Montesinos-López Abelardo, Montesinos-López Osval A, Cuevas Jaime, Mata-López Walter A, Burgueño Juan, Mondal Sushismita, Huerta Julio, Singh Ravi, Autrique Enrique, González-Pérez Lorena, Crossa José
Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, 44430 Guadalajara, Jalisco Mexico.
Facultad de Telemática, Universidad de Colima, Colima, Mexico.
Plant Methods. 2017 Jul 27;13:62. doi: 10.1186/s13007-017-0212-4. eCollection 2017.
Modern agriculture uses hyperspectral cameras that provide hundreds of reflectance data at discrete narrow bands in many environments. These bands often cover the whole visible light spectrum and part of the infrared and ultraviolet light spectra. With the bands, vegetation indices are constructed for predicting agronomically important traits such as grain yield and biomass. However, since vegetation indices only use some wavelengths (referred to as bands), we propose using all bands simultaneously as predictor variables for the primary trait grain yield; results of several multi-environment maize (Aguate et al. in Crop Sci 57(5):1-8, 2017) and wheat (Montesinos-López et al. in Plant Methods 13(4):1-23, 2017) breeding trials indicated that using all bands produced better prediction accuracy than vegetation indices. However, until now, these prediction models have not accounted for the effects of genotype × environment (G × E) and band × environment (B × E) interactions incorporating genomic or pedigree information.
In this study, we propose Bayesian functional regression models that take into account all available bands, genomic or pedigree information, the main effects of lines and environments, as well as G × E and B × E interaction effects. The data set used is comprised of 976 wheat lines evaluated for grain yield in three environments (Drought, Irrigated and Reduced Irrigation). The reflectance data were measured in 250 discrete narrow bands ranging from 392 to 851 nm (nm). The proposed Bayesian functional regression models were implemented using two types of basis: B-splines and Fourier. Results of the proposed Bayesian functional regression models, including all the wavelengths for predicting grain yield, were compared with results from conventional models with and without bands.
We observed that the models with B × E interaction terms were the most accurate models, whereas the functional regression models (with B-splines and Fourier basis) and the conventional models performed similarly in terms of prediction accuracy. However, the functional regression models are more parsimonious and computationally more efficient because the number of beta coefficients to be estimated is 21 (number of basis), rather than estimating the 250 regression coefficients for all bands. In this study adding pedigree or genomic information did not increase prediction accuracy.
现代农业使用高光谱相机，其可在许多环境中的离散窄波段提供数百个反射率数据。这些波段通常覆盖整个可见光光谱以及部分红外和紫外光光谱。利用这些波段构建植被指数，以预测诸如谷物产量和生物量等农学上重要的性状。然而，由于植被指数仅使用某些波长（称为波段），我们建议同时使用所有波段作为主要性状谷物产量的预测变量；多个多环境玉米（阿瓜特等人，《作物科学》，2017年，第57卷第5期：1 - 8页）和小麦（蒙特西诺斯 - 洛佩斯等人，《植物方法》，2017年，第13卷第4期：1 - 23页）育种试验的结果表明，使用所有波段比植被指数产生更好的预测准确性。然而，到目前为止，这些预测模型尚未考虑纳入基因组或系谱信息的基因型×环境（G×E）和波段×环境（B×E）相互作用的影响。
在本研究中，我们提出了贝叶斯函数回归模型，该模型考虑了所有可用波段、基因组或系谱信息、品系和环境的主效应以及G×E和B×E相互作用效应。所使用的数据集由在三种环境（干旱、灌溉和减灌）下评估谷物产量的976个小麦品系组成。反射率数据在392至851纳米（nm）的250个离散窄波段中测量。所提出的贝叶斯函数回归模型使用两种类型的基函数实现：B样条和傅里叶基函数。将所提出的贝叶斯函数回归模型（包括用于预测谷物产量的所有波长）的结果与有波段和无波段的传统模型的结果进行了比较。
我们观察到具有B×E相互作用项的模型是最准确的模型，而函数回归模型（具有B样条和傅里叶基函数）和传统模型在预测准确性方面表现相似。然而，函数回归模型更简约且计算效率更高，因为要估计的β系数数量为21（基函数数量），而不是为所有波段估计250个回归系数。在本研究中，添加系谱或基因组信息并未提高预测准确性。
