Bulletin of the American Physical Society
APS March Meeting 2012
Volume 57, Number 1
Monday–Friday, February 27–March 2 2012; Boston, Massachusetts
Session J42: Focus Session: Stochastic Population Dynamics I - Cyclic competition and population stability
11:15 AM–1:51 PM,
Tuesday, February 28, 2012
Sponsoring Units: DBIO GSNP
Chair: Michel Pleimling and Uwe Tauber, Virginia Polytechnic Institute and State University
Abstract ID: BAPS.2012.MAR.J42.1
Abstract: J42.00001 : Cyclic competition of four or more species: Results from mean field theory and stochastic simulations*
11:15 AM–11:51 AM
(Physics Department, Virginia Tech, Blacksburg, VA 24061)
Population dynamics is a venerable subject, dating back two centuries to Malthus, Verhulst, Lotka, Volterra, and many others. Nonetheless, new and interesting phenomena are continually being discovered. For example, the recent discovery of ``Survival of the Weakest'' in cyclic competition between 3 species with no spatial structure (Berr, Reichenbach, Schottenloher, and Frey, Phys. Rev. Lett. 102, 048102 (2009)) attracted considerable attention, e.g., http://www.sciencedaily.com/releases/2009/02/090213115127.htm. Considering a similar system with 4 or more species, we find a more intuitively understandable principle which appears to underpin all systems with cyclically competing species. We will present several interesting aspects of the 4 species system -- from non-linear dynamical phenomena in a deterministic mean-field approach to remarkable extinction probabilities in the stochastic evolution of a finite system. Some insights into the deterministic dynamics, gained from generalizing this system to one with any number of species with arbitrary pairwise interactions, will also be discussed.
*Supported in part by NSF-DMR-0904999 and 1005417.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2012.MAR.J42.1
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