Life and death near a windy oasis.
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 --> A + A, die A --> 0, and annihilate A + A --> 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.
Dahman
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Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA. dahmen@uiuc.edu
Nelson
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Shnerb
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D001419:Bacteria / Q000254:growth & development*; D016014:Linear Models; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted