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.