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Correlated characters

Correlated characters. Sanja Franic VU University Amsterdam 2008. Relationship between 2 metric characters whose values are correlated in the individuals of a population. Relationship between 2 metric characters whose values are correlated in the individuals of a population

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Correlated characters

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  1. Correlated characters Sanja Franic VU University Amsterdam 2008

  2. Relationship between 2 metric characters whose values are correlated in the individuals of a population

  3. Relationship between 2 metric characters whose values are correlated in the individuals of a population • Why are correlated characters important? • Effects of pleiotropy in quantitative genetics • Pleiotropy – gene affects 2 or more characters • (e.g. genes that increase growth rate increase both height and weight) • Selection – how will the improvement in one character cause simultaneous changes in other characters?

  4. Relationship between 2 metric characters whose values are correlated in the individuals of a population • Why are correlated characters important? • Effects of pleiotropy in quantitative genetics • Pleiotropy – gene affects 2 or more characters • (e.g. genes that increase growth rate increase both height and weight) • Selection – how will the improvement in one character cause simultaneous changes in other characters? • Causes of correlation: • Genetic • mainly pleiotropy • but some genes may cause +r, while some cause –r, so overall effect not always detectable • Environmental • two characters influenced by the same differences in the environment

  5. We can only observe the phenotypic correlation • How to decompose it into genetic and environmental causal components?

  6. (phenotypic correlation) (phenotypic covariance) (phenotypic covariance expressed in terms of A and E) (substitution gives) (because σ2P= σ2A+ σ2E σP= σA+ σE σP=hσP+eσP) (substitution gives) (phenotypic correlation expressed in terms of A and E) • We can only observe the phenotypic correlation • How to decompose it into genetic and environmental causal components?

  7. (phenotypic correlation) (phenotypic covariance) (phenotypic covariance expressed in terms of A and E) (substitution gives) (because σ2P= σ2A+ σ2E σP= σA+ σE σP=hσP+eσP) (substitution gives) (phenotypic correlation expressed in terms of A and E) • We can only observe the phenotypic correlation • How to decompose it into genetic and environmental causal components?

  8. Estimation of the genetic correlation • Analogous to estimation of heritabilities, but instead of ANOVA we use an ANCOVA

  9. Estimation of the genetic correlation • Analogous to estimation of heritabilities, but instead of ANOVA we use an ANCOVA Half-sib families • Design: a number of sires each mated to several dames (random mating) • A number of offspring from each dam are measured

  10. Estimation of the genetic correlation • Analogous to estimation of heritabilities, but instead of ANOVA we use an ANCOVA Half-sib families • Design: a number of sires each mated to several dames (random mating) • A number of offspring from each dam are measured s=number of sires d=number of dames per sire k=number of offspring per dam

  11. Estimation of the genetic correlation • Analogous to estimation of heritabilities, but instead of ANOVA we use an ANCOVA Half-sib families • Design: a number of sires each mated to several dames (random mating) • A number of offspring from each dam are measured s=number of sires d=number of dames per sire k=number of offspring per dam observational components

  12. Estimation of the genetic correlation • Analogous to estimation of heritabilities, but instead of ANOVA we use an ANCOVA Half-sib families • Design: a number of sires each mated to several dames (random mating) • A number of offspring from each dam are measured s=number of sires d=number of dames per sire k=number of offspring per dam observational components causal components

  13. σ2S= variance between means of half-sib families (phenotypic covariance of half-sibs) = ¼ VA

  14. σ2S= variance between means of half-sib families (phenotypic covariance of half-sibs) = ¼ VA σ2W VT = VBG + VWG VWG = VT – VBG VBG = covFS covFS = ½ VA + ¼ VD σ2W=VWG = VT -½ VA - ¼ VD = VA + VD +VE -½ VA - ¼ VD = ½ VA + ¾ VD + VEW

  15. σ2S= variance between means of half-sib families (phenotypic covariance of half-sibs) = ¼ VA σ2W VT = VBG + VWG VWG = VT – VBG VBG = covFS covFS = ½ VA + ¼ VD σ2W=VWG = VT -½ VA - ¼ VD = VA + VD +VE -½ VA - ¼ VD = ½ VA + ¾ VD + VEW σ2D= σ2T-σ2S -σ2W = VA + VD +VE -¼ VA -½ VA – ¾ VD - VEW = ¼ VA + ¼ VD + VEC (VE = VEC +VEW)

  16. σ2S= variance between means of half-sib families (phenotypic covariance of half-sibs) = ¼ VA σ2W VT = VBG + VWG VWG = VT – VBG VBG = covFS covFS = ½ VA + ¼ VD σ2W=VWG = VT -½ VA - ¼ VD = VA + VD +VE -½ VA - ¼ VD = ½ VA + ¾ VD + VEW σ2D= σ2T-σ2S -σ2W = VA + VD +VE -¼ VA -½ VA – ¾ VD - VEW = ¼ VA + ¼ VD + VEC (VE = VEC +VEW) • In partitioning the covariance, instead of starting from individual values we start from the product of the values of the 2 characters covS= ¼ covA

  17. covS= ¼ covA • varSX = ¼ σ2AX • varSY = ¼ σ2AY

  18. covS= ¼ covA • varSX = ¼ σ2AX • varSY = ¼ σ2AY Offspring-parent relationship • To estimate the heritability of one character, we compute the covariance of offspring and parent • To estimate the genetic correlation between 2 characters we compute the “cross-variance”: product of value of X in offspring and value of Y in parents • Cross-variance = ½ covA

  19. covS= ¼ covA • varSX = ¼ σ2AX • varSY = ¼ σ2AY Offspring-parent relationship • To estimate the heritability of one character, we compute the covariance of offspring and parent • To estimate the genetic correlation between 2 characters we compute the “cross-variance”: product of value of X in offspring and value of Y in parents • Cross-variance = ½ covA

  20. Correlated response to selection • If we select for X, what will be the change in Y?

  21. Correlated response to selection • If we select for X, what will be the change in Y? • The response in X – the mean breeding value of the selected individuals • The consequent change in Y – regression of breeding value of Y on breeding value of X

  22. Correlated response to selection • If we select for X, what will be the change in Y? • The response in X – the mean breeding value of the selected individuals • The consequent change in Y – regression of breeding value of Y on breeding value of X

  23. Correlated response to selection • If we select for X, what will be the change in Y? • The response in X – the mean breeding value of the selected individuals • The consequent change in Y – regression of breeding value of Y on breeding value of X because:

  24. [11.4]

  25. [11.4]

  26. [11.4]

  27. [11.4]

  28. [11.4]

  29. [11.4] Coheritability

  30. [11.4] Coheritability [11.3] Heritability

  31. Questions?

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