Analysis of repeated measures data through mixed models: An application in Theobroma grandiflorum breeding

Theobroma grandiflorum is a perennial fruit tree native to the Amazon region. As a perennial species with continuous production throughout the years, breeders should seek well-conducted trials, accurate phenotyping and adequate statistical models for genetic evaluation and selection that can leverage the information provided by the repeated measures. We evaluated 13 models with different covariance structures for genetic and residual effects for T. grandiflorum evaluation, using an unbalanced dataset with 34 hybrids from the triple-crossing of nine parents, planted in a randomized complete block design. For nine consecutive years, the fruit yield of these hybrids was evaluated. Each model had its goodness-of-fit tested by the Akaike information criterion. The most adequate model for estimating the variance components and the breeding values were modelled with the first-order heterogeneous autoregressive for residual effects and third-order factor analytic for genetic effects. From this model, we used the factor analytic selection tools for selecting the top 10 families, providing a genetic gain of 10.42%. These results are important not only for T. grandiflorum breeding but also to show that in any repeated measures' data from fruit-bearing perennial species the modelling of genetic and residual effects should not be neglected.