  The position of propagating population fronts fluctuates because of the
discreteness of the individuals and stochastic character of processes of birth,
death and migration. Here we consider a Markov model of a population front
propagating into a metastable state, and focus on the weak noise limit. For
typical, small fluctuations the front motion is diffusive, and we calculate the
front diffusion coefficient. We also determine the probability distribution of
rare, large fluctuations of the front position and, for a given average front
velocity, find the most likely population density profile of the front.
Implications of the theory for population extinction risk are briefly
considered.
