1. Planning rice breeding programs for impact Correlated response to selection

2. IRRI: Planning breeding Programs for Impact Introduction  undesired changes in traits that are important but that are not under direct selection  May be more effective to conduct indirect selection for a low-H trait by selecting for a correlated high-H trait  Selection in SE for performance in TPE is a form of indirect selection. Response in the TPE to selection in the SE is a correlated response Question: Why are breeders concerned with genetic correlations?

3. IRRI: Planning breeding Programs for Impact Learning objectives Genetic and env. correlations will be defined for traits measured on the same plot, and an estimation method presented Genetic and environmental correlations will be defined for traits measured in different environments, and an estimation method presented Models for predicting correlated response to selection will be presented  Examples of use of correlated response methods to answer practical breeding questions

4. IRRI: Planning breeding Programs for Impact Basic statistics The product-moment correlation: For 2 variables, A and B, the product-moment correlation is: r = σ AB /( σ A σ B )[9.1] The variance of a sum If Y = A + B, then σ 2 Y = σ 2 A + σ 2 B + 2 σ AB [9.2]

5. IRRI: Planning breeding Programs for Impact Genetic covariances and correlations for traits measured on the same plot For 2 traits, A and B, measured on the same plot Y A = m A + G A + e A Y B = m B + G B + e B σ G(AB) r G(AB) = √ (σ 2 G(A) σ 2 G(B) )

6. IRRI: Planning breeding Programs for Impact Genetic covariances and correlations for traits measured on the same plot For 2 traits, A and B, measured on the same plot Y A = m A + G A + e A Y B = m B + G B + e B σ e(AB) r e(AB) = √ (σ 2 e(A) σ 2 e(B) )

7. σ P(AB) r PAB = √ (σ 2 P(A) σ 2 P(B) ) σ G(AB) + {σ E(AB) /r] = √ (σ 2 G(A) + σ 2 E(A) /r ) √(σ 2 G(B) + σ 2 E(B) /r ) As r increases, the phenotypic correlation approaches the genotypic correlation! Phenotypic correlation (correlation of line means)

8. IRRI: Planning breeding Programs for Impact Remember: σ 2 Gy = σ 2 GA + σ 2 GB + 2 σ GAB [9.2] Therefore, σ G(AB) = [σ 2 GY –(σ 2 GA + σ 2 GB )]/2 [9.5] 1. Estimating r G for traits measured on the same plot

9. IRRI: Planning breeding Programs for Impact Method 1.Add measurements A and B for each plot, to make a new combined variable a new name (say Y). Poss. with Excel 2.Perform ANOVA on the new combined variable, then estimate the genetic variance component using the method described in Unit 8 3.Use Equation [9.5] : σ G(AB) = [σ 2 GY –(σ 2 GA + σ 2 GB )]/2 Estimating r G for traits measured on the same plot

10. IRRI: Planning breeding Programs for Impact For each plot, add HI to GY  Call new variable GYHI Rep Plot EntryGYHIGYHI 11IR60080-46A3.4180.3803.798 12IR71524-443.3450.3323.677 Example: Calculating r G for GY & HI in 40 lines

11. IRRI: Planning breeding Programs for Impact Do ANOVA, then calculate variance components Example: Calculating r G for GY & HI in 40 lines SourceDfMS for HI MS for GY MS for GYHI EMS Rep 2 Entry390.01172.43772.7215σ 2 e + r σ 2 G Error780.00220.14700.1537σ2eσ2e

12. IRRI: Planning breeding Programs for Impact Y A = m A + G A + e A Y B = m B + G B + e B Correlated Not correlated Therefore, r P across environments has no environmental covariance: cov P = cov G 2. Estimating r G for traits measured in different environments

13. IRRI: Planning breeding Programs for Impact σ G(AB) r P(AB) = √ (σ 2 P(A) σ 2 P(B) ) When means for same trait are estimated in different trials:  the phenotypic covariance is due to genetic causes only

14. IRRI: Planning breeding Programs for Impact r G’ = r P /√( H A x H B ) [9.6] Estimating r G for traits measured in different environments SO

15. IRRI: Planning breeding Programs for Impact r P = 0.36 H short = 0.51 H long = 0.65 r G = 0.36/(0.51*0.65).5 Example: Calculating r G for short-season and long-season sites in the eastern Indian shuttle network OYT

16. IRRI: Planning breeding Programs for Impact To find out if we could make more gains by selecting for a correlated trait with higher H To find out if selection done in our SE will result in gains in target environment Question: Why do we want to predict correlated response?

17. IRRI: Planning breeding Programs for Impact Predicting correlated response For 2 traits, A and B, OR for same trait in 2 environments, A and B: Correlated response (CR) in A to selection for B is: CR A = k r G √ H B σ G(A) Where: k is selection intensity in phenotypic standard deviation units

18. IRRI: Planning breeding Programs for Impact Any questions or comments?

19. IRRI: Planning breeding Programs for Impact r P is corr. of line means for different traits, or for same trait in different environments r G is corr. of genotypic effects free from confounding with the effect of plots or pots 2 main kinds of genetic correlation (corr. for 1 trait in 2 envs versus corr. for 2 traits in 1 env.) have to be estimated differently Summary

20. IRRI: Planning breeding Programs for Impact Main reason to estimate r G is to predict correlated response r G in combination with H, can be used to evaluate different selection strategies by predicting CR in the TPE to selection in different SE Summary