"Speed and shape of population fronts with density dependent diffusion"Stokes, BethUnderstanding how and why animal populations disperse is a key question in movement ecology. There are many reasons for dispersal, such as overcrowding and searching for food, territory or potential mates. These behaviours are often dependent on the local density of the population. Motivated by this, we investigate an FKPP equation with density dependent diffusion. Using a combination of linear stability analysis and variational arguments, we derive bounds on the minimum realisable wavespeed of travelling wave solutions for different diffusion functions. We find that the linear stability analysis suggests that the wavespeed is entirely determined by diffusion at zero density, regardless of how the function behaves on the rest of the domain. Applying the variational arguments, we then see how the selected wavespeed may differ from this, depending in more detail on the diffusion profile across all densities. We explore the system dynamics across both discrete and continuous domains, and present results for the wavespeed and shape of travelling wave fronts with diffusion functions describing a variety of cases of both positive and negative density dependence. |
« back