Aggregation methods in food chains with nutrient recycling
Kooi, B.W., Poggiale, J.C., Auger, P. and Kooijman, S. A. L. M. 2002.
Aggregation methods in food chains with nutrient recycling.
Ecological Modelling, 157: 69 - 86
This paper is devoted to the study of food chain models under batch
and chemostat conditions where nutrient recycling is taken into
account. The food chain is formed by a nutrient and two populations,
prey and predator (producers and consumers). Species at both trophic
levels digest their food source only partly. The unusable parts of the
food not used for growth is ejected in the reactor as faeces together
with metabolic products. The excreted material together with death
material, detritus, is decomposed and this gives the recycling of the
nutrient. In closed (batch-type environment) systems the elemental
matter needed by producers must be provided through recycling where
light energy from the environment supplies the necessary energy that
fuels the life processes. In open (chemostat-type environment) systems
this energy is added to the system via the chemical energy stored in
the organic compounds in the inflow.
An aggregation method is developed for situations in which each
trophic level is characterized by differing time scales. This allows
us the reduce the dimension of the model which gives good
approximations after the fast transient. We will show that in the
chemostat case first-order approximations are needed in order to get
the same qualitative long-term dynamics for both the full and the