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Phase separation explains a new class of self-organized spatial patterns in ecological systems
Liu, Q.X.; Doelman, A.; Rottschäfer, V.; de Jager, M.; Herman, P.M.J.; Rietkerk, M.; van de Koppel, J. (2013). Phase separation explains a new class of self-organized spatial patterns in ecological systems. Proc. Natl. Acad. Sci. U.S.A. 110(29): 11905-11910. dx.doi.org/10.1073/pnas.1222339110
In: Proceedings of the National Academy of Sciences of the United States of America. The Academy: Washington, D.C.. ISSN 0027-8424, more
Peer reviewed article  

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Author keywords
    mussels; mathematical model; spatial self-organization; animal aggregation

Authors  Top 
  • Liu, Q.X., more
  • Doelman, A.
  • Rottschäfer, V.
  • de Jager, M., more
  • Herman, P.M.J., more
  • Rietkerk, M.
  • van de Koppel, J., more

Abstract
    The origin of regular spatial patterns in ecological systems has long fascinated researchers. Turing's activator-inhibitor principle is considered the central paradigm to explain such patterns. According to this principle, local activation combined with long-range inhibition of growth and survival is an essential prerequisite for pattern formation. Here, we show that the physical principle of phase separation, solely based on density-dependent movement by organisms, represents an alternative class of self-organized pattern formation in ecology. Using experiments with self-organizing mussel beds, we derive an empirical relation between the speed of animal movement and local animal density. By incorporating this relation in a partial differential equation, we demonstrate that this model corresponds mathematically to the wellknown Cahn-Hilliard equation for phase separation in physics. Finally, we show that the predicted patterns match those found both in field observations and in our experiments. Our results reveal a principle for ecological self-organization, where phase separation rather than activation and inhibition processes drives spatial pattern formation.

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