predation and harvesting in a closed system

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1 Ecology , Modelling wildebeest population dynamics: implications of Blackwell Publishing, Ltd. predation and harvesting in a closed system CRAIG J. TAMBLING and JOHAN T. DU TOIT Mammal Research Institute, Department of Zoology and Entomology, University of Pretoria, Pretoria 0002, South Africa Summary 1. Predation upon ungulates is generally considered to have a stronger regulatory effect on sedentary than migratory populations, with migratory populations maintaining higher densities. The blue wildebeest Connochaetus taurinus is a migratory species that has suffered a general decline in numbers and distribution across its species range. Wildebeest suffer from a fragmented distribution together with isolation of populations in closed reserves, preventing migratory movements and potentially allowing predators to benefit from a captive prey resource. 2. In Pilanesberg National Park, South Africa, the declining blue wildebeest population (from 1074 in 1995 to 594 in 2001) is sedentary because the park ( ha) is completely enclosed by fencing. This population was used to model the potential effects of predation and harvesting. The Pilanesberg population was then compared with other wildebeest populations in southern Africa. 3. The model outputs demonstrated that increased levels of predation by lions Panthera leo on a captive population of prey such as wildebeest, in combination with regular harvesting by park managers, can drive the population towards extinction. At lower levels of predation some other factor needs to act in combination with predation to drive the population into a decline. 4. During our study the lion biomass density in Pilanesberg was almost three times greater than that predicted by regression models of the stable relationship between lion and prey biomass densities across African savannas. Furthermore, the ratio of lion numbers to prey numbers was substantially higher than in most other African reserves. 5. Synthesis and applications. In African savannas, artificial closed systems provide advantages to large predators. If wildlife-cropping schemes are implemented in such systems without careful monitoring and regulation of large predators, then ungulate populations can decline more rapidly than managers expect. Key-words: Connochaetus taurinus, lion density, lion predation, migratory and sedentary ungulates, prey density, wildlife cropping Ecology (2005) 42, doi: /j x Ecological Society Introduction Historically, many grassland regions of the world supported vast herds of migratory ungulates. Although most migratory ungulate populations have become reduced in abundance and range, mainly because of overhunting, they still often occur in much higher densities than can Correspondence: Craig J. Tambling, Mammal Research Institute, Department of Zoology and Entomology, University of Pretoria, Pretoria 0002, South Africa ( cjtambling@zoology.up.ac.za). be attained by conspecific sedentary populations (Fryxell & Sinclair 1988). The reasons are unclear but Fryxell, Greever & Sinclair (1988) proposed that migratory populations benefit from (i) escaping year-round predation by migrating out of the territories of large resident predators and (ii) responding to seasonal and spatial heterogeneity in food quality. Populations of both sedentary and migratory wildebeest Connochaetus taurinus still persist in various parts of the African savanna biome, although both population types have suffered declines in various parts of the species range. The resident wildebeest population of the

2 432 C. J. Tambling & J. T. du Toit Masai Mara ecosystem declined by 81% from in 1977 to in 1997 (Ottichilo, de Leeuw & Prins 2001). The migratory population in Botswana declined by 90% in the early 1980s because of veterinary fences, hunting and competition with livestock (Spinage 1992). In the Kruger National Park, the western boundary subpopulation suffered an 87% decline between 1965 and 1979 as a result of a veterinary fence restricting them to half their original range (Whyte 1985; Whyte & Joubert 1988). The Etosha wildebeest population declined from to 2500 between 1954 and 1978 because of an anthrax epidemic and elevated predation rates arising from the abundance of weak animals (Berry 1981a,b). The wildebeest population in Pilanesberg National Park in South Africa declined by 47% between 1997 and There are a number of possible explanations for the decline. First, an increase in predator numbers associated with wildebeest harvesting could have caused the decline (Starfield, Smuts & Shiell 1976). Secondly, the decline may have been related to nutritional factors dependent on intra-annual rainfall patterns, such as dry season rainfall (Mduma, Sinclair & Hilborn 1999). Thirdly, wildebeest numbers are negatively correlated with annual rainfall in Kruger (Smuts 1978; Whyte 1985; Mills, Biggs & Whyte 1995) and so the Pilanesberg decline may have been a lagged response to rainfall patterns, such as wet dry cycles. Many protected areas in Africa are under increasing pressure to supply meat to local human communities, both through traditional subsistence hunting (Pascual & Hilborn 1995) and quota harvesting (Pascual, Kareiva & Hilborn 1997). In addition many small reserves, and even some large ones, actively manage their large mammal communities to achieve a mix of charismatic species that appeal to the tourist market. However, the interactions between management interventions and natural ecosystem processes (many of which are stochastic) need to be evaluated whenever an adequate set of monitoring data becomes available, and models allow this to be done relatively quickly (Starfield, Smuts & Shiell 1976). Models are often best utilized when follow-up studies can be undertaken to help answer questions that arise as a result of model development. Even within protected areas managers need to be aware that wildebeest populations can undergo rapid declines through natural processes and/or anthropogenic sources. There is a need to understand how sedentary wildebeest populations respond to harvesting and natural predation, because protected areas are increasingly becoming closed systems as a result of fencing and/ or habitat loss outside. In this study we investigated the recent decline of the Pilanesberg wildebeest population by modelling the effects (in isolation and in combination) of natural predation and harvesting by management. We compared the Pilanesberg data with that from other southern African wildebeest populations, and used the Pilanesberg case study to gain further insights into the effects of predation and harvesting on sedentary wildebeest populations. Methods STUDY AREA Pilanesberg National Park (25 8 S S, E E) is a ha circular reserve situated in the remains of an extinct volcano (Slotow & van Dyk 2001) in the North-west Province, South Africa. The moist savanna vegetation consists of Acacia spp. (mainly Acacia mellifera and Acacia tortilis), broad-leaf bushveld (notably Combretum spp.) and pediment grasslands (Brockett 2002). Pilanesberg has an average rainfall of 624 mm year 1, mostly falling in the summer months. The dry period between April and September contributes c. 11% of the annual rainfall. The monthly rainfall figures used in our study were obtained from six recording stations. For each year ( ) the rainfall in that and the previous 2 years was averaged over the six stations to derive a 3-year running mean. If the rainfall data for 1 month were missing from a station, the entire year for that station was removed from the analysis. WILDEBEEST POPULATION TRENDS Wildebeest introductions took place in 1978 and In 1983 the park management reduced the population by 67% to allow a natural population increase to take place. Since 1982 an annual aerial count has been conducted during August and September for all large mammal populations in Pilanesberg (Brockett 2002). Harvesting of various ungulate populations takes place from October, after the completion of aerial counting. Annual population estimates (n) and numbers of wildebeest harvested each year were obtained from Pilanesberg park records and the population trend was plotted from 1984 to The observed rate of population change was determined for an increasing phase ( ) and a decreasing phase ( ). The observed rate of population change was estimated from the slope of a regression of log n against time (t) in years (Caughley & Birch 1971). During September 2002, before the onset of the spring rains, all wildebeest encountered when driving systematically on all accessible roads in Pilanesberg were scanned through binoculars (8 40) or a spotting scope (20 ). Each individual was aged and sexed only if it could be observed clearly enough to obtain a definite classification. Departure from parity in the sex ratio of adults was tested for using a chi-squared test. Age sex classification was based on Attwell (1980), Skinner & Smithers (1990) and Estes (1991). Three social groupings were identified: territorial males, breeding herds and bachelor herds. Territorial males are single individuals maintaining a territory. Breeding herds consist of a territorial male, breeding females and associated calves and yearlings. Bachelor herds consist of non-territorial males. During the field observations the body condition of territorial and bachelor herd males was scored visually as good, medium or poor (Riney 1960).

3 433 Wildebeest population dynamics LION POPULATION TRENDS Lions Panthera leo are the dominant large predators in Pilanesberg, having been reintroduced in The age and sex of each individual lion was extracted from lion genealogy records maintained by the Pilanesberg management. All births, introductions, deaths and removals of lions were recorded, enabling all individuals alive at the end of each year to be counted, and the age and sex structure of the population to be determined for each year. Regression analysis was undertaken to determine if variation in observed lion numbers (total, total adults and adult females) could explain the variation in observed wildebeest numbers between 1995 and THE POPULATION MODEL A population model based on that of Starfield, Smuts & Shiell (1976) was developed to determine which factors could be driving the decline in the Pilanesberg wildebeest population. The model simulates the population size and structure near the end of the calving season. Pilanesberg has had a harvesting programme for most ungulates since the park s inception in We assumed that wildebeest of all age classes and both sexes are harvested (cropped) in equal proportions. The cropping rate (c t ) was calculated as the proportion of animals removed from the wildebeest population following the aerial census. Predation was included in the model for all years after 1993 and all wildebeest mortality from predators was assumed to be from lions. For simplicity we assumed that lions take equal proportions of all age and sex classes (Mills & Shenk 1992). The proportion of wildebeest killed at a time t + 1 is expressed as: p t+1 = (γ l t )/w t eqn 1 where γ is the number of wildebeest taken per adult lion per year, and l t and w t are the number of adult lion and wildebeest in the reserve at time t, respectively. The model tracks changes in four age classes at time t: juveniles ( j t ), yearlings ( y t ), 2-year-olds (d t ) and adults (a t ). The numbers of each age class at time t + 1 is then calculated to determine the total population at t + 1. The number of calves in year t + 1 is a result of reproduction of both adult females and 2-year-old females and can be expressed by: j t+1 = (a t b a ) + (d t b t ) eqn 2 where b a is the reproductive rate of adults and b t is the reproductive rate of 2-year-olds. The number of yearlings at t + 1 is dependent on the calf survival rate from the previous year. The number of yearlings can be calculated by: y t+1 = ( j t β j ) (1 c t ) eqn 3 before the introduction of lions and y t+1 = ( j t β j ) (1 (p t + c t )) eqn 4 after the introduction of lions, where β j is the calf survival rate and c t is the proportion of calves cropped. The 2-year-olds that survive from the yearling group minus the proportion lost to both cropping and predation determine the 2-year-old population size at t + 1: d t+1 = ( y t β y ) (1 c t ) eqn 5 before the introduction of lions and d t+1 = ( y t β y ) (1 (p t + c t )) eqn 6 after the introduction of lions, where β y is the survival rate of the yearlings. Mortality that is not the result of predation includes death from fence electrocution, fighting and poaching. The adults at time t + 1 are those surviving adults and 2-year-olds after accidental deaths have occurred minus the proportions lost to cropping and lions: a t+1 = ((a t β a ) (1 c t )) + ((d t β t ) (1 c t )) eqn 7 before the introduction of lions and a t+1 = ((a t β a ) (1 ( p t + c t ))) + ((d t β t ) (1 ( p t + c t ))) eqn 8 after the introduction of lions. Survival of adults and 2- year-olds independent of predation by lions is given by β a and β t, respectively. Wildebeest population data were limited for Pilanesberg and predation on wildebeest was not specifically monitored in the park. Nevertheless, accurate lion numbers were obtained from genealogical records, which are well maintained in Pilanesberg. We assumed that each adult Pilanesberg lion kills two to four wildebeest per year, as in the Kruger ecosystem (Starfield, Smuts & Shiell 1976; Peel & Montagu 1999). We simulated both low and high kill rates to investigate how differing predation pressure may affect the wildebeest population. It is feasible that each lion removes four wildebeest per year because of the enclosed and therefore more sedentary and (presumably) vulnerable nature of the population in comparison with Kruger. Predation was assumed to be even across age classes, excluding calves (Starfield, Smuts & Shiell 1976; Mills & Shenk 1992). Predation on calves was incorporated into the calf survival rates. The proportion of the wildebeest population removed by management each year was calculated from the Pilanesberg harvesting records and aerial census data. All analyses involving lions used the number of adult and subadult lions, i.e. those capable of killing and consuming wildebeest. Equal age distribution across sexes was assumed for wildebeest cohorts less than 2 years of age, after which

4 434 C. J. Tambling & J. T. du Toit male-biased mortality was expected (Estes 1968), and an estimate of 60% females (confirmed by field surveys) was adopted for the adult cohorts. Before lions were introduced to the park, adult female wildebeest fecundity should have been high, approaching the 95% recorded for western Masailand (Talbot & Talbot 1963). Assuming 95% of the adult females conceived each year, and 60% of adults were females, the adult reproductive rate for the model is 57% (i.e. excluding in utero and neonatal mortalities). Conception rates for 2-year-old wildebeest vary widely across Africa, reaching as high as 87% in western Masailand (Talbot & Talbot 1963), but ranging between 0% in Etosha, Namibia (Berry 1981b) and 32% in Kruger (Starfield, Smuts & Shiell 1976) for southern Africa. There is evidence that young female fecundity in ungulates is related to habitat quality (Gaillard et al. 2000), which is in turn related to rainfall (Owen-Smith & Ogutu 2003). The average annual rainfall in Pilanesberg was c. 620 mm year 1, which is greater than the long-term mean annual rainfall for Kruger (589 mm; Mills & Shenk 1992). Therefore, without data on the calving rate of 2-year-old wildebeest in Pilanesberg, we assumed that 2-year-olds have a conception rate of 30%, similar to that observed in Kruger. The 2- year-old age class in the wildebeest population consists of approximately 60% females, so, in combination with a conception rate of 30%, the reproductive rate for all 2- year-olds is 18%. For simplicity the reproductive rates of adult and 2-year-old wildebeest were kept the same before and after lions were introduced. Calf mortality was set at 50% (Starfield, Smuts & Shiell 1976; Berry 1981b) throughout all stages of the population s history and in all modelled scenarios. We used a step-ahead analysis to evaluate how different predation scenarios perform in predicting observed values one time step ahead (Turchin 2003). Specifically, if we use the model retrospectively to predict an outcome (e.g. population level in a specific year) y* at time t in the past, from initial conditions defined at time t 1, then letting y t be the value actually observed at time t and the mean or estimate of the total counts over the census history (average population size over a set period of time), the quantity: r 2 n 2 ( y* y t 1 t ) = = 1 n 2 ( yt ) t= 1 eqn 9 provides a measure of the performance of the model. In particular, r 2 = 1 implies the model fits the observed data perfectly, r 2 = 0 implies that the model fit is no more informative than using the mean or estimate of the total counts, and r 2 < 0 implies that the model fits the data worse than the mean or estimate of the total counts (Turchin 2003). Once the model was parameterized, two management scenarios (MS i ) were simulated: MS 1 assumed no lion introductions into the park; MS 2 assumed that wildebeest harvesting was terminated following lion introductions in The model was also run under two predation scenarios: PS 1 assumed a low predation rate by lions (each lion kills two wildebeest per year); PS 2 assumed a larger predation rate (each lion kills four wildebeest per year). Under each predation scenario, a further subset of four experimental scenarios was considered: ES 1 allowed the adult lion population to increase at approximately 12% per year and maintained the average rate at which the park management removed wildebeest since lions were introduced (7% per year); ES 2 stopped wildebeest harvesting and maintained the lion kill rate at a constant level per year (densitydependent predation; Hirst 1969); ES 3 stopped wildebeest harvesting and kept the lion population constant at its present level (density-independent predation); ES 4 stopped wildebeest harvesting and maintained the lion population at 50% of its present level. The ES j scenarios were run from 2001 until 2006 to predict what could happen under each scenario and to represent cases from the worst-case scenario (ES 1 ) to the best-case scenario (ES 4 ). The model was simulated for a further 5 years until 2006 using the parameters outlined by PS 2 with no harvesting and parameter values adjusted to determine the sensitivity of the model to changes in the parameter space (Starfield & Bleloch 1991). Parameters tested included lion numbers, juvenile survival and reproductive rates (2-year-old and adult rates). The parameters were increased and decreased by 10% to test how the projected population would react to changes in parameter values (Berry 1981b). The sensitivity of the parameters was investigated over a short time frame (1 year) and a longer time frame (5 years). Results WILDEBEEST POPULATION DYNAMICS Between 1984 and 1995 the wildebeest population grew by 12% per annum despite continual harvesting (Fig. 1). Lions were introduced in From 1995 to 1998 the wildebeest population levelled off and then went into a steady decline of c. 8% per annum. This cannot be explained by resource limitation because the 3-year mean annual rainfall has remained stable since 1997 at c. 780 mm, which is 25% higher than the long-term mean annual rainfall. The survival of wildebeest calves in Pilanesberg was very low, with calves comprising only 5 6% of the sampled population (Table 1), and so the cow : calf ratio was very high (8 : 1). This cannot be accounted for by resource limitation because, in addition to the rainfall trend described above, the body condition of adult wildebeest was generally good. In the sample of territorial males, 63% were in good condition and none were in poor condition, even though most were found in areas of tall, low-nutrient, grass rather than on the higher quality burnt patches. The adult sex ratio (females : males) was 1 : 1 5, indicating a clear bias towards females (χ 2 = 9 71, d.f. = 1, P < 0 05), which was unchanged from a 1998 survey in Pilanesberg.

5 435 Wildebeest population dynamics Fig. 1. Aerial counts for wildebeest in Pilanesberg National Park showing the observed rate of growth (r) as well as the yearly and average 3-year mean annual rainfall (mm). Table 1. Population structure of the Pilanesberg (PNP) wildebeest population compared with populations in Etosha, Zululand and Kruger National Park central district population Area Criteria PNP* Etosha Zululand Kruger Wildebeest sampled (n) Wildebeest in the breeding herds (%) Mean breeding herd size (no.) Adult females in the sample (%) Yearlings in the sample (%) Calves in the sample (%) Yearlings in the breeding groups (%) Calves in the breeding groups (%) Males in the bachelor herds (%) Mean bachelor herd size (no.) Lone territorial bulls (%) Breeding herd bulls (%) Adult males in the sample (%) Males : females 1 : : : : 1 67 Calves : females 1 : : : : 1 73 Yearlings : females 1 : : 2 12 *Present study, based on ground counts (September 2002). Berry (1981b), based on ground counts ( ). Attwell (1977), based on aerial counts (August 1974). Mason (1991), based on ground counts (August October 1990). LION POPULATION TRENDS The lion population increased from c. 25 animals in 1994 to 59 in 2001 (Table 2), equivalent to an annual population growth rate of 10 6% over this period. The number of adult females (> 2 years of age) also increased during this period and significantly explained a large percentage of the variation in the wildebeest numbers (R 2 = 0 63, n = 8, P < 0 05). There were, however, no statistical significant relationships between wildebeest population size and the total lion population size (R 2 = 0 45, n = 8, P = 0 068), or wildebeest population size and the number of adult lions in the population (R 2 = 0 41, n = 8, P = 0 087). THE POPULATION MODEL The scenario assuming higher predation pressure (four wildebeest taken per year per lion) tracked the three population phases (growth, level, decline) indicated from the field-derived aerial counts. However, at lower predation pressure (two wildebeest taken per year per lion) there was no decline from 1998 onwards (Fig. 2). The step-ahead analysis revealed that the least accurate

6 436 C. J. Tambling & J. T. du Toit Table 2. Lion population structure (n) in Pilanesberg National Park since lion introductions in 1993 Year Adults (total) Adult males Adult females 1 2 years olds Cubs Total Fig. 2. Population estimates from the model for no lion introductions from 1994 (MS 1 ), no harvesting after lion introduction (MS 2 ) assuming low predation pressure (PS 1, two wildebeest eaten per lion per year) and no harvesting after lion introduction (MS 2 ) assuming high predation pressure (PS 2, four wildebeest eaten per lion per year), vs. actual numbers from aerial counts for Pilanesberg National Park. Fig. 3. Population estimates from the model for low predation pressure (PS 1, two wildebeest eaten per lion per year) and high predation pressure (PS 2, four wildebeest eaten per lion per year), vs. actual numbers from aerial counts for Pilanesberg National Park. correlation between predictions and observed counts occurred when the impact of predation was low (r 2 = 0 376). When the impact of predation was high, the modelled population predicted a 76 5% better fit to the observed data than the mean estimate for total counts (r 2 = 0 765). This indicated that the model explained population trends better when parameterized with higher predation rates. When the model was run under management scenarios MS 1 and MS 2, it predicted population increases from 1994 onwards instead of the observed decline (Fig. 3). Under management scenario MS 2, at both high and low predation pressures, the model predicted that low predation would result in a much quicker population increase, almost to the point that the wildebeest population increased exponentially (Fig. 3). Assuming harvesting continued at approximately 7% and the lions continued to increase in numbers (ES 1 scenario), the model predicted a decline in the wildebeest population under both PS 1 and PS 2 scenarios (Figs 4

7 437 Wildebeest population dynamics Fig. 4. Predictions for future trends in Pilanesberg National Park until 2006 assuming low predation pressure (PS 1 ) under four experimental scenarios: maintaining the current growth in the lion population and 7% harvesting (ES 1 ); maintaining the kill rate (density-dependent mortality) and allowing no harvesting (ES 2 ); maintaining lion numbers (density-independent mortality) with no harvesting (ES 3 ); halving the lion numbers and allowing no harvesting (ES 4 ). Fig. 5. Predictions for future trends in Pilanesberg National Park until 2006 assuming heavy predation pressure (PS 2 ) under four experimental scenarios: maintaining the current growth in the lion population and 7% harvesting (ES 1 ); maintaining the kill rate (density-dependent predation) and allowing no harvesting (ES 2 ); maintaining lion numbers (density-independent predation) with no harvesting (ES 3 ); halving the lion numbers and allowing no harvesting (ES 4 ). and 5), with a more drastic decline, to approximately 100 individuals, under the PS 2 conditions (Fig. 5). When harvesting was terminated and the lion predation rate was maintained (ES 2 scenario), the populations did not deviate from the 2001 level, assuming both PS 1 and PS 2 scenarios (Figs 4 and 5). If lion numbers remained constant and wildebeest harvesting ceased (ES 3 scenario), under PS 2 the population would decline slightly (Fig. 5). However, under PS 1 the population recovered and started increasing (Fig. 4). The best-case scenario for the wildebeest population was when lion numbers were halved and harvesting was terminated (ES 4 scenario), resulting in population increases under both PS 1 and PS 2 (Figs 4 and 5). The effects of the 10% increase and decrease in the parameters are given in Fig. 6. The most sensitive parameter over the short term (1 year) was adult wildebeest reproductive rate, whereas over the long term (5 years) the most sensitive parameter was lion population size (Fig. 6). A 10% decrease in the adult wildebeest reproductive rate resulted in a 2 62% decline in the wildebeest population in 1 year. The cumulative effects of a 10% increase in lion numbers until 2006 caused the population to decline by 22% over the 5-year period. The least sensitive parameter was the 2-year-old reproductive rate, causing a 0 16% change in both directions in a single year and a 1 14% decrease and 1 15% increase by The order of increasing sensitivity for the model over 1 year was: 2-year-old reproductive rate, lion number, calf survival and adult reproductive rate. Considering the cumulative effects over 5 years, the least sensitive parameter was: 2-year-old reproductive rate, followed by calf survival, adult reproductive rate and lion number. Discussion Wildebeest populations had been reported to be declining in Pilanesberg (this study), Etosha (Berry 1981b) and Zululand (Attwell 1977) but stable in Kruger

8 438 C. J. Tambling & J. T. du Toit Fig. 6. Sensitivity analysis to determine what affect a 10% increase or decrease in parameter (2-year-old reproductive rate, adult reproductive rate, calf survival and lion population size) value will have on the projected population modelled until (Whyte 1985). The annual rate of decline of the Etosha and Zululand populations was approximately 3 8%, whereas the Pilanesberg population had declined at c. 8 6% year 1 since The Pilanesberg, Etosha and Zululand populations were considered sedentary, but the Kruger population still maintained seasonal movements (Mason 1991) despite the influence of artificial water supplies (Gaylard, Owen-Smith & Redfern 2003). The Pilanesberg and Zululand populations showed a similar percentage (10 1% and 9%, respectively) of lone territorial males. This was considerably higher than in Etosha (3 7%) and Kruger (5 3%), where the populations move over larger areas and where selective predation on lone territorial males would be expected when breeding herds move away to new grazing areas. In contrast, the most vulnerable part of the Pilanesberg population was the calves. A 25% increase in rainfall over the period of wildebeest decline would have facilitated grass growth, a factor known to improve lion hunting success (Funston, Mills & Biggs 2001). Furthermore, in the absence of evidence of resource limitation, it seems likely that the high calf mortality was the result of increased numbers of predators, aided by more cover. A similar reduction in wildebeest calf survival was described in Phinda Reserve (Northern Kwa-Zulu Natal, South Africa) and was thought to be a consequence of lion and cheetah Acinonyx jubatus introductions into the reserve (Hunter 1998). In 1998 juveniles (calves and yearlings) comprised 28 6% of the wildebeest population, in comparison with our estimate of 24 8%. However, the 1998 survey did not differentiate between calves and yearlings so we cannot be certain if calf survival has always been as low as it is now, or if fluctuations in calf numbers have occurred from year to year. The lion : prey biomass (kg) ratio for Pilanesberg increased from 1 : 173 in 1996 to 1 : 95 in 2001, while in Etosha this ratio varied between 1 : 107 and 1 : 153. This is high compared with values of 1 : : 300 in other areas (Berry 1981a). The lion biomass density of 14 5 kg km 2 in Pilanesberg was more than three times greater than the 4 38 kg km 2 predicted by East s (1984) regression model describing the relationship between prey and predator biomass. The lion biomass density in Pilanesberg was higher than Etosha (1 96 kg km 2 ; East 1984), Kruger (11 8 kg km 2 ; Smuts 1976) and Zululand (9 21 kg km 2 ; Myers 1975). THE PILANESBERG CASE STUDY: IMPLICATIONS FROM MODELLING The development of the model arose from the need to assess rapidly the potential factors that may play a role in the decline of the wildebeest population in Pilanesberg. Lion predation was included a priori because of an observed relationship between lion numbers and wildebeest population size, and the model allowed for variation in predation pressure. We used a simple model to reduce the impact of parameter uncertainty (Starfield, Smuts & Shiell 1976). Nevertheless, we acknowledge that by excluding the interacting influences of drought, disease and competition we may have missed some additional factors contributing to the wildebeest population decline. The simulation of two levels of predation pressure resulted in different outcomes. When simulated with low predation pressure, the population did not decline from 1998 onwards. The observed decline was only evident when predation rates were high (four wildebeest killed per lion per year). Therefore, if lion predation occurs at low levels then other factors must contribute to the population decline. In Kruger, wildebeest and zebra Equus burchelli numbers are negatively correlated with rainfall, whereas other species (waterbuck Kobus ellipsiprymnus, kudu Tragelaphus strepsiceros, buffalo Syncerus caffer and impala Aepyceros melampus)

9 439 Wildebeest population dynamics show the opposite trend (Starfield, Smuts & Shiell 1976; Whyte 1985; Mills, Biggs & Whyte 1995). If this relationship holds for Pilanesberg, increased rainfall should lead to declines in wildebeest and zebra numbers, whereas kudu, waterbuck, buffalo and impala should increase in numbers. There has been a 25% increase in rainfall since 1997, yet zebra and impala numbers remained constant until large numbers were removed in (16% of the impala population, 35% of the zebra population). Large declines have also occurred in eland Tragelaphus oryx (76%), waterbuck (67%) and kudu (65%) since rainfall increased in Therefore, competition with zebra and impala may have played a part in the initial stages of the wildebeest decline but it is unlikely that this competition was important following the decline in ungulate populations. The possible consequence of no management actions (ES 4 ) if predation pressure remains high is an obvious concern. However, assuming the best-case scenario (ES 1 ), the present decline can be halted under both high and low levels of predator pressure. The wildebeest population showed a further decline between 2001 (n = 594) and 2002 (n = 471), indicating that population numbers are not stabilizing and some management actions will be needed to halt the current decline. The model was most sensitive to lion predation. This trend only became apparent over several years because of the lag effect often found between predators and prey. Adult reproductive rates and calf survival were most important to population stability, therefore management interventions should ensure that females are not targeted. In this study, the predation rate on both sexes has not changed since 1998 and the sex ratio is known to be similar to other areas (Table 1). This suggests that all segments of the population are declining, and the reduction in numbers of females and associated calves, as a result of predation and harvesting programmes, may be driving the decline. The Pilanesberg wildebeest population declined at c. 8% per annum through 6 years of above-average rainfall, while managers were unaware that the population was unable to sustain both natural predation and harvesting. The results from our analysis indicate that if lions had not been reintroduced the population would have continued to follow its previous upwards trend until controlled by density dependence. Conversely, if the harvesting operations had ceased following the introduction of lions the population would still have increased until limited by density dependence. The potential impact of elevated predation pressure on the wildebeest population, and the rapid increase in the lion population to an unusually high density in Pilanesberg, offers support for the hypothesis that sedentary wildebeest populations may be especially vulnerable to high levels of predation (Fryxell & Sinclair 1988; Fryxell, Greever & Sinclair 1988). Of the three hypotheses put forward to explain the decline of the Pilanesberg wildebeest numbers, predation on this sedentary and enclosed ungulate population emerges as the most plausible. Inadequate rainfall during a critical phase of the intra-annual cycle can be ruled out, as the population has declined consistently since 1995 in common with other ungulate species. Resource limitation is unlikely given that no loss of body condition was detected and rainfall in Pilanesberg has been above average since The model was designed to provide a simple simulation of wildebeest population dynamics, open to improvement and refinement (Starfield & Bleloch 1991). If populations continue to decline following a reduction in lion numbers, research should be directed at the ungulate resource interface and other factors identified. IMPLICATIONS FOR MANAGEMENT The Pilanesberg case study adds to previous evidence that sedentary ungulate populations are susceptible to high levels of predation (Starfield, Smuts & Shiell 1976; Sinclair 1985; Mills 1990; Sinclair 1995; Peel & Montagu 1999). The implications for managed savanna ecosystems are: (i) when ungulate species with migratory tendencies (such as wildebeest) are enclosed, their potential to sustain predation and harvesting may be overestimated; (ii) when lions have access to sedentary staple prey, their population growth may be underestimated. These findings underscore the importance of maintaining corridors between conservation areas to allow source sink dynamics to operate for prey and predator populations, although human demographics and land transformation in Africa are rendering this impractical. The maintenance of the natural spatiotemporal heterogeneity of habitats within large wildlife reserves is also important, although this can be jeopardized by artificial water provisioning (Gaylard, Owen-Smith & Redfern 2003). The introduction of artificial water points is a common management intervention in African wildlife areas, and savanna ungulates that typically attain high biomass densities, such as wildebeest, zebra and buffalo, are most responsive to water provisioning (Owen-Smith 1996). These are staple prey species for large predators (Radloff & du Toit 2004). Where staple prey become resident around permanent artificial water supplies, the lion density may quickly build up and impose severe spill-over effects on rare prey species (e.g. roan antelope Hippotragus equinus; Harrington et al. 1999). Finally, the mounting requirement to provide benefits such as meat to local communities living outside African wildlife reserves (du Toit, Walker & Campbell 2004) places pressure on park managers to consider game harvesting schemes. 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