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Uwe C. Tauber (Virginia Tech)

Stochastic predator-prey models: population oscillations,
spatial correlations, and the effect of randomized rates

 

Abstract

It is now well established that including spatial structure and stochastic
noise in models for predator-prey interactions invalidates the classical
deterministic Lotka-Volterra picture of neutral population cycles. In contrast,
stochastic models yield long-lived, but ultimately decaying erratic population
oscillations, which can be understood through a resonant amplification
mechanism for density fluctuations. Monte Carlo simulations of spatial
stochastic predator-prey systems yield striking complex spatio-temporal
structures. These spreading activity fronts induce persistent correlations
between predators and prey. Fluctuation-induced renormalizations of the
oscillation frequency and damping can be studied through field-theoretic
methods. In this talk, I shall also address the influence of spatially varying
reaction rates on a stochastic two-species Lotka-Volterra lattice model. The
effects of this quenched randomness on population densities, transient
oscillations, spatial correlations, and invasion fronts are investigated
through Monte Carlo simulations. We find that spatial variability in the
predation rate results in more localized activity patches. Population
fluctuations in rare favorable regions in turn cause a remarkable increase in
the asymptotic population densities of both predators and prey, and also lead
to accelerated front propagation.

References:

- M. Mobilia, I.T. Georgiev, and U.C.T., Phys. Rev. E 73, 040903(R) (2006)
[q-bio.PE/0508043]
- M. Mobilia, I.T. Georgiev, and U.C.T., J. Stat. Phys. 128, 447 (2007)
[q-bio.PE/0512039]
- M.J. Washenberger, M. Mobilia, and U.C.T., J. Phys. Condens. Matter 19,
065139 (2007) [cond-mat/0606809]
- U. Dobramysl and U.C.T., Phys. Rev. Lett. 101, 258102 (2008)
[arXiv:0804.4127]

Presentation

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