Genomic-Enabled Prediction in Maize Using Kernel Models with Genotype × Environment Interaction

Abstract

Multi-environment trials are routinely conducted in plant breeding to select candidates for the next selection cycle. In this study, we compare the prediction accuracy of four developed genomic-enabled prediction models: (1) single-environment, main genotypic effect model (SM); (2) multi-environment, main genotypic effects model (MM); (3) multi-environment, single variance G×E deviation model (MDs); and (4) multi-environment, environment-specific variance G×E deviation model (MDe). Each of these four models were fitted using two kernel methods: a linear kernel Genomic Best Linear Unbiased Predictor, GBLUP (GB), and a nonlinear kernel Gaussian kernel (GK). The eight model-method combinations were applied to two extensive Brazilian maize data sets (HEL and USP data sets), having different numbers of maize hybrids evaluated in different environments for grain yield (GY), plant height (PH), and ear height (EH). Results show that the MDe and the MDs models fitted with the Gaussian kernel (MDe-GK, and MDs-GK) had the highest prediction accuracy. For GY in the HEL data set, the increase in prediction accuracy of SM-GK over SM-GB ranged from 9 to 32%. For the MM, MDs, and MDe models, the increase in prediction accuracy of GK over GB ranged from 9 to 49%. For GY in the USP data set, the increase in prediction accuracy of SM-GK over SM-GB ranged from 0 to 7%. For the MM, MDs, and MDe models, the increase in prediction accuracy of GK over GB ranged from 34 to 70%. For traits PH and EH, gains in prediction accuracy of models with GK compared to models with GB were smaller than those achieved in GY. Also, these gains in prediction accuracy decreased when a more difficult prediction problem was studied.

Keywords: Gaussian nonlinear kernel; GenPred; Genomic Best Linear Unbiased Predictor (GBLUP) linear kernel; Genomic Selection; Genotype× Environment interaction (G×E); Shared Data Resources.

Figure 1

Box plot of grain yield (ton per hectare) (GY), plant height (centimeter) (PH), and ear height (centimeter) (EH) for (A) HEL data set and (B) USP data set. Environments for the HEL data set are IP, Ipiaçú; NM, Nova Mutum; PM, Pato de Minas; SE, Sertanópolis; and SO, Sorriso. Environments for the USP data set are: P-LN, Piracicaba low nitrogen; P-IN, Piracicaba ideal nitrogen; A-LN, Anhumas low nitrogen; and A-IN, Anhumas ideal nitrogen.

Figure 2

HEL data set. Correlation between phenotypes and prediction values (average of 50 random CV partitions) for single-environment, main genotypic effect model with GBLUP kernel method (SM-GB), and single-environment, main genotypic effect model with GK method (SM-GK) for: (A) five environments (horizontal axis) for grain yield, (B) three environments for plant height, and (C) three environments for ear height. Environments are: Ipiaçú (IP), Nova Mutum (NM), Pato de Minas (PM), Sertanópolis (SE) and Sorriso (SO). Error bars show SD.

Figure 3

HEL data set. Mean correlation between observed and predictive values (average of 50 random CV partitions, CV2) for multi-environment, main genotypic effect model GBLUP kernel (MM-GB), multi-environment, main genotypic effect GK (MM-GK), multi-environment, single variance G×E deviation model GBLUP kernel (MDs-GB), multi-environment, single variance G×E deviation model GK (MDs-GK), multi-environment, environment-specific variance G×E deviation model GBLUP kernel (MDe-GB), multi-environment, environment-specific variance G×E deviation model GK (MDe-GK) for (A) five environments (horizontal axis) for grain yield, (B) three environments for plant height, and (C) three environments for ear height. Environments are: Ipiaçú (IP), Nova Mutum (NM), Pato de Minas (PM), Sertanópolis (SE) and Sorriso (SO). Error bars show SD.

Figure 4

USP data set. Mean correlation between phenotypes and predictions (average of 50 random CV partitions) for single-environment, main genotypic effects model with GBLUP kernel method (SM-GB), and single-environment, main genotypic effects model with GK method (SM-GK) in four environments (horizontal axis) for (A) grain yield, (B) plant height, and (C) ear height. Environments are: Anhumas ideal Nitrogen (A-IN), Anhumas low Nitrogen (A-LN), Piracicaba ideal Nitrogen (P-IN) and Piracicaba low Nitrogen (P-LN). Error bars show SD.

Figure 5

USP data set. Mean correlation between observed and predictive values (average of 50 random CV partitions, CV2) for multi-environment, main genotypic effect model GBLUP kernel (MM-GB), multi-environment, main genotypic effect Gaussian kernel (MM-GK), multi-environment, single variance G×E deviation model GBLUP kernel (MDs-GB), multi-environment, single variance G×E deviation model Gaussian kernel (MDs-GK), multi-environment, environment-specific variance G×E deviation model GBLUP kernel (MDe-GB), multi-environment, environment-specific variance G×E deviation model Gaussian kernel (MDe-GK) in four environments (horizontal axis) for: (A) grain yield, (B) plant height, and (C) ear height. Environments: Anhumas ideal Nitrogen (A-IN), Anhumas low Nitrogen (A-LN), Piracicaba ideal Nitrogen (P-IN), and Piracicaba low Nitrogen (P-LN). Error bars show SD.