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Published online 16 January 2008
Published in Crop Sci 48:317-330 (2008)
© 2008 Crop Science Society of America
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Testing Wheat in Variable Environments: Genotype, Environment, Interaction Effects, and Grouping Test Locations

Kraig L. Roozebooma,*, William T. Schapaugha, Mitchell R. Tuinstraa, Richard L. Vanderlipa and George A. Millikenb

a Dep. of Agronomy, 2004 Throckmorton Hall, Kansas State Univ., Manhattan, KS 66506-5504
b Dep. of Statistics, 101 Dickens Hall, Kansas State Univ., Manhattan, KS 66506-5504. Contribution No. 07-226-J Kansas Agricultural Experiment Station, Kansas State Univ

* Corresponding author (kraig{at}ksu.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
Selection of winter wheat (Triticum aestivum L.) genotypes requires testing programs with complementary locations that sample environments of interest with minimal duplication. The goal of the current study was to improve prediction of genotype performance in the highly variable environments of the central Great Plains in the United States by estimating the contributions of genotype, location, and year to wheat yield variability and identifying subgroups of test locations that minimize crossover genotype-by-environment interaction. Variance components were estimated from Kansas wheat performance data from 17 locations from 1982 to 2002. Annual data sets balanced for genotypes and environments were used to generate genotype, genotype-by-environment biplots that could objectively separate locations into groups with the same top-yielding genotype. Location, year, and their interaction introduced the greatest proportion of the variability in wheat performance test yields. Frequency of common grouping during the 21-year period was used to construct six groups of test locations representing unique target environments. Evaluation of the six groups using results from two subsequent years revealed that they generally agreed with location groups observed in the previous 21 years. Smaller regional genotype-by-environment variance component estimates compared with statewide estimates further confirmed the effectiveness of the pro posed six regions for reducing genotype-by-environment interaction.

Abbreviations: AMMI, additive main effects and multiplicative interaction • G, genotype • GE, genotype-by-environment • GGE, genotype, genotype-by-environment • GL, genotype-by-location • GLY, genotype-by-location-by-year • GY, genotype-by-year • L, location • LY, location-by-year • MSE, mean square error • SREG, sites regression model • SS, sum of squares • TSS, total sum of squares • Y, year


   ACKNOWLEDGMENTS
 
The authors would like to acknowledge the consistent quality and quantity of work supplied by the cooperating agronomists who conducted the field studies that supplied the data for this study: Dr. Mark Claassen, Pat Evans, Dr. Allan Fritz, Dr. Barney Gordon, Dr. Bill Heer, Dr. Keith Janssen, Dr. James Long, Dr. T. Joe Martin, Dr. Vic Martin, Dr. Alan Schlegel, Ted Walter, and Dr. Merle Witt.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication April 13, 2007.

Testing Wheat in Variable Environments: Genotype, Environment, Interaction Effects, and Grouping Test Locations

Kraig L. Roozebooma,*, William T. Schapaugha, Mitchell R. Tuinstraa, Richard L. Vanderlipa and George A. Millikenb

a Dep. of Agronomy, 2004 Throckmorton Hall, Kansas State Univ., Manhattan, KS 66506-5504
b Dep. of Statistics, 101 Dickens Hall, Kansas State Univ., Manhattan, KS 66506-5504. Contribution No. 07-226-J Kansas Agricultural Experiment Station, Kansas State Univ

* Corresponding author (kraig{at}ksu.edu).

Selection of winter wheat (Triticum aestivum L.) genotypes requires testing programs with complementary locations that sample environments of interest with minimal duplication. The goal of the current study was to improve prediction of genotype performance in the highly variable environments of the central Great Plains in the United States by estimating the contributions of genotype, location, and year to wheat yield variability and identifying subgroups of test locations that minimize crossover genotype-by-environment interaction. Variance components were estimated from Kansas wheat performance data from 17 locations from 1982 to 2002. Annual data sets balanced for genotypes and environments were used to generate genotype, genotype-by-environment biplots that could objectively separate locations into groups with the same top-yielding genotype. Location, year, and their interaction introduced the greatest proportion of the variability in wheat performance test yields. Frequency of common grouping during the 21-year period was used to construct six groups of test locations representing unique target environments. Evaluation of the six groups using results from two subsequent years revealed that they generally agreed with location groups observed in the previous 21 years. Smaller regional genotype-by-environment variance component estimates compared with statewide estimates further confirmed the effectiveness of the pro posed six regions for reducing genotype-by-environment interaction.

Abbreviations: AMMI, additive main effects and multiplicative interaction • G, genotype • GE, genotype-by-environment • GGE, genotype, genotype-by-environment • GL, genotype-by-location • GLY, genotype-by-location-by-year • GY, genotype-by-year • L, location • LY, location-by-year • MSE, mean square error • SREG, sites regression model • SS, sum of squares • TSS, total sum of squares • Y, year


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
SELECTION OF WINTER WHEAT (Triticum aestivum L.) genotypes for advancement in breeding programs or for planting in producer fields requires information about genotype performance. That information typically is generated through a series of field tests designed to sample the target environments and predict genotype performance in those environments (Cooper et al., 1993). In the United States, most states with significant hard red winter wheat acreage conduct performance tests with the stated goal of providing information on genotype performance to producers to assist in their genotype selection decisions (Johnson et al., 2004; Roozeboom et al., 2004; Nelson et al., 2005). Typically, test results are presented for each location and often for subsets of locations. These subsets are derived from geographic location (e.g., southeast, south central) or management system (e.g., dryland, irrigated) or a combination of both. It is implied that the results from a given subset of locations best represent or predict genotype performance for a specific target environment.

Efficient testing of genotypes in variety testing or breeding programs requires a set of complementary test locations that adequately sample environments of interest with minimal duplication (Hamblin et al., 1980). Only one test would be needed if genotypes performed similarly in all environments. However, genotypes and environments interact such that different rankings often exist for the same set of genotypes tested over a range of environments (Hill, 1975; DeLacy et al., 1990). Although efforts have been made to identify superior selection environments (Vela-Cardenas and Frey, 1972; Allen et al., 1978), most plant breeding and performance testing programs opt to test genotypes in a number of locations to document genotype performance in different environments.

The highly variable wheat growing environments found in Kansas provide ample opportunity for differentiation of target environments and manifestation of genotype-environment interactions. The normal annual precipitation from 1961 to 1990 ranged from just over 116 cm in the southeast corner to less than 40 cm in southwest Kansas (National Climatic Data Center, 2002). A change in elevation of more than 1000 m (Kansas Geological Survey, 2005) and a 3° change in latitude result in a growing season that is up to 7 wk shorter in the northwest than in the southeast (Goodin et al., 1995). In 2003 the 4.21 x 106 ha of wheat planted in Kansas consisted of 2.32 x 106 ha in a continuously cropped, dryland system, 1.65 x 106 ha in a wheat-fallow, dryland system, and 0.23 x 106 ha under irrigation (Thiessen, 2004). Soil texture, pH, depth, organic matter content, fertility, diseases, and insect pests provide additional dimensions of variability.

The multilocation, multiyear trials used in plant breeding programs and crop performance tests are subject to three main sources of variation; genotype (G), location (L), year (Y), and their interactions: location-by-year (LY), genotype-by-year (GY), genotype-by-location (GL), and genotype-by-location-by-year (GLY) (Petersen, 1994). Sums of squares, mean squares, and estimates of variance components ({sigma}2g, {sigma}2l, {sigma}2y, {sigma}2ly, {sigma}2gy, {sigma}2gl, {sigma}2gly) reveal relationships between genotype, location, and year effects, their interactions, and their relative importance (Park, 1987; DeLacy et al., 1990; Frensham et al., 1998). Several studies have demonstrated larger location and year effects compared to genotype effects (Campbell and Lafever, 1977; Kong et al., 1987; DeLacy et al., 1990). Others have presented evidence for significant GL interactions but a minimal contribution of year to variation in yield (Liang et al., 1966; Shorter et al., 1977; Park, 1987). In some cases, genotype can have a greater influence than year or location (Cullis et al., 1996; Frensham et al., 1998).

When GL interactions are predictable, they can be exploited by targeting specific genotypes to appropriate subregions (Gauch and Zobel, 1997; Yue et al., 1997; Collaku et al., 2002). Atlin et al. (2000) indicated that if {sigma}2gl is large relative to {sigma}2g, the potential exists to increase response to selection by subdividing a larger region into two or more subregions. Genotype-by-year interactions typically are less predictable, complicating genotype selection and forcing the use of multiyear data to identify stable genotypes that are resilient in the face of changing environmental conditions (Allard and Bradshaw, 1964; Yan and Rajcan, 2002).

A number of techniques have been used to identify groups of test locations for the purpose of targeting genotypes to unique environments. Minimizing the genotype-by-environment (GE) component from the traditional combined analysis of variance identifies groups of locations with few genotype rank changes (Horner and Frey, 1957; McCain and Schultz, 1959; Park, 1987). Guitard (1960) constructed location groupings by correlating genotype performance between pairs of locations, and Hamblin et al. (1980) correlated individual locations or groups of locations with state means to determine which were better predictors of statewide performance. Others have used correlation coefficients as measures of similarity for cluster analysis of test locations (Abou-El-Fittouh et al., 1969; Campbell and Lafever, 1977) or for factor analysis (Peterson and Pfeiffer, 1989; Peterson, 1992). Clustering techniques using squared Euclidean distance as the dissimilarity measure and incremental sum of squares as the clustering strategy have been used extensively (DeLacy and Cooper, 1990; Abdalla et al., 1996; DeLacy et al., 2000). Kong et al. (1987) and Collaku et al. (2002) used similar classification strategies with different clustering techniques. Often the clustering strategies have been complemented by ordination methods that attempt to represent the proximity of locations in fewer dimensions by using principal component or principal coordinate analysis (DeLacy et al., 1994; Abdalla et al., 1996). Brown et al. (1983) used multiple regression to identify predictive environmental variables that were in turn used to develop groups of similar test locations. Principal components analysis provided the clearest delineation of location groupings when compared with regression, phenotypic correlation, and rank-change techniques, according to Fox and Rathjen (1981). They cautioned against emphasizing marginal means because they may be weighted by a set of similar locations, effectively negating potentially useful information from more independent locations. These methods rely on traditional statistical approaches to group test locations by analyzing similarity of genotype performance across a number of locations.

The additive main effects and multiplicative interaction (AMMI) model attempts to improve yield estimates and genotype selection through separating meaningful pattern and distracting noise in the data (Gauch, 1992). This model uses analysis of variance (ANOVA, an additive model) to characterize genotype and environment main effects and principal components analysis (a multiplicative model) to characterize interactions. Biplots from AMMI analysis concisely summarize a large body of information to characterize genotypes, environments, and their interactions. Ebdon and Gauch (2002) used AMMI analysis to examine GE in national turfgrass tests and were able to identify location groups within which the predictive value of the individual locations for the others was higher than for locations outside of the group.

Attempts have been made to minimize crossover interactions among subsets of locations. Baker (1988) applied the Azzalini–Cox (Azzalini and Cox, 1984) and Gail–Simon (Gail and Simon, 1985) tests for significant changes in rank order to agronomic experiments. Truberg and Hühn (2000) recommended the Azzalini–Cox test for detecting significant crossover interactions among genotypes. Russell et al. (2003) suggested applying the Gail–Simon test to genotypes with above-average performance in situations where the primary goal is to recommend genotypes for specific groups of environments. Crossa et al. (2002) identified similar groups of locations with low levels of interaction using both shifted multiplicative model and sites regression model (SREG) biplots with and without crossover interaction restraints and data transformation.

The GGE (G and GE) biplot used by Yan et al. (2000) and Yan and Rajcan (2002) was equivalent to SREG (Crossa et al., 2002). Gabriel (1971) demonstrated the ability of biplots to display the essential features of a two-way data set. Kempton (1984) applied biplots to the analysis and interpretation of multilocation agronomic data and GE interactions. Cooper and DeLacy (1994) demonstrated the power of biplots to present multilocation data in the context of plant breeding and genotype selection. The GGE biplots are similar to AMMI biplots but differ in that the genotype main effect is included as a multiplicative effect rather than as an additive main effect (Yan and Kang, 2003). Yan and Hunt (2001) argued that genotypic main effects depend on environmental conditions and flow from GE, justifying use of the GGE model. Biplots of GGE facilitate the rapid identification of groups of locations with minimal crossover interaction—particularly with the same highest-yielding genotype or treatment (Yan et al., 2001; Ma et al., 2004; Rubio et al., 2004). Laffont et al. (2007) proposed a method for partitioning the variation into that due to G and that due to GE, enhancing the information that can be derived from a GGE biplot.

With such a wide array of techniques available for forming location groups that may produce similar results, which one to use depends on the goals of the investigator, the strengths of each technique, and the nature of the data available for analysis. Most approaches that attempt to group locations by minimizing GE require replicated data from each location and fail to differentiate between crossover and noncrossover interactions. Phenotypic correlations can use unreplicated data and place more emphasis on crossover interactions, but they apply just as much weight to crossovers among the lower ranks as to those among the higher-ranking genotypes. Clustering techniques can use unreplicated data, but they involve a number of subjective decisions (e.g., choice of similarity/dissimilarity measure, specific clustering strategy) that can influence the ultimate outcome. Genotype, genotype-by-environment biplots are limited to two dimensions and may ignore important variation. Genotypes or environments located near the origin may be either nonresponsive or nondiscriminating, or their variability may exist in higher dimensions (Kroonenberg, 1995). van Eeuwijk et al. (2001) recommended that biplots be used only as screening tools when searching for an appropriate model to describe the data. However, GGE biplots provide two important benefits: they do not require replicated data and they emphasize crossover interactions among the highest-ranking genotypes (Yan et al., 2001; Ma et al., 2004).

Improving the prediction of genotype performance requires a thorough understanding of the interactions between genotype, location, and year as well as an objective approach for grouping test locations to maximize their effectiveness. The relative importance of genotypes, years, and locations as sources of variation can provide insight into the potential for their interactions to complicate genotype selection in variable environments. The relationships between sources of variation in multilocation tests also supply information about the possibility of improving results from selection by dividing test locations into more homogeneous subgroups. Identification of homogeneous subgroups should facilitate identification of superior genotypes for a wide range of wheat-growing environments (Liang et al., 1966; Kong et al., 1987). Previous attempts have examined only a few years (Kong et al., 1987) or have used data from areas with climate and crops substantially different from that of the central Great Plains (Shorter et al., 1977; Park, 1987; Cullis et al., 1996).

The current objectives are (i) to estimate the relative contributions of genotype, location, and year to yield variability in wheat performance tests conducted in variable environments and (ii) to test a method for identifying subgroups of test locations that minimize crossover GE interactions in variable environments.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 REFERENCES
 
Data Set
Yield data from 21 yr of Kansas wheat performance tests were used for the analysis. The data set included location means for 102 genotypes in various combinations at 17 locations from 1982 to 2002, representing 300 separate tests and 4495 GLY combinations. Individual yield means were generated from performance tests with a randomized complete block design and three or four replications. Since 1994 nearest neighbor analysis (Stroup et al., 1994) or mixed models with spatial covariance (Littell et al., 1996) have been used to adjust genotype means to account for within-test spatial variability. Because many of the means were adjusted in recent years and individual replicate data for earlier years were unavailable, we were obliged to the use of genotype means from each location rather than individual replicate data.

The multiyear data set was highly unbalanced (Table 1 ). The data set was balanced for genotypes and locations within each year but unbalanced for each from year to year. The degree of overlap in genotypes generally decreased as the difference in years increased, but the degree of overlap in locations depended on the specific year pair. A minimum of nine genotypes and 10 locations was present in every year. Genotypes were included if they were present in all possible locations in a given year. Genotypes typically were present in all locations if they were widely adapted and occupied a large fraction of the total wheat acreage or if they were new releases or experimental lines with poorly defined areas of adaptation. The number of genotypes changed each year as new genotypes were introduced and obsolete genotypes were phased out. Locations were not consistent from year to year because some were lost to environmental extremes (e.g., hail, drought, flood, freeze) or management problems (e.g., volunteer wheat, uncontrolled insect pests).


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  		Table 1. Number of genotypes and locations for each year and number in common for each pair of years for Kansas winter wheat performance tests, 1982 to 2002 (genotypes lower left, locations upper right).

 
Kansas wheat tests are located on formal research facilities or on privately owned farms to represent the primary growing regions of Kansas (Fig. 1 ) (Roozeboom et al., 2004). Location codes and descriptive information are presented in Table 2 . Previous and present location groupings based on geographic location and management parameters are indicated. A four-region grouping was used to summarize test results from 1993 to 1998. Beginning in 1999, the previous groups were gradually subdivided so that an eight-region grouping was in place by 2005.


Figure 1
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  		Figure 1. Winter wheat test locations and their location codes in Kansas. C, central region; E, east region; I, irrigated region; W, west region.

 

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  		Table 2. Kansas winter wheat test location codes, descriptions, and regional groupings.

 
Variance Components
Variance components were estimated using the SAS VARCOMP procedure (SAS Institute, 2003). Levene's test (Milliken and Johnson, 1984) provided evidence for heterogeneous variances (F = 4.17, df = 299 and 3664, P > F < 0.0001), so genotype means from each trial were weighted using weight = r/MSE (Steel and Torrie, 1980). Weights ranged from 8.69 x 10–6 to 3.62 x 10–4 with a median of 4.80 x 10–5. Of the 300 tests, 10 had weights exceeding 1.90 x 10–4. Genotype means from these ten tests were assigned a weight of 1.90 x 10–4 to prevent undue emphasis on this small number of tests in the analysis. The restricted maximum likelihood (REML) method is less likely than maximum likelihood (ML) to underestimate variance parameters (Gogel et al., 1995) and was selected for the analysis.

Grouping Test Locations
The full data set including all 102 genotypes was used to form groups of test locations. For each of the 21 years, a balanced genotype (g) by environment (e) yield data set was used to generate annual GGE biplots with a polygon and perpendiculars that were used to objectively separate locations into groups with the same top-yielding genotype (Yan et al., 2000). Each annual data set was converted to matrix, Y, with genotypes represented in the rows and environments in the columns. Each matrix was centered on environment by subtracting the environment means from each value. The dimensionality of the variation present in the environment-centered Y was reduced via singular value decomposition, yielding principal component scores for each genotype and each location (Yan and Kang, 2003). If Y is a g by e matrix of rank r ≤ min(g,e), its singular value decomposition is given by Y = U{Lambda}V' where {Lambda} is an r by r diagonal matrix with singular values {lambda}1 ≥ {lambda}2 ... ≥ {lambda}r and U and V are orthogonal matrices with dimensions of g by r and e by r, respectively (Laffont et al., 2007). Each element of Y can be represented as

Formula
where Yij = yield of genotype i in location j, i = 1 to g, j = 1 to e, r = min(g,e), {lambda}k = singular value of the kth principal component, the square of {lambda}k is the sum of squares explained by the kth principal component, k = rank of a principal component (k = 1 to r), {xi}ik = eigenvector of genotype i for the kth principal component, and {eta}kj = eigenvector of location j for the kth principal component.

If G = U{Lambda}{alpha}, and H = V{Lambda}1–{alpha}, then the first two columns of G provide genotype coordinates and the first two columns of H provide environment coordinates for a two-dimensional biplot (Laffont et al., 2007). The value of {alpha} in the exponent determines the partitioning of the singular values and can range from 0 to 1 to provide different interpretations of the resulting biplots. For this study, singular values were partitioned symmetrically to genotype and environment scores ({alpha} = 0.5) to preserve both genotype and environment relationships in the resulting biplots (Yan, 2002).

The variation presented in each GGE biplot was partitioned into the G and GE components as demonstrated by Laffont et al. (2007). Using the previous notation, Y = YG + YGE, where YG represents the genotype effects as a matrix with e columns, each containing the genotype (row) means from Y (Formula1.,Formula2.,···,Formulag), and YGE = Y – YG, where each element can be represented by yij–yi.. Given the above, the kth diagonal element of {Lambda}2, {lambda}2k, can be represented as {lambda}2k = uk‘YY’uk = uk‘YGYG’uk + uk ‘YGEYGE’uk where uk is the kth left singular vector of U. If the square of {lambda}k is the sum of squares (SS) explained by the kth principal component (TSSk), where TSS = total sum of squares, the previous relationships allow the partitioning of TSSk into that attributable to genotype and that attributable to the genotype by environment interaction: TSSk = SSGk + SSGEk.

The frequency that two locations grouped together was determined as the number of years that two locations were in the same group divided by the number of years that both locations were present. Frequency of grouping of a given location in a region (Table 2) was determined as the number of times that location grouped with any location from the region of interest divided by the number of times the location appeared in the same annual data set with any location from the region of interest. A single degree of freedom {chi}2 test (Steel and Torrie, 1980) was used to determine if frequencies were significantly greater or less than 0.5. Four- and eight-region formats (Table 2) were evaluated based on how frequently individual locations grouped with other locations from their region. Genotype, genotype-by-environment biplots were generated for two additional years, 2003 and 2004, to test predictability of location groupings.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
REFERENCES
 
Variance Components
All variance component estimates were significantly different from zero (Table 3 ), demonstrating the importance of genotype, location, year, and their interactions in contributing to the variation present in the data set. Estimates for location and year were significantly greater than that for genotype. Estimates of the variation due to interactions of location and year with genotype were significantly smaller than that for year or location alone but were not different from that for genotype. As with DeLacy et al. (1990) and Kong et al. (1987), environmental components ({sigma}2l, {sigma}2y, {sigma}2ly) were larger than those involving genotype ({sigma}2g, {sigma}2gl, {sigma}2gy). The largest estimate was for the year-to-year variance in location means, {sigma}2ly, which was more than 26 times larger than the year-to-year variance in genotype means, {sigma}2gy, and 27 times larger than the location-to-location variance in genotype means, {sigma}2gl, and accounted for 47.9% of the total variance. Year-to-year variance, {sigma}2y, and location-to-location variance, {sigma}2l, were roughly a third to half as large as {sigma}2ly. This differs from Park (1987) and Liang et al. (1966), who reported a minimal importance for year in their analyses. This may be due to the different climate regime and crop involved in Park's (1987) analysis and the number and/or particular set of years included in Liang's et al. (1966) analysis. Genotype variance, {sigma}2g, was roughly five- to sevenfold smaller than that for location or year, accounting for only 3.1% of the total. The second-order interaction variance, {sigma}2gly, was three times larger than the genotype variance. The relative magnitude of the entire set of variance components followed a pattern similar to that reported by Kong et al. (1987) for wheat in Kansas. The pattern of the interaction variance component estimates indicated that location and year and their interaction introduce the greatest proportion of the variability in wheat performance test wheat yields in Kansas as represented by the current data set. Examination of genotype, location, and their interaction effects within each year avoids the large variance introduced by year.


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  		Table 3. Estimates of variance components from winter wheat performance tests in Kansas, 1982 to 2002.

 
Grouping Test Locations
Table 4 summarizes the results from the annual biplots, four of which are presented in Fig. 2 to illustrate extremes of percentage of total SS captured, GE SS/G SS ratios, and number of groups. On average, the biplots accounted for 66% of G and GE variation present in the original residual matrices, similar to that reported by Yan et al. (2000) for winter wheat in Ontario, but lower than values reported by Yan and Rajcan (2002) for soybean [Glycine max (L.) Merr.] in Ontario. Although not a complete representation, the biplots captured enough of the variation present in the data sets to illustrate the overall pattern of relationships between genotypes, between environments, and between genotypes and environments. The relative importance of G and GE varied tremendously with year. The ratio of GE SS to G SS ranged from 0.44 in 1985 to 3.20 in 1994 (Table 4, Fig. 2). The GE SS/G SS ratio was close to or greater than one in more than half the years, indicating the potential for improvement in the effectiveness of genotype selection by subdividing environments into subregions (Atlin et al., 2000). In their examination of multi-location trials for several crops conducted all over the world, DeLacy et al. (1990) seldom reported a GE SS/G SS ratio of less than one. It appears that year had a large influence on the relative importance of G and GE effects in the current data set. This agrees with the relatively large variance component estimates for year and its interactions with genotype and location (Table 3).


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  		Table 4. Summary of annual biplots for winter wheat performance tests in Kansas, 1982 to 2002.{dagger}

 

Figure 2
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  		Figure 2. Annual genotype, genotype-by-environment (GGE) biplots for Kansas wheat performance tests, 1982, 1985, 1994, and 1996. TSS = total sum of squares; PC1, first principle component; PC2, second principle component.

 
Location groups were not entirely repeatable from one year to the next (Fig. 2). All location vectors fell into one sector in 1996, with 2137 as the top-yielding genotype. In 1982, location vectors fell into five different sectors, forming five location groups as follows (top-yielding genotypes for each location group in italics):
  1. Arkan: I4
  2. TAM 105: I1, I2, W1, E1, E3, C1
  3. Wings: C2, E4, W2, C3
  4. Hawk: W4, W3, C4
  5. Scout 66: E2

Examination of the frequencies of common grouping for all pairs of locations revealed some interesting patterns (Table 5 ). Locations were sorted into the four-region format to assist in visualizing geographic relationships between locations (Fig. 1). In the east region, E1 and E4 seldom grouped together. The C1 and E1 locations grouped together significantly more than half the time. Among the central locations, C4 had the lowest frequencies of common grouping with other central locations. Frequencies of common grouping for east or central locations with locations in the West or Irrigated regions were almost all less than 0.50 and often were significantly less. No frequencies of common grouping for locations in the west region with other west locations were less than 0.50, revealing some consistency of genotype ranking for that set of locations. Among the locations in the irrigated region, I3 showed little consistency of genotype ranking with the others by grouping with them significantly less than half the time. I1 had higher frequencies of common grouping with west locations than with other locations in the Irrigated region. The remaining locations in the irrigated region (I2, I3, I4) generally grouped with the west locations less than half the time.


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  		Table 5. Frequency of common grouping for all pairs of locations (upper right) and number of possible common groupings (lower left) for winter wheat performance test locations in Kansas, 1982 to 2002.{dagger}

 
Frequencies of common grouping for each location with other locations from its region (Table 6 ) were similar to the patterns observed for the individual location-pair frequencies (Table 5). With four regions, frequency of grouping with other east locations was less for E1 and E4 than for the other east locations. C4 was the only central location with a frequency significantly less than 0.50. In the west region, all locations had frequencies at or greater than 0.50. Three of the four locations in the irrigated region had frequencies less than 0.50. I3 seldom grouped with other locations in the Irrigated region. With eight regions, the frequency of common grouping with other locations in each region generally improved except for the Northeast, Southwest Dryland, and Southwest Irrigated regions. E1 and E2, although geographically close, grouped together only half the time at best. The same could be said for C4 and W4, although they are more widely separated in distance and soil type (Fig. 1, Table 2). I3 and I4 grouped together significantly less than half the time. Although eight regions appeared to be an improvement over four regions, additional improvement could be made by realigning locations that grouped with others in their region less than half the time.


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  		Table 6. Frequency of grouping for each location with other locations in its region for winter wheat performance tests in Kansas, 1982 to 2002—four and eight regions.

 
Grouping frequencies for six regions that attempt to address the problems noted above are presented in Table 7 . Among other shifts in alignment, the most notable was that the two Stafford County locations, C4 and I3, were separated into a new region (STAF). Although other factors are likely involved, it should be noted that C4 and I3 have distinctly more coarse soils than the other locations (Table 2) and may indeed represent a unique environment. Table 7 includes the frequency of grouping for each location with other locations in its region on the diagonal, as well as the frequency of grouping for each location with locations in other regions on either side of diagonal. These additional frequencies provide information about a given location's relationship with other regions. Examination of the diagonal frequencies associated with locations within each region reveals that most were either not different than 0.50 or were greater than 0.50. The irrigated region had the lowest frequencies, but they were not significantly different than 0.50. The off-diagonal frequencies were generally at or less than 0.50, indicating that most locations were grouped appropriately. Two exceptions bear noting: the C1 location grouped more frequently with locations in the south central region than with the E1 location, and the I1 location grouped more frequently with locations in the west region than with other locations in the irrigated region. The difference in frequency was statistically significant only in the latter case. This may indicate that the I1 location should be realigned to the west region or that changes in management or other site characteristics are required.


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  		Table 7. Frequency of grouping for each location with other locations in its region and locations in other regions for winter wheat performance tests in Kansas, 1982 to 2002, six regions.

 
Evaluation of the six-region format using test results from 2003 and 2004 reveals similar patterns of location grouping with the same inconsistency from year to year that was evident in the 1982 to 2002 data set (Fig. 3 ). Both northeast locations were present only in 2003 when they were in separate groups. However, the acute angle between the two northeast location vectors indicated a positive correlation for genotype ranks (Kroonenberg, 1995). Two of the three east locations were in the same group in 2003, but all three were in different groups in 2004. A potential fourth east location that was not included in the 1982 to 2002 data set, CRD, grouped with another East location, E4, in 2003. All three south central locations were in the same group in 2003 with small angles between the location vectors. In 2004 C2 ranked genotypes quite differently than the other two south central locations. Three of four west locations were in the same group in 2003, with W3 ranking genotypes differently than the other three. All west locations were in the same group in 2004, including two potential additions to the west region (SMD and FDD). Two of three irrigated locations grouped together in 2003, with the third in an adjacent group. The two previously defined Irrigated locations present in 2004 grouped together with a new location that could logically belong to the irrigated region (SVI). Only one STAF location produced usable test results in 2003 and 2004, so no assessments of that region were possible. Although all locations from each region did not group together consistently, the six-region format developed using data from 1982 to 2002 generally agreed with how locations ranked genotypes in 2003 and 2004.


Figure 3
Figure 3
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  		Figure 3. Annual genotype, genotype-by-environment (GGE) biplots for Kansas wheat performance tests, 2003 and 2004. TSS = total sum of squares; PC1, first principle component; PC2, second principle component.

 
Estimates of variance components within each region also were used to evaluate the effectiveness of the six-region format in reducing genotype by environment interaction. On a regional basis, the relative magnitude of variance component estimates tended to follow the same pattern as that for all locations (Table 8 ). For instance, {sigma}2ly was usually the largest estimate, and the genotype component and its interactions ({sigma}2g, {sigma}2gy, {sigma}2gl) tended to be smaller than the other terms. A notable deviation from the pattern was that {sigma}2y and {sigma}2gy were often much larger for an individual region than for all locations, likely because including means from a large number of locations acted to dampen the yearly variation on a statewide basis. Another exception was that {sigma}2l was much smaller for the east and irrigated regions, implying similarity of overall performance over time for locations in those regions. The Stafford region was the only region with a larger {sigma}2gl than the statewide estimate. Given that for five of the six regions, {sigma}2gl was roughly half or less than that for all locations, the six-region format successfully grouped locations that ranked genotypes similarly.


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  		Table 8. Estimates of variance components from winter wheat performance tests in Kansas by region, 1982 to 2002.

 
The large annual variation in genotype performance, location yields, and GL interactions complicated identification of uniform regions for testing wheat genotypes in variable environments of Kansas. Genotype, genotype-by-environment biplots reduced complex annual data sets to two-dimensional forms that facilitated identification of subsets of test locations with little crossover interaction among top-yielding genotypes. Frequency of common grouping between pairs of locations over a 21-yr period facilitated identification of locations that tended to rank top-yielding genotypes similarly at least half the time. Evaluation of Kansas wheat performance test location groupings with four, eight, or six regions indicated that four and eight regions grouped together some locations that tended to rank top-yielding genotypes differently. Six regions maximized the frequency of common grouping between pairs of locations over a 21-yr period. Yield data from two subsequent years showed some annual inconsistency but generally confirmed the location groups in the proposed six regions. Regional GL variance component estimates that were smaller than statewide estimates for five of the six proposed regions provided additional confirmation of the effectiveness of the proposed six regions for reducing GL interactions.

The authors would like to acknowledge the consistent quality and quantity of work supplied by the cooperating agronomists who conducted the field studies that supplied the data for this study: Dr. Mark Claassen, Pat Evans, Dr. Allan Fritz, Dr. Barney Gordon, Dr. Bill Heer, Dr. Keith Janssen, Dr. James Long, Dr. T. Joe Martin, Dr. Vic Martin, Dr. Alan Schlegel, Ted Walter, and Dr. Merle Witt.

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication April 13, 2007.


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