Availability of a three-way data analysis to characterize two consecutive tomato (Solanum lycopersicum) generations is necessary to continue a plant breeding program with less uncertainty. The aim of this work was to analyze tomato fruit quality from F 2 and F 3 populations by two three-way data analysis: multiple factorial analysis (MFA) and generalized procrustes analysis (GPA). These techniques have the same main objective, searching for a common structure, but they achieve it in different ways. This work evaluated 18 tomato genotypes, represented by individual plants in F 2 and selfed families in F 3. The same quantitative traits related to fruit quality were measured in both generations. The first two axes of the MFA represented 51.0% of the total variability. From the representation of the genotypes on these axes, traits differing from one generation to another were identified. The first two axes of the GPA represented 56.4% of the total variability. This analysis provided a table of analysis of variance (ANOVA), which corroborated the graphic and analytical interpretations of the MFA, a technique that provides the composition of the obtained axes. The comparison between the results obtained from these techniques indicated that both MFA and GPA allowed the detection of genotypes with discrepancies between the two generations. The MFA technique presented the advantage of studying graphically and analytically the nature and degree of phenotypic differences among genotypes in both generations, while the GPA complemented the analysis with an ANOVA, achieving the quantification of statistical significances for the discrepancies or similarities between them.

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The objective of this work was to evaluate a multiple factor analysis approach to estimate heritability for quality traits in tomatoes (Solanum lycopersicum), taking as a reference the values of heritability obtained through the classical method offspring-parent regression. A total of 18 F3 tomato families originated from the selfing of 18 individuals from a second-cycle hybrid were evaluated. In both generations, ten quantitative traits related to fruit quality were assessed. The multiple factor analysis showed that some of the evaluated traits performed differently and others similarly between generations. Heritability is low or null for some traits, such as shelf life and reflectance percentage, and high for others, as weight and shape. That analysis also enables the study of the global connection between both generations through the RV (F3, F2) coefficient, which measures the correlation between two matrix configurations. RV was 0.503 and may be associated with the general heritability of all data. The multiple factor analysis is a valid multivariate technique to evaluate heritability for quality traits in tomatoes.