Density outbursts in a food web model with closed nutrient cycle

TL;DR

This study models a spatial food web with a closed nutrient cycle, revealing two long-term states and identifying nutrient detritus percolation and top predators as key factors in system stability and density outbursts.

Contribution

The paper introduces a novel spatial food web model with a closed nutrient cycle and analyzes the emergence of density outbursts and stability mechanisms through Monte Carlo simulations.

Findings

Density outbursts (waves) are linked to detritus percolation.

Two asymptotic states: extinction and coexistence.

Top predators are crucial for food web stability.

Abstract

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).