  Stochastic simulations of cyclic three-species spatial predator-prey models
are usually performed in square lattices with nearest neighbor interactions
starting from random initial conditions. In this Letter we describe the results
of off-lattice Lotka-Volterra stochastic simulations, showing that the
emergence of spiral patterns does occur for sufficiently high values of the
(conserved) total density of individuals. We also investigate the dynamics in
our simulations, finding an empirical relation characterizing the dependence of
the characteristic peak frequency and amplitude on the total density. Finally,
we study the impact of the total density on the extinction probability, showing
how a low population density may jeopardize biodiversity.
