Learning how a tree branches out: A statistical modeling approach

The increasingly large size of the graphical and numerical data sets collected with modern technologies requires constant update and upgrade of the statistical models, methods and procedures to be used for their analysis in order to optimize learning and maximize knowledge and understanding. This is the case for plant CT scanning (CT: computed tomography), including applications aimed at studying leaf canopies and the structural complexity of the branching patterns that support them in trees. Therefore, we first show after a brief review, how the CT scanning data can be leveraged by constructing an analytical representation of a tree branching structure where each branch is represented by a line segment in 3D and classified in a level of a hierarchy, starting with the trunk (level 1). Each segment, or branch, is characterized by four variables: (i) the position on its parent, (ii) its orientation, a unit vector in 3D, (iii) its length, and (iv) the number of offspring that it bears. The branching structure of a tree can then be investigated by calculating descriptive statistics on these four variables. A deeper analysis, based on statistical models aiming to explain how the characteristics of a branch are associated with those of its parents, is also presented. The branching patterns of three miniature trees that were CT scanned are used to showcase the statistical modeling framework, and the differences in their structural complexity are reflected in the results. Overall, the most important determinant of a tree structure appears to be the length of the branches attached to the trunk. This variable impacts the characteristics of all the other branches of the tree.