The end of the last Ice Age (Pleistocene) saw: 1)§significant climate and vegetation changes, 2) the§introduction of humans to the New World, and 3) major§megafaunal extinctions.§The leading theories of these extinctions climate§change and overkill are inadequate neither explains§why: 1) ruminants survived better than non-ruminants;§2) many mammal species were diminished in size; or 3)§why vegetative environments shifted.§Climate change does not explain why climate changes§of similar magnitude did not lead to similar§extinctions. §Overkill links extinction with humans hunting§herbivores, but omits the reciprocal impact, of prey§decline on predators, yet kanon predator/prey§models show predators cannot hunt prey to extinction.§The Second Order Predation theory handles these§concerns. It holds that humans reduced predator§populations, leading to a megaherbivore boom,§over-consumption of plants, environmental exhaustion,§and extinctions. The mathematical model developed to§test this hypothesis is the only one to date that can§be used to compare all three extinction theories.