Few cultivars of papaya from the Formosa group are available to producers, and the development of new genotypes is indispensable. Thus, the use of effective selection strategies to obtain more productive cultivars and better quality fruits is also necessary. The aim of this study was to select of half-sib families (HSF) of papaya using the methodology of mixed models. Nineteen HSFs from the Incaper’s papaya breeding program were evaluated in a randomized block design with five replicates and nine plants per plot. The selection was made based on fruit mass (FM), pulp thickness (PT), soluble solids content in pulp (SS) and number of fruits (NF). The genetic parameters and genotypic values were estimated by the REML/BLUP procedure. The selected HSFs increased FM by 26.1%; the PT in 10.5%; the SS in 7.5% and; the NF in 13.0%. The additive heritability within the progenies and the individual variation coefficient obtained indicate that the selection between and within the HSFs can provide greater genetic gains. The selection based on the REML/BLUP methodology was efficient to obtain simultaneous genetic gains for all variables under study despite the negative correlation between them.

Soybean has a recognized narrow genetic base that often makes it difficult to visualize available genetic and phenotypic variability and identify superior genotypes during the selection process. However, the phenotypic expression of soybean plants is highly affected by photoperiod and the cultivation of a given variety is performed in the latitude range that presents ideal conditions for its development based on its relative maturity group (RMG) for the optimization of the phenotypic expression of its genotype. Based on the above, this study aimed to evaluate the efficiency of artificial neural networks (ANNs) as a tool for the correct discrimination and classification of tropical soybean genotypes according to their relative maturity group during the population selection process with the aim of optimizing the phenotypic performance of these selected genotypes. For this purpose, three biparental populations were synthesized, one with a wide genetic variability for the RMG character obtained from the hybridization between genitors of maturity groups RMG 5 (Sub-tropical 23° LS) × RMG 9.4 (Tropical 0° LS) and two populations with a narrow variability obtained between genitors RMG 7.3 (Tropical 20° LS) × RMG 9.4 and RMG 5.3 × RMG 6.7, respectively. Criteria for comparing the developed ANN architecture with Fisher’s linear and Anderson’s quadratic parametric discriminant methodologies were applied to the data for the discrimination and classification of the genotypes. ANN showed an apparent error rate of less than 8.16% as well as a low influence of environmental factors, correctly classifying the genotypes in the populations even in cases of reduced genetic variability such as in the RMG 5 × RMG 6 population. In contrast, the discriminant functions were inefficient in correctly classifying the genotypes in the populations with genealogical similarity (RMG 5 × RMG 6) and wide genetic variability, with an error rate of more than 50%. Based on the results of this study, ANN can be used for the discrimination of genotypes in the initial generations of selection in breeding programs for the development of high performance cultivars for wide and reduced photoperiod amplitudes, even with fewer selection environments, more efficiently, and with fewer time and resources applied. As a result of similarity between the parents, ANN can correctly classify genotypes from populations with a narrow genetic base, in addition to pure lines and genotypes with a high degree of inbreeding.

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