A note on population growth in a variable environment.

Some properties of diffusion approximations to models of population dynamics in a variable environment are noted and discussed. A counter-intuitive feature of these models is that a larger mean population can lead to instability, given a particular level of variation. The need to consider different types of stochastic variation is stressed. Migration is shown to be either stabilising or destabilising, depending on the balance of effects of different types of variation.