Study design

We conducted the study in a 400 km² square area, north of the Michigamme Reservoir in the Upper Peninsula of Michigan (46°15' N, 88°14' W). Land cover included deciduous forests (38%), woody wetlands (29%), mixed forests (13%), conifer forests (6%), open water (4%), grassland/herbaceous (3%), developed (3%), and other (3%). Dominant tree species include sugar maple (Acer saccharum) and trembling aspen (Populus tremuloides) in upland deciduous forests, black spruce (Picea mariana) in lowland coniferous forests, and red pine (Pinus resinosa) in plantations. Average annual snowfall in the study area is about 180 cm and average annual rainfall is about 69 cm. State and US highways border the study area with secondary roads interspersed throughout. Land within the study area is state, commercial forest association, or privately owned.

We divided the study area into 64 2.5 x 2.5 km cells, and selected a station in each cell that we considered suitable bobcat habitat, following Stricker et al. [29]. At each station, we constructed a circular barrier 0.7–1.0 m high and containing 4 entrances, then baited stations using vehicle- or hunter-killed white-tailed deer (Odocoileus virginianus) or beaver (Castor canadensis) carcasses wired to a central tree. We applied a commercial skunk-based lure to the central tree about 1.7 m above ground. At each station, we attached a remote camera (Bushnell Infrared Trophy Cameras; Bushnell Outdoor Products, Overland Park, Kansas, USA) to a tree, 70 to 100 cm above ground and positioned to capture all animal activity within the station. We programmed cameras to obtain images of animals with a 5-minute delay between detections. We conducted an 11 week survey from December 2012 to February 2013 with visits to each station every 7 days. We replaced image cards and batteries each visit and added bait and lure as necessary. We recorded the date and time of each image containing bobcat or hare detected and summarized by week and species the number of days the species was detected, and the number of days each camera operated (i.e., number of sampling replicates). In this context, we assumed occupancy to be constant during each week, and used each day in a week as a temporal replicate. Therefore, most cells received 7 temporal replicates (i.e. days) each week.

Covariates

Using remote-sensing data, we extracted covariates for each cell in our survey grid. To model bobcat occupancy, we used the following covariates: road and water densities at the scale of the cell and of the first-order neighborhood (defined as the eight cells surrounding the target cell), and distance from the station to the nearest water source. Full neighborhood information for cells in the border of the study area was provided via a one-cell buffer area surrounding our target region. We obtained river, stream and road data from Topologically Integrated Geographic Encoding and Referencing system files [31]. We modeled snowshoe hare occupancy as a function of vegetation cover type. We used 2011 National Landcover Data (30-m resolution; [32]) that we reclassified from 15 original landcovers to 9 (Table 1). For each cell, we then estimated the percentage of the cell covered by each vegetation cover type. Each covariate was scaled and centered for analyses, and no strong or moderate multicollinearity was detected [33]. The range of each covariate, once scaled, is presented in S1 Table.

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Table 1. Land cover designations as defined in the 2011 national land cover database with percentage land cover within study area, Iron County, Upper Peninsula Michigan (from [32]).

https://doi.org/10.1371/journal.pone.0143347.t001

Statistical analysis

We estimated bobcat and snowshoe hare occupancies using a hierarchical co-occurrence model [34]. We first modeled snowshoe hare occupancy in cell i during week t as following a Bernoulli distribution with a mean , that we modeled as a linear function of landcover covariates on the logit scale, such as: where b^H is the intercept and β_x corresponds to the ‘x’ vegetation type specific slope. The intercept was given a flat prior, while the slopes for cover type covariates were given non-informative Normal priors with mean 0 and variance 100. We accounted for any residual spatial and time variations using the random effect , following a normal distribution such as:

Similarly, bobcat occupancy followed a Bernoulli distribution with a mean . In turn, is defined conditionally on hare presence, as we expected bobcat occupancy probability to be greater when its prey is present. where and represent bobcat occupancy when hare is present and absent, respectively. We then modeled those probabilities as a linear function of water and road covariates on the logit scale:

Thus, and are intercepts for bobcat occupancy probabilities when hare are present and absent, respectively. When hare are present, slopes for the cell road and water densities (D_road(c)i and D_water(c)i), neighborhood road and water densities (D_road(n)i and D_water(n)i), and distance to nearest water source (d_i) are represented by α_{1 road}, α_{1 water}, β_{1 road}, β_{1 water} and γ₁, respectively. When hare are absent, α_{0 road}, α_{0 water}, β_{0 road}, β_{0 water} and γ₀ are the corresponding slopes. Intercepts were given flat priors, while slopes for road and water covariates were given non-informative Normal priors with mean 0 and variance 10000. Finally, and are random cell-week effects. This formulation allows bobcat occupancy, as well as its relationship to the covariates, to vary with hare presence.

We used a hierarchical approach to model bobcat and snowshoe hare and their potential ecological determinants independently of the effects of imperfect detection and sampling [35]. We modeled bobcat and snowshoe hare detections, and , respectively, in cell i during week t as following a binomial distribution such that: where is the daily hare detection probability during week t in cell i, and is the daily bobcat detection probability in cell i. K_i,t indicates the number of days in week t during which the camera in cell i was operating, and therefore corresponds to 7 temporal replicates for most cell-week combinations.

Implementation

We implemented the model using program WinBUGS [36], called from R (v.3.0.1, [37]) with the package R2WinBUGS [38] (S1 File, corresponding data available in S1 Dataset). We ran three chains using non-informative priors, for 100,000 iterations after a 300,000 iteration burn-in period (to insure convergence) with a thinning of 10. We monitored convergence by visual inspection of the MCMC chains and using the Gelman-Rubin convergence statistic [39].

Model selection was done following a two-step process: 1) selecting the general observation process modeling structure and 2) selecting the relevant set of covariates used in the ecological process part of the model. First, we determined a suitable general model structure for our observation process by assessing goodness-of-fit based on Bayesian p-values both for bobcat and hare weekly total detection [40]. Our original model considered daily bobcat and hare detection probabilities (p^B and p^H, respectively) to be constant over time and space since we did not expect variation in our monitoring using cameras. However, fitting this initial model resulted in poor goodness-of-fit (Bayesian p-values [41] of 0.00 for hare and 0.01for bobcat; S1 Fig). We therefore revised the model to allow the daily bobcat detection probability to vary across space and the daily hare detection probability across both space and time (i.e. between weeks), resulting in satisfactory goodness-of-fit (Bayesian p-values of 0.77 for hare and 0.38 for bobcat; S2 Fig). We tested a final model where bobcat and hare detection probabilities varied across space and time, but the improvement in goodness-of-fit for bobcat did not warrant the additional parameters, with Bayesian p-value of 0.77 and 0.69 for hare and bobcat, respectively. Secondly, to determine which covariates were important to explain bobcat and hare occupancy, we specified a set of latent indicator variables w_k (one for each model effect k) [41]. By imposing a Bernoulli prior on each indicator variable, we can dictate the probability of each set of model covariates, and therefore their probability of being included in the final model [42] [35]. Consider the set of later indicator variables with prior distributions: assumed to be mutually independent. We can then reformulate the occupancy probabilities definitions such as:

Finally, based on the posterior distribution each w_k, we estimated the likelihood of each corresponding k covariate to be included in the final model.

To provide a simple summary of co-occurrence probabilities, we estimated a posterior co-occurrence contingency table indicating how many times across cells and weeks bobcat and hare were each present, present together, or neither present. Based on this posterior contingency table, we then estimated the probability that the proportion of cells occupied by bobcats when hares were present was greater than, equal to, or less than the proportion of cells occupied by bobcats when hares were absent. Let y₁ and y₂ be the number of cells occupied by bobcats when hare is present or absent, respectively. Let n₁ and n₂ be the total number of cells occupied or not occupied by hares, respectively. Then, the number of cells occupied by bobcats depending on hare occupancy can be defined as: with θ₁ and θ₂ representing the proportion of sites that are occupied by bobcat when hare is present and absent, respectively. Assuming Beta(1,1) priors (equivalent to a uniform distribution) on the proportions θ₁ and θ₂, and given the conjugacy of the beta for the binomial, we have:

From there, we can estimate by simulation the posterior density of δ = θ₁-θ₂, the probability that θ₁ is greater than θ₂, i.e. the probability that cells are more likely to be occupied by bobcats when hare are present (compared to when hare are absent). This simulation is done by taking M = 10000 samples from the joint posterior and then use the approximation where , if is greater than , and 0 otherwise. More details concerning this approach can be found following Carpenter [43] and Gelman [44] [39]. We conducted a similar assessment of hare occupancy response to bobcat presence/absence.

Ethics statement

This research was conducted with approval from The Mississippi State University Institutional Animal Care and Use Committee, Animal Ethics Committee, Animal Ethics Permit number CMLR/304/13/QLD GOVT Protocol Number 09–004, was carried out in the field according to the conditions of Michigan Department of Natural Resources scientific collector permit number 1376.

Detectabilities

Mean hare detection probability was 0.46 ± 0.28 (mean ± standard deviation) averaged across weeks and cells) and mean bobcat detection probability was 0.36 ± 0.27 (averaged across cells). As expected, following model selection, both bobcat and hare detection probabilities vary across space (Fig 1).

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Fig 1. Bobcat (A) and snowshoe hare (B) detection probabilities averaged over weeks, Upper Peninsula Michigan, December 2012–February 2013.

Roads and streams are represented by grey and blue lines, respectively.

https://doi.org/10.1371/journal.pone.0143347.g001

Hare occupancy

Overall mean hare occupancy probability (averaged over weeks and cells) was 0.29± 0.15 with greatest occupancy in the northeast and southwest portions of the study area (Fig 2). While overall mean hare occupancy probability did not vary greatly over time, cell specific probabilities varied in space and time. Hare occupancy was positively correlated to grassland cover type, and had a probability of being selected in the model of 0.95 (Table 2).

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Fig 2. Bobcat occupancy probability (and corresponding standard deviations) (A & B) and snowshoe hare occupancy (and corresponding standard deviations) (C & D) averaged over weeks for each cell, Upper Peninsula Michigan, December 2012–February 2013.

Roads and streams are represented by grey and blue lines, respectively.

https://doi.org/10.1371/journal.pone.0143347.g002

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Table 2. Intercepts and slopes on the logit scale for the selected bobcat-snowshoe hare hierarchical co-occurrence model in Upper Peninsula Michigan, during December 2012—February 2013.

Model selection probability corresponds to the percentage of iterations in which the corresponding covariate was selected to be part of the model. Corresponding parameter values are only indicated for model selection probabilities higher than 0.5.

https://doi.org/10.1371/journal.pone.0143347.t002

Bobcat occupancy

Overall mean bobcat occupancy probability (averaged over weeks and cells) was 0.11 ± 0.14. Occupancy was greatest near the center of the study area and occupancy of most cells varied little over time (Fig 2). When hares were absent, bobcat occupancy probability was negatively correlated with road density at the cell scale, and positively correlated at the neighborhood scale (Table 2), and both of these parameters had a probability of being selected in the model equal to 1. When hares were present, bobcat occupancy probability was not influenced by other covariates and mean bobcat occupancy (averaged over weeks and cells) appeared lower when hares were present (0.07 ± 0.07 against 0.12 ± 0.16 with hares absent).

Co-occurrence

When hares were present, bobcats were present only 7.4% of the time (12.6% when hare was absent; Table 3). According to our model, and based on the observed data, there was a 94% [64%; 99%] chance that the proportion of cells occupied by bobcats was greater than the proportion of cells without bobcat when hares were absent. Conversely, when bobcat were present, hares were present only 19.6% of the time (30.5% when bobcat was absent). The probability that the proportion of cells occupied by hare was greater than the proportion of cells without hare when bobcats were present was only a 0.06 [0; 0.36]. Greater average bobcat occupancy when hare was absent appeared driven by a subset of cells in the center of our study area where occupancy probability was greater (Fig 3). The remainder of the study area had a lower bobcat occupancy probability when hare was absent, but occupancy probabilities for those cells increased when hare was present. The central area of high bobcat occupancy probability when hares were absent appeared to influence overall bobcat occupancy when hare occupancy was considered.

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Table 3. Contingency table of the total number of cells and corresponding 95% credible intervals (summed across weeks) summarizing bobcat and snowshoe hare presence, Upper Peninsula Michigan, December 2012–February 2013.

https://doi.org/10.1371/journal.pone.0143347.t003

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Fig 3. Bobcat occupancy probability when snowshoe hare are present (A) and absent (B), Upper Peninsula Michigan, December 2012–February 2013.

Roads and streams are represented by grey and blue lines, respectively.

https://doi.org/10.1371/journal.pone.0143347.g003

Snowshoe hare occupancy

Snowshoe hare selected for grassland cover types. Snowshoe hare presence has been associated with landcover [45], food and cover [46], habitat fragmentation [47], and predator presence and density [48][49]. Hares vacate suboptimal habitats during population declines and during population increases, use less-preferred habitats once higher-quality habitats are saturated [48]. The first cover types to be deserted are usually open or marginal habitats, then mature birch or aspen stands [46][48][50]. In contrast, hare occupancy is positively correlated with presence of dense brushy understory and conifers [40][42][43][51] as well as young forests [52]. One reason why evergreen was not selected might be that cells contained adequate amounts of this land cover such that our model would have identified it as a baseline. It is also possible that coniferous forests, while offering a dense cover, can also lack suitable amounts of preferred browse, especially during winter [51], causing hares to move among those habitat patches to more successional forests to find food.

Large scale patterns of extinction and colonization by snowshoe hares are influenced by cover characteristics, with habitat quality having greatest effect at local scales [49]. Hares exhibit daily variation in use of vegetation types, even when food and cover appear abundant in a single habitat [46][51]. Similarly, temporal variation in hare detectability arises from variation in availability for detection. For example, we demonstrated use of stations varied in response to bobcat occurrence. Consequently, including factors such as predator avoidance should be considered in future models to better understand species habitat relationships.

Bobcat occupancy

Bobcat occupancy probabilities varied across space and time and were related to local hare presence and (when hares were absent) to road density at both local spatial scales. Local presence of snowshoe hare was the main driver for bobcat occupancy, but when hare were absent, road density influenced variation in occupancy probabilities. We demonstrated an adverse effect of roads on bobcats at the local scale. Increases in road density can negatively affect bobcat populations [53][22] through habitat loss, altering landscape structure and function, and increasing access for humans [54]. Interestingly, bobcats do not always avoid roads [55], and sometimes use them to conserve energy by avoiding walking in deeper snow [56][57]. This could explain the slight positive association we observed between bobcat occupancy probabilities and road density at the neighborhood scale. Saunders et al. suggested the potential effects of road density should be examined at appropriate scales and across different forest types and can be used to indicate the level of human disturbance [54]. Further, mature forests typically are of lower suitability for hares than successional forests [45]. As timber harvesting in our study area occurs near or adjacent to roads, subsequent greater habitat suitability for hares in these areas may facilitate selection for roads by bobcats at the coarser resolution.

Bobcat habitat selection was not only scale specific, but context specific. While road density influenced bobcat occupancy in two different ways depending on if looking at the local (i.e. cell) or larger (i.e. neighborhood) scale, this occurred only when hares were absent at the local scale. When present, hare occupancy at the local scale was the only relevant parameter to predict bobcat presence. Prey abundance and availability is an important driver of bobcat populations [58][59][60][61][62][10]. Though prey presence explained bobcat occupancy at the local scale, other factors can be more important at a larger scale (or when preys are absent). Godbois, Conner & Warren demonstrated that bobcat habitat selection at a smaller spatial scale was driven by food, whereas habitat composition was more important at coarser spatial scale, concluding that prey and refugia are important to bobcats [18]. We similarly suggest that prey presence is important to bobcats at fine spatial scales and that environmental factors become important at larger scales and when an important prey species is absent.

Cooccurrence

In contrast to our prediction, overall bobcat occupancy was lower when hares were present. Snowshoe hare experience dramatic variation in weather, food availability, and predation pressure [51]. Hares will select habitat with denser cover when more predators are present [46][63], trading preferred browse for reduced predation risk [64][65][51]. This could explain why in our study hare occupancy appeared to be lower when bobcats were present. Avoidance of bobcats by hares at the scale of bait stations is likely to lead to lower availability of hares when bobcats are present in an area. Hare would avoid the area around the bait station when bobcats area present, but could still be present in the cell. This behavior would affect our results by lowering hare apparent occupancy probability and lowering the chances of hare detection by our cameras when bobcats were present. Consequently, the lower detection probability for hares when bobcats were present could lead to underestimation of the simultaneous presence of both species. Our results support this hypothesis as hares actively avoided bobcats.

Other factors could influence bobcat occupancy, including alternate prey. In Massachusetts, white-tailed deer were used more by bobcats than snowshoe hares, despite hares being more abundant [56]. In this same study, once a deer had been killed, due to its large body size bobcats would apparently feed for up to 3–4 days. Finally, bobcats could stay in areas of their home range offering better refugia, only occasionally leaving them for hunting in cells where preys are more readily available. Similarly, space use of lynx in Alberta was not related to snowshoe hare density; rather, lynx met their food requirements by switching to alternate prey including carrion.

Several improvements for our approach are possible. Currently, the conclusions drawn from our modeling approach and methods are limited by several factors. First, the current resolution of our sampling design limits our inferences of the relationship between bobcat and hare presence. Snowshoe hare home range sizes have been report to be up to 6 ha [51], while our study design resolution (i.e. cell size) correspond to 625 ha. Therefore, the importance of potential relationships, among hare presence, bobcat presence, and habitat covariates summarized at this resolution might not accurately reflect the effect of these covariates at the scale of snowshoe hare’s home range. Moreover, since we only have one bait station per cell, our results rely on the assumption that each station provides a valid representation of the processes occurring in its corresponding cell. Increasing our sampling effort by augmenting the total number of bait stations should help regarding these issues. Moreover, setting several stations in each cell could facilitate i) achieving more accurate estimates of cell occupancy and ii) estimating variation in hare use of bait stations within weeks in response to bobcat presence. However, increasing the number of bait station could also cause another problem. One essential feature of this design is that each station should accurately sample bobcat occupancy in its corresponding cell, i.e. it should not attract individuals from neighboring cells. In this context, the widely accepted use of bait stations for carnivore studies represents a challenge for habitat use under the occupancy modeling paradigm. However, this approach can prove to be especially useful in the case of rare or hard-to-detect species [66] and has been proven to be a viable method for estimating occupancy at both local and landscape scales for at least some carnivores [67]. Any subsequent design should account for the risk of affecting perceived habitat use (via the attraction of individual from other cells) by optimizing the bait station density against their attractiveness. To our knowledge, there is not good data on bobcat detection distances of lures. However, it has been suggested black bears could likely detect lures up to about 135m away [68], and we have circumstantial evidences of bobcats not detecting our scented and baited traps from just a few meters away, depending on the wind direction. For all our carnivore trapping, we have not seen evidence of attraction of more than several meters, and this confirms why trap/site location is so important. Finally, future extensions of this model could benefit from modeling hare detection probability conditionally on bobcat presence, or conversely bobcat detectability in function of hare presence [34]. This could improve our understanding of the relationship between bobcat (or hare) presence and hare (or bobcat) presence and detectability. One final consideration could be to directly account for occupancy (presence/absence over weeks) and use (variation in occupancy among days within a week) to further our understanding of the dynamic use of their habitat by our target species [69].

Habitat use by bobcats [52] and other carnivore species is hierarchical [17][7]. We identified some factors driving bobcat and snowshoe hare occupancies and the importance of understanding interactions among these factors across multiple spatial scales. Importantly, we demonstrated that the effects of those factors on bobcat occupancy were context specific to predation and the presence of a primary prey species. While our model would benefit by the addition of more dynamic covariates to explain weekly variations in bobcat and snowshoe hare occupancy, we demonstrate how scale, environment, and prey presence can interact to explain carnivore occupancy. When trying to understand the factors underlying carnivore distributions, we recommend addressing landscape attributes in addition to factors controlling prey species dynamics and at which spatial scales those factors are acting.