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This study presents a novel approach for the optimization of genomic parental selection in breeding programs involving categorical and continuous-categorical multi-trait mixtures (CMs and CCMMs). Utilizing the Bayesian decision theory (BDT) and latent trait models within a multivariate normal distribution framework, we address the complexities of selecting new parental lines across ordinal and continuous traits for breeding. Our methodology enhances precision and flexibility in genetic selection, validated through extensive simulations. This unified approach presents significant potential for the advancement of genetic improvements in diverse breeding contexts, underscoring the importance of integrating both categorical and continuous traits in genomic selection frameworks.

Selecting and mating parents in conventional phenotypic and genomic selection are crucial. Plant breeding programs aim to improve the economic value of crops, considering multiple traits simultaneously. When traits are negatively correlated and/or when there are missing records in some traits, selection becomes more complex. To address this problem, we propose a multitrait selection approach using the Multitrait Parental Selection (MPS) R package-an efficient tool for genetic improvement, precision breeding, and conservation genetics. The package employs Bayesian optimization algorithms and three loss functions (Kullback-Leibler, Energy Score, and Multivariate Asymmetric Loss) to identify parental candidates with desirable traits. The software's functionality includes three main functions-EvalMPS, FastMPS, and ApproxMPS-catering to different data availability scenarios. Through the presented application examples, the MPS R package proves effective in multitrait genomic selection, enabling breeders to make informed decisions and achieve strong performance across multiple traits., (© 2024 International Maize and Wheat Organization (CIMMYT). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

The infrared spectrum of bovine milk is used to predict many interesting traits, whereas there have been few studies on goat milk in this regard. The objective of this study was to characterize the major sources of variation in the absorbance of the infrared spectrum in caprine milk samples. A total of 657 goats belonging to 6 breeds and reared on 20 farms under traditional and modern dairy systems were milk-sampled once. Fourier-transform infrared (FTIR) spectra were taken (2 replicates per sample, 1314 spectra), and each spectrum contained absorbance values at 1060 different wavenumbers (5000 to 930 × cm -1 ), which were treated as a response variable and analyzed one at a time (i.e., 1060 runs). A mixed model, including the random effects of sample/goat, breed, flock, parity, stage of lactation, and the residual, was used. The pattern and variability of the FTIR spectrum of caprine milk was similar to those of bovine milk. The major sources of variation in the entire spectrum were as follows: sample/goat (33% of the total variance); flock (21%); breed (15%); lactation stage (11%); parity (9%); and the residual unexplained variation (10%). The entire spectrum was segmented into five relatively homogeneous regions. Two of them exhibited very large variations, especially the residual variation. These regions are known to be affected by the absorbance of water, although they also exhibited wide variations in the other sources of variation. The average repeatability of these two regions were 45% and 75%, whereas for the other three regions it was about 99%. The FTIR spectrum of caprine milk could probably be used to predict several traits and to authenticate the origin of goat milk.

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population's genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10 th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle., (Copyright © 2018 de Jesus et al.)