Life and death near a windy oasis. (English) Zbl 0999.92038

Dahmen, Karin A.; Nelson, David R.; Shnerb, Nadav M.

J. Math. Biol. 41, No. 1, 1-23 (2000).

Summary: We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near a patch of nutrient or favorable illumination (“oasis”) in the presence of a drift term (“wind”) is computed. The bacteria, described by a simple generalization of the Fisher equation, diffuse, divide \(A\to A+A\), die \(A\to 0\), and annihilate \(A+A\to 0\).
At high wind velocities all bacteria are blown into an unfavorable region (“desert”), and the colony dies out. At low velocity a steady state concentration survives near the oasis. In between these two regimes there is a critical velocity at which bacteria first survive. If the “desert” supports a small nonzero population, this extinction transition is replaced by a delocalization transition with increasing velocity. Predictions for the behavior as a function of wind velocity are made for one and two dimensions.

MSC:

92D40	Ecology
35Q92	PDEs in connection with biology, chemistry and other natural sciences

Keywords:

delocalization; extinction; Fisher equation

Software:

OASIS