1. Breeding Value Estimation Chapter 7

2. Single information source What is the breeding value of this cow for milk production? A cow produces 9000 kg milk population mean is 8000 kg. +1000 = A + E One equation, two unknowns Solution: Regression of breeding value on the phenotype

3. Breeding value estimation is about regression........ (P- P) Estimated breeding value value A True breeding value

4. the regression coefficient of breeding value on phenotype: own performance

5. Single information source h 2 =0.3 P = 9000 Population mean = 8000 Selection based on the own performance of an animal is called mass selection.

6. Single information source What is the breeding value of the offspring of this cow for milk production? A cow produces 9000 kg milk population mean is 8000 kg.

7. Single information source We want to estimate the breeding value of the offspring based on the performance of the mother.

9. Single information source The breeding value of the offspring based on the performance of the mother:

10. Single information source h 2 =0.3 P = 9000 Population mean = 8000 Compare with first result (+300 kg): was this result expected?

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

12. 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 = r IH Unbiased = true value should on average be equal to the estimated value.

13. In-accurate Unbiased Accurate Biased Selection index theory

14. Multiple information sources No!!! We have to take into account dependence between information sources in order to avoid double counting.

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

16. Selection index theory Extension to multiple information sources What values should we use for b 1, b 2 ….. in order to have an optimal weighing of all the information that is available?  Is information from a dam more important than information from one full sib?  Is a measurement on one full sib just as important as a measurement on one offspring?

17. Selection index theory How to solve for b?

18. Selection index theory

19. 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 all those variances and covariances?

20. Selection index theory

21. The covariance take into account that some information sources partly contain the same information: no double counting!!

22. How to solve the equations: P-matrix (X = the deviation of information source P from an overall mean)

23. How to solve the equations: P-matrix

24. Cov(P 1, P 2 ) = the “correlation” between the breeding values * σ 2 A The covariance between a trait measurement on individual 1 and a trait measurement on individual 2:

25. How to solve the equations: P-matrix Grandsire sireDam X 2 Progeny A,X 1 ?????

26. The covariance between a trait measurement on individual 1 and a trait measurement on individual 2: How to solve the equations: P-matrix Grandsire sireDam X 2 Progeny A,X 1 1 23 1

27. How to solve the equations: P-matrix In general: 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 when c 2 is present Common environment model