...................................................................... Mathematical Ecology "Open Problems Forum": Modeling Animal Movement with Arbitrarily Complicated Constraints Department of Biological Sciences & Department of Mathematical Sciences, NJIT AbstractHow do animals move from patch to patch in New York City? The city has a large number of green patches of various sizes, separated by a very complex urban mosaic that restricts movement to varying degrees. In the simplest view, buildings can be considered to either block movements or not (depending on their height and the kind of organism in question). The complete building footprint of NYC is available as vector outlines with associated heights, or alternatively, as raster of heights at some arbitrary resolution (currently I have it at 3m). Either way, this is a very large dataset describing a very complex spatial structure.) We would like to be able to generate estimates of relative movements rates between green patches, given the 'resistance' of the urban infrastructure between them. The approach I have taken so far is directed diffusion, using a discrete array approximation. First I model the diffusion of some 'orienting substance' out of green patches, ignoring the buildings and the 'origin' patch. Then I overlay the building raster footprint. Finally, I use Monte-Carlo simulations to model the movement of organisms from the periphery of the origin patch, with the movement steps biased to move up-gradient, and to bounce back from buildings. This works ok, but is slow and inelegant (in my opinion), and organisms can too easily get stuck in cul-de-sacs. I am wondering of there might be a much better approach at modeling 'flow' through the city streets. For example, can some of the 'classic' numerical methods for modeling diffusion, or fluid flow, be scaled up to such a complicated structure? Is there a completely different framework that might be better? This topic could be of interest to lots of people in the Department, especially those with expertise in fluid dynamics.
Last Modified: Nov 28, 2007 Horacio G. Rotstein h o r a c i o @ n j i t . e d u Last modified: Tue Sep 14 10:28:13 EDT 2010 |