Análises discriminantes não paramétricas aplicadas ao estudo da diversidade genética baseado em dados fenotípicos quantitativos

Abstract

The multivariate discriminant analysis methods aim to identify the populations in which an individual should belong, admitting previously, that the individual composes one of the evaluated populations. Methods based on linear discriminant functions have been used in predictive studies of diversity in genetic improvement, when the data are quantitative phenotype. However, this type of analysis presupposes the multinormality of populations. The objective of this study was to evaluate the effectiveness of the non-parametric discriminant methodologies of the middle neighbor and k-Nearest Neighbour in the predictive study of diversity in genetic improvement, when applied to quantitative variables, in order to satisfactorily (re) classify the genotypes in their respective populations defined a priori. Two sets of data were used: i) 83 pupunha matrices, previously allocated in three primitive races, for seven variables of the fruit; ii) 122 clones of coffee trees, previously allocated among three botanical varieties, for ten agronomic characteristics. The non-parametric methods of the middle neighbor and the k-Nearest Neighbour were evaluated under various scenarios, according to possible combinations between non-parametric analysis technique x genetic distance measure x k x probability a priori of the genotypes belonging to the populations. The genotype allocation was compared in the different scenarios and the one obtained by Anderson's discriminant functions (considered standard) from the global apparent error rates (TEA) of classification of the individuals in the respective populations. The GENES software was used. The nonparametric methods were effective to classify the genotypes in their respective populations when compared with Anderson's discriminant analysis method. There were no significant differences between Euclidean distances measurements. The Gower distance provided apparent error rates different from the other studied distances. The method of discriminant analysis of the k-Nearest Neighbour proved to be adequate for populations whose genetic divergence within is smaller. The middle neighbor method, however, classifies the genotypes better in populations where there is greater inter- or intra-population diversity.