  Understanding whether a population will survive and flourish or become
extinct is a central question in population biology. One way of exploring this
question is to study population dynamics using reaction-diffusion equations,
where migration is usually represented as a linear diffusion term, and
birth-death is represented with a bistable source term. While linear diffusion
is most commonly employed to study migration, there are several limitations of
this approach, such as the inability of linear diffusion-based models to
predict a well-defined population front. One way to overcome this is to
generalise the constant diffusivity, $D$, to a nonlinear diffusivity function
$D(C)$, where $C>0$ is the density. While it has been formally established that
the choice of $D(C)$ affects long-term survival or extinction of a bistable
population, working solely in a classical continuum framework makes it
difficult to understand precisely how the choice of $D(C)$ affects survival or
extinction. Here, we address this question by working with a simple discrete
simulation model that is easy to interpret. The continuum limit of the discrete
model is a nonlinear reaction-diffusion equation, where the flux involves a
nonlinear diffusion term and the source term is given by the strong Allee
effect bistable model. We study population extinction/survival using this very
intuitive discrete framework together with numerical solutions of the
reaction-diffusion continuum limit equation. This approach provides clear
insight into how the choice of $D(C)$ either encourages or suppresses
population extinction relative to the classical linear diffusion model.
