# Bivariate Genetic Analysis Practical

Bivariate Genetic Analysis Practical Lucia Colodro Conde, Elizabeth Prom-Wormley, and Hermine Maes with thanks to Meike Bartels and Dorret Boomsma \\workshop\Faculty\lucia\Wednesday_biv_prac Open twoACE_vc_nl_biv_2gr.R Twin Covariances/ Correlations What are our initial expectations after looking at the covariance and

correlation matrices by zygosity? MZCov gff_T1 hap_T1 gff_T2 hap_T2 gff_T1 0.96 0.40 0.56 0.31 hap_T1 0.40 1.08 0.33 0.40 gff_T2 0.56 0.32 1.14 0.35 hap_T2 0.30 0.40 0.35 0.94 DZCov gff_T1 hap_T1 gff_T2 hap_T2

gff_T1 hap_T1 gff_T2 hap_T2 1.08 0.44 0.46 0.18 0.44 1.04 0.31 0.15 0.46 0.30 1.09 0.34 0.18 0.15 0.34

0.92 Conclusions Twin Covariances/ Correlations Within individual cross-trait covariance implies common aetiological influences Cross-twin cross-trait covariance implies common aetiological influences are familial Whether familial influences genetic or environmental shown by MZ:DZ ratio of cross- twin cross-trait covariances Bivariate Genetic Model

Important Questions to Answer What is the variance due to genetic and environmental contributions for a measure? Variance Decomposition -> Heritability, (Shared) environmental influences How much of the phenotypic correlation is accounted for by genetic and environmental influences? Covariance Decomposition -> The influences of genes and environment on the covariance between the two variables

Is there a large overlap in gene/ environmental sets? covA <- mxMatrix( type="Symm", nrow=nv, ncol=nv, free=TRUE, values=valDiag(svPa,nv), labels=labLower("VA",nv), name="VA" ) Looking at VA fitACE\$matrices\$VA SymmMatrix 'VA' \$labels

[,1] [,2] [1,] "VA11" "VA21" [2,] "VA21" \$values "VA22" [,1] [,2] [1,] 0.27159025 0.17308458 [2,] 0.17308458 \$free

[,1] [,2] [1,] TRUE TRUE [2,] TRUE TRUE 1- What is the variance is due to genetic and environmental contributions for a specific measure? Variance Decomposition -> Heritability, (Shared) environmental influences STANDARDIZED VARIANCES fitACE\$algebras\$SV \$SV

mxAlgebra 'SV' \$formula: cbind(VA/V, VC/V, VE/V) \$result: SA SA SC SC SE SE SV 0.25 0.45 0.30 0.38 0.44 0.16 SV 0.45 0.51 0.38 -0.11 0.16 0.60

Important Questions to Answer What is the variance due to genetic and environmental contributions for a measure? Variance Decomposition -> Heritability, (Shared) environmental influences How much of the phenotypic correlation is accounted for by genetic and environmental influences? Covariance Decomposition -> The influences of genes and environment on the covariance between the two variables

Is there a large overlap in gene/ environmental sets? A Cross-Twin Covariances Genetic Correlation rg= 12

11 22 ) corA

Careful! If a11 and a22 are near zero then shared genes do not contribute to correlation Genetic Correlation High genetic correlation = large overlap in genetic effects on the two phenotypes Does it mean that the phenotypic correlation between the traits is largely due to genetic effects? No: the substantive importance of a particular rG depends the value of the correlation and the value of VAs i.e. importance is also determined by the heritability of each phenotype

Extra ConsiderationsGenetic Correlations Two Paper and Pencil Tasks Consider two traits with a rP = 0.40 : h2P1 = 0.7 and h2P2 = 0.6 with rG = .3 What is the correlation due to additive genetic effects = ? What is the contribution to phenotypic correlation attributable to additive genetic effects = ? Consider again two traits with a rP = 0.40 : h2P1 = 0.2 and h2P2 = 0.3 with rG = 0.8 Correlation due to additive genetic effects = ?

Contribution to phenotypic correlation attributable to additive genetic effects = ? Correlation due to A: vide by rP to find contribution to phenotypic correlatio

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