Localization and extinction of bacterial populations under inhomogeneous growth conditions.pdf

a r X i v : q - b i o / 0 3 1 0 0 3 2 v 1 [ q - b i o .P E ] 2 4 O c t 2 0 0 3 Localization and extinction of bacterial populations under inhomogeneous growth conditions Anna L. Lin??, Bernward A. Mann, Gelsy Torres-Oviedo, Bryan Lincoln, Josef Ka?s, Harry L. Swinney Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, TX 78712 ? To whom correspondence should be addressed. email: alin@phy.duke.edu ? Current address: Center for Nonlinear and Complex Systems and Department of Physics, Duke University, Durham, NC 27708 The transition from localized to systemic spreading of bacteria, viruses and other agents is a funda- mental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple one-dimensional system to determine the spreading of bac- terial populations that occurs for an inhomogeneous environment under the influence of external convection. Our system consists of a long channel with growth inhibited by uniform UV illumination except in a small “oasis”, which is shielded from the UV light. To mimic blood flow or other flow past a localized infection, the oasis is moved with a constant velocity through the UV-illuminated “desert”. The experiments are modeled with a convective reaction-diffusion equation. In both the experiment and model, localized or extinct populations are found to develop, depending on condi- tions, from an initially localized population. The model also yields states where the population grows everywhere. Further, the model reveals that the transitions between localized, extended, and extinct states are continuous and non-hysteretic. However, it does not capture the oscillations of the localized population that are observed in the experiment. The growth, spreading, and extinction of a population in an inhomogeneous environment is of interest given the global decline in biodiversity. Under what conditions does a population c