Vicariance biogeography, i.e., the erection of barriers causing speciation is the other school. Although the argument continues, no doubt both schools have played roles. Dispersal is the tendency for an organism to move from its natal or breeding site. Don't confuse this with dispersion which is the spatial distribution of individual organisms within a population. Three methods of dispersal Jump dispersal -long distance dispersal to remote areas by one or few individuals.
Examples are islands, remote mountains.
Chance or stochastity plays a large role. Humans accelerate this process. Think of how rapidly disease and invasive organisms can now spread. A flu pathogen is only a few hours, comparatively, to anywhere on earth. Spread of pathogens to New World by Europeans during exploration and colonization.