[POS] Ecology and Enviromment

[POS-39] Detecting symmetry in the process of tree growth

*Takaaki Fujimoto¹, Eita Shimizu¹ (1. Tottori University (Japan))

Keywords:

Sustainability,Riemannian geometry,Characteristic class,Geodesic,Analytical mechanics

Since forests are large ecosystems that cover 30% of the world's land area, their management and conservation will have a huge impact on the global environment. Growing concerns about the conservation of ecosystem have led to a strong demand for sustainable forest management. A cycle of forest management with high symmetry should minimize disturbances to the ecosystem, which would therefore lead to sustainable forest management. The aim of this study is to find symmetry in long-term forest dynamics by comparing the geometric quantities of the surface between groups of artificial and natural forest samples. If the quantity representing the state of the system does not depend on time, then it is nothing other than a conserved quantity from a physical point of view. In terms of differential forms, the conserved quantity is recognized as being represented in an exact form. We have attempted to evaluate the symmetry of the tree growth process using de Rham cohomology, which is the quotient vector space measuring the failure of a closed form to be exact. First, to confirm the amount of curvature of the surface, we computed the parallel translation along a curve, a notion equivalent to a geodesic. The cumulative sum of the norms of the geodesic was calculated to compare the length of the geodesic between the artificial forest and the natural forest. The natural forest had a longer geodesic length than the artificial forest, indicating that the variation in the state of xylem in the natural forest behaved more meandering, resulting in a longer geodesic. The Pfaffian of the curvature matrix, i.e., the characteristic class, was found to increase with age and the artificial forest remained higher values than the natural forest throughout the growth process. This suggests that the growth process of the natural forest was more symmetrical, that is, more sustainable, than that of the artificial forest. Because the geometric quantities are invariant under coordinate transformations, the proposed methods provide us with the intrinsic behavior of the tree growth process independent of a specific coordinate system, that is, a concrete space spanned by the measured wood properties.