Mathematical Model for the Population Dynamics of the Serengeti Ecosystem

Abstract

Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased.