
STOCHASTIC SPATIAL LOTKAVOLTERRA PREDATORPREY MODELSUwe C. Täuber (Personal webpage)Department of Physics, Virginia Tech
Dynamical models of interacting populations have recently become offundamental interest for the spontaneous formation of patterns andother intriguing features in nonequilibrium statistical physics.In turn, theoretical physics provides a toolbox for quantitative analysis for many paradigmatic models employed in biology and ecology.Stochastic, spatially extended models for predatorprey interactiondisplay striking spatiotemporal structures [1,2] that are not capturedby the LotkaVolterra meanfield rate equations. These spreading activity fronts induce persistent correlations between predators and prey that can be studied through fieldtheoretic methods [3]. Introducing local restrictions on the prey population induces predator extinction. The critical dynamics at this continuous absorbing state transition is governed by the scaling exponents of critical directed percolation [4]. This lecture will also address the influence of spatially varying reaction rates: Fluctuations in rare favorable regions cause a remarkable increase in both predator and prey populations [5]. Intriguing novel features are found when variable interaction rates are affixed to individual particles rather than lattice sites. The ensuing stochastic dynamics combined with inheritance rules causes rapid time evolution for the rate distributions, with however overall neutral effect on stationary population densites [6]. When we subject the systemto a periodically varying carrying capacity that describes seasonally oscillating availability of resources for the prey population, we observe intriguing stabilization of the twospecies coexistence regime [7]. The lecture will finally briefly discuss noiseinduced spontaneous pattern formation and the stabilization of vulnerable ecologies through immigration waves in systems with three cyclically competing speciesakin to spatial rockpaperscissors games [8]. This research is supported by the U.S. National Science Foundation, Division of Mathematical Sciences under Award No. NSF DMS2128587.
References:
[1] M. Mobilia, I.T. Georgiev, and U.C.T., J. Stat. Phys. 128, 447 (2007); arXiv:qbio.PE/0512039. 