Crop Science 43:608-617 (2003)
© 2003 Crop Science Society of America
CROP ECOLOGY, MANAGEMENT & QUALITY
Effect of Environmental Variates on Genotype x Environment Interaction of Winter Wheat
A Comparison of Biadditive Factorial Regression to AMMI
M. Brancourt-Hulmel*,a and
C. Lecomteb
a INRA, Unité de Génétique et d'Amélioration des Plantes, 80200 Estrées-Mons, France
b INRA, Station de Génétique et d'Amélioration des Plantes, 17 rue Sully, BP 86510, 21065 Dijon Cedex, France
* Corresponding author (hulmel{at}mons.inra.fr)
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ABSTRACT
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Genotype x environment interaction is a commonly observed phenomenon in experiments in plant breeding and genetics. This interaction can be modeled by different statistical models which can include covariates, such as in biadditive factorial regression, or in other ways, such as in the classical additive main effect and multiplicative interaction (AMMI) model. The aim of this paper was to explain genotype x environment interaction in multienvironment trials of winter wheat (Triticum aestivum L.) by environmental variates to assess the genotype sensitivities to the environmental conditions and to compare the results from biadditive factorial regression (BIAREG) and AMMI. Data consisted of 13 lines grown in France in 14 environments (combinations of two years, four locations and two treatments). Grain yield and heading date were measured and the environments were characterized by climatic data (water deficit, radiation, temperature above 25°C) and by observations of powdery mildew infection (caused by Erysiphe graminis DC F. sp. tritici), lodging, and nitrogen status. AMMI model explained most of the genotype x environment interaction (77.4%) but did not provide a direct biological explanation. BIAREG explained a slightly smaller part (74.0%) but with fewer degrees of freedom. The contributions of the environmental variates to the synthetic variates revealed two important subsets of initial covariates—biotic variates and nitrogen status in contrast to climatic ones—associated with the interaction. The interactive pattern of the genotypes and the environments was similar for both models. BIAREG is more powerful than AMMI because it provides a description of the sensitivities of the genotypes in regard to the observed environmental covariates. When environments can be characterized by variates, we suggest that BIAREG can complement AMMI because it provides direct biological explanation of the interaction.
Abbreviations: AMMI, additive main effect and multiplicative interaction • BIAREG, biadditive factorial regression • BK, ratio between nitrogen absorbed during the whole cycle and kernel number • E, environment • ETa, actual evapotranspiration • ETm, maximal evapotranspiration • -F, medium sowing date without fungicides • G, genotype • GY, grain yield • HTT, high temperature during grain-filling • IN, medium sowing date with fungicides • LodgT, lodging during grain-filling • PMK, powdery mildew during grain number formation • PMT, powdery mildew during grain-filling • RK, radiation during grain number formation • RKm, radiation ± 3 d at meiosis • RT, radiation during grain-filling • LS, late sowing date with fungicides • S, site • SSI, sum of squares of interaction • WDK, water deficit during grain number formation • WDT, water deficit during grain-filling • Y, year
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INTRODUCTION
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EXPERIMENTS IN PLANT BREEDING AND GENETICS generally require several locations, years, and genotypes. In most cases, genotype x environment interaction is observed and needs to be modeled and interpreted. Models can be linear formulations such as joint-regression (Yates and Cochran, 1938; Finlay and Wilkinson, 1963; Eberhart and Russell, 1966; Perkins and Jinks, 1968), factorial regression (Denis, 1980, 1988) or multiplicative formulations such as AMMI (Gollob, 1968; Mandel, 1971; Gauch, 1992), or BIAREG (Denis 1988, 1991). This last model is also called reduced rank regression (van Eeuwijk, 1995).
AMMI and BIAREG belong to bilinear models (Denis, 1991), also termed biadditive models (Denis and Gower, 1992). AMMI models do not use directly measured environmental variates. In contrast, BIAREG uses measured environmental variates (van Eeuwijk, 1995). Just as with AMMI, BIAREG provides axes or synthetic environmental variates to which genotypes differ maximally in sensitivity, but under the restriction of being linear combinations of the initial environmental variates. BIAREG can be considered as a generalization of both AMMI and factorial regression.
Biadditive factorial regression can be interpreted from the environmental viewpoint via the correlations between the synthetic variates and the initial environmental covariates. These correlations can be displayed in Cartesian diagrams as it is done in principal component analysis. The biplot can contain three types of vectors whose coordinates are determined by the genotype sensitivities, the environmental characterizations, and coefficients for the environmental covariates within the synthetic axes (van Eeuwijk, 1995). Environmental characterizations come from the linear combinations of the initial environmental covariates. To clarify such a biplot, these three types of vectors can be considered in two separate plots (Brancourt-Hulmel et al., 2000): one including the genotype sensitivities and the coefficients of the environmental covariates and the other containing the same genotype sensitivities and the environmental characterizations. The results of AMMI can be presented graphically in the form of biplots which contain genotype and environment scores on the multiplicative (bilinear) terms. A comprehensive description of the method is given by Vargas et al. (1999).
The aim of this paper is to explain genotype x environment interaction in multienvironment trials of winter wheat x environmental variates to assess the genotype sensitivities to the environmental conditions and to compare the results from BIAREG and AMMI.
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MATERIALS AND METHODS
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Description of the Data
Genotypes included three wheat cultivars (APOLLO, SOISSONS, and THESEE) and 10 lines bred by several units of INRA (DI003, RE001, RE006, RE009, RE813, RE914, VM002, VM003, VM014, VM017). The cultivars differed for heading date: APOLLO was the latest and headed on average 9 d after RE914, which was the earliest line.
All these genotypes were grown in 14 environments. The environments were obtained by combining three factors: two years (1991 or 1992); four French sites, Mons (49°56' N, 2°56' E, silt loam soil, orthic Luvisol), La Minière (48°48' N, 2°08' E, silt loam soil, haplic Luvisol), data available only in 1991, Rennes (48°05' N, 1°41' W, silt loam soil, haplic Luvisol) and Dijon (47°19' N, 5°01' E, clay loam soil, clayey eutric Cambisol); and two treatments, medium–late sowing date at Dijon (F, LS), with and without fungicides at other sites (F,-F). Each year, the experiment was arranged in a randomized complete block design with two replicates. Indications about growing season (sowing and harvest dates) and fungicides treatments (chemicals, rates, and applications) are given in Table 1.
After a preliminary analysis, environmental variances were not homogeneous and that was mostly due to 91MINF. This environment was removed in the final analysis. Table 2 shows the yields of the 13 genotypes in the 13 remaining environments.
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Table 2. Grain yield (t/ha) for the 13 genotypes in the 13 environments, 91 and 92 code for the year, DIJ, MIN, MON, and REN code, respectively, for Dijon, La Minière, Mons, and Rennes. F, -F, LS code for treatments, respectively, with fungicides, without fungicides, and late sowing date.
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More details dealing with additional characteristics of the environments, plant sampling, and measurements are reported elsewhere (Brancourt-Hulmel, 1999). Further information about the genotypes is also given by Brancourt-Hulmel and Lecomte (1994).
Environmental covariates were related to two distinct periods: the grain-number formation (before flowering) and the grain filling (after flowering). Covariates of the first period were sum of daily water deficit (ETm-ETa) from the beginning of stem elongation (precisely when the distance between the base of the first leaf and the top of the young ear reached 10 mm) to flowering (WDK), sum of daily radiation from the beginning of stem elongation to flowering (RK), sum of daily radiation ± 3 d at meiosis (RKm), ratio between total nitrogen absorbed by the plant and kernel number (BK)—this ratio was an indicator of the nitrogen status, infection of powdery mildew (PMK), and lodging (LodgK). We added the letter "K" (for kernel number) at the last position of these variates code. For the grain-filling period, we added the letter "T" (for 1000-kernel weight) at the end of the code. The variates were sum of daily water deficit (WDT), daily radiation (RT), high temperature assessed by the sum of degree-days based on 25°C (HTT), infection of powdery mildew (PMT), and pressure of lodging (LodgT). For this period, the three climatic covariates were calculated from flowering to maturity. For more details about the determination of these variates, see Brancourt-Hulmel et al. (1999). In addition, the environmental effect (EFFECT) was introduced as an environmental covariate as it is done in joint-regression model (Finlay and Wilkinson, 1963).
An initial selection of a subset of environmental covariates was performed on the analysis of yield components measured on four independent genotypes, called probe genotypes, by means of the biadditive factorial regression model. These probe genotypes are used to probe, i.e., to capture, the influence of environmental constraints. Probe genotypes would produce yield components close to the optimal values in favorable environments and small values in unfavorable ones. More information about their description and choice can be found in Brancourt-Hulmel et al. (2001). They were grown in the same environments as the 13 genotypes. The analysis of their yield components helped to discard two environmental covariates not strongly involved in interaction: LodgK and RT. The corresponding selection procedure is described by Brancourt-Hulmel et al. (2000). Simple statistics of the retained environmental covariates are summarized in Table 3.
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Table 3. Mean across locations and range for yield-limiting factors. Scale for powdery mildew and lodging: 1 (without infection pressure) to 9 (heavily damaged).
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Statistical Developments
Genotype x environment interaction for grain yield was first analyzed according to a classical multiplicative model or AMMI (Gollob, 1968; Mandel, 1971; Gauch, 1992) with three multiplicative terms. It is written as follows:
where E[Yge] is the expectation of performance Yge for Genotype g grown in Environment e, µ is the general mean, 
g is the Genotype main effect, ße is the environment main effect; each of the multiplicative term has the same structure: 
1 is the size, 
g1 is the normalized genotype vector of the genotype scores or sensitivities, 
e1 is the normalized environmental vector of the scores describing the environments, all assigned to the first term. The parameters of the second and third terms follow the same definition. For each genotype, interaction was described in terms of ecovalence (von Wricke, 1962) and the interaction pattern with genotype scores provided by the AMMI model.
Then genotype x environment interaction was analyzed by biadditive factorial regression with three terms. This model was applied here introducing only environmental covariates, in the same manner as Wood (1976):
where E[Yge], µ, g, ße have the same definitions as previously; each of the multiplicative term has the same structure: '1 is the size, 'g1 is the normalized genotype vector of the genotype sensitivities, 
'h1Eeh is a normalized linear combination of the HB environmental covariates Eeh, assigned to the first term. The parameters of the following terms are defined in the same way.
All analyses were performed with BiaReg, a set of SPlus-functions developed by Denis (1998). The environmental covariates were first centered and scaled to unit variance.
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RESULTS
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Analysis of Variance
The analysis of variance showed significant effects for genotype, environment, and genotype x environment interaction (Table 4a). Site, treatment, and year were all significant and contributed to the environment effect. Site x year and site x treatment x year interactions were significant. The genotype x environment interaction was mostly due to the genotype x site effect. Genotype mean yields varied from 6.5 to 7.3 Mg/ha (at 0% moisture content). Four genotypes showed high ecovalences and contributed the most to the interaction (Fig. 1): APOLLO (16.4%), VM014 (15.7%), THESEE (11.8%), and RE001 (10.4%).
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Table 4. Analysis of variance with interactive model (a) and partitioning of interaction with AMMI (b) and BIAREG (c).
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AMMI analysis of variance indicated that three multiplicative terms were significant (P < 0.05). These multiplicative terms accounted for 40.8, 26.3, and 10.3% of the genotype x environment interaction sum of squares with 23, 21, and 19 degrees of freedom, respectively (Table 4b). These terms accounted for a total of 77.4% of the interaction with 43.7% for the corresponding degrees of freedom. Most interaction was described by these three terms since the remaining interaction was not significant.
Results obtained with BIAREG were of the same kind: the three first multiplicative terms accounted for 39.1, 24.8, and 10.1% with 21, 19, and 17 degrees of freedom, respectively (Table 4c). This represented a total of 74.0% of the interaction with 39.6% degrees of freedom. As previously, most interaction was described by these three terms since the remaining interaction was not significant.
Correlations between the Environmental Scores and the Initial Covariates
To help interpret AMMI results from the environmental viewpoint, the correlations between the environmental scores and the initial covariates were computed. Similarly, the correlations were calculated between the environmental characterizations obtained by BIAREG, which come from the linear combinations of the initial environmental covariates and the initial covariates themselves. These two series of correlations were similar in absolute value between AMMI and BIAREG (Table 5) because scores were similar in absolute value between the two models (Fig. 2). The first synthetic variate was correlated mostly with PMT (0.83 for AMMI/0.86 for BIAREG in Table 5), LodgT (0.73/0.75), PMK (0.72/0.73), BK (0.71/0.73), and EFFECT (-0.67/-0.66). Environmental variates were not strongly correlated with the second synthetical variate. Nevertheless, climatic variates (WDK, RK, WDT, and HTT) recorded the higher correlations in contrast to the other variates. The third variate was correlated with RK (0.66/0.68), WDT (0.59/0.55), and HTT (0.55/0.47). In summary, these synthetic variates were related to distinct types of yield-limiting factors: powdery mildew, lodging, and nitrogen status for the first one and climatic variates for the last two ones (Fig. 3).
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Fig. 3. Contributions of each covariate to the synthetic environmental variates defined with BIAREG: 1st and 2nd synthetic variates (a) 1st and 3rd variates (b) Significant variates are given in bold. Codes of environment covariates are the same as in Table 3.
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Explaining the Behavior of the Most Interactive Genotypes
The analysis of the genotype and environment parameters resulting from either AMMI or BIAREG, because these parameters were similar between both models, helps to describe the behavior of the genotypes. Dashed lines refer to genotypes (Fig. 4). Genotypes near the origin show little interaction, while genotypes distant from it represent the most interactive genotypes. APOLLO, VM014, THESEE, and RE001 were the most interactive, while VM002, VM003 (hidden by VM002 on all plots of Fig. 4), RE813, and VM017 were the least interactive. Points near each other, such as VM002 and VM003, have similar interaction pattern (in both Fig. 4a and 4b). Out of the four most interactive genotypes, APOLLO and VM014 had the most similar interaction pattern. APOLLO showed positive interaction effects at 91DIJF, 92DIJF, 92MONF, and 91DIJLS and negative interaction effects at 92REN-F, 91REN-F, 92RENF, 91MON-F, and 91MIN-F (Fig. 4a and 4b). THESEE showed positive interaction effects at 91RENF and 91REN-F and negative ones at 91MIN-F, 92REN-F, and 92REINF (Fig. 4a). VM014 displayed positive effects at 91DIJLS, 91MIN-F, 91DIJF, and 92DIJF and negative ones at 91REN-F, 92REN-F, and 91RENF (Fig. 4a). RE001 showed positive interaction effects at 91MON-F, 91DIJLS, and 92REN-F and negative effects at 91RENF and 92MONF (Fig. 4b).
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Fig. 4. Biadditive factorial regression biplots with 1st and 2nd synthetic variates (a and c) and 1st and 3rd synthetic variates (b and d). Parameters of genotypes (dashed lines) are depicted in all the plots while environmental characterizations are displayed on a and b and environmental covariates (arrows) on c and d. Genotypes names are given in italic. The genotype "VM003" was hidden by the genotype "VM002" in all plots. Environment codes are the same as in Table 2. Codes of environment covariates are the same as in Table 3. Plots c and d are on the following page.
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An additional feature of the BIAREG biplot, in comparison with the AMMI biplot, is to give approximations about the coefficients for factorial regression (van Eeuwijk et al., 1995). This helps to explain the particular behavior of the four interactive genotypes. Arrows refer to the initial environmental variates (Fig. 4c and 4d). Projecting the genotype line on the concomitant variable arrows, it can be seen that VM014 and APOLLO had the highest positive effects on EFFECT, BK, and LodgT and a negative effect on PMT, while RE001 showed opposite effects (Fig. 4c). THESEE showed a negative effect for HTT (Fig. 4c and 4d). APOLLO, VM014, and THESEE also displayed the highest positive effects for RK and negative effect for WDT (Fig. 4d), while RE001 showed opposite effects.
In the experiments under consideration, VM014 and APOLLO thus had positive interactions in environments with high yield potential and a long period before flowering. These environments could be subjected to lodging. In contrast, the interaction pattern of VM014 and APOLLO is negative in environments subject to late infection of powdery mildew and water deficit. These genotypes are adapted to fertile environments and poorly adapted to environments with late infection of powdery mildew. THESEE behaved similarly but was also subjected to hot temperatures. The opposite was partly observed for RE001: this genotype behaved well in environments subject to late infection of powdery mildew but not in those with high yield potential.
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DISCUSSION AND CONCLUSION
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BIAREG and AMMI accounted for an important part of the interaction, with a slight superiority of AMMI in terms of sum of squares of interaction but a slight inferiority in terms of degrees of freedom. The interactive pattern of the genotypes and the environments was similar for both models. The contributions of the environmental variates to the synthetic variates revealed some important subsets of initial covariates related to the interaction. The interaction was related to distinct types of yield-limiting factors: climatic variates in contrast to infection of powdery mildew, nitrogen status, and lodging.
BIAREG is more powerful than AMMI because it combines features of AMMI model and factorial regression by means of linear functions of true measured covariates. The biplots not only provide the interactive patterns of the genotypes and the environments, but also a description of the sensitivities of the genotypes in regard to the environmental covariates. BIAREG can then complement AMMI biplots in the analysis of genotype x environment interaction.
In our study, AMMI analyses revealed similar patterns as BIAREG, indicating that the major interactions in the data were clearly related to the environmental variates chosen. These variates were initially chosen through crop diagnosis and were subsets which were the most related to the interaction during the whole cycle of the plant (Brancourt-Hulmel et al., 2000). When AMMI and BIAREG solutions differ, van Eeuwijk et al. (1995) suggest that it should be considered whether all relevant environmental information has been introduced in the analysis or not. We further suggest that the manner used to determine the covariates should be reconsidered as well.
Winter wheat is widely grown in France and is subject to diverse climatic conditions. This diversity complicates the characterization of the environments and the statistical analysis of the interaction as covariates can be countless. If parsimony is defined as the number of free parameters used in the model (Brancourt-Hulmel et al., 1997), BIAREG is then of interest because it can introduce numerous covariates with parsimony. In contrast, linear factorial regression is not adapted because it demands many parameters, although these parameters are better estimated by linear factorial regression than by BIAREG.
Although BIAREG is parsimonious, a selection procedure may be needed in some cases. The correlations of each environmental covariate to the synthetic variates help to discard those poorly related to the interaction (Brancourt-Hulmel et al., 2000). When the analyzed trait is complex, it can be dissected into more simple traits and the environmental covariates can be selected according to these traits. This procedure also helps to assess with more insight the effect of environmental factors. For instance, wheat grain yield comes from two main yield components which are determined over two distinct periods: kernel number per square meter and 1000-kernel weight. These components or comparisons of the components to potential values can be used as more simple traits (Brancourt-Hulmel et al., 1999).
This study revealed that BIAREG is a useful tool for interpreting genotype x environment interaction in multienvironment trials especially when a large number of covariates is concerned. It demonstrated that BIAREG and AMMI complement each other and can help plant breeders and researchers not only in explaining genotype x environment interaction but also in selecting subsets of environmental variates.
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ACKNOWLEDGMENTS
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We express gratitude to Denis Beghin, Michel Leleu, Claude Sausseau, and the staff of the Domaines INRA of Dijon, La Minière, Mons, and Rennes for their technical assistance. We also express thanks to Jean-Baptiste Denis for the development of BIAREG; Eric Hanocq and Jacques Le Gouis for their careful reading of the manuscript; and Hervé Monod, Jean-Baptiste Denis, and Nathalie Robert for their helpful suggestions. We thank also the two reviewers for their helpful comments.
Received for publication July 12, 2001.
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ABSTRACT
INTRODUCTION
