Evolution of stepping-stone dispersal rates

We present a general model of the evolution of dispersal in a population wi th any distribution of dispersal distance. We use this model to analyse evo lutionarily stable (ES) dispersal rates for the classical island model of d ispersal and for three different stepping-stone models. Using general techn iques to compute relatedness coefficients in the different dispersal models which we consider, we find that the distribution of dispersal distance may affect the ES dispersal rate when the cost of dispersal is low In this cas e the ES dispersal rate increases with the number of demes that can be reac hed by one dispersal event. However, for increasing cost the ES dispersal r ate converges to a value independent of the distribution of dispersal dista nce. These results are in contrast to previous analyses of similar models. The effects of the size (number of demes) and shape (ratio between the widt h and the length) of the population on the evolution of dispersal are also studied. We find that larger and more elongated populations lead generally to higher ES dispersal rates. However, both of these effects can only be ob served for extreme parameter values (i.e. for very small and very elongated populations). The direct fitness method and the analytical techniques used here to compute relatedness coefficients provide an efficient way to analy se ES strategies in subdivided populations.