  Ecological modelling of increasingly more complex microbial populations is
necessary to reflect the highly functional and diverse behaviour inherent to
many systems found in reality. Anaerobic digestion is one such process that has
benefitted from the application of mathematical analysis not only for
characterising the biological dynamics, but also to investigate emergent
behaviour not apparent by simulation alone. Nevertheless, the standard
modelling approach has been to describe biological systems using sets of
differential equations whose kinetics are generally described by some
empirically derived function of growth. The drawbacks of this are two-fold; the
growth functions are derived from empirical studies that may not be
representative of the system to be modelled and whose parameters may not have a
mechanistic meaning, and mathematical analysis is restricted by a conformity to
an assumption of the dynamics. Here, we attempt to address these challenges by
investigating a generalised form of a three-tier chlorophenol mineralising
food-web previously only analysed numerically. We examine the existence and
stability of the identified steady-states and find that, without a decay term,
the system may be characterised analytically. However, it is necessary to
perform numerical analysis for the case when maintenance is included, but in
both cases we verify the discovery of two important phenomena; i) the washout
steady-state is always stable, and ii) the two other steady-states can be
unstable according to the initial conditions and operating parameters.
