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Computer Simulation of Wolf-removal Strategies for Animal Damage Control

Results


Single strategies

The 3 removal strategies reduced mean depredation by at least 40% compared with the no-action strategy (Table 1). With no action, the populations doubled from 320 wolves in 32 packs (year 0) to an average of 661 wolves in 64 packs (year 20), with depredation occurring in 30 of the 32 farm territories. Preventive and reactive strategies reduced the number of farm territories with depredation to 15-17 packs. Depredation decreased because each strategy removed wolves in territories overlapping farms. As a result, 40-50 % of the territories near farms were either free of wolves or included wolves that did not have a tendency for depredation. The population-size strategy reduced depredation to an average of 10 packs because it had fewer restrictions on wolf removal and therefore fewer wolves lived near farms.

Table 1.  Mean performance (n = 1,000) in year 20 of hypothetical wolf-removal strategies with the following base-case assumptions: 5 immigrants per year, 60% capture probability for pups and yearlings and 30% for adults, and 20% annual probability of wolves in a farm territory becoming prone to depredation. Standard errors are in parentheses.
Performance measure Strategy a
N P R S P-R S-R
Packs active in depredation 30
(0.04)
15
(0.11)
17
(0.10)
10
(0.12)
9
(0.09)
5
(0.08)
Wolves removed 0
(0.00)
21
(0.21)
80
(0.58)
17
(0.22)
38
(0.44)
20
(0.34)
Population size 661
(0.98)
382
(1.84)
463
(1.53)
271
(2.41)
357
(1.90)
216
(2.13)
Probability population size <100 0.00 0.00 0.00 0.02
(0.004)
0.00 0.04
(0.006)
Compensation cost ($ thousand) 50.4 25.2 28.6 16.8 15.1 8.4
Removal cost ($ thousand) 0.0 10.5 120.0 8.5 45.0 19.0
Total cost ($ thousand) 50.4 35.7 148.6 25.4 60.1 27.4
a Management strategies: N = no action, P = preventive, R = reactive, S = population size reduction.

Preventive and population-size strategies removed 70-80% fewer wolves than the reactive strategy (Table 1) because removal occurred in winter before birth (Figure 1). On average, about 1 wolf per pack was captured and removed. Because the reactive strategy took place in summer after pups were born, >4 wolves were removed per pack on average, most of which were pups and yearlings.

None of the 3 strategies, applied alone, threatened to extirpate the wolf populations because wolf removal was limited to packs near farms, and the majority of packs lived in the wild area and totaled >100 wolves (Table 1). The population-size strategy reduced the number of wolves in farm territories from 160 in year 0 to an average of 73 in year 20 with annual removal rates of 20-25% of the population in farm territories. Those removal rates were lower than sustainable harvest levels estimated for free-ranging populations (30-50%; Mech 1970, Gasaway et al. 1983, Peterson et al. 1984, Bollard et al: 1987, Larivière et al. 2000).

Combined strategies

Combining preventive or population-size management with reactive management doubled the trapping effort on packs with tendencies for depredation, resulting in <10 packs with such tendencies after 20 years (Table 1). Under such scenarios, >70% of farm territories were either free of wolves or included wolves without tendencies for depredation. Combined strategies reduced wolf removals by 50-75% in year 20 compared with reactive management alone because there were fewer packs with tendencies for depredation. Combined strategies also increased turnover in territories near farms, resulting in smaller packs. Combined strategies did not threaten to extirpate populations, although they produced smaller populations than the single strategies.

Cost

In year 20 compensation payments averaged $50,400 under the no-action scenario (Table 1). The 2 single strategies in which we removed wolves in winter before birth (i.e., preventive and population-size management) reduced costs 30-50% because they resulted in fewer depredating packs and removed fewer wolves. Reactive management was the most expensive because of the large number of wolves removed and the high unit cost of wolf removal.

The 2 combined strategies had different impacts on costs relative to no action (Table 1). Population-size reduction combined with reactive removal reduced costs 46%, while the combination of preventive and reactive removals increased casts 19%. Population-size reduction resulted in fewer wolves in farm territories, thereby reducing the number of high-cost reactive removals.

Standard errors

Number of depredating packs, wolves removed, and population size were averages of outcomes in year 20 obtained from 1,000 independent simulations of the wolf model. With 1,000 replications, standard errors were <2% of the means (Table 1). The estimator for the probability that population size was <100 waives was the proportion of simulations with populations <100 wolves in year 20. With 1,000 simulations, standard errors of estimated probabilities between 0.20 and 0.80 were 0.012-0.016. Standard errors of estimated probabilities between 0.01 and 0.20 were 0.003-0.012. White we could not compute a standard error for cases in which the estimated probability was 0.00, we can say that if the probability were really >0.01, it would be very unlikely (less than one chance in 10,000) we would observe no instances of these events in 1,000 simulations. Standard errors of the means obtained in the sensitivity analyses were of the same magnitude, so we did not report them.

Sensitivity analyses

The absence of immigration (Table 2) resulted in smaller wolf populations after 20 years under all removal strategies compared with population projections with 5 immigrants per year (Table 1). As a result, fewer wolves colonized territories near farms, fewer packs had tendencies for depredation, and fewer wolves were removed. Without immigration, population growth was very sensitive to the type of wolf removal, the growth rate remaining positive only with reactive removal or no action. The two strategies involving population-size management (S and S-R) resulted in populations with <100 wolves in >60% of the simulations. Without immigration, populations declined without stabilization because many wolves from wild areas dispersed to farm range and were removed before they could reproduce. The wolves remaining in the wild area were not numerous or productive enough to sustain the population.

Table 2.  Mean performance (n = 1,000) in year 20 of hypothetical wolf-removal strategies under 2 scenarios of the immigration rate; other assumptions as in the base case.
Performance measure Strategy a
N P R S P-R S-R
0 immigrants per year
Packs active in depredation 30 11 14 3 6 1
Wolves removed 0 13 58 5 21 4
Population size 652 254 351 87 214 52
Probability population size <100 0.00 0.10 0.05 0.63 0.17 0.82
Compensation cost ($ thousand) 50.4 18.5 23.5 5.0 10.1 1.7
Removal cost ($ thousand) 0.00 6.5 87.0 2.5 25.5 4.0
Total cost ($ thousand) 50.4 25.0 110.5 7.5 35.6 5.7
20 immigrants per year
Packs active in depredation 30 18 18 17 11 10
Wolves removed 0 28 89 30 52 48
Population size 669 463 514 438 438 383
Probability population size <100 0.00 0.00 0.00 0.00 0.00 0.00
Compensation cost ($ thousand) 50.4 30.2 30.2 28.6 18.5 16.8
Removal cost ($ thousand) 0.0 14.0 133.5 15.0 60.0 50.0
Total cost ($ thousand) 50.4 44.2 163.7 43.6 78.5 66.8
a Management strategies: N = no action, P = preventive, R = reactive, S = population size reduction.

The influx of 20 immigrants per year amplified trends observed under the scenario of 5 immigrant per year, and wolf populations were larger after 2 years under a31 removal strategies (Table 2). This resulted in more wolves colonizing territories near farms, more packs with tendencies for depredation, and greater wolf removal. The preventive strategy produced the same results as population-size management under the high-immigration scenario because most territories in farm range contained depredating packs.

With an increase in probability of capture (Table 3), relative performance of removal strategies remained the same as in the base case (Table 1). However, increasing the capture probability resulted in fewer depredating packs and fewer wolf removals compared with projections in the base case. Repeated and effective trapping near farms kept the number of packs and the size of those packs relatively small. With fewer depredating packs and wolf removals, the projected cost of each removal strategy was lower than its counterpart with lower capture probability. Strategies involving population-size management cost 75-80% less than the no-action strategy because of lower, depredation costs. Finally, increased capture probability reduced population-size projections relative to the base case, especially when wolves were removed near farms without regard for the pack's depredation history.

Table 3.  Mean performance (n = 1,000) in year 20 of hypothetical wolf-removal strategies under 80% capture probability for pups and yearlings and 50% for adults; other assumptions as in the base case.
Performance measure Strategy a
N P R S P-R S-R
Packs active in depredation 30 9 12 3 6 2
Wolves removed 0 19 76 11 33 12
Population size 661 344 474 162 340 156
Probability population size < 100 0.00 0.00 0.00 0.16 0.00 0.15
Compensation cost ($ thousand) 50.4 15.1 20.1 5.0 10.1 3.4
Removal cost ($ thousand) 0.0 9.5 114.0 5.5 36.5 9.0
Total cost ($ thousand) 50.4 24.6 134.1 10.5 46.6 12.4
a Management strategies: N = no action, P = preventive, R = reactive, S = population size reduction.

Increasing the annual probability of a wolf becoming prone to depredation from 20% to 40% produced only small increases in numbers of depredating packs, numbers of wolves removed, and costs. In this case the relative performance of removal strategies remained the same as in the baseline simulations, and we do not present the tabular results. However, decreasing the switching probability to 1% had a dramatic effect (Table 4). Because fewer packs switched to depredation, each removal strategy nearly eliminated the wolves with tendencies for depredation by year 20. As a result, each of the removal strategies produced <5 depredating packs and removed <20 wolves. Strategies involving preventive and reactive removal, which took wolves only in depredating packs, removed fewer wolves than strategies involving population-size management, which took wolves from all packs near farms regardless of depredation tendency. As a result, projected population sizes under preventive and reactive removal were higher than those projected under population-size management.

Table 4.  Mean performance (n = 1,000) in year 20 of hypothetical wolf-removal strategies under a 1% annual probability of wolves in a farm territory becoming prone to depredation; other assumptions as in the base case.
Performance measure Strategy a
N P R S P-R S-R
Packs active in depredation 29 4 2 2 1 1
Wolves removed 0 10 11 18 6 18
Population size 661 588 643 288 635 278
Probability population size <100 0.00 0.00 0.00 0.01 0.00 0.01
Compensation cost ($ thousand) 48.7 6.7 3.4 3.4 1.7 1.7
Removal cost ($ thousand) 0.0 5.0 16.5 9.0 7.0 10.0
Total cost ($ thousand) 48.7 11.7 19.9 12.4 8.7 11.7
a Management strategies: N = no action, P = preventive, R = reactive, S = population size reduction.


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