Bayesianand Frequentist Estimation of Adaptability and Stability Parameters of Cucumis melo L. Genotypes Using the Toler Model Under Semi-Arid Conditions

Melon (Cucumis melo L.) production in Brazil is concentrated in the semi-arid Northeast region, where environmental variability hinders the selection of stable, high-yielding genotypes. This study evaluated the adaptability and phenotypic stability of experimental hybrids of yellow melon, cantaloupe melon, and Galia melon under contrasting environmental conditions, using Toler’s bi-segmented and simple linear models under frequentist and Bayesian approaches. The experiments were conducted in the Brazilian semi-arid region, comprising 8 environments for the first Yellow melon group, 12 for the second Yellow melon group, 9 for Cantaloupe, and 12 for Galia. Bayesian inference was implemented using nested sampling with the UltraNest package to estimate the intercept (α)and regression coefficients (β1 and β2) of the bi-segmented model, as well as the common regression coefficient (βcommon) of the simple linear model, together with their posterior uncertainty. The Bayesian analysis provided 95% highest-density intervals (HDIs) for these parameters, with convergence assessed using trace and corner plots. The frequentist and Bayesian approaches showed consistent classifications for 37 of the 38 genotypes (97.37%), with an isolated difference observed for AM-12. Based on the Bayesian analysis, Group A genotypes were identified among the Yellow melon and Cantaloupe materials, whereas the Galia genotypes were classified into Groups C and E. Group A genotypes exhibited a convex and doubly desirable response pattern, characterized by low sensitivity in unfavorable environments and high responsiveness under favorable conditions; Group C represented broad adaptability, whereas Group E represented a concave and doubly undesirable response. The results indicate that Bayesian inference provides complementary information to traditional analyses by explicitly quantifying parameter uncertainty, supporting the interpretation of genotype adaptability and phenotypic stability in melon breeding under semi-arid conditions.