INTEGRATING BIOMECHANICAL AND MARKOV CHAIN MODELS INTO AN L-SYSTEM SIMULATION OF ARCHITECTURAL DEVELOPMENT OF APPLE TREES

Abstract

In this paper, we present a new apple tree model, MAppleT, which integrates a statistically-based model of architectural tree development and a biomechanical model of axis shape. Our goal is to predict both the topology and the geometry of a developing tree: these two factors contribute strongly to a tree's architecture. This goal is motivated by the role of tree architecture in light interception, carbon acquisition and tree training. Our study was carried out on the 'Fuji' cultivar. MAppleT is developed using L-studio on the basis of previous L-system models of tree topology and biomechanics. Growth rules generate branching patterns according to hidden semi-Markov chains, with parameters depending on the shoot type. The type of the shoot developing from a terminal bud is determined between the successive annual growth cycles, as a function of tree age. A distribution of shoot lengths, measured in the number of internodes, is attributed to each shoot type in either terminal or lateral position. Organ dimensions and mass, wood properties, branching angles and the calendar of events during a growing season are based on experimental data. The radial growth of internodes is estimated by the pipe model, slightly modified to account for our experimental data. Topological and geometric descriptors of the simulated trees and real, digitised trees were compared at different scales (the crown, the branches and the shoots) using multi-scale tree graph representations and tools from the OpenAlea platform. Graphical and numerical outputs from MAppleT are discussed. (Resume d'auteur)