#### study area

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 km^{2}) 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 km^{2} (34% on cattle and 66% on sheep ranches). About 37% of land in the surrounding region (5236 km^{2}) 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).

#### 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 *D*_{ij} 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.