Multiple centroid method to evaluate the adaptability of alfalfa genotypes

Metodologia dos centroides múltiplos para avaliação da adaptabilidade em genótipos de alfafa

Abstracts

This study aimed to evaluate the efficiency of multiple centroids to study the adaptability of alfalfa genotypes (Medicago sativa L.). In this method, the genotypes are compared with ideotypes defined by the bissegmented regression model, according to the researcher's interest. Thus, genotype classification is carried out as determined by the objective of the researcher and the proposed recommendation strategy. Despite the great potential of the method, it needs to be evaluated under the biological context (with real data). In this context, we used data on the evaluation of dry matter production of 92 alfalfa cultivars, with 20 cuttings, from an experiment in randomized blocks with two repetitions carried out from November 2004 to June 2006. The multiple centroid method proved efficient for classifying alfalfa genotypes. Moreover, it showed no unambiguous indications and provided that ideotypes were defined according to the researcher's interest, facilitating data interpretation.

principal components; genotype x environment interaction; Medicago sativa L.

Este trabalho teve como objetivo avaliar a eficiência do método dos centroides múltiplos em um estudo de adaptabilidade de genótipos de alfafa (Medicago sativa L.). Neste método os genótipos são comparados a ideótipos definidos de acordo com o interesse do pesquisador por meio do modelo de regressão bissegmentada. Desta forma a classificação dos genótipos é realizada conforme objetivo do pesquisador e a estratégia de recomendação desejada. Apesar do grande potencial do método há a necessidade que o mesmo seja avaliado sob o aspecto biológico (com dados reais). Assim, diante deste contexto foram utilizados dados provenientes de um experimento em blocos casualizados com 2 repetições, que constituiu-se da avaliação da produção de matéria seca de 92 cultivares de alfafa em 20 cortes, realizados no período de novembro de 2004 a junho de 2006. A metodologia dos Centroides Múltiplos mostrou-se eficiente na classificação de genótipos de alfafa. Além de não apresentar duplicidade de indicações e proporcionar que ideótipos fossem definidos de acordo com o interesse do pesquisador facilitando a interpretação dos dados.

componentes principais; interação genótipos x ambientes; Medicago sativa L.

Introduction

In the presence of genotype by environment interaction, it is necessary to obtain detailed information on the performance of each cultivar across environmental variations (Cruz et al., 2004). Thus, the adaptability and stability analyses become extremely important and necessary in order to identify and recommend superior genotypes for different environments.

A number of methods of adaptability and stability analyses are described in the literature, including the Eberhart & Russell (1966) and the Bayesian method proposed by Nascimento et al. (2011) that use the simple regression analysis as statistical principle. Non-parametric methods, such as those developed by Lin & Binns (1988), Nascimento et al. (2010), centroid (Rocha et al., 2005) and its subsequent developments the multiple centroid (Nascimento et al., 2009a) and the extended centroid (Nascimento et al., 2009b) are also reported.

Adaptability and stability analyses have been used to identify genotypes of interest in various crops. Lédo et al. (2005) conducted studies to select alfalfa genotypes with improved adaptability and stability for dry matter production. Mohebodini et al. (2006) used several methods to study in detail the genotype x environment interaction of 11 lentil genotypes (Lens culinaris M.). Pelúzio et al. (2008) evaluated the performance, adaptability and stability of soybean genotypes in four sowing dates, in the municipality of Gurupi, Tocantins. Mahammed & Amri (2008) compared and evaluated the results of 20 parametric and non-parametric methods for selection of Triticum durum genotypes. In addition to these, Barreto et al. (2011) estimated the adaptability and stability of sweet potato genotypes in three environments in the South Central region of the State of Tocantins.

Among the cited methodologies, the multiple centroid method stands out in the literature as having a great potential for genotype recommendation, since the choice of the ideotypes (ideal references) is defined according to the researcher's interest using the bissegmented regression model. The method provides the researcher with a greater flexibility and genotype classification is carried out as determined by the objective of the researcher and the proposed recommendation strategy. However, despite the great potential of the method, it has not been used on actual data, hence the need to evaluate its applicability in the biological context (with real data).

Thus, this study aimed to evaluate the efficiency of the multiple centroid method in an adaptability study using real data from alfalfa genotypes (Medicago sativa L.).

Material and Methods

The multiple centroid method requires that the environments are classified into favorable and unfavorable using the environmental index proposed by Finlay & Wilkinson (1963):

where: Yij is the average of the genotype i in the environment j; Y.. is the total number of observations; a is the number of environments; and g is the number of genotypes.

After the classification of the environments, the ideal hypothetical cultivar (ideotype), or reference, is defined by the bissegmented regression model with the following parameters: mean b0i and the linear response to unfavorable environments b1i and favorable environments (b1i + b2i) (Cruz et al., 1989).

Using the model Y_ij = β_0i + β_1i I_j + β_2iT(I_j),

where: Yij is the ideal response of the hypothetical genotype in the environment j; b0i is the value provided so that the ideal response is maximum in all sites; Ij is the environment coded index; T(I_j) = 0 if I_j < 0; and T(I_j) = I_j - + if I_j > 0, with the mean of the positive indices.

After establishing the centroids based on the researcher's interest, the principal component analysis is applied to obtain scores for plotting the graphs. Genotypes are classified by their position on the graphs in relation to the centroids and the Cartesian distances between points (genotypes) and each of the centroids defined by the researcher. As in the centroid method and its subsequent developments, a measure of spatial probability is calculated, which is defined as the inverse of the distance between a treatment and the ideotype defined by the researcher:

where: Pd(i, k) is the probability of showing a pattern of stability similar to the kth centroid; and dik is the distance from the ith genotype to kth centroid.

Dry matter production data used in this study were obtained from an alfalfa evaluation experiment carried out by Southeast-Embrapa Livestock Research Center to develop alfalfa genotypes adapted to the different Brazilian ecosystems. The experiment evaluated the dry matter production of 92 alfalfa genotypes in 20 cuttings in a randomized block design with two replications. The cuttings were considered to be representative of different environmental conditions because they were performed at different times during the period from November 2004 to June 2006.

The ideotypes for the method were defined according to Pereira & Ferreira (2008), considering that when the interest is the genetic improvement, one selects alfalfa genotypes in which a good performance for dry matter production is coupled with a high response to environment improvement and highly predictable behavior. Thus, using the bissegmented regression model, the following references of interest were created: ideotype I - mean higher than the overall mean of the assessed alfalfa genotypes and with general adaptability as

;

ideotype II - mean higher than the overall mean and responsive to environmental changes

;

and for discard: ideotype III - general adaptability with mean lower than the general mean

,

mathematically:

The results obtained from the multiple centroid method were also compared with the non-parametric methodology by Lin & Binns (1988).

The statistical analyses were carried out using the GENES software (Cruz, 2006) available at http://www.ufv.br/dbg/genes/gdown.htm.

Results and Discussion

There was significant difference among dry matter production means of the alfalfa cultivars and significant cultivar (Cv) x cutting (Ct) interaction, at 5 and 1% probability levels, respectively (Table 1). The significance of the cultivar x cutting interaction shows that the cultivars had different performances in the various environmental conditions. Therefore, this interaction was studied in more detail using the analyses of adaptability and stability.

Table 1:
Summary of the analysis of variance for the trait dry matter production of 92 alfalfa cultivars in 20 environments (cuttigs), in the municipality of São Carlos / SP, from November 2004 to June 2006

The ideotypes based on the work of Pereira & Ferreira (2008) and defined by the bissegmented regression model were characterized as follows:

Ideotype I is a genotype with general adaptability with mean higher than the overall mean, which is of interest for breeding programs with a wide range of environments. Ideotype II is responsive to environment improvement and of great interest for alfalfa breeding (Pereira & Ferreira, 2008). Ideotype III has lower mean than the overall mean and can be discarded.

In the Principal Components Analysis, the cumulative percentage of variance in the first three components explained 75.44% of the variability in the data (Table 2), which, according to Johnson & Wichern (1992) and Melém Júnio. et al. (2008), is sufficient to a satisfactory interpretation of the results.

Table 2:
Variance estimates (eigenvalues) of principal components and cumulative percent of variance explained by the components

The genotypes were classified according to the multiple centroid method (Table 3). Of the 92 alfalfa genotypes, 49 were classified as having high general adaptability with means higher than the overall mean of the experiment (ideotype I), four were classified as specific for favorable environments (ideotype II) and 39 as having general adaptability with means lower than the overall mean (ideotype III) (Table 3).

Table 3:
Classification and probability associated with the genotypes in each of the three groups characterized by the ideotypes defined by Multiple Centroid Method (MCM) and estimates of stability and adaptability by the Lin & Binns (1988) method for the trait dry matter production

Among the 49 genotypes classified as ideotype I, ten showed greater probabilities, including Siriver 2 (0.503); P 30 (0.501); WL 442 (0.490); Monarca INTA (0.489); 5 683 (0.486); Sequel HR (0.486); 13 R Supreme (0.486); 58 N 58 (0.485); 5 929 (0.484); and Perla (0.485). These genotypes can be recommended to sites with large environmental variability. The genotypes classified as ideotype II of great interest for alfalfa breeding programs were: 5939 (0.393); Califonia 60 (0.366); P 105 (0.362); and WL 516 (0.338).

Among the 39 genotypes classified as ideotype III, which can be discarded, the ten with the largest probabilities were: Monarca (0.535); Crioula (0.530); Gala (0.520); Esmeralda (0.516); Tahoe (0.513); Gapp 969 (0.512); F 708 (0.505); DK 181 (0.501); WL 414 1 (0.501); and Winter (0.501).

The first three principal components scatterplot of the 92 genotypes in twenty environments (cuttings) showed a mass of genotypes around the ideotypes I and III, which confirms the results presented (Figure 1).

Figure 1:
Scatterplot of the first three principal components of 92 genotypes for the response of dry matter production to twenty environments (cuttings). The three points numbered with Roman numerals represent the centroids.

The genotypes were also analyzed by the method of Lin & Binns (1988) (Table 3). The results showed that the first five genotypes classified as of general adaptability were: WL 516; P 105; 5939; California 60; and Maricopa. The first five genotypes classified as adaptable to favorable environment were: P 107; Sundor. 5 939; California 60; and Maricopa. The genotypes WL 516, F 686, P 105, 5 939 and Maricopa were the first five classified as adaptable to unfavorable environments.

The four genotypes classified as adaptable to favorable environments by the multiple centroid method were also classified as of general adaptability by the method of Lin & Binns (1988). Besides, of these four genotypes, two, 5 939 and California 60, were also classified as of specific adaptability to favorable environments. Among those that can be discarded, which were classified as ideotype III by the multiple centroids and of specific adaptability to unfavorable environments by Lin & Binns (1988), none showed equivalent classification.

The results of this study corroborate the work of Nascimento et al. (2009a) and demonstrate the ease of analysis and interpretation of adaptability by the multiple centroid method compared to the method of Lin & Binns (1988). This easiness is due to the non-occurrence of possible ambiguous indications in the multiple centroid method, as it happens in the Lin & Binns (1988) method, as well as the direct comparison with the ideotype of interest.

were also classified as of general adaptability by the method of Lin & Binns (1988). Besides, of these four genotypes, two, 5 939 and California 60, were also classified as of specific adaptability to favorable environments. Among those that can be discarded, which were classified as ideotype III by the multiple centroids and of specific adaptability to unfavorable environments by Lin & Binns (1988), none showed equivalent classification.

Conclusions

The multiple centroid method was efficient to classify alfalfa genotypes without showing ambiguous information as it occurs with the Lin & Binns (1988) method. Furthermore, the definition of ideotypes according to the researcher's interest facilitated data interpretation.

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Publication Dates

• Publication in this collection
  Feb 2015

History

• Received
  03 May 2012
• Accepted
  19 Nov 2014