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We study bifurcations in a spatially extended nonlinear system representingpopulation dynamics with the help of analytic calculations based on thetime-independent Schr\"{o}dinger equation for a quantum particle subjected to auniform gravitational field. Despite the linear character of theSchr\"{o}dinger equation, the result we obtain helps in the understanding ofthe onset of abrupt transitions leading to extinction of biologicalpopulations. The result is expressed in terms of Airy functions and sheds lighton the behavior of bacteria in a Petri dish as well as of large animals such asrodents moving over a landscape.

Extinction of Populations and the Schr\"{o}dinger Equation: Analytic Calculations for Abrupt Transitions