Modeling long-distance signals in complex branching structure: Application to the control of floral induction in apple trees

Flowering is the main process that determines yield in fruit trees, and a negative relationship between crop load and floral induction has been observed in many species. In apple tree, hormonal signals coming from seeds, mainly gibberellins, which can be transported over long distances within the tree, are suspected to inhibit floral induction. Apple trees display a complex architecture with large genotypic variability. This genotypic variability results in differences in organ morphology and topology (succession of shoots and branching pattern) that can directly modify the amount of “inhibiting” signal reaching each meristem. To analyze the intertwined effects of plant architecture, crop load and inhibiting signal on floral induction we developed a model based on the L-system formalism. In the model, the plant is represented as a set of interconnected metamers and organs, in which the amount of inhibiting signal coming from each fruit is transferred to the next metamer depending on its length and on a constant proportion of the incoming flux of inhibiting signal. The model assumes that the amount of inhibiting signal produced every day depends on the stage of fruit development. The model simulates both the basipetal and acropetal movement of the signal as well as its partitioning at each branching point. An iterative procedure was used to reach model convergence in order to partition the total amount of inhibiting signals in the whole tree structure. Simulations were performed on sub-tree structures (shoot and branch) to analyze the response of the model to three main parameters (α: the transfer rate, proportion of signal moved to the next metamer, σ: the parameter driving the partition of the signal into acropetal and basipetal fluxes, and L: the internode length). Then, simulations were performed during one growth season on 4-year-old trees simulated using the MappleT model with a range of crop loads. The model reveals its accuracy to simulate well-known results at the tree scale (e.g. higher amount of inhibiting signal when crop load increases) and at the shoot scale (e.g. higher amount of inhibiting signal in reproductive shoots than in vegetative ones). More interestingly, if we assumed thresholds for signals that inhibit floral induction, we observed that changing α values and the crop load led to contrasted floral induction patterns that can be related to genotype bearing behavior (regular vs alternate). So far, the model has been only compared to qualitative results from literature. But it gives new insights into interactions between plant development, architecture and floral induction in a context of genotypic variability. Experiments are currently being performed to validate this model at different scales of plant organization. Furthermore, the model developed in this study seems to be generic enough to be easily adapted to other plants for simulating moving signals that can affect growth and developmental processes