Bivariate Genetic Analysis
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1 Bivariate Genetic Analysis Boulder Workshop 2018 Hermine H. Maes, Elizabeth Prom-Wormley, Lucia Colondro Conde, et. al.
2 Questions Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance? Bivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between two traits?
3 Two Traits
4 Causes of covariation Two or more traits can be correlated because they share common genes or common environmental influences same genetic/environmental factors influencing traits? With twin data on multiple traits it is possible to partition the covariation into its genetic and environmental components Goal is to understand what factors make sets of variables correlate or co-vary
5 Bivariate Twin Data individual twin within between trait within between within-twin within-trait co(variance) (within-twin cross-trait) covariance (cross-twin within-trait) covariance cross-twin cross-trait covariance
6 Sources of Information Within-twin Cross-trait covariance: phenotypic covariance Cross-twin Cross-trait covariance: between twins MZ:DZ ratio of Cross-twin Cross-trait covariance Ratio of Cross-twin to Within-twin Cross-trait covariance
7 s Phenotype 1 (P1) P1T2 P2T2 P1T2 P2T2 P1T2
8 s Phenotype 2 (P2) P1T2 P2T2 P1T2 P2T2 P1T2 P2T2
9 Phenotypic P1-P2 Within-Twin Cross-Trait P1T2 P2T2 P1T2 P2T2 P1T2 P1T2P2T2 P1T2P2T2 P2T2
10 Cross-Twin Within-Trait P1 P1T2 P2T2 Within-Trait P1T2 P1T2 P2T2 Within-Trait P1T2 P1T2 P1T2P2T2 P1T2P2T2 P2T2
11 Cross-Twin Within-Trait P2 P1T2 P2T2 Within-Trait P1T2 Within-Trait P2T2 P1T2 P2T2 Within-Trait P1T2 Within-Trait P2T2 P1T2 P1T2P2T2 P1T2P2T2 P2T2
12 Cross-Twin Cross-Trait X1Y2 P1T2 P2T2 Within-Trait P1T2 Cross-Trait P2T2 Within-Trait P2T2 P1T2 P2T2 Within-Trait P1T2 Cross-Trait P2T2 Within-Trait P2T2 P1T2 P1T2P2T2 P1T2P2T2 P2T2
13 Cross-Twin Cross-Trait X2Y1 P1T2 P2T2 Within-Trait P1T2 Cross-Trait P1T2 Cross-Trait P2T2 Within-Trait P2T2 P1T2 P2T2 Within-Trait P1T2 Cross-Trait P2T2 Cross-Trait P1T2 Within-Trait P2T2 P1T2 P1T2P2T2 P1T2P2T2 P2T2
14 Bivariate Twin Matrix P1T2 P2T2 V C CP1T2 CP2T2 C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
15 Within Twin s P1T2 P2T2 V C CP1T2 CP2T2 Within-Twin C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 Within-Twin P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
16 Cross-Twin s P1T2 P2T2 V C CP1T2 CP2T2 Within-Twin Cross-Twin C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 Cross-Twin Within-Twin P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
17 Two Phenotypes/Twin - Within-Twin s
18 Cross-Twin s
19 A Cross-Twin s
20 C Cross-Twin s
21 E Cross-Twin s
22 Bivariate Twin Matrix
23 Bivariate Twin Matrix VA11
24 Bivariate Twin Matrix VA11 VA21
25 Bivariate Twin Matrix VA11 VA21 VA21
26 Bivariate Twin Matrix VA11 VA21 VA21 VA22
27 Bivariate Twin Matrix VA11 + VE11 VA21 + VE21 VA21 + VE21 VA22 + VE22
28 Bivariate Twin Matrix P1T2 P2T2 Within-Trait P1T2 Cross-Trait P1T2 Cross-Trait P2T2 Within-Trait P2T2
29 Bivariate Twin Matrix P1T2 P2T2 1/0.5 * VA11 Cross-Trait P1T2 Cross-Trait P2T2 Within-Trait P2T2
30 Bivariate Twin Matrix P1T2 P2T2 1/0.5 * VA11 1/0.5 * VA21 Cross-Trait P2T2 Within-Trait P2T2
31 Bivariate Twin Matrix P1T2 1/0.5 * VA11 1/0.5 * VA21 P2T2 1/0.5 * VA21 Within-Trait P2T2
32 Bivariate Twin Matrix P1T2 1/0.5 * VA11 1/0.5 * VA21 P2T2 1/0.5 * VA21 1/0.5 * VA22
33 Predicted Twin Matrix P1T2 P2T2 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE22 1/0.5 * VA11 + VC11 1/0.5 * VA21 + VC21 1/0.5 * VA21 + VC21 1/0.5 *VA22 + VC22 P1T2 P2T2 1/0.5 * VA11 + VC11 1/0.5 * VA21 + VC21 1/0.5 * VA21 + VC21 1/0.5 *VA22 + VC22 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE22
34 Predicted MZ Twin P1T2 P2T2 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE22 VA11 + VC11 VA21 + VC21 VA21 + VC21 VA22 + VC22 P1T2 P2T2 VA11 + VC11 VA21 + VC21 VA21 + VC21 VA22 + VC22 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE22
35 Predicted DZ Twin P1T2 P2T2 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE * VA11 + VC * VA21 + VC * VA21 + VC *VA22 + VC22 P1T2 P2T2 0.5 * VA11 + VC * VA21 + VC * VA21 + VC *VA22 + VC22 VA11 + VC11 + VE11 VA21 + VC21 + VE21 VA21 + VC21 + VE21 VA22 + VC22 + VE22
36 Bivariate Twin Matrix P1T2 P2T2 V C CP1T2 s of CP2T2 & P2 same across twins and C V zygosity groups CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
37 Bivariate Twin Matrix P1T2 P2T2 V C CP1T2 s CP2T2 of P1& P2 same across twins and C V zygosity groups CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
38 Bivariate Twin Matrix P1T2 P2T2 Cross-Twin Within- V C CP1T2 CP2T2 Trait s differ by zygosity C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
39 Bivariate Twin Matrix P1T2 P2T2 Cross-Twin Cross- V C CP1T2 CP2T2 Trait s differ by zygosity C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2
40 Example MZ Matrix P1T2 P2T P1T P2T
41 Example DZ Matrix P1T2 P2T P1T P2T
42 Cross-Trait s Within-twin Cross-trait covariances imply common etiological influences (phenotypic covariance) Cross-twin Cross-trait covariances imply familial common etiological influences MZ/DZ ratio of Cross-twin Cross-trait covariances reflects whether common etiological influences are genetic or environmental Ratio of Cross-twin to Within-twin Cross-trait covariance reflects on role of unique environment
43 Genetic to Genetic Correlation calculated by dividing genetic covariance by square root of product of genetic variances of two variables 1 r g r g 1 = 1 σ 2 A σ 2 A22 * σ 2 A11 σ 2 A21 σ 2 A12 σ 2 A22 * 1 σ 2 A σ 2 A22
44 Contribution to Phenotypic Correlation if VA21=~VA11 & VA22, then two sets of genes overlap completely if however VA11 & VA22 are near zero, genes do not contribute much to phenotypic correlation contribution to phenotypic correlation is function of both heritabilities and rg
45 OpenMx Specification P1T2 P2T2 V C CP1T2 CP2T2 C V CP1T2 CP2T2 P1T2 CP1T2 CP1T2 VP1T2 CP1T2P2T2 P2T2 CP2T2 CP2T2 CP1T2P2T2 VP2T2 OpenMx script
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