Genomic-Enabled Prediction Kernel Models with Random Intercepts for Multi-environment Trials

Abstract

In this study, we compared the prediction accuracy of the main genotypic effect model (MM) without G×E interactions, the multi-environment single variance G×E deviation model (MDs), and the multi-environment environment-specific variance G×E deviation model (MDe) where the random genetic effects of the lines are modeled with the markers (or pedigree). With the objective of further modeling the genetic residual of the lines, we incorporated the random intercepts of the lines (bold-italicl) and generated another three models. Each of these 6 models were fitted with a linear kernel method (Genomic Best Linear Unbiased Predictor, GB) and a Gaussian Kernel (GK) method. We compared these 12 model-method combinations with another two multi-environment G×E interactions models with unstructured variance-covariances (MUC) using GB and GK kernels (4 model-method). Thus, we compared the genomic-enabled prediction accuracy of a total of 16 model-method combinations on two maize data sets with positive phenotypic correlations among environments, and on two wheat data sets with complex G×E that includes some negative and close to zero phenotypic correlations among environments. The two models (MDs and MDE with the random intercept of the lines and the GK method) were computationally efficient and gave high prediction accuracy in the two maize data sets. Regarding the more complex G×E wheat data sets, the prediction accuracy of the model-method combination with G×E, MDs and MDe, including the random intercepts of the lines with GK method had important savings in computing time as compared with the G×E interaction multi-environment models with unstructured variance-covariances but with lower genomic prediction accuracy.

Benchmarking between item based collaborative filtering algorithm and genomic best linear unbiased prediction (GBLUP) model in terms of prediction accuracy for wheat and maize//Estudio comparativo en términos de capacidad predictiva para datos de trigo y maíz entre el algoritmo de filtrado colaborativo y el modelo genómico mejor predictor lineal insesgado (GBLUP)

“…This data set is based on the data used in the study of Cuevas et al (2018). It consists of a sample of 247 maize lines evaluated in 2015 in three environments corresponding to Nova Mutum (NM) in the state of Mato Grosso, Pato de Minas (PM) and Ipiaçú (IP) in the state of Minas Gerais, Brazil.…”

“…This data set is based on the data used in the study of Cuevas et al (2018). It consists of 720 lines of corn evaluated in Piracicaba and Anhumas, Brazil, each with two levels of nitrogen fertilization (N): Ideal N (IN) and Low N (LN) for a total of four artificial environments (PIN, PLN, AIN and ALN), for three traits (EH, PH, GY).…”

BGGE: A New Package for Genomic-Enabled Prediction Incorporating Genotype × Environment Interaction Models

“…Different multi-environment models are defined based on the construction of the kernel matrices, using information available on genotypes, molecular markers and the environment (Jarquín et al 2014; Sousa et al 2017; Cuevas et al 2018). The construction of multi-environment kernels depends on two primary processes: the choice of covariance function and the multi-environment model.…”

“…The first multi-environment model added to $\mu$and ${\mathrm{bold-italicX}}_{\mathrm{bold-italicf}}\mathit{\beta }$ a random vector of main genotypic effects (MM) (Jarquín et al 2014), assuming these genetic effects across environments are constant, with a variance-covariance structure of ${\mathrm{bold-italicZ}}_u\mathit{K}{\mathrm{bold-italicZ\text{'}}}_u^{\prime }$ (Table 1), where ${\mathrm{bold-italicZ}}_u$ is a known incidence matrix that relates the genotypes to the observations in the environments (Jarquín et al 2014). The second model MM l adds to the MM model a random intercept l (Table 1) with variance-covariance structure ${\mathrm{bold-italicZ}}_u\mathit{I}{\mathrm{bold-italicZ\text{'}}}_u^{\prime }$ (Cuevas et al 2018). The third model is the multi-environment, single variance genotype × environment deviation model (MDs), which is an extension of the main genetic effect model (MM), but incorporates a random deviation effect of GE.…”

“…In MDe, a vector of specific environment effects is added with a known variance-covariance structure such that the blocks that correspond to the columns and rows of environment $j\text{th} (j=(1,\dots ,m)$ are a matrix ${\mathrm{bold-italicK}}_{\mathrm{bold-italicj}}\mathit{ }$with the other elements equal to zero (Sousa et al 2017). Again, when a random intercept component is added, a new model is generated, the MDe l (Cuevas et al 2018). …”