19-22 October 2011
Hotel Roanoke, Roanoke VA
US/Eastern timezone
<font color=red><b>To upload your file, log in (@ top right), then click on your talk title, then click "Add Material" at the bottom of the page.</b></font>

Stochastic population oscillations in spatial predator-prey models

21 Oct 2011, 14:30
30m
Crystal Ballroom DE (Hotel Roanoke, Roanoke VA)

Crystal Ballroom DE

Hotel Roanoke, Roanoke VA

Speaker

Uwe TÄUBER (Virginia Tech)

Description

It is 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. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase. [See Preprint arXiv:1105.4242, and further refs. therein.]

Presentation Materials

Your browser is out of date!

Update your browser to view this website correctly. Update my browser now

×