ACE Problems Greg Carey BGA, 2009 Minneapolis, MN

Thought Experiment 1: Future technology identifies all loci and alleles that contribute to a phenotype. Genotype a very large sample for all these loci. Code the alleles for additive effects. Regress the phenotypes on the additive codes. Predicted values of the phenotypes are the additive genetic values = numerical estimates of latent variable A.

^ P A11 A1i Locus 1 A21 A2j Locus 2 An1 Ank Locus n a11 a1i a21 a2j    A11 A1i Locus 1 A21 A2j Locus 2 An1 Ank Locus n P a11 a1i a21 a2j an1 ank ^

Assumption 1: Phenotypes are influenced by concrete environmental events or Xs.

Thought Experiment 2: Measure all the Xs for a large sample of individuals. Regress the phenotype on all the Xs. Predicted values equal the total environmental values = numerical estimates of the sum of latent variables C + E.

X1 X2 Xn b1 b2 bn ^ P

Problem at Hand: If (C + E) = SbiXi, we should be able to find weights for C and weights for E so that: (1) C and E are uncorrelated in an individual; (2) the Es for siblings are uncorrelated.

X11 E1 X12 C1 P1

Necessary Condition 1: Every X variable can be placed into one of two mutually exclusive classes—those predicting E and those predicting C. (X variables can be either green or red).

X1e E1 X1c C1 P1

Necessary Condition 2: X variables predicting the unique environment cannot be correlated with X variables predicting the common environment within an individual. (No magenta correlations).

P1 X1e E1 X1c C1 X2c C2 X2e E2 P2

Necessary Condition 3: No sibling correlations among the Xs for the unique environment. (Green Xs cannot correlate across siblings or no green correlational paths).

P1 X1e E1 X1c C1 X2c C2 X2e E2 P2

Necessary Condition 4: No X for sib 1’s unique environment can correlate with any X for sib 2’s common environment. (No magenta correlational paths)

P1 X1e E1 X1c C1 X2c C2 X2e E2 P2

Necessary Condition 5: When C1 = C2,

Necessary Condition 5: When C1 = C2, (With some algebra), a red X for sib 1 and its counterpart for sib 2 must correlate 1.0.

X11e X1ke X1c X12 Xjc X21e X2ke E1 C E2 P1 P2

ACE Model Assumption: Select any X variable.

ACE Model Assumption: Select any X variable. That X must correlate either 0.0 or 1.0 for the relatives.

ACE Model Assumption: Select any X variable. That X must correlate either 0.0 or 1.0 for the relatives. It is not possible to have an X that correlates, say, .43 between sibs.

ACE Model Assumption: Conversely, if peer substance abuse correlates .38 among sibs, then

ACE Model Assumption: Conversely, if peer substance abuse correlates .38 among sibs, then Peer substance abuse can NOT be an environmental influence on substance abuse.

What Happened? In the beginning,

What Happened? In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).

What Happened? In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). E2 variance component morphed into variable C in path analysis.

What Happened? In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). E2 variance component morphed into variable C in path analysis. E1 variance component morphed into variable E in path analysis.

What Happened? In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). E2 variance component morphed into variable C in path analysis. E1 variance component morphed into variable E in path analysis. Variance components G1 and G2 were eliminated and replaced with variable A.

What Happened? In the process, we overlooked the fact that correlation (variance components) does not necessarily imply causality.

School Pupil1 Pupil2 Res1 Res2

Can legitimately calculate: Variance component for School.

Can legitimately calculate: Variance component for School. Orthogonal variance component for Error.

Can legitimately calculate: Variance component for School. Orthogonal variance component for Error. Test of significance of the variance component for School.

Can legitimately calculate: Variance component for School. Orthogonal variance component for Error. Test of significance of the variance component for School. Intraclass correlation for School.

But is this causal?

But is this causal? Not necessarily!

School Pupil1 Pupil2 Res1 Res2 Family1 Family2

How Important Is This? For the simple analysis of a single phenotype, no problem. For some models of GE correlation, how does a variable (G) correlate with a variance component? What about multivariate models?

Solution?

Common and Unique Environment Solution? Common and Unique Environment

Shared and Nonshared Environment Solution? Shared and Nonshared Environment

Use Total Environment = C + E Solution? Use Total Environment = C + E

P1 b A1 E1 a e P2 E2 A2 h

$5,000 prize

$5,000 prize Bouchard Prize

$5,000 prize Bouchard Prize Prove me wrong or irrelevant

$5,000 prize Bouchard Prize Prove me wrong or irrelevant Equations, not words