4301.pdf ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 13 MODELING THE IMPACT OF MOOSE AND WOLF MANAGEMENT ON PERSISTENCE OF WOODLAND CARIBOU Réhaume Courtois1,2 and Jean-Pierre Ouellet3 1Ministère des ressources naturelles et de la faune, Direction du développement de la faune, 880, ch. Ste-Foy, 2e étage, Québec, PQ, Canada G1S 4X4; 2Université Laval, Département de foresterie et de géomatique, Cité Universitaire, Ste-Foy, PQ, Canada G1K 7P4; 3Jean-Pierre Ouellet, Université du Québec à Rimouski, Département de biologie, Centre d’études nordiques, 300, allée des Ursulines, Rimouski, PQ, Canada G5L 3A1 ABSTRACT: Limiting factors of caribou (Rangifer tarandus) populations vary regionally. In tundra environments, this species appears to be regulated by food, either because wolves (Canis lupus) are absent or because migration of caribou allows escape from predation during part of the year. In the boreal forest, the main limiting factors are hunting and predation but because of low caribou densities, no regulation mechanism seems to exist between caribou and wolves. Moose (Alces alces) is the primary prey species of wolves and consequently, if moose abundance increases, wolves should also increase, independently of the caribou population. Thus, caribou could experience high predation rates and be eliminated in high wolf densities. Here we attempted to identify the necessary conditions to maintain caribou numbers in the presence of moose. To do so, we built a deterministic model that simulated the relationship between a caribou population regulated by food competition and limited by predation, a moose population regulated by predation, and a wolf population, the abundance of which is determined by moose abundance. At current hunting rates for caribou and moose in the boreal forest, and in the absence of wolf trapping, the model predicted that the caribou population would be extirpated in ap- proximately 100 years. Wolf trapping was not adequate to conserve the caribou population unless very intensive control was undertaken. In the absence of trapping, cessation of caribou hunting allowed a 3-fold increase in caribou numbers over the long term, if the moose population remained low. According to our model, the best management measure for caribou consisted of maintaining a low moose density through appropriate population and habitat management strategies, which prevented expansion of the wolf population and limited predation on caribou. ALCES VOL. 43: 13-27 (2007) Key words: caribou, hunting, interactions, moose, predation, simulation, trapping, wolf The hypothesis of exploitation ecosystems predicts that the number of trophic levels and population regulating factors depend on the primary productivity of an ecosystem (Oksanen et al. 1981, Oksanen and Oksanen 2000). In very poor environments (e.g., high arctic and deserts, where productivity is < 40 g/m2/year), ecosystems consist of vegetation communities that are regulated by competi- tion for resources. In poor environments (e.g., tundra: 40 – 700 g/m2/year), plants are regulated by herbivores. In contrast, more productive environments are made up of three trophic levels that are regulated from the top. Here, herbivores are regulated by carnivores that have only a limited impact on vegetation (Oksanen 1988), so both carnivores and plants Because regulating factors of caribou (Rangifer tarandus) vary between ecotypes, the exploitation ecosystem model seems appropriate for prediction of caribou popula- tion changes. In tundra environments, low productivity and low carrying capacity con- biological communities. Predators are even absent on certain Arctic islands (Klein 1968, Ouellet et al. 1996) and in such cases, caribou IMPACT OF MOOSE AND WOLVES ON CARIBOU – COURTOIS AND OUELLET ALCES VOL. 43, 2007 14 populations are regulated by competition for food and population changes can be described by a logistic model (Caughley 1977). Net population growth rate varies with density: and then growth rate gradually slows down as populations approach carrying capacity. In such environments, the carrying capacity seems to be on the order of 60 – 100 caribou per 100 km2, as observed on Coats Island in Hud- son Bay where caribou have occurred since at least the beginning of the 20th century (Ouellet et al. 1996). Massive mortalities from starva- tion sometimes take place overwinter due to food overexploitation or density-independent factors, such as climatic conditions prevent- ing access to food (e.g., ice crust; Klein 1968, Reimers 1982). In continental tundra, caribou populations also seem to be regulated by food. Caribou may undertake very long migrations that al- low escape from predation most of the year, partly because wolf (Canis lupus) packs are because wolf packs cannot move away from a den site when raising pups during summer (Bergerud 1996). In tundra environments, pre- predation rate does not increase as a function of caribou abundance. Caribou numbers can therefore increase and, at high density, they can overexploit food available during summer (Bergerud 1996, Crête and Doucet 1998) or winter (Ouellet et al. 1994, 1996, 1997). As resources available per animal diminish with increasing population, a decrease in birth rate and an increase in adult and calf mortal- ity are noted. Densities averaging 60 – 110 caribou per 100 km2 have been observed in this environment (Messier et al. 1988, Seip 1991). Using the annual increase in lichen biomass, which is the primary food source for caribou (Gauthier et al. 1989), along with losses caused by animal trampling, Arsenault et al. (1997) have estimated the carrying ca- pacity of caribou in tundra at approximately 20 animals per 100 km2. In the boreal forest, the carrying capacity for caribou is not precisely known. Based on lichen biomass, Crête and Manseau (1996) estimated that carrying capacity should be at least that observed in tundra, because alter- native food sources (such as leaves, twigs, and deciduous shrubs) are abundant and the climate is milder in that environment. For example, in east-central Québec, carrying capacity based solely on terrestrial lichen has recently been estimated at 4.1 – 7.7 cari- bou per 100 km2 (Courtois 2003). Despite a relatively high potential carrying capacity, woodland caribou populations experience very low densities of between 1 and 3 individuals per 100 km2 (Seip 1991, Courtois 2003) and most are declining in North America (Mal- lory and Hillis 1998). Those observations suggest that woodland caribou populations for winter food. Moreover, as caribou food habits are much less restrictive in summer, the main limiting factors seem to be hunting and predation (Stuart-Smith et al. 1997, Rettie and Messier 1998). Caribou densities in the boreal forest (1 – 3 per 100 km2; Seip 1991, Courtois et al. 2003) are typically incapable of supporting wolf populations. Wolves in the boreal for- est therefore depend on moose (Alces alces), a larger and more abundant ungulate that generally lives at densities of between 10 and 20 individuals per 100 km2 (Messier 1985). Due to the absence of a regulating mechanism between caribou and wolves in the boreal forest (Seip 1991), an increase in moose abundance should provoke a wolf population increase, independent of caribou abundance. In such a situation, more frequent encounters between wolf and caribou should be expected leading to an increased predation rate on caribou that could decline, eventually down to extirpation (Seip 1991). Caribou abundance decreases when there are more than 0.60 – 0.65 wolves per 100 km2 (Bergerud and Elliot 1986, Berg- ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 15 erud 1996) and caribou populations increase when wolf numbers are controlled (Boertje et al. 1996, Hayes et al. 2003). The necessity for caribou to adopt avoid- ance strategies of both predators and other ungulates in order to survive is now recog- et al. 1984; Bergerud 1985, 1996; Seip 1991, 1992; Cumming et al. 1996; Stuart-Smith et al. 1997; Rettie and Messier 1998). However, the mechanisms underlying caribou, moose, and wolf interactions still remain obscure. In this study, we built a deterministic model that mimicked the relationships between moose, wolves, and caribou and then simu- lated how variation in hunting of caribou and caribou abundance. Model results should help to determine which management strate- gies are most suitable to maintain equilibrium between these three species in order to help maintain caribou, a threatened species in the boreal forest. METHODS The Model The model simulates changes in caribou, moose, and wolf numbers in a 1,000-km2 study area of the Québec boreal forest where the three species live in sympatry. According to the model, in the absence of wolves, the moose and caribou populations are regulated by food competition and follow a logistic equation (Nt+1 = Nt r 1 - Nt/KCC , where Nt and Nt+1 = numbers at time t and time t+1, re- spectively, r = maximum population growth rate, and KCC = food carrying capacity; Caughley 1977). In the presence of wolves, the moose population is regulated by preda- tion in accordance with the predation model of Messier (1994). Wolf numbers are deter- mined by moose numbers, as predicted by the Michaelis-Menten hyperbolic equation of Messier (1994). In the combined model, where the three species interact, wolves have access to caribou and carry out density-independent survival of calves and adults, as predicted by the Bergerud and Elliot (1986) model. We completed the model by adding management parameters, which allowed changing the moose and caribou hunting and wolf trapping mortalities that were additive to natural mortal- ity. Additional parameters allowed stochastic variation of moose and caribou productivity due to uncontrolled environmental conditions (Crête and Courtois 1997). The model (Appen- dix I) was elaborated using Stella 4.0 software (ISEE Systems, Lebanon, NH, USA). In summary, our combined model is of predation or when predators are controlled, caribou and moose populations are regulated by competition for food (Messier 1994, Crête and Manseau 1996); (2) in the presence of wolves, the moose population is regulated by wolf predation (Messier 1994); (3) wolf numbers are determined by moose abundance (Messier 1994), but there is no dependance of wolves on caribou numbers (Seip 1991); (4) caribou predation increases non-linearly with wolf abundance (Bergerud and Elliot 1986); and (5) there is no immigration or emigration in the system or these two opposite processes are equal. Caribou Population Parameters Due to the paucity of woodland caribou population dynamics data, maximum growth rate and food carrying capacity were taken from published data for barren-ground caribou. Maximum population growth rate of caribou was based on observations of a population reintroduced on Southampton Island in Hud- son Bay (Ouellet et al. 1996, 1997). In 1991, this population was estimated at 13,700 1,580 adults, with an annual growth rate (r) of 0.245 since the introduction of 38 one-year- old individuals in 1967 (Nt = N0 e rt, hence 13,700 = 38 er 24; where Nt = number of cari- bou at time t, N0 = number of caribou in 1967, and t = time in years). No decline in growth IMPACT OF MOOSE AND WOLVES ON CARIBOU – COURTOIS AND OUELLET ALCES VOL. 43, 2007 16 rate was observed over the 24 years, so this value of r should be close to the maximum attainable by a caribou population that is sub- ject to negligible hunting (< 1% per year) and lacks wolf predation. Maximum growth rate is comparable to that reported for the caribou herd introduced on St. Matthew Island in the Bering Sea (17 – 29%; Klein 1968). Carrying capacity based on availability of terrestrial lichens was estimated at 20 caribou per 100 km2 (Crête and Manseau 1996, Ar- senault et al. 1997). Caribou can eat various items (arboreal lichens, deciduous leaves, sedges, forbs, etc.), but these were not included in the carrying capacity estimates to avoid overestimation since winter diet is largely dominated by terrestrial lichens (Gauthier et al. 1989) and this season is the most likely to be limiting caribou (Klein 1968). Initial winter density was set at 1.63 individuals per 100 km2, with 16% calves in the population, as noted in a recent aerial survey (Courtois et al. 2003). Annual losses due to predation and hunting (adults only) were initially established at 3% and 8%, respectively, as noted in central Québec (Courtois 2003). We considered that using empirical data would allow more realistic simulations for the Québec boreal forest. Moose Population Parameters Maximum annual growth rate of the moose population was estimated to be 25%, based on observations in Newfoundland in the absence of predation (Fryxell et al. 1988). Similar rates of increase were reported in south-central Québec (23-24%, Laurian et al. 2000). Other parameters were taken from studies carried out in east-central Québec where densities are ap- proximately 3.0 moose per 100 km2 (Gingras et al.1989). The habitat carrying capacity was estimated at 84 moose per 100 km2, based on annual production of deciduous twigs available during winter (Courtois et al. 1993). Although this estimate may appear low, it is four times higher than the minimum density required to maintain viable wolf populations (20 moose per 100 km2; Messier 1985). Natural mortality rate was set at 9.2% per year (of which 4.5% was due to causes other than predation) while annual hunting mortality was estimated to be 9.0% (Courtois et al. 1994b). As for caribou, these estimates were the only ones available for the Québec boreal forest. Additional simu- lations involved annual stochastic variation in birth rate in order to mimic productivity changes (0.56 – 1.00) that were caused by variations in snowfall and summer tempera- ture (Crête et Courtois 1997). It would have been possible to use stochastic variability in all parameters but we preferred using actual estimates to allow realistic simulations for the study site. Besides, anthropogenic mortality does not vary substantially from year to year because hunting regulation remains stable in the area. Finally, interpretation would have many parameters. Wolf Population Estimation Our model considers wolf population size to be determined by moose population size, according to the predation model developed by Messier (1994, 1995) from 27 North American studies. This author demonstrated that it was possible to predict wolf abundance as a func- tion of moose density (numerical response: number of wolves/1,000 km2 = 58.73 [number of moose/km2 – 0.031]/[0.76 + number of moose/km2], r2 = 0.62). The number of moose exponentially as a function of prey density then decelerates and starts declining at 0.65 moose/km2 (functional response: number of moose killed per wolf per 100 days = 3.3 number of moose per km2/[0.46 + number of moose per km2], r2 = 0.53; Messier 1994). In this model, the total response is the product of numerical and functional responses. Fol- lowing recommendations of Messier (1994), a correction factor of 0.71 was applied to winter predation rates to obtain annual rates and values for 100 days were converted to ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 17 annual values. The impact of wolves on the caribou population was estimated using the Bergerud and Elliot (1986) density-independent model that was based on 17 North American studies. We thus predicted annual recruitment rate (percentage calves during winter = e(3.340-0.127 wolves/1,000 km2), r2 = 0.69) and annual mortality rate of adults (percentage adult mortality = 4,766 + (0.699 wolves per 1,000 km2)1,275, r2 = 0.73). Simulations Parameters and initial and calculated variables are presented in Appendix II. Preliminary simulations were performed on caribou and moose populations separately illustrated the trajectories of populations that - petition for food. In a second trial, we used the moose-wolf model of Messier (1994) to illustrate the reaction of wolves in the pres- ence of moose only. After these preliminary trials, we ran the combined model using the three species’ interactions to investigate the outcome of a limited number of realistic man- agement scenarios over a 100-year span. Four deterministic scenarios were conducted. In trajectories under management strategies that had prevailed in central Québec until autumn 2000 (i.e., moose and caribou hunting at 9% and 8%, respectively, but no wolf trapping). Then we successively simulated effects of (2) a caribou hunting ban; (3) intensive wolf trapping (at 30%; Larivière et al. 2000), and (4) moose hunting increased to 15% (in order to allow only a light population increase) without wolf trapping. Finally (5), in order to experiment with the effects of changes not controlled by harvest regulation, we included negative effects of stochastic environmental variations on productivity (Crête and Courtois 1997) of moose (from 0% – 40%) and caribou (20%), on scenarios 1 and 2. RESULTS Simple Models for Caribou, Moose, and Wolf Populations In the absence of hunting and predation, caribou reached their carrying capacity (K) in 53 years, with numbers increasing from 16 to 200 individuals in the 1,000-km2 site. Half of the carrying capacity (optimal density 0.5K) was reached in 10 years, allowing a maximum sustainable yield of 12 caribou per year in a stable population of 100 individuals. Adding a natural mortality of 3% resulted in 0.5 K being reached in 12 years, with a maximum sustainable yield of 9 individuals per year. When an additional anthropogenic harvest of 8% was included, the population reached 0.5 K after 28 years and did not exceed 112 caribou after 100 years. In the absence of hunting and predation, the 30 initial moose reached their carrying capacity (840 individuals) in 62 years. The maximum sustainable yield (52 moose) was at- tained with a population of 420 moose (optimal density: 42 moose per 100 km2) in 13 years. Including a natural mortality of 9% resulted in 0.5 K being reached in 25 years, but the total population did not exceed 537 moose after 100 years. After adding another 9% hunting mortality, the population comprised only 234 moose (0.28 K) after 100 years. According to the predation model (Messier 1994), the wolf population was sustained by the moose population and also regulated moose numbers. Both wolf abundance and predation rate increased with moose abundance. Without hunting, the moose population stabilized at 650 individuals (65 moose per 100 km2). At this plateau, predator density reached 2.58 wolves per 100 km2, as predicted by the numerical response equation of Messier (1994). IMPACT OF MOOSE AND WOLVES ON CARIBOU – COURTOIS AND OUELLET ALCES VOL. 43, 2007 18 Combined Model Incorporating Interac- tions Between Moose, Wolves and Cari- bou Scenario 1: moderate moose (9%) and caribou (8%) hunting but no wolf trapping.— When moose and caribou were exploited at moderate rates and in the absence of wolf trapping, moose abundance increased from 30 to 110 individuals in 55 years and then remained stable (Fig. 1). Simultaneously, wolves increased from 0 at the start of the run to 5 individuals after 30 years only to stabilize afterwards. Moose predation rate reached 8% per year, which stabilized the moose-wolf system. Caribou abundance increased from 16 to 40 individuals in 14 years and then gradu- ally declined to quasi-extirpation in 100 years (2 caribou remaining). The caribou decline initiated when moose and wolf reached 76 and 32 individuals (7.6 and 0.32 individuals per 100 km2), respectively. Scenario 2: ban on caribou hunting with 9% moose hunting and no wolf trapping.— the moose and wolf population trajectories, since the relevant population parameters remained the same (Fig. 2). The caribou hunting ban allowed the caribou population to increase and reach 94 individuals after 22 years; however, despite this increase, the caribou population started to decline as soon as moose numbers attained 95, thus supporting 4.5 wolves (9.5 moose and 0.45 wolves per 100 km2). Caribou were not extirpated and the population stabilized at approximately 64 individuals (6.4 per 100 km2). Scenario 3: intensive wolf trapping (30%) with 9% moose and no caribou hunting.— Introducing intensive trapping of wolves (30%) to parameters of the previ- ous simulation did not markedly improve the situation for caribou. Wolf abundance increased steadily despite exploitation, in parallel with the increase in moose abundance (Fig. 3). Abundance after 100 years was 5 wolves and 141 moose (0.5 and 14.7 per 100 km2, respectively). The caribou population reached 109 individuals after 23 years, but then declined and stabilized at (75 individuals 7.5 per 100 km2). Scenario 4: increased moose hunting (15%) with no wolf and caribou harvest- ing.— Intensifying moose harvest to 15% but discontinuing wolf trapping maintained the moose population at a relatively low level of 61 individuals (6.1 moose per100 km2), which directly reduced the wolf population to less than 2.2 individuals (< 0.22 wolves per 100 km2; Fig. 4). This management strategy was very favourable for caribou and the popula- tion reached 146 individuals after 30 years and then stabilized at 141 caribou (14.1 per 100 km2). Scenario 5: stochastic environmental variations.— With random annual variation in birth rates, each simulation followed a new trajectory (Fig. 5). Stochastic variation - 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100 TIME (years) N O .I N D IV ID U A L S Moose Caribou Wolf Fig. 1. Moose, wolf, and caribou population tra- jectories with moderate moose (9% per year) and caribou (8% per year) hunting but no wolf trapping (Scenario 1). 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100 TIME (years) N O .I N D IV ID U A LS Moose Caribou Wolf Fig. 2. Moose, wolf, and caribou population tra- jectories with moderate moose hunting (9% per year) but no caribou hunting or wolf trapping (Scenario 2). ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 19 tions in both moose and wolf numbers, which always remained lower than in previous simulations. These variations had a positive impact on caribou numbers. In the presence of moderate moose harvesting (9%) but no wolf trapping or caribou hunting (previous scenario 2), the caribou population reached 125-135 individuals and stabilized at this level (Fig. 5a). If caribou hunting was also introduced into this model (previous scenario 1), the caribou population stabilized at approxi- mately 50 – 60 individuals (Fig. 5b). When environmental stochasticity was allowed to increase the variation in caribou birth rate in addition to the moose birth rate, the caribou population declined to approximately 35 in- dividuals (Fig. 5c). Equilibrium Points of the Combined Models Theoretical equilibrium points of the simple moose-wolf model were 65.0 moose and 2.58 wolves per 100 km2. In the moose- wolf-caribou model, equilibrium points were much lower than these values. In simulations without stochastic environmental variation, equilibrium points were approximately 7 – 10 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 60 70 80 90 100 TIME (years) N O .I N D IV ID U A L S Moose Caribou Wolf Fig. 3. Moose, wolf, and caribou population tra- jectories with moderate moose hunting (9% per year) and intensive wolf trapping (30% per year) but no caribou hunting (Scenario 3). 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 60 70 80 90 100 TIME (years) N O .I N D IV ID U A L S Moose Caribou Wolf Fig. 4. Moose, wolf, and caribou population trajectories with moose hunting set at 15% per year but no caribou hunting or wolf trapping (Scenario 4). A) 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 TIME (years) N O .I N D IV ID U A LS _ B) 0 20 40 60 80 100 120 140 0 20 40 60 80 100 TIME (years) N O .I N D IV ID U A LS _ C) 0 20 40 60 80 100 120 140 0 20 40 60 80 100 TIME (years) N O .I N D IV ID U A LS _ Moose Caribou Wolf Fig. 5. Typical moose, wolf, and caribou population trajectories according to different management strategies and by including random variations in moose (all simulations) and caribou birth rates (last simulation) (Scenario 5). (A) Moderate moose hunting (9% per year), with no caribou hunting or wolf trapping; moose birth rate vary- ing up to 40% a year; (B) Moderate moose (9% per year) and caribou (8% per year) hunting with no wolf trapping; moose birth rate varying randomly (0 – 40%); (C) Moderate moose (9% per year) and caribou (8% per year) hunting with no wolf trapping; both moose and caribou birth rates varying randomly, between 0 and 40% and 0 and 20%, respectively. IMPACT OF MOOSE AND WOLVES ON CARIBOU – COURTOIS AND OUELLET ALCES VOL. 43, 2007 20 moose, 0.3 – 0.5 wolves, and 3 – 14 caribou per 100 km2. In the last simulation, which appears a plausible situation in nature, populations stabilized at 6 – 8 moose, 0.2 – 0.3 wolves, and 3.5 – 4 .0 caribou per 100 km2. DISCUSSION Usefulness of the Combined Model in Cari- bou, Moose, and Wolf Management Our moose-wolf-caribou model suggests interesting alternatives for the management of these three species. Seip (1991, 1992) pro- posed that predation could eliminate woodland caribou whenever wolves are sustained by another species because there is no retroactive mechanism that decreases the impact of wolves when the caribou population declines. Our simulations suggest that certain management strategies could help maintain caribou numbers by limiting wolf expansion. Wolf control could be considered (Bergerud and Elliot 1986, Seip 1991), but this strategy would only have a minor impact on caribou, unless a very intensive control is performed. Weclaw and Hudson (2004) obtained similar results using another model based on responses of wolves, moose, caribou, lichens, and vascular plants to various natural and anthropogenic factors. A 30% harvest rate exerted by trappers is not high birth rate, wolf populations can increase quickly if moose abundance is high. Cessation of caribou hunting seems more of the caribou population in the long term if the moose (and wolf) population does not the habitat carrying capacity for moose is relatively low. Moose densities are generally higher in disturbed habitats and young for- ests rich in deciduous browse than in mature spruce forests (Timmermann and McNicol 1988). Moose expansion could therefore be controlled by limiting forest exploitation in sites used by caribou or by promoting spruce wolves, our simulations suggest that caribou can be maintained in natural ecosystems, at least in the absence of human disturbance as suggested by Weclaw and Hudson (2004). The best strategy, however, would consist of maintaining low moose densities through population and habitat management. Low moose densities imply low wolf densities and, therefore, low predation rates on caribou. Increasing the harvest of moose would be the easiest and most convenient management measure to adopt. Moose hunting is highly popular. With a 3- to 4-week hunting season, the harvest rate could reach 15% if all seg- ments of the population (both sexes of adults and calves) were targeted without setting a limit on the number of hunting permits issued (Courtois et al. 1994a). In such a situation, our simulation suggests that moose density would stabilize at about than 7 – 8 individuals per 100 km2 and wolf density at less than 0.2 – 0.3 individuals per 100 km2. Annual caribou recruitment would then be approximately 19 – 20% and adult predation rate would be around 7 – 8%. A population increase in caribou to 3 – 14 individuals per 100 km2 could thus be seen in several decades. Even if conservative caribou hunting was maintained, a doubling or tripling of the population could be ob- served over the long term, depending on the magnitude of variations due to environmental factors. This scenario supports the growing evidence that moose management may be an integrated aspect of caribou management, as indicated by controlled experiments in the moose hunting rates higher than 15% in order to maintain a stable or slightly increasing popu- lation. Management that encourages declining moose populations will lead to lower hunting success rate, which in the long term may be a less popular decision among hunters. Our simulations seem optimistic in com- parison with actual woodland caribou densities (1 – 3 individuals per 100 km2, Seip 1991, Courtois 2003); however, historical densities ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 21 were much higher. Brassard (1967) measured a density of 26.2 caribou per 100 km2 in a 25,723 km2 study site in the boreal forest of the Québec North Shore. In Labrador, Bergerud (1967) estimated the 1958 density of the Mealy Mountain herd at 7.9 individuals per 100 km2 over 30,303 km2. Both these densities rapidly declined following intensive hunting during the 1960s and 1970s following the invention of snowmobiles that greatly facilitated hunter access. Similarly, caribou density was ap- proximately 4 – 5 individuals per 100 km2 in 1992 in the Charlevoix herd, north of Québec City, in the absence of hunting and restricted forest exploitation (Sebbane 2003). Caribou declines followed anthropogenic and natural habitat disturbance in the absence of hunt- ing, presumably due to increased predation. Controlled experiments (Boertje et al. 1996, Hayes et al. 2003) and other simulation models (Weclaw and Hudson 2004) also suggest that caribou densities can attain 10 individuals per 100 km2, depending on the extent of wolf predation and hunting-related mortality. Effects of Increase in Caribou Biomass We intentionally developed a simple model based on empirical data from the Qué- order to avoid including variables that were depended exclusively on moose density. This - ence of ungulates is necessary to sustain wolf populations (Messier 1994, 1995) and also caribou density was too low to constitute a white-tailed deer, could be an important prey for wolves during winter, but this deer is not found where caribou live in the northern bo- real forest. In sites used by woodland caribou, for wolves. Although wolves certainly con- sume beavers in summer, which presumably increases pup survival, beavers are not readily available in winter because beaver movements are mostly restricted to beneath the ice where Nevertheless, we tested the effect of a pos- sible caribou-wolf retroaction mechanism. We the carrying capacity of wolves depended on the total biomass of available ungulates (Fuller 1989) and we considered that 1 caribou was equivalent to 0.29 moose, based on respective masses. As a result, the wolf population in- creased by 2% compared to scenario 2 (harvest rates: 9%, 0%, and 0% for moose, caribou, and wolves, respectively), which created population declines of 14% in moose and 6% in caribou. Assuming that wolves make hunt- ing decisions based solely on prey biomass, not risk associated with their capture (which is lower for caribou than moose), the impact of an increase in wolves would probably be greater on moose than caribou. Seip (1991) and Bergerud (1996) have suggested that caribou could be extirpated from an area in the presence of high moose densities due to increased predation on caribou from increased wolf densities. In contrast, Hayes et al. (2003) have suggested that reduced moose densities would lead to caribou extirpation in areas where wolves, moose, and caribou use similar habitats in summer because in such a case caribou lose the advantage of their spac- ing strategy to avoid predation. In the model including both moose and caribou biomass to support wolves, increasing the moose harvest rate to 22% led to extirpation of this species in 100 years, while caribou increased to 156 individuals. Despite a 10-fold increase, the caribou biomass (4.5 moose-equivalent per 100 km2 a viable wolf population that subsequently declined to 1 animal after 100 years, suggest- ing that an abundant primary prey (moose or deer) is required to maintain wolves in the boreal forest. Our model implies that natural and anthropogenic mortality are additive. This assumption is probably valid for ungulates, IMPACT OF MOOSE AND WOLVES ON CARIBOU – COURTOIS AND OUELLET ALCES VOL. 43, 2007 22 but wolf trapping could be partly compensa- tory (Fuller 1989). Harvesting wolves would indeed leave more food available for each surviving wolf, which could contribute to a wolf population increase. We did not have any empirical evidence to quantify this pos- sibility, however. Moreover, if trapping is extensive, the reduced wolf packs should be biomass per animal. Limits of the Model Simulation results are strongly dependent on which combinations of parameters are used and on the accuracy of the parameters included. Caribou and moose densities, food carrying capacity, and hunting mortalities were based on empirical data from the Québec boreal forest (Courtois 2003), but wolf densities and their related impact on caribou numbers could be greater than those predicted by our model. Larivière et al. (2000) used the num- ber of wolf howls heard by hunters to predict wolf density. For the Port-Cartier – Sept-Îles Wildlife Reserve, which is located in the main distribution area of woodland caribou, these authors estimated a density of 0.85 wolves per 100 km2. Using Fuller’s model (1989), 0.48 wolves per 100 km2 would be obtained. The model we used (Messier 1994) predicted 0.22 wolves per 100 km2 for a similar moose abundance (6 individuals per 100 km2), and maximum density of 0.38 wolves per 100 km2 at carrying capacity (84 moose per 100 km2). Only an inventory could provide accurate wolf numbers in the study area. However, if the wolf densities predicted by Larivière et al. (2000) and Fuller (1989) are correct, more restric- tive measures would be needed to conserve caribou in the presence of moose and wolves. Similarly, the population growth rate for both by certain environmental variables, such as snow conditions (Schaefer and Messier 1991). Therefore, simulations that do not include the impact of such stochastic limiting factors are likely to yield optimistic results. Bergerud and Elliot (1986) estimated that caribou abundance should decline when wolf density exceeds 0.65 individuals per 100 km2. In our simulations, caribou numbers started declining as soon as the wolf population ex- ceeded 0.45 individuals per 100 km2. Caribou declines always followed an expansion phase, which means that food density-dependent mechanisms intervened when caribou numbers increased and that these mechanisms were ad- ditive to predation effects. The carrying capac- ity that we selected (20 caribou per 100 km2, Arsenault et al. 1997) could also be too high based on recent estimates (4.1 – 7.7 individuals per 100 km2, Courtois 2003), and recent stud- ies suggest that caribou avoid human-related infrastructures leading to loss of available habitat (see Weclaw and Hudson 2004 for a review). Black bear (Ursus americanus) are not abundant in prime caribou habitat, but this species can exert an important additional density-independent pressure on caribou in some areas (Ballard 1994), particularly the southern region of the boreal forest. Therefore, the model may be inappropriate in areas with bears, cougars, or other predators. Taken management decisions. Model Improvements Improvements could be made to our model. For example, the wolf population could be considered as a reservoir, rather than as a parameter linked to the moose population. This change would allow consideration of other variables that affect wolves, such as the presence of other prey species or demographic uncontrolled variables and measurement errors were responsible for approximately 40% of the variance in wolf density between studies consulted by Messier (1994). The regulation mechanism between moose and wolves in our ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 23 model, however, seems more appropriate to mimic natural predator-prey dynamics than a priori parameters. Furthermore, instead of considering ungu- late populations as homogeneous reservoirs, we could categorize populations by age and only if proportions of males and females vary substantially. According to sensitivity analy- ses performed by Fancy et al. (1994), moose and caribou population growth rates are not highly sensitive to age structure, but rather depend on recruitment rate, which is strongly and their survival. More importantly, a spatially explicit model would be particularly useful to investi- gate the possibility of excluding wolves from areas used by caribou, for example through habitat management that renders areas unsuit- able for moose. Such a model could be based on the movement rate and direction of wolves could help to determine the minimal size of a protected area for caribou that would permit avoidance of most encounters between wolves and caribou. 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Rectangles represent reservoirs (populations), double arrows identify sources (births) and sinks - tions tested the impact of changes in caribou and moose hunting rates (CaribouHuntingRate and MooseHuntingRate, respectively), wolf trapping rate (WolfTrappingRate) and changes in caribou and moose productivity due to random variations in environmental conditions (CaribouRandomEnvCdn and MooseRandomEnvCdn) on caribou and moose reproductive rates. Other parameters and equations were obtained from the literature (see methods). Min- ProdCaribou and MinProdMoose indicate the minimum productivity of the species under the worst environmental conditions. Other acronyms are self explanatory. ALCES VOL. 43, 2007 COURTOIS AND OUELLET - IMPACT OF MOOSE AND WOLVES ON CARIBOU 27 Appendix II Parameters and variables used in the models, values employed in the simulations, and data sources. Parameter or variable Values employed Data source MOOSE Habitat carrying capacity 840 in the study area (84 per 100 km2) Courtois et al. (1993) Population 30 in the study area at time 0; calculated by the model afterwards Gingras et al. (1989) Maximum growth rate 25% per year Fryxell et al. (1988) Annual predation rate Calculated from Messier’s predation model (depends on moose density) Messier (1994) Annual hunting rate 9% (simulations 1, 2, 3, 5) or 15% (simulation 4) Courtois et al. (1994b) Annual rate of mortality due to other causes 4.50% Courtois et al. (1994b) Annual variability of recruitment 0% (simulations 1 to 4); random variation between 0 and 40% (simulation 5) Crête and Courtois (1997) WOLF Population Calculated from Messier’s Michaelis- Menten hyperbolic equation (depends on moose population) Messier (1994) Trapping rate 0% (simulations 1, 2, 4, 5) or 30% (simulation 3) Larivière et al. (2000) CARIBOU Habitat carrying capacity 200 in the study area (20 per 100 km2) Arsenault et al. (1997) Population 163 in the study area at time 0; calculated by the model afterwards Courtois et al. (2003) Maximum growth rate 24.5% per year Estimated from Ouellet et al. (1996, 1997) data Annual recruitment rate Calculated from Bergerud and Elliot’s model (depends on wolf density) Bergerud and Elliot (1986) Annual rate of adult natural mortality Calculated from Bergerud and Elliot’s model (depends on wolf density) Bergerud and Elliot (1986) Annual hunting rate 9% (simulations 1, 2, 3, 5) or 15% (simulation 4) Courtois et al. (2003) Annual variability of recruitment 0% (simulations 1 to 4, 5a and 5b); random variation between 0 and 20% (simulation 5c) Arbitrary