Multiple centroid method to evaluate the adaptability of alfalfa genotypes

Submitted on 3/05/2012 and appr oved on 1/19/2014. 1 Universidade Federal de Viçosa, Departamento de Estatística, Viçosa, Minas Gerais, Brasil. moysesnascim@ufv .br 2 Universidade Federal do Espírito Santo, Centro de Ciências Agrárias, Alegre, Espírito Santo, Brasil. adesioferreira@gmail.com 3 Universidade Federal de Viçosa, Departamento de Estatística, Viçosa, Minas Gerais, Brasil. ana.campana@ufv .br 4 Universidade Federal de Viçosa, Departamento de Estatística, Viçosa, Minas Gerais, Brasil. fabyano.fonseca@ufv .br 5 Embrapa Pecuária Sudeste, São Carlos, São Paulo, Brasil. reinaldo@cppse.embrapa.br 6 Universidade Federal de Viçosa, Departamento de Biologia Geral, Viçosa, Minas Gerais, Brasil. cdcruz@ufv .br *Corresponding author: moysesnascim@ufv .br Multiple centroid method to evaluate the adaptability of alfalfa genotypes


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.Nonparametric 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: Y ij 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 β 0i and the linear response to unfavorable environments β 1i and favorable environments (β 1i + β 2i ) (Cruz et al., 1989).
where: Y ij is the ideal response of the hypothetical genotype in the environment j; β 0i is the value provided so that the ideal response is maximum in all sites; Ι j is the environment coded index; T(Ι j ) = 0 if Ι j < 0; and T(Ι j ) = Ι j -+ if Ι 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: P d(i, k) is the probability of showing a pattern of stability similar to the kth centroid; and d ik 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 Rev. Ceres, Viçosa, v. 62, n.1, p. 030-036, jan/fev, 2015 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 IIIgeneral adaptability with mean lower than the general mean , mathematically: II.

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

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.
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) andMelém Júnio. et al. (2008), is sufficient to a satisfactory interpretation of the results.
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).
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.

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.

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 NS non-significant; * and ** -significant at 5 and 1% probability levels, respectively, by the F test

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

Table 3 .
Lin & Binns (1988) 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 theLin & Binns (1988)method for the trait dry matter production Rev. Ceres, Viçosa, v. 62, n.1, p. 030-036, jan/fev, 2015