Association of Variables as Markers for the Classification of Accessions of the Cuban Cocoyam Collection Xanthosoma spp . (Araceae)

as Markers for the Classification of Accessions of the Cocoyam Collection Abstract The present work was carried out on the basis of the previously obtained results where a total of 71 accessions of the Cuban cocoyam collection of the genus Xanthosoma in Cuba were used, which were characterized through the 24 minimum descriptors selected among those that included the number of chromosomes and the color of rhizome The isoenzyme systems esterases, peroxidases and polyphenol oxidases also The isoenzimatic bands associated with the present cytotypes and the color rhizome flesh were through the CHAID method (Chi-squared Automatic In teraction Detector). the chromosome decision


Introduction
In cocoyam, genus Xanthosoma, morphoagronomic data have been traditionally used for the characterization and identification of accessions [1] and they have been complemented with information on isoenzymatic markers and RAPD-type DNA polymorphism in integrated analysis, and 24 important minimum descriptors in the differentiation of cultivated accessions of this genus have been recommended recently (2 y 3); However, the possible association between some variables that allow the classification of accessions to be more efficient has not been determined, making use of the available characterization information. There is a variability that is detected with the naked eye and another that requires special techniques to be detected; for this reason, it is important to identify which of them is intended to be measured in order to be able to choose the appropriate statistical methods to analyze the data resulting from a characterization study. In general, publications on the subject contain little information about these methods and their use is not practical for most users. The main objective of this work is to determine the association between variables in the Cuban collection of cocoyam, genus Xanthosoma to classify the accessions and detect associated characteristics early with the use of statistical techniques.

Materials and Methods
The present work was carried out on the basis of the results obtained previously [2,3]. These authors used a total of 71 accessions from the Cuban cocoyam collection of the genus Xanthosoma in Cuba, which they characterized through the 24 minimum descriptors selected among those that included the number of chromosomes and the color of rhizome flesh. They also analyzed the isozyme systems esterases, peroxidases and polyphenoloxidases. The isoenzymatic esterase (Best)bands, peroxidase (Bprx) and polyphenoloxidase

Results
The CHAID technique allowed to determine the possible association of the isoenzymatic bands with the two cytotypes found and with the color of rhizome flesh of the accessions of the studied collection. This technique was able to segment the population into groups according to the presence (1) or absence (0) of the isoenzymatic bands and their interactions, which differentiate essential differences between the cytotypes and between the accessions with different color of rhizome flesh optimally. Using the CHAID method, it was also possible to detect the bands (of the three isoenzymatic systems studied) which have statistically significant associations with the two cytotypes found and with the color of rhizome flesh (Tables 1 & 3). A decision tree corresponds to each of these bands, in which the first segmentation of the population made at the root node is performed using this band (Figures 1-3).       (Table 1).
Next, the classification rules of the accessions with 2n = 24 and 2n = 26 chromosomes are exposed. An accession has 24 chromosomes if the following logical expression is true:

It is written literally:
If it is true that (Best_4 = 1 or Bprx_7 = 1) and Bppo_12 = 1) or if it is true that Best_10 = 1, then the accession has 24 chromosomes.
On the other hand, an accession has 26 chromosomes if the following logical expression is true: That is to say, if the given rule for n = 24 chromosomes is not met, then the denial of rule (1) is true1.In symbolic and simplified form it can be written: ¬ (1) = (2) or as in the previous case, it is written literally: If it is true that (Best_4 = 0 or Bprx_7 = 0) and Bppo_12 = 0) or if it is true that Best_10 = 0, then the accession has 26 chromosomes.
Then, the presence of Best_4, Bprx_7, Bppo_12 and Best_10 bands is associated in a biological and significant statistically way with accessions that have 2n = 24 chromosomes, and its absence is manifested in the accessions with a chromosome number of 2n = 26, so which it can be affirmed that these bands constitute isoenzymatic markers for the chromosome number in the studied collection ( Figure 3).

An association between the chromosome number and flesh
color is also observed, which is revealed in the presence of purple It is written literally: If it is true that Best_7 = 1 or Best_16 = 1 or Best_20 = 1 or Bprx_8 = 1, then the accession produces rhizomes of white flesh.
The accession produces rhizomes of purple flesh, if the following logical expression is true: That is to say, if the following restrictions are met simultaneously:

It is written literally:
If it is true that Best_7 = 0 and (Bppo_5 = 0 or Best_4 = 1) and Best_16 = 0 and Bprx_13 = 0, then the accession produces rhizomes of purple flesh. The accession produces rhizomes of yellow flesh, if the following logical expression is true: It is written literally:  (Tables 4 & 5), it is observed how these results are confirmed; when this accession is included, the correct total percentage of classification is reduced from 98.6% to 97.2%.  The 'Criolla1 1' accession is not well classified by the decision trees obtained, which prevents reaching 100% of correct classification (Table 5) to segment populations and detect their interactions to distinguish essential differences. The CHAID method has already been used successfully [5] in the characterization of risk factors and diagnosis of diseases, but in the available literature there were not found references on its application in plants.

Conclusion
The created multiclassification rules allowed to achieve 100% of correct classification of the accessions according to the association of the isoenzymatic bands with the chromosome numbers and with the color of rhizome flesh, so they can be used as useful markers in the early determination of these characteristics.