Trees have a fractal-like branching architecture that determines their structural complexity. We used terrestrial laser scanning technology to study the role of foliage in the structural complexity of urban trees. Forty-five trees of three deciduous species, Gleditsia triacanthos, Quercus macrocarpa, Metasequoia glyptostroboides, were sampled on the Michigan State University campus. We studied their structural complexity by calculating the box-dimension (Db) metric from point clouds generated for the trees using terrestrial laser scanning, during the leaf-on and -off conditions. Furthermore, we artificially defoliated the leaf-on point clouds by applying an algorithm that separates the foliage from the woody material of the trees, and then recalculated the Db metric. The Db of the leaf-on tree point clouds was significantly greater than the Db of the leaf-off point clouds across all species. Additionally, the leaf removal algorithm introduced bias to the estimation of the leaf-removed Db of the G. triacanthos and M. glyptostroboides trees. The index capturing the contribution of leaves to the structural complexity of the study trees (the ratio of the Db of the leaf-on point clouds divided by the Db of the leaf-off point clouds minus one), was negatively correlated with branch surface area and different metrics of the length of paths through the branch network of the trees, indicating that the contribution of leaves decreases as branch network complexity increases. Underestimation of the Db of the G. triacanthos trees, after the artificial leaf removal, was related to maximum branch order. These results enhance our understanding of tree structural complexity by disentangling the contribution of leaves from that of the woody structures. The study also highlighted important methodological considerations for studying tree structure, with and without leaves, from laser-derived point clouds.
Sarnak’s conjecture for sequences of almost quadratic word growth
