Table_1_Integrating a growth degree-days based reaction norm methodology and multi-trait modeling for genomic prediction in wheat.XLSX

Multi-trait and multi-environment analyses can improve genomic prediction by exploiting between-trait correlations and genotype-by-environment interactions. In the context of reaction norm models, genotype-by-environment interactions can be described as functions of high-dimensional sets of markers and environmental covariates. However, comprehensive multi-trait reaction norm models accounting for marker × environmental covariates interactions are lacking. In this article, we propose to extend a reaction norm model incorporating genotype-by-environment interactions through (co)variance structures of markers and environmental covariates to a multi-trait reaction norm case. To do that, we propose a novel methodology for characterizing the environment at different growth stages based on growth degree-days (GDD). The proposed models were evaluated by variance components estimation and predictive performance for winter wheat grain yield and protein content in a set of 2,015 F6-lines. Cross-validation analyses were performed using leave-one-year-location-out (CV1) and leave-one-breeding-cycle-out (CV2) strategies. The modeling of genomic [SNPs] × environmental covariates interactions significantly improved predictive ability and reduced the variance inflation of predicted genetic values for grain yield and protein content in both cross-validation schemes. Trait-assisted genomic prediction was carried out for multi-trait models, and it significantly enhanced predictive ability and reduced variance inflation in all scenarios. The genotype by environment interaction modeling via genomic [SNPs] × environmental covariates interactions, combined with trait-assisted genomic prediction, boosted the benefits in predictive performance. The proposed multi-trait reaction norm methodology is a comprehensive approach that allows capitalizing on the benefits of multi-trait models accounting for between-trait correlations and reaction norm models exploiting high-dimensional genomic and environmental information.多性状与多环境分析可通过利用性状间相关性及基因型-环境互作（genotype-by-environment interactions）提升基因组预测（genomic prediction）的性能。在反应范型模型（reaction norm model）的框架下，基因型-环境互作可被描述为高维标记集与环境协变量的函数。然而，当前仍缺乏兼顾标记×环境协变量互作的综合多性状反应范型模型。本文提出将一种通过标记与环境协变量的（共）方差结构刻画基因型-环境互作的反应范型模型，拓展至多性状反应范型场景。为此，我们提出一种基于生长度日（growth degree-days, GDD）的不同生育阶段环境表征新方法。所提模型在包含2015个F6代株系的冬小麦籽粒产量与蛋白质含量数据集上，通过方差组分估计与预测性能评估完成了验证。交叉验证分析采用留一年份-地点交叉验证（leave-one-year-location-out, CV1）与留一育种周期交叉验证（leave-one-breeding-cycle-out, CV2）两种策略。基因组[单核苷酸多态性（SNPs）]×环境协变量互作的建模，可显著提升两种交叉验证方案下冬小麦籽粒产量与蛋白质含量的预测能力，并降低预测遗传值的方差膨胀。针对多性状模型开展性状辅助基因组预测后，该方法在所有场景中均显著提升了预测能力并降低了方差膨胀。通过基因组[SNPs]×环境协变量互作进行基因型-环境互作建模，并结合性状辅助基因组预测，进一步放大了预测性能的提升收益。本文所提出的多性状反应范型方法是一种综合方案，可充分利用多性状模型借助性状间相关性带来的优势，以及反应范型模型借助高维基因组与环境信息的优势。