  Lately, experimental research on microbial symbioses based on nutrient
exchange and interdependence has yielded a number of interesting findings,
however an in-depth mathematical description of the exact underlying dynamics
of such symbiotic associations is still missing. Here, we derive and analyse a
mechanistic mathematical model of such a relationship in a continuous chemostat
culture based on five coupled differential equations. The influence of the
biological traits of the involved organisms on the position and stability of
the equilibrium states of the system is examined. We also demonstrate how
manipulating the external metabolite concentrations of the system can shift the
species interaction on a continuous spectrum ranging from mutualism over
commensalism to parasitism.
