One major concern of global warming is that the rate of climate change may be too rapid to allow populations to adapt, causing higher rates of extinction. In this talk, I modify a pre-existing mathematical model to examine how the rate of environmental change can affect the dynamics of local adaptation and extirpation. The model, first introduced by Doebeli and Dieckmann (2003, nature), assumes that an environmental gradient exists which interacts with individuals in a population, where mortality rates determined by both the gradient and local population densities. They showed that the gradient allows the population to adapt locally, resulting in polymorphism in the population due to evolutionary branching.

In this talk, We explore how environmental change affects the population through habitat shift and local adaptation. We assumed that the environmental gradient keeps a constant slope but shifts in a parallel fashion at a specified, constant rate. We find that the population-level responses to the speed of environmental change can be classified into four types (extinction, habitat shift & extinction, habitat shift & multiple branching, and viable). This result promotes a better understanding of ecological and evolutionary responses to climate change.