Date of Award

Spring 2017

Project Type

Departmental Honors Paper/Project


Department of Mathematics & Statistics


There are multiple hypotheses as to why the Columbian Mammoth (Mammuthus columbi) and other megafauna in North America went extinct relatively recently and relatively quickly. The most popular of which are disease, climate change, meteorite strikes, and over hunting by humans [2, 9]. There is evidence to show that a combination of factors contributed to the megafaunal extinction, but ”overkill” explores the idea that early humans migrated onto the continent and then hunted the mammoths and other megafauna to extinction. The overkill hypothesis was first proposed by anthropologist Paul Martin in 1973 [8]. Evidence from radiocarbon dating shows that the extinction of megafauna in North America was a geologically very sudden event. Not only was it very sudden, but it lines up well with our current estimations of when humans migrated onto the continent of North America about 13,000 BP (years before present) [8]. Jared Diamond’s 1997 Guns, Germs, and Steel popular science book was the first time to bring the overkill theory to the general public [4]. Then, paleobiologist John Alroy’s work published in 2001 was the first evidence using computer simulations that overkill was the likely cause of the megafaunal extinctions of North America. He found that extinction was inevitable for a large number of species, but matching the true fates (extinction vs survival) of species was only partially accurate; 32 of 41 species fates were correctly determined in the best preforming simulation run [1]. In 2015, Frank et al published the paper Investigating Anthropogenic Mammoth Extinction with Mathematical Models. This paper attempted to determine extinction dates using a continuous ordinary di↵erential equations model [5]. This model uses di↵erential equations to calculate rates at which humans and mammoths were born, died, and migrated. The goal of their project was to find any stable equilibria, therefore determining whether the populations stabilize either at extinction or at survival. One potential flaw of this model is that it has continuous state variables. This allows the movement of fractions of humans or mammoths throughout the simulation. These fractions, while simply being unrealistic, also lead to erroneous results such as when extinction is not declared due to mammoth population being just a fraction above the extinction criteria. The exact timeline of when humans first migrated and how they migrated is a heavily debated topic. Throughout this paper, we will be following the assumption that the first humans migrated into North America through Berignia by means of an “ice-free corridor” around 13,000 BP [3, 6, 13]. The earliest Clovis (or early human) artifacts to be found in North America date around 12,000 BP to 11,500 BP [13]. Most megafaunal extinctions in North America were complete by 10,000 BP [7], and there is evidence to suggest that North America was completely settled by humans by 9,000 BP [14]. Using these dates and information, we conservatively assumed that the shortest time frame for human migration would be between 13,000 BP and 12,000 BP, while the longest time frame for human migration would be between 13,000 BP and 9,000 BP. This resulted in a possible range of human migration through North America of between 1000 and 4000 years. These migration time-spans were used to calibrate the migration rates throughout our final simulations. In this paper, we expand on this research in anthropogenic mammoth extinction by creating a discrete stochastic model. The goal is to create a model that is analogous to the ordinary differential equations (ODE) model in Frank’s paper while reducing computation time and finding more realistic migration rates. Reducing the computation time will allow us to run simulations representing a larger land mass so that we will not have to make the assumption to scale up our predictions linearly.