Robustness of cheetah asymptotic growth rate and implications to population models∗

The endangered cheetah (Acinonyx jubatus) is in decline due to hunting, poaching, loss of habitat, lack of genetic diversity and death of cubs due to natural predators such as lions and hyenas. Previous cheetah population models contend that increasing the survivorship of adult cheetahs is the best conservation method to ensure long term viability of this endangered species. The age-structured matrix model of the Serengeti Plain cheetahs by Crooks, et al.[5] suggests the asymptotic population growth rate is most sensitive to adult survivorship. Using linear algebra and robustness techniques, we analyze this previously published model and the robustness of its conclusion. Our results reveal a 5% increase in the adult survivorship is necessary in order to achieve a positive growth. Since the mortality of Serengeti cheetahs occur predominately during the first six months of life, we also explore how large an increase in this survivorship is necessary in order to achieve a positive growth rate. Our results show only an 7.7% increase in cub survivorship is necessary in order to achieve positive growth rate; a figure certainly within reach of concerted conservation efforts. In this paper we present a new population model for the Serengeti cheetahs. Our model examines the effect of capturing pregnant cheetahs, then releasing them back into the wild with their cubs six months after birth. This strategy dramatically increases the survivorship of the cubs in the initial six months of their lives. Using this model in combination with the current conservation strategy of increasing the adult survivorship yields a positive robust population growth rate.