Darwin attributed the absence of species transitions in the fossil record to his hypothesis that speciation occurs within isolated habitat patches too geographically restricted to be captured by fossil sequences. Mayr's peripatric speciation model added that such speciation would be rapid, further explaining missing evidence of diversification. Indeed, Eldredge and Gould's original punctuated equilibrium model combined Darwin's conjecture, Mayr's model and 124 years of unsuccessfully sampling the fossil record for transitions. Observing such divergence, however, could illustrate the tempo and mode of evolution during early speciation. Here, we investigate peripatric divergence in a Miocene stickleback fish, Gasterosteus doryssus. This lineage appeared and, over approximately 8000 generations, evolved significant reduction of 12 of 16 traits related to armour, swimming and diet, relative to its ancestral population. This was greater morphological divergence than we observed between reproductively isolated, benthic-limnetic ecotypes of extant Gasterosteus aculeatus. Therefore, we infer that reproductive isolation was evolving. However, local extinction of G. doryssus lineages shows how young, isolated, speciating populations often disappear, supporting Darwin's explanation for missing evidence and revealing a mechanism behind morphological stasis. Extinction may also account for limited sustained divergence within the stickleback species complex and help reconcile speciation rate variation observed across time scales.