title: How turbulence regulates biodiversity in systems with cyclic competition.
abstract: Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended systems with a limited range of dispersal, whereas in well-mixed environments models for cyclic competition often lead to a loss of biodiversity. Here we consider the dispersal of biological species in a fluid environment, where mixing is achieved by a combination of advection and diffusion. In particular, we perform a detailed numerical analysis of a model composed of turbulent advection, diffusive transport, and cyclic interactions among biological species in two spatial dimensions and discuss the circumstances under which biodiversity is maintained when external environmental conditions, such as resource supply, are uniform in space. Cyclic interactions are represented by a model with three competitors, resembling the children's game of rock-paper-scissors, whereas the flow field is obtained from a direct numerical simulation of two-dimensional turbulence with hyperviscosity. It is shown that the space-averaged dynamics undergoes bifurcations as the relative strengths of advection and diffusion compared to biological interactions are varied.
authors: Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany.
authors: Daniel
authors: D
authors: Grošelj
authors: Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany.|Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA.
authors: Frank
authors: F
authors: Jenko
authors: Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany.
authors: Erwin
authors: E
authors: Frey
mesh_terms: D044822:Biodiversity; D004058:Diffusion; D057446:Hydrodynamics; D008962:Models, Theoretical; D062211:Spatio-Temporal Analysis