PBG 650 Advanced Plant Breeding

1. PBG 650 Advanced Plant Breeding • Module 11: Multiple Traits • Genetic Correlations • Index Selection

2. Genetic correlations • Correlations in phenotype may be due to genetic or environmental causes • May be positive or negative • Genetic causes may be due to • pleiotropy • linkage • gametic phase disequilibrium • The additive genetic correlation (correlation of breeding values) is of greatest interest to plant breeders • “genetic correlation” usually refers to the additive genetic correlation (rG is usually rA ) • We measure phenotypic correlations Falconer and Mackay, Chapt. 19; Bernardo, Chapt. 13

3. Components of the phenotypic correlation Includes covariance among residuals and non-additive genetic covariances

4. Components of the phenotypic correlation • When heritabilities are high, most of the observed phenotypic correlation is due to genetics • When heritabilities are low, most of the observed rP is due to the environment • If rA and rE are opposite in sign, rP may be close to zero • example: stalk strength and ear number in corn divide by

5. Extimating the genetic correlation • Genetic correlations can be estimated from the same mating designs used to estimate genetic variances • Perform analysis of covariance rather than ANOVA • Mixed model approaches can also be used (ref. below) Example: half-sib families r = #reps, e = #environments MCP is the Mean Cross Products between trait X and Y Piepho, H-P and J. Mӧhring. 2011. Crop Sci. 51: 1-6.

6. Estimates of the genetic correlation • Genetic correlations vary greatly with gene frequency • estimates are unique for each population • Standard errors of estimates of rA are extremely large • Can also estimate genetic correlations from double selection experiments • observe direct response (R) and correlated response (CR) to selection for each trait

7. Correlated response to selection • Consequence of genetic correlation • selection for one trait will cause a correlated response in the other • May be unfavorable • example: selection for high yield in corn increases maturity, plant height, lodging, and grain moisture at harvest • May be helpful • a correlated trait may have a higher heritability or be easier and/or less costly to measure than the trait of interest; indirect selection may be more effective than direct selection

8. Correlated response to selection • Change in breeding value of Y per unit change in breeding value of X Direct response to selection for X coheritability: analagous to h2 in response to direct selection

9. Indirect selection • Can we make greater progress from indirect selection than from direct selection? • In theory, molecular markers should be useful tools for indirect selection because they have an h2=1 • Need to consider other factors (time, cost) • Is there a benefit to practicing both direct and indirect selection at the same time? is hYrA > hX?

10. Strategies for multiple trait selection • So far, we have only considered the case where one trait has economic value, and the secondary (correlated) trait either has no value or should be held at a constant level • We usually wish to improve more than one trait in a breeding program. They may be correlated or independent from each other. • Options: • independent culling • tandem selection • index selection

11. 10 9 8 7 6 Trait Y 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Trait X Independent culling • Minimum levels of performance are set for each trait

12. 10 9 8 7 6 Trait Y 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Trait X Tandem selection • Conduct one or more cycles of selection for one trait, and then select for another trait Select for trait X in the next cycle

13. Selection indices • Values for multiple traits are incorporated into a single index value for selection 10 9 8 7 6 Trait Y 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Trait X

14. Effects of multiple trait selection • Selection for n traits reduces selection intensity for any one trait • Reduction in selection intensity per trait is greatest for tandem selection, and least for index selection • Expected response to selection: index selection ≥ independent culling ≥ tandem selection

15. Smith-Hazel Index • Also called the “optimum index” • Incorporates information about • heritability of the traits • economic importance (weights) • genetic and phenotypic correlations between traits

16. Smith-Hazel Index • We want to improve the aggregate breeding value • Calculate an index value for each individual H = a1A1 + a2A2 + …. anAn = ΣaiAi ai’s are the economic weights and Ai’s are the breeding values for each trait I = b1X1 + b2X2 + …. bnXn = ΣbiXi bi’s are the index weights and Xi’s are the phenotypic values for each trait Ga = Pb G is a matrix of genetic variances and covariances P is a matrix of phenotypic variances and covariances b = P-1Ga solve for the index weights

17. Expected gain due to index selection

18. Selection index example Traits are oil (1), protein (2), and yield (3) in soybeans on a per plot basis b = P-1Ga I = 1.74Xoil – 1.66Xprotein + 0.60Xyield Brim et al., 1959

19. Selection indices to improve single traits • Family index • selection for a single trait using information from relatives • related to BLUP • Covariate index • selection is practiced on a correlated trait that has no economic value • aim is to maximize response (direct + indirect) for the trait of interest

20. Other selection indices for multiple traits • Desired gains index • Restricted index • holds certain traits constant while improving other traits • Multiplicative index • does not require economic weights • cutoff values established for each trait (similar to independent culling) • Retrospective index • measures weights that have been used by breeders b = G-1d d is a matrix of desired gains for each trait b = P-1s s is a matrix of selection differentials

21. Base index • Proposed by Williams, 1962 • Economic weights are used directly as weights in the index • May be better than the Smith-Hazel index when estimates of variances and covariances are poor. • It’s quick and easy – can be done on a spreadsheet I = a1X1 + a2X2 + …. anXn = ΣaiXi

22. Base index I = a1X1 + a2X2 + …. anXn = ΣaiXi Suggestions (more of an art than a science) • Use results from ANOVA and estimates of h2 and rg when prioritizing traits for selection and setting weights • For traits of greatest importance, use blups or adjust weights to account for differences in h2 • For secondary traits, emphasize traits with high quality data for the particular site or season • Consider applying some selection pressure to correlated traits • Standardize genotype means or blups • Monitor selection differentials for all traits • Verify desired gains • Avoid undesirable changes in correlated traits (these will be based on phenotypic correlations, but that’s better than nothing)