Bi-trophic food chain dynamics with multiple component populations

Kooi, B.W. and Hanegraaf, P.P.F. 2001. Bi-trophic food chain dynamics with multiple component populations. Bull. Math. Biol., 70: 271 - 299.


Food web models describe the patterns of material and energy flow in communities. In classical food web models the state of each population is described by a single variable which represents, for instance, the biomass or number of individuals that make up the population. However, in a number of models proposed recently in the literature the individual organisms consist of two components. In addition to the structural component there is an internal pool of nutrients, lipids or reserves. Consequently the population model for each trophic level is described by two state variables instead of one. As a result the classical predator--prey interaction formalisms have to be revised. In our model time budgets with actions as searching and handling provide the formulation of the functional response for both components. In the model, assimilation of the ingested two prey components is done in parallel and the extracted energy is added to a predators reserve pool. The reserves are used for vital processes; growth, reproduction and maintenance. We will explore the top-down modelling approach where the perspective is from the community. We will demonstrate that this approach facilitates a check on the balance equations for mass and energy at this level of organisation. Here it will be shown that, if the individual is allowed to shrink when the energy reserves are in short to pay the maintenance costs, the growth process has to be 100\% effective. This is unrealistic and some alternative model formulations are discussed. The long-term dynamics of a microbial food chain in the chemostat are studied using bifurcation analysis. The dilution rate and the concentration of nutrients in the reservoir are the bifurcation parameters. The studied microbial bi-trophic food chain with two-component population models shows chaotic behaviour.

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