The phenotypic data acquired were subjected to quality control of residuals, assessing normal distribution through graphical inspection (Q–Q plot), the existence of outliers, and homogeneity of variance. A square-root transformation was applied when needed so that the residuals more closely meet the normality assumptions.

A linear mixed model was fitted per trait as trait = block + treatment + origin + accession + treatment × origin + treatment × accession using the restricted maximum likelihood (REML) variance component analysis framework of Genstat software55. Accession, water treatment, the gene pool of the origin of accessions, treatment × accession, and water treatment × gene pool of origin interaction were fitted as fixed, and block as random effects. A Wald test for the significance of fixed effects was performed. Only the Portuguese common bean accessions were included in the statistical model. Tukey’s multiple-comparison tests were applied for mean comparison of 16 photosynthesis-related traits measured among the accession gene pool of origin for each water treatment.

Phenotypic data obtained under WW and WD were analyzed separately. REML was used to fit a mixed model per trait as trait = block + accession + error. This model, with accession and block fixed, was applied to estimate the best linear-unbiased estimates (BLUEs) for each accession, used as input for the GWAS. Phenotypic correlations of BLUEs were calculated between traits, followed by a principal component analysis (PCA).

With our original experimental setup, the variance components for accession and error were not correctly estimated. So, a complementary experiment was performed in the same conditions, using ten accessions and five replications, following an alfa-lattice design. This new experiment was combined with the original experiment in the estimation of variance components for accession and error. Broad-sense heritabilities were calculated using vheritability procedure in Genstat software, based on the same model above, but with block and accession as random, and using the combined experiments.

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