Discrete-time growth-dispersal models with shifting species ranges

Many species are responding to global climate change by shifting their ranges poleward in latitude or upward in elevation. We analyze an integrodifference equation that combines growth, dispersal, and a constant-speed, climate-induced range shift and find that a shifting population can die out, even if the width of its range remains constant. We show how to determine the critical range-shift speed (for extinction) and study the effects of the growth rate and of the shape and scale of the dispersal kernel on persistence.