The statistical analysis of multi-environment data: modeling genotype-by-environment interaction and its genetic basis

Abstract

Genotype-by-environment interaction (GEI) is an important phenomenon in plant breeding. This paper presents a series of models for describing, exploring, understanding, and predicting GEI. All models depart from a two-way table of genotype by environment means. First, a series of descriptive and explorative models/approaches are presented: Finlay-Wilkinson model, AMMI model, GGE biplot. All of these approaches have in common that they merely try to group genotypes and environments and do not use other information than the two-way table of means. Next, factorial regression is introduced as an approach to explicitly introduce genotypic and environmental covariates for describing and explaining GEI. Finally, QTL modeling is presented as a natural extension of factorial regression, where marker information is translated into genetic predictors. Tests for regression coefficients corresponding to these genetic predictors are tests for main effect QTL expression and QTL by environment interaction (QEI). QTL models for which QEI depends on environmental covariables form an interesting model class for predicting GEI for new genotypes and new environments. For realistic modeling of genotypic differences across multiple environments, sophisticated mixed models are necessary to allow for heterogeneity of genetic variances and correlations across environments. The use and interpretation of all models is illustrated by an example data set from the CIMMYT maize breeding program, containing environments differing in drought and nitrogen stress. To help readers to carry out the statistical analyses, GenStat® programs, 15th Edition and Discovery® version, are presented as "Appendix."

Keywords: QTL by environment interaction; QTL mapping methodology; REML; adaptation; genotype by environment interaction; multi-environment trials.

Figure 1

Genotype-by-environment interaction in terms of changing mean performances across environments: (A) additive model, (B) divergence, (C) convergence, (D) cross-over interaction.

Figure 2

(A) Boxplot for yield of a maize F2 population in eight environments displaying total range, interquartile range (box) and median (line). Environment names are coded as: LN, low nitrogen; HN, high Nitrogen; SS, severe water stress; IS, intermediate water stress; NS, no water stress. The two digits indicate the year of the trial, and the letters a and b the cropping season: a, winter; b, summer. (B) Scatter plot matrix for two stress environments (IS92a, and IS94a) and two non-stress environments (HN96b and NS92a).

Figure 3

Finlay–Wilkinson regression curves of five maize genotypes. The vertical line indicates the average environment. Next to genotype labels, the corresponding Finlay-Wilkinson regression equation is given.

Figure 4

(A) Biplot from the AMMI model used to describe GEI in the maize example data. Gray circles represent genotypes, and filled triangles environments, with triangles pointing in the direction of increasing GEI (at origin GEI = 0). The projection of two genotypes (G041 and G091) on the NS92a axis is shown by a dashed line. (B) GGE biplot for the maize data set, with same characteristics as of the AMMI biplot, except that triangles point in the direction of increasing overall performance (G + GEI), so the origin corresponds to the average performance of all genotypes in the particular environment. Projections for genotypes G041 and G091 are given.

Figure 5

Plot produced by a SIM QTL scan in a maize F2 population. The upper panel shows the P value of the Wald test (on a –log10 scale) for the effect of a QTL along the chromosomes (solid line). The horizontal line indicates a threshold value for significance. The lower panel gives an indication of magnitude of QTL effects (higher intensity, larger effect), and parental line contributing the superior allele (blue, maternal; red, parental line).

Figure 6

Plot produced by a CIM QTL scan in a maize F2 population. The upper panel shows the P value of the Wald test (on a –log10 scale) for the effect of a QTL along the chromosomes (solid line). The horizontal line indicates a threshold value for significance. The lower panel gives an indication of magnitude of QTL effects (higher intensity, larger effect), and parental line contributing the superior allele (blue, maternal; red, parental line).

Figure 7

Effect on yield (ton ha-1) of the QTL on chromosome 1 at 141 cM in relation to the minimum temperature (°C) during flowering time.