Modelling Late Pleistocene megafaunal extinction and critical cases: A simple prey-predator perspective

Using a nonlinear prey-predator model, we establish the extinction threshold for megafauna in the Late Pleistocene and predict extinction times since the arrival of hunters. The threshold is related to growth and depredation rates. From archaeological data, ecological findings, and the overkill hypothesis, the elapsed extinction times in Australia and North America are roughly estimated as 4800 and 3000 years, respectively. In Africa, the extinction times follow a particular power-law behavior with a critical time of the order of 185,000 years, roughly corresponding to the emergence of anatomically modern humans. Most of the parameters are estimated from a living representative megafauna prototype; the African elephant (Loxodonta africana). The elapsed time becomes a function of the effective area and the human diffusion coefficient. From allometric considerations, we can understand why small species were not decimated by depredation in the Late Pleistocene.