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“Development”. Lindon Eaves, NIDA Workshop, October 2010. Issues and Questions. Things change with time Systems learn, remember and forget How do we incorporate these processes in genetic models for behavioral development a nd aging?. Causal, Developmental Network. Some Data.

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development

“Development”

Lindon Eaves,

NIDA Workshop,

October 2010

slide2

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?

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

slide17

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

slide18

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)

slide21

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

slide22

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

slide23

Twin correlations in social attitudes across the life-span

Correlation

Source:

MCV Cardiovascular Twin Study (9-17);

Virginia 30,000 (18-80)

types of model
Types of Model
  • Growth Curves
  • Autoregression
  • Contingent expression
growth curve

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)

autoregression

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.)

matrix formulation
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

slide34

No random growth differences

Autoregression (b=0.9/year)

slide37

Independent constants (l=6) and

Linear growth (l=2). No autoregression

slide38

Correlated constants and

Linear growth (r=0.8). No autoregression

slide39

Correlated constants and

Linear growth (r=-0.8). No autoregression

slide40

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)

slide41

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.

slide42

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.

and this is only the genetic bit

…and this is only the genetic bit

…imagine what can happen if you start to include the environment

does the same type of developmental mechanism apply to genetic and environmental components

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

slide46

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

slide47

First-order Autoregressive Model for the Effects of the Shared and Unique Environment

on the Liberalism-Conservatism Index during Childhood and Adolescence

slide48

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)
slide49

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)
slide50

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”).

slide51

ML parameter estimates for principal parameters

of developmental models for MFQ depression scores (Final model).

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