Abstract
Using ideas similar to Simpson's selection landscape, we set up a model of a population in a homogenous environment which varies gradually with time and location. This model exhibits allopatric speciation at the periphery of its range and reinvasion by the descendant species, without postulating the appearance and disappearance of geographic barriers. Thom's celebrated theory of catastrophes implies that it can be safely assumed in this model that any allopatric speciation must arise from the fold catastrophe. The theory also predicts that the morphological variation in the vicinity of the speciation obeys a square root law, which in principle can be tested.
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