From genotype × environment interaction to gene × environment interaction

Abstract

Historically in plant breeding a large number of statistical models has been developed and used for studying genotype × environment interaction. These models have helped plant breeders to assess the stability of economically important traits and to predict the performance of newly developed genotypes evaluated under varying environmental conditions. In the last decade, the use of relatively low numbers of markers has facilitated the mapping of chromosome regions associated with phenotypic variability (e.g., QTL mapping) and, to a lesser extent, revealed the differetial response of these chromosome regions across environments (i.e., QTL × environment interaction). QTL technology has been useful for marker-assisted selection of simple traits; however, it has not been efficient for predicting complex traits affected by a large number of loci. Recently the appearance of cheap, abundant markers has made it possible to saturate the genome with high density markers and use marker information to predict genomic breeding values, thus increasing the precision of genetic value prediction over that achieved with the traditional use of pedigree information. Genomic data also allow assessing chromosome regions through marker effects and studying the pattern of covariablity of marker effects across differential environmental conditions. In this review, we outline the most important models for assessing genotype × environment interaction, QTL × environment interaction, and marker effect (gene) × environment interaction. Since analyzing genetic and genomic data is one of the most challenging statistical problems researchers currently face, different models from different areas of statistical research must be attempted in order to make significant progress in understanding genetic effects and their interaction with environment.

Keywords: Genomics-enable prediction and selection.; Genotype × environment interaction (GE); Quantitative Trait Loci (QTL); environmental and genotypic covariables; gene × environment interaction; molecular markers (MM).

Fig. (1)

Standard errors of BLUPs of 29 wheat genotypes (1-29) within 16 sites for grain yield for four linear-bilinear models (models 1, 2, 3, and 4). Sister lines are in bold (5,6), (4,19,20), (14,15), (21,23,24), (28,29). For model 15, each graph line represents one of the 16 sites. Model 1 is the standard fixed linear-bilinear model (SREG), model 2 is a simple mixed linear-bilinear model without A (not modeling GE), model 3 is a simple mixed linear-bilinear model using A (not modeling GE), and model 4 is a mixed linear-bilinear model that models the GE using the FA and includes information on relatives (A) (adapted from Crossa et al. [16]).

Fig. (2)

Biplot of the standard fixed effect linear-bilinear model 1 for grain yield. Lines are 1-29. Sister lines are in bold (5,6), (4,19,20), (14,15), (21,23,24), (28,29). The 16 sites are MEX, USA1, USA2, TKY, ISR, BGD, IND, PKT, SYR, SPN1, SPN2, NPL, KNY, ZBW, NZL, and CHL (adapted from Crossa et al. [16]).

Fig. (3)

Biplot of the mixed linear-bilinear model 4 with FA for GE and pedigree information (A) for grain yield. Lines are 1-29. Sister lines are in bold (5,6), (4,19,20), (14,15), (21,23,24), (28,29). The 16 sites are MEX, USA1, USA2, TKY, ISR, BGD, IND, PKT, SYR, SPN1, SPN2, NPL, KNY, ZBW, NZL, and CHL (adapted from Crossa et al. [16].

Fig. (4)

Profile of R² for the additive effects of QTL (solid line), QEI (dotted line), and QTL+QEI (broken line) on grain yield for chromosome 10 (additive). The horizontal lines show the appropriate threshold for the effects QTL+QEI, QTL, and QEI (adapted from Vargas et al. [51]).

Fig. (5)

Profile of LOD of chromosome 3A from the multi-trait analysis. The LOD profile of the joint analysis of all four traits (red) and the LOD profile of the marginal analyses for Karnal bunt (green), leaf rust (blue), tan spot (light blue), and yellow rust (black). The LOD threshold for the joint profile is the red horizontal line and the LOD threshold for the traits is the blue horizontal line.

Fig. (6)

Profile of LOD of chromosome 5B from the multi-trait analysis. The LOD profile of the joint analysis of all four traits (red) and the LOD of the marginal analyses for Karnal bunt (green), leaf rust (blue), tan spot (light blue) and yellow rust (black). The LOD threshold for the joint profile is the red horizontal line and the LOD threshold for the traits is the blue horizontal line.

Fig. (7)

Biplot of the first and second principal component axes (Comp. 1 and Comp. 2) of maize female flowering (FFL) and male flowering (MFL) effects of the 1148 SNPs estimated from the full data model M-BL of the maize dataset in each of two environments, severe water stress (SS) and well watered (WW). A total of six trait-environment combinations (FFL-SS, FFL-WW, MFL-SS, MFL-WW, SS-ASI, and WW-ASI) was formed. Only the effects of the 19 SNPs that are located far from the center of the biplot were identified with their corresponding SNP’s name (filled-in circles) (from Crossa et al. [32]).

Fig. (8)

Biplot of the first and second principal component axes (Comp. 1 and Comp. 2) of the Exserohilum turcicum (NCLB) disease effect of 1152 SNPs estimated from the full data M-BL model for the maize dataset in each of three environments: El Batán (México) (BA), Harare (Zimbabwe) (HA), and Mpongwe (Zambia) (MP). Only the effects of 24 SNPs located far from the center of the biplot were identified with the names of their corresponding SNPs. Three groups of environments and molecular markers are delineated as groups 1, 2, and 3 (from Crossa et al. [33]).