Abstract
One extinction hypothesis of the Columbian mammoth (Mammuthus columbi ), called overkill, theorizes that early humans overhunted the animal. We employ two dierent approaches to test this hypothesis mathematically: analyze the stability of the equilibria of a 2D ordinary dierential equations (ODE) system and develop a metapopulation dierential equations model. The 2D ODE system is a modied predator-prey model that also includes migration. The metapopulation model is a spatial expansion of the rst model on a rectangular grid. Using this metapopulation system, we model the migration of humans into North America and the response in the mammoth population. These approaches show evidence that human-mammoth interaction would have aected the extinction of the Columbian mammoth during the late Pleistocene.
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