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Issue Math. Model. Nat. Phenom.
Volume 2, Number 4, 2007
Patterns and waves in ecology and evolution
Page(s) 74 - 104
DOI 10.1051/mmnp:2008023

Math. Model. Nat. Phenom. Vol. 2, No. 4, 2007, pp. 74-104
DOI: 10.1051/mmnp:2008023

Pattern Formation of Competing Microorganisms in Sediments

Y. Schmitz1, M. Baurmann2, B. Engelen2 and U. Feudel2

1  Systems Biology and Bioinformatics Group, Department of Computer Science, University of Rostock, Germany
2  Institute of Chemistry and Biology of the Marine Environment, University of Oldenburg, Germany

schmitz@informatik.uni-rostock.de

Abstract
We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature. We focus on the interaction between pattern formation and non-uniform forcing, which naturally occurs in our model, since layers closer to the sea water are richer in particular chemicals than deeper layers. We find that heterogeneous forcing has a strong impact on the structures that evolve, leading to the formation of banded structures or even pulses instead of the well-known Turing patterns.


Mathematics Subject Classification. 70K50, 37G35, 92D25, 92D40, 34C60

Key words: Turing instability -- pattern formation -- population dynamics -- competition




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