A Model of Population Growth, Dispersal and Evolution in a Changing Environment

The climatic and biotic conditions at any geographic location will change through time, for example, because of the advance of glaciers. If it is to avoid extinction, a species adapted to a moving habitat must either track its habitat spatially, or adapt genetically to the new environmental conditions. These processes of migration and evolution are important in determining continental biogeographic patterns. We develop a model to explore the relative contributions of adaptation and dispersal as alternative mechanisms whereby a population can respond to changing environmental conditions. In our model the environment to which the species is adapted moves across the landscape at a constant velocity, and a quantitative trait determines each individual's fitness as a function of the local environmental conditions. Local populations are allowed to adapt genetically to the environmental conditions at each point in space, so that a cline develops in the quantitative character. We find that if the rate of environmental movement is slow, the species will track its environment across space, otherwise it will go extinct. Additionally, the higher the genetic variance in the character, the easier it is for the species to maintain itself in a moving environment. Our results generalize previous models that predict a critical patch size of suitable habitat necessary for population persistence.