Dispersal and interbreeding as survival strategies for species exposed to environment change

The success of individual species under a change to the environment is dependent on a number of factors, which include the changes to habitat, competition with other species and adaptability. Here we investigate the impact of differing dispersal characteristics of two competing species responding to the change using an idealized spatio-temporal model. The rate of dispersion is given by a combination of the growth term and the form of the diffusion term, which is set to give either normal diffusion or anomalous (super) diffusion. The later is brought about by employing fractional diffusion and we characterize the population as being more adventurous than the population undergoing normal diffusion. The more adventurous population is found, not surprisingly, to reach and occupy uninhabited ground before the population undergoing normal diffusion can get there. Interbreeding is found to be important in that it can aid the spread of the less adventurous population preventing its extinction. The response to an abrupt environment change, taken here to be a change in the distribution of the growth rate, is dependent on the initial conditions, the dispersion characteristics, and the level of interbreeding, leading to very different intermediate and final states. Our results highlight instances when a particular dispersal strategy gives a population an edge over another. In the cases considered here we find states where the more adventurous population can dominate across the domain, the two populations exist in separate parts of the domain separated by fronts, and both populations coexist across the domain in the medium term with one or other of the populations dominating across the domain in the long term. Given the long time to reach equilibrium where one or other of the populations dominate, consideration needs to be put to the time scale of change, as sufficiently frequent change can allow coexistence. We demonstrate the need to include dispersion characteristics when considering the factors affecting the response of species to a change in the environment.