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Understanding Genetic and Environmental Contributions to Trait Variance and Covariance in Twins

This analysis explores the contributions of additive genetic, dominance/shared environmental, and unique environmental factors to the variance of traits. It also investigates the covariance between traits using bivariate analysis within twin data. By partitioning the covariation into genetic and environmental components, the study aims to identify whether traits are influenced by common genetic/environmental factors. Utilizing a multivariate saturated model for twin data, this work sheds light on the underlying genetic and environmental structures that contribute to concurrent trait variations over time.

kasper-wolfe
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Understanding Genetic and Environmental Contributions to Trait Variance and Covariance in Twins

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  1. Twin Analysis 104 • October 2010

  2. Bivariate Questions I • 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. Bivariate Questions II • Two or more traits can be correlated because they share common genes or common environmental influences • e.g. Are the same genetic/environmental factors influencing the traits? • With twin data on multiple traits it is possible to partition the covariation into its genetic and environmental components • Goal: to understand what factors make sets of variables correlate or co-vary

  5. Bivariate Twin Data

  6. Bivariate Twin Covariance Matrix

  7. Genetic Correlation

  8. Alternative Representations

  9. Cholesky Decomposition

  10. Bivariate AE Model

  11. MZ Twin Covariance Matrix a112+e112 a112 a21*a11+ e21*e11 a222+a212+ e222+e212 a21*a11 a222+a212

  12. DZ Twin Covariance Matrix a112+e112 .5a112 a21*a11+ e21*e11 a222+a212+ e222+e212 .5a21*a11 .5a222+ .5a212

  13. Within-Twin Covariances [Mx]

  14. Within-Twin Covariances

  15. Cross-Twin Covariances

  16. Cross-Trait Covariances • Within-twin cross-trait covariances imply common etiological influences • 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

  17. Practical Example I • Dataset: MCV-CVT Study • 1983-1993 • BMI, skinfolds (bic,tri,calf,sil,ssc) • Longitudinal: 11 years • N MZF: 107, DZF: 60

  18. Bivariate • Saturated Model • equality of means/variances • Genetic Models (ACE) • bivariate -> Cholesky Decomposition

  19. > parameterSpecifications(bivACEFit)model:ACE, matrix:a [,1] [,2] [1,] [a11] 0 [2,] [a21] [a22]model:ACE, matrix:c [,1] [,2] [1,] [c11] 0 [2,] [c21] [c22]model:ACE, matrix:e [,1] [,2] [1,] [e11] 0 [2,] [e21] [e22]model:ACE, matrix:Mean [,1] [,2][1,] [NA] [NA]

  20. Multivariate • Saturated Model • equality of means/variances • Genetic Models (ACE) • multivariate -> Cholesky Decomposition • Independent Pathway • Common Pathway

  21. Scientific Questions • Are these measures influenced by the same genes (single common factor)? • Is there more than one factor (overall fat- fat distribution)? • What is the structure of C and E? • Contribution of A, C, E factors to covariance between traits

  22. Cholesky F1 F2 F3 F4 P1 f11 P2 f21 P3 f31 P4 f41 Text Text

  23. F1 F2 F3 F4 P1 f11 0 P2 f21 f22 P3 f31 f32 P4 f41 f42

  24. F1 F2 F3 F4 P1 f11 0 0 P2 f21 f22 0 P3 f31 f32 f33 P4 f41 f42 f43

  25. F1 F2 F3 F4 P1 f11 0 0 0 P2 f21 f22 00 P3 f31 f32 f33 0 P4 f41 f42 f43 f44

  26. Phenotypic

  27. Cholesky Decomposition Estimate covariance matrix, fully saturated F1 F2 F3 F4 P1 f11 0 0 0 P2 f21 f22 00 P3 f31 f32 f33 0 P4 f41 f42 f43 f44 F1 F2 F3 F4 P1 f11 f21 f31 f41 P2 0 f22 f32 f42 P3 00 f33 f43 P4 0 00 f44 %*% F %*% t(F)

  28. Genetic

  29. & Environmental

  30. model:ACE, matrix:a [,1] [,2] [,3] [,4] [,5] [1,] [a11] 0 0 0 0 [2,] [a21] [a22] 0 0 0 [3,] [a31] [a32] [a33] 0 0 [4,] [a41] [a42] [a43] [a44] 0 [5,] [a51] [a52] [a53] [a54] [a55]model:ACE, matrix:c [,1] [,2] [,3] [,4] [,5] [1,] [c11] 0 0 0 0 [2,] [c21] [c22] 0 0 0 [3,] [c31] [c32] [c33] 0 0 [4,] [c41] [c42] [c43] [c44] 0 [5,] [c51] [c52] [c53] [c54] [c55]model:ACE, matrix:e [,1] [,2] [,3] [,4] [,5] [1,] [e11] 0 0 0 0 [2,] [e21] [e22] 0 0 0 [3,] [e31] [e32] [e33] 0 0 [4,] [e41] [e42] [e43] [e44] 0 [5,] [e51] [e52] [e53] [e54] [e55]model:ACE, matrix:Mean [,1] [,2] [,3] [,4] [,5][1,] [NA] [NA] [NA] [NA] [NA]

  31. IP

  32. Common Factor

  33. F1 P1 f11 P2 f21 P3 f31 P4 f41 F1 F2 F3 F4 P1 f11 f21 f31 f41 %*% F %*% t(F)

  34. Residuals

  35. E1 E2 E3 E4 P1 f11 0 0 0 P2 0 f22 00 P3 0 0 f33 0 P4 0 0 0 f44 E1 E2 E3 E4 P1 f11 0 0 0 P2 0 f22 00 P3 0 0 f33 0 P4 0 0 0 f44 %*% E %*% t(E)

  36. F %*% t(F) + E %*% t(E)

  37. with Twin Data

  38. twin 1

  39. GeneticCommon Factor

  40. Shared environmentalCommon Factor

  41. Unique environmental Common Factor

  42. Genetic Residuals& C & E Residuals

  43. A1 P1 a11 P2 a21 P3 a31 P4 a41 P1 P2 P3 P4 A1 a11 a21 a31 a41 %*% ac %*% t(ac)

  44. A1 A2 A3 A4 P1 a11 0 0 0 P2 0 a22 00 P3 0 0 a33 0 P4 0 0 0 a44 P1 P2 P3 P4 A1 a11 0 0 0 A2 0 a22 00 A3 0 0 a33 0 A4 0 0 0 a44 %*% as %*% t(as)

  45. model:ACE, matrix:as [,1] [,2] [,3] [,4] [,5] [1,] [as11] 0 0 0 0 [2,] 0 [as21] 0 0 0 [3,] 0 0 [as31] 0 0 [4,] 0 0 0 [as41] 0 [5,] 0 0 0 0 [as51]model:ACE, matrix:cs [,1] [,2] [,3] [,4] [,5] [1,] [cs11] 0 0 0 0 [2,] 0 [cs21] 0 0 0 [3,] 0 0 [cs31] 0 0 [4,] 0 0 0 [cs41] 0 [5,] 0 0 0 0 [cs51]model:ACE, matrix:es [,1] [,2] [,3] [,4] [,5] [1,] [es11] 0 0 0 0 [2,] 0 [es21] 0 0 0 [3,] 0 0 [es31] 0 0 [4,] 0 0 0 [es41] 0 [5,] 0 0 0 0 [es51]model:ACE, matrix:M [,1] [,2] [,3] [,4] [,5][1,] [NA] [NA] [NA] [NA] [NA] model:ACE, matrix:ac [,1] [1,] [ac11][2,] [ac21][3,] [ac31][4,] [ac41][5,] [ac51]model:ACE, matrix:cc [,1] [1,] [cc11][2,] [cc21][3,] [cc31][4,] [cc41][5,] [cc51]model:ACE, matrix:ec [,1] [1,] [ec11][2,] [ec21][3,] [ec31][4,] [ec41][5,] [ec51]

  46. Independent Pathway • Biometric model • Different covariance structure for A, C and E

  47. IP Model

  48. CP

  49. Latent Phenotype

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