Planning rice breeding programs for impact

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

2. Introduction Question: Why are breeders concerned with genetic correlations? • 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 IRRI: Planning breeding Programs for Impact

3. 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 IRRI: Planning breeding Programs for Impact

4. Basic statistics The product-moment correlation: For 2 variables, A and B, the product-moment correlation is: r = σAB/( σA σB) [9.1] The variance of a sum  If Y = A + B, then σ2Y = σ2A + σ2B + 2 σAB[9.2] IRRI: Planning breeding Programs for Impact

5. Genetic covariances and correlations for traits measured on the same plot For 2 traits, A and B, measured on the same plot YA = mA + GA + eA YB = mB + GB + eB σG(AB) rG(AB) = √ (σ2G(A) σ2G(B) ) IRRI: Planning breeding Programs for Impact

6. Genetic covariances and correlations for traits measured on the same plot For 2 traits, A and B, measured on the same plot YA = mA + GA + eA YB = mB + GB + eB σe(AB) re(AB) = √ (σ2e(A) σ2e(B) ) IRRI: Planning breeding Programs for Impact

7. Phenotypic correlation (correlation of line means) σP(AB) rPAB = √ (σ2P(A) σ2P(B) ) σG(AB) + {σE(AB)/r] = √ (σ2G(A) + σ2E(A)/r ) √(σ2G(B) + σ2E(B)/r ) As r increases, the phenotypic correlation approaches the genotypic correlation!

8. 1. Estimating rG for traits measured on the same plot • Remember: • σ2Gy = σ2GA + σ2GB + 2 σGAB[9.2] • Therefore, • σG(AB) = [σ2GY –(σ2GA + σ2GB )]/2 [9.5] IRRI: Planning breeding Programs for Impact

9. Estimating rG for traits measured on the same plot • Method • Add measurements A and B for each plot, to make a new combined variable a new name (say Y). Poss. with Excel • Perform ANOVA on the new combined variable, then estimate the genetic variance component using the method described in Unit 8 • Use Equation [9.5] : • σG(AB) = [σ2GY –(σ2GA + σ2GB )]/2 IRRI: Planning breeding Programs for Impact

10. Rep Plot Entry GY HI GYHI 1 1 IR60080-46A 3.418 0.380 3.798 1 2 IR71524-44 3.345 0.332 3.677 Example: Calculating rG for GY & HI in 40 lines For each plot, add HI to GY  Call new variable GYHI IRRI: Planning breeding Programs for Impact

11. Source Df MS for HI MS for GY MS for GYHI EMS Rep 2 Entry 39 0.0117 2.4377 2.7215 σ2e + r σ2G Error 78 0.0022 0.1470 0.1537 σ2e Example: Calculating rG for GY & HI in 40 lines Do ANOVA, then calculate variance components IRRI: Planning breeding Programs for Impact

12. 2. Estimating rG for traits measured in different environments Not correlated YA = mA + GA + eA YB = mB + GB + eB Correlated Therefore, rP across environments has no environmental covariance: covP = covG IRRI: Planning breeding Programs for Impact

13.  the phenotypic covariance is due to genetic causes only When means for same trait are estimated in different trials: σG(AB) rP(AB) = √ (σ2P(A) σ2P(B) ) IRRI: Planning breeding Programs for Impact

14. Estimating rG for traits measured in different environments SO rG’ = rP/√( HAx HB) [9.6] IRRI: Planning breeding Programs for Impact

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

16. Question:Why do we want to predict correlated response? • 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 IRRI: Planning breeding Programs for Impact

17. 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: • CRA = k rG √ HBσG(A) • Where: k is selection intensity in phenotypic standard deviation units IRRI: Planning breeding Programs for Impact

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

19. Summary • rP is corr. of line means for different traits, or for same trait in different environments • rG 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 IRRI: Planning breeding Programs for Impact

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