Water stress affects crop productivity, especially maize, with water deficit studies associated with genetic improvement as well as the understanding of genetic mechanisms involved in drought tolerance being of primary importance. Thus the present work was carried out with the objective of evaluating the genetic divergence and the potential of the PioneiraCerrado maize population for the extraction of superior strains and populations. In addition to estimating genetic parameters of progenies of half sibs of corn, in order to select progenies of maize adapted to the edaphoclimatic conditions of Tocantins. The experiment was conducted in Gurupi -TO, at the Experimental Farm of UFT, belonging to the Federal University of Tocantins. Sixty-six progenies of half-siblings of the PioneiraCerrado maize population (Serrated grains) were used, from the breeding program of the company Pioneira Ltda. Progenies were evaluated in two replicate experiments. The experimental design used was the 13 x 13 lattice, with two replicates. In thefirst chapter we considered the characteristics of plant height, spike weight without straw, spike weight with straw, ear length and grain yield to be performed the analysis of variance and test of grouping means between progenies and later analysis of Using indexes based on ranks. Selection intensities of 22% were applied, corresponding to the number of thirty progenies. Significant effect of corn half-sib progenies on all traits was observed. The mean of the original population was 1.80 m in height of plants, 0.183 kg in weight of spike without straw, 0.233 kg in weight of spike with straw, 17.53 cm in length of spike and 6550.94 kg ha-1 Productivity. While in the selected population the selection gain in these characteristics was 12.49; 16.13; 11.96; 2.24 and 22.21%, respectively. In the second chapter, the same 169 progenies were used, however, considering the height characteristics of plants, height of spike, broken plants, bedded plants, tang weight without straw, tang weight with straw, ear length, ear diameter, number of rows, number of grain row pain and grain yield. In the study of the genetic divergence between the progenies, the dissimilarity measures were determined, according to the multivariate analysis model, which allowed to obtain the matrixof dissimilarity and residual covariance. For this, the Generalized Distance of Mahalanobis was used as a measure of dissimilarity and in obtaining the groups, we used the Hierarchical Neighboring Neighbor Method and the Tocher Optimization Method. The cluster analysis by the Tocher method separated the progenies into seven groups, and in group I most of the genetically similar progenies remained. All characteristics contributed to the determination of genetic divergence, to a greater or lesser extent. However, grain yield was the one that contributed the most to the dissimilarity among the progenies, and should be prioritized in the selection in breeding programs. In the grouping adopted by the hierarchical method of the nearest neighbor, even statistically similar, small distances between the progenies are observed. This information is of utmost importance within breeding programs and to complement the results obtained with the Tocher analysis. With this, it can be concluded that the PioneiraCerrado maize population shows genetic divergence and genetic potential to be used in breeding programs aimed at obtaining superior strains and populations. The progenies of selected half-sibs of maize in southern Tocantins present satisfactory averages of all traits.
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