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a Department of Agricultural, Food, and Nutritional Science, University of Alberta, Edmonton, AB, T6G 2P5, Canada
b Field Crop Development Centre, Second Floor, Agriculture Building, 5030- 50 Street, Lacombe, AB, T4L 1W8, Canada
* Corresponding author (dean.spaner{at}ualberta.ca)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Abbreviations: GEI, genotype by environment interaction • COI, crossover interaction • SREG, site regression model • SHMM, shifted multiplicative model
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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One approach to COI is to characterize the environments in terms of the way they influence the relative performance of the genotypes and to identify environmental groupings with negligible COI. Although several statistical models have been proposed to study GEI (DeLacy et al., 1996), only a few of them are known to be capable of distinguishing between significant genotypic rank change (COI) and no genotypic rank change. Two types of models are defined as being suitable for grouping sites within which there is negligible COI (Crossa et al., 2002): the shifted multiplicative model (SHMM) by Seyedsadr and Cornelius (1992) and the sites regression model (SREG) by Cornelius et al. (1996). Crossa et al. (1993) used the SHMM model with an associated cluster method in a study of multilocation trials and confirmed that such a model is able to identify subsets of sites with statistically negligible genotypic rank change. Yan et al. (2000), Yan and Hunt (2001), and Crossa et al. (2002) demonstrated that the application of SREG model with the use of biplots of primary and secondary effects can identify groups of sites with low COI.
Considering that the need to grow different varieties in different environments is mainly due to the existence of GEI, Gauch and Zobel (1996, 1997) defined megaenvironments as a portion of a crop species' growing region with a homogenous environment causing some genotypes to perform similarly. Yan et al. (2001) suggested that if the GEI patterns identified in biplots of the SREG analyses are repeatable over years, megaenvironments can be identified. If such patterns are not repeatable then tested environments belong to a single megaenvironment.
Padbury et al. (2002) categorized the agroecoregions of the land resources of the northern Great Plains and identified five ecoregions in Alberta. For the purpose of cultivar recommendation, however, spring wheat growing regions in Alberta have traditionally been divided into six subregions on the basis of the soil type, geographical, and climatic factors (Alberta seed guide at: http://www.seed.ab.ca; verified 17 January 2006). These divisions are henceforth referred to as "agro-climatic zones." Each year, multilocation data from regional variety testing in the province are summarized on the basis of this geographical classification. This method of summarizing the data gives the impression that each agroclimatic zone is uniform in terms of relative performance of cultivars throughout the region. However, a great amount of within-zone variability is commonly observed and these zones do not truly reflect differential spring wheat adaptations in Alberta. Recently, a new approach has been taken, whereby yearly multilocation data are summarized on the basis of yielding ability of individual sites, regardless of their geographical location. Yang et al. (2005) described a performance-based approach to identify groups of sites with similar yielding ability (isoyield groups), which might not necessarily be contiguous, and recommended the use of this approach for choosing appropriate genotypes for a given environment with a known target yield.
We report here on a study of a dataset of 22 yr of multilocation regional spring wheat variety trials in Alberta, using SHMM and SREG models. This study was undertaken to (i) identify groups of sites with statistically negligible genotypic rank change for each of the 22 yr, (ii) investigate whether there is a repeatable GEI pattern which may lead to the identification of wheat growing megaenvironments, as described by Gauch and Zobel (1996 and 1997), and (iii) identify responsive sites representative of the average varietal performance over the years.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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ij. is the mean of the ith cultivar in the jth environments; ß is the shift parameter; 
k (1 
2 ... t) are scaling constants (singular values) that allow the imposition of orthonormality constraints on the singular vectors for cultivars, 
ik = (1k,...,gk) and sites, 
jk = (1k,...,ek), such that 
i ik2 = j jk2 = 1 and i ik ik' = j jk jk' = 0 for k 
k'; ik and jk for k = 1, 2, 3,... are called "primary," "secondary," "tertiary,.".. etc. effects of cultivars and sites, respectively; 
ij. is the residual error assumed to be normally and independently distributed with the mean being zero and the variance being 
2/r, where 2 is the pooled error variance from the combined ANOVA; and r is the number of replications. The distances for all possible pairs of sites were calculated as the residual sum of squares after SHMM1 was fitted to the data from all the site pairs. Dendrograms were constructed using complete linkage clustering methods as implemented in SAS PROC CLUSTER (SAS Institute 1999). For the dendrograms generated for each of the 22 yr, frequencies of COI in each cluster of sites were calculated using a modification of the Azzalini-Cox test for improved sensitivity (Cornelius et al., 1992). In each of the yearly dendrograms, a cut-off point was selected to group sites into subsets with an average COI frequency of less than 10%. This was often the third or forth fusion level in dendrograms. A summary table was then made to represent the association of sites with other sites in each of the agroclimatic zones and the overall association of each site with other sites in Alberta. For this purpose, the association of each site with the sites in each zone was calculated as the number of times this site was clustered together with other sites within the same agroclimatic zones, divided by the total number of site occurrences of the given zone. These values were then averaged over agroclimatic zones to represent the overall association of each site with other sites in the province.
SREG Analysis
The yearly multilocation data were subjected to analyses by the SREG model with two principle components (Cornelius et al., 1996; Yan et al., 2000). The SREG model is:
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It should be noted that in the SREG model, only the main effects of genotypes (G) plus genotype x location (GL) are absorbed into the bilinear terms but in the SHMM model, all effects, G, L, and GL are absorbed into the bilinear terms.
The genotype main effect (G) plus genotype x location (GL) biplots (henceforth referred to as GGL biplots) were constructed by use of the SREG model (Cornelius et al., 1996; Yan et al., 2000) with the first two principle components (PCs). From the yearly GGL biplots, using the graphical method described by Yan et al. (2000) and Crossa et al. (2002), subsets of sites with common winning (highest yielding) genotypes were identified to classify each year's testing sites into subsets with negligible COI.
The SREG and SHMM analyses, like other GEI analyses, are based on a common assumption that individual ij. values are normally and independently distributed (NID). The consequence of failures to NID assumptions often result in a larger pooled error, thereby rendering the GEI analysis less sensitive. Conversely, error variances often differ considerably over test environments. Such heterogeneity from pooling error variances across environments tends to increase levels of significance of the F test. Thus, the net outcome is that the two opposing effects often offset one another (Cochran and Cox 1957, Ch. 14).
The SAS codes used for the SHMM and SREG analyses and graphing the GGL biplots are provided by CIMMYT Biometrics Group and are available at: http://www.cimmyt.org/english/wps/biometrics/index.htm; verified 10 February 2006.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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SREG
The relatively large contribution of L to yield variation, which is irrelevant to cultivar evaluation and megaenvironment investigation, justifies the application of SREG model as it focuses on G and GL but discards L that is irrelevant for genotype rankings. The large GL relative to G indicates the possible existence of different megaenvironments (Yan et al., 2000). Application of the SREG model is especially beneficial given the large contribution of L to the total variation. The SREG model with two principal components was used in all years as they accounted for a large portion of GE.
Table 4 summarizes the results of the SREG analyses of the multilocation yearly data. Both PC1 and PC2, derived from subjecting the multilocation data of each year to singular value decomposition, were significant (p < 0.01) for all years. The PC1 accounted for 28 to 63% and PC2 for 14 to 28% of the total G + GL. In total, PC1 and PC2 together accounted for 45 to 83% of the G + GL, which make up a given GGL biplot. Therefore, the SREG model with the first two PCs was the most predictively accurate member of its model family in all years. The correlation coefficient for PC1 scores with the genotypic main effects was always greater than 0.80 (p < 0.01), except for years 1992 and 1997 with r = 0.72 (p < 0.01) and r = 0.69 (p < 0.01), respectively (Table 4).
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With regards to genotypes, an ideal genotype is one with a large PC1 (high average yield) and near zero PC2 scores (stable across most sites). In 1998, with near perfect correlation between PC1 and genotypic main effect (r = 0.94; p < 0.01), AC Barrie had the highest PC1 (average yield) and near zero PC2 scores (most stable) and can be considered the ideal genotype for recommendation across the province in that year. Unlike the GEI patterns that were not repeatable, there seems to be some repeatability for the genotypes that were selected as ideal genotypes in the GGL biplots. Varieties Neepawa and Katepwa in early 1980s, Laura in late 1980s, CDC Teal and AC Barrie in 1990s, and AC Superb in early 2000s were varieties that were repeatedly selected as high yielding and stable genotypes for the spring wheat growing areas in Alberta. It is noteworthy that these cultivars were chosen by prairie farmers in Canada and were generally grown on vast hectarages throughout the prairies during and following their testing purposes. For example AC Barrie was still grown on 25% of the Canadian prairie wheat growing area in 2004 (Canadian Wheat Board, pers comm.).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Considering that the need to grow different cultivars in different environments is due to the existence of GEI, Gauch and Zobel (1996) defined a megaenvironment as a portion of a crop species' growing region with a homogeneous environment that causes some genotypes to perform similarly. They later presented a methodology for identifying megaenvironments, which was based on the winning genotypes in different environments (Gauch and Zobel, 1997). Taking a similar strategy, Yan et al. (2000) identified yearly "which-won-where" patterns in GGL biplots from SREG analysis to identify subsets of sites with common winning genotypes. They identified a repeatable pattern across years and concluded that the wheat growing areas in Ontario can be divided into two megaenvironments. Crossa et al. (2002) discussed that such grouping of sites, using SHMM and (or) SREG models can identify subsets of sites with low-level COI for multilocation data. In the present study, the yearly multilocation data were subjected to the SHMM cluster analysis. Furthermore, following the graphical method based on the GGL biplots (Yan et al., 2000; Crossa et al., 2002), the yearly which-won-where patterns were outlined.
For each year, in both models, testing sites fell into several subsets, often two or three major groups of sites. The pattern of the site groupings, however, was not consistently repeatable in terms of sites which grouped together, and such groupings varied over years. These groupings generally did not correspond with traditional wheat growing area divisions in Alberta, nor with the classification of agroecosystems of the land resources of northern Great Plains (Padbury et al., 2002). Quite often sites in the southeast corner of the province (area 1), grouped with sites in the northern part of the province (area 6). This indicated that GEI patterns were inconsistent over the years, mainly because of complex, highly variable, and unpredictable year effects in the northern Great Plains which accounted for an extremely large portion of GEI. In four year interval combined analyses (results not shown), while location seems to be the main contributor to total variation, year x location accounted for 21 to 40% of the total sums of squares.
It can therefore be concluded that the classification of spring wheat growing areas in Alberta and defining spring wheat growing megaenvironments, as defined by Gauch and Zobel (1997), on the basis of GEI patterns, seems to be unrealistic, mainly because of the lack of repeatability of such patterns over years. Rather it should be regarded as a single megaenvironment with unpredictable COI pattern. Results are congruent with findings of other studies suggesting that there is little or no repeatability of site groupings across years in this region of North America (Yang et al., 2005). As an alternative to classification of sites into megaenvironments as subsets of sites with minimal COI (Gauch and Zobel, 1997), Yang et al. (2005) introduced the term "isoyield environments" in their study of multilocation field pea data from Alberta. They recommended site groupings based on yielding ability of sites. Results of the present study indicate that COI patterns are independent of yielding ability of sites for spring wheat. This suggests that genotypic rank change may occur within a group of sites with nonsignificant yield differences. Under such a situation, identification of genotypes well adapted to a wide range of environments with different levels of yielding ability can be recommended. This is not only important to breeders wishing to identify best performing genotypes in a range of environments but also to producers wishing to choose varieties with a reduced risk for the unpredictable year.
The SREG model is known to explain what is commonly called genotype main effects in terms of a noncrossover GEI (Yan and Hunt, 2001) and has been used to identify superior cultivars and test environments facilitating the identification of such cultivars (Yan et al., 2000). Results of the SREG analysis in the present study pointed to sites Olds, Lacombe, Vegreville, and Trochu as being the most discriminating sites, representative of the average genotypic performance across the province over the years.
Moreover, the SHMM model has also been used to study the association among testing sites in multilocation–year trials on the basis of the frequency that sites grouped together in negligible COI groups (e.g., Lillemo et al., 2004; Trethowan et al., 2001) and to identify sites with high association with other sites. The summary of SHMM clusters in the present study identified the testing sites Lethbridge, Oyen, Strathmore, Lacombe, Beaverlodge, Fort St. John, and Fort Vermilion as the most representative sites in Alberta with overall high association with other sites in the province. It is concluded that although there is no predictability for the GEI patterns, some sites are better for variety testing in terms of their discriminating ability and (or) being representative of average varietal performance. This indicates that the regional variety testing in Alberta and other regions of the northern Great Plains may be conducted at a fewer locations with better discriminating ability and (or) more representative of the average performance.
There were differences between results obtained from the two models in terms of classifying sites with reduced COI. This was largely because the GGL biplots site groupings are mainly on the basis of similar winning genotypes (Yan et al., 2000), while in the SHMM model the overall response of all genotypes determines the COI groups. While differences were notable between the two models, our conclusion of the absence of repeatability in site groupings is independent of the statistical models.
With near perfect correlation between PC1 and genotypic yield in most years, GGL biplots can also be used to identify the high yielding and stable genotypes (Crossa et al., 2002). These genotypes with large PC1 (higher average yield) and near zero PC2 (more stable) were repeatedly selected over the years. Varieties Neepawa and Katepwa in the early 1980s, Laura in the late 1980s, CDC-Teal and AC-Barrie in the 1990s, and Superb in the early 2000s were the varieties that were repeatedly selected as ideal genotypes (high yielding and stable) across all locations. These varieties were also the most popular spring wheat cultivars grown by farmers across the province during the respective time periods. As an example of this phenomenon, AC Barrie was still grown on 25% of wheat-growing land in the Canadian Prairies in 2004, and Superb was already the second most popular cultivar at 14% of the wheat-land (Canadian Wheat Board, pers. Comm.). This may indicate that variety selection by plant breeders and (or) farmers on the basis of genotypic main effects have resulted in selection for wide adaptation over random events and hence a greater popularity of such genotypes.
Genetic similarity of the high yielding and stable genotypes over years may suggest that this genetic background needs to be maintained while introducing new genetic diversity in germplasm development programs. Katepwa is a backcross derivative of Neepawa (coefficient of parentage = 0.98), and AC Barrie is also derived from crosses involving Neepawa (coefficient of parentage = 0.79). Neepawa has relatively less genetic similarity with Laura (coefficient of parentage = 0.37) and CDC Teal (coefficient of parentage = 0.44). The genetic similarity among the stable varieties indicate that maintaining the genetic background of the high yielding and stable cultivars while introducing new genetic diversity through crossing may result in further development of well-adapted varieties for the Canadian prairies.
In some years, groups of one or two sites with clear COI with all other sites were identified in both SHMM and SREG model analyses. Examples of such sites can be seen in SHMM dendrogram of year 1998 (Fig. 1) and in the GGL biplot of the same year (Fig. 2; 1998). In both models site BKS has shown a clear COI pattern with all other sites. If these sites had repeatedly shown the clear COI pattern with other sites in the province, a group(s) of marginal sites in Alberta could have been identified. However, as it seems that this is a randomly occurring phenomenon for only a few sites and only in a few years, it can be concluded that this marginal COI pattern is also year-dependant. For the purpose of variety selection and recommendation, inclusion of these sites may result in bias estimates of genotypic performance. It can therefore be recommended that in the analysis of yearly multilocation regional variety tests, data from such sites be dropped before the analysis.
Implications for Future Regional Cultivar Evaluation
Analysis using the SHMM cluster method and the GGL biplots of the SREG model indicated that GEI effects do not follow a repeatable pattern in Alberta. Although COI was frequently observed within the yearly data, megaenvironments cannot be identified because of lack of repeatability and therefore unpredictability of the GEI patterns. It can be concluded that the spring wheat growing regions in Alberta, and on a greater scale, in the northern Great Plains, belong to a single megaenvironment with inconsistent GEI patterns.
Under the highly variable and unpredictable year effect, typical of the Canadian prairies in the higher latitudes of the northern Great Plains, variety selection should focus on selecting for wide adaptation to random events and not on selection for specific adaptation. This is mainly because the random year effect makes it impossible to select for a specific environment. Selection for general adaptation and yield stability should be feasible through selection for genotypic main effects from multilocation–year data. Despite the lack of repeatability in GEI patterns over years, repeated selection of the same genotypes and selection of genotypes with high genetic similarity, over years, as the best performing genotypes (high yield and stable) was notable. This indicated that the only way to deal with the unpredictable GEI is through selection for wide adaptation.
In the analysis of some years, one or two testing sites were identified with clear COI pattern with all other locations. Since this marginal response of some sites in some years seems to be randomly occurring with no consistent pattern, it is recommended that the yearly data from such locations be removed before summarizing the data, to avoid unwanted bias estimates of the varietal performance. Such marginal sites can be identified each year, by the use of models capable of identifying COI patterns such as SHMM and (or) SREG. Moreover, identification of sites with a greater predictability of the average varietal performance suggests that regional trials may be conducted at fewer locations. Such sites would generally be more discriminating and more representative of the average varietal performance in the region.
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ACKNOWLEDGMENTS |
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Received for publication June 24, 2005.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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