Density outbursts in a food web model with a closed nutrient cycle

A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The food web consists of three trophic levels. The basal level species (called resources  , R$R$) corresponds to primary producers in real ecosystems. The species at an intermediate level (consumers  , C$C$) relates to herbivores. It feeds on the resources. The consumers themselves constitute food for the top level species (predators  , P$P$), which corresponds to carnivores. The remains of the consumers and predators (detritus  , D$D$) provide nutrient for the resources. 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$R$, C$C$ and D$D$ 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).