Title: Fluctuations and Phase Transitions in Lattice Models for
Predator-Prey Interaction

Authors: M. Mobilia, I. T. Georgiev and U. C. Taeuber

Abstract: Including spatial structure and stochastic noise invalidates
the classical Lotka-Volterra picture of stable regular population cycles
emerging in models for predator-prey interactions. Growth-limiting terms
for the prey induce a continuous extinction threshold for the predator
population whose critical properties are in the directed percolation
universality class, as indicated by field-theoretic arguments supported 
by Monte Carlo simulation results.
     We discuss the robustness of this scenario by considering 
an ecologically inspired stochastic lattice predator-prey model variant
where the predation process includes next-nearest-neighbor interactions.
We find that the corresponding stochastic model reproduces the above
scenario in dimensions 1< d \leq 4, in contrast with mean-field theory
which predicts a first-order phase transition. However, the mean-field
features are recovered upon allowing for nearest-neighbor particle
exchange processes, provided these are sufficiently fast.

References 

M. Mobilia, I. T. Georgiev, U. C. Taeuber, Phys. Rev. E 73, 04903(R) (2006)
M. Mobilia, I. T. Georgiev, U. C. Taeuber, accepted in Journal of
Statistical Physics,  (http://arxiv.org/q-bio.PE/0512039)