Emergent behaviour in a chlorophenol-mineralising three-tiered microbial `food web'

Generalised approach to modelling a three-tiered microbial food-web

“…In Section 5 we perform local stability analysis of the steady-states without maintenance, and in Section 6, perform a comprehensive numerical stability analysis of the four cases for both the model with and without a decay constant. We show that our approach leads to the discovery of five operating regions, in which one leads to the possibility of instability of the positive steady state, where all three organisms exist, a fact that has not be reported by [10]. Indeed, we prove that a stable limit-cycle can occur in this region.…”

“…The model developed in [10] has six components, three substrate (chlorophenol, phenol and hydrogen) and three biomass (chlorophenol, phenol and hydrogen degraders) variables. The substrate and biomass concentrations evolve according to the six-dimensional dynamical of ODEs…”

“…Although the authors were not able to determine the general conditions under which this four dimensional syntrophic consortium was stable, further work has shown that a model with generality can be used to answer the question posed, determining that the two-tiered food-chain is always stable when maintenance is included [9]. In a more recent example, the model described by [8] was extended by the addition of a third organism and substrate to create a three-tiered 'food-web' [10]. In this model, the stability of some steady-states could be determined analytically, but due to the complexity of the Jacobian matrix for certain steady-states, local solutions were necessary using numerical analysis, when considering the full system behaviour.…”

“…In this model, the stability of some steady-states could be determined analytically, but due to the complexity of the Jacobian matrix for certain steady-states, local solutions were necessary using numerical analysis, when considering the full system behaviour. Although the results were important in revealing emergent properties of this extended model, the motivation of this work is to determine whether the approach carried out in [9], can be applied to the three-tiered model from [10], to provide some general properties of that system.…”

“…The paper is organised as follows. In Section 2, we present a description of the model to be investigated, before providing an alternative reduction of its structure than that given by [10], in Section 3. With Section 4 we demonstrate the existence of the three steadystates and define four interesting cases for specific parameter values that are investigated using the analytical solutions, whilst also indicating the regions of existence of the steady-states for the operating parameter values (dilution rate and substrate input concentration).…”