Life and death near a windy oasis

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Jul 2000


  • Delocalization
  • Disorder
  • Extinction
  • Fisher equation

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)


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