Multiscale functional-structural plant modelling at the example of apple trees

基于过程的作物模型允许预测在均匀条件和农业实践下的植物区室的生长。它们不太适合于以单个植物器官为重点的应用。功能结构植物模型（FSPM）的目的是克服这一限制，代表三维植物结构和生理功能与它们的相互依赖关系。然而，当它们包括几个过程并在器官水平上代表植物时，FSPM的计算时间可能变得令人望而却步，特别是对于大型植物。另一个问题是由复杂性引起的：由于大量的参数和建模过程之间的非线性依赖关系，参数估计和灵敏度分析的必要步骤是不平凡的。我们将在一个由四个团队组成的项目中解决这些问题，这些团队代表了植物学，园艺作物建模，数学和计算机科学方面的专业知识。我们的项目将致力于两个研究重点：F1 -“模型开发，校准，分析，和相应的软件工具”，和F2 -“案例研究：模拟苹果树的器官，分支和整树规模的生长”。在F1中，我们将建立数学和算法工具，用于弥合空间和时间尺度之间的差距（空间：器官-分支轴-个体树-果园;时间：小时到年）。同步设备表示的放大、缩小和维护方法（包括将使用开放源码模拟软件开发若干规模级别的工艺。此外，还将开发和实施一个工具箱，用于对这种多尺度模型进行参数拟合、敏感性分析和验证。与尺度之间的差距密切相关的另一个差距是机械模型和基于数学的模型之间的差距。我们将在F2的案例研究中弥合这一差距，来自双方：现有的经验，基于L系统的苹果树生长模型将适合不同的基因型和环境条件。与此同时，将利用现有的软件，在器官和分支尺度上开发一个基于生物农药的水通量和碳运输模型，以便于说明和稳定求解网络上的微分方程。该模型将允许在不同的水情景下评估水果质量。最后，这两条线的工作将合并在一个集成的，多尺度的苹果树生长模型与液压和C运输组件。它将使用F1的工具进行构建、分析和验证。与此同时，F1研究人员与F2建模人员需求的持续对抗将指导方法和工具的开发及其在FSPM平台中的集成。项目的一致性将通过几个小组就一些任务开展联合工作、定期会议、年度讲习班、联合数据库和对学生的联合监督得到进一步保证。

Process-based crop models allow the prediction of the growth of plant compartments under homogeneous conditions and agricultural practices. They are less adapted to applictions where single plant organs are in the focus. Functional-structural plant models (FSPMs) were designed to overcome this limitation by representing 3-dimensional plant structure and physiological functioning with their mutual dependencies. However, when they include several processes and represent the plant at organ level, calculation times for FSPMs can become prohibitive, particularly for large plants. A further problem is caused by complexity: The necessary steps of parameter estimation and sensitivity analysis are nontrivial, due to the large number of parameters and the often non-linear dependencies between the modelled processes. We will address these problems in a project of four teams, representing expertise in botany, horticultural crop modelling, mathematics and computer science. Our project will be devoted to two research foci: F1 - "Model development, calibration, analysis, and corresponding software tools", and F2 - "Case study: Modelling apple tree growth at organ, branch and whole-tree scale". In F1, we will build mathematical and algorithmic tools for bridging the gap between spatial and temporal scales (spatial: here organ - branch axis - individual tree - orchard; temporal: hour to year). Methods for upscaling, downscaling and maintenance of simultaneous plant representations (incl. processes) at several scale levels will be developed using open-source simulation software. Furthermore, a toolbox for parameter fitting, sensitivity analysis and validation for such multiscale models will be developed and implemented. A further gap, closely related to that between scales, is that between mechanistic and empirically-based models. We will bridge this gap in the case study in F2, coming from both sides: An existing empirical, L-system-based model of apple tree growth will be fitted to different genotypes and environmental conditions. In parallel, a biophysically-based water flux and carbon transport model will be developed at the organ and branch scale, utilizing an existing software for an easy specification and stable solution of differential equations on networks. This model will allow assessments of fruit quality under different water scenarios. In the end, both lines of work will be merged in an integrated, multiscale apple tree growth model with a hydraulic and a C transport component. It will be built, analyzed and validated using the tools from F1. At the same time, the continuous confrontation of the researchers in F1 with modellers' demands from F2 will guide the development of methods and tools and their integration in FSPM platforms. Project coherence will be further assured by joint work of several teams on some of the tasks, regular meetings, annual workshops, a joint database, and joint supervision of students.