Effects of variations in adaptation potential on invasion speeds and species ranges

Confronted with global changes and their potential impacts on biodiversity, an important question is to understand the ecological and evolutionary determinants of species geographical distributions. In order to understand how adaptation in heterogeneous environments constrains such distributions, we analyze how the potential of adaptation along an environmental cline affects the geographical distribution and propagation dynamics (invasion or extinction) of a single species. We re-analyse a model initially proposed by Kirkpatrick and Barton using propagation speed to assess whether species distribution is spatially limited or not. We found that for big adaptation potentials, the species invades space following Fishers model, whereas for small adaptation potentials the propagation depends on the evolutionary challenge to overcome. We have explicit approximations for the propagation speeds in both cases. We discuss the utility of these propagation speeds as an eco-evolutionary index based on empirical studies.