Actually, I suspect the combination was a major factor. Even trees have shifted their range north to south in response to the various phases of the ice age. Extinctions seem to be the result of sudden, drastic changes to which the organisms in question do not have time to adapt by natural selection.
Man is such an agent of drastic change.
Another example would be the interfaunal exchange that took place between North and South America. Sure, one may see that a species was in decline in that area.