“Development”

1. “Development” Lindon Eaves, NIDA Workshop, October 2010

2. Issues and Questions Things change with time Systems learn, remember and forget How do we incorporate these processes in genetic models for behavioral development and aging?

4. Causal, Developmental Network

5. Some Data

7. We will focus on single variables • But same mathematics extends to more complex problems and processes…e.g. cross-temporal networks of causality.

8. Tasks 1. Get a feel for some data • Outline elements of a formal model • Explore how changes in model lead to changes in structure of data 4. Illustrate some applications 5. Try an example analysis in OpenMx (Nathan)

9. Average Trends

12. Individual Differences

14. Age Changes inVariances and Correlations

17. Phenotypic correlations for total Olweus scores across ages Age 8 9 10 11 12 13 14 15 16 17 18 8 1.00000 0.40599 0.48920 0.37489 0.42908 0.44412 0.33718 0.32222 0.10788 . . 9 0.40599 1.00000 0.58677 0.52948 0.23738 0.49436 0.42475 0.37785 0.41377 0.31299 . 10 0.48920 0.58677 1.00000 0.55042 0.55460 0.65617 0.38359 0.35088 0.41824 0.29044 -0.05075 11 0.37489 0.52948 0.55042 1.00000 0.44463 0.48617 0.56144 0.39357 0.48213 0.35473 0.31592 12 0.42908 0.23738 0.55460 0.44463 1.00000 0.30763 0.57259 0.53623 0.49282 0.52786 0.47710 13 0.44412 0.49436 0.65617 0.48617 0.30763 1.00000 0.72990 0.54786 0.55997 0.51216 0.54057 14 0.33718 0.42475 0.38359 0.56144 0.57259 0.72990 1.00000 0.54756 0.63722 0.65555 0.63536 15 0.32222 0.37785 0.35088 0.39357 0.53623 0.54786 0.54756 1.00000 0.64921 0.64388 0.53136 16 0.10788 0.41377 0.41824 0.48213 0.49282 0.55997 0.63722 0.64921 1.00000 0.73018 0.73167 17 . 0.31299 0.29044 0.35473 0.52786 0.51216 0.65555 0.64388 0.73018 1.00000 0.61137 18 . . -0.05075 0.31592 0.47710 0.54057 0.63536 0.53136 0.73167 0.61137 1.00000 Source: Virginia Twin Study of Adolescent Behavioral Development October 2010

18. Age trends in twin correlations for anti-social behavior (Olweus BAQ) Correlation Age (yr) Source: Virginia Twin Study of Adolescent Behavioral Development (Child self-reports)

19. Conduct Disorder: Age changes in genetic effects)

20. Expression Contingent on Milestone

21. Age-dependent in Varriance and Twin Resemblance when Gene Expression is Contingent on Genetic or Environmental Differences in Attainment Of Developmental Milestone Source: Eaves and Silberg, Behavior Genetics, 2002

22. Age-dependent Contributions of Shared Environment and Epistasis to Twin Resemblance when Gene Expression is Contingent on Genetic or Environmental Differences in Attainment Of Developmental Milestone Source: Eaves and Silberg, Behavior Genetics, 2002

23. Twin correlations in social attitudes across the life-span Correlation Source: MCV Cardiovascular Twin Study (9-17); Virginia 30,000 (18-80)

28. Types of Model • Growth Curves • Autoregression • Contingent expression

29. Growth Curve Yit = mi+bitXit + eit Outcome = constant+slope x age + other stuff i=person, t=time 1.Can make it more fancy (non-linear) 2. Slope depends on person (genes and environment) 3. Same basic model for GxE (see e.g. Mather and Jinks, 1982)

30. Autoregression Yit = m+bYi(t-1) + eit Now = constant + slope x last time + new stuff i=person, t=time 1.Can make it more fancy (higher order, random b) 2. “Slope” is the effect of “last time” on “now” (remembering, forgetting, learning etc.)

31. Putting it Together in a Structural Model

32. Matrix Formulation “Loadings” “Variances” “Correlations” “Residuals” • = A L 1/2 RL 1/2 A’ + Y Growth model • = (I-B)-1 W (I-B)’ -1 + U Autoregression “Autoregression” Notes: W and S may be different for genetic and environmental structure Loadings (A) are fixed a priori (covariate values) bi,i+1 are free (may be equal), other elements of B are usually zero

33. No random growth differences No autoregression

34. No random growth differences Autoregression (b=0.9/year)

35. Cross-temporal genetic covariances: autoregressive model (b=0.9)

36. Cross-temporal genetic correlations: autoregressive model (b=0.9)

37. Independent constants (l=6) and Linear growth (l=2). No autoregression

38. Correlated constants and Linear growth (r=0.8). No autoregression

39. Correlated constants and Linear growth (r=-0.8). No autoregression

40. You can get almost any pattern if you change the parameters Correlated constant (l=6), linear(l=1) and quadratic (l=2) growth (rcl=0.4, rlq=0.5), autoregression (b=0.8)

41. Cross-temporal genetic covariances Correlated constant (l=6), linear(l=1) and quadratic (l=2) growth (rcl=0.4, rlq=0.5), Y=0.8, autoregression (b=0.8), U=0.

42. Cross-temporal genetic correlations Correlated constant (l=6), linear(l=1) and quadratic (l=2) growth (rcl=0.4, rlq=0.5), Y=0.8, autoregression (b=0.8), U=0.

43. …and this is only the genetic bit …imagine what can happen if you start to include the environment

44. Does the same type of developmental mechanism apply to genetic and environmental components?

45. Applications (1) “Autoregressive” Model for Development of Conservative Attitudes

46. The Relative Influence of Shared and Unique Environmental Influence on Liberalism-Conservatism during Childhood and Adolescence

47. First-order Autoregressive Model for the Effects of the Shared and Unique Environment on the Liberalism-Conservatism Index during Childhood and Adolescence

48. Cross-age Correlations Showing Modest Change in Unique Environment Effects on Conservative Attitudes during Childhood and Adolescence Note: Figure portrays cross-age correlations over time in unique environmental effects on the liberalism-conservatism index • Source: MCV Cardiovascular Twin Study • (see Hatemi et al., The Journal of Politics, Vol. 71, No. 3, July 2009, Pp. 1141–1156)

49. Cross-age Correlations Showing Shared Environment Effects Persist and Accumulate during Childhood and Adolescence • Note: Figure portrays cross-age correlations over time in unique environmental effects • on the liberalism-conservatism index • Source: MCV Cardiovascular Twin Study • (see Hatemi et al., The Journal of Politics, Vol. 71, No. 3, July 2009, Pp. 1141–1156)

50. Model comparison statistics for VTSABD longitudinal MFQ depression scores 1 k=# of free parameters in model for covariance structure (i.e. ignoring mean parameters). 212 parameters fixed to zero (no data available for extimation of remote correlations). 3 Denotes number of model used for comparison. Note: elements of Y and U are assumed to be constant over time unless noted otherwise (“free”).