  We propose a formal framework based on collective coordinates to reduce
infinite-dimensional stochastic partial differential equations (SPDEs) with
symmetry to a set of finite-dimensional stochastic differential equations which
describe the shape of the solution and the dynamics along the symmetry group.
We study SPDEs arising in population dynamics with multiplicative noise and
additive symmetry breaking noise. The collective coordinate approach provides a
remarkably good quantitative description of the shape of the travelling front
as well as its diffusive behaviour, which would otherwise only be available
through costly computational experiments. We corroborate our analytical results
with numerical simulations of the full SPDE.
