The cane toads invasion in Australia: front slowdown due to non-local interactions

At the beginning of the 20th century, the cane toads were introduced to Australia in the hopes that they would curb the population of a pest that was destroying sugar cane crops (they did not).  Instead, this poisonous, competitively advantaged species caused ecological disruption and became the subject of interest from biologists who noticed that their habitat was growing at increasing over time.  In this talk, I will discuss a mathematical model for the population density of the cane toads that, by incorporating evolution of a dispersal trait, allows for the observed acceleration of the habitat.  Our goal in analyzing this model is to establish precise estimates on the invasion speed; however, the reaction-diffusion-evolution model involves long-range non-local interactions that cause serious technical difficulties and alter the long-time dynamics from what might be naively predicted.