Woman who works with my wife at the college brought one of those chocolate stirring devices back from Mexico for me, because she knew I was a turner. Elaborately burned and perforated on the one I have. The turning itself is both wheel and axle in the circumstance. The rotary motion about an axis or axle needed to define a wheel is there, though it is also clear that this component of two of the Greeks' four fundamental machines was not developed, or if developed, not documented in Amerind cultures.
I'll stick with the AHD, where " wheel (hw¶l, w¶l) n. 1. A solid disk or a rigid circular ring connected by spokes to a hub, designed to turn around an axle passed through the center. 2. Something resembling such a disk or ring in appearance or movement or having a wheel as its principal part or characteristic, as: a. The steering device on a vehicle. b. A potter's wheel. c. A water wheel. d. A spinning wheel. ...."
The evidence for drought cited is only part of the picture. Populations decline to the level the food supply, which includes the available game, can support, then rise again with the food supply. Clearly this did not happen in this case. I'll stick with disease and/or warfare over available resources as the actual nail in the coffin. Most sources I've seen make a good deal of the fact that a static population easily decimates the undomesticated fauna within the distance required to sortie forth, kill, and bring back anything resembling edible high-quality protein. Fairly short distance in the tropics.