Multi-trophic resource selection function enlightens the behavioural game between wolves and their prey

Authors

  • Nicolas Courbin,

    Corresponding author
    1. Chaire de recherche industrielle CRSNG-Université Laval en sylviculture et faune, Département de biologie, Université Laval, Québec, QC, Canada
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  • Daniel Fortin,

    1. Chaire de recherche industrielle CRSNG-Université Laval en sylviculture et faune, Département de biologie, Université Laval, Québec, QC, Canada
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  • Christian Dussault,

    1. Ministère des Ressources naturelles et de la Faune, Direction de la faune terrestre et de l'avifaune, Québec, QC, Canada
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  • Viviane Fargeot,

    1. Chaire de recherche industrielle CRSNG-Université Laval en sylviculture et faune, Département de biologie, Université Laval, Québec, QC, Canada
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  • Réhaume Courtois

    1. Ministère des Ressources naturelles et de la Faune, Direction de la biodiversité et des maladies de la faune, Québec, QC, Canada
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Summary

  1. Habitat selection strategies translate into movement tactics, which reckon with the predator–prey spatial game. Strategic habitat selection analysis can therefore illuminate behavioural games. Cover types at potential encounter sites (i.e. intersections between movement paths of predator and prey) can be compared with cover types available (i) within the area of home-range-overlap (HRO) between predator and prey; and (ii) along the path (MP) of each species. Unlike the HRO scale, cover-type availability at MP scale differs between interacting species due to species-specific movement decisions. Scale differences in selection could therefore inform on divergences in fitness rewarding actions between predators and prey.
  2. We used this framework to evaluate the spatial game between GPS-collared wolves (Canis lupus) versus caribou (Rangifer tarandus), and wolf versus moose (Alces alces).
  3. Changes in cover-type availability between HRO and MP revealed differences in how each species fine-tuned its movements to habitat features. In contrast to caribou, wolves increased their encounter rate with regenerating cuts along their paths (MP) relative to the HRO level. As a consequence, wolves were less likely to cross caribou paths in areas with higher percentage of regenerating cuts than expected based on the availability along their paths, whereas caribou had a higher risk of intersecting wolf paths by crossing these areas, relative to random expectation along their paths. Unlike for caribou, availability of mixed and deciduous areas decreased from HRO to MP level for wolves and moose. Overall, wolves displayed stronger similarities in movement decisions with moose than with caribou, thereby revealing the focus of wolves on moose.
  4. Our study reveals how differences in fine-scale movement tactics between species create asymmetric relative encounter probabilities between predators and prey, given their paths. Increase in relative risk of encounter for prey and decrease for predators associated with specific cover types emerging from HRO to MP scale analysis can disclose potential weaknesses in current movement tactics involved the predator–prey game, such as caribou use of cutovers in summer–autumn. In turn, these weaknesses can inform on subsequent changes in habitat selection tactics that might arise due to evolutionary forces.

Introduction

Predator–prey interactions are shaped by the habitat selection games taking place between them (Sih 1998; Lima 2002). Although most studies focus on the viewpoint of either the predator or the prey while considering the other group as motionless (Lima 2002), both predators and prey respond to one another's distribution and behaviour (Dupuch, Dill & Magnan 2009; Valeix et al. 2009). For example, many predators make selective use of their habitat to increase their chances of encountering a prey (Laundré 2010), including coursing predators such as wolves (Canis lupus) (Mech & Boitani 2003; Mao et al. 2005). In response, prey use anti-predator behaviours to limit their vulnerability (reviewed in Lima & Dill 1990; Brown, Laundré & Gurung 1999), including habitat selection (Gilliam & Fraser 1987; Valeix et al. 2009) and movement tactics (Mitchell & Lima 2002; Hodson, Fortin & Bélanger 2010). In response to the risk of wolf predation, for example, ungulates can adopt short-term anti-predator behaviours (e.g. Creel et al. 2005; Fortin & Fortin 2009), or they may alter their habitat selection during extended periods of time by selecting safer land-cover types (Fortin et al. 2005), by seeking refuges (Schmitz 2005), by avoiding habitats prized by alternative prey (James et al. 2004) or by selecting wolf territorial boundaries (Mech & Boitani 2003). In fact, the predator–prey space race (Sih 1998, 2005) can be such that prey may undermatch their own resources to decrease predation risk (Sih 1998; Hammond, Luttbeg & Sih 2007; Laundré 2010), while predators may match the distribution of the prey's resource (plants) but not that of the prey's abundance (i.e. the leapfrog effect; Sih 1998).

The space race between predators and prey also depends on food web complexity (Sih, Englund & Wooster 1998; Rosenheim 2004). In multi-prey systems, the breadth of a predator's diet influences the outcomes of the predator–prey game (Lima 2002; Laroche et al. 2008). As the predator expands its diet, its selection of habitat may become increasingly decoupled from that of any of its prey (Rosenheim 2004). The differences can be such that, when a predator and a prey travel across a given land-cover type, they may experience different ‘relative’ risks of encountering each other, even though the encounter points are the same for both animals. Here, we address this paradox.

Habitat selection is generally assessed based on the comparison between used and available (or unused) habitat units (Manly et al. 2002), and there is no unique spatial domain over which availability can be estimated. Comprehensive ecological studies provide insights into hierarchical habitat selection by defining availability over multiple spatial extents (Johnson 1980; Boyce et al. 2003), but what has yet to be considered is that we could gain insights regarding species interactions also by strategically defining availability. Non-random movement trajectories among land-cover types partly represent an animal's habitat selection strategy in the adaptive game that it plays with its predators or its prey. We can thus assess how visiting different land-cover types along an animal's movement path (i.e. third-order selection, sensu Johnson 1980) alters the likelihood of encountering the other species (Fig. 1). To do so, the availability of the various land-cover types can be quantified along the movement path (MP) of each species, which would yield a species-specific definition of availability at the MP level (Fig. 2). Then, the characteristics of the points where the predator's and prey's paths intersect (i.e. potential encounter locations) can be contrasted with species-specific availability, thereby defining relative risk of encounter along their paths based on the viewpoint of each of the two interacting species. We propose that this approach can clarify the adaptive game taking place between interacting species and could have a broad-range of ecological applications, such as orienting wildlife conservation and management.

Figure 1.

Predator–prey encounters result from both predator and prey habitat selection strategies displayed in a multi-scale process [i.e. Johnson's (1980) order selection]. Habitat availability changes between spatial scales [i.e. landscape, home range, home-range-overlap (HRO), movement path] or between trophic levels (i.e. predator and prey). Third-order selection reflects the search tactic used by each species and can provide specific outcomes for the predator or the prey. For each species, the changes in habitat availability between the area of HRO of predator and prey and the movement-path determine the tactic efficiency. The differences in the tactic efficiency and the asymmetry of the tactic outcomes between predator and prey should help to improve our understanding of the predator–prey game.

Figure 2.

The habitat features of the wolf–prey encounter sites in the Côte-Nord region of Québec (Canada) were evaluated using resource selection functions at both home-range-overlap (HRO) and movement-path (MP) levels. The observed wolf–prey path intersections (image_n/jane12093-gra-0001.png), resulting from both wolf and prey movements, were identical for both species. In contrast, habitat availability was scale-dependent and was separately assessed for each species at the MP level. Random sites were drawn within the overlap of 95% MCP for wolves and 100% MCP for prey (image_n/jane12093-gra-0002.png) at the HRO level, and along the movement paths of wolves (image_n/jane12093-gra-0003.png) or prey (image_n/jane12093-gra-0004.png) at the MP level. For each wolf–prey pair, RSFs evaluated where the intersection step non-randomly occurred given the species movement trajectory, the one of wolf (Wolf–Prey) or the one of prey (Prey–Wolf) and revealed the asymmetry of the outcomes of the tactic used.

A predator–prey behavioural game of interest for conservation and management involves interactions between the grey wolf and woodland caribou (Rangifer tarandus) and moose (Alces alces) in the managed boreal forests of eastern Canada. Woodland caribou are threatened in the Canadian boreal forest (COSEWIC 2002) and are under top-down control by wolves (Seip 1992; Wittmer, Sinclair & McLellan 2005). Forest succession following timber harvest can lead to increased predation risk of caribou (Seip 1992) by creating suitable habitats for moose (Courtois, Ouellet & Gagné 1998), an ‘apparent’ competitor (Wittmer, Sinclair & McLellan 2005). Indeed, as shrubs and deciduous trees invade harvested stands during early successional stages, the density of moose increases, followed by increasing wolf density (Messier 1994), which results in increased predation risk of caribou. Understanding the behavioural game between wolves and their prey in relation to logging activities could help to maintain threatened caribou populations in managed areas.

Our general objective was to gain insights into the spatial game taking place among wolves, caribou and moose from multiple habitat selection analyses (Fig. 1). First, we determined the habitat selection of wolves, caribou and moose within their home ranges (HRs). This selection is a function of multiple factors, including the distributions of the other species. Secondly, we assessed habitat covariates favouring a wolf–prey encounter in the HR of the latter to identify which land-cover types entail high relative risk of the prey, given the proportion of time spent there. Thirdly, we identified the land-cover types where wolves had a relatively high probability of crossing the path of moose or caribou, given land-cover availability along the predator's movement trajectories (i.e. the predator's viewpoint). Finally, we identified the land-cover types where moose or caribou experienced a relatively high probability of crossing the path of wolves, given land-cover availability along the movement trajectories of each of these prey (i.e. the prey's viewpoint).

Material and methods

Study Area

The study was carried out from March 2005 to March 2010 and was centred on the Manicouagan hydroelectric reservoir (51°00′ N, 69°00′ W) in the boreal forest of the Côte-Nord region of Québec, Canada. The study landscape (31 350 km2) is typical of the Canadian Precambrian Shield, with rolling and hilly terrain, and elevations varying between 300 m and 1000 m. Mean daily temperature ranges from -20°C in February to 15°C in July. Mean annual precipitation is 715 mm, with one-third falling as snow (Environment Canada) that reaches a mean depth of ca. 1 m in February–March (Courbin et al. 2009). The forest overstory is dominated by black spruce [Picea mariana (Mill.) BSP] and balsam fir [Abies balsamea (L.) Mill.]. Jack pine (Pinus banksiana Lamb.), trembling aspen (Populus tremuloides Michaux), white or paper birch (Betula papyrifera Marsh.) and tamarack or eastern larch [Larix laricina (Du Roi) K. Koch] are other common tree species. Forest harvesting has been the major source of anthropogenic disturbance since the mid-1990's.

Caribou density was estimated from aerial surveys to be 3·3 individuals/100 km2 in March 2007. Moose density was 4·3 individuals/100 km2 (Gingras, Audy & Courtois 1989). Four wolf packs were present, each comprised of three to six individuals. The Matonipi, Guinecourt, Reservoir and Manic5 packs occupied the study area following aerial surveys between 2005 and 2007. In summer, wolves also hunt beaver (Castor canadensis) and snowshoe hare (Lepus americanus) that are present in the area. Ungulates (especially yearlings and calves) still compose, however, the large part of the biomass consumed by wolves in summer (Mech & Boitani 2003). Density of black bear (Ursus americanus) was unknown for the area, but bears rarely prey upon adult caribou and moose.

Telemetry Data

Telemetry was performed from March 2005 to March 2010, but we focused on the summer and autumn periods (1 July to 14 November), which is when we observed most path intersections between radio-collared wolves and their prey. We captured 29 female caribou in winter with a net gun fired from a helicopter and monitored them during five summer–autumn periods (from 2005 to 2009) with GPS and Argos/GPS collars (GPS 3300L, Lotek Engineering Inc., Newmarket, ON, Canada; TGW-3680, Telonics Inc., Mesa, AZ, USA). Collars were programmed to collect locations at 1-, 3-, 4- or 8-h intervals depending on individuals. Caribou were followed for an average of 8·1 months (range ≤1–22 months per individual). We followed 10 female moose for an average of 8·3 months (range = 4·5–9 months per individual) during 2006 and 2007 summer–autumn periods with GPS collars (GPS 3300L), taking a location every hour. Finally, two male and five female wolves belonging to the four local packs were monitored from 2005 to 2009 summer–autumn periods with GPS collars (GPS 3300SW), by collecting locations at a 4-h interval 5 days a week, and every hour the rest of the week, or with Argos/GPS collars (TGW-3580) collecting locations at 10-h intervals. Wolves were followed for an average of 22·4 months (range = 5–34 months per individual). We delineated a wolf territory in a given year based on the 95% minimum convex polygon (MCP) that was estimated from the GPS locations of all pack members followed that year (Courbin et al. 2009). Any location falling outside of the territory was removed from the resource selection function (RSF) analysis (see below).

Habitat Covariates

Habitat was characterized from a Landsat Thematic Mapper image taken in 2000 with a 25-m resolution grid (Natural Resources Canada, Canadian Forest Service). We considered four land-cover types: dense and open conifers with mosses (covering 56·3% of the study area); mixed and deciduous stands (8·1%); open areas (9·5%, including wetlands); and others (i.e. lake, conifer forests with lichens, lichen–heath community, 21·1%). The reclassified Landsat map was updated every year by adding regenerating cuts (2·5%), recent cuts (2·0%) and roads (0·5%), using the information provided by the local forest companies. Roads were not simply considered as linear structures, but they consisted of a continuous number of adjacent cells. Therefore, the percentage of a given area covered by road could be estimated, as was the case for the other land-cover types.

Our intent was not to only describe the exact location where the trajectory of a wolf crossed that of a prey, but to characterize the general areas where the paths intersected. We thus used spatial autocorrelation analysis to identify the spatial extent beyond which spatial similarities in habitat attributes vanished (Boyce et al. 2003; Fortin et al. 2008). Semi-variograms revealed that the range was < 200 m for five land-cover types and that the sixth cover type was only weakly autocorrelated at 200 m. Overall, the habitat shared similarities within a 200-m radius. Accordingly, we developed RSFs (see the next two sections) based on the proportions of land-cover types within a 200-m radius buffer around each observed and each random location. We did not consider the proportion of the category ‘others’ to maintain relative independence between the proportions of the six other land-cover types (r2 < 0·45 between land-cover types). All RSFs had low multi-collinearity (condition index < 10), allowing valid statistical inferences (Cohen et al. 2003).

Evaluation of Wolf and Prey Habitat Selection

We used RSFs (Manly et al. 2002) to assess habitat selection of wolf, caribou and moose in the summer–autumn period (1 July to 14 November) within their HR (HR level). RSFs compared resource covariates at GPS locations with an equal number of random locations drawn within 95% MCP for wolves and within the summer–autumn 100% MCP of each individual prey. We estimated RSF parameters using a generalized linear mixed model (GLMM), with a binomial distribution. We approximated the maximum likelihood using an adaptive Gaussian quadrature procedure to estimate GLMM parameters (Bolker et al. 2009). We included a random intercept for each individual to take into account the non-independence among observations for a given caribou or moose, while also accounting for the unbalanced sampling design (Gillies et al. 2006). We used GLMM with standard errors that are robust to both within- and between-animal correlations (Koper & Manseau 2009) and to sample size. Mixed-effects RSF models were developed for both prey species with the GLIMMIX procedure in SAS (SAS 9.2 Institute 2008) and had the form:

display math(eqn 1)

where w(x)PREY is the relative probability of use for a given prey species, βn is the estimated coefficient for covariate xn, γ0j is the random intercept for caribou j or moose j. We modelled wolf response using three-level mixed-effects RSF models to accommodate the hierarchical structure of wolves within packs, with nested random intercepts pack|individual (Hebblewhite & Merrill 2008), following:

display math(eqn 2)

where w(x)WOLF is the relative probability of use for wolves, γ0jk is the random intercept for wolf j belonging to pack k and γ0k is the random intercept for pack k. We evaluated model robustness of all species using k-fold cross-validation, by developing RSFs with 80% of the locations (training set), and then by testing the predictive power of these RSFs with the 20% withheld locations (testing set), as suggested by Boyce et al. (2002) and Koper & Manseau (2009). For wolves, caribou and moose, habitat selection was modelled using the proportions of the six different land-cover types in a 200-m radius buffer around locations.

Evaluation of Predator–Prey Encounter Risk

We identified the locations where the paths of wolves intersect those of each of their prey during the summer–autumn period. We only used locations with a 1-h interval to increase the accuracy of the potential encounter sites, from a subset of 8064 locations from five wolves, 83 335 locations from 15 caribou and 46 804 locations from 10 moose. GPS locations that were taken at regular 1-h intervals for all species were converted into steps (i.e. straight-line segments linking successive locations, Fortin et al. 2005). The intersection points between the steps of a wolf and a caribou or a moose represented sites where wolf–caribou or wolf–moose encounters could have occurred. Our objective was to identify the spatial habitat features where ‘potential’ wolf–prey encounters could occur during summer–autumn period of the same year, but the two species did not necessarily have to meet one another (i.e. no obligation for the steps to cross one another at the exact same time) to provide unbiased information on potential encounter locations.

We used RSFs at two levels: (i) the home-range-overlap (HRO) level to identify the land-cover types in which the wolf–caribou and wolf–moose step intersections were more likely to occur given the time that was spent there relative to elsewhere in individual HRs; and (ii) the MP level to evaluate whether these step intersections were more likely to occur in some cover types given the time that was spent there relative to elsewhere along the movement trajectories of wolves or their prey (Fig. 2). The wolf–prey step intersections were identical for both the predator and its prey, whereas availability could vary according to the level of investigation and, therefore, availability was measured separately for each of the three species at the MP level (Fig. 2). We then built three RSFs for each wolf–prey pair, the first by defining availability within the overlap of the HR of wolves and their prey (HRO level, Fig. 2), the second by defining availability along the wolf path and the third along the prey path (MP level, Fig. 2). HRO- and MP level RSFs compared resource covariates at the intersection points of wolf–prey steps with those found at random sites (10 for each observed intersection for both levels). RSFs provided the relative wolf–prey encounter risk in the landscape (HRO level) and indicated whether wolf–prey intersection points were non-randomly placed given the time a particular species had spent in the different cover types that were encountered along its path, thereby providing relative encounter risk from the viewpoint of the predator or the prey (MP level).

We used logistic regressions with a GLMM to estimate RSF parameters as previously explained (see Evaluation of wolf and prey habitat selection) using SAS 9·2. At the HRO level, the wolf–prey encounter models had the form:

display math(eqn 3)

where w(x)WOLF–PREY is the relative probability of occurrence of wolf–prey step intersection, βn is the estimated coefficient for covariate xn and γ0j is the random intercept for a given wolf–prey pair j. At the MP level, the wolf–prey encounter models given the prey movement and the wolf–prey encounter models given the wolf movement were developed from equations (eqn 1) and (eqn 2), respectively. Model robustness was evaluated based on a cross-validation procedure (Boyce et al. 2002). RSF models included the same set of independent variables as in the previous analyses of habitat selection, that is, the proportions of the six land-cover types in a 200-m radius buffer around the step intersections.

About 50% of the wolf steps that intersected a caribou or a moose step were based on locations recorded on the same day or on different days, but at a similar time of day (≤6 h apart). We also built the HRO and MP models based only on the wolf–prey step intersections occurring during the same period of the day (≤6 h apart). Despite reduced power, we obtained similar results, and our conclusions are therefore robust to these differences. We only report the results obtained with the larger of the two datasets.

Results

We observed 197 wolf–caribou step intersections among four wolves and six caribou, and 214 wolf–moose step intersections resulting from the movements of two wolves and six moose (Fig. 3). These wolves, caribou and moose were representative of all individuals that had been radio-tracked (i.e. seven wolves, 29 caribou and 10 moose) in the study area, as they displayed similar patterns of habitat selection. Indeed, the k-fold cross-validation procedure indicated that, for every species, habitat selection models (Table 1) that had been built based only on this subsample of individuals could successfully explain habitat selections made by the others (mean Spearman rank correlations: inline image = 0·73 for wolves, inline image = 0·92 for caribou, and inline image = 0·70 for moose).

Table 1. Mixed-effects logistic regression models of habitat selection of seven wolves, 29 caribou and 10 moose during the summer–autumn period (1 July to 14 November) in the Côte-Nord region, Québec (Canada), with their selection coefficients (β ± SE). Models were robust to cross-validation, as indicated by high mean Spearman rank correlations (inline image)
VariableResource selection function
WolfCaribouMoose
  1. a

    < 0·05.

Mixed and deciduous−0·81 ± 0·61−0·27 ± 0·863·75 ± 0·76a
Conifer with mosses−0·66 ± 0·522·15 ± 0·25a1·64 ± 0·50a
Open area0·99 ± 0·47a1·42 ± 0·43a2·58 ± 0·65a
Road7·93 ± 0·87a−14·03 ± 3·85a−5·57 ± 1·60a
Regenerating cut (≥5 years old)−0·20 ± 0·32−1·99 ± 1·342·37 ± 0·61a
Recent cut (<5 years old)0·35 ± 0·66−5·40 ± 1·63a2·68 ± 0·45a
k-fold inline image0·980·900·95
Figure 3.

Minimum convex polygons of wolves (95% MCP) and those of caribou and moose (100% MCP) used in the wolf–caribou and wolf–moose step encounter analyses during summer–autumn period in the Côte-Nord region of Québec (Canada). Step encounter analyses only considered the home-range-overlap (MCP overlap) areas between wolves and their prey. White areas represented the harvested areas (roads, regenerating and recent cuts).

The relative probability of occurrence of caribou and wolves was not related to the availability of mixed and deciduous stands within their individual HRs (Table 1). The steps of caribou, however, were marginally (= 0·06) more likely to intersect those of wolves in areas (200-m radius buffer) comprised of a high rather than a low percentage of mixed and deciduous stands (PercMD), given the PercMD availability at the HRO level (Table 2). This higher relative probability of intersection of wolf–caribou steps in areas rich in PercMD was even stronger relative to PercMD availability along their respective MPs (MP level, Table 2). Given that the intersection locations are exactly the same at the HRO and the MP levels, this increase directly reflected the slight decrease in availability between the HRO (8·80%) and the MP (5·83% for wolves and 7·42% for caribou) levels, which in turn reflects fine-scale movement adjustments made by wolf and caribou. In contrast, moose selected areas of their HR that were largely comprised of PercMD (Table 1). The relative probability that wolf and moose steps intersected was independent of PercMD, given PercMD availability within the HRO area (HRO level, Table 2) or along each of their own paths (MP level, Table 2).

Table 2. Models of wolf–caribou (= 197 sites, four wolves and six caribou) and wolf–moose (= 214 sites, two wolves and six moose) step intersections at the home-range-overlap (HRO) and movement-path (MP) levels during the summer–autumn period (1 July to 14 November) in the Côte-Nord region, Québec (Canada). The models were evaluated using mixed-effects logistic regressions based on a used/available design of RSF. Availability was evaluated (i) within the intersection of home ranges of both wolves and their prey (HRO level); and (ii) along the movement path of each species (MP level), either along the predator path (Wolf–caribou and Wolf–moose) or along the prey path (Caribou–wolf and Moose–wolf). We show parameter coefficients (β ± SE). Models were robust to cross-validation, as indicated by relatively high inline image
VariableHome-range-overlap levelMovement-path level
Wolf–caribouWolf–mooseWolf–caribouCaribou–wolfWolf–mooseMoose–wolf
  1. *< 0·05 and = 0·06.

Mixed and deciduous1·34 ± 0·71−1·62 ± 2·341·52 ± 0·43*2·63 ± 0·49*2·35 ± 2·34−1·64 ± 1·44
Conifer with mosses0·62 ± 0·60−2·50 ± 1·09*0·17 ± 0·60−0·26 ± 0·541·07 ± 0·46*−3·32 ± 0·64*
Open area0·06 ± 1·35−1·71 ± 0·73*−5·32 ± 2·77*−0·54 ± 1·68−2·28 ± 0·51*−2·93 ± 0·27*
Road−2·10 ± 3·23−3·42 ± 7·29−11·25 ± 0·87*2·81 ± 5·67−7·14 ± 1·09*−0·70 ± 7·13
Regenerating cut (≥5 years old)0·43 ± 1·010·14 ± 1·26−3·51 ± 1·32*3·34 ± 0·59*−0·57 ± 0·60−0·08 ± 1·42
Recent cut (<5 years old)0·46 ± 0·731·07 ± 0·83−0·77 ± 0·892·77 ± 0·29*1·95 ± 0·52*2·79 ± 0·62*
k-fold inline image0·390·480·870·660·850·82

All three species selected sites with higher percentage of open areas (PercOA) than was available within their HR (Table 1). The relative probability of wolf–caribou step intersection was independent of the local (200-m radius buffer) PercOA, given PercOA availability at the HRO level (Table 2). Their MPs were such that PercOA availability only increased along wolf paths relative to the area of HRO between the two species (MP level relative to HRO level, Table 3). Because of this increase, wolves became less likely to intersect a caribou step in areas with relatively high PercOA, relative to random expectation along their paths (MP level, Table 2). In comparison, the risk that a caribou intersected a wolf path remained independent of PercOA, given the availability along this ungulate's paths. Unlike in the case of caribou and wolf, the wolf–moose steps had a lower relative probability of intersecting in areas with high rather than low PercOA, given the availability at both the HRO and MP levels (Table 2).

Table 3. Percent (mean ± SE) of land-cover type available within a 200-m radius buffer, as determined from random locations drawn (i) within the home range (HR) of wolves, caribou and moose (HR level); (ii) within the intersection between the HRs of wolves and caribou or of wolves and moose (HRO level); and (iii) along the predator paths (Wolf–caribou and Wolf–moose) or the prey paths (Caribou–wolf and Moose–wolf) (MP level), during the summer–autumn period (1 July to 14 November) in the Côte-Nord region, Québec (Canada)
VariableHome-range levelHome-range-overlap levelMovement-path level
WolfCaribouWolfMooseWolf–caribouWolf–mooseWolf–caribouCaribou–wolfWolf–mooseMoose–wolf
Mixed and deciduous08·55 ± 0·1409·00 ± 0·0708·54 ± 0·1810·40 ± 0·0908·80 ± 0·3214·14 ± 0·4505·83 ± 0·2407·42 ± 0·2406·24 ± 0·2411·60 ± 0·37
Conifer with mosses45·08 ± 0·3155·39 ± 0·1539·95 ± 0·4356·56 ± 0·1950·16 ± 0·7044·73 ± 0·7634·98 ± 0·6761·14 ± 0·6624·38 ± 0·5939·07 ± 0·74
Open area12·80 ± 0·2208·78 ± 0·0920·92 ± 0·3810·35 ± 0·1206·07 ± 0·3325·94 ± 0·7122·39 ± 0·6905·80 ± 0·3339·74 ± 0·7135·24 ± 0·81
Road01·29 ± 0·0300·50 ± 0·0100·85 ± 0·0400·72 ± 0·0200·95 ± 0·0700·35 ± 0·0402·59 ± 0·1100·19 ± 0·0301·16 ± 0·0800·13 ± 0·03
Regenerating cut (≥5 years old)07·36 ± 0·1901·69 ± 0·0504·69 ± 0·2100·79 ± 0·0401·37 ± 0·2100·69 ± 0·1508·87 ± 0·5100·10 ± 0·0304·40 ± 0·3600·83 ± 0·17
Recent cut (<5 years old)05·14 ± 0·1602·21 ± 0·0502·99 ± 0·1703·22 ± 0·0805·48 ± 0·4100·79 ± 0·1508·37 ± 0·490·63 ± 0·142·04 ± 0·240·33 ± 0·09

At the HRO level, the relatively probability that a wolf crossed the path of a caribou or a moose was independent of the local (200-m radius buffer) percentage of roads (PercRD) or cuts (Table 2). Movement decisions, however, led these intersections to being non-randomly located along the MPs of the different species. Wolves selected areas with higher PercRD than expected, based on its availability within their HR, whereas caribou and moose avoided these areas (Table 1). The difference in selection was such that PercRD was 13 times higher along wolf (2·59%) than caribou (0·19%) paths and nine times higher along wolf (1·16%) than moose (0·13%) paths (MP level, Table 3). Because of these strong differences, wolf–caribou and wolf–moose step intersections were more likely to occur in areas with lower PercRD, relative to random expectation based on availability along wolf paths. In contrast, the relative probability that caribou or moose intersected the path of a wolf was independent of PercRD, given its availability along the paths of either prey species (MP level, Table 2).

Relative to its availability in their HR, caribou avoided areas comprised of a high percentage of recent cuts (PercRCC), whereas moose selected these, together with areas comprised of a relatively high percentage of regenerating cuts (PercRGC) (Table 1). Wolves, in contrast, simply used both types of cuts in proportion to their availability. This difference in habitat selection between the two prey species, combined with the fact that HRs of caribou and wolves overlapped in areas with a higher availability of cuts relative to those of moose and wolves (HRO level, Table 3), resulted in the MPs of both caribou and moose being comprised of a small PercRCC and PercRGC (MP level, Table 3). The distinct response of caribou and wolves to cutovers induced differences in the availability of these features along their MPs (MP level, Table 3). The intersection of wolf–caribou steps, therefore, was more likely to occur in areas with higher PercRCC and PercRGC than expected based on their availability along the paths of caribou, but less likely to occur in areas with higher PercRGC than expected based on its availability along the paths of wolves (MP level, Table 2). Moose selected areas of their HR with relatively high PercRCC (Table 1). Nevertheless, their MP was such that they still had a relatively high probability of intersecting wolf paths in areas largely comprised of PercRCC, (MP level, Table 2), relative to its availability along their paths (Table 3). Wolves were more likely to cross the path of moose in areas where PercRCC was relatively high along their own paths.

Discussion

Our assessment of habitat selection by the members of the wolf–caribou–moose food web demonstrates that the use of specific land-cover types may represent completely different ‘relative’ risks of encounter for the predator with its prey than for a prey with its predator. For example, caribou had a higher risk of encountering wolves by crossing areas largely comprised of regenerating cuts, relative to the proportion of time they spent in these areas along their paths (e.g. these cuts had only a 0·10% overlap with their MPs, while 3% of step intersections occurred in areas that included regenerating cuts). Wolves had a relatively low probability of crossing a caribou's path in areas that were comprised of a high PercRGC, relative to the time they spent there along their paths. Our framework provides the opportunity to detect such asymmetry in relative predator–prey encounter risks along their paths and, therefore, to reveal differences in the outcomes of their movement tactics. In contrast to predator–prey co-occurrence studies (e.g. Courbin et al. 2009) that only inform on the locations suitable to predator–prey encounters, we are able to evaluate outcomes of the tactics used by the predator and its prey from their relative probability of encounter given their MPs.

On the Use of a Multi-Trophic Framework

Predator and prey respond to one another's distributions in a dynamic game (Lima 2002; Sih 2005), and their movement decisions directly influence the outcomes of their spatial game (Lima 2002; Hammond, Luttbeg & Sih 2007; Laundré 2010). Unlike most studies on large mammal food webs, our study considers that both predators and their prey have dynamical distributions reflecting the game that they play. Species-specific movements across the various land-cover types may be such that predators and prey do not spend the same amount of time in each cover type. This time can serve as a basis for comparing the frequency with which the paths of predator and prey cross in each land-cover type, which in turn can reveal the relative risk of encountering each other in a particular cover type, given the specificity of their individual MPs (i.e. movement tactic outcome). If the intersection of a wolf–prey path occurs more often in a given cover type than expected, based on the availability along the path of a given prey, travelling in this land-cover type will yield a relatively high risk of co-occurrence with the predator from the standpoint of that prey. The same principle applies from the standpoint of the predator.

Our quantitative approach highlights elements of the spatial game between predator and prey on the basis that changes in availability between spatial scales or between trophic levels generally reflect changes in encounter rates with the different land-cover types due to habitat selection strategies. Figures 1 and 2 illustrate how the combination of analyses at different spatial scales and trophic levels can clarify the behavioural predator–prey game. At the broadest scale (HRO level, Fig. 2), we assessed availability of land-cover types within the area of sympatry in the distributions of radio-collared wolves and caribou or wolves and moose. At the HRO level, the availability is, by definition, the same between wolf and its prey within this shared space. HRO availability reflects the outcome of second-order selection (sensu Johnson 1980; Fig. 1) by both the wolf and its prey, including the strategy of any broad-scale avoidance of predation risk used by caribou (Rettie & Messier 2000) and moose (Dussault et al. 2005a). Selection at that scale determines the relative availability of land-cover types at finer scales and, therefore, can limit further opportunities of prey to adjust their movements to habitat features. At the finest scale of investigation (MP level, Fig. 2), we quantified availability along the MPs of wolves and their prey, which then reflects third-order selection by each species (Johnson 1980; Fig. 1) and the spatial organization of resource patches (Bastille-Rousseau, Fortin & Dussault 2010). While the tactic used by wolves and their prey has hidden properties, its outcome is clear in terms of relative encounter rates with the different land-cover types at the MP level. For each species, the differences in availability between the two scales reflect adjustments of the time spent in the different land-cover types, given the outcome of the wolf–prey game.

Different Outcomes of Movement Decisions Between Wolves and Their Prey in Human-Disturbed Areas

The main consequence of the fine-scale habitat selection tactic used by wolves was a strong increase in the availability of cutovers and roads along their MPs relative to their availability over the entire area of overlap with their prey. Unlike wolves, caribou and moose avoided areas with high road density within their summer–autumn HR, resulting in their low availability at the HRO level. Movement tactics of caribou and moose strongly decreased the encounter rate with cuts (except with regenerating cuts for moose) and roads along their paths, relative to the HRO level. Such road avoidance is commonly reported for ungulates (Fortin et al. 2008; Courbin et al. 2009) and is stronger in high than low wolf-use areas (Labbé 2012). The different movement tactics of wolves and their prey caused differences in the relative probability of encounter when wolves, caribou or moose entered an area with a higher PercRD than expected, given the road availability of these features along their paths. Wolves were less likely to cross the paths of either prey species in areas of their path that were comprised of high rather than low road densities. Wolves thus did not seem to use areas of high road density to encounter caribou or moose. Instead, wolves may use roads as convenient travel routes to patrol their territory or to identify locations that their prey recently crossed along a road (Eriksen et al. 2009).

The movements of caribou were such that, relative to the time they spent in areas largely comprised of cutovers, individuals experienced a relatively high risk of encountering a wolf in areas that were largely comprised of recent and regenerating cuts than elsewhere along their paths. In the wolf–caribou game, we found no evidence that human-disturbed areas provide a spatial refuge for prey during the summer–autumn period, unlike other wolf–prey studies (Muhly et al. 2011).

Hunting Tactic of Wolves

The hunting tactic of wolves resulted in higher potential encounter rates with moose than caribou (0·05 and 0·03 step intersections per kilometre of wolf trajectory for moose and caribou, respectively). The encounter probability between the wolf and each of its prey species may appear low, but boreal caribou populations are under top-down control (Wittmer, Sinclair & McLellan 2005), and moose populations are commonly limited by wolf predation (Messier 1994; Mech & Boitani 2003). Scale-dependent changes (from HRO to MP) in land-cover availability had more similarities between wolves and moose than between wolves and caribou, as also was implied by the closer timing of wolves terms of their in seasonal shifts in habitat-use patterns with the former compared with the latter prey (Basille et al. 2013). The movement tactic of wolves led to a higher availability of open areas and human-disturbed areas along their paths than in the HRO, but like moose, to lower availability of conifer with mosses and mixed and deciduous stands. In contrast, caribou experienced a large increase in the availability of conifer with mosses along their paths relative to the availability in HRO, but a decrease in all other land-cover types (except open areas). The result of the concurrent movement tactics of the three species was such that, given the time spent in the different land-cover types, it is by entering into areas with higher percentages of conifer with mosses or recent cuts than would be expected along their paths that wolves increased their relative chance of coming across a moose (29% and 4% of their step intersections with moose, respectively). Further, by entering into sites that consisted of a higher percentage of mixed and deciduous stands than elsewhere along their paths, wolves increased their relative chances of crossing the path of a caribou (9% of their encounters with caribou). Given the search tactic of wolves and relative to the time spent in the different land-cover types (i.e. the outcome of the wolf hunting process), 33% of the wolf–moose step intersections would result from a non-random process, whereas 91% of their step intersections with caribou randomly occurred and should be viewed as opportunistic events. Overall, the outcomes of their hunting tactic indicate that wolves focus their search more on moose than on caribou. Direct observations and scat analysis in south-central Alaska (Mech & Boitani 2003) imply that wolves prefer: adult moose > calf moose > adult caribou.

Different Movement Tactics Between Caribou and Moose

Previous research in our study area found that caribou make gradual changes in their movement tactics in response to spatial variation in the probability of wolf presence (Labbé 2012). Our framework reveals that caribou and moose displayed different tactics in response to the risk of wolf predation. Open areas seemed to play an important role in the wolf–caribou–moose game, as all three species selected these areas within their summer–autumn HR. During the summer–autumn period, open areas provide forage such as terrestrial plants for moose (Dussault et al. 2005b) and caribou (Rettie & Messier 2000), whereas wolves patrolling these areas not only to find the ungulates, but also encounter other prey, such as beaver (Mech & Boitani 2003), particularly in wetlands. Because caribou spent a limited amount of time (5·80% of their time) in open areas, caribou–wolf encounter locations randomly occurred in open areas along their paths. Unlike the case for caribou, the movement tactics of wolves and moose led to an increase in the availability of open areas along their paths relative to the availability of these features found at the HRO level. The wolf–moose game in open areas is not characterized by a mismatch between predator and prey distributions (Sih 1998; Hammond, Luttbeg & Sih 2007; Dupuch, Dill & Magnan 2009), because wolves and moose both spent more than a third of their time in sites with open areas (39·74 and 35·24%, respectively). According to the predator–prey space race (Sih 2005), a positive pattern of spatial association between predator and prey indicates that the predator wins the space race. The outcome of the game depends not only on the predator–prey spatial association but also on other fitness-related factors (Sih 2005). Even if moose seem to lose the spatial game, given their spatial association with wolves, their higher capacity for detecting wolves in open areas than in forest, and the fact that wolves may search for alternate prey such as beaver in some open areas during summer, could balance the relative high encounter risk with wolves for moose in such areas.

Conclusions

Our study demonstrates how habitat selection patterns are fine-tuned among species at each scale according to the predator–prey game. The changes in availability between scales reflect the movement tactics of each species and highlight behavioural mechanisms underlying the predator–prey game. Our framework clarifies, on one hand, the differences in the tactics used between wolves and their prey, and between caribou and moose, and, on the other hand, wolf preferences in their hunting tactics. Moreover, given that movement decisions reflect the current state of the habitat selection game between predators and prey, the relative risk of encounter that is outlined by our analyses can inform us regarding subsequent changes in habitat selection tactics that might arise due to evolutionary forces, by exposing potential weaknesses in their current tactics, such as areas of high relative probability of encounter given the current movement tactic.

Acknowledgements

Financial support for field work and data analysis were funded by Natural Sciences and Engineering Research Council of Canada (NSERC)-Sylviculture and Wildlife Research Chair, the Ministère des Ressources naturelles et de la Faune du Québec (MRNF), the Canadian Foundation for Innovation, the Fondation de la faune du Québec, and the Fondation Anne Vallée. We thank the members of our field team: B. Baillargeon, L. Breton, S. Couturier, D. Gay, D. Grenier, J.-Y. Lacasse, and B. Rochette. Thanks to W.F.J. Parsons and two anonymous reviewers for comments on the paper. The Comité de protection des animaux de l'Université Laval provided the required authorizations for this study (2005-004, 2005-004-2, 2008026-1, 2008026-2).

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