MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models

Abstract

Construction of tree architectural databases over years is time consuming and cannot easily capture event dynamics, especially when both tree topology and geometry are considered. The present project aimed to bring together models of topology and geometry in a single simulation such that the architecture of an apple tree may emerge from process interactions. This integration was performed using L-systems. A mixed approach was developed based on stochastic models to simulate plant topology and mechanistic model for the geometry. The succession of growth units (GUs) along axes and their branching structure were jointly modelled by a hierarchical hidden Markov model. A biomechanical model, derived from previous studies, was used to calculate stem form at the metamer scale, taking into account the intra-year dynamics of primary, secondary and fruit growth. Outputs consist of 3-D mock-ups – geometric models representing the progression of tree form over time. To asses these models, a sensitivity analysis was performed and descriptors were compared between simulated and digitised trees, including the total number of GUs in the entire tree, descriptors of shoot geometry (basal diameter, length), and descriptors of axis geometry (inclination, curvature). In conclusion, despite some limitations, MAppleT constitutes a useful tool for simulating development of apple trees in interaction with gravity.