Food web model with detritus path

We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agents on the lowest level produce food from dead agents (detritus) of the upper levels and are themselves eaten by the first level species, which in turn are prey for the top level species. Agents which do not find food in a given time, die with a given probability, while eating enables them to produce offspring in their neighborhood. This rule applies to species on all levels, including the lowest one. The dynamics is therefore nutrient limited. We are considering two pathways - grazers and detritus (using dead organic matter). We show that the emerging dynamics is more complex than the ordinary predator-prey systems in which bottom species are indestructible. We investigate the viability of our model and we construct appropriate (extinct-alive) phase diagrams. We demonstrate how the temporal fluctuations in the densities of the three populations are correlated. We show also that the density of the middle level agents plays the key role in the viability of the investigated food web.