Study of Branching Responses of One Year Old Branches of Apple Trees to Heading Using Hidden Semi-Markov Chains

A model of branching structures of apple trees (Malus domestica cv. Fuji) in an intensive orchard for different levels of heading intensities is presented. The model, based on a statistical analysis, essentially simulates the numbers and distributions of the axillary production along one-year-old parent branches using the Hidden Semi-Markov Chain (HSMC), and has been validated against observed data with excellent results. A numerical study was made for simulating the heading effects on the branching response of one-year-old branches of apple trees. With different levels of heading schemes, our results show that (a) the proportion of axillary budbreak in heavy heading and severe heading was significantly different from that in light heading and moderate heading, (b) the proportion of the long shoot in heavy and severe heading was more than the medium shoot, while the medium shoot was more for the moderate heading and light heading, and (c) the numbers of latent buds along the parent branch for light heading were higher than heavy and moderate heading. The modeling method of this paper aims at providing a quantitative tool for orchard management, particularly with regard to pruning practices.