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      Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

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          Abstract

          Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Such non-transitive relations lead to an evolution with central features represented by the `rock-paper-scissors' game, where rock crushes scissors, scissors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity. However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity. When mobility exceeds a certain value, biodiversity is jeopardized and lost. In contrast, below this critical threshold all subpopulations coexist and an entanglement of travelling spiral waves forms in the course of temporal evolution. We establish that this phenomenon is robust, it does not depend on the details of cyclic competition or spatial environment. These findings have important implications for maintenance and evolution of ecological systems and are relevant for the formation and propagation of patterns in excitable media, such as chemical kinetics or epidemic outbreaks.

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          Author and article information

          Journal
          03 September 2007
          2008-04-09
          Article
          10.1038/nature06095
          0709.0217
          7fa60d30-a0e1-4e98-908c-03d460da21b7
          History
          Custom metadata
          LMU-ASC 62/07
          Nature 448, 1046-1049 (2007)
          Final submitted version; the printed version can be found at http://dx.doi.org/10.1038/nature06095 Supplementary movies are available at http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie1.AVI and http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie2.AVI
          q-bio.PE cond-mat.stat-mech physics.bio-ph

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