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Department of Plant Agriculture, University of Guelph, Guelph, Ontario, Canada N1G 2W1
wyan{at}uoguelph.ca
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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Abbreviations: AMMI, Additive Main Effect and Multiplicative Interaction Effect • CHU, Corn Heat Units • E, environment main effect • G, genotypic main effect • GE, genotype x environment interaction • GGE, G plus GE • GGL, G plus GL • GL, genotype x location interaction • L, location main effect • MET, multiple environment trials • OCCC, Ontario Cereal Crops Committee • OWWP, Ontario winter wheat performance trials • PC, principal component(s) • SREG, sites regression • SVD, singular value decomposition
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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Winter wheat regions in North America, and throughout the world, are typically divided into a number of subregions for cultivar recommendation purposes. Often this is based on traditional thinking (on geographical, climatic, or administrative factors) rather than on available MET data, presumably due to lack of appropriate analytical methods. For example, the winter wheat growing region in Ontario is traditionally divided into four subareas based on yearly Corn Heat Units (CHU). Area I in this classification encompasses much of southern Ontario, Area II and IV, western Ontario, and Area III, eastern Ontario, with the greatest CHU being in Area I and the least in Area IV, which has higher elevations than the other areas. Based on the belief that these subareas are sufficiently different, and thus require different wheat cultivars for optimum performance, each year the Ontario winter wheat performance (OWWP) trial data are summarized separately for each area (Publication no. 296 OMAFRA). However, it is not known if these subareas truly reflect differential winter wheat adaptations.
The work reported here was undertaken to address the question of mega-environment identification using Ontario MET data and a biplot technique. Because the technique is not widely known, our first objective is to present the GGE biplot methodology to graphically summarize the effects of G and GE interaction, and to address the question of "which won where" in a MET dataset. The second objective is to use the GGE biplot technique to examine the possible existence of different mega-environments in the Ontario winter wheat growing region.
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Material and methods |
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TOPABSTRACTINTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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Locations and genotypes in the OWWP trials varied each year, resulting in highly unbalanced year x genotype and year x location data, although the yearly genotype x location data were largely balanced. Ten cultivars were common to trials from 1989 to 1993, 13 cultivars were common to trials from 1996 to 1998, and seven cultivars were tested in most or all of the 10 yr. A total of 52 cultivars were tested in at least one of the 10 yr.
Model and Biplot Selection
To make possible the display in a single graph of the performance of each genotype at each location, the biplot technique developed by Gabriel (1971) was used. Through singular value decomposition (SVD), a g x e matrix of mean yield of g cultivars in e environments can be approximated as the product of a genotype matrix and an environment matrix, so that the yield of genotype i at environment (location) j, Yij, is approximated as
 | (1) |
min(g,e); 
n is the singular value of PCn, the square of which is the sum of squares explained by PCn. 
in and jn are the ith genotype score and the jth environment score, respectively, for PCn. The SVD allows the g x e table of means to be displayed in a plot having g points for the genotypes plus e points for the environments. Each genotype is represented by a point, called a marker, defined by the genotype's scores on all PCs, and each environment is represented by a marker defined by the environment's scores on all PCs. Such a plot is called a biplot because both the genotypes and the environments are plotted in a single plot. Biplots can be multidimensional, but two-dimensional biplots, using only the first and the second PCs, are most common, both for biological reasons as well as for easy comprehension. To achieve symmetric scaling between the genotype scores and the environment scores, Eq. [1] is usually written in the form:
 | (1a) |
and
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The mean yield of genotype i in environment j is commonly described by a general linear model
 | (2) |
i is the main effect of ith genotype, ßj is the main effect of jth environment, and 
ij is the interaction between genotype i and environment j. Deletion of i and/or ßj or all of µ + i + ßj allows variation explainable by the deleted term(s) to be absorbed into the ij term. It is the matrix of ij values that is subjected to SVD. Subjecting the ij in Eq. [2] to SVD results in the Additive Main effects and Multiplicative Interaction (AMMI) model (Gauch, 1988; Zobel et al., 1988).
We use the sites regression (SREG) model (Cornelius et al., 1996; Crossa and Cornelius, 1997) obtained from Eq. [2] by deleting the i term and subjecting the ij (which are now environment-centered yields) to SVD. Explicitly,
 | (3) |
A biplot based on Eq. [3] contains only G plus GE, and will be characterized as a GGE biplot. In contrast, a biplot based on SVD of ij in Eq. [2] contains only GE interaction and can be referred to as a GE biplot. Kempton (1984) applied the GE biplot in an analysis of a wheat MET, and the GGE biplot to a wheat variety x fungicide study.
The SREG model can have an environment-standardized version
 | (3a) |
Considering that test locations are basic units of mega-environments, and that the genotype x year and the location x year data were highly unbalanced, the GL relation was the focus of analysis. Starting from 1989, the yearly GL data were analyzed using Eq. [3] and a GGL biplot constructed using the first two PCs. The yearly results were then collectively summarized and interpreted.
The biplots and data in Table 1 were based on the published cell means, but the model tests in Table 2 were based on the replicated data. Since not all replicates were available, and since the number of replicates varied from three to six depending on the test locations, the values in Tables 1 and 2 do not exactly match.
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Results |
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TOPABSTRACTINTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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The GGL Biplot
A two-dimensional, symmetrically scaled GGL biplot graphically approximates the location-centered yield data (Fig. 1)
. For a specific genotype at a specific location, the location-centered yield is approximated by the product of the genotypic PC1 score by the location PC1 score, plus the product of the genotypic PC2 score by the location PC2 score. Geometrically, this is the length of the location vector (the absolute distance from the plot origin to the marker of the location) multiplied by the length of the genotype vector (the absolute distance from the plot origin to the marker of the genotype) and by the cosine of the angle between them (Kroonenberg, 1995). This property allows the following information to be readily visualized: (i) the similarity and difference among the locations in their differentiation of the genotypes, (ii) the similarity and difference among the genotypes in their response to the locations, and (iii) the nature (positive vs. negative) and magnitude of the interaction between any genotype and any location.
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Comparing the Performance of Two Genotypes at All Locations
Based on the same principle, the performance of two genotypes can be easily compared on the GGL biplot. To compare two cultivars, here cultivars AC Ron and Rebecca in Fig. 1C, first connect their markers by a straight line; then draw a perpendicular line that passes through the plot origin. This perpendicular divides the locations into two groups, each of these two cultivars yielding better than the other at locations with markers on its side of the perpendicular, and vice versa. Thus, Rebecca yielded better than AC Ron at WE, WK, and MH, while AC Ron yielded better at the other locations (namely NN, HW, BH, RN, ID, LN, and EA). The perpendicular through the origin represents virtual locations at which AC Ron and Rebecca would yield the same.
Winning Genotypes and Mega-Environment Identification
On each biplot, some corner or vertex genotypes, which are the most responsive ones, can be visually identified. These are either the best or the poorest genotypes at some or all locations; they can be used to identify possible mega-environments. The corner genotypes for the 1992 dataset were AC Ron, Rebecca, Ena, and Harmil (Fig. 1D). By connecting the markers of these corner genotypes a polygon is formed. By drawing perpendiculars to each side of the polygon passing through the origin, the locations are divided among several sectors, each with a different corner cultivar. In Fig. 1D, the locations are divided between two sectors. The first sector contains locations WE, WK, and MH, with cultivar Rebecca being the winner. The other locations make up the second sector, cultivar AC Ron being the winner. With Rebecca winning at three locations and AC Ron at seven locations, AC Ron gave higher average yield across the locations. Cultivar Delaware was located at an intermediate point on the line connecting AC Ron and Rebecca; therefore, it performed intermediately between AC Ron and Rebecca at all locations. The two other corner cultivars, Harmil and Ena, were the poorest-yielding cultivars. They located far away from the markers of all locations, reflecting the fact that they yielded poorly at all locations. Cultivars within the polygon were less responsive to the locations than the corner cultivars.
If mega-environments are defined by different winning cultivars (Gauch and Zobel, 1997), Fig. 1D suggests the existence of two mega-environments for winter wheat in Ontario, namely the Rebecca-winning niche and the AC Ron-winning niche. However, such a subdivision can be regarded only as a suggestion insofar as it is based solely on one year's data.
Winter Wheat Mega-Environments in Ontario
The GGL biplots for the other 9 yr were similarly constructed and are not presented. Each year the locations fell into different groups but the pattern of the location groupings varied across years. In most cases, the suggested mega-environments based on the location grouping did not correspond with the traditional area divisions (Table 3). However, examination of the yearly location groupings revealed that the eastern Ontario location OA tended to be grouped separately from the majority of other locations (1989, 1993, 1994, 1995, 1996, and 1998). It was always grouped with another eastern Ontario location KE (1993–1995 and 1997). This suggests that the two eastern Ontario locations, OA and KE, form a single mega-environment, which is different from the other locations (Table 3).
The GGL biplots based on multi-year data (Fig. 2 and 3) seem to support this suggestion. Ten cultivars were common to trials in 1989 to 1993 and 12 locations were used in the test for at least two of the 5 yr. The GGL biplot based on the averaged 10 cultivar by 12 location data separated the two eastern Ontario locations OA and KE from the other locations (Fig. 2). Similarly, 21 cultivars were common to trials in 1996 to 1998 and eight locations were used in the test for at least two of the 3 yr. The GGL biplot based on the averaged 21 cultivar by 8 location data separated OA from the other locations (Fig. 3). Location WE was separated from other locations in Fig. 2 but this was not repeated in Fig. 3. Likewise, locations ID and RN were separated from other locations in Fig. 3, but this was not seen in Fig. 2. Thus, there are two winter wheat mega-environments in Ontario: the eastern Ontario mega-environment represented by OA and KE, and the western and southern Ontario represented by other locations.
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Genotype xLocation Interaction Due to Disproportionality of Cultivar Response across Locations
In contrast to PC1, the location PC2 takes both positive and negative values. Consequently, it is impossible for a genotype to have large positive PC2 interactions with all locations. If it has large positive interactions with some of the locations (due to a large genotypic PC2 score of same sign), it must simultaneously have large negative interactions with some other locations. Thus PC2 summarizes the most important sources of variation of a MET that lead to disproportionate genotype yield differences across locations. If this disproportionality is sufficiently severe, it can lead to the net combined effects of PC1 and PC2 revealing crossover GE interactions. The GGL biplots clearly demonstrate crossover GL interactions for all years. For example, Fig. 1C shows AC Ron is better than Rebecca at locations above the dashed line and Rebecca better than AC Ron below it. It is the crossover GL interaction involving the better cultivars that leads to mega-environment differentiation.
Better Locations for Cultivar Evaluation
In case of random GL interaction, a GGL biplot displays the tested genotypes in terms of average yield across locations (approximated by the genotype PC1 scores) and yield stability (represented by the genotype PC2 scores). Thus, high- and stable-yielding genotypes should have large PC1 scores but near-zero PC2 scores. These genotypes are most easily identified at locations with large PC1 scores and near-zero PC2 scores. For example, EA was such a location in 1992 (Fig. 1). The better testing locations visually identified based on the GGL biplots for each of the 10 yr are labeled with "
" in Table 3. Among all 16 locations involved in the 10 yr of testing, location EA was identified as a better location for cultivar evaluation for four of the 10 yr. Other locations that were identified as a better testing location include KE (three out of 6 yr), RN (two out of 10 yr), HW (two out of 7 yr), WE (two out of 6 yr), BH (one out of 5 yr), OA (one out of 7 yr), and MH (one out of 3 yr). The other eight locations were not identified as a good testing location in any of the years.
Under limited resources and the need to conduct cultivar evaluation in a limited number of environments, the better locations will be those with high values of the PC1 and small values of PC2. The locations so selected should constitute a sample of environments that adequately cover the range of environmental conditions of the target geographical region.
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Discussion |
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TOPABSTRACTINTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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The validity of the GGE (or GGL) biplot can be inferred by the bulk of evidence from applying the AMMI model. Upon reviewing the application of AMMI in MET data analysis in recent years, Gauch and Zobel (1996) concluded that in 70% of the cases, AMMI1 (with one multiplicative term) is the best model, and for the rest, AMMI2 (with two multiplicative terms) is the best. A best model is considered to best capture the pattern but reject the noise contained in the data (Gauch, 1988; Piepho, 1994; Cornelius et al., 1993, 1996). From both theory and actual calculation, a two-dimensional GGE biplot based on SREG2 always uses an intermediate number of degrees of freedom and explains an intermediate portion of G + GE variation between AMMI1 and AMMI2. Thus, a GGE biplot should always be close to the best model. Using the simplified method suggested in Gauch and Zobel (1996) to estimate the pattern vs. noise contained in the data, it was revealed that the best model was SREG2 for 1993, 1994, and 1998 and SREG3 for 1996 and 1997. Thus, in many cases a GGE biplot displays the location-centered yield data not only graphically, but also more accurately than the raw data. The merit of using a GGE biplot would be increasingly manifest as more genotypes are tested in more environments and as the GE interaction pattern becomes more complicated.
Compared with AMMI, the GGE biplot presents the genotypic main effect as a multiplicative effect in terms of GE interaction (called the cultivar "primary" effect by Crossa and Cornelius, 1997). Since the PC1 scores of all locations tend to be of the same sign, PC1 presents a noncrossover GE interaction. Because typically the genotypic PC1 scores are highly correlated with genotype main effects, for practical purposes they can substitute for the main effects; however, conceptually the two are quite different. By definition, "genotypic main effect" is a constant genotypic effect in any environment, but yield predictions from PC1 in the GGE biplot for a given genotype are not constant. They vary across environments in direct proportion to the environment PC1 scores. We believe that this proportionality of genotype yield response is more logical and biologically plausible than the concept of additive main effects. Moreover, a unique property of this concept is that locations that facilitate identification of genotypes with greater main effect are simultaneously indicated (locations labeled with "" in Table 3). Another strength of the GGE biplot is the differentiation between proportionate and disproportionate cultivar responses and their implications for crossover and noncrossover GE interactions. Understanding of these interactions may be achieved by relating PC1 and PC2 scores to genotypic and/or environmental covariates.
Implications for Future Cultivar Evaluation and Selection
Analysis using the GGE biplot method revealed two winter wheat mega-environments in Ontario: eastern Ontario, which is a small mega-environment, and southern and western Ontario, which makes up the majority of the Ontario winter wheat–growing region. This has several implications for future breeding and cultivar evaluation in Ontario. First, different cultivars should be deployed for the two mega-environments to achieve optimal adaptation. Second, although crossover GL interaction was frequently observed within the southern and western Ontario mega-environments, it could not be effectively exploited due to its unpredictability. The unpredictable annual GL interaction introduces uncertainty (instability) to cultivar performance and therefore should be avoided or minimized through breeding. This must be achieved through cultivar evaluation and selection focusing on genotype main effects or general adaptation. Any measured yield at a given location in a given year is a mixture of the year, location, and genotype main effects plus various interaction effects. Reliable selection for the genotype main effect requires removal of all other unfixable variations, that is, the various year and location related effects. The only way to achieve this is to conduct multiple-location trials in multiple years. The finding that some testing locations may be better than others for cultivar evaluation suggests that the genotypes may be evaluated at fewer but better locations while still achieving the same or even better evaluation.
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ACKNOWLEDGMENTS |
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Received for publication February 9, 1999.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMaterial and methodsResultsDiscussionREFERENCES |
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