The dynamics of a tri-trophic food chain with two-component populations from a biochemical perspective

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.