April 1999 By John Hearne There is a saying, "If it pays it stays." By making game ranching more profitable, operations research is contributing toward the conservation of our wildlife heritage. Private game ranching is a rapidly growing enterprise in South Africa. Many former cattle farms have been converted to game ranches. A number of factors have contributed to this increase, including the reduction of subsidies to cattle farmers and the increase in tourism after the ending of apartheid and the lifting of sanctions. In 1979 private fenced game ranches covered less than 10,000 square kilometers. Now there are some 4,000 fenced ranches in the country with a combined area of 80,000 square kilometers. While game ranches undoubtedly contribute to conservation, an important reason for their establishment in South Africa is the profit motive. There are reports of game ranches realizing much greater profits than cattle farms. In one instance, a seven-fold increase in profits over cattle ranching was reported (Bothma and Van Hoven, [1993]). Sources of revenue include gate fees from visitors, accommodation fees, live sales, and fees for meat and sport hunting. The average game ranch size of 20 square kilometers is not large enough to accommodate large predators. Rough calculations show that a population of 1,200 wildebeest is the standing stock required to generate, on a sustainable basis, sufficient prey for a pride of only five lion. In a semi-arid region, the grazing requirements of such a wildebeest population would necessitate a dedicated area of land at least 28 square kilometers. It is apparent that most private ranches are not able to accommodate large predators. As a consequence, the various populations of browsers, grazers and mixed feeders must be harvested each year to avoid overstocking and the negative impacts on vegetation that would result. This harvesting also represents an opportunity for generating revenue from hunting. One needs fewer hunters than tourists to make a game operation viable. A study in Tanzania showed that one hunter is equivalent to 100 tourists in terms of the revenue brought in (Nel, [1995]). Each year about 5,000 foreign hunters visit South Africa to partake in trophy hunting. A trophy or safari hunter aims to shoot an impressive male. When a safari hunter shoots an animal, the reserve normally retains the meat of the animal. The skin and trophy of the animal belong to the hunter. Meat hunters, on the other hand, are paying for the opportunity to experience a hunt and for the meat of the animals they shoot. Generally speaking, meat hunters shoot female animals. In South Africa most meat hunters are local citizens. Trophy hunters are willing to pay large sums for certain trophy animals — up to $28,000 for a white rhino and $10,000 for a buffalo. In contrast to these high prices, some species such as impala and warthog fetch less than $200. The question then arises: Can we manipulate the balance of species to optimize the returns from harvesting surplus animals? In other words, what should be the population number of each species? An ecological consultant will visit a ranch and determine the species that are suitable for the local region. Rainfall, terrain, soil type, vegetation and water availability are all factors that are taken into consideration. Once the species are chosen, the numbers of each species must be determined. In choosing these numbers, there are a number of constraints that need to be considered. Species are divided into broad feeding classes: browsers, selective grazers and non-selective grazers. Within each of these classes, species are assumed to compete for the same resource. For example, white rhino, buffalo, zebra and waterbuck are regarded as being in competition for the bulk graze; similarly, hartebeest, reedbuck and wildebeest share the nutritious shorter grasses — the concentrate graze. The total food requirements of each feeding class must be less than or equal to the food resources available to that class. Further, a white rhino consumes about two-and-a-half times the food required by a buffalo. These differing needs of individuals of each species have to be taken into account in determining the total food requirements of a group. The finite resource in each food class constrains the numbers of animals in that group. So, for example, increasing numbers of buffalo might require the waterbuck population to be decreased. Although the food constraint effectively places a ceiling on populations, there are additional constraints on populations due to habitat considerations that the ecologists usually want imposed. Furthermore, a minimum number of each species is required to ensure a quality wilderness experience important for attracting visitors. Thus, for example, it is necessary to have a viable zebra population, although they do not fetch high prices. A sufficiently large genetic pool is another consideration in determining minimum numbers of the less valuable species. With the above constraints, an optimization problem can be formulated. We constrain the offtake of each species to be equal to the growth rate for that species. Revenue is then calculated by summing the product of offtake and price for each species. The mathematical details can be found in Hearne, Korrubel and Koch (in press). Maximizing revenue can be formulated as a knapsack problem, but in practice the results from an LP formulation are satisfactory. This procedure has been used to determine stocking rates for each species on five different ranches in South Africa (see, for example, Hearne and McKenzie, in press). Land Use With the change in government in South Africa, people who had been forcibly removed from traditional land have been able to lay a claim for the return of their land. How should this land be used? There is always some pressure toward using the land for communal grazing, but some of these claims have involved parts of game reserves or land adjacent to reserves. Would it be economically more profitable to use the land as a game ranch or to use it for a subsistence pastoral system? This is a politically sensitive but important question. To get some insight into the most profitable land use in semi-arid areas we did a cost-benefit analysis of the two systems: game ranching and a subsistence pastoral system. Obviously, the area of land involved is relevant to this analysis. Furthermore, the shape of the property will affect certain costs, particularly fencing. We proceeded by considering square properties. The optimization problem discussed earlier can be formulated with the area of a ranch used as a parameter. A number of additional constraints are necessary in this formulation. For example, we stipulated that the ranch must be at least 40 square kilometers before white rhino could be introduced. With this formulation, maximal revenue from hunting (both trophy and meat hunting), can be determined as a function of ranch area. There are a number of other sources of revenue for game ranches such as entrance fees, accommodation and food sales. There are also a number of costs. Some costs such as fencing and road maintenance depend on the size of the property, while other costs are fixed. Costs and revenue from non-hunting sources are difficult to quantify without making a huge number of assumptions about the specific ranch such as the availability of water. We therefore proceeded by collecting data. Constrained by the time frame of the project, we were able to collect data on 15 game ranches and game reserves in the province of KwaZulu-Natal. A detailed inspection of these data, some regression analysis and other calculations followed. Finally, the hunting revenue was included in these calculations to yield profit as a function of property size. The profit curve rises quite sharply when the area of the property is large enough to accommodate the larger animals such as buffalo and eventually white rhino. A similar cost-benefit analysis of a subsistence pastoral system was undertaken. A number of non-marketable benefits from the system had to be given an economic value. For example, in many remote regions it is not possible to market the milk produced. This milk, however, is an important food for households, and they would have to pay a premium price for its replacement. Cattle are also used as draft power both for transport and for plowing fields. These systems have very few fixed costs so profit can be obtained from relatively small areas of land. The profit curve, however, is almost linear. The results show that game ranches are clearly more profitable than pastoral systems for property sizes in excess of 20 square kilometers (Tomlinson, [1998]). The Makasa Nature Reserve While the profit motive is important, it is not an overriding factor. Until recently the South African government owned the land now known as the Makasa Nature Reserve. On the southern border of the reserve is the communally owned land of the Makasa Tribe. The fence on this border had begun to disintegrate, and the Makasa community began harvesting resources from the area and using the land for grazing their cattle. Nkosi Gumede, leader of the Makasa Tribe, then made a request that control of the land be transferred to the Makasa Tribe in order to establish a Tribal Conservation area on the land (Goodman and Blok, [1996]). However, control of the land was placed in the hands of the Natal Parks Board who attempted to establish a conservation initiative that provided tangible benefits to the Makasa Tribe. This tribe was the original owner of the land on which the reserve had been established (Goodman and Blok, [1996]). A management committee was established for the reserve with equal representation from the community and from the Natal Parks Board. Funding was obtained from the Green Trust to pay for the initial management costs of the reserve. A number of game species — goodwill gifts from the Natal Parks Board — had been introduced into the reserve, including: white rhino, buffalo, waterbuck, zebra, nyala, impala, giraffe, warthog, reedbuck and blue wildebeest. Small populations of kudu, suni, red duiker and grey duiker were also present in the reserve. Three years ago the Makasa Reserve was not generating any income. The annual running costs were approximately $63,000. A decision needed to be made on what combination of strategies would lead to the highest economic returns for the reserve. The neighboring Phinda Resource Reserve had made an offer for the lease of the land. Was this a good offer? Could the Makasa people derive greater benefit by running the reserve themselves? An investigation showed that non-consumptive tourism would not be viable (Hearne and McKenzie, in press) so it was left to decide whether game hunting could provide income comparable to that offered by leasing. White rhino are the most lucrative species to sell, but with the low numbers of white rhino that could be accommodated in the reserve, it is unlikely that rhino hunts could occur more than once every 10 years. The next most lucrative species is the buffalo. It is not only lucrative to sell male trophy buffalo, but it is also lucrative to sell females for meat hunts. Since buffalo are also a species that will attract hunters to the reserve, they will be the most important species in determining the profitability of the reserve. Hence, a detailed analysis was done, using mathematical modeling, to determine the likely offtake of buffalo from the reserve. The analysis involved a two-stage approach. The first stage involved developing a deterministic model for buffalo to find an age structure that will maximize the offtake of buffalo. This involved a linear programming problem. The second stage involved the development of a dynamic, stochastic model that used the age structures determined by the deterministic model as targets in an offtake strategy. The results of the stochastic model indicated that the average yearly offtake of male and female buffalo would be less than three from each group. Using a simpler but less accurate model to calculate the offtake from other species, it was found that in a "good" year (three trophy buffalo available) the reserve could earn between $19,300 and $22,500 from hunting on 77 days in the year. It was clear that hunting alone would not be able to meet the cost of running the reserve. With the Green Trust money coming to an end, there was also no further capital available for establishing lodges or other income-generating schemes. The Phinda Resource Reserve, however, has the financial resources and the local infrastructure necessary to complete the transition of the land to a viable reserve and ensure a lease income to the Makasa people exceeding that of agriculture. Starting Up A Game Ranch As alluded to above, a major hurdle to overcome in setting up a game ranch is raising the large amount of initial capital required. For a typical farm of about 20 square kilometers, the start-up costs comprising game fencing, tourist huts, and other infrastructure and equipment range from $300,000 to $400,000 (Eloff, [1996]). The acquisition of game necessitates an additional sum of the order of $300,000. Since the capital available is a major constraint in establishing game ranches, it is vital to utilize this limited resource optimally. It can take between three and five years to acquire and build up stock to their optimal levels before a game ranch becomes operational. During this time the optimal numbers of some species, especially buffalo and white rhino, cannot be attained overnight. While the numbers of such species are below optimal levels, there are surplus grazing resources available. This graze can be exploited by the faster-growing or more readily available species. These species can then be harvested down again, generating revenue, when the resources are required by the more profitable species. The question, then, is, What is the optimal sequence of stock acquisitions and offtake that minimizes net capital outlay during the start-up period? This is a discrete optimal control problem and under certain circumstances can be formulated as a multiperiod LP problem. Constraints include capital availability, growth rates of species, maximum annual acquisition rates and other constraints used to calculate the optimal population numbers. Together with the optimal schedule for acquisitions and offtake, the results generate a full cash flow statement over the start-up period. Using this procedure, a reduction of more than 20 percent in capital required for the game component of setting up a ranch can be achieved. This can affect the decision whether to proceed or not with the establishment of a game ranch. Conclusion The profit motive is driving the move from cattle to game in certain semi-arid areas. By helping to maximize the profit from game in a sustainable way OR is contributing toward the survival of African wildlife. One of the enjoyable aspects of OR is seeing the similarities between problems that at first appear to be very diverse. Choosing population numbers of different species to fill a game ranch is like filling a knapsack! As we get more sophisticated in managing game ranches we see that optimal portfolio theory is going to be useful. Given that species grow at different rates and have different probabilities of survival, and also are subject to species-specific price fluctuations, how should we invest in the different species to be on a Pareto optimal risk-return curve? Stock markets and game ranches — the OR is the same. References Eloff. T., 1996,"Farming with a Future," SA Game and Hunt, 2/3 Bothma, J., Du, P. and W. Van Hoven, 1993. "Planning Game Ranching Systems In Livestock Production Systems, Principles and Practice." Eds. Maree, C. and N.H. Casey, pp. 281-299. Hearne, J.W. and Mckenzie, M.,"Compelling reasons for game ranching in Maputaland," in: H H T Prins & J G Grootenhuis (eds.), "Valuation of benefits and costs of wildlife in Africa," chapter 13, Chapman and Hall, London (in press). Hearne, J.W., Korrubel, J.L. and Koch, K.J.,"Modelling to optimize consumptive use of game," Annals of OR (in press). Nel, M., 1995,"Hunting and conservation - legitimate partners or a contradiction in terms?" Africa: Environment and Wildlife, Vol. 3, No. 5, pp. 31-34. Tomlinson, K.W.,"Modelling the effect of property size on the opportunity cost incurred by wildlife production," M.Sc. Thesis, University of Natal, 1998. Goodman, PS and Blok, R. , 1996, "Makasa Nature Reserve Concept Plan: Draft," unpublished report. John Hearne is a professor in the School of Mathematics, University of Natal, Pietermaritzburg, South Africa, and president of the Operations Research Society of South Africa. 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