Number of harvest years and selection for productivity, witches’ broom resistance, stability, and adaptability in cacao

A suitable statistical model for the analysis of repeated measures is a prerequisite for an accurate genetic selection of cacao (Theobroma cacao L.) genotypes. Thus, the objectives of this study were to (a) evaluate homoscedastic and heteroscedastic repeatability models, (b) estimate the optimal number of harvest years for genetic selection, and (c) identify and select biparental crosses with high productivity, witches' broom (Moniliophthora perniciosa Stahel & Philips‐Mora) resistance, stability, and adaptability. Twenty biparental crosses were evaluated in a complete randomized blocks design, with seven replications and 12 trees per plot for 10 harvest years. Evaluated traits were number of healthy fruits (NHF), number of symptomatic fruits for witches' broom (NWBF), dry bean weight (DBW), and fruit index (FI). Variance components were estimated by restricted maximum likelihood, and genotypic values were predicted by best linear unbiased prediction. The best‐fitted repeatability model for each trait was indicated by Akaike's information criterion. The additive index was used for simultaneous selection for productivity, witches' broom resistance, stability, and adaptability. The heteroscedastic repeatability model showed the best fit for all traits. For HF, WBF, and FI, two and seven harvest years were sufficient for selection aiming at recombination and recommendation, respectively. For NWBF, evaluated only from the seventh year onwards, one harvest year was enough for recombination and three for recommendation. Five biparental crosses with high productivity, witches' broom resistance, stability, and adaptability were selected for recombination and/or for competition trials for recommendation. Such results can help define efficient strategies and optimize cacao breeding programs. Core Ideas Heteroscedastic repeatability model was more suitable than homoscedastic repeatability model. Two and seven harvest years were necessary for selection for recombination and recommendation, respectively. Additive index allowed genetic gains for productivity and disease resistance traits.