ABSTRACT 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 F2 and F3 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 F2 and selfed families in F3. 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.

Resumo: O objetivo deste trabalho foi avaliar uma abordagem de análise de fator múltiplo para estimar a herdabilidade de características de qualidade em tomates (Solanum lycopersicum), tendo como referência os valores de herdabilidade obtidos por meio do método clássico de regressão parental descendente. Foi avaliado um total de 18 famílias de tomate F3 originadas do autocruzamento de 18 indivíduos de um híbrido de segundo ciclo. Em ambas as gerações, foram avaliadas dez características quantitativas relacionadas à qualidade da fruta. A análise de fator múltiplo mostrou que algumas das características avaliadas apresentaram desempenho diferente e outras semelhante entre as gerações. A herdabilidade é baixa ou nula para algumas characterísticas, como vida útil e percentagem de refletância, e alta para outras, como peso e forma. Essa análise também permite o estudo da conexão global entre ambas as gerações por meio do coeficiente RV (F3, F2), que mede a correlação entre duas configurações de matriz. O RV foi 0,503 e pode estar associado à herdabilidade geral de todos os dados. A análise de fatores múltiplos é uma técnica multivariada válida para avaliar a herdabilidade de características de qualidade em tomates.

Abstract: 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.