| The paper used Markov stochastic process theory to study the branching patterns of the 2-year-old branches of mature peach trees (Prunus persica (L.) Batsch). The stochastic model of branching architecuture was established based on the field survey data. The study focused on quantifing the main architectural features of peach trees after being pruned, providing the definitions of specific shoot types and their distribution within the branching framework, visualizing three-dimensionally the modeling results of pruning measures. The main progress has been made as follows:1. We used hidden semi-Markov model with four states to model the branching patterns of peach trees {Prunus persica (L.) Batsch) after being pruned. A hidden semi-Markov chain was defined by the following parameters: the initial probability, the transition probability, the occupancy distribution, the first occurrence distribution, the recurrence distribution and the sojourn distribution.The model parameters were estimated by a maximum likelihood algorithm, which maximizes the likelihood of the observed data. The theoretical characteristic distributions were calculated from the estimated parameters of the underlying semi-Markov chain (initial probabilities, transition probabilities, and occupancy distribution).2. The effects of the different pruning measures on branching patterns were analyzed and compared by examining model parameters and observation probabilities of diverse one-year-old shoots. The modeling results of the branching patterns for different models showed the proximity and difference of pruning measures, hi the case of light heading back, more branching shoots occurred along the central and distal portion of the parent branches. Sylleptic shoots had their highest probability at most distal nodes on parent branch, while the most proximal nodes remained unbranched. The increase in the probability of sylleptic branching towards the proximal end was more notable in parent branches being heavy heading back than in those being light and medium heading back. The degree of pruning on two year-old parent branch was thus probably important in orientating the development of the one-year-old shoots and branching patterns. The most distal node of each parent branch being pruned is the one with the highest probability of producing the sylleptic shoot. A better knowledge of these effects of pruning should lead to an improvement in the pruning program of mature trees. Our work suggested that light heading back was not recommended to alleviate shoot crowding, to improve fruit size and quality, as well as to maintain an optimum light exposure on all tree parts, whereas moderate heading back was a sustainable management strategy that growers can adopt to improve profitability of the orchard. From a practical point of view, our result suggested that the effectiveness of heavy heading back, usually recommended on weak ageing trees, could be improved if it was carried out on the parent branches.3. The presented hidden semi-Markov chain model (HsMM) was able to take into account structural and stochastic characteristics of the parent branches of peach trees. The simulated results showed that theoretical probability distributions of diverse one-year-old shoots of the parent branches calculated on the basis of the parameters of the hidden semi-Markov chain model were in good agreement with probabilities extracted from the observed data. The study offered the evidence of the variation in shoot growth within a population of mature peach trees and enabled us to recognize discrete shoot types. Unlike the usual methods for simply estimating branching densities, the HsMM approach led us to capture the embedded architecture and contributed to a more precise analysis of the branching pattern for parent branches. The model was therefore a useful tool to characterize shoot distribution inside a branching zone according to function of the diverse one-year-old shoot, e.g. vegetative and/or reproductive branching shoots. The determination rules of t...
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