Villar-Hernández Bartolo de Jesús, Pérez-Elizalde Sergio, Martini Johannes W R, Toledo Fernando, Perez-Rodriguez P, Krause Margaret, García-Calvillo Irma Delia, Covarrubias-Pazaran Giovanny, Crossa José
Colegio de Postgraduados, Montecillos, Edo. de Mexico, CP 56264,Mexico.
Universidad Autonoma de Coahuila, Saltillo, CP 25280, Mexico.
G3 (Bethesda). 2021 Feb 9;11(2). doi: 10.1093/g3journal/jkab012.
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.
在所有育种计划中，决定选择哪些个体进行杂交以形成下一个选择周期至关重要。鉴于经济价值和净遗传价值取决于多个性状，遗传种群的改良需要同时考虑多个性状；因此，随着计算和统计工具以及基因组选择（GS）的发展，研究人员正专注于多性状选择。选择最佳个体很困难，尤其是在性状呈负相关的情况下，其中一个性状的改善可能意味着其他性状的降低。有一些方法有助于多性状选择，最近有人提出了贝叶斯决策理论（BDT）。鉴于BDT总结了所有相关的数量遗传学概念，如遗传力、选择反应和性状之间的依赖结构（相关性），使用BDT进行亲本选择在多性状选择中可能有效。在本研究中，我们应用BDT，使用三种多元损失函数（LF），即库尔贝克-莱布勒（KL）、能量得分和多元不对称损失（MALF），来处理多性状亲本选择的复杂性，以便在两个广泛的真实小麦数据集中为下一个育种周期选择表现最佳的亲本。结果表明，某些性状的基因组估计育种值（GEBV）排名高的品系，其后验期望损失（PEL）并不总是很低。对于这两个数据集，KL损失函数对包括籽粒产量在内的所有性状赋予了相似的重要性。相比之下，能量得分和MALF在四个不同于籽粒产量的性状中的三个性状上表现更好。BDT方法应有助于育种者不仅根据要选择的亲本本身的GEBV来做出决策, 还能根据贝叶斯范式依据不确定性水平进行决策。
