HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (8) Citing Articles via Google Scholar Google Scholar Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Search for Related Content PubMed Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Agricola Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Related Collections Maize Biometrics Plant and Environment Interactions

CROP BREEDING, GENETICS & CYTOLOGY

Clustering Environments to Minimize Change in Rank of Cultivars

^a Dep. of Agronomy and Horticulture, Univ. of Nebraska, Lincoln, NE 68583-0915
^b Dep. of Biometry, Univ. of Nebraska, Lincoln, NE 68583-0712
^c Northwestern Agric. Res. Center, 4575 Hwy. 35, Kalispell, MT 59901

^* Corresponding author (krussell3{at}unl.edu)

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Crossover interactions occur in evaluation trials when ranks of cultivars change across environments. Determining groups of environments within which crossover interactions are minimized may facilitate making cultivar recommendations. The goal of this research was to test a new approach for determining these environmental groups in which crossover interaction between a pair of cultivars was defined across all environments. The number of groups was based both on reduction in crossover interaction and repeatability of cultivar means within groups. The validity of this procedure was tested on three simulated data sets with known crossover interactions. For each data set, the approach divided the environments into the two groups that minimized crossover interactions. The approach also was applied to yield data from a maize (Zea mays L.) trial in which 59 environments previously had been clustered by a different measure of crossover interaction. Three groups of 12 environments and one group of 23 environments were defined. The previous clustering had identified six clusters. The amount of crossover interaction within the four environmental groups was reduced by 53% from the total crossover interaction in all 59 environments. The results of the clustering depended on whether all pairwise comparisons among cultivars or only the significant crossover interactions among the higher yielding cultivars were used. The latter method was deemed more appropriate when the goal is to recommend specific cultivars for specific groups of environments. Regardless of the approach used, clustering based on crossover interactions only has practical significance if these interactions are repeatable.

Abbreviations: SimA, simulated data set A • SimB, simulated data set B • SimC, simulated data set C • CC, Crossa-Cornelius • GS, Gail-Simon

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
THE TYPE of genotype x environment interaction in which a change in rank occurs between a pair of cultivars is known as a crossover interaction. When crossover interactions exist in evaluation trials, a single cultivar may not be the best in every environment. One approach to this problem is to divide the environments into two or more groups within which crossover interactions are minimized.

Cornelius et al. (1992), Crossa et al. (1993)(1995), and Crossa and Cornelius (1997) identified such environmental clusters by using various multiplicative models in which the distance between two environments is equal to the residual sum of squares after the model is fit to the genotypic means in those environments. Each of the models used by Crossa and Cornelius (1997) has a single multiplicative term and is a noncrossover model if all the primary environmental effects in the multiplicative term are of the same sign.

Several tests have been proposed to determine the statistical significance of crossover interactions. Azzalini and Cox (1984) developed a test for changes in rank between two treatments in two environments. The joint t test of Cornelius et al. (1992) is similar in that crossover interaction is defined as a change in rank in a 2 x 2 treatment x environment quadruplet. The test developed by Gail and Simon (1985) is different from either of these foregoing tests because the significance of crossover interaction between a pair of treatments is based on their relative performance across a series of independent trials. In a large trial with many environments, a crossover interaction between a pair of cultivars across all environments may not be declared significant even though one or more 2 x 2 crossover interactions between the same pair of cultivars are statistically significant. Defining groups of environments based on the Gail-Simon test is desirable when plant breeders are more interested in the relative performance of two culivars across a series of environments than in only two environments.

Another consideration when grouping environments to minimize crossover interactions is which interactions to use. If the primary goal of a trial is to make specific recommendations for the cultivars actually tested, then minimizing interactions between cultivars that have below average performance across all environments is not as relevant as minimizing interactions between high performing cultivars. This would be true even though both types of interaction are statistically significant. Thus, a desirable method of clustering should allow the researcher to choose the pairwise interactions on which to base the clustering of environments.

Our purpose is to describe and test a new approach for clustering environments that is based on reducing crossover interactions as defined by Gail and Simon (1985). Unlike the procedure used by Crossa and Cornelius (1997), our approach is not model based. The validity of this new approach for clustering environments is tested on several simulated data sets with known crossover interactions. Also, the approach is applied to yield data from a maize trial, which were previously analyzed by Crossa and Cornelius (1997). Finally, the issues of when to terminate clustering, basing clustering only on selected pairs of cultivars, and the practical significance of clustering are considered.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Clustering Procedure
The Gail-Simon test is a likelihood-ratio test in which the level of crossover interaction between the ith and jth cultivars is defined as,

D_ij,k = the difference between the ith and jth cultivar in the kth environment, ²_k = variance of the difference between cultivars in the kth environment, and e = the number of environments. When the number of cultivars is large, the test is valid if consistent estimates of ²_k are used instead of the parameter itself. Gail and Simon (1985) presented a partial table of critical values for this test. They also described the derivation of these values so that critical values for any combination of environments and Type 1 error rate could be calculated.

To cluster the environments, we based the distance between any two environments both on the sign of the difference between pairs of cultivars grown in those environments and on the relative magnitudes of the crossover interaction across all environments for each pair of cultivars, as measured by Q_ij. For example, let the difference between cultivars A and B be positive in environments 1 and 2 but negative in environments 3 and 4. Then on the basis of this cultivar pair, the distance between environments 1 and 2 and between 3 and 4 is 0, whereas the distances between environmental pairs 1 and 3, 1 and 4, 2 and 3, and 2 and 4 are > 0. This result does not depend on whether the difference considered is A–B or B–A. The actual distance between environments 1 and 2 was determined by considering all pairs of cultivars with Q_ij as the weighting factor. This definition of distance is similar to that used by Guillen-Portal (2000), except he considered only the sign of the difference.

This criterion for defining distance was applied to both hierarchical and nonhierarchical methods of clustering. For nonhierarchical clustering, we used Proc Fastclus (SAS Institute, 1989). The clustering was done on an e x n matrix, where e was the number of environments and n was the total number of cultivar pairs. The value of all elements in the column of this matrix associated with the ijth pair of cultivars was +Q_ij if the difference between the cultivars was positive in an environment or -Q_ij if the difference was negative.

For the hierarchical clustering, we used Proc Cluster (SAS Institute, 1989). The input matrix was an e x e distance matrix. The distance between environments x and y was defined as

Q^'_ij = Q_ij, if the differences between the ith and jth cultivars in both environments x and y were of the same sign, Q^'_ij = -Q_ij, if the differences between the ith and jth cultivars in environments x and y were of different sign, and

The distance of an environment from itself was 0, and the maximal distance between two environments was 2.

The criterion used to determine when clustering should be stopped was

H = repeatability of cultivar means, and X refers to a series of environmental clusters that collectively form a pool of environments, Y. In a multi-environmental trial, repeatability is the proportion of the phenotypic variability that is attributable to genetic differences among cultivars (Falconer and Mackay, 1996). It is a direct measure of the precision with which a cultivar mean is determined in a set of environments. We propose that clustering be discontinued when this product increases in value. The rationale behind this criterion is presented in the Results and Discussion section. The approach to defining environmental clusters that uses the aforementioned definition of distance and this criterion for deciding the appropriate number of clusters is subsequently referred to as the GS approach because it is based on the Gail-Simon definition of crossover interaction.

Data Sets
Three simulated data sets (Table 1) were used to measure the ability of the GS approach to correctly identify the two environmental groups for which the value of QSUM within groups was a minimum. The values in Table 1 are dimensionless and are actual parameter values rather than measured values (i.e., these values contain no error component). Unique patterns of crossover interactions occur in each of the data sets. In the first simulated data set (SimA), crossover interactions exist between 20 of the 45 pairs of cultivars. The value of min ranges from 1 to 24. All crossover interactions in SimA can be eliminated by dividing the environments into two groups, environments 1 to 6 and environments 7 to 12. Crossover interactions in SimB exist between cultivars 1 and 2, cultivars 3 and 4, and cultivars 5 and 6. Considering each crossover separately will result in a different division of the environments into two groups. For example, the crossover interaction between cultivars 1 and 2 can be eliminated by putting environments 1 and 2 into one group and environments 3 and 4 into another. However, for cultivar pair 3 and 4, the appropriate division of the environments is 1 and 3 in one group and 2 and 4 in another. In SimC, cultivars 1 to 4 have identical performance and cultivars 5 to 8 have identical performance. Crossover interactions exist between every pair of non-identical cultivars. For each interaction, the differences between non-identical cultivars in environments 1, 2, and 3 are 8, 2, and -2, respectively. On the basis of the actual, absolute separation between these differences, environments 2 and 3 are the most similar environmental pair [i.e., 2 - (-2) = 4, whereas 8 - 2 = 6 and 8 - (-2) = 10]. However, on the basis of the signs of the differences, environments 1 and 2 are the most similar pair.

For SimB and SimC, ²_k purposely was set to 3.09 and 2.31, respectively. These values make the expected value of Q for each true crossover interaction equal to c_.20. As with SimA, 1500 independent, nonhierarchical cluster analyses in which environments were divided into two groups were run on each of these simulated data sets. In the analyses of all three simulated data sets, only the ability of the GS approach to correctly identify patterns of crossover interaction at the first splitting of the environments into two groups was tested. The criterion for determining when to discontinue clustering was not used.

The Trial 1 data set used by Crossa and Cornelius (1997) was from an international maize yield trial with eight cultivars and 59 locations in one year. The total number of 2 x 2 quadruplets is 47908, of which 19682 exhibited crossover interactions. Using a sites regression model on scaled data and a hierarchical clustering method with complete linkage, they defined six environmental groups ranging in size from 1 to 21 environments. When the lack-of-fit of the model becomes nonsignificant, clustering is discontinued. This approach to defining environmental clusters will be referred to as the CC approach. To compare the GS and CC approaches, the Trial 1 data set was analyzed with the same clustering method (i.e., hierarchical, complete linkage) but with distance between environments defined as described above to minimize the value of QSUM and with the QSUM x ^0.5 criterion used to determine the appropriate number of clusters.

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Simulated Data Sets
In SimA, frequency of Type 1 errors was much less than expected on the basis of critical values provided by Gail and Simon (1985) (Table 2). For example, the values of cultivars 2 and 3 were identical in all environments, and hence no crossover interaction existed between these cultivars. However, the frequency at which the value of Q was greater than c_.20 was only 0.03 for this cultivar pair. The reason for the discrepancy between this observed frequency and the expected frequency of 0.20 is not known. When the difference between cultivars was 1 in all environments (cultivar pair 2,4 and cultivar pair 3,4), the frequency at which Q exceeded c_.20 was less than 0.01. This result showed that the greater the mean difference between two cultivars for which a crossover interaction did not exist, the less was the probability of a Type 1 error with the Gail-Simon test. In no case was the frequency of a Type 1 error greater than 0.07 when the critical value was c_.20.

In SimA, the frequency at which environment 1 was in the same group as environment 2, 3, 4, 5, or 6 ranged from 0.81 to 0.90 (Table 3). Similarly high frequencies occurred for all pairs of environments within environments 1 to 6 or within environments 7 to 12. On the other hand, the frequency of pairings between environment 1 and any environment from environments 7 to 12 was never greater than 0.15. For environment 6 and any environment from 7 to 12, this frequency of pairing increased but only to 0.30. The frequencies of correct and incorrect pairings were substantially increased and decreased, respectively, when clustering was based only on those cultivar pairs for which the calculated value of Q_ij was greater than the value of c_.20 (data not shown). For example, the frequency of pairing between environments 1 and 6 increased from 0.81 to 0.92 and between environments 6 and 7 decreased from 0.30 to 0.08. This improvement in clustering occurred because in SimA every crossover interaction was similar in that each could be eliminated by dividing the environments into the same two clusters. Therefore, using only the data from the largest crossover interactions did not change which pairs of environments clustered together most frequently, but it did improve the precision of the clustering. When not all interactions are similar in this way, completely ignoring those interactions that are not statistically significant also will affect which pairs of environments cluster together most frequently.

Data set SimC provided a test of the clustering procedure to group correctly the environments on the basis of the sign of the crossover (Table 1). The frequency of pairing for environments 1 and 2 was 0.91 compared to only 0.09 for environments 2 and 3. This occurred even though environments 2 and 3 were more similar than environments 1 and 2 on a quantitative basis. The results from all three simulated data sets indicated that the clustering procedure was effective in identifying the pair of environmental groups within which crossover interactions were minimized. As expected, the clustering procedure became more precise as both the size of the crossover interactions and the differences between pairs of cultivars without crossover interaction increased.

Maize Trial Data Set
There were 28 pairs of cultivars in this data set. With = 0.20, nine of these pairs exhibited significant crossover interactions (Table 4). All cultivars were involved in at least one significant crossover interaction. Cultivar 8, which across all environments ranked fifth in yield, was involved in five of the nine significant crossovers and in the two largest crossovers. One of these interactions was with cultivar 1, which ranked sixth across all environments, and the other was with cultivar 4, which ranked third overall. In general, significant crossover interactions were associated with pairs of cultivars for which the absolute difference between mean yield was small.

With both the CC and GS approaches, the goal is to define homogeneous groups of environments within which crossover interactions are minimized. The ultimate set of homogeneous groups occurs when each environment is a cluster. Clearly this is undesirable, because the precision of measuring the genotypic value of a cultivar is directly related to the number of environments in which that cultivar is evaluated (Atlin et al., 2000). In the CC approach, clustering is halted when lack-of-fit of the model is not statistically significant. In the GS approach, there is not a comparable lack-of-fit criterion to determine the appropriate number of clusters. We propose use of the product, QSUM x ^0.5 because the first term measures the reduction in crossover interaction as the number of clusters increases whereas the second term measures the loss in precision in determining the genetic value of a cultivar as the number of environments in clusters declines.

This criterion is similar to the expression, r_GXY x ^0.5, where r_GXY is the genetic correlation between performance in environments X and Y. This expression is a prediction of the relative advantage of indirectly selecting for performance in a set of environments X by basing selection on performance in a different set of environments Y (Atlin et al., 2000). Therefore, our proposed criterion implies a relationship between r_GXY and the percent reduction in QSUM. When r_GXY = 1.0, there is no genotype x environment interaction. No changes in ranks between X and Y and no reduction in QSUM will result from clustering. When r_GXY < 0, crossover interaction exists and a reduction in QSUM from clustering will occur. Using computer simulation to create 250 randomly generated multienvironmental data sets (each set included 15 cultivars evaluated in each of 4 environments), we found that the correlation between r_GXY (X = 1 environment; Y = all 4 environments) and the percent reduction in QSUM from forming clusters of 1 and 3 environments was –0.54 (data not shown). The correlation was not –1.00 because r_GXY is a measure of genotype x environment interaction, but not all genotype x environment interaction is of the crossover type. The percent reduction in QSUM is actually a more direct measure than is r_GXY of how closely the rankings of cultivars in Y predict the rankings of those same cultivars in X. A less conservative approach to determining the appropriate number of clusters (i.e., more clusters formed) would be to substitute H_X(avg), the average repeatability across the clusters, for H_X(min) in the criterion. If the goal is to determine with good precision the best cultivar(s) for each cluster, then any single cluster with a low repeatability is undesirable. Therefore, we favor H_X(min) over H_X(avg). Also, because QSUM must go to 0 when each cluster is a single environment, we recommend that clustering be halted when the criterion first increases in value even though it may subsequently decline again at the next level of clustering.

Application of this criterion to the clusters defined in the maize data set based on the GS approach indicated that clustering should be stopped at the four-cluster stage (Table 5). The initial division of the 59 environments into 2 clusters resulted in a substantial reduction in QSUM, whereas in each cluster the loss in precision in measuring genotypic value, as measured by repeatability, was minimal. At the 3- and 4-cluster stages, the loss in precision in one cluster was 18.3% compared with that obtained with data from all 59 environments, but the reduction in QSUM more than compensated for this lower precision. At the 5-cluster stage, the loss in precision in the smallest cluster (six environments) was an additional 45.0%. QSUM also was reduced by going from four to five clusters but by a lesser percentage.

In the clusters defined by the CC approach, application of this same criterion again indicated that clustering should be terminated at the four-cluster stage (Table 5). This is less than the six clusters recognized by Crossa and Cornelius (1997). For each level of clustering from two through four, the value of the criterion was slightly less for the clusters defined by the GS approach than those defined by the CC approach.

In the maize data set, two of the significant crossover interactions were between cultivars 3 and 6 and between 1 and 8 (Table 4). Whereas both cultivars 3 and 6 had above average performance across all environments, cultivars 1 and 8 had below average performance. Considered separately, each of these pairwise interactions defined sets of two environmental groups. These two sets were not closely related. For example, in both environments 1 and 2, cultivar 6 was superior to cultivar 3. With cultivars 1 and 8, one cultivar was better in environment 1 and the other in environment 2. Across all possible pairs of environments, this differential classification of environments occurred at a frequency of 0.51. This result shows that if the primary goal of forming clusters is to find environmental groups within which the crossover interactions between the cultivars with the highest means are minimized, including crossover interactions between cultivars with lower means in the cluster analysis may be detrimental to defining these groups.

Selecting a specific set of crossover interactions to define distances between environments is straightforward when clustering is not model-based, as with the GS approach. When the maize data set was clustered using only the four significant crossover interactions occurring among the cultivars that ranked in the top half across all environments, the QSUM value for these four interactions was reduced from 169.1 to 55.4 by splitting the environments into two clusters (Table 6). This compared to a reduction in QSUM for these four crossover interactions from 169.1 to only 147.4 when clustering was based on all data. In the latter case, two of the four interactions were still statistically significant at the two-cluster stage. When clustering was based on only these four interactions, none of them was significant at the two-cluster stage. In cluster 2a defined on the basis of only the four selected cultivar pairs (Table 6), the ranking of the cultivars from highest to lowest yielding was 3, 6, 4, 5, 1, 8, 2, and 7. In cluster 2b of the same analysis, the ranking was 6, 5, 4, 8, 3, 2, 1, and 7. The best cultivar in cluster 2a was only the fifth best in cluster 2b.

	CONCLUSIONS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The results from the simulated data sets and from the maize data set showed that the proposed GS approach for clustering identified groups of environments in which the level of crossover interaction, as defined by Gail and Simon (1985), was substantially reduced. The researcher must decide whether to use all the crossover interactions or only those between selected pairs of cultivars to define the environmental clusters. If the cultivars are a fixed set and the primary goal is to recommend specific cultivars for specific groups of environments, using only crossover interactions in which both cultivars of the pair have above average performance is appropriate. When the primary goal is to identify specific environmental factors that cause rank changes between cultivars or to define environmental groups that will be used in evaluating a different set of cultivars, using all the data to define the clusters is more appropriate.

In the maize data set, four clusters were defined when the value of QSUM x ^0.5 was the criterion on which discontinuation of clustering was based. These four clusters removed 53.0% of the total crossover interaction, as measured by QSUM. The six clusters defined by Crossa and Cornelius (1997) in the same data set removed 82.3% of the 2 x 2 crossover interactions. However, removing crossover interactions by forming many clusters of environments may lower the precision at which genetic value is estimated in a given cluster. In the maize data set, this loss of precision was more detrimental than the reduction in crossover interaction was beneficial after four clusters were defined. By allowing researchers to consider the effect of clustering both on reducing crossover interactions and on altering the precision of estimating genetic values, we believe the criterion we have proposed for halting the clustering is valuable. Also, clustering should be based only on repeatable crossover interactions.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Nebraska Agric. Res. Div., Journal Series No. 13794.

Received for publication August 8, 2002.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

• Atlin, G.N., R.J. Baker, K.B. McRae, and X. Lu. 2000. Selection response in subdivided target regions. Crop Sci. 40:7–13.[Abstract/Free Full Text]
• Azzalini, A., and D.R. Cox. 1984. Two new tests associated with analysis of variance. J. Roy. Statist. Soc. B 46:335–343.
• Cornelius, P.L., M.S. Seyedsadr, and J. Crossa. 1992. Using the shifted multiplicative model to search for "separability" in crop cultivar trials. Theor. Appl. Genet. 84:161–172.[ISI]
• Crossa, J., and P.L. Cornelius. 1997. Sites regression and shifted multiplicative model clustering of cultivar trial sites under heterogeneity of error variances. Crop Sci. 37:406–415.[Abstract/Free Full Text]
• Crossa, J., P.L. Cornelius, M.S. Seyedsadr, and P. Byrne. 1993. A shifted multiplicative model cluster analysis for grouping environments without genotypic rank change. Theor. Appl. Genet. 85:577–586.[ISI]
• Crossa, J., P.L. Cornelius, K. Sayre, and J.I. Ortiz-Monasterio R.A. 1995. Shifted multiplicative model fusion method for grouping environments without cultivar rank change. Crop Sci. 35:54–62.[Abstract/Free Full Text]
• Falconer, D.S., and T.F.C. Mackay. 1996 Introduction to quantitative genetics. Addison Wesley Longman Limited, Essex, UK.
• Gail, M., and R. Simon. 1985. Testing for qualitative interactions between treatment effects and patient subsets. Biometrics 41:361–372.[ISI][Medline]
• Guillen-Portal, F.R. 2000. Maize hybrid adaptability to drought stress assessed with combining ability and genotype-by-environment effects. Ph.D. diss. Univ. of Nebraska, Lincoln (Diss. Abstr. AA19991989) (Diss. Abstr. Int. 61B:5065.
• SAS Institute Inc. 1985. SAS user's guide: basics (version 5 ed.). SAS Institute Inc., Cary, NC.
• SAS Institute Inc. 1989. SAS/STAT user's guide (version 6, 4th ed.). SAS Institute Inc., Cary, NC.

This article has been cited by other articles:

				K. L. Roozeboom, W. T. Schapaugh, M. R. Tuinstra, R. L. Vanderlip, and G. A. Milliken Testing Wheat in Variable Environments: Genotype, Environment, Interaction Effects, and Grouping Test Locations Crop Sci., January 16, 2008; 48(1): 317 - 330. [Abstract] [Full Text] [PDF]

				P. S. Baenziger, W. K. Russell, G. L. Graef, and B. T. Campbell Improving Lives: 50 Years of Crop Breeding, Genetics, and Cytology (C-1) Crop Sci., September 8, 2006; 46(5): 2230 - 2244. [Abstract] [Full Text] [PDF]

				R. Mishra, P. S. Baenziger, W. K. Russell, R. A. Graybosch, D. D. Baltensperger, and K. M. Eskridge Crossover Interactions for Grain Yield in Multienvironmental Trials of Winter Wheat Crop Sci., April 25, 2006; 46(3): 1291 - 1298. [Abstract] [Full Text] [PDF]

				R.-C. Yang, S. F. Blade, J. Crossa, D. Stanton, and M. S. Bandara Identifying Isoyield Environments for Field Pea Production Crop Sci., January 1, 2005; 45(1): 106 - 113. [Abstract] [Full Text] [PDF]

				F. R. Guillen-Portal, W. K. Russell, K. M. Eskridge, D. D. Baltensperger, L. A. Nelson, N. E. D'Croz-Mason, and B. E. Johnson Selection Environments for Maize in the U.S. Western High Plains Crop Sci., September 1, 2004; 44(5): 1519 - 1526. [Abstract] [Full Text] [PDF]

This Article Abstract Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (8) Citing Articles via Google Scholar Google Scholar Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Search for Related Content PubMed Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Agricola Articles by Russell, W. K. Articles by Guillen-Portal, F. R. Related Collections Maize Biometrics Plant and Environment Interactions