This paper deals with the genotypic evaluation of Theobroma grandiflorum progenies in the Pará State for the characters number of fruits (NF) in four harvests, intensity of occurrence of witch's broom disease in the inflorescences (WBI) and in the fruits (WBF) and weight of branches with witch's broom (WWB). Also, it presents estimates of genetic parameters that allow to infer on the genetic control and level of genetic variability in the appraised germplasm. All the characters presented considerable genetic variability, with coefficients of genetic variation varying from 27% to 88% at progenies level and from 38% to 123% at individual level. This reveals excellent possibilities for the selection in that hybrid experimental population. The estimates of individual narrow sense heritabilities, in a harvest, varied from 25% to 54% and the individual repeatabilities for NF was equal at 35%. With the four accomplished harvests the individual heritability increased to 48%, providing selective accuracy of 70%, for the individuals' selection. The gain in efficiency, when using more than five crops is practically worthless. For NF, genetic gains above 60% can be obtained with the selection of the best five individuals. Individuals with annual production of 17 fruits can be selected, value which is much more superior to the general average of 10 fruits, found in the commercial plantations. Superior genetic gains can be obtained with clone propagation of the best individuals in relation to the sexual propagation and for the best individual the genetic gain increases from 75.5% to 88.3%, that is to say, from 17 to almost 19 fruits per plant. This reveals a great potential for the commercial cloning of Theobroma grandiflorum. For the characters VBI and VBF high individual narrow sense heritabilities were verified with values ranging from 30% to 54%. This reveals the excellent potential of the recurrent selection to improve the resistance level. It seems enough to consider in the selection just the number of brooms, without being necessary to consider the weight. The correlation between resistance in the fruit and in the inflorescence was high (0.84) indicating some genetic control common to the two characters. Superior progenies were identified for production of fruits and resistance to the broom simultaneously.
T. grandiflorum breeding; heritability; repeatability; genetic parameters; selection methods; Reml/Blup