A dynamic model of xylem and phloem flux in an apple branch

Abstract

We present here the framework for a Functional-structural plant model (FSPM) of the water and sugar transport in an apple (Malus domestica (L.) Bartsch.) branch. The model is parameterized at the spatial level of the organ (leaf blade, leaf petiole; internode; fruit, and fruit peduncle), explicitly describing water and sugar flows between all possible organ combinations. In order to do so, an object-oriented representation of each organ was introduced, containing the functional description of xylem and phloem elements within the respective organs, and between each organ pair, using the dedicated modelling platform GroIMP. The geometry and topology of the branch and its elements were based on measurements of ‘Fuji’ cv. apple trees, located in an experimental orchard in Angers, France, whereas the coefficients of the transport model system were derived from the literature. Branch architecture is an input to the model therefore not supposed to change during the simulated period (June to September). First results are promising: 1) a fully functional, quantitative simulation of water flux based on biophysical principles (leaf transpiration coupled to photosynthesis rate and stomatal conductance) is driving the water transport from the base of the branch to the peripheral organs (leaves) according to the Darcy flow principle. At the same time sugars are transported from sources (leaves) to sinks (fruits) based on Münch flow in the phloem. Such a simulation is possible in real time (temporal resolution one second); 2) even for extreme situations the network of xylem and phloem with its numerous interconnections shows reasonable and stable behaviour.