  We investigate travelling wave solutions in reaction-diffusion models of
animal range expansion in the case that population diffusion is
density-dependent. We find that the speed of the selected wave depends
critically on the strength of diffusion at low density. For sufficiently large
low-density diffusion, the wave propagates at a speed predicted by a simple
linear analysis. For small or zero low-density diffusion, the linear analysis
is not sufficient, but a variational approach yields exact or approximate
expressions for the speed and shape of population fronts.
