It seems to me that for Darwin the pulsing of evolutionary rates was a strictly vertical phenomenon.
Ernst MayrNew gene pools are generated in every generation, and evolution takes place because the successful individuals produced by these gene pools give rise to the next generation.
Ernst MayrA 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.
Ernst MayrThe reduced variability of small populations is not always due to accidental gene loss, but sometimes to the fact that the entire population was started by a single pair or by a single fertilized female. These 'founders' of the population carried with them only a very small proportion of the variability of the parent population. This 'founder' principle sometimes explains even the uniformity of rather large populations, particularly if they are well isolated and near the borders of the range of the species.
Ernst Mayr