When Toba blew it's top 75,000 years ago, I've seen it quoted a number of times that only 2,000-5,000 humans worldwide survived. The only difference in the statements is how many humans survived. Not once do they mention how many squirrels, grizzlies, buffalo, elephants, etc. survived.
I can believe Vollmond's idea that all humans may have done is polish off already declining populations.
I recently read that for 99% of the time that there have been humans, the average life span was about 18 years, that does not support large populations of humans. But, contrary to that, we do know that some of the oldest human skeletons ever found in the Americas (Spirit Cave Man, Kennewick Man) died in their mid-40's. The women skeletons found (Buhl Woman, Luzia) died before the age of 25.