Pilanesberg National Park (25°8′S−25°22′S, 26°57′E−27°13′E) is a 50 000-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 (1984–2001) 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 1979. 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 2002. The observed rate of population change was determined for an increasing phase (1984–95) and a decreasing phase (1995–2002). 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).
lion population trends
Lions Panthera leo are the dominant large predators in Pilanesberg, having been reintroduced in 1993. 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 2001.
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 1979. We assumed that wildebeest of all age classes and both sexes are harvested (cropped) in equal proportions. The cropping rate (ct) 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:
( eqn 1)
where γ is the number of wildebeest taken per adult lion per year, and lt and wt 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 (jt), yearlings (yt), 2-year-olds (dt) and adults (at). 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:
( eqn 2)
where ba is the reproductive rate of adults and bt 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:
( eqn 3)
before the introduction of lions and
( eqn 4)
after the introduction of lions, where βj is the calf survival rate and ct 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:
( eqn 5)
before the introduction of lions and
( eqn 6)
after the introduction of lions, where βy 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:
( eqn 7)
before the introduction of lions and
( eqn 8)
after the introduction of lions. Survival of adults and 2-year-olds independent of predation by lions is given by βa and βt, 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 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 yt be the value actually observed at time t and ȳ the mean or estimate of the total counts over the census history (average population size over a set period of time), the quantity:
( eqn 9)
provides a measure of the performance of the model. In particular, r2= 1 implies the model fits the observed data perfectly, r2= 0 implies that the model fit is no more informative than using the mean or estimate of the total counts, and r2 < 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 (MSi) were simulated: MS1 assumed no lion introductions into the park; MS2 assumed that wildebeest harvesting was terminated following lion introductions in 1993. The model was also run under two predation scenarios: PS1 assumed a low predation rate by lions (each lion kills two wildebeest per year); PS2 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: ES1 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); ES2 stopped wildebeest harvesting and maintained the lion kill rate at a constant level per year (density-dependent predation; Hirst 1969); ES3 stopped wildebeest harvesting and kept the lion population constant at its present level (density-independent predation); ES4 stopped wildebeest harvesting and maintained the lion population at 50% of its present level. The ESj scenarios were run from 2001 until 2006 to predict what could happen under each scenario and to represent cases from the worst-case scenario (ES1) to the best-case scenario (ES4).
The model was simulated for a further 5 years until 2006 using the parameters outlined by PS2 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).