βZM)2