Steve points me to this article which reports on a paper in PNAS (not online) that falsifies a climate-only hypothesis for North American megafaunal extinctions 11,000 years B.P. by using the islands of Cuba and Hispaniola as controls. Ground sloths disappeared from these islands 6,000 years ago, at about the time humans arrived. In After the Ice: A Global Human History 20,000-5000 BC Steve Mithen also points out that the Wrangel Island Mammoths disappeared at around the time that the first evidence of human occupation can be discerned. Mithen also reports that he and a graduate student designed a computer model which simulated the effects on population size of megafauna due to climate change, and noted that when human hunting was added into system the population predictably tended to not recover from periods of simultaneous hunting and environmental stress. The fact that the megafuna of African still survive is likely a testament to the coevolution that must have occurred between the various ungulates and other assorted herbivores and hominid groups over the eons. The only quibble I might have with the narrative above is that it seems to presuppose a Clovis kill off, and Mithen seems to reflect that the consensus in the archeological profession that Monte Verde, at least, predates Clovis by thousands of years, so that particular chapter of the book is rather unsatisfying if you are looking for answers since the author basically moots confusions and mysteries that need to be resolved in the next few years.