The dynamics of a tri-trophic food chain with two-component populations from a biochemical perspective
Hanegraaf, P.P.F. and Kooi, B.W. 2002.
The dynamics of a tri-trophic food chain with two-component populations from a biochemical perspective.
Ecol. Modell., 152: 47 - 64.
Theoretical considerations and curve fitting of data support the
proposition that models for heterotrophic organisms are more realistic
when individuals consist of two components: reserves and structure.
Predators that prey on a population of such individuals can choose to
assimilate the reserves or the structure of the prey, or both. As a
consequence, the Holling type II description we use for predator-prey
interaction has to be revised. In this article we study
tri-trophic food chains with two-component populations in a chemostat.
The influence of different degrees of assimilation of reserves and
structure on the long-term dynamics of the food chain is studied with
bifurcation analysis of the governing system of ODEs. The
results presented in bifurcation diagrams show large quantitative
effects. The modelling will start at the individual level. The two
components of the prey are assimilated in parallel and the usable
portions are added to a common storage pool, the reserves. The energy
stored in these reserve materials is used for maintenance and growth.
The three processes, assimilation, maintenance and growth, are
modelled as chemical reactions where mass and energy conservation laws
are obeyed. With stationary solutions the growth rate has to be
positive in order to compensate for predation and other causes of
depletion. However with oscillatory solutions, reversed growth can
occur when time-periods exist where the reserves are less than needed
to pay maintenance costs. When reversed growth is allowed, the two
components can be transformed into each other without heat or product
formation, which is unrealistic. This calls for a constraint on the
maintenance requirements so that reversed growth does not occur.
This constraint yields a new cause for extinction by nutrient enrichment
for the two-component model.