Estimating fruit tree growth curves in breeding field using fragmented longitudinal data: An application to citrus hybrid seedlings

Vegetative and reproductive growth in fruit trees is interconnected, and analyzing this relationship can provide valuable insights into fruit quality. However, characterizing vegetative growth through growth models is challenging because of the difficulty in obtaining longitudinal data, given the slow growth rate. In breeding fields, in contrast, seedlings of different ages are planted, allowing for simultaneous measurements that yield a dataset resembling longitudinal data with missing values --termed "fragmented longitudinal data." Because longitudinal data are obtained from a single measurement, they can potentially shorten the period required for growth curve estimation. Bayesian nonlinear models offer advantages in estimating curves from incomplete data. In this study, we generated fragmented longitudinal data using genome data with 45,929 markers from 624 citrus hybrid seedlings and applied a Bayesian nonlinear model to explore its potential. We also incorporated genomic information into the model to assess the impact of the estimation accuracy. Our simulations indicated that the Bayesian nonlinear models ability to interpolate missing values significantly improved the estimation performance. At best, the mean square error of the parameter characterizing the later growth stage was reduced by 84.3 mm2. Although the improvement from incorporating genomic information was modest, it still surpassed models that lacked genomic data. We also predicted the curves of untested individuals using the estimated parameters. Although the prediction accuracy of each parameter measured by the correlation coefficient was lower than 0.5, one parameter consistently showed a better accuracy. Further research is required to reveal the advantages of integrating genomic data for better predictions.