Fractal Geometry of Succession

Mathematical representation of vegetation growth:

As an undergrad, I worked with Dr. Gregg Hartvigsen and Dr. Chris Leary to try and develop a process to measure the growth of large stands of vegetation as accurately and efficiently as possible. I worked in a summer research program with them where we focused on the use of fractal geometry to emulate biological processes. I was also an assistant manager of the SUNY Geneseo Roemer Arboretum, so I had first hand observations of the way grasslands transformed into woods over time.

Obviously trees are much more long-lived than humans, so we had to sacrifice a long-term study of a single area for a multi-site design in which each site represented a different stage of succession. We replicated these sites for inferential rigor. What we found is that as a patch of vegetation succeeds from grass to shrubs to young-growth trees (saplings) to old-growth trees, the 'shape' of the patch is conserved.

We developed a technique to relatively easily (one person, an hour or two in the field) obtain critical metrics of a patch of vegetation (e.g., average height of the lowest live branch, average height of the tallest vegetation, coordinate position of large (>5" diameter) trunks, etc.) and convert that to an estimate of that patch's 'fractal dimension'. Basically, that means determining what the dimension of a patch would be, similar to the dimension of a box being 3D.

Fractal geometry allows for the reality of an object taking up less than the full 3-dimensions of space it exists in (i.e. a tree canopy can be approximated as an ellipsoid, but there are actually a huge number of gaps between leaves and branches, so it's not completely '3D', but more like '2.71D').

Read more in Applied Mathematics.