Genetic evaluation of Theobroma grandiflorum hybrid families for fruit yield and resistance to witches’ broom

Abstract Theobroma grandiflorum is a perennial fruit-bearing species with a long breeding cycle (~ 12 years). In multi-harvest data analyses, one frequently observes heteroscedasticity and genetic/statistical imbalance, which requires adequate statistical methods. This study aimed to compare the adequacy of multi-harvest models with homogenous and heterogeneous residual variance and to define the optimal number of harvests for an accurate genetic selection of T. grandiflorum families with high fruit yield persistence and resistance to witches’ broom. We used a generalized linear mixed model to analyse the resistance to witches’ broom. The data refers to an unbalanced trial with 34 triple-cross hybrid families, arranged in a randomized complete block design. We evaluated these families throughout nine consecutive harvests regarding fruit yield and resistance to witches’ broom. The variance components, genetic parameters and genotypic values were estimated/predicted through residual maximum likelihood/best linear unbiased prediction methodologies. The model with heterogeneous residuals had a better fit than the homogeneous model for the fruit yield trait, according to Akaike information criterion. The results attest to the genetic variability in the evaluated population. To select the best individual for the next breeding cycle, three and two harvests are enough for selecting accurately for fruit yield and resistance to witches’ broom, respectively. For commercial release, nine harvests are necessary for both traits. We identified ten high-performance families regarding fruit yield persistence and resistance to witches’ broom.