The study area was a mixed steppe of grass and shrubs in north-western Patagonia (40°S, 71°W), Argentina (see Appendix 1). Six ranches (80–400 km2) were chosen to represent dominant land uses in the region. Collun-Co and La Rinconada were cattle ranches where culpeo hunting was rare or non-existent, and Catan Lil, La Papay, Los Remolinos and Cerro de los Pinos were predominantly sheep ranches where hunting was intense. Hunting occurred primarily during late autumn and early winter (1 Ma.−31 August), although some occurred throughout the year. The total area of all six ranches was 1420 km2 (34% on cattle and 66% on sheep ranches). About 37% of land in the surrounding region (5236 km2) was cattle ranches, so our main study area was representative of the proportion of land with and without hunting in this region (see Appendix 1).
Biomass of culpeo prey, except for sheep, was similar on sheep and cattle ranches, and sheep represented 20% of the biomass of the culpeo diet on sheep ranches (Novaro, Funes & Walker 2000). Thus we did not expect differences in prey productivity between ranches to influence culpeo survival or fecundity.
Culpeos have been hunted in this area since the introduction of sheep in the early 1900s (Crespo & de Carlo 1963), sustaining high hunting pressure when fur demand increased during the 1960s and 1970s (Novaro 1995). Prior to 1994, all ranches studied had maintained consistent practices with respect to hunting and livestock for at least 30 years. As a result of declining sheep wool prices, the owners of Cerro de los Pinos and Los Remolinos began raising only cattle in early 1994 and banned culpeo hunting. This ban during our study (1989–97) allowed us to test for compensatory mortality (see below).
test of the source–sink model
We tested the following predictions of the source–sink hypothesis.
Prediction 1: rates of increase
The rate of increase of the culpeo population based on schedules of survival and fecundity (rc; Caughley & Sinclair 1994) is significantly < 0 on hunted ranches and significantly > 0 on unhunted ones, but the observed rates of increase (ro) are not significantly different from 0 if the regional population level is stable (Hanski & Simberloff 1997). To evaluate which demographic parameter determined differences between rc and ro, we compared rates of survival and fecundity between ranches.
Prediction 2: dispersal direction
Most culpeos disperse from unhunted to hunted ranches.
Prediction 3: non-compensatory mortality
If hunting mortality is removed from a previously hunted ranch, culpeo survival should increase significantly because any increase in natural mortality would not be sufficient to compensate for hunting mortality (Caughley & Sinclair 1994).
ro for culpeos was estimated from population trends obtained at the beginning of the hunting season between 1989 and 1997 with scent stations (Roughton & Sweeny 1982). Forty scent stations (eight lines of five stations each) were operated along all internal roads and trails of each ranch during one day and night. We calculated culpeo densities from scent station indices (SSI) using a conversion factor [density = SSI/(32·8 ± 3·0)] obtained from a simultaneous calibration with line transect estimates (Novaro et al. 2000). Rates of increase between 1989 and 1994 were calculated with the Caughley & Sinclair (1994) linear regression method. Densities for 1995–1997 were not used because of the ban on hunting in two of the ranches in 1994.
rc was calculated with data from radio-telemetry and analysis of 362 culpeo carcasses collected during the hunting season between 1989 and 1994. We captured 47 culpeos on Collun-Co (unhunted control, hereafter UCC) and adjacent Cerros de los Pinos (hunted, HCP) between January and May of 1993 and 1994 using padded foot-hold traps (Victor 1.5 soft-catch; Woodstream Corp., Lititz, Pennsylvania). Ages of culpeos were estimated according to tooth wear (Zapata, Funes & Novaro 1997). A total of 23 adults and 21 juveniles, which weighed at least 50% of adult body mass (4 months old; Crespo & de Carlo 1963), were fitted with radio-collars (ATS Inc., Isanti, MN; weighing up to 5% of body mass). Fifty per cent of radio-collared culpeos were females. Twenty-seven culpeos were captured and radio-tracked in 1993 (11 at UCC and 16 at HCP). In 1994, 13 survivors from 1993 and 17 newly captured culpeos were radio-tracked (16 at UCC and 14 at HCP). Eighteen culpeos that survived throughout 1994 were radio-tracked until they died or until 15 March 1996. Culpeos were located during the daytime at least twice every week from a vehicle or from a fixed-wing aircraft. We did not locate culpeos at night because we did not attempt to describe habitat use or activity patterns. We interviewed hunters to establish when and where culpeos were killed. Carcasses of non-hunted culpeos that died were necropsied to determine cause of death.
Survival rates were estimated from dates of capture and death with the Kaplan–Meier method (White & Garrott 1990; Bechet et al. 2003) and cause-specific mortality rates with the Mayfield estimator using program micromort (Heisey & Fuller 1985). Survival of juveniles and adults were different, so they were analysed separately. Yearly survival of adults was estimated between 15 November (the mid-point of the birth pulse; Crespo & de Carlo 1963) of one year and 14 November of the following year. Survival of radio-tracked juveniles 4–12 months of age was estimated between 15 March and 14 November. Some culpeos dispersed from HCP and UCC to other ranches. Survival data on other ranches were grouped with data from HCP and UCC according to hunting pattern to estimate overall survival of hunted and unhunted populations. Survival rates were compared using the log–rank test in SAS (SAS Institute Inc. 1996).
Culpeo fecundity rate was the product of the proportion of breeding females and the number of female pups produced per female (Caughley & Sinclair 1994). Radio-tracked females were identified as breeding if they denned and if signs of pups (e.g. faeces, tracks) were observed. Survival of juveniles between 0 and 4 months of age was estimated by dividing the average litter size seen at 4 months by in-utero embryo counts. Nine pups from three litters were captured and ear tagged. We estimated litter size by combining counts of pups at dens and embryos in female reproductive tracts (Gese, Rongstad & Mytton 1989). Fecundity of culpeos that dispersed was analysed following the criteria for grouping ranches for survival analysis. Because not all pregnant females in the carcass sample might have given birth to live litters, we may have overestimated rates of fecundity and population increase for hunted ranches. This overestimation, however, would result in a more conservative test of the predictions. Fecundity rates were compared using a randomization test because of the small sample sizes and lack of independence among samples (because data for the same females on different years were grouped; Bruce, Simon & Oswald 1995).
We estimated the age of dead animals by counting cementum annuli on canine teeth (Zapata, Funes & Novaro 1997). Culpeos were grouped into yearly age classes up to 6 year olds; older culpeos were grouped into one age class. Sex ratio was compared with a 1 : 1 ratio using a chi-square test.
The rc of culpeos was calculated using the Lotka (1907a,b) iterative equation:
∑lx e − rx mx = 1
where lx and mx are the survival and fecundity, respectively, of age class x. We assumed constant fecundity rates for 1-year-old and older females. Rates of increase were also expressed as finite rates per year (λ = er).
We estimated dispersal rates from the proportion of radio-tracked culpeos that dispersed from one ranch to another. We recorded dates of departure from natal range and arrival at new range, dispersal distance, and type of ranch (unhunted or hunted) for the new range.
culpeo population dynamics and landscape changes
We studied population dynamics of culpeos using the RAMAS/Metapop simulation model (Akçakaya 1994). The model had a spatial structure defined by the geographical location of populations, dispersal among populations and correlation among their vital rates. To simulate dynamics on a continuous landscape, we modelled the populations of the six ranches studied and of the 17 additional ranches to the north and south, for which we recorded size and culpeo hunting pattern (see Appendix 1). The area was delimited to the west by the Andes Mountains and the east by the limit of culpeo distribution. More distant ranches to the south were included because two radio-collared culpeos dispersed 86 and 90 km south (see the Results).
Percentage change in population size was the dependent state variable. Input data were demographic parameters estimated on the six ranches. Initial age structures and abundances on the additional ranches were calculated using average age structures and densities from the former six ranches (0·49 ± 0·12 and 0·31 ± 0·09 culpeos km−2 on the four hunted and two unhunted ranches, respectively). We assumed age structures did not change during the simulation, modelled all individuals in the population (females and males, ratio 1 : 1), and used a matrix model with three stages (juveniles, 1 year olds and older). We used two adult age classes because survival of 1-year-old adults was lower and because some 1 year olds dispersed.
Vital rates were calculated following methods proposed by Caswell (1989) and Akçakaya (1994). Reproductive data were analysed as maternity rates. Transition matrices were constructed assuming age structures from a pre-breeding census because most carcasses were collected during winter, before the culpeo birth pulse (Caswell 1989). The transition matrix for populations on ranches without hunting, built with vital rates from UCC (see the Results),was , and for ranches with hunting,with vital rates from HCP and other hunted ranches,was . The matrix for hunted rancheswas assigned using the catastrophe feature of RAMAS, with local probability of 1.
Environmental stochasticity was simulated by choosing vital rates at random from a normal distribution with means from each transition matrix and standard deviations from a matrix calculated from annual variation of vital rates. The matrix of standard deviations of vitalrates was . Demographic stochasticitywas included because it could be significant if there were sharp declines in abundance, which was likely on small hunted ranches.
Dispersal rates among ranches were calculated assuming that dispersal declined monotonically with distance (Akçakaya 1994), which was reasonable based on our radio-telemetry data. Dispersal rate between ranches i and j was:
where Dij was the distance between the geographical centre of ranches i and j. Maximum dispersal distance (D) was that recorded with radio-telemetry (see the Results).
We did not include density dependence in the simulations for two reasons. First, when populations are subject to ‘systemic’ pressures such as regular and intense hunting, inclusion of density dependence in simulations can lead to an underestimation of extinction risks (Ginzburg, Ferson & Akcakaya 1990). Secondly, we did not have information on density-dependence parameters of culpeo populations. Because hunting was decreasing in the area, we presumed that density dependence might become a more significant factor in the future, and therefore ran the simulations for only 8 years, the duration of the study of demographic parameters, assuming these parameters incorporated density dependence effects at current densities. We used 1000 replications in each simulation and validated the model by comparing output population trends with trends estimated between 1989 and 1997.
The implication of changes in the proportion of hunted and unhunted areas was analysed by simulating changes in the proportion between cattle and sheep ranches. To study the effect of a declining unhunted area, we switched unhunted to hunted ranches one at a time and ran the model with remaining parameters unchanged. We also evaluated a combination of changes in landscape proportions and vital rates. To assess which vital rates may have a stronger influence on population dynamics we did a sensitivity analysis. We changed survival, fecundity and dispersal rates by 10%, 20% and 30% and measured changes in population trend.