Modelling branching patterns on 1-year-old trunks of six apple cultivars

Abstract

The structure resulting from branching on 1-year-old apple tree trunks was analysed in a set of apple cultivars with diverse branching and fruiting habits. Four different lateral types borne on successive nodes were observed when vegetative and flowering fates, as well as sylleptic and proleptic branching, were taken into account. The location and grouping of lateral types along the trunk were analysed for all cultivars, but are detailed for one cultivar only. This cultivar showed a succession of zones, each zone being characterized by its composition of lateral types. Statistical models-hidden semi-Markov chains-were built to take this structure into account and to characterize the cultivar's specific branching pattern. The models showed that most of the branching zones had a similar location in the different cultivars, even though zone composition and zone length differed among cultivars. On a more detailed scale, the nodes bearing a lateral, regardless of its type, were frequently followed by latent buds. The validity of the models and their biological interpretation are discussed with respect to parent shoot dynamics, hormonal gradients and competition between neighbouring buds.

Fig. 1. Probability of the different types of laterals according to the node rank observed on 1‐year‐old trunks in ‘Reinette Blance du Canada’.

Fig. 2. Example of differentiated zones on three sequences corresponding to three 1‐year‐old trunks of ‘Reinette Blanche du Canada’. 0, latent bud; 1, proleptic spur; 2, long proleptic shoot; 3, bourse; 4, sylleptic shoot.

Fig. 3. Number of successive nodes bearing a long shoot on 1‐year‐old trunks of ‘Reinette Blanche du Canada’.

Fig. 4. Modelling branching on 1‐year‐old trunks of ‘Reinette Blanche du Canada’ using a hidden semi‐Markov chain. Each state, corresponding to a branching zone, is represented by a circle. Transient states are edged by a single line while the final state is edged by a double line. The possible transitions between states are represented by arcs with the attached probabilities noted nearby (for legibility, only transitions with probabilities exceeding 0·02 are shown). Thick arcs entering states indicate initial states. The attached initial probabilities are noted nearby. The occupancy distributions are shown above the corresponding states, as are the possible lateral types observed in each state. Each lateral type is represented by a symbol: 0, latent bud; 1, proleptic spur; 2, proleptic long shoot; 3, bourse; 4, sylleptic shoot.

Fig. 5. Model assessment: comparison of the characteristics extracted from the observed sequences with those computed from model parameters, i.e. intensity (A), interval (B) and counting (C) points of view.

Fig. 6. Schematic representations of the hidden semi‐Markov chains estimated for each cultivar. The branching zones are represented by different motifs and their length corresponds to the mean value of the occupancy distribution. The observed lateral types are represented by histograms (except for the top and bottom zones where only latent buds are observed). The oriented edges represent the possible transitions between the zones and their respective probabilities are noted nearby. The mean total number of nodes is indicated in parentheses at the bottom of each diagram.