Correlations Between Characters In “Genetics and Analysis of Quantitative traits” by Lynch, M. and Walsh, B. Presented Sansak Nakavisut

Topics Covariance and Correlation Genetic Covariance Estimation of the Genetic Correlation Pairwise Comparison of Relatives Nested Analysis of Variance and Covariance Regression of Family Means

Covariance Covariance measures how much 2 variables vary together wt & age, age & grey hair; ADG & NBA If 2 variables vary in opposite direction, Cov can be –ve eg. ADG & FCR Cov of a variable with itself = Variance

Covariance & Variance

Example

Correlation A measure of the strength of a bivariate linear relationship –1 < r < +1

Correlation & Regression

Properties of covariance "The expected value of the cross product" Cov(a,Y) = 0 Cov(aX,Y) = aCov(X,Y) Cov(X+W,Y) = Cov(X,Y) + Cov(W,Y) Cov(X,X) = Var(x) Cov(a+X,Y) = Cov(a,Y) + Cov(X,Y) = Cov(X,Y) Cov(X,Y) = Cov(Y,X)

Correlations between Characters Phenotypic correlations ie height & feet size Environmental correlations Genetic correlations  pleiotropy  gametic phase disequilibrium

Genetic covariance G1 G2

Estimation of the genetic correlation Three methods Pairwise Comparison of Relatives Nested Analysis of Variance and Covariance Regression of Family Means Extra method not in the book

Pairwise Comparison of Relatives Data from pairs of relatives ie mid-parent (x) values for Trait1 and Trait2 And progeny means (y) for Trait1 and Trait2 Four phenotypic Cov. can be computed Cov(x1,y1); Cov(x2,y2) >>> heritabilities T1&T2 Cov(x1,y2); Cov(x2,y1) >>> r g(1,2)

Pairwise Comparison of Relatives

Genetic correlation

Example from my real data

Estimate of additive genetic correlation between ADG & FCR

Nested Analysis of Var and Cov Nested full-sib and half-sib designs (Ch 18) Provide nested analysis of genetic variance Mean squared deviations of individual traits A parallel analysis > add. genetic covariance Mean cross-products of the deviations of traits 1 and 2 rather than MS

Full-sib design T1 T T1 T2 21

Half-sib design T1 T T1 T2 21

Analysis of Variance (half-sib) Factordf SS MS E(MS) SireN-1 SSs/(N-1) Within sireT-N SSs/(T-N) TotalT-1 SSt(T-1)

Analysis of Covariance (half-sib) Factordf Sum cross-prod. MCP E(MCP) SireN-1 SCPs/(N-1) Within sireT-N SCPe/(T-N) TotalT-1 SCPt(T-1)

ANOVA (half-sib) ADG & FCR Factordf SS MS E(MS) Sire Within sire Total Factordf SS MS E(MS) Sire Within sire Total ADG FCR

Analysis of Cov(ADG,FCR) (half-sib) FactordfS cross-prod. MCP E(MCP) Sire Within sire Total

Regression of Family means Correlation between family mean phenotypes The Family size , the sampling errors  Family mean phenotype  Family mean genotype value

Regression of family means in practice

This is how we do it now (REML) correlation between ADG & FCR Anim !P Sire !P Dam !P ADG FCR chapter21.ped !ALPHA data.dat !MAXIT 30 ADG FCR ~ Trait !r Tr.Anim Tr 0 US Tr.Anim 2 Tr 0 US Anim h1 =  h2 =  rp =  rg = 

THE END