Self-organized map: the new aproach for study of genetic divergence in kale

Abstract

The objective of this study was to study the genetic divergence between genotypes of kale, to propose a methodology for the use of neural networks of the SOM type and to test its efficiency through Anderson's discriminant analysis. We evaluated 33 families of half-siblings of kale and three commercial cultivars. The design was a randomized block with four replications with six plants per plot. A total of 14 plant-level quantitative traits were evaluated. Genetic values were predicted at family level via REML / BLUP. For the study of divergence, neural networks of the SOM type (Selforganizing Map) were adopted. We evaluated different network architectures, whose consistencies of the clusters were identified by the Anderson discriminant analysis and by the number of empty clusters. After selecting the best network configuration, a dissimilarity matrix was obtained, from which a dendrogram was constructed using the UPGMA method. The best network architecture was formed with five rows and one column, totaling five neurons and consequently five clusters. The greatest dissimilarity was established between clusters I and V. The crossing between the genotypes of cluster I and those belonging to clusters III and V are the most recommended, since they aim to recombine families with characteristics of interest to the improvement and high dissimilarity. Anderson's discriminant analysis showed that the genotype classification was 100% correct, indicating the efficiency of the methodology used. Map (SOM) neural networks are a type of exploratory multivariate analysis tool that allows, through artificial computational intelligence, to design high-dimensional data in a smaller dimensional space, without loss of information [12]. This new organization prioritizes maintaining the structure, such as clusters and information relationships [13]. This reinforces its constant use in several