Geographic Range Shifts under Climate Warming
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Rapid climate warming has caused species across the globe to shift their geographic ranges, and ecologists are increasingly concerned about whether species are able to track climate warming. Early efforts to predict species ranges used statistical correlation models that neglected population dynamics. Recently, theoretical ecologists have begun to incorporate both population growth and dispersal in their models. Integrodifference equations are useful in describing spatiotemporal dynamics of species with distinct growth and dispersal stages. These equations can accommodate a diverse assortment of dispersal mechanisms. I incorporated climate warming into some classic examples of integrodifference equations by letting the niche curve, a curve describing environmental suitability for population growth on a spatial gradient, shift in one direction. The equations thus become non-autonomous. Using a series of these non-autonomous integrodifference equations, I investigate the impact of changing climatic conditions on a single-species population. These integrodifference equations can prescribe climate-warming scenarios and environmental heterogeneity in a versatile way. These new models capture the range-shift phenomenon. A population experiencing niche-curve shifts exhibits traveling pulse solutions when it persists. The population may, however, lag behind the shifting niche curve, and carry a niche deficit. The niche deficit may stabilize at a level, or keep accumulating, depending on the acceleration of climate warming. Acceleration of climate warming is shown to impose extra burden on the species, compared with constant-speed warming, even if the amount of warming is the same over the same period of time for a fair comparison. The population experiencing climate warming may also fail to persist, and go extinct, if climate warming is too rapid. The threshold speed for persistence, or the critical speed, c*, can be viewed as the species' ability to keep up with climate warming. This critical speed depends both on the species' growth or recruitment, and its dispersal.
- Applied mathematics