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Computer Simulation of Wolf-removal Strategies for Animal Damage Control


Considerations for model design

Wolves live in packs and defend exclusive territories (Mech 1973). Generally, packs are family groups, with 1 dominant breeding pair and their offspring (Mech 1970). In the western Great Lakes region, midwinter pack size averages 4-8 wolves, with about half being pups (Fuller 1989). Because of territoriality, population density and reproductive rate depend on number and size of territories. Wolves depend on prey availability and can live wherever large herbivores are present, provided humans can tolerate them (Fuller 1995, Mech 1995). Population turnover rates are naturally high, with G pups born per pack (Mech 1970) and more than half of pack members lost each year to mortality and dispersal (Mech 1977, Fritts and Mech 1981, Fuller 1989, Gese and Mech 1991). A dispersing wolf might pair with the opposite sex and colonize a vacant territory, or join another pack and replace a missing breeding member (Rothman and Mech 1979, Fritts and Mech 1981, Fuller 1989). Wolf populations are characterized by discrete but interacting packs. In the western Great Lakes region, midwinter pack territories average 150-180 km² (Fuller et al. 1992, Wydeven et al. 1995).

Formulation of the wolf simulation model

We designed a stochastic, demographic model of a wolf population consisting of 64 pack territories living in a large, semi-wild landscape with abundant, well-distributed prey. The model was spatially structured (Beissinger and Westphal 1998) because the population was subdivided into packs, which were located in either wild- or farm range; however, the model was not spatially explicit because territory shapes and locations were not included. The model was individually based because demographic events were computed 1 wolf at a time. The model was a variant of one developed by Haight and Mech (1997).

Our model simulated mortality, dispersal, and birth of wolves in each pack using estimates obtained in Minnesota (Fuller 1989) and Wisconsin (Wydeven et al. 1995). State variables for each pack included number of wolves of each sex in 3 age classes: pup (0-12 months), yearling (12-24 months), and adult (>24 months). Individuals of the last 2 age classes could belong to 2 categories: nonbreeding and breeding. The model allowed 1 breeding pair per pack (Meth 1970). Packs in farm territories could have 2 states: a tendency for depredation or not, based on wolf behavior in farm territories (Fritts and Mech 1981). The model assumed an annual probability of 20% that packs with no history of depredation in farm territories initiated this activity.

The annual cycle of events (Figure 1) began in autumn, and all modeled mortality occurred in winter. Whether each wolf died was a Bernoulli random variable with probability depending on wolf age. Mortality rates were 65% and 32% far pups and older animals, respectively (Fuller 1989, Wydeven et a1. 1995).

Figure 1
Figure 1.  Annual sequence of wolf-removal and demographic events in the wolf-removal model used to evaluate 4 hypothetical removal strategies.

Modeled dispersal occurred in late winter, with probability = 1.0 if the breeding pair died. Otherwise, whether each wolf dispersed was a Bernoulli random variable with probability depending on wolf age: pups (25%),.yearlings (50916),and nonbreeding adults (90%; Gese and Mech 1991). Breeders had no probability of dispersal. The model assumed 20% long-distance dispersals, with those wolves being lost from the population. The model annually included 5 immigrants that joined the dispensers.

Each disperses searched the area for a suitable territory (i.e., a vacant one or one with an available mate). The model assumed that each dispersing wolf randomly explored 6 territories (Lande 1987, Lamberson et al. 1994). Unsuccessful dispensers died. The probability of finding a suitable territory was as follows:

Figure 2: equation

Successful dispensers were assigned to the most suitable territory among the 6 they explored, suitability depending on depredation history. Dispensers coming from packs without tendencies for depredation were assumed to prefer territories with available mates to empty territories without preference for territories in wild or farm areas. The model assumed dispensers originating from packs with a tendency for depredation to select first for territories with available mates and second for territories in farm range.

Breeding pairs produced their pups in spring, and we modeled litter size using a discrete probability distribution, with a mean of 6.5 pups and a range of 0-10 pups (Fuller 1989). The sex of each pup was determined with equal probabilities. When only one member of the breeding pair occupied a territory, it head its territory without reproducing (Smith et al. 1997). The age distribution of each pack was updated after birth.

The propensity for depredation of packs near farms was updated following reproduction. All packs with a history of depredation were assumed to maintain that tendency. Each pack with no history of depredation could switch to a tendency for depredation in one of two ways: if a dispersing wolf with a tendency for depredation joined the pack, or if proximity to farms induced depredation (P = 0.20).

Removal strategies

We modeled wolf-removal strategies over a 20-year horizon, assuming 32 farm territories and 32 wild territories. The initial autumn population had 320 wolves in 32 packs, where each pack had 6 pups, 2 yearlings, and 1 breeding pair of adults. Six teen packs inhabited farm territories, half of theta having tendencies for depredation.

We simulated 3 types of wolf removal: preventive (P), reactive (R), and population-size (S) management. We also evaluated 2 mixed strategies: preventive and reactive management (P-R) and population-size and reactive management (S-R). In addition to these 5 active management strategies, we considered a sixth strategy of no action (N).

We assumed that each removal strategy used trapping or snaring, methods that were not 100 effective. Simulations assumed capture probabilities of 60% for pups and yearlings and 30% for adults. Trapping stopped when the fate of every wolf in targeted territories had been determined.

The model included two kinds of density dependence. There was partial compensation between natural and human causes of mortality because those two types of mortality events were applied at different points in time. In addition, the fate of dispersers depended on the rate of territory occupancy (i.e., population density).

Analysis of management strategies

We evaluated removal strategies over a 20-year horizon based on livestock loss, wolf removal, and sustainability of the strategies. We ran simulations 1,000 times and computed each performance measure for the final year of the 20-year horizon. Livestock loss from wolf depredation was estimated by counting farm territories in June that were occupied by packs with a tendency for depredation. We determined sustainability of management strategies using mean population size and probability that population size decreased to <100 wolves.

The cost of each removal strategy was also computed for the final year of the 20-year horizon (1998 United States dollars) and included compensation payments for animals lost to wolf depredation and costs of trapping and removing wolves. We assumed that each wolf pack involved in depredation affected 3 Farms, which represented $1,680 (assuming compensation averaged $550 per farm; Mech 1998). We also assumed that the cost of trapping and removing each wolf under reactive management was $1,500, based on data collected in Minnesota (Mech 1998). For preventive and population-size management, we used an administrative removal cost of $500 per wolf because such removal imposed fewer restrictions on the location and timing of wolf removal.

Sensitivity analysis

We analyzed the impacts of one-at-a-time changes in selected model parameters. To determine the impacts of changing the immigration rate, we evaluated removal strategies with 0 and 20 immigrants per year. To determine the impacts of increasing trapping success, we increased capture probabilities to 80% for pups and yearlings, and 60% for adults. Finally, we evaluated the removal strategies under 1% and 40% annual probabilities of wolves becoming prone to depredation.

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