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Breeding Value Estimation

Breeding Value Estimation. Chapter 7, part 2. Selection index theory. How do we combine all sorts of information sources in order to get the “best” EBV of our target individual?. Selection index theory. Solution: multiple regression = selection index.

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Breeding Value Estimation

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  1. Breeding Value Estimation Chapter 7, part 2

  2. Selection index theory How do we combine all sorts of information sources in order to get the “best” EBV of our target individual?

  3. Selection index theory • Solution: multiple regression = selection index. • Note that we set up a selection index to estimate the breeding value (EBV) of one particular individual. For another individual the available information might be different and therefore the selection index might be different • “best EBV” • Most accurate = rIH • Unbiased = true value should on average be equal to the estimated value.

  4. Selection index theory Notation: I = the index value (the estimated breeding value) b1 = the weighing factor for information source 1 X1 = the deviation of information source 1 from an overall mean

  5. Selection index theory

  6. Selection index theory

  7. Selection index theory • P is variance-covariance matrix of information sources • G is the vector with covariances between the information sources and the breeding value that we want to estimate. • b is the vector with weighing factors How to calculate the variances and covariances?

  8. Selection index theory

  9. How to solve the equations: P-matrix Var(X1, X2) = the “phenotypic variance” Cov(X1, X2) = the “additive genetic relationship” * σ2A

  10. How to solve the equations: P-matrix • Use the right genetic model! • 1) covariance between (the same) traits measured on the same individual: • repeated measurements model • 2) trait measured on a different individual • Common environment model • Depending upon whether a c2 is present.

  11. How to solve the equations: G-matrix • The covariance between the breeding value A of individual X1 • and a trait measurement on individual X2 ?????

  12. Selection index theory Example: own milk production and milk production of a half-sister I = b1X1 + b2X2

  13. Selection index theory Exc: Lets fill in the variances and covariances…..

  14. Selection index theory

  15. Selection index theory See matrix calculations lecture notes • = 8000 kg milk, Own = 9000 kg milk, HS = 6000 kg milk What is the breeding value of X1? I = b1X1 + b2X2 I = 0.345(9000-8000)+0.057(6000-8000) = 345-114 = +231 kg milk

  16. = 8000 kg milk I = EBV=+231 kg milk Own = 9000 kg milk HS = 6000 kg milk Selection index theory • I = 0.345X1 + 0.057X2 • This selection index is specific for: • the situation with 2 information sources: Own performance and production of 1 HS • The genetic parameters used (h2 = 0.35)

  17. = 8000 kg milk Own = 9000 kg milk HS = 6000 kg milk Selection index theory • If interest is in the EBV of the sire, a new selection index needs to be derived!! • I = b1X1 + b2X2 or • I = bXAverage

  18. = 8000 kg milk Own = 9000 kg milk HS = 6000 kg milk Selection index theory • For the other HS the same index (b-values) can be used: own performance and the performance of one HS!! • I =0.345(6000-8000)+0.057(9000-8000) = - 633 kg

  19. Selection index theory I = 0.345X1 + 0.057X2 • b-values indicate the relative importance of each information source: • own performance: 0.345 • Half sib: 0.057

  20. Accuracy of index selection • The accuracy of index selection is the correlation between the true and the estimated breeding value and is indicated as rIH • I = the Index (EBV), H = A = the true breeding value (single trait) • rIH varies between 0 and 1

  21. Accuracy of index selection

  22. Accuracy of index selection

  23. General considerations • Selection index finds the optimal weights (b) of information sources: • optimal: the accuracy (rIH) of the EBV is maximised. • Selection index results in unbiased Estimated Breeding values: • no direction of change Large number of animals with EBV=100  on average the true breeding value will be +100 • individual EBV will change if rIH<1, (error) variance:

  24. Select Select General considerations Use EBV (=Index values) to predict level of next generation: Males Females +500 +1000 +400 +900 +300 +800 -100 0 -200 -100 Average of EBV male and female selected parents: +400 and +900

  25. Accuracy of index selection Accuracy of selection for progeny testing (Table 7.3) • Function of • number of offspring (n) • heritability (h2)

  26. General considerations - progeny testing

  27. General considerations Which animal do I select? highest EBV or highest rIH ?? I = +100 rIH = 0.90 I = +200 rIH = 0.70 Select animals with highest EBV independent of the rIH!!

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