OJE  Vol.5 No.4 , April 2015
Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem
Abstract: We develop a two-species prey-predator model in which prey is wildebeest and predator is lion. The threats to wildebeest are poaching and drought while to lion are retaliatory killing and drought. The system is found in the Serengeti ecosystem. Optimal control theory is applied to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for poaching, construction of strong bomas for retaliatory killing and construction of dams for drought control. The possible impact of using a combination of the three controls either one at a time or two at a time on the threats facing the system is also examined. We observe that the best result is achieved by using all controls at the same time, where a combined approach in tackling threats to yield optimal results is a good approach in the management of wildlife populations.
Cite this paper: Sagamiko, T. , Shaban, N. , Nahonyo, C. and Makinde, O. (2015) Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem. Open Journal of Ecology, 5, 110-119. doi: 10.4236/oje.2015.54010.

[1]   Chakraborty, K., Chakraborty, M. and Kar, T. (2011) Optimal Control of Harvest and Bifurcation of a Prey-Predator Model with Stage Structure. Applied Mathematics and Computation, 217, 8778-8792.

[2]   Dubey, B. (2007) A Prey-Predator Model with a Reserved Area. Nonlinear Analysis: Modeling and Control, 12, 479-494.

[3]   Peterson, M.J. (1991) Wildlife Parasitism, Science and Management Policy. Wildlife Management, 55, 782-789.

[4]   Walker, B., Carpenter, S., Anderies, J., Abel, N., Cumming, G., Janssen, M., Lebel, L., Norberg, J., Peterson, G. and Pritchard, R. (2002) Resilience Management in Social-Ecological Systems: A Working Hypothesis for a Participatory Approach. Conservation Ecology, 6, 14.

[5]   Sinclair, A.R.E., Packer, C., Mduma, S.A.R. and Fryxell, J.M. (2008) Serengeti III, Human Impacts on Ecosystems Dynamics. The University of Chicagopress, Chicago.

[6]   Kideghesho, J.R. (2010) “Serengeti Shall Not Die”: Transforming an Ambition into a Reality. Tropical Conservation Science, 3, 228-248.

[7]   Bolger, D., Newmark, W., Morrison, T. and Doak, D. (2008) The Need for Integrative Approaches to Understand and Conserve Migratory Ungulates. Ecology Letters, 11, 63-77.

[8]   Haris, G., Thirgood, S., Hopcraft, J., Cromsigt, J. and Berger, J. (2009) Global Decline in Aggregated Migrations of Large Terrestrial Mammals. Endangered Species Research, 7, 55-76.

[9]   GEAS (2013) Saving the Great Migrations: Declining Wildebeest in East Africa?

[10]   Hopcraft, J., Sinclair, A., Holdo, R., Mwangomo, E., Mduma, S., Thirgood, S., Borner, M., Fryxell, J. and Olff, H. (2013) Why Are Wildebeest the Most Abundant Herbivore in the Serengeti Ecosystem? Serengeti IV: Sustaining Biodiversity in a Coupled Human-Natureal System. University of Chicago Press, Chicago.

[11]   Ikanda, D. and Packer, C. (2008) Ritual vs. Retaliatory Killing of African Lions in the Ngorongoro Conservation Area, Tanzania. Endangered Species Research, 6, 67-74.

[12]   Kissui, B.M. (2008) Livestock Predation by Lions, Leopards, Spotted Hyenas and Their Vulnerability to Retaliatory Killing in the Maasai Steppe, Tanzania. Animal Conservation, 11, 422-432.

[13]   Kolowski, J.M. and Holekam, K.E. (2006) Spatial, Temporal and Physical Characteristics of Livestock Depradations by Large Carnivores along a Kenyan Reserve Border. Biological Conservation, 128, 529-541.

[14]   Kar, T. and Gosh, B. (2012) Sustainability and Optimal Control of an Exploited Prey-Predator System through Provision of Alternative Food to Predator. Biosystems, 109, 220-232.

[15]   Holling, C.S. (1965) The Functional Response of Predators to Prey Density and Its Role in Mimicry and Popuation Regulation. Memoirs of the Entomological Society of Canada, 97, 1-60.

[16]   Fryxell, J.M., Mosser, A., Sinclair, A.R.E. and Packer, C. (2007) Group Formation Stabilizes Predator-Prey Dynamics. Nature, 449, 1041-1043.

[17]   Schaller, G.B. (1972) The Serengeti Lion: A Study of Predator-Prey Relations. University of Chicago Press, Chicago.

[18]   Mduma, S.R. (1996) Serengeti Wildebeest Population Dynamics: Regulation, Limitation and Implication for Harvesting. Ph.D. Thesis, University of British Columbia, Canada.