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

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

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

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

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. 2011. Crop Sci. 51: 1-6.

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

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

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

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

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?

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

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

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

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

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

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

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

Expected gain due to index selection

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

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

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

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

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)