Integration of a System Dynamics Model and 3D Tree Rendering—VISmaF Part II: Model Development, Results and Potential Agronomic Applications

Abstract

Biological–mathematical models of trees can be exploited for a wide range of agronomic applications including crop management, visualization of ecosystem changes over time, in-field phenotyping, crop load effects, testing of plant functions, biomechanics, and many others. Some models propose a 3D output of tree that, in addition to having functionality to visualize the result, offers an additional tool for the evaluation of some parameters of the model itself (interception and amount of light, temperature, obstacles, physical competition between multiple trees). The present study introduces a biological–mathematical model of tree growth with a 3D output of its structure in a realtime 3D rendering environment (Unity©). Thanks to the virtual environment created in Unity©, it was possible to obtain variable environmental parameters (amount of light, temperature) used as inputs to the mathematical simulation of growth. The model is based on ordinary differential equations (ODEs) that compute the growth of each single internode in length (primary growth) and width (secondary growth) and the accumulation of growth inhibitors regulating the seasonal cyclicity of the tree. Virtual experiments were conducted varying environmental conditions (amount of light and temperature), and the species-specific characteristics of the simulated tree (number of buds, branching angle). The results have been analyzed showing also how the model can be adapted for the creation of different tree species and discussing the potential agronomic applications of model.

Keywords

• FSPM
• ordinary differential equations
• system dynamics
• 3D tree rendering
• <i>Unity</i>©