One extinction hypothesis of the Columbian mammoth (Mammuthus columbi), called overkill, theorizes that early humans overhunted the animal. We employ two different approaches to test this hypothesis mathematically: analyze the stability of the equilibria of a 2D ordinary differential equations (ODE) system and develop a metapopulation differential equations model. The 2D ODE system is a modified predator-prey model that also includes migration. The metapopulation model is a spatial expansion of the first 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 affected the extinction of the Columbian mammoth during the late Pleistocene.
Frank, Michael; Slaton, Anneliese; Tinta, Teresa; and Capaldi, Alex
"Investigating Anthropogenic Mammoth Extinction with Mathematical Models,"
Spora: A Journal of Biomathematics: Vol. 1
Available at: https://ir.library.illinoisstate.edu/spora/vol1/iss1/3