Extensions to a Lagrangian model of animal aggregation

Virginia Pasour, North Carolina State University

I have extended an existing simple Lagrangian model developed by Yamazaki and Haury (1993) which uses a nonparametric density estimation technique to study animal aggregation. The essence of the original model is its two parameters: a, which describes the perception distance of the organisms, and b, which relates to their motivation to aggregate. In the original model an attractive component caused individuals to move toward higher densities of organisms with strength b. This revised model also includes a tendency to be repulsed, instead of attracted, by densities of organisms above a certain threshold level, represented by a third parameter, g. Numerical simulations were performed in two-dimensional space using 100 organisms and a range of values for the three parameters. While including repulsion leads, in general, to more dispersal of organisms with time, the interplay between perception distance and motivation to aggregate can be quite complex with some surprising results, including initial super-diffusion.

Abstract Author(s): Virginia Pasour