Mathematical Model of the Roan Antelopes, Ruma Park

Abstract

Roan antelopes that were once abundant in the country in the 1880s have been reduced to a remnant population of less than fifty individuals in the last estimate,November 2009. Oksendal and Lungu developed population growth model in a crowded environment by introducing randomness in their differential equation via additional noise term. Magin and Kock in their roan antelope recovery plan in the Ruma National Park considered poaching as a major factor affecting population growth of roans which saw a slight population growth before experiencing stagnation since the year 2003 to date. The Kenya Wildlife Service (KWS) has since taken neces sary measures to curb poaching. This reduced the risk of poaching as a major factor that accelerated roans' population decay. Lambwe valley is believed to have uranium deposits that could affect fertility. Inbreeding in small populations is known to have substantial effects on population growth rate. We have therefore incorporated in our model genetic defect that was not incorporated by Magin and Kock. This was made possi ble by making appropriate adjustments to Vortex Version 9.99 which is a computerized program for the simulation of the extinction processes. We noted that there is a high correlation between inbreeding and popu lation growth in small populations. It is hoped that this study will help The Kenya Wildlife Service (KWS) in the management of their complex ecosystem.