On the Causes of the Extinction of Some Animals at the end of the Pleistocene

A mathematical theory is developed to demonstrate the disputed hypothesis that hunting tribes of the Upper Paleolithic in Europe did play a decisive role in bringing about the extinction of the mammoth and other large herbivorous animals at the end of the Pleistocene. Formulas for the periods of time during which hunting did not greatly affect animal numbers and during which the numbers declined to zero are used to show that mammoth numbers remained relatively stable during most of the Upper Paleolithic (a period of 10,000 to 25,000 years) and then dropped rapidly within a few centuries to complete extinction. The theory is used to explain why only the largest animals became extinct and why elephants continued to survive in tropical areas while the mammoth vanished in the north.