Aggregation methods in food chains

Abstract

The aim of this paper is to apply aggregation methods to food chains under batch and chemostat conditions. These predator-prey systems are modelled using ODEs, one for each trophic level. Because the models are based on mass conservation laws, they are conservative and this allows perfect aggregation. Furthermore, it is assumed that the ingestion rate of the predator is smaller than that of the prey. On this assumption, approximate aggregation can be performed, yielding further reduction of the dimension of the system. We will study a food chain often found in wastewater treatment plants. This food chain consists of sewage, bacteria, and worms. In order to show the feasibility of the aggregation methods, we will compare simulated results for the reduced and the full model of this food chain under chemostat conditions.