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Model Fitting and Analysis of the Cost-effectiveness of Control Strategies in the Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem
Journal of Humanities & Social Science (JHSS),
Vol. 10 No. 4 (2021)
Abstract
In this paper, a wildebeest-lion prey-predator model for the Serengeti ecosystem was adopted from a previous publication. The threats to the model system were poaching, retaliatory killings, and droughts. The proposed threat control strategies for these threats were anti-poaching patrol to mitigate poaching, construction of strong bomas to reduce retaliatory killings, and construction of dams to mitigate the impact of droughts. Data on the lion population density in the Serengeti ecosystem were used to fit the model by using the maximum likelihood method. The impact of different control strategies for a period of five years was analysed using the incremental costeffectiveness ratio (ICER). An analysis of the dynamical behaviour of the adopted model was carried out. Results indicated that the model fitted well the data and the construction of dams using the ICER was the most cost-effective strategy. Nevertheless, at the implementation level, the management may decide to adopt either of the two programs.
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- Baxter, P. W., C. Wilcox, M. Mccathy & H. Possingham. 2008. Cost Effectiveness Suppression and Eradication of Invasive Predator. Conservation Biology, 22(1): 89–98. Cao, J., G. F. Fussman & J. O. Ramsay. 2008. Estimating a Predator-Prey Dynamical Model With the Parameter Cascades Method. Biometrics, 64(3): 959–967. Chakraborty, K., M. Chakraborty & T. Kar. 2011. Optimal Control of Harvest and Bifurcation of a PreyPredator Model With Stage Structure. Applied Mathematics and Computation, 217: 8778–8792. Fryxell, J. M., A. Mosser, A. R. Sinclair & C. Packer. 2007. Group Formation Stabilizes Predator-Prey Dynamics. Nature, 449. Grzimek, B. & M. Grzimek. 1960. Serengeti Shall Not Die. London, UK: Hamish Hamilton. Ikanda, D. & C. Packer. 2008. Ritual vs. Retaliatory Killing of African Lions in the Ngorongoro Conservation Area, Tanzania. Endangered Species Research, 6: 67–74. Ionides, E. L., C. Betro & A. A. King. 2006. Inference for Nonlinear Dynamical Systems. Proceedings of the National Academy of Sciences, 103 – 18438–18443. Kar, T. & B. Gosh. 2012. Sustainability and Optimal Control of an Exploited Prey-Predator System Through Provision of Alternative Food to Predator. Journal of Biosystems, 109: 220–232. Kideghesho, J. R. 2010. ‘Serengeti Shall Not Die’: Transforming an Ambition into a Reality. Tropical Conservation Science, 3: 228–248. Mduma, S. R. 1996. Serengeti Wildebeest Population Dynamics: Regulation, Limitation and Implications for Harvesting. Canada: University of British Columbia. Myung, I. J. 2003. Tutorial on Maximum Likelihood Estimation. Journal of Mathematical Psychology, 47: 90–100. Okosun , K., O. Richard & N. Marcus. 2013. Optimal Control Strategies and Cost-Effectiveness Analysis of a Malaria Model. Biosystems, 111(2): 83–101. Sagamiko, T. D., N. Shaban, C. L. Nahonyo & O. D. Makinde. 2015. Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem. Open Journal of Ecology, 5: 110–119. Schaller, G. B. 1972. The Serengeti Lion: A Study of Predator-Prey Relations. Chicago: University of Chicagopress. Sinclair, A. R., C. Packer, S. A. Mduma & J. M. Fryxell. 2008. Serengeti III, Human Impacts on Ecosytems Dynamics. Chicago: The University of Chicago Press.
References
Baxter, P. W., C. Wilcox, M. Mccathy & H. Possingham. 2008. Cost Effectiveness Suppression and Eradication of Invasive Predator. Conservation Biology, 22(1): 89–98. Cao, J., G. F. Fussman & J. O. Ramsay. 2008. Estimating a Predator-Prey Dynamical Model With the Parameter Cascades Method. Biometrics, 64(3): 959–967. Chakraborty, K., M. Chakraborty & T. Kar. 2011. Optimal Control of Harvest and Bifurcation of a PreyPredator Model With Stage Structure. Applied Mathematics and Computation, 217: 8778–8792. Fryxell, J. M., A. Mosser, A. R. Sinclair & C. Packer. 2007. Group Formation Stabilizes Predator-Prey Dynamics. Nature, 449. Grzimek, B. & M. Grzimek. 1960. Serengeti Shall Not Die. London, UK: Hamish Hamilton. Ikanda, D. & C. Packer. 2008. Ritual vs. Retaliatory Killing of African Lions in the Ngorongoro Conservation Area, Tanzania. Endangered Species Research, 6: 67–74. Ionides, E. L., C. Betro & A. A. King. 2006. Inference for Nonlinear Dynamical Systems. Proceedings of the National Academy of Sciences, 103 – 18438–18443. Kar, T. & B. Gosh. 2012. Sustainability and Optimal Control of an Exploited Prey-Predator System Through Provision of Alternative Food to Predator. Journal of Biosystems, 109: 220–232. Kideghesho, J. R. 2010. ‘Serengeti Shall Not Die’: Transforming an Ambition into a Reality. Tropical Conservation Science, 3: 228–248. Mduma, S. R. 1996. Serengeti Wildebeest Population Dynamics: Regulation, Limitation and Implications for Harvesting. Canada: University of British Columbia. Myung, I. J. 2003. Tutorial on Maximum Likelihood Estimation. Journal of Mathematical Psychology, 47: 90–100. Okosun , K., O. Richard & N. Marcus. 2013. Optimal Control Strategies and Cost-Effectiveness Analysis of a Malaria Model. Biosystems, 111(2): 83–101. Sagamiko, T. D., N. Shaban, C. L. Nahonyo & O. D. Makinde. 2015. Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem. Open Journal of Ecology, 5: 110–119. Schaller, G. B. 1972. The Serengeti Lion: A Study of Predator-Prey Relations. Chicago: University of Chicagopress. Sinclair, A. R., C. Packer, S. A. Mduma & J. M. Fryxell. 2008. Serengeti III, Human Impacts on Ecosytems Dynamics. Chicago: The University of Chicago Press.