Statistical analysis and modeling of root measures for the description of spatiotemporal root patterns, using experimental and simulated image data gained by X-ray CT and root architecture models

根的三维微结构在驱动根际和根结构形成和功能的生物、化学和物理过程中起着关键作用。X射线计算机断层扫描（CT）是一种强大的技术，研究时空根生长模式的三维。然而，模拟的根结构提供了额外的见解，例如通过更快的数据采集和更高的时间分辨率。在这两种情况下，即在根生长模式的实验和虚拟研究中，产生大量复杂的图像数据，需要使用尽可能少的模型参数对其进行统计分析和建模。 在最近的一份出版物中，与D. Vetterlein（UFZ）模型的基础上，提出了一个能够描述蚕豆（Vicia faba）生长初期各阶段根系生长规律的根距模型。在与A. Schnepf（FZJ），我们研究了三维根构型模型CRootBox的输入参数与模拟根系的各种度量（如根长密度和凸船体体积）之间的联系，本项目的目的是继续和扩展与Vetterlein和Schnepf小组富有成效的合作。首先，我们继续从土壤的角度统计分析（实验观察和模拟）根的生长模式。除了通过根距离模型分析整个根系，我们开发本地根距离模型相对于特定类别的根段，例如，段是老的（接近种子）或段是在，或附近，根尖。这将使我们更详细地了解根系生长和功能的动态。此外，将建立定量关系的三维根构型模型CRootBox的输入参数和各种根的措施。多变量方法，如copula提供的数学工具，建立参数元模型的向量（相关）根的措施。研究结果将被用来开发一个普遍适用的方法，以目标为导向的根系结构模型的校准。特别是，我们将展示如何将机器学习方法与所获得的结果相结合，以便通过断层根部图像数据或衍生措施来校准CRootBox。另一个主题是几何根模式的统计描述，以区分纯粹随机，均匀和聚类形态。随机几何的方法提供了另一个角度在分析生长的根系，并将被用来研究，例如，在平面（例如垂直或水平）部分的土壤与化学2D地图的根穿刺点模式的相关性。最后但并非最不重要的是，我们将在约束和无约束的根架构中执行根度量的比较统计分析。

The 3D microstructure of roots plays a key role for biological, chemical and physical processes that drive rhizosphere and root structure formation and function. X-ray computed tomography (CT) is a powerful technology to study spatiotemporal root growth patterns in 3D. However, simulated root architectures provide additional insights, e.g. through faster data acquisition and higher temporal resolution. In both cases, i.e. in experimental and virtual investigations of root growth patterns, large amounts of complex image data are generated, which need to be statistically analyzed and modeled using as few as possible model parameters. In a recent publication together with the group of D. Vetterlein (UFZ), we proposed a root distance model, which is able to describe root growth patterns throughout all stages in the first weeks of growth of Vicia faba. In a further paper with the group of A. Schnepf (FZJ), we investigated the connection between the input parameters of the 3D root architecture model CRootBox and various measures of the simulated root systems, like root length density and volume of the convex hull.The aim of the present project is to continue and extend the fruitful collaborations with the Vetterlein and Schnepf groups. First, we continue to statistically analyze (experimentally observed and simulated) root growth patterns from the soil perspective. In addition to analyzing entire root systems via root distance models, we develop local root distance models with respect to specific classes of root segments, e.g. segments which are older (proximal to the seed) or segments being at, or near, the tips of roots. This will give us more detailed insight into the dynamics of root growth and function. Furthermore, quantitative relationships will be established between the input parameters of the 3D root architecture model CRootBox and various root measures. Multivariate approaches such as copulas provide the mathematical tools to build parametric meta-models for vectors of (correlated) root measures. The results will be used to develop a universally applicable approach for the target-oriented calibration of root architecture models. In particular, we will show how methods of machine learning can be combined with the results obtained, in order to calibrate CRootBox by means of tomographic root image data or derived measures. An additional topic is the statistical description of geometrical root patterns to distinguish between purely random, even and clustering morphologies. Methods of stochastic geometry provide yet another perspective in the analysis of growing root systems and will be used to study, e.g. the correlation of root piercing point patterns in planar (e.g. vertical or horizontal) sections of soil with chemical 2D maps. Last but not least, we will perform a comparative statistical analysis of root measures in constrained and unconstrained root architectures.