Correlations Between Characters

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Correlations Between Characters

• In Genetics and Analysis of Quantitative traits
• by
• Lynch, M. and Walsh, B.
• Presented
• Sansak Nakavisut

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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

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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

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Covariance Variance
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Example
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Correlation
A measure of the strength of a bivariate linear
relationship 1 lt r lt 1
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Correlation Regression
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Properties of covariance

• "The expected value of the cross product"
• Cov(a,Y) 0
• Cov(aX,Y) aCov(X,Y)
• Cov(XW,Y) Cov(X,Y) Cov(W,Y)
• Cov(X,X) Var(x)
• Cov(aX,Y) Cov(a,Y) Cov(X,Y) Cov(X,Y)
• Cov(X,Y) Cov(Y,X)

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Correlations between Characters

• Phenotypic correlations ie height feet size
• Environmental correlations
• Genetic correlations ? pleiotropy ? gametic phase
  disequilibrium

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Genetic covariance
G1
G2
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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

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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) gtgtgt heritabilities T1T2
• Cov(x1,y2) Cov(x2,y1) gtgtgt rg(1,2)

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Pairwise Comparison of Relatives
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Genetic correlation
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Example from my real data
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Estimate of additive genetic correlation between
ADG FCR
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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 gt add. genetic covariance
• Mean cross-products of the deviations of traits 1
  and 2 rather than MS

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Full-sib design
T1 T2
T1 T2
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T1 T2
T1 T2
T1 T2
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T1 T2
T1 T2
T1 T2
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T1 T2
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Half-sib design
T1 T2
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T1 T2
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T1 T2
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Analysis of Variance (half-sib)
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Analysis of Covariance (half-sib)
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ANOVA (half-sib) ADG FCR
ADG
FCR
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Analysis of Cov(ADG,FCR) (half-sib)
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Regression of Family means

• Correlation between family mean phenotypes
• The Family size ?, the sampling errors ?
• Family mean phenotype ? Family mean genotype value

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Regression of family means in practice
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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 1 2 1 0 Tr
0 US 1 0.1 1 Tr.Anim 2 Tr 0 US 1 0.1 1 Anim
h1 0.5998 ? 0.0198 h2
0.5109 ? 0.0229 rp -0.4391? 0.0111
rg -0.4001? 0.0302
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THE END