It seems to me that for Darwin the pulsing of evolutionary rates was a strictly vertical phenomenon.
Ernst MayrBiology can be divided into the study of proximate causes, the study of the physiological sciences (broadly conceived), and into the study of ultimate (evolutionary) causes, the subject of natural history.
Ernst MayrThe major novelty of my theory was its claim that the most rapid evolutionary change does not occur in widespread, populous species, as claimed by Most geneticists, but in small founder populations.
Ernst Mayr