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In this paper, we study the influence of an Allee effect on the spreadingrate in a local reaction-diffusion-mutation equation modelling the invasion ofcane toads in Australia. We are, in particular, concerned with the case whenthe diffusivity can take unbounded values. We show that the accelerationfeature that arises in this model with a Fisher-KPP, or monostable,non-linearity still occurs when this non-linearity is instead bistable, despitethe fact that this kills the small populations. This is in stark contrast tothe work of Alfaro, Gui-Huan, and Mellet-Roquejoffre-Sire in related models,where the change to a bistable non-linearity prevents acceleration.

Super-linear spreading in local bistable cane toads equations