Extinction Growth Model

Main Article Content

Daniel Ochieng Achola


Objectives: To develop a mathematical model that incorporates genetic defect in estimating the growth rate of roan antelopes in Ruma National Park,Kenya.
Methodology: This study has developed an improved Oksendal and Lungu’s stochastic logistic model to estimates population growth rate of roans by incorporating genetic defect that were not considered by Magin and Cock. Appropriate adjustments were made to Vortex version 9.99 a computer simulation programme to simulate the extinction process.
Results: There is a high-level impact between inbreeding and population growth(survival) in small populations. Supplementation of both juvenile and adult roans ensured population survival for longer period.
Conclusion: Due to unpredictable consequences to the ecosystem and conflict with wildlife management policies in protected areas, this paper recommends supplementation instead of predator control to curb inbreeding which is a major threat to small populations. Supplementation should be done in phases without causing disruption to social groups.

Population dynamics, growth models, stochastic models.

Article Details

How to Cite
Achola, D. O. (2020). Extinction Growth Model. Asian Research Journal of Mathematics, 16(8), 93-107. https://doi.org/10.9734/arjom/2020/v16i830212
Original Research Article


Griensen R. Public and urban economics. MassLexington Books, Lexington; 1976.

Shaffer M. Minimum population sizes for species conservation. Biosciences. 1981;31:131-134.

Lacy RH, Hughes KA, Miller PS. Vortex- a stochastic simulation of the extinction process.

Version 9.99 Users’ Manual; 2005. IUCN/SSC Captive Breeding Specialist Group, Apple Valley, Minesota; 2005.

Falconer DS. Introduction to quantitative techniques. 2nd Ed Longman, New York; 1981.

Selander R. Evolution consequences in genetics and conservation; A reference for managing wild animals and plant populations. Benjamin/Cummings, Carlifornia; 1983.

Gilpin M. Minimum viable population,process of extinction in conservation biology. (S.M.E, Ed) Sanderland Massachusets; 1998.

Wilson,W. Simulating ecological and evolution systems. London, Cambridge University Press, London; 2000.

Oksendal B. Stochastic differential equation. An introduction with applications 6thEd.

Springer-Verlag,New York; 2000.

Magin C, Kock R. Roan antelopes recovery plan. IUCN; 1997.

Pivato M. Stochastic processes and stochastic integration. Lecture Notes; 1999.

Pollet P. Diffusion approximation for ecological model. Canberra Proceedings of International Congress On Modelling And Simulation Society Of Australia and New Zealand. 2001;14-19.

Friedman A. Stochastic differential equations & applications. Academic Press, New York;;1.