Extinction Growth Model
Daniel Ochieng Achola *
Department of Mathematics, Kabarak University, Private Bag-20157, Nakuru, Kenya.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Population dynamics, growth models, stochastic models.