Combining 3D digitizing data and architectural modelling to simulate shoot growth and geometry in apple

Abstract

Various models have been developed to predict tree growth and architecture over years, but few of them are capable of simulating 3D geometry development and shoot typology from a pre-existing crown geometry. In this study, we developed an approach for simulating 3D apple tree structure by combining 3D digitizing data with topological rules adapted from MappleT, an existing architectural model. In this modelling approach, bud fates were simulated with a first and second order Markov chain for terminal successions and using a hidden semi-Markov chain for the branching pattern on the one-year-old shoots. In these Markov models, five bud/shoot types were considered (small, medium, long, floral and dormant). Parametric laws and allometric relationships for each shoot type were used to simulate shoot length and leaf area. Shoot spatial position was set according to branching angle and phyllotaxis of the simulated cultivar. One nine-year-old apple tree (Malus ×domestica 'Jubile®') grown in 110L pots was digitized in 2013 and 2014. The model was calibrated on data recorded in 2012 and 2013. The calibration allowed (i) deriving distribution parameters of shoot length according to their types; (ii) establishing allometric relationships between the internode number, leaf area and the total shoot length; and (iii) evaluating the parameters of the Markov and semi-hidden Markov chains. To validate the model, simulations were performed using the tree digitized in 2013 as inputs of the model. The results were compared to the same tree digitized in 2014, comparing within tree shoot demography and the shoot leaf areas according to their type and length. Using this approach we were able to simulate tree growth on year n+1 from observed architectures at the adult stage. This opens the way for the optimization of management practices on observed trees in orchards conditions.