Multiscaling analysis of a slowly varying single species population model displaying an Allee effect

We consider the growth of a single species population modelled by a logistic equation modified to accommodate an Allee effect, in which the model parameters are slowly varying functions of time. We apply a multitiming technique to construct general approximate expressions for the evolving population in the case where the population survives to a (slowly varying) finite positive limiting state, and that where the population declines to extinction. We show that these expressions give excellent agreement with the results of numerical calculations for particular instances of the changing model parameters.