A "Quasi-Rapid" Extinction Population Dynamics and Mammoths Overkill
  In this work we suggest and consider an original, simple mathematical model of a "quasi-rapid" extinction population dynamics. It describes a decrease and final extinction of the population of one prey species by a "quasi-rapid" interaction with one predator species with increasing population. This "quasi-rapid" interaction means ecologically that prey species behaves practically quite passively (since there is no time for any reaction, i.e. defense), like an appropriate environment, in respect to "quasi-rapid" activity of the predator species that can have different "quasi-rapid" hunting abilities. Mathematically, our model is based on a non-Lotka-Volterraian system of two differential equations of the first order, first of which is linear while second, depending of a parameter that characterizes hunting ability is nonlinear. We compare suggested "quasi-rapid" extinction population dynamics and the global model of the overkill of the prehistoric megafauna (mammoths). We demonstrate that our "quasi-rapid" extinction population dynamics is able to restitute successfully correlations between empirical (archeological) data and overkill theory in North America as well as Australia. For this reason, we conclude that global overkill theory, completely mathematically modelable by "quasi-rapid" extinction population dynamics can consistently explain the Pleistocene extinctions of the megafauna. 
Vladan Pankovic, Rade Glavatovic, Nikola Vunduk, Dejan Banjac, Nemanja   Marjanovic, Milan Predojevic