According to the concept of transformational evolution, first clearly articulated by Lamarck, evolution consists of the gradual transformation of organisms from one condition of existence to another.

A new species develops if a population which has become geographically isolated from its parental species acquires during this period of isolation characters which promote or guarantee reproductive isolation when the external barriers break down.

Indeed, I was unable to find any evidence whatsoever of the occurrence of a drastic evolutionary acceleration and genetic reconstruction in widespread, populous species.

Paleontologists had long been aware of a seeming contradiction between Darwin's postulate of gradualism, confirmed by the work of population genetics, and the actual findings of paleontology. Following phyletic lines through time seemed to reveal only minimal gradual changes but no clear evidence for any change of a species into a different genus or for the gradual origin of an evolutionary novelty. Anything truly novel always seemed to appear quite abruptly in the fossil record.

Wherever we look at the living biota … discontinuities are overwhelmingly frequent…The discontinuities are even more striking in the fossil record. New species usually appear in the fossil record suddenly, not connected with their ancestors by a series of intermediates.

Evolution ... is opportunistic, hence unpredictable.

I had found again and again that the most aberrant population of a species - often having reached species rank, and occasionally classified even as a separate genus - occurred at a peripheral location, indeed usually at the most isolated peripheral location.