  We describe a continuous-time modelling framework for biological population
dynamics that accounts for demographic noise. In the spirit of the methodology
used by statistical physicists, transitions between the states of the system
are caused by individual events while the dynamics are described in terms of
the time-evolution of a probability density function. In general, the
application of the diffusion approximation still leaves a description that is
quite complex. However, in many biological applications one or more of the
processes happen slowly relative to the system's other processes, and the
dynamics can be approximated as occurring within a slow low-dimensional
subspace. We review these time-scale separation arguments and analyse the more
simple stochastic dynamics that result in a number of cases. We stress that it
is important to retain the demographic noise derived in this way, and emphasise
this point by showing that it can alter the direction of selection compared to
the prediction made from an analysis of the corresponding deterministic model.
