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• W1678983186 abstract "NYALA AND BUSHBUCK I: A COMPETING SPECIES MODEL 1. INTRODUCTION A very real over-population problem is occurring in the Ndumu Game Reserve in KwaZulu-Natal, South Africa. One species of antelope, the Nyala, is crowding out another species, the Bushbuck. In this article, we construct a competing species model which permits us to describe mathematically what is occurring in Ndumu. In a second companion article, we use the model for the investigation of various harvesting strategies which might suggest a solution to the problem. The advantage of this approach is immediately evident for we can see the effects of a particular harvesting strategy without actually culling any animals. We first give a general description of the biological and mathematical underpinnings of a competing species model. Then secondly, we use the available data on Nyala and Bushbuck to derive the coefficients for our model to represent the situation in Ndumu. To achieve this, the logistic growth patterns will be discussed with specific reference to the Ndumu problem. The model accurately predicts the ultimate extinction of the Bushbuck. Competing species models are mentioned in most beginning differential equations texts. They provide excellent examples hosting a variety of types of critical points: stable and unstable nodes, saddle points, and the like. Thus, this model we develop herein is suitable for discussion in a beginning course on differential equations or in a first course in mathematical ecology. A further objective is to point out the underlying assumptions that add to the plausibility of the model and to emphasize the interpretation of what the model describes mathematically. It is our feeling that students have more difficulty in interpretation than in performing calculations, perhaps because they have little opportunity to do so and thus are inexperienced. An attractive feature of our model is that it immediately lends itself to physical interpretation and should therefore be of interest to students and instructors alike. 2. BIOLOGICAL BACKGROUND The Ndumu Game Reserve (10,117 hectares) is situated at the southern end of the Mozambique plain on the international boundary between South Africa and Mozambique [10]. The reserve is well suited for forest loving animal species like Nyala (Tragelaphus angasii), Bushbuck (Tragelaphus scriptus) and Suni (Neotragus moschatus). The predator species present in Ndumu are of the smaller type like Hyena (Hyaenidae crocuta). They hunt on rabbits (Pronolagus crassicaudatus), Suni and Duikers (Cephalophus natalensis) and have no impact on the population of bigger animals. However, the Nyala, through sheer numbers, impact heavily on the success of the other browsing species, especially Bushbuck which feed on the same browse line'. The data of Nyala and Bushbuck population estimates and numbers of actual removals are indicated in Table 2.1. Since the calculated carrying capacity of the area is 2,000 for Nyala and 140 for Bushbuck [10], the reason for concern is apparent. The Nyala not only impact on other species through direct competition for available browse, but also indirectly through their negative impact on vegetation structures. Due to the range utilization by the Nyala, palatable plant species are being crowded out by unpalatable ones. An additional concern, noted by W. S. Matthews [6], is that there is a significant bush encroachment problem in the reserve. He ascribes the low biomass in the thickets to trampling by the many Nyala. This encroachment problem can only be dealt with if the aboveground plant biomass can be increased in order to use fire as a managing tool. Officials did consider exportation of a number of Nyalas, but since Ndumu was situated behind the so-called red line2, a period of quarantine was essential before they can be introduced to other reserves. Experience has shown that the mortality rate is exceptionally high when these animals are kept in quarantine. …" @default.
• W1678983186 created "2016-06-24" @default.
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• W1678983186 date "1999-09-01" @default.
• W1678983186 modified "2023-09-26" @default.
• W1678983186 title "Nyala and Bushbuck I: a competing species model" @default.
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