Economical optimization of a breeding scheme by selective phenotyping of the calibration set in a multi-trait context: application to bread making quality

Abstract

Key message

Trait-assisted genomic prediction approach is a way to improve genetic gain by cost unit, by reducing budget allocated to phenotyping or by increasing the program’s size for the same budget.

Abstract

This study compares different strategies of genomic prediction to optimize resource allocation in breeding schemes by using information from cheaper correlated traits to predict a more expensive trait of interest. We used bread wheat baking score (BMS) calculated for French registration as a case study. To conduct this project, 398 lines from a public breeding program were genotyped and phenotyped for BMS and correlated traits in 11 locations in France between 2000 and 2016. Single-trait (ST), multi-trait (MT) and trait-assisted (TA) strategies were compared in terms of predictive ability and cost. In MT and TA strategies, information from dough strength (W), a cheaper trait correlated with BMS (r = 0.45), was evaluated in the training population or in both the training and the validation sets, respectively. TA models allowed to reduce the budget allocated to phenotyping by up to 65% while maintaining the predictive ability of BMS. TA models also improved the predictive ability of BMS compared to ST models for a fixed budget (maximum gain: + 0.14 in cross-validation and + 0.21 in forward prediction). We also demonstrated that the budget can be further reduced by approximately one fourth while maintaining the same predictive ability by reducing the number of phenotypic records to estimate BMS adjusted means. In addition, we showed that the choice of the lines to be phenotyped can be optimized to minimize cost or maximize predictive ability. To do so, we extended the mean of the generalized coefficient of determination (CD_mean) criterion to the multi-trait context (CD_multi).

Appendix

We extended here the generalized CD (Laloë 1993) to the multi-trait context. The objective is to compute the expected reliability (before phenotyping) in a multi-trait context for contrasts corresponding to the prediction objectives. To give an example, it is clear that if the objective is to accurately predict the difference (contrasts) between families, or to focus on predictions within families, the contrasts to be considered will be different and the optimal calibration sets as well. By defining contrasts corresponding to the prediction objectives, one can adapt the CD_multi criterion to the specific prediction objectives (see Rincent et al. 2017 for more details in the single-trait context).

For a given contrast c, the generalized prediction error variance (PEV(c)) in the multi-trait context is equal to:

$${\text{PEV}}\left( c \right) \, = c^{T} \left( {Z^{T} MZ + \left( {\Sigma_{a}^{ - 1} \otimes K^{ - 1} } \right)} \right)^{ - 1} c$$

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$${\text{With}}\;M = \left( {\Sigma_{\varepsilon }^{ - 1} \otimes I} \right) - \left( {\Sigma_{\varepsilon }^{ - 1} \otimes I} \right)X\left( {X^{T} \left( {\Sigma_{\varepsilon }^{ - 1} \otimes I} \right)X} \right)^{ - 1} X^{T} \left( {\Sigma_{\varepsilon }^{ - 1} \otimes I} \right)$$

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where X and Z are the design matrices for the fixed and random effects, respectively, K is the kinship matrix, Σ_a is the genetic variance–covariance matrix between traits, and Σ_ε is the residual variance–covariance matrix between traits. ⊗ indicate the Kronecker product operator between matrices.

The generalized multi-trait CD for a given contrast c is equal to:

$${\text{CD}}_{{{\text{multi}}}} \, \left( c \right) = \frac{{c^{T} \left( {(\Sigma_{a} \otimes K) - \left( {Z^{T} MZ + \left( {\Sigma_{a}^{ - 1} \otimes K^{ - 1} } \right)} \right)^{ - 1} } \right)c}}{{c^{T} \left( {\Sigma_{a} \otimes K} \right)c}}$$

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As a reminder, a contrast is a vector whose elements sum to 0 and indicating the difference in which we are interested. For example, if we are interested in accurately predicting the difference between individual 1 and individual 2, the contrast to consider will be: $c^{T} = \left[ {1, - 1,0,0,0,0, \ldots } \right]$.