  A spatial three level food web model with a closed nutrient cycle is
presented and analyzed via Monte Carlo simulations. The time evolution of the
model reveals two asymptotic states: an absorbing one with all species being
extinct, and a coexisting one, in which concentrations of all species are
non-zero. There are two possible ways for the system to reach the absorbing
state. In some cases the densities increase very quickly at the beginning of a
simulation and then decline slowly and almost monotonically. In others, well
pronounced peaks in the $R$, $C$ and $D$ densities appear regularly before the
extinction. Those peaks correspond to density outbursts (waves) traveling
through the system. We investigate the mechanisms leading to the waves. In
particular, we show that the percolation of the detritus (i. e. the
accumulation of nutrients) is necessary for the emergence of the waves.
Moreover, our results corroborate the hypothesis that top-level predators play
an essential role in maintaining the stability of a food web (top-down
control).
