Thanks for the ping. I found this especially interesting: "A prolonged arid phase from about 70,000 to 12,000 years ago apparently drove humans out of the region, but then the rains returned along with the people."
The prolonged arid phase from about 70,000 to 12,000 years ago corresponds to the last "ice age" in North America, and the return of the rains corresponds to the melting of the North American ice sheet.
The lack of ice in Africa at that time suggests it wasn't a global ice age, but an arctic ice cap centered on what is now Hudson Bay, Canada.
I've read that it collapsed/melted in the 7-8,000 year time frame.