Cut off from the larger gene pool by geographic barriers, a small amount of variation would be amplified by selection. The problem with this theory is that there isn't any positive evidence to support it. It claims that gradual evolution happens so quickly, in such limited areas, that the chances of finding any transitional fossils is essentially zero. Transitional fossils haven't been found, which is what the theory of Punctuated Equilibrium predicts. So, the fossils that haven't been found are claimed as support for the theory.
Many people think that transitional fossils have been found.
They usually cite the evolution of the horse as an example. It showed a sequence of mounted skeletons, each one larger and with a more well-developed hoof than the last. Almost a century later, paleontologist George Gaylord Simpson reexamined horse evolution and concluded that generations of students had been misled. I don't know if those science teachers tell their students that this is an obsolete theory that has been discredited, but both books present the figures as if this development of the horse is still believed to be true by paleontologists. It may be possible that generations of students are still being misled.