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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


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)




Age changes in variances and correlations
Age Changes inVariances and Correlations


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


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)




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


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


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


No random growth differences

No autoregression


No random growth differences

Autoregression (b=0.9/year)


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



Independent constants ( (b=0.9)l=6) and

Linear growth (l=2). No autoregression


Correlated constants and (b=0.9)

Linear growth (r=0.8). No autoregression


Correlated constants and (b=0.9)

Linear growth (r=-0.8). No autoregression


You can get almost any pattern if you change the parameters (b=0.9)

Correlated constant (l=6), linear(l=1) and quadratic (l=2) growth (rcl=0.4, rlq=0.5),

autoregression (b=0.8)


Cross-temporal genetic (b=0.9)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.


Cross-temporal genetic correlations (b=0.9)

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 (b=0.9)

…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?


Applications 1 autoregressive model for development of conservative attitudes
Applications (1) genetic and environmental components? “Autoregressive” Model for Development of Conservative Attitudes


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


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

on the Liberalism-Conservatism Index during Childhood and Adolescence


Cross-age Correlations Showing Modest Change in Shared and Unique EnvironmentUnique 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)


Cross-age Correlations Showing Shared Environment Effects Shared and Unique EnvironmentPersist 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)


  • Model Shared and Unique Environment 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”).


ML parameter estimates for principal parameters Shared and Unique Environment

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


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