Effects of gradual spatial variation in resources on population extinction: Analytic calculations for abrupt transitions

We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations. The result we obtain helps in the understanding of the onset of abrupt transitions leading to the extinction of biological populations. The result is expressed in terms of Airy functions and sheds light on the behavior of bacteria in a Petri dish as well as of large animals such as rodents moving over a landscape.