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
divide by
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

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 traits X and Y
Piepho, H-P and J. Mӧhring 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

7. Estimates of the genetic correlation - alternatives
Genetic correlations can be estimated from parent-offspring regression
Can also estimate genetic correlations from double selection experiments
observe direct response (R) and correlated response (CR) to selection for each trait
Parent-offspring covariance for traits X and Y
Parent-offspring covariance for trait X
Falconer and Mackay, Chapt. 19

8. 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

9. 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

10. 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?

11. 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

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

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

14. 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 1 2 3 4 5 6 7 8 9 10
Trait X

15. 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

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

17. We want to improve the aggregate breeding value
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

18. Expected gain due to index selection

19. 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 Xyield
Brim et al., 1959

20. 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

21. 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

22. 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

23. 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)