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Potential paths for male-mediated gene ﬂow to and from an isolated grizzly bear population 1,4 1, 2 1 CHRISTOPHER P. P ECK, FRANK T. VAN MANEN, CECILY M. COSTELLO, MARK A. HAROLDSON, 1 2 3 2 LISA A. LANDENBURGER, LORI L. ROBERTS, DANIEL D. BJORNLIE, AND RICHARD D. MACE

1Interagency Grizzly Bear Study Team, Northern Rocky Mountain Science Center, U.S. Geological Survey, 2327 University Way, Suite 2, Bozeman, Montana 59715 USA 2Montana Department of Fish, Wildlife and Parks, 490 North Meridian Road, Kalispell, Montana 59901 USA 3Large Carnivore Section, Wyoming Game and Fish Department, 260 Buena Vista, Lander, Wyoming 82520 USA

Citation: Peck, C. P., F. T. van Manen, C. M. Costello, M. A. Haroldson, L. A. Landenburger, L. L. Roberts, D. D. Bjornlie, and R. D. Mace. 2017. Potential paths for male-mediated gene ﬂow to and from an isolated grizzly bear population. Ecosphere 8(10):e01969. 10.1002/ecs2.1969

Abstract. For several decades, grizzly bear populations in the Greater Yellowstone Ecosystem (GYE) and the Northern Continental Divide Ecosystem (NCDE) have increased in numbers and range extent. The GYE population remains isolated and although effective population size has increased since the early 1980s, genetic connectivity between these populations remains a long-term management goal. With only ~110 km distance separating current estimates of occupied range for these populations, the potential for gene flow is likely greater now than it has been for many decades. We sought to delineate potential paths that would provide the opportunity for male-mediated gene flow between the two populations. We first developed step-selection functions to generate conductance layers using ecological, physical, and anthropogenic landscape features associated with non-stationary GPS locations of 124 male grizzly bears (199 bear-years). We then used a randomized shortest path (RSP) algorithm to estimate the average number of net passages for all grid cells in the study region, when moving from an origin to a destination node. Given habitat characteristics that were the basis for the conductance layer, movements follow certain grid cell sequences more than others and the resulting RSP values thus provide a measure of movement potential. Repeating this process for 100 pairs of random origin and destination nodes, we identified paths for three levels of random deviation (h) from the least-cost path. We observed broad-scale concordance between model predictions for paths originating in the NCDE and those originating in the GYE for all three levels of movement exploration. Model predictions indicated that male grizzly bear movement between the ecosystems could involve a variety of routes, and verified observations of grizzly bears outside occupied range supported this finding. Where landscape features concentrated paths into corridors (e.g., because of anthropogenic influence), they typically followed neighboring mountain ranges, of which several could serve as pivotal stepping stones. The RSP layers provide detailed, spatially explicit information for land managers and organizations working with land owners to identify and prioritize conservation measures that maintain or enhance the integrity of potential areas conducive to male grizzly bear dispersal.

Key words: connectivity; corridor; dispersal; gene ﬂow; Greater Yellowstone Ecosystem; grizzly bear; movements; Northern Continental Divide Ecosystem; randomized shortest path; step-selection model; Ursus arctos.

Received 1 May 2017; revised 4 August 2017; accepted 29 August 2017. Corresponding Editor: Eric M. Geese. Copyright: © 2017 Peck et al. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 4 Present address: Colorado Cooperative Fish and Wildlife Research Unit, Colorado State University, 205 J.V.K. Wagar Building, 1484 Campus Delivery, Fort Collins, Colorado 80523 USA. E-mail: [email protected]

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INTRODUCTION 2006) and Southwest Montana (Montana Depart- ment of Fish, Wildlife and Parks 2013). Facilitation Landscape connectivity has become a central of natural movement, through habitat manage- tenet of biodiversity conservation and the number ment, is favored over translocation of bears of published studies on this topic has increased between ecosystems (Dood et al. 2006). substantially since 2008, largely because of new For several decades, grizzly bear populations in methodologies (Correa Ayram et al. 2016). Large the GYE and NCDE have increased in numbers mammalian carnivores have received particular and range extent (Schwartz et al. 2006, Kendall attention because they have large home ranges et al. 2009, Mace et al. 2012, Bjornlie et al. 2014, and dispersal distances, occur at relatively low Costello et al. 2016, Haroldson et al. 2016). Addi- densities, have fragmented distributions, and often tionally, the presence of grizzly bears has been function as flagship species for conservation (Beier verified for 21 locations in the area between the et al. 2008, Correa Ayram et al. 2016). Conserving occupied ranges of the NCDE and GYE. Unlike movement corridors for mammalian carnivores is core habitats for these two populations, which are challenging because they frequently span large dominated by large expanses of public land with geographic areas comprised of complex landscape grizzly bear-specific habitat protections, areas of mosaics with varied land ownerships and uses. recent expansion are characterized by greater Limited funds and logistical constraints often anthropogenic influence, and even more so are necessitate prioritization of lands deemed vital for the landscapes between the two populations. The conservation, but identification of important habi- likelihood of future demographic linkage of these tat is often hampered by the lack of relevant move- two populations is uncertain. However, dispersal ment data for focal species. Advances in analytical in grizzly bears is male-biased (Blanchard and techniques combined with extensive, long-term Knight 1991, McLellan and Hovey 2001, Proctor Global Positioning System (GPS) data for grizzly et al. 2004) and the potential for male-mediated bears (Ursus arctos) provided the opportunity to genetic linkage between the NCDE and GYE is identify potential paths that may facilitate gene likely greater now than it has been for many dec- flow between populations in the Northern Conti- ades. The estimate of closest proximity between nental Divide Ecosystem (NCDE) and the Greater current occupied ranges for these populations is Yellowstone Ecosystem (GYE). This important ~110 km, which is within maximum dispersal dis- information need was identified by federal, state, tances (67–176 km) documented for males in the and tribal managers (U.S. Fish and Wildlife Service region (Blanchard and Knight 1991, McLellan and 1993, 2017, Dood et al. 2006, Montana Department Hovey 2001, Proctor et al. 2004). Given that bear of Fish, Wildlife and Parks 2013). dispersals typically occur over time periods of one Whereas the NCDE population is contiguous to multiple years, our goal was to identify paths with grizzly bear populations in the Canadian between the NCDE and GYE populations with Rocky Mountains (U.S. Fish and Wildlife Service habitat conditions conducive to male dispersal. 1993, Schwartz et al. 2003), current genetic data Although potential habitat linkages and move- indicate the GYE population remains isolated (i.e., ment corridors for grizzly bears (Picton 1986, no evidence of recent immigrants; Haroldson Walker and Craighead 1997, Dilkina et al. 2016) et al. 2010, Proctor et al. 2012; Fig. 1; Appen- and black bears (Ursus americanus; Cushman et al. dix S1: Fig. S1). Concerns for the genetic health of 2009) have been identified for this region, no such the GYE population have lessened considerably studies have been conducted using grizzly bear with recent findings of a three- to fourfold location data from either ecosystem. The random- increase in effective population size since the early ized shortest path (RSP) algorithm, introduced to 1980s (Kamath et al. 2015), exceeding the theoreti- the field of movement ecology by Panzacchi et al. cal number for avoiding inbreeding depression (2016), is a new methodological approach to pre- (Frankham et al. 2014). Nonetheless, genetic con- dict the location of paths between functional areas nectivity between these populations remains a based on step-selection functions (SSF) derived long-term management goal for the state of Mon- from individual-based movement data. By modu- tana as described in the Grizzly Bear Manage- lating the degree of randomness in simulated ment Plan for Northwest Montana (Dood et al. movements, the algorithm has the potential to

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Fig. 1. Study area for delineating potential paths for male-mediated gene ﬂow between the Northern Conti- nental Divide Ecosystem (NCDE) and Greater Yellowstone Ecosystem (GYE) grizzly bear populations. Map (red rectangle in inset map) displays area between estimated occupied range in the NCDE to the north and the GYE to the south, where the randomized shortest path algorithm was applied. Green polygon in inset map shows the full extent of the study area where data informing the step-selection functions were collected from independent- age (≥2 yr old) male bears during 2000–2015 (also see Appendix S1: Fig. S1). Mountain ranges that appear in the text are named (Montana State Library 2014). Occupied range based on data through 2014 (Bjornlie et al. 2014, Costello et al. 2016). better capture the movement ecology of species approach was particularly appropriate for our compared with optimal least-cost path (Walker objective to delineate potential paths for gene and Craighead 1997, Cushman et al. 2009) or ran- ﬂow between the GYE and NCDE populations. It dom-walk approaches (Clark et al. 2015). This allowed us to explore the trade-off between

❖ www.esajournals.org 3 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. optimal, short paths (likely important for success- cultivated crops. Road densities are generally ful immigration given the current distance greater in this area than in the NCDE and GYE, between populations) vs. more exploratory paths and two interstate highways, I-90 and I-15, may (characteristic of a dispersing bear traversing act as potential barriers to grizzly bear move- unfamiliar landscapes). ments. Private land ownership in this area (39%) is greater compared with the NCDE and GYE. STUDY AREA METHODS The study area encompassed 357,773 km2 and spanned 49 counties within western Montana, GPS data eastern Idaho, and northwestern Wyoming Grizzly bears were captured for research and (Fig. 1). We used recent delineations of occupied management purposes using culvert traps or grizzly bear range in the NCDE (Costello et al. Aldrich leg-hold snares (Blanchard 1985), and a 2016 [55,200 km2;2004–2014 data]) and GYE sample of independent-age (≥2 yr old) bears were (IGBST, unpublished data [58,314 km2;2000–2014 fitted with radio transmitters (Telonics, Mesa, Ari- data]), estimated based on Bjornlie et al. (2014), as zona, USA). Grizzly bear capture and handling the basis for our analyses. The NCDE consists of procedures used for this study were reviewed and rugged mountain topography shaped by glacia- approved by the respective Animal Care and Use tion. West of the Continental Divide, vegetation at Committees of the U.S. Geological Survey (ACUC lower elevations is dominated by Douglas-fir no. 201201) and Montana Department of Fish, (Pseudotsuga menziesii), lodgepole pine (Pinus con- Wildlife and Parks (2004). Procedures conformed torta), subalpine fir(Abies lasiocarpa), and spruce to the Animal Welfare Act and to U.S. Govern- (Picea spp.). Non-forested, alpine habitats gener- ment principles for the use and care of vertebrate ally occur above 2000 m. Mountains abruptly animals used in testing, research, and training. transition to short-grass prairie and limber pine Captures were conducted under U.S. Fish and (Pinus flexilis) savannas along the eastern edge of Wildlife Service Endangered Species Permit [Sec- the Rocky Mountains. The GYE consists of a high- tion (i) C and D of the grizzly bear 4(d) rule, 50 elevation plateau surrounded by 14 mountain CFR17.40(b)], with additional state research per- ranges with elevations >2130 m and contains the mits for Wyoming, Montana, and Idaho, and headwaters of three continental-scale rivers. National Park Service research permits for Yellow- Lower elevations (<1900 m) are characterized by stone, Grand Teton, and Glacier national parks. grasslands or shrub steppes interspersed with We restricted our analyses to male grizzly open stands of juniper (Juniperus scopulorum), bears monitored with GPS transmitters during Douglas-fir, and limber pine. Douglas-firforms May 2000–October 2015. Because some remotely the lowest-elevation forest community at around downloaded GPS data did not include activity 1900–2200 m, whereas lodgepole pine dominates data and may have lower precision than data at mid-elevations. Engelmann spruce (Picea engel- stored in internal memory, we based all analyses mannii), subalpine fir, and whitebark pine (Pinus on GPS data from the downloaded, on-board albicaulis) form the upper tree line around 2900 m. memory after collar retrieval, irrespective of Alpine tundra occurs at the highest reaches of all transmitter type. We excluded three-dimensional major mountain ranges. and two-dimensional GPS fixes with PDOP >10 The area of interest for potential paths between (D’Eon and Delparte 2005) or horizontal error the NCDE and GYE consists of a complex of >150 m to ensure fixes had minimal positional forested mountain ranges and open grassland error relative to the spatial resolution of covari- and sagebrush valleys, interspersed with agricul- ates (i.e., 300 m). Additionally, fixes collected tural lands and human settlements at lower eleva- during the typical denning months of December– tions (Fig. 1). Elevations range between 738 and April were excluded. 3883 m. The area contains about 43% forest cover, primarily distributed in the northern portion, Step-selection function whereas the southern portion contains more open We used SSF to quantify habitat selection for grasslands with patches of shrub–scrub land and grizzly bears in the NCDE and GYE. As defined

❖ www.esajournals.org 4 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. by Fortin et al. (2005), the SSF is exponential in We considered an extensive set of spatial form: w(x) = exp(xb), where x represents a vector covariates known or hypothesized to be associ- of environmental covariates and b the associated ated with grizzly bear habitat selection and move- coefficient vector estimated by conditional logis- ments to construct a candidate model set for the tic regression. Grid cells with higher SSF scores step-selection analysis. Our focus was on identify- (w(x)) have greater relative probabilities of being ing paths that show potential for male dispersal chosen by an animal. In circuit theory terminol- between the two populations. Zeller et al. (2012) ogy, the spatial predictions of the SSF scores suggested that estimation of resistance surfaces reflect a conductance surface (McRae et al. 2008). for pathways should take into account that ani- All statistical analyses were carried out in the R mals may make movement decisions based on computing environment (v3.3.1; R Core Team factors other than resource selection. However, 2016). For each observed step (i.e., straight-line grizzly bear dispersal often involves an extended segment linking two successive GPS locations), period of several years, reflective of exploratory we computed the step length and turning angle habitat selection behaviors of resident animals, using the adehabitatLT package (v0.3.20; Calenge rather than a rapid, long-distance movement 2006). We excluded consecutive fixes <100 m (McLellan and Hovey 2001). Data on documented apart from analysis because we were interested in dispersal events are rare, so we used GPS data characterizing habitat selection associated with from a large sample of males from each popula- active movements rather than passive movements tion and assumed that habitat selection associated or stationary states (Latham et al. 2011, Clark with non-stationary GPS locations (i.e., consecu- et al. 2015). Because our GPS data were from two tive fixes ≥100 m apart) within their home ranges different ecosystems and spanned two decades, was generally reflective of how male grizzly bears GPS fix intervals varied. Most GPS transmitters explore the landscape. We classified covariates were programmed to sample at intervals of ≤3.5 h into the following themes (Singleton et al. 2004): so we included all steps that occurred within land cover, road features, hydrological features, ≤4 h. We then applied an additional constraint of human presence, and topography (Appendix S1: ≥100 valid steps for any bear within any year to Table S1). Using ArcGIS 10.2 (ESRI, Redlands, ensure that data were representative of typical Washington, USA), we generated each covariate movements by individual bears for reliable esti- as a raster layer with 300-m resolution. We chose mation of individual-specificregressionparame- this resolution as a compromise between the need ters (Fieberg et al. 2010). to accurately characterize habitats selected, the Next, we paired each observed step with 10 large extent of our study area, and computer pro- steps that shared the same step origin, but with cessing capabilities. We measured several covari- varying step lengths and turn angles, to compare ates using circular moving windows with a the habitat chosen by the bear to those that were radius of 1500 m from the centroid of the center available (Thurfjell et al. 2014, Clark et al. 2015). pixel based on typical daily movements of males We first computed a linear-circular correlation (Schwartz et al. 2010). coefficient (Mardia 1976) between step length and For land cover, we reclassified the 2011 turning angle to determine whether available National Land Cover Database (NLCD; U.S. steps could be generated by sampling step length Geological Survey 2014) to construct a forest ras- independent of turning angle (Thurfjell et al. ter comprised of deciduous, evergreen, and 2014). To fit a distribution to the range of observed mixed forests, as well as woody wetlands. step lengths (i.e., 100–15,000 m), we standardized Because grizzly bear movements and habitat use all step lengths to a [0,1] interval. We then fita are often associated with the interface of forested beta distribution, chosen for its flexibility, to the and open habitats, we derived a covariate based transformed step lengths via maximum-likelihood on Euclidean distance to the nearest forest poly- estimation (MLE) using the fitdistrplus package gon (Nielsen et al. 2004, May et al. 2008, Stewart (v1.0-7; Delignette-Muller and Dutang 2015). We et al. 2013). Positive and negative distance values fit a von Mises distribution, via MLE, to the were associated with grid cells either outside or observed turning angles using the circular pack- inside forest polygons, respectively. We used age (v0.4-7; Agostinelli and Lund 2013). Fragstats (McGarigal et al. 2012) to generate a

❖ www.esajournals.org 5 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. contagion index of natural land cover (i.e., all 1500-m radius circular neighborhood. For human land-cover types from the reclassified 2011 presence, we computed the density of housing NLCD data, but excluding cropland and urban units per census block, as defined by the U.S. areas) using a moving window with a 10-km Census Bureau (2010), using 2010 housing data radius representative of seasonal to annual male (U.S. Department of Commerce 2010). We log10- home ranges. We used this index to measure the transformed these data because the relative prob- extent to which patch types with natural land ability of bears moving through increasingly cover were aggregated or clumped. Higher val- anthropogenic-influenced landscapes is not lin- ues of contagion may result from landscapes ear (Schwartz et al. 2010). For elevation, we with a few large, contiguous patches of natural resampled 30-m National Elevation Data (U.S. land cover, whereas lower values generally char- Geological Survey 2009) to a 300-m resolution acterize landscapes with many small and dis- and included a quadratic term to allow for a persed patches; contagion is inversely related to non-linear response. Because terrain features and edge density (McGarigal et al. 2012). We gener- topography may affect movement, we computed ated a normalized difference vegetation index vector ruggedness measure using a 1500-m (NDVI), a relative measure of vegetative green- radius to provide a broad-scale measure of varia- ness (Mace et al. 1997), using the Google Earth tion in aspect and slope (Sappington et al. 2007). Engine (GEE; Google Earth Engine Team 2015) Using the covariates specified in Appendix S1: as a median composite of Landsat 8 (U.S. Geo- Table S1, we constructed a candidate set of 10 logical Survey 2016) imagery acquired between ecologically plausible models (Table 1). Our 2013 and 2015, during peak greenness (15 June– approach was to maximize predictive power of 15 July); GEE processing corrected for geometric, the model instead of estimating covariate effects. radiometric, and atmospheric errors and individ- We addressed autocorrelation by fitting regres- ual pixels corresponding to clouds were sion models to data from individual animals excluded from the analysis. For road features, we followed by averaging to determine popula- used the National Transportation Dataset to tion-level responses (Fieberg et al. 2010). All 10 derive distance and density covariates (U.S. Geo- candidate models contained six covariates that logical Survey 2015b). Grizzly bears generally we considered essential for modeling grizzly avoid close proximity to roads, but this may vary bear habitat selection (Roever et al. 2010, Proctor depending on road type and, correspondingly, et al. 2015, Ziołkowska et al. 2016): distance to traffic volume (Mace et al. 1996, Chruszcz et al. forest edge, natural contagion, NDVI, home den- 2003, Waller and Servheen 2005, Roever et al. sity, elevation (including its quadratic term), and 2010). Therefore, we computed the Euclidean ruggedness (Table 1). We then added landscape distance to the nearest road separately for pri- and habitat covariates in different combinations mary or secondary roads. Additionally, we to reflect different hypotheses of how such fea- derived linear density for primary or secondary tures may influence grizzly bear exploration of roads per km2, as measured within a 1500 m the landscape. For water features, we included radius circular neighborhood. Primary roads the distance to rivers and distance to perennial were U.S., state, and county highways, whereas streams as an additive pair and as a combined secondary roads encompassed all other roads, covariate. Similarly, within the road feature including unimproved roads. For hydrological theme, we included several combinations of road features, we used the high-resolution National density and distance to roads covariates. We Hydrography Dataset (1:24,000 scale; U.S. Geo- hypothesized that grizzly bear response to roads logical Survey 2015a) to derive distance and den- is a function of both traffic volume and road density covariates. Empirical evidence suggests that sity, so we also included an additive covariate grizzly bear movements are often associated pair consisting of distance to highway and den- with riparian habitats, particularly on the open sity of roads and highways combined. plains (Wilson et al. 2005). We computed the Although we treated individual bears as the Euclidean distance to the nearest river or peren- experimental unit, we performed model selection nial stream, and the linear density of rivers or at the population level because our objective was perennial streams per km2 as measured within a to characterize typical habitat selection patterns

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Table 1. Covariates included in candidate step-selection function models to predict habitat selection of independent-age (≥2 yr old) male grizzly bears monitored with GPS collars in the Northern Continental Divide Ecosystem and Greater Yellowstone Ecosystem, 2000–2015.

Model

Covariate M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 Distance to forest edge 999999999 9 Natural contagion 999999999 9 Normalized difference vegetation index 999999999 9 Distance to highway or secondary road 99 Distance to highway + distance to secondary road 99 Highway density + secondary road density 99 Road and highway density 99 Distance to highway + road and highway density 99 Distance to river or stream 9999 9 Distance to river + distance to stream 99999 999999999 9 Home density (log10) Elevation + elevation2 999999999 9 Vector ruggedness measure 999999999 9 associated with bear movements (Fieberg et al. predicted SSF scores for each grid cell within the 2010). We estimated SSF parameters (b) sepa- respective areas of grizzly bear occupied range rately for the two populations. We used condi- and obtained scores for the locations within the tional logistic regression via the survival package withheld test partition. We divided all mapped (v2.39-4; Therneau 2015) and evaluated candi- (i.e., expected) scores into 10 bins based on quan- date models using corrected Akaike’s informa- tiles and calculated the proportion of test location criterion (AICc) scores (Hurvich and Tsai tions (i.e., observed) that fell within each bin 1989, Burnham and Anderson 2002). To account (Boyce et al. 2002, Thurfjell et al. 2014, Clark et al. for heterogeneity in bear habitat selection and to 2015). For a model with good predictive capabili- equally weight each individual bear, we imple- ties, observed proportions are expected to mented a two-stage modeling approach: After increase with successively higher bins of SSF specifying the covariate structure of the SSF for scores. We computed the Spearman rank correla- each population, we fit the model to each indi- tion between the proportion and bin rank for each vidual bear (pooled over years) and then aver- cross-validated model. We repeated the entire aged the b values across individual bears to fivefold cross-validation procedure 100 times to obtain population-level b values. examine whether model performance was consis- To evaluate the fitofeachpopulation’stop tent among alternative partitions of the data. model, we used the k-fold cross-validation procedure outlined in Boyce et al. (2002). We parti- Randomized shortest path tioned individual bears in each population into We used the RSP algorithm in conjunction five subsamples. To ensure that sample sizes with the SSF models to identify potential paths among partitions were comparable, we first strati- for dispersal of grizzly bears between the NCDE fied bears based on sample size (i.e., stratum one and GYE (Panzacchi et al. 2016). The algorithm contained the top five bears with the largest sam- is analogous to a least-cost path analysis but sub- ple sizes, stratum two included the next five ject to a given level of randomness that is con- bears, and so on) and then randomly assigned trolled by the parameter h. Lower values of h bears within each stratum to a partition. We then result in greater exploration around the shortest estimated the SSF using four of the five partitions path (h = 0 equivalent to pure random walk), as training data, and averaging b values across whereas larger values approach the equivalent of individual bears to obtain population-level mod- a least-cost path. By specifying a range of values els. For each population and test partition, we for h, paths can be identified for varying levels of

❖ www.esajournals.org 7 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. trade-off between exploration and optimal locations (origin nodes) within the 25-km buffer exploitation of the landscape exhibited by indi- with a random location (destination node) in the vidual bears. Animal movements occur through opposing buffer. We computed RSP values for all a sequence of linked nodes, as represented by grid cells in the study region for each pair of grid cells. The RSP algorithm uses a conductance origin and destination nodes using the gdistance surface (i.e., the inverse of a friction surface) and package (v1.1-9; van Etten 2015) with parameter h to estimate the average number of net passages values for h of 0.01, 0.001, and 0.0001. Given the through each grid cell when moving from an study area’s spatial resolution and associated con- origin to a destination node. Given the conduc- ductance values, we visually determined a h value tance layer derived from the spatial covariates in of 0.1 to be approaching the least-cost path. the SSF model, paths follow certain grid cell Bounded by h values of 0 and 0.1 at the extremes, sequences more than others and the resulting we chose three intermediate h values by multi- RSP values thus provide a measure of movement plicatively decreasing the defined maximum of potential. Collectively, the RSP values for all grid 0.1 by consecutive powers of 10. cells in the study region provide an assessment For each level of h and node pair, we obtained of potential paths for male dispersal. a raster layer containing the average net number Using the estimated SSF model for each popu- of passages through each grid cell. For each h,we lation, we predicted a conductance surface for then summed the RSP raster layers for all 100 the entire study region based on 300-m grid cells. node pairs as an index of movement potential for Conductance values for each cell i were based on simulated dispersal events from the NCDE to the À1 the logit (xib), where xi is the vector of covariate GYE, and vice versa. Finally, for each value of h, values associated with cell i and b the vector of we multiplied the cumulative RSP layers for both estimated SSF model coefficients. To avoid con- populations together to delineate areas where ductance values compressing against the bound- predictions intersected, weighted by the respec- ary of the [0,1] interval, we shifted each xib value tive number of net passages. Higher values iden- fi by subtracting the median xib value for the entire ti ed areas where the NCDE and GYE models study area (i.e., the median xib value thus corre- predicted a high number of passages, and lower sponds to a relative probability of 0.5; Panzacchi values reflected fewer predicted paths for one or et al. 2016). We then computed a transition both models. matrix using a Moore neighborhood (i.e., cells No data existed for a robust external validation connected with their eight orthogonal and diago- of our predictions. However, 21 confirmed obser- nal nearest neighbors) with the transition value vations of grizzly bears ≥8kmoutsideof,and between cells i and j within the neighborhood between, the two estimated grizzly bear occupied À equal to f(ci,cj) = max(ci,cj) ci + cj, where ci ranges (Montana Department of Fish, Wildlife and cj are the conductance values associated with and Parks, unpublished data; IGBST, unpublished each cell. Under this specification, the transition data) provided an opportunity to corroborate value is non-commutative and the transition model predictions. For each location, we com- matrix is asymmetric. puted its quantile value based on the distribution We used the 300-m grid cells to represent the of all non-zero, cumulative RSP values from all collection of nodes through which animal move- grid cells within the rectangular area encompass- ments occur. To define origin and destination ing all primary paths and outlier observations nodes, we delineated a 25-km buffer zone span- (Figs. 2–4). Because we predicted movements in ning 500 km on the southern and northern areas different from where these data were sam- boundaries within estimated grizzly bear occu- pled, this analysis offered an ad-hoc, external vali- pied range in the NCDE and GYE, respectively dation of the paths. (Fig. 1). We chose the eastern and western extents of each buffer to encompass locations where RESULTS dispersal events were most likely to originate or terminate, based on our collective knowledge of We obtained GPS telemetry data from 173 grizzly bear movements in the two populations. male bears (NCDE = 33, GYE = 140) for a total For each population, we paired 100 random of 309 bear-years (NCDE = 47, GYE = 262) over

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Fig. 2. Randomized shortest path (RSP) predictions of male grizzly bear movements from the Northern Conti- nental Divide Ecosystem (NCDE) to the Greater Yellowstone Ecosystem (GYE) based on GPS movement data for males monitored in the NCDE, 2000–2015. Color gradient is based on cumulative values of RSPs for 100 pairs of origin–destination nodes, representing the average number of net passages for each grid cell. Three levels of h are shown, representing different trade-offs between exploration and optimal exploitation of the landscape: (A) h = 0.0001, (B) h = 0.001, and (C) h = 0.01. Locations of 21 conﬁrmed records of grizzly bear presence are shown as blue triangles. Black arrow indicates direction of paths. Occupied range based on data through 2014 (Bjornlie et al. 2014, Costello et al. 2016).

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Fig. 3. Randomized shortest path (RSP) predictions of male grizzly bear movements from the Greater Yellow- stone Ecosystem (GYE) to the Northern Continental Divide Ecosystem (NCDE) based on GPS movement data for males monitored in the GYE, 2000–2015. Color gradient is based on cumulative values of RSPs for 100 pairs of origin–destination nodes, representing the average number of net passages for each grid cell. Three levels of h are shown, representing different trade-offs between exploration and optimal exploitation of the landscape: (A) h = 0.0001, (B) h = 0.001, and (C) h = 0.01. Locations of 21 conﬁrmed records of grizzly bear presence are shown as blue triangles. Black arrow indicates direction of paths. Occupied range based on data through 2014 (Bjornlie et al. 2014, Costello et al. 2016).

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Fig. 4. Intersect of randomized shortest path (RSP) predictions of male grizzly bear movements between the Northern Continental Divide Ecosystem (NCDE) and Greater Yellowstone Ecosystem (GYE), 2000–2015. Color gradient is based on multiplication of cumulative values of RSPs for 100 pairs of origin–destination nodes for each population (Figs. 2, 3). Three levels of h are shown, representing different trade-offs between exploration and optimal exploitation of the landscape: (A) h = 0.0001, (B) h = 0.001, and (C) h = 0.01. Locations of 21 con- ﬁrmed records of grizzly bear presence are shown as blue triangles. Black arrow indicates direction of paths. Occupied range based on data through 2014 (Bjornlie et al. 2014, Costello et al. 2016).

❖ www.esajournals.org 11 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. the period May 2000–October 2015. Telemetry Table 2. Model selection results for step-selection mod- monitoring resulted in 58,737 and 237,680 GPS els to predict movements of independent-age (≥2yr fixes in the NCDE and GYE, respectively. After old) male grizzly bears monitored with GPS collars in removing steps and individual bears that failed the Northern Continental Divide Ecosystem (NCDE) to meet our inclusion criteria, we retained 131 and Greater Yellowstone Ecosystem (GYE), 2000–2015. male bears (NCDE = 15, GYE = 116) spanning Population Model k AIC DAIC w logL 212 bear-years (NCDE = 22, GYE = 190). Ages of c c i À bears ranged from two to 16 with a median of NCDE M6 10 83,537.6 0.0 0.44 41,758.8 À four years in the NCDE, and from two to 30 with M10 10 83,538.3 0.7 0.31 41,759.1 À M8 9 83,539.4 1.8 0.18 41,760.7 a median of eight years in the GYE. The NCDE À M2 10 83,542.2 4.6 0.04 41,761.1 dataset contained 17,624 steps with step counts À M4 9 83,543.1 5.5 0.03 41,762.5 among individuals ranging from 112 to 4445. À M9 11 83,582.1 44.5 0.00 41,780.0 À The GYE dataset contained 108,309 steps with M5 11 83,583.5 45.9 0.00 41,780.8 À step counts among individual bears ranging M7 10 83,584.6 47.0 0.00 41,782.3 À from 106 to 4491. Median step length was 520 m M1 11 83,585.9 48.3 0.00 41,781.9 À (range = 100–10,420) in the NCDE and 724 m M3 10 83,588.2 50.6 0.00 41,784.1 À GYE M9 11 515,059.2 0.0 1.00 257,518.6 (range = 100–14,520) in the GYE. Because longer À M7 10 515,110.2 51.0 0.00 257,545.1 step lengths occurred more frequently among À M10 10 515,110.5 51.3 0.00 257,545.3 GYE bears than NCDE bears, and because of À M5 11 515,111.8 52.6 0.00 257,544.9 fi À landscape differences, we t separate step-length M1 11 515,158.1 98.9 0.00 257,568.0 À distributions for each population (beta distribu- M8 9 515,161.1 101.9 0.00 257,571.6 À tion parameter MLEs: a = 0.792, b = 16.532 for M6 10 515,163.1 103.9 0.00 257,571.5 À NCDE; a = 0.708, b = 9.027 for GYE). Mean step M3 10 515,194.4 135.2 0.00 257,587.2 À duration was 68.7 min (range = 26.6–240.0) for M2 10 515,206.1 146.9 0.00 257,593.1 M 9 515,240.3 181.1 0.00 À257,611.2 NCDE bears and 106.4 min (range = 26.7–240.0) 4 ’ for GYE bears. Turning angles exhibited directional Note: Shown are differences in Akaike s information criteria for small sample sizes (AICc) between the model and lowest persistence and were independent of step length AICc in the model set (DAICc), number of estimable parame- (R = 0.007). Plots of turning angles indicated no ters (k), model weight (wi), and the log-likelihood (logL). practical difference between bears in the two populations. Because we had no ecological basis to zero variation in either the natural contagion or assume directionality of movements would be road–highway density covariate. Thus, popula- different for the NCDE and GYE, we estimated a tion-level covariates were based on 109 male bears single, pooled turning angle distribution (von for a total of 177 bear-years and 98,655 steps. Mises parameter MLEs: l = 0.020, j = 0.607). Model M9 wasmostparsimoniousamongthecan- Median cumulative step length among individ- didate set by a large margin (DAICc = 50.991; ual bears was 484.4 km (range = 103.0–2013.0) Table 2). Average Spearman rank correlations for NCDE and 610.9 km (range = 57.2–2072.0) from fivefold cross-validation ranged from 0.678 to for GYE bears. 0.969 (median = 0.862) for the 100 iterations, indi- For the NCDE, several population-level models cating good predictive capacity within the GYE. were parsimonious based on DAICc values <2 The cumulative RSP layer based on the NCDE (models M6,M10, and M8; Table 2). We chose conductance map depicted numerous potential fl model M10 because it re ected biologically rele- paths from the NCDE to the GYE. These vant covariates based on the hypothesis that bear included areas of dense paths that formed inter- response may be a function of both trafficvolume secting corridors linking mountain ranges in the associated with highways and overall density of center of the study area, and broader areas with roads and highways. Average Spearman rank more diffuse paths on the periphery (Fig. 2). Two correlations for the 100 iterations of fivefold corridors consisting of dense paths converged on cross-validation ranged from 0.743 to 0.990 the Tobacco Root Mountains. One originated in (median = 0.939), indicating good predictive the Rattlesnake–Garnet ranges and traversed the capacity within the NCDE. Individual-level mod- John Long, Flint Creek, Anaconda, Pioneer, and els could not be fit for seven GYE bears because of Highland ranges, whereas the other originated in

❖ www.esajournals.org 12 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. the Nevada–Garnet ranges and traversed the portions of the area between the two ecosystems, Boulder Mountains. After traversing the Tobacco generally reflecting wide, open, inter-mountain Root Mountains, paths entered the GYE through valleys encompassing human settlements and the Madison or Gravelly ranges. Two other agriculture (Fig. 4). Models also agreed on a high routes with dense paths originated in the south- density of paths forming several distinct routes ern Lewis and Clark Range and converged on in the central portion of the area, where path the Bridger Range prior to entering the GYE. options were limited due to habitat fragmenta- One followed the Nevada, Boulder, Elkhorn, and tion. Additionally, areas with high intersection of southern Big Belt Mountains, and the other tra- model predictions were associated with the versed the Big Belt Mountains. Longer, more Bridger and Big Belt Mountains in the east and meandering paths were evident on the western the previously described routes between the and eastern peripheries, especially for models Rattlesnake–Garnet ranges south of the NCDE with h = 0.0001. Paths on the western periphery and the Tobacco Root Mountains northwest of extended from the Bitterroot and Anaconda the GYE (Fig. 4). ranges and traversed the Pioneer and Blacktail Confirmed locations of grizzly bears beyond ranges before reaching the Gravelly or Centen- the occupied ranges generally were in grid cells nial ranges. Paths on the eastern periphery fol- predicted to have relatively high net passage lowed the Little Belt, Castle, and Crazy ranges. rates (median quantile values = 0.75–0.87; For the GYE, the cumulative raster layers of Figs. 2–4), with generally higher values for the the 100 RSP models also showed many potential NCDE model compared with the GYE model paths leading from the GYE to the NCDE (Table 3). Within each model, differences in (Fig. 3). Areas with a high density of paths quantiles across h values were small, indicating formed two corridors that originated in the Grav- little influence due to varying levels of move- elly, Madison, or Gallatin ranges, converged on ment exploration between nodes. Three locations the Tobacco Root and Highland ranges, but then (locations 8, 20, and 21) for the NCDE model and split to follow the Pioneer, Anaconda, Flint five locations (locations 4, 8, 16, 20, and 21) for Creek, and John Long Mountains or the Boulder the GYE model were in areas with lower pre- Mountains to enter the NCDE. Predicted paths dicted passage rates, whereas four locations originating in the Absaroka and Gallatin ranges (locations 8, 16, 20, and 21) had a low passage were concentrated and formed a corridor along rate according to the intersection of model pre- the Bridger and Big Belt Mountains or branched dictions (Table 3; Appendix S1: Fig. S2). at the southern portion of the Big Belt Mountains to the Elkhorn and Boulder Mountains. Several DISCUSSION alternative routes interconnecting these areas were evident as well. Predicted paths were Although we observed fine-scale differences in moderately dense and formed a corridor that our predicted paths, spatial concordance was originated from the southern Madison Range high between models based on the NCDE vs. the and Centennial Mountains, and subsequently GYE grizzly bear location data. Close agreement traversed the Snowcrest, Blacktail, Pioneer, Ana- between the models is particularly germane conda, and Sapphire Mountains. More diffuse when judging the validity of our results, given paths on the western periphery also included that we applied the models to areas beyond the the Tendoy, Beaverhead, and Bitterroot ranges. origins of the training data (Boyce et al. 2002). Diffuse paths on the eastern periphery included Reliability of our model output was also sup- the Crazy Mountains and, to a lesser extent, the ported by positive results of the fivefold cross- Castle and Little Belt ranges. validation of the SSF component and our ad-hoc We observed broad-scale concordance between external validation of the RSP component using model predictions for paths originating in the verified outlier observations of grizzly bears. NCDE and those originating in the GYE for all Model predictions, particularly those based on values of h (Figs. 2, 3). Based on the weighted, lower values of h, indicated that grizzly bear spatial intersection of model predictions, there paths between the populations might involve was low potential for movement within large any number of routes. This result is not

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Table 3. Information about conﬁrmed grizzly bear locations observed between the occupied ranges of the Northern Continental Divide Ecosystem (NCDE) and Greater Yellowstone Ecosystem (GYE) populations, and individual and median quantile values of their location grid cells (as computed from the distributions of all non-zero, cumulative randomized shortest path [RSP] cell values within the rectangular area encompassing all predicted paths and outlier observations [Figs. 2–4]).

Distance from Quantile of RSP distribution 2014 occupied range (km) NCDE model GYE model Intersect model Loc. Cohort‡ number (origin; if h = h = h = h = h = h = h = h = h = (yr) Type† known) NCDE GYE 0.0001 0.001 0.01 0.0001 0.001 0.01 0.0001 0.001 0.01

1 (1998) M SM (GYE) 141 19 0.54 0.59 0.65 0.64 0.62 0.59 0.60 0.63 0.62 2 (2005) M SM (NCDE) 43 113 0.87 0.92 0.92 0.92 0.98 1.00 0.91 0.97 0.98 3 (2010) DNA AM (NCDE) 8 137 0.91 0.86 0.86 0.67 0.67 0.67 0.85 0.80 0.78 4 (2010) M AM (NCDE) 40 80 0.88 0.83 0.77 0.42 0.52 0.53 0.56 0.66 0.65 5 (2014) BP S 163 34 0.66 0.76 0.72 0.93 0.92 0.89 0.84 0.86 0.79 6 (2015) TO AFC 22 100 0.99 0.98 0.97 0.93 0.93 0.93 0.97 0.96 0.96 7 (2016) TO S 32 93 0.76 0.68 0.63 0.57 0.57 0.52 0.68 0.64 0.57 8 (2016) I S 8 192 0.33 0.49 0.59 0.19 0.24 0.20 0.21 0.33 0.30 9 (2016) BP, TP S 89 120 0.73 0.79 0.84 0.75 0.80 0.84 0.78 0.83 0.87 10 (2016) TP S 96 119 0.67 0.75 0.77 0.74 0.82 0.86 0.75 0.81 0.82 11 (2016) BP S 60 83 0.93 0.93 0.89 0.67 0.64 0.59 0.86 0.81 0.74 12 (2016) BP S 25 106 0.94 0.94 0.93 0.92 0.91 0.94 0.94 0.93 0.94 13 (2016) BP S 18 96 0.97 0.96 0.95 0.90 0.91 0.92 0.95 0.94 0.95 14 (2016) BP, C SM (NCDE) 17 100 0.96 0.95 0.93 0.94 0.93 0.92 0.95 0.95 0.93 15 (2016) BP, TO S 10 104 0.98 0.95 0.95 0.94 0.93 0.94 0.97 0.95 0.95 16 (2016) TP S 37 85 0.57 0.60 0.61 0.38 0.44 0.41 0.45 0.50 0.48 17 (2016) BP S 131 115 0.60 0.56 0.53 0.80 0.73 0.66 0.73 0.68 0.60 18 (2017) TP S 132 9 0.99 0.99 0.97 0.93 0.94 0.95 0.97 0.98 0.97 19 (2017) BP S 49 137 0.91 0.90 0.91 0.94 0.91 0.82 0.93 0.92 0.90 20 (2017) BP SM§ 90 167 0.37 0.32 0.30 0.28 0.25 0.14 0.31 0.28 0.16 21 (2017) M SM§ 110 164 0.17 0.16 0.15 0.20 0.19 0.09 0.19 0.18 0.08 Median 43 104 0.87 0.83 0.84 0.75 0.80 0.82 0.84 0.81 0.79 Notes: Values of h represent different trade-offs between exploration and optimal exploitation of the landscape, with greater exploration movements at lower values. Several within-year observations may be of the same individual bear. † Type: BP, bear photographed; C, capture; M, mortality; DNA, hair DNA sample; I, investigated; TO, tracks observed; TP, tracks photographed. ‡ Cohort: AFC, adult female with cub-of-the-year; AM, adult male; S, solitary bear, unknown sex or age class; SM, subadult male. § Locations 20 and 21 are multiple records of two sibling males traveling together. unexpected given that grizzly bears are general- exploration allowed us to identify the more ists and occur in a wide variety of habitats, both direct routes that bears may use to move across and within populations (Stirling and between the ecosystems, areas with greater pre- Derocher 1990). Therefore, with the exception of dicted passage rates do not necessarily reflect areas with low numbers of predicted passages superior habitat characteristics compared with (e.g., wide open valleys), we anticipate that spo- areas with more diffuse paths. In fact, areas radic bear sightings and possible interactions where paths are more scattered seem to reflect with humans may occur almost anywhere along more contiguous habitats, as opposed to areas the gradient of our model predictions. Still, the where anthropogenic influence is greater and exploration vs. optimal exploitation trade-off path options are limited. For example, despite component of the RSP procedure (i.e., modula- longer routes, the pattern of diffuse paths on the tion based on h) enhanced our understanding of western periphery suggests ample movement the range of potential paths available to grizzly options, likely as a function of large, contiguous bears. Whereas paths with the lowest level of areas of natural landscapes (forest and range

❖ www.esajournals.org 14 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. land) with limited anthropogenic influence. As range are possible (Table 3). Nonetheless, the indicated by Panzacchi et al. (2016), RSP analyses probability of successful dispersal may still be are based on the assumption that animals have low, despite recent population expansion. In fact, prior knowledge of the entire landscape but results of a first attempt to model movement move neither optimally (i.e., following the short- between the populations support this notion: est path) nor entirely at random, often exhibiting Based on the SSF we reported here, we initially exploratory movements. This assumption is used a correlated random-walk method similar likely met for male grizzly bears moving within to Clark et al. (2015). However, among 20,000 their home range, but may involve more explo- simulations consisting of 3000 steps (equivalent ration among dispersing bears. Therefore, we to one active season), very few simulated walks caution against a sole focus on the most heavily reached the vicinity of the destination popula- predicted corridors based on the larger h value tion, and none were fully successful. It was only (i.e., Figs. 2C, 3C, 4C), and encourage considera- by constraining the starting and end nodes of tion of alternative paths that reflect a greater paths using the RSP approach (Panzacchi et al. level of exploration (panels A and B in Figs. 2–4). 2016) that we were able to predict potential paths We also emphasize that areas where we identi- linking the two populations. Thus, although our fied potential paths should not be interpreted as results delineate many possible paths for disper- habitat linkages that provide conditions con- sal between the two ecosystems, successful ducive to permanent grizzly bear occupancy as immigration events will likely remain rare given they may not represent the most likely areas for the current distance between the populations. If future range expansion. Identification of such the two populations continue to expand and this areas will require a different approach, involving distance decreases, the likelihood of successful additional data (e.g., female locations, resting immigration will increase accordingly. and denning locations) and likely different spa- We identified several interconnected areas with tial covariates. The two types of connectivity concentrated paths along neighboring mountain were illustrated by Proctor et al. (2012). They ranges that may serve as stepping stones to male reported that grizzly bear populations along the grizzly bear dispersal between the two ecosys- Canada–U.S. border area remained genetically tems. Concentrated paths following the Big Belt connected through male immigration, but lacked and Bridger Mountains and the Boulder and demographic connectivity because habitat frag- Tobacco Root Mountains were similar to those mentation (primarily transportation infrastruc- identified by Picton (1986), Walker and Craighead ture and human settlements) severely inhibited (1997), and Cushman et al. (2009). However, our movement of females. analyses placed much greater emphasis on poten- Although our models provide information tial paths following the Rattlesnake, Garnet, John about possible routes for male-mediated gene Long, Flint Creek, Anaconda, Pioneer, and High- flow, a key question is how high the likelihood of land Mountains. The Tobacco Root Mountains successful immigration is. Total distances of may be a particularly pivotal stepping stone, as predicted paths in the central region range from many different paths converged on this mountain approximately 135 to 210 km, whereas paths in range. To date, no recent observations of grizzly the western periphery may exceed 350 km. These bears have been confirmed within the Tobacco distances surpass average dispersal distances for Root Mountains, despite DNA sampling efforts male grizzly bears recorded in the northern Rocky (Lukins et al. 2004) and surveillance based on Mountains (30–42 km), but overlap the range observation reports (K. Frey, Montana Depart- of maximum distances observed (67–176 km; ment of Fish, Wildlife and Parks, personal commu- Blanchard and Knight 1991, McLellan and Hovey nication). Corridors delineated by Dilkina et al. 2001, Proctor et al. 2004). To date, the most (2016) for grizzly bears only partially aligned with remote verified observations of grizzly bears those we identified in our study. One reason for within the region between the populations were this difference is likely related to different analyti- located ~110 km from the GYE and ~95 km cal approaches. Whereas our study relied on from the NCDE (locations 9, 10, 11, and 17), con- extensive GPS data to predict how bears may firming that movements within this distance explore the landscape between the NCDE and

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GYE, Dilkina et al. (2016) used optimization pro- individual bears was large, the concordance of cedures based on landscape resistance to bear results based on two independent datasets, the movement, defined based on qualitative weight- similarity of RSP quantiles associated with the 21 ing of habitat types and road density, combined outlier locations across the three values of h,and with estimated costs of land acquisition given our careful selection of covariates associated with specificbudgetconstraints. movement steps, we believe these assumptions In our analyses, we assumed the conductance were generally met. In drawing from the pooled surface values represent the willingness of a bear distribution of step lengths and turning angles to traverse a given spatial unit, but we did not but estimating SSF parameters for each individ- specifically evaluate the potential for transporta- ual, we implicitly assumed that sampled bears tion infrastructure to act as local barriers to move- exhibited similar movement behaviors but made ment. For example, our models were capable of individual choices depending on habitat availabil- accounting for grizzly bear avoidance of areas ity within the reach of one step length. Finally, with high road density (Mace et al. 1996, given the spatial resolution of the covariates, we Chruszcz et al. 2003, Waller and Servheen 2005, assumed those choices were not affected by varia- Roever et al. 2010), but were not equipped to tion in our GPS fix rates (Thurfjell et al. 2014). identify specific multi-lane, high-volume high- Our study provides detailed, spatially explicit ways that may impede movement (e.g., interstate information for land managers and organizations highways I-90 and I-15). Nevertheless, our results working with land owners to identify and priori- can be used to identify sections of these highways tize conservation measures to maintain or enhance where crossings might occur similar to Cushman the integrity of areas supporting potential disper- et al. (2009), who identified 21 potential barriers sal of male grizzly bears, such as conservation to animal movement along predicted black bear easements and land purchases; mitigation of high- corridors within our study region. Those barriers way and other infrastructure barriers across key represented gaps in federal land ownership and paths; and proactive education and attractant major highways, areas in federal ownership but management programs to prevent or reduce traversed by major highways, and areas where human–bear conflict. The predicted RSPs are major highways paralleled corridors. available as GIS data layers (300 m pixel size) and Interpretation of our analyses required a num- can be used in landscape planning decisions (see ber of additional assumptions. First, we assumed https://doi.org/10.5066/f72v2f2w). that the sample used in our analyses adequately represented the population of male bears in each ACKNOWLEDGMENTS population. We also assumed that dispersing male bears explore new terrain in a manner similar to We thank the many personnel from the NCDE trend the observed movements of bears in our sample. monitoring team and the Interagency Grizzly Bear Median ages for bears in our sample were four Study Team who directly or indirectly contributed to and eight for the NCDE and GYE, respectively, so the collection of data we used in this study, including observed movements were likely representative the Blackfeet Nation; the Confederated Salish and of bears within established home ranges, as well Kootenai Tribes; Idaho Fish and Game; Montana as more exploratory movements among young Department of Fish, Wildlife and Parks; National Park males. Given that dispersal is typically a gradual Service (Glacier, Grand Teton, and Yellowstone process, we believe this assumption was reason- national parks); U.S. Geological Survey; U.S. Fish and able. Additionally, because of range expansion, Wildlife Service; U.S. Forest Service; the Wind River landscape conditions on the periphery of occu- Fish and Game of the Eastern Shoshone and Northern Arapaho Tribes; and Wyoming Game and Fish Depart- pied range are not substantially different from ment. This study was funded by the U.S. Fish and areas between the two ecosystems. We also Wildlife Service, Office of the Grizzly Bear Recovery assumed that selection of covariates was similar Coordinator. We thank Chris Servheen for his support across seasons and across years for bears with of this study. We appreciate the review comments from multiple years of data and that any changes in Justin Gude and Robert Inman and two anonymous covariate values during the period of 2000–2015 reviewers. We thank David Gustine for conducting the were negligible. Given that our sample size of U.S. Geological Survey Fundamental Science Practices

❖ www.esajournals.org 16 October 2017 ❖ Volume 8(10) ❖ Article e01969 Embargoed until 10/23/2017 PECK ET AL. review. Any use of trade, firm, or product names is for Cushman, S. A., K. S. McKelvey, and M. K. Schwartz. descriptive purposes only and does not imply endorse- 2009. Use of empirically derived source-destination ment by the U.S. Government. models to map regional conservation corridors. Conservation Biology 23:368–376. LITERATURE CITED Delignette-Muller, M. L., and C. Dutang. 2015. fitdistrplus: an R package for fitting distributions. Journal Agostinelli, C., and U. Lund. 2013. R package circular: of Statistical Software 64:1–34. circular statistics (version 0.4-7). https://r-forge. D’Eon, R. G., and D. Delparte. 2005. Effects of radio- r-project.org/projects/circular/ collar position and orientation on GPS radio-collar Beier, P., D. R. Majka, and W. D. Spencer. 2008. 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