Simulation Study of Stratified Diffusion Model

Fugo Takasu¹, Kohkichi Kawasaki² and Nanako Shigesada¹

¹Department of Information and Computer Sciences, Nara Women's University, Kita-Uoya Nishimachi, Nara 630, Japan
²Department of Knowledge Engineering and Computer Sciences, Doshisha University, Tanabe-cho, Kyoto 610-03, Japan

(Received April 12, 1996; Accepted June 28, 1996)

Keywords: Keywords: Range Expansion, Invasion, Stratified Diffusion, Long Range Dispersal, Colonization

Abstract. Biological range expansion is studied by using a stratified diffusion model that incorporates both the short range and long range dispersals. The distance of long range dispersal is taken from a constant, Gaussian, or exponential distribution. The expansion rate of range distribution is analyzed numerically and compared with that from the previous study, which was based on simpler but artificial assumptions. Analysis shows that long range dispersal contributes much in increasing the expanding speed; the greater are the mean distance and dispersing rate, the faster is the speed. When the distance has a Gaussian distribution, a greater variance results in a faster expanding speed, but the speed is higher when the distance is taken from exponential distribution with the same mean and greater variance. These results suggest the importance and the need of assessing distribution form of the long range dispersal to estimate the expanding speed in practical problems.