  This paper formulates two 3D stochastic differential equations (SDEs) of two
microbial populations in a chemostat competing over a single substrate. The two
models have two distinct noise sources. One is general noise whereas the other
is dilution rate induced noise. Nonlinear Monod growth rates are assumed and
the paper is mainly focused on the parameter values where coexistence is
present deterministically. Nondimensionalising the equations around the point
of intersection of the two growth rates leads to a large parameter which is the
nondimensional substrate feed. This in turn is used to perform an asymptotic
analysis leading to a reduced 2D system of equations describing the dynamics of
the populations on and close to a line of steady states retrieved from the
deterministic stability analysis. That reduced system allows the formulation of
a spatially 2D Fokker-Planck equation which when solved numerically admits
results similar to those from simulation of the SDEs. Contrary to previous
suggestions, one particular population becomes dominant at large times.
Finally, we brie y explore the case where death rates are added.
