  Microbial populations in the natural environment are likely to experience
growth conditions very different from those of a typical laboratory xperiment.
In particular, removal rates of biomass and substrate are unlikely to be
balanced under realistic environmental conditions. Here, we consider a single
population growing on a substrate under conditions where the removal rates of
substrate and biomass are not necessarily equal. For a large population, with
deterministic growth dynamics, our model predicts that this system can show
transient (damped) oscillations. For a small population, demographic noise
causes these oscillations to be sustained indefinitely. These oscillations
arise when the dynamics of changes in biomass are faster than the dynamics of
the substrate, for example, due to a high microbial death rate and/or low
substrate flow rates. We show that the same mechanism can produce sustained
stochastic oscillations in a two-species, nutrient-cycling microbial ecosystem.
Our results suggest that oscillatory population dynamics may be a common
feature of small microbial populations in the natural environment, even in the
absence of complex interspecies interactions.
