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Published online 27 March 2006
Published in Crop Sci 46:1100-1106 (2006)
© 2006 Crop Science Society of America
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CROP BREEDING & GENETICS

Nonparametric Methods for Interpreting Genotype x Environment Interaction of Lentil Genotypes

Naser Sabaghniaa, Hamid Dehghania,* and Syyed Hossain Sabaghpourb

a Dep. of Plant Breeding, Tarbiat Modares Univ. Tehran, P.O. Box 14115-336, Tehran, Iran
b Dryland Agricultural Research Institute, Kermanshah, Iran

* Corresponding author (dehghanr{at}modares.ac.ir)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Analysis of multienvironment trials (METs) of crops for cultivar evaluation and recommendation is an important issue in plant breeding research. Evaluating both stability of performance and high yield is essential in MET analyses. The objective of this investigation was to compare 10 nonparametric stability methods and apply nonparametric tests (which do not require distributional assumptions) for genotype-by-environment (G x E) interaction to 11 lentil (Lens culinaris Medik) genotypes. Nine improved lentil genotypes and two local cultivars were grown in 20 semiarid environments in Iran from 2002 to 2004. Results of nonparametric tests of G x E interaction and a combined ANOVA across environments showed there were both crossover and noncrossover G x E interactions and genotypes varied significantly for yield. In this study, high values of TOP (proportion of environments in which a genotype ranked in the top third) and low values of rank-sum (sum of ranks of mean yield and Shukla's stability variance) were associated with high mean yield, but the other nonparametric methods were not positively correlated with mean yield and instead characterized a static concept of stability. The results of principal component (PC) analysis and correlation analysis of nonparametric stability statistics and yield indicated that only rank-sum and TOP methods would be useful for simultaneously selecting for high yield and stability. These methods recommended FLIP 92–12L as stable and FLIP96–6L as unstable genotypes. A biplot of the first two PCs also revealed that the nonparametric methods grouped as three distinct classes that corresponded to different agronomic and biological concepts of stability.

Abbreviations: G x E, genotype x environment interaction • ICARDA, International Center for Agricultural Research in Dry Areas • MET, multienvironment trial


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
LENTIL is an annual legume best adapted to cool climate conditions and is traditionally grown as a rainfed crop in the Middle East. Legumes and especially lentil are the most important food crops in developing countries such as Iran. Lentil seed is a rich source of good protein (up to 28%) in human diets in arid and semiarid areas of west Asia (Sarker et al., 2003). Iranian farmers currently use landraces (e.g., Kermanshah) and pure lines (e.g., Gachsaran), which have good seed size and are adapted to local rainfed conditions. The yield performance of these varieties is very low (typically about 475 kg ha–1) compared with the highest global yields (1306 kg ha–1, produced in Canada; FAO, 2001). Iran has had an important lentil-breeding program in recent years, supported by the International Center for Agricultural Research in Dry Areas (ICARDA). Increasing the genetic potential of yield is an important objective of lentil breeding programs in Iran and other countries. The improved lentil genotypes are evaluated in METs to test their performance across different environments and to select the best genotypes in specific environments. In most cases, G x E interaction is observed, complicating selection for improved yield.

Interpretation of G x E interaction can be aided by statistical modeling. Models can be linear formulations such as joint-regression (Yates and Cochran, 1938; Eberhart and Russell, 1966), multivariate clustering techniques (Lin and Butler, 1990), multiplicative formulations such as additive main effects and multiplicative interaction (AMMI; Zobel et al., 1988; Gauch, 1992), or nonparametric methods (Huehn, 1979). Modeling G x E interaction in METs helps to determine phenotypic stability of genotypes, but this concept has been defined in different ways and increasing numbers of stability parameters has been developed (Gauch and Zobel, 1996).

Huehn (1996) indicated that there are two major approaches to studying G x E interaction and determining adaptation of genotypes. The first and most common approach is parametric, which relies on distributional assumptions about genotypic, environmental, and G x E effects. The second major approach is the nonparametric or analytical clustering approach, which relates environments and phenotypes relative to biotic and abiotic environmental factors without making specific modeling assumptions. For practical applications, however, most breeding programs incorporate some elements of both approaches (Becker and Leon, 1988).

The parametric stability methods have good properties under certain statistical assumptions, like normal distribution of errors and interaction effects; however, they may not perform well if these assumptions are violated (Huehn, 1990). That means parametric tests for significance of variances and variance-related measures could be very sensitive to the underlying assumptions. Thus, it is wise to search for alternative approaches that are more robust to departures from common assumptions, such as nonparametric measures (Nassar and Huehn, 1987; Huehn and Nassar, 1989).

Several nonparametric procedures proposed by Huehn (1979), Nassar and Huehn (1987), Kang (1988), Fox et al. (1990), and Thennarasu (1995) are based on the ranks of genotypes in each environment and genotypes with similar ranking across environments are classified as stable. Huehn (1979) and Nassar and Huehn (1987) proposed four nonparametric measures of phenotypic stability (1) Si(1) is the mean of the absolute rank differences of a genotype over the n environments, (2) Si(2) is the variance among the ranks over the n environments, (3) Si(3) and Si(6) are the sum of the absolute deviations and sum of squares of rank for each genotype relative to the mean of ranks, respectively. Kang (1988) assigned ranks for mean yield, with the genotype with the highest yield receiving the rank of 1, and ranks for the stability variance of Shukla (1972), with the lowest estimated value receiving the rank of 1. The sum of these two ranks provides a final index, in which the genotype with lowest rank-sum is regarded as the most desirable. Fox et al. (1990) suggested a nonparametric superiority measure for general adaptability. They used stratified ranking of the cultivars and ranking was done at each environment separately; the proportion of sites at which the cultivar occurred in the top, middle, and bottom third of the ranks was computed to form the nonparametric measures TOP, MID, and LOW, respectively. A genotype that occurred mostly in the top third (high value of TOP) was considered as a widely adapted genotype. Thennarasu (1995) proposed as stability measures the nonparametric statistics NPi(1), NPi(2), NPi(3), and NPi(4) based on ranks of adjusted means of the genotypes in each environment, and defined stable genotypes as those whose position in relation to the others remained unaltered in the set of environments assessed.

According to Huehn (1990), the nonparametric procedures have the following advantages over the parametric stability methods: they reduce the bias caused by outliers, no assumptions are needed about the distribution of the observed values, they are easy to use and interpret, and additions or deletions of one or few genotypes do not cause much variation of results.

Many statistical procedures have been proposed to study G x E interactions (Westcott, 1986; Crossa, 1990; Lin and Binns, 1994; Kang and Gauch, 1996). Most of these procedures, however, fail to distinguish between significant crossover and noncrossover (usual) interactions (Baker, 1990). Nonparametric statistical procedures for the test of crossover interactions have been developed in the field of medicine and can be applied to G x E interactions in METs (Truberg and Huehn, 2000). Nonparametric measures for the test of interactions provide a useful alternative to parametric methods such as the ANOVA currently used, which is based on original data values.

Huehn and Leon (1995) compared four nonparametric analyses of interactions and grouped them into two different concepts of interactions. While the Bredenkamp, Hildebrand, and Kubinger procedures depend on usual interactions, the van der Laan–de Kroon method depends on crossover interactions. Truberg and Huehn (2000) studied five statistical methods for the analysis of G x E interactions and suggested that for analysis of usual noncrossover interactions, the methods of Hildebrand and Kubinger are closely connected with the ANOVA. If some of the necessary assumptions are violated, the validity of the inferences obtained from the standard statistical techniques, for example, ANOVA, may be questionable or lost. In such cases, however, the results of nonparametric estimation and testing procedures, which are based on ranks, can be more reliable (Truberg and Huehn, 2000).

The objectives of this study were (i) to identify lentil genotypes that have both high mean yield and stable yield performance across different environments for semiarid areas of Iran, (ii) to apply nonparametric tests to investigate of crossover and noncrossover interaction in METs, and (3) to study the relationships among nonparametric stability statistics.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Data Source
This research data set involves 11 lentil genotypes tested in 20 environments (year–location combinations during 2002–2004), extracted from the Iran lentil performance trial programs. Of 11 lentil genotypes used, nine were from the ICARDA lentil improvement program and two were local check cultivars typically grown by Iranian farmers (Table 1). Seven locations were used for yield trials: Ilam, Kermanshah, and Lorestan in western Iran; Gorgan and Shirvan in northeastern Iran; Qazvin, in the northwest; and Gachsaran in southern Iran. In all test locations, yield trials were performed for 3 yr except the trial at the Qazvin test location, which was conducted for only 2 yr.


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  		Table 1. The names and origins of 11 lentil genotypes tested at 20 environments.

 
At each location, a completely randomized block design with four replicates was used. The experiments were planted according to local practice with planting rate of about 50 seeds m–2. Plots were 4 m2 with four rows each 4 m long and 25 cm between rows. The harvested plot size was 1.75 m2 (two 3.5-m rows at the center of each plot). Mean grain yield was estimated for each genotype at each location (environment).

Statistical Analysis
In this investigation, four nonparametric statistical methods were applied to test the significance of G x E interaction. The methods of Bredenkamp (1974), Hildebrand (1980), and Kubinger (1986) are based on the usual linear model for interactions: interactions are defined as deviations from the additivity of main effects. The procedure of the van der Laan-de Kroon (1981) was used for test of crossover G x E interactions. The test statistics of above methods are approximately {chi}2 distributed with (k – 1)(n – 1) degrees of freedom, where k = number of genotypes, and n = number of environments. These statistical methods have been described in detail by Huehn and Leon (1995) and Truberg and Huehn (2000).

Huehn (1979) and Nassar and Huehn (1987) proposed four nonparametric stability statistics that combine mean yield and stability. For a two-way data with k genotypes and n environments, we denote rij as the rank of the ith genotype in the jth environment, and ri. as the mean rank across all environments for the ith genotype. The statistics based on yield ranks of genotypes in each environment are expressed as follows:

Formula

Formula

Formula

Formula
Kang's (1988) rank-sum is another nonparametric stability procedure where both yield and Shukla's (1972) stability variance are used as selection criteria. This index assigns a weight of one to both yield and stability statistics to identify high-yielding and stable genotypes. The genotype with the highest yield is given a rank of 1 and a genotype with the lowest stability variance is assigned a rank of 1. All genotypes are ranked in this manner, and the ranks by yield and by stability variance are added for each genotype. The genotype with the lowest rank-sum is the most desirable one.

The stratified ranking technique of Fox et al. (1990) consists of scoring the number of environments in which each genotype ranked in the top, middle, and bottom third of trial entries. A genotype that occurred mostly in the top third (high TOP value) was considered as a widely adapted cultivar.

Thennarasu's (1995) nonparametric stability analysis considers adjusted ranks of genotypes within each test environment. The adjusted rank, rij*, is determined on the basis of the adjusted phenotype values (xij* = xij – xi.), where xi. is the mean performance of the ith genotype. The ranks, obtained from these adjusted values (xij*), depend only on G x E interaction and error effects. Using the adjusted rank values defined above, Thennarasu (1995) proposed the four following nonparametric stability measures:

Formula

Formula

Formula

Formula
In the above formulas, rij* is the rank of xij*, Formula and Mdi* are the mean and median ranks for adjusted values, while ri. and Mdi are the same parameters computed from the original (unadjusted) values. The yield data were subjected to nonparametric analysis using SAS software (SAS, 1996). The effects of environments and replications were considered random but the genotype effect was assumed fixed. Lu (1995) developed a SAS-based computer program that computes Si(1) and Si(2) nonparametric measures. A comprehensive SAS program called SASG x ESTAB has become available, which calculates different parametric and nonparametric stability statistics (Hussein et al., 2000). Both of these programs were used to calculate different nonparametric stability statistics.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Analysis of Genotype x Environment Interaction
Analysis of variance was conducted to determine the effects of environment (year x location combination), genotype, and interactions among these factors, on grain yield of lentil genotypes (Table 2). Effects of environments (E) and G x E interaction were highly significant (P < 0.01) and genotype main effect was significant (P < 0.05). Environment and G x E interaction effects accounted for most of the sums of squares (Table 2).


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  		Table 2. Analysis of variance for lentil grain yield in 20 environments.

 
The numerical values of the test statistics for the different nonparametric statistical procedures are presented in Table 3. The null hypothesis for Hildbrand and Kubinger is no noncrossover G x E interactions and for van der Laan-de Kroon is no crossover G x E interaction. Results of these indicated that both significant noncrossover and crossover interactions were found in this MET according to Hildbrand and Kubinger procedures (for noncrossover) and the van der Laan-de Kroon test (for crossover). This result is in agreement with the ANOVA, but provides more specific information about the nature of G x E interactions.


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  		Table 3. Analysis of G x E interaction using different nonparametric tests on 11 lentil genotypes grown in 20 environments.

 
Stability Analysis
The results of 10 nonparametric stability measures and genotypes mean yield are summarized in Table 4. The significance tests for Si(1) and Si(2) were developed by Nassar and Huehn (1987) and were highly significant (P < 0.01) for all genotypes (data not shown). The Si(1) and Si(2) statistics are based on ranks of the genotypes across environments and they give equal weight to each environment. Genotypes with fewer changes in rank are considered to be more stable (Becker and Leon, 1988). The Si(1) estimates are based on all possible pair-wise rank differences across environments for each genotype, whereas Si(2) is based on variances of ranks for each genotype across environments (Nassar and Huehn, 1987). Nevertheless, these two statistics ranked genotypes similarly for stability. For example, according to both Si(1) and Si(2), G2 had the smallest changes in ranks and is thus regarded as the most stable genotype unlike G10, which was significantly (P < 0.01) unstable. The next most stable genotype was G1, followed by G5, which had the highest mean yield across environments (Table 4).


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  		Table 4. Mean values (Y) and nonparametric stability parameters (NP) for grain yield of 11 lentil genotypes evaluated in 20 environments.

 
Two other nonparametric statistics of Huehn (1979), Si(3) and Si(6) combine yield and stability based on yield ranks of genotypes in each environment. These parameters measure stability in units of the mean rank of each genotype (to see the differences in the work of Huehn, 1979). The lowest value for each of these statistics indicates maximum stability for a certain genotype. Like Si(1) and Si(2), G2 was the most stable according to the Si(3) parameter, but according to Si(6), G4 was the most stable genotype. The mean yield of G2 was relatively high, but the mean yield of G4 was lowest among the cultivars tested. The most unstable genotype according to all four of these statistics was G10, which ranked second for mean yield (Table 5).


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  		Table 5. Ranks of 11 lentil genotypes after yield data from 20 environments were analyzed for G x E interaction and stability using 10 different nonparametrics methods.{dagger}

 
Kang's (1988) nonparametric stability parameter (rank-sum) uses both yield and stability variance (Shukla, 1972). The genotype with the lowest rank-sum is the most favorable one. According to the rank-sum statistic, G5 had the minimum value for rank-sum and therefore was the most stable genotype, followed by G1 and G2 (Table 4). According to the rank-sum statistic, the undesirable genotypes were G4 and G6.

The nonparametric superiority parameter of Fox et al. (1990) consists of scoring the percentage of environments in which each genotype ranked in the top, middle, and bottom third of trial entries. A genotype usually found in the top third of entries across environments can be considered relatively well adapted and stable. Thus, G5 was stable because it ranked in the top third of genotype in a high percentage of environments (high TOP value), and was followed by G10, G11, and G1 (Table 4). The undesirable genotypes in this method were G4 and G7, followed by G6 genotypes. The results of this method for stable and unstable genotypes are relatively in agreement with the rank-sum procedure.

Results of Thennarasu's nonparametric stability statistics, which are calculated from ranks of adjusted yield means, are shown in Table 4, and the ranks of genotypes according to these parameters are given in Table 5. According the fist method [NPi(1)], genotypes G2, G4, and G5 were stable in comparison with other genotypes, but genotypes G5 and G10 were unstable and had the lowest value of NPi(1).

Genotype G4 had the lowest value of NPi(2) and was stable, followed by G11 and G1. Because of the high values for NPi(2), the stabilities of G5 and G10 were low, although they had high mean yield (Table 4). NPi(3), like NPi(2), identified G4 as the most stable genotype, although is had the lowest mean yield. The next most stable genotypes were G7, G1, and G3, which also had relatively low mean yield performances. The unstable genotypes based on NPi(3) were G5, G10, and G8, which had highest mean yields. Therefore, NPi(3) had a negative relationship with yield.

Stability parameter NPi(4) identified G4 as a stable genotype, followed by G6 and G7; but like NPi(2) and NPi(3), identified G1 and G10 as unstable. The results of three NPs (NPi(2), NPi(3), and NPi(4)) were very similar to each other and identified G4 as stable, although it had lowest minimum mean yield performance. According to NPi(4), G5 was an unstable genotype, although it had the highest mean yield performance.

Relationship among Different Stability Statistics
Each one of the nonparametric methods produced a unique genotype ranking (Table 5). The Spearman's rank correlations between each pair of nonparametric stability parameters were calculated (Table 6) and demonstrate a highly significant (P < 0.01) rank correlation between Si(1) and Si(2), Si(3), and NPi(1). The Si(6) parameter was positively correlated with Si(1), NPi(2), and NPi(3), and NPi(4) was negatively correlated with the percentage of environments in which it ranked in the top third of genotypes (TOP).


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  		Table 6. Spearman's rank correlation coefficients between the different nonparametric stability parameters for grain yield of 11 lentil genotypes.{dagger}

 
The stability parameters NPi(2), NPi(3), and NPi(4) were positively correlated with each other and with Si(3), but the NPi(1) measure was not correlated with other NPs. Two parameters, NPi(2) and NPi(3), were negatively correlated with TOP. The correlations were also significant (P < 0.01) between rank-sum and mean yield of genotypes (r = 0.84**). Mean yield was significantly positively correlated with TOP and significantly negatively correlated with NPi(4) (Table 6).

To better understand the relationships among the nonparametric methods, a PC analysis based on the rank correlation matrix (Table 6) was performed. Table 7 shows the loadings of the first two PCs of ranks of different nonparametric stability methods. When applying the PC analysis, the two first PCs explained 86.54% (55.01 and 31.54% by PC1 and PC2, respectively) of the variance of the original variables. The relationships among the different stability statistics are graphically displayed in a biplot of PC1 and PC2 (Fig. 1 ).


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  		Table 7. First two principal components loadings of ranks obtained from 10 nonparametric methods used to analyze G x E interaction of lentil genotype yields.

 

Figure 1
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  		Fig. 1. Principal component analysis (PC1 and PC2) plot of ranks of stability of yield, estimated by 10 methods using yield data from 11 lentil genotypes grown in 20 environments and showing interrelationships among these parameters.

 
In this biplot, the PC1 axis mainly distinguishes the methods of TOP and rank sum from the other methods. Mean yield (Y) also groups near these statistics, and we refer to these as Class 1 (C1) stability measures. The second PC axis separates Si(1), Si(2), Si(3), and NPi(1) (which we will refer to as Class 3, C3) from Si(6), NPi(2), NPi(3), and NPi(4) (Class 3, C3).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
Genotype-by-environment interactions are important sources of variation in any crop, and the term stability is sometimes used to characterize a genotype, which shows a relatively constant yield, independent of changing environmental conditions. On the basis of this idea, genotypes with a minimal variance for yield across different environments are considered stable. This idea of stability may be considered as a biological or static concept of stability (Becker and Leon, 1988). This concept of stability is not acceptable to most breeders and agronomists, who prefer genotypes with high mean yields and the potential to respond to agronomic inputs or better environmental conditions (Becker, 1981). The high yield performance of released varieties is one of the most important targets of breeders; therefore, they prefer a dynamic concept of stability (Becker and Leon, 1988).

Using nonparametric tests for G x E interactions was equivalent with parametric method (ANOVA) in this investigation. Similar were results reported by Truberg and Huehn (2000), who recommended Hildbrand and Kubinger tests for usual interaction and the van der Laan-de Kroon test for crossover interaction.

Figure 1 shows that the first PC axis separates TOP, rank-sum, and mean yield (Y) from the other methods. This PC distinguishes methods based on two different concepts of stability: the static (biological) and dynamic (agronomical) concepts. The parameters TOP and rank-sum are related with dynamic stability, and other remaining methods are associated with static stability. Flores et al. (1998) pointed out that the TOP procedure is associated with mean yield and the dynamic concept of stability. Kang and Pham (1991) found that the rank-sum method is related with high yield performance, and therefore this stability parameter defines stability with dynamic concept.

We found that three nonparametric statistics of Huehn (1979) and the NPi(1) parameter of Thennarasu (1995) clustered together on the biplot, and we grouped them together as Class 2 (C2) statistics. These methods classify genotypes as stable or unstable in a similar fashion. The stability parameters Si(2), Si(3), and NPi(1) were positively and significantly correlated (P < 0.01), indicating that the three measures were similar in classifying the genotypes according to their stability under different environmental conditions (Table 6). Consequently, only one of these parameters would be sufficient to select the stable genotypes in a breeding program. Scapim et al. (2000) also found significantly positive correlations among Si(1), Si(2), and Si(3) nonparametric methods. Similarly, Flores et al. (1998) reported high rank correlations between Si(1) and Si(2) in faba bean (Vicia faba L.) and pea (Pisum sativum L.) METs. Nassar and Huehn (1987) reported that the Si(1) and Si(2) are associated with the static biological concept of stability, as they define stability in the sense of homeostasis. The C2 stability statistics represent a static concept of stability, and were correlated neither positively nor negatively with mean yield or the C1 statistics. Therefore, the C2 statistics could be used as compromise methods that select genotypes with moderate yield and high stability.

The Si(6) nonparametric methods of Huehn (1979) and three NPs statistics (NPi(2), NPi(3), and NPi(4)) of Thennarasu (1995) were in same class (C3). Like the C2, these methods identify genotypes that are stable based on the static or biological concept of stability, but unlike C2, they were also strongly negatively correlated with high yield. Therefore, we do not recommend use of these statistics for cultivar selection.

The nonparametric stability measurements do not require any assumptions about the normality of the distribution and variance homogeneity. The interaction concepts of the classification they represent are strongly related to that of selection in which breeders are interested and can define static and dynamic concepts of stability. In conclusion, nonparametric stability measurements seem to be useful alternatives to parametric measurements (Yue et al., 1997), although they do not supply information about genotype adaptability.

For several reasons, we prefer the use of nonparametric stability models. First, these methods avoid the bias caused by outliers and no assumptions are needed about the distribution of the observations. Second, these methods are easy to use and to interpret; therefore, estimation of stability seems to be an appropriate approach. Many parametric and nonparametric measures of stability have been presented and compared in the literature (Lin et al., 1986; Flores et al., 1998). For making recommendations, it is essential to investigate the relationship among these parameters and compare their powers for different stability models. This topic will be considered in detail in a subsequent paper.


   ACKNOWLEDGMENTS
 
Thanks to Prof. Dr. A. Bjornstad, Prof. Dr. M.S. Kang, and Prof. Dr. H.Y. Lu for their helpful comments and providing SAS programs used for this research. Sincere gratitude goes to Iran's Agricultural Research Center and its Agricultural Research Stations for providing plant materials, experimental sites, and technical assistance. We thank anonymous reviewers for their helpful comments, suggestions, and corrections of the manuscripts.

Received for publication June 13, 2005.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 




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