Non-invasive mark–resight surveys for brown bears: Incorporating spatial information to improve landscape-scale monitoring of density and distribution

Abstract

1. Effective wildlife monitoring and management are reliant on unbiased estimators of population parameters. Most standard survey approaches ignore spatial pattern in the data although spatial relationships can be leveraged to produce more efficient designs for future surveys, thereby reducing project cost. Landscape-scale surveys for brown bears are notoriously expensive and difficult to complete, leading to the development of a non-invasive mark–resight aerial survey approach as a practical alternative to more commonly employed approaches for estimating brown bear density across large areas.
2. Here we extend that model to accommodate spatial covariate information and explicitly model residual spatial autocorrelation. Using brown bear survey data from northwestern Alaska, USA from 2015 to 2021, we demonstrate how our extension can be useful in exploring ecological factors related to spatial variation in bear density and detection probability.
3. We found that detection probability was higher in more rugged terrain, and occurrence probability was higher at mid-elevations where denning habitat was more prevalent and in areas with more salmon streams. The descriptive model of residual autocorrelation confirmed that additional unmeasured factors were associated with bear distribution. While these findings were not unexpected, they are very useful when considering future survey effort.
4. Using this information, we explored a hypothetical redesign of the 2021 brown bear survey that removed 50% of the survey subunits with elevation values below the mean, where bears were least likely to occur. We demonstrated that the resulting estimates were unbiased, suggesting that adopting the spatial approach to analysis could reduce overall project costs by ~20%–30% going forward.
5. Overall, our work indicates that directly accounting for spatial pattern within the non-invasive mark–resight framework has substantive advantages over the original non-spatial approach and may be useful in increasing the amount of information available for brown bear populations.

1 INTRODUCTION

Effective wildlife monitoring and management are reliant on efficient, effective and feasible survey techniques (Reynolds, 2012; Reynolds et al., 2011) that address the issue of incomplete detection (Thompson, 2004; Williams et al., 2002). Correcting for incomplete detection is a primary component of capture–recapture (Otis et al., 1978; Pollock et al., 1990), distance sampling (Buckland et al., 2001; Burnham et al., 1980) and occupancy modelling (MacKenzie et al., 2002, 2018) approaches, which are commonly used to estimate core population parameters (i.e. density, abundance, survival, occupancy, etc). However, the spatial distribution of the detected individuals contains information that can be used to improve estimation and provide meaningful information on population distribution and ecological relationships.

The idea of recasting common approaches to population parameter estimation in a spatial framework has led to an explosion in the development of spatial versions of capture–recapture methods (Borchers & Efford, 2008; Efford, 2004; Royle et al., 2014), distance sampling (Hedley & Buckland, 2004; Miller et al., 2013) and occupancy models (Johnson et al., 2013). One of the primary advantages of incorporating the spatial location of detected individuals is that it provides a direct link between the population parameter of interest (e.g. density) and the spatial distribution of the parameter values on the landscape. A common example is a density surface model whereby density is predicted over a gridded study area based on known covariate values (e.g. elevation, snow depth, soil type) for each grid cell. The link between the spatial covariates and density allows the researcher to identify factors influencing animal distribution in space (Royle et al., 2014, 2018; Tourani, 2022). Descriptive models of the remaining spatial autocorrelation (e.g. Gaussian process models, generalized additive models, conditionally autoregressive models) can also be added to improve predictions of variation on the landscape and help form future hypotheses related to species distribution (Kery & Royle, 2021). As an added benefit, when the underlying relationship between animal density and landscape characteristics is known, model-based inference can be used to design more efficient sampling schemes without introducing bias (Johnson et al., 2010; Schmidt & Deacy, 2021). Together, these advances can be used to produce efficient survey designs that provide key information on the ecological underpinnings of a species' distribution, as well as estimators of important population parameters (Camp et al., 2021, 2023).

Landscape-scale surveys for bears (Ursus spp.) are logistically difficult and expensive given the characteristics of their life history (e.g. low density, large home ranges, elusive behaviour). Over time, researchers have developed effective capture–mark–resight (Miller et al., 1997), genetic mark–recapture (Kendall et al., 2008, 2009; Mowat & Strobeck, 2000; Murphy et al., 2016) and distance sampling (Becker & Crowley, 2021; Becker & Quang, 2009; Walsh et al., 2010) methods for assessing brown bear (Ursus arctos) populations at large spatial scales. However, the need for a more economical landscape-scale survey approach for brown bears led to the recent development of an aerial non-invasive mark–resight approach that uses photographs and spatial locations as temporarily identifiable marks that allow bears to be identified during replicate survey events conducted within a short time interval (Robison et al., 2017; Schmidt et al., 2017). One specific advantage of the mark–resight survey protocol is that a brief resurvey interval limits movement of individuals, allowing the model to be cast in a simple non-spatial framework (see Schmidt et al., 2017) rather than a more complex spatially explicit mark–resight framework which must account for movement between sampling events (e.g. Royle et al., 2014). Primarily applicable to unforested habitats, the approach of Schmidt et al. (2017) was used to estimate brown bear density across an approximately 85,000 km² area in northwestern Alaska, USA (Schmidt et al., 2021). Although the non-spatial approach to these surveys was adequate to achieve the original objectives, we expected it would be beneficial to extend the approach to incorporate spatial covariate information, such as landscape characteristics and indices of food availability, to help explain the distribution of brown bears on the landscape. Doing so would provide the opportunity to explore spatial patterns in bear occurrence and facilitate further optimization of survey designs.

Here we extend the mark–resight model of Schmidt et al. (2017) to allow the incorporation of spatial covariate information and residual spatial autocorrelation. We demonstrate the utility of the extended model using brown bear survey data from northwestern Alaska, USA collected between 2015 and 2021. In doing so, we integrate several recent advances in survey design and spatial analysis to estimate brown bear density and distribution in relation to spatial predictors (i.e. elevation, proximity to salmon streams). We also demonstrate how a model-based analytical approach can be used to reduce effort during subsequent surveys without causing bias. Our main objectives were to identify patterns in bear distribution that may be useful in supporting positive monitoring and management outcomes and to support ongoing survey efforts by reducing overall survey cost going forward. Although the resulting mark–resight model was developed specifically for our brown bear surveys, the basic principles could be easily extended to other similar applications.

2 MATERIALS AND METHODS

2.1 Study area

Our study area consists of four distinct subareas [central Seward Peninsula; lower Noatak River drainage; upper Noatak River drainage; Gates of the Arctic National Park and Preserve] covering approximately 85,000 km² in northwest Alaska, USA (Figure 1). The area includes elevations ranging from sea level to 2400 m and is characterized by long cold winters (~0°C to −55°C) and short summers (~0°C to 30°C) with low annual precipitation (~20–45 cm/year). Terrain ranges from flat tussock tundra, to rolling hills, and steep mountains. Woody vegetation is generally limited to shrub patches (Salix spp., Alnus spp.) concentrated along riparian corridors, although closed spruce (Picea spp.) and deciduous (Populus balsamifera and Betula neoalaskana) forest does occur in the southern portion of the Seward Peninsula and along the lower Noatak River. In addition to brown bears, populations of Dall's sheep (Ovis dalli dalli), caribou (Rangifer tarandus), muskoxen (Ovibos moschatus), moose (Alces alces) and black bears (Ursus americanus) occur in portions of the study area. Pacific salmon (Oncorhynchus spp.) are also present in portions of the study area, although their abundance and availability to bears as a food resource is highly variable in space and time. Additional details can be found in Schmidt et al. (2021).

FIGURE 1

Map showing the spatial locations of the four brown bear survey subareas in northwestern Alaska, USA 2015–2021 and the layout of the systematic sampling grids (a). Blue grid cells were surveyed once, and red grid cells were surveyed twice. The distribution of the sampling effort for the 2021 resurvey of the Seward Peninsula subarea is shown in the inset (b).

2.2 Field methods

We used the aerial non-invasive mark–resight design and survey protocol developed by Schmidt et al. (2017) to survey for bears in each of the four subareas 2015–2018 (1 subarea/year), and again in the Seward Peninsula subarea in 2021. We began by generating a 31 km² grid of pixels across each subarea, and then created a sampling design consisting of a series of systematically placed 124 km² units, consisting of four pixels each (i.e. subunits) within each subarea (Figure 1). During each survey, a pilot-observer team intensively searched each assigned subunit for bears from a fixed-wing tandem-seat aircraft, typically spending ≤1 h covering each subunit. Within a short time (generally within 1 h), a second pilot-observer team would resurvey the same subunit. The short time interval between the first and second survey helped meet the assumption of closure. Whenever a bear group was detected, the observer took multiple high-resolution digital photographs of the group and recorded the spatial location (using a global positioning system), composition (i.e. cubs, adults) and other distinguishing features (e.g. distinctive coloration) of the group that might aid identification. Given the close resurvey interval, the spatial location of each group and its unique characteristics allowed teams to determine which bear groups were detected in common. We then used the paired detection information to form a capture history for each observed group. Schmidt et al. (2017, 2021) provide additional details on survey procedures and justification for the underlying methodological assumptions. Our surveys adhered to the guidelines provided by the American Society of Mammologists for the conduct of aerial surveys of vertebrate mammals and therefore did not require permitting.

The mark–resight model of Schmidt et al. (2017, 2021) relied on a systematic sampling design with a random start to ensure that all habitats were surveyed in proportion to their occurrence, meaning that the target population and the sampled population were assumed to be aligned (e.g. Williams et al., 2002). Under that assumption, the product of the mean probability of group occurrence and mean group size across the collection of sampled pixels represents an unbiased estimator of density for the entire area of interest. However, habitat variables and population density are unlikely to be uniformly distributed in space, and variation in density can reduce estimator precision. Adding a spatial component to the model allows density to vary among pixels as a function of spatial covariates and facilitates predictions of density at the spatial grain of the individual pixel. Given that our design was already grid based, it was relatively straightforward to formulate the spatial version of the model in the context of the entire population of pixels (i.e. all potential subunits, both sampled and unsampled) within each subarea, rather than the subset of sampled pixels. Doing so allowed us to estimate parameters associated with brown bear density and detection in the context of spatially varying covariate values.

2.3 Analysis

As in past applications (Schmidt et al., 2017, 2021), we used data augmentation (Royle, 2009; Royle et al., 2007) to create additional 00 capture histories for groups within each pixel, with a total of five potential groups/pixel (observed plus augmented groups). We then used the model to estimate how many of these potential groups were actually present in each pixel. The generalized version of our model can be written as:

$$$$ {y}_{ij k}\sim Bernoulli\left({z}_{ij}\times {p}_{ij k}\right), $$$$

$$$$ {z}_{ij}\sim Bernoulli\left({\varPsi}_{ij}\right), $$$$

$$$$ logit\left({\varPsi}_{ij}\right)={\boldsymbol{x}}_{ij}^{\prime}\boldsymbol{\beta} +\sum \limits_m^{60}{\mu}_m\left( Pixel.{loc}_i-{\boldsymbol{\kappa}}_m\right), $$$$

$$$$ logit\left({p}_{ijk}\right)={\boldsymbol{w}}_{ijk}^{\prime}\boldsymbol{\alpha}, $$$$

$$$$ {s}_{ij}\sim Poisson\left({\boldsymbol{v}}_{ij k}^{\prime}\boldsymbol{\gamma} \right), $$$$

$$$$ {\hat{N}}_i=\sum \limits_{j=1}^n\left({z}_{ij}\times {s}_{ij}\right), $$$$

where the observations, $$$ {y}_{ijk} $$$, for each pixel, i, potential group, j, and visit, k, are a function of the true state, $$$ {z}_{ij} $$$, and the probability of detecting a group given it was present, $$$ {p}_{ijk} $$$. The probability of occurrence for each group within each subarea (and year in cases where a subarea is surveyed in multiple years), $$$ {\varPsi}_{ij} $$$, can be modelled as a function of a vector of known covariate values, $$$ {\boldsymbol{x}}_{ij} $$$, where $$$ \boldsymbol{\beta} $$$ is the associated coefficients. A spatial generalized additive model (GAM) addresses residual spatial autocorrelation in $$$ {\varPsi}_{ij} $$$ among pixels (Collier et al., 2012; Hedley & Buckland, 2004; Hefley et al., 2017; Schmidt et al., 2022). The spatial effects, $$$ {\mu}_m $$$, are modelled as a function of the spatial location of each pixel, $$$ Pixel.{loc}_i $$$, in relation to the placement of fixed knots (i.e. spatial locations over which predictions are smoothed), $$$ {\boldsymbol{\kappa}}_m $$$, located throughout the study area. In our case, we set $$$ m=60 $$$ to ensure adequate coverage. Our spatial GAM was comprised of a series of basis functions in the form of random effects that smoothed predictions across the collection of pixels using radial basis splines (Crainiceanu et al., 2005; Gimenez et al., 2006, 2009; Peron et al., 2011; Schmidt et al., 2022).

Detection probability and group size, $$$ {s}_{ij} $$$, are modelled as functions of vectors of known covariate values, $$$ {\boldsymbol{w}}_{ijk} $$$ and $$$ {\boldsymbol{v}}_{ijk} $$$, and associated coefficients, $$$ \boldsymbol{\alpha} $$$ and $$$ \boldsymbol{\gamma} $$$ respectively. The estimated number of individuals in each pixel ($$$ {\hat{N}}_i $$$) is derived by summing the product of the true state and the predicted group size for all n potential groups within each pixel (in our application n = 5). Estimates of density are then simply calculated by summing the $$$ {\hat{N}}_i $$$ across all the pixels of interest (e.g. all pixels within a defined subarea) and dividing by the total area encompassed by those pixels.

For our specific brown bear application, we assumed unique intercepts for $$$ {\varPsi}_{ij} $$$ and $$$ {s}_{ij} $$$ for each subarea and a common intercept for detection probability. These choices were based on our expectation that the average probability of group occurrence and mean group size differed among the subareas, while the overall detection process was broadly consistent across the study area. We also explored a small suite of covariates that we suspected were related to variation in density or detection on the landscape. Specifically, we considered the number of kilometres of salmon streams within 25 km of each pixel as a possible predictor of bear occurrence (recognizing that salmon were not available to bears at the time of the survey and that bears can move long distances to access limited food resources) based on the hypothesis that bear densities might be higher in areas with more access to salmon (Hilderbrand et al., 1999). We considered mean elevation within each pixel as a quadratic effect given that the timing of our survey corresponded closely with the end of the den emergence period and steeper slopes at higher elevation provide more denning habitat (Libal et al., 2011; Sorum et al., 2019; Van Daele et al., 1990). We also included the spatial GAM, structured to smooth spatial autocorrelation across all four subareas simultaneously, to better predict spatial pattern in bear distribution on the landscape. For the 2021 resurvey of the Seward Peninsula subarea, we fit a separate spatial smoothing term, allowing us to assess variation in distribution through time. To help account for heterogeneity in detection probability, we considered the standard deviation of the slopes within each pixel as a measure of terrain ruggedness which we expected to act as an index of sighting complexity. We expected higher ruggedness values may decrease the observer's ability to detect bears.

We calculated mean elevation for each pixel from a 5 m Digital Elevation Model using ArcMap (ESRI, Redlands, California, USA), and the standard deviation of the collection of slope values within a given subunit. We determined the salmon covariate values based on the Anadromous Streams Catalog maintained by the Alaska Department of Fish and Game (https://www.adfg.alaska.gov/sf/SARR/AWC/index.cfm?ADFG=maps.dataFiles). We filtered waterbodies by species (pacific salmon) and life history stage (i.e. spawning or migrating) to produce a coarse estimate of the possible salmon resources available in the vicinity of each survey unit pixel. We then summed the total kilometres of anadromous waters within a 25 km buffer around each unit.

We focused our initial analysis on all five surveys; one initial survey across each subarea and the 2021 resurvey of the Seward Peninsula subarea. To provide a comparison among methods, we first fit a model without covariates or the spatial GAM and estimated density across all pixels within each subarea (i.e. the constant model). This allowed us to compare estimates from 2015 to 2018 with those of Schmidt et al. (2021) under a similar model structure to demonstrate their equivalence. We then fit the covariate model with and without the spatial GAM as described above and produced estimates of density by subarea and year. We also produced a predictive map based on the underlying covariate relationships and residual spatial pattern in the fully spatial model.

Finally, to provide some guidance on how surveys may be redesigned to increase efficiency using the spatial approach, we explored a hypothetical reduced sampling scenario that focused sampling in areas where bears were more likely to be detected. In doing so, we endeavoured to maintain systematic coverage throughout the study area to mitigate the risk of bias or the potential to miss density hotspots if entire regions were not sampled. Specifically, we removed all observations from 51 subunits located in the northwest and southeast corner of a sampled unit with mean elevation values <132 m (i.e. the median elevation of the pixels in the Seward Peninsula subarea) in the 2021 Seward Peninsula dataset. We did so based on the results of the overall analysis that suggested that the lowest elevation areas were least likely to contain brown bear groups. The objective being to reduce sampling effort in low density areas while maintaining a sufficient sample size for analysis. It is important to note that we removed only two of four potential subunits (i.e. ≤50% of subunits at <132 m elevation were eligible for removal) within each unit because modelling of simple spatial autocorrelation implicitly relies on the assumption that sampled locations and animal abundance are conditionally independent (Conn et al., 2017; Diggle et al., 2010). After downsampling the dataset, we then refit the model and compared the estimates of density and distribution. Doing so allowed us to explore a hypothetical scenario where analysis of the first round of surveys is used to reduce sampling in areas where fewer bears occur (i.e. low elevation).

We analysed the data in a Bayesian framework, using JAGS 4.3.1 (Plummer, 2003) for model fitting and R 4.2.1 (R Core Team, 2022). We specified vague priors on all parameters and ran two chains for 10,000 iterations each, discarding the first 5000 as burn-in and retaining the rest for inference. Exploration suggested this number of iterations produced sufficient effective sample sizes for reliable inference (not shown). We used the Gelman–Rubin diagnostic (Brooks & Gelman, 1998) and a visual inspection of the chains to ensure convergence had been reached. We present all parameter estimates as means with 95% credible intervals.

3 RESULTS

The results of the non-spatial covariate model showed that the probability of brown bear occurrence in any given pixel was related to both elevation (β_elev = 0.46, 95% CrI = [0.20–0.74]; β_elev² = −0.36, 95% CrI = [−0.51 to −0.22]) and the number of kilometres of salmon streams within 25 km (β_salmon25km = 0.18, 95% CrI = [0.06–0.30]). The curvilinear elevation effect indicated peak group occurrence probabilities arose at mid-elevations (i.e. approximately 800 m; Figure 2). With half of the pixels in the study area at elevations <370 m (Figure 3), the systematic survey design resulted in much of the survey effort being focused in areas where the probability of bear occurrence was relatively low. Detection probability was positively related to the standard deviation of slope ($$$ {\alpha}_{ruggedness}=0.29 $$$, 95% CrI = [0.07–0.52]). The addition of the spatial GAM to the covariate model suggested less certainty in the covariate effects, but in all cases the probability of the effect being different from 0 was ≥94%. Therefore, we based our inference on the full model.

FIGURE 2

Plot showing the relationship between elevation and the probability of brown bear group occurrence for the Seward Peninsula (solid black), lower Noatak (solid grey), upper Noatak (dotted black) and Gates of the Arctic (dotted grey) subareas in northwestern Alaska, USA. The curves are limited to the observed elevation values for each subarea.

FIGURE 3

Spatial distribution of the covariate values used for analysis: the standard deviation of the slope values within each pixel (SD slope), the mean elevation (in meters) within each pixel (Elevation), and the number of kilometres of identified salmon streams within 25 km of each pixel (Salmon 25 km) for all grid cells within each of the four brown bear survey subareas (Seward Peninsula, lower Noatak, upper Noatak, Gates of the Arctic; rows 1–4, respectively) in northwestern Alaska, USA.

Density estimates based on the constant model were comparable to those presented by Schmidt et al. (2021) for the equivalent model structure given the differences in datasets used in the two analyses (Table 1). The addition of spatial covariates and the descriptive spatial component (i.e. the spatial GAM) resulted in modest apparent increases in estimated densities in some subareas, although estimator precision was generally comparable (Table 1). Spatial predictions generally corresponded with the spatial pattern of the covariates, particularly elevation (Figure 3), although there was clearly some residual spatial autocorrelation that was captured by the descriptive spatial GAM (Figure 4). Prediction uncertainty was greatest along study area edges, as would be expected given that the spatial GAM has less information in these areas (Figure 4). Uncertainty was also greater in areas where sampling was incomplete or where few bears were detected (e.g. northwestern and southeastern Gates of the Arctic).

TABLE 1. Estimated total brown bear density (bears of all ages/1000 km²) for each of four subareas in northwestern Alaska, USA, under three different model structures.

Subarea and year	Constant model			Covariate model			Covariates + GAM model
	Density	95% CrI	CV (%)	Density	95% CrI	CV (%)	Density	95% CrI	CV (%)
Seward Peninsula 2015	27.7	20.0–37.1	16	30.7	21.7–42.1	17	28.3	20.1–38.9	17
Lower Noatak 2016	70.7	54.6–89.7	13	79.0	60.5–100.4	13	81.3	62.4–104	13
Upper Noatak 2017	34.4	24.2–47.1	17	35.0	24.9–48.2	17	34.0	24.3–46.3	16
Gates of the Arctic 2018	20.6	13.8–29.3	19	20.1	13.7–28.5	19	20.4	13.8–28.8	19
Seward Peninsula 2021	39.4	29.2–52	15	44.5	31.8–62.3	18	41.7	29.7–57.6	17

• Note: The constant model assumed constant detection and occurrence probability, the covariate model included the effects of elevation and the proximity of known salmon streams on group occurrence and the standard deviation of slope on detection probability, and the final model included these covariates as well as a spatial GAM describing remaining spatial autocorrelation in group occurrence. Estimates are presented with 95% credible intervals (CrIs) and the coefficient of variation (CV).

FIGURE 4

Predicted pixel-level brown bear density and the coefficient of variation (CV) for the four brown bear survey subareas (Seward Peninsula, lower Noatak, upper Noatak, Gates of the Arctic; rows 1–4, respectively) in northwestern Alaska, USA from 2015 to 2018. Predictions are based on the full spatial model including covariates and the spatial GAM.

Comparison of the two survey events for the Seward Peninsula subarea suggested that the spatial pattern of bear abundance was generally consistent through time, with the exception of a concentration of bears along the northwestern coast in 2021 that was not observed during the 2015 survey (Figures 4 and 5). The spatial GAM captured this pattern despite the lack of a specific identifiable spatial covariate (Figure 5). Under the reduced effort scenario for the 2021 survey, our <132 m elevation cutoff value removed 51 subunits from the sample, reduced potential effort by 27%, and reduced the total number of group detections in the dataset from 79 to 60. Our reanalysis using the downsampled 2021 data produced a density estimate of 40.6 bears/1000 km², essentially the same as the estimate based on the full dataset (Table 1). Estimator precision was reduced (i.e. CV = 17% full vs. CV = 20% reduced), however, the predicted spatial pattern in occurrence probability was largely unchanged despite the large reduction in effort (Figure 5), suggesting that there was enough information remaining in the reduced dataset to capture broad patterns in bear distribution.

FIGURE 5

Predicted pixel-level brown bear density and the coefficient of variation (CV) for the Seward Peninsula subarea in northwestern Alaska, USA in 2021 based on the full dataset (Full), and under a hypothetical scenario (Reduced) where 51 subunits with elevations <132 m were assumed to have been excluded from sampling. Predictions are based on the full spatial model including covariates and the spatial GAM.

4 DISCUSSION

The development of spatially explicit versions of common analytical approaches has provided the means to reliably extract information on both density and distribution from a variety of datasets (Miller et al., 2013; Royle et al., 2014). Here we have demonstrated how the mark–resight model for aerial brown bear surveys (Schmidt et al., 2017, 2021) can be extended to incorporate spatial information, resulting in multiple advantages to the practitioner. By incorporating spatial covariates and directly modelling residual spatial autocorrelation in group occurrence, we demonstrated how the resulting formulation can be a powerful tool for estimating brown bear density and distribution on the landscape, as well as helping to identify ecologically meaningful covariate relationships. We also established that the spatial approach could be used to reduce sampling in areas where brown bears are less likely to occur, thereby substantially reducing future survey cost with little impact on estimation. Together, these features will help to increase the amount of information available for brown bear populations in remote areas.

As we suspected, the broad index of salmon availability was related to bear distribution in our study area despite the temporal mismatch between the survey timing (early spring) and salmon run timing (late summer). Our measure of salmon availability was also admittedly coarse because salmon abundance varies dramatically across anadromous waters and are only available to bears if they migrate past an obstacle (e.g. waterfall) or spawn in shallow water (Quinn et al., 2017). Despite these limitations, we suspected a relationship might be present because access to salmon has been shown to correlate with density in other brown bear populations (Hilderbrand et al., 1999). Moreover, bears are highly mobile animals which can have large home ranges when their resources are dispersed (Joly et al., 2022). However, as we found, their spatial distribution during spring surveys is more strongly related to variables representing potential denning habitat than the gross distribution of salmon resources. Elevation was a strong predictor of bear occurrence, likely because survey timing was coincident with the post-den emergence period when bears may be more likely to occur at mid-elevations with more topographic relief (Libal et al., 2011; Sorum et al., 2019; Van Daele et al., 1990). In particular, female bears with young cubs often stay close to their dens in early spring (Haroldson et al., 2002) as a hedge against poor weather and to reduce the risk of predation or infanticide.

The positive relationship between terrain ruggedness within a pixel and detection probability was surprising to us as we expected that higher values would correspond to more complex terrain that may be more difficult to search. We suspect two possible explanations. First, simpler terrain tends to occur at low elevations where shrubs are more common. Although surveys are conducted prior to leaf out, the presence of shrubs increases search complexity. Second, in more complex, mountainous terrain, the search distance is restricted due to topography, forcing the pilot to spend more time to cover the subunit. We speculate that this natural increase in search effort, combined with increased shrub cover at low elevations, may explain the counterintuitive relationship. However, further exploration of the factors affecting detection probability is certainly warranted.

We found that the addition of a descriptive model of residual spatial autocorrelation can be quite helpful in identifying areas where the covariates do a poor job of prediction and can lead to new hypotheses about animal distribution. By modelling variation in spatial pattern across the study area, we acknowledge additional heterogeneity in occurrence probability. Doing so allows the practitioner to identify spatial variation in habitat use that would not be evident when covariate predictors are used alone (Camp et al., 2021, 2023). This is particularly useful for generalist animals like brown bears, which exhibit flexible life history strategies (Mangipane et al., 2020). For example, the descriptive spatial component of our model showed a concentration of bears along the northwest coast of the Seward Peninsula in 2021 that was not evident during the 2015 survey of the same area. This inconsistent pattern might represent an intermittently available food resource (e.g. carcasses of marine mammals, birds or fish) or some other clustering process that deserves more investigation. The non-spatial formulation provides no information on distribution, and if we had limited our inference to the covariates alone in the current analysis, we would not have detected this difference in distribution between years.

The original non-spatial version of the mark–resight approach of Schmidt et al. (2017, 2021) used a systematic design with a random start. In general, we implicitly assume that the probability of detecting individuals is constant (or that any heterogeneity is fully addressed by covariates) and that the sampled units are independent of the state variable of interest. If unmodeled heterogeneity in detection probability remains, or if a non-random design is used, the resulting estimator will be biased (Link, 2003; Williams et al., 2002). Schmidt et al. (2017, 2021) determined the assumption of constant detection probability throughout the study area was unlikely to be met, and therefore included random effects at the level of the subunit to address potential heterogeneity in detection probability. The incorporation of spatial predictors to address heterogeneity in the observed data was a natural extension and has been used with spatial capture–recapture models to assess spatial pattern in bear densities (Boulanger et al., 2018; Kendall et al., 2019; Lamb et al., 2018; Stetz et al., 2019). Our extension to the mark–resight approach for brown bears similarly allowed us to incorporate more directly interpretable predictors of variation in detection and group occurrence, which in turn allowed us to make predictions across the study area. The identification of additional covariates related to detection probability would help to further explain heterogeneity and provide a more mechanistic understanding of variation in detection within and among surveys.

One important consideration when using descriptive models of spatial pattern is that they are reliant on the assumption of unbiased spatial coverage (Conn et al., 2017; Diggle et al., 2010). In the case of spatially indexed covariates, values are observed for every pixel. Therefore, even in the absence of sampling we still have information from which we can make predictions. For the descriptive spatial component of the model, predictions are based on the spatial relationship among the observations. That means that if there are no data from some portion of the study area, predictions must be made based on the nearest sampled units (which may be far away and unrepresentative of the unsurveyed pixels). This phenomenon explains the higher prediction uncertainty we observed along some subarea edges where each pixel has fewer neighbours from which the GAM can draw spatial information. Similarly, when sampling is incomplete in some portion of the study area, the uncertainty surrounding the estimates for that region will be elevated. To prevent this problem in our downsampling scenario, we only deleted ≤2 subunits from each unit. Doing so ensured that some sampling occurred in all parts of the area of interest, thereby decreasing the risk of missing important spatial patterns. We caution practitioners that optimal sampling configurations should include some effort in all portions of the area of interest when using descriptive spatial models and non-randomized survey designs. Although we used a simple approach to reduce survey effort, a spatially balanced sample could also be selected by using sampling inclusion probabilities (e.g. Foster et al., 2017; Robertson et al., 2013).

Finally, one of the primary benefits of incorporating spatial information was our ability to consider more efficient sampling schemes that focused more of the total survey effort in areas where brown bears are more likely to occur. Our simulated scenario suggested that targeted sampling could reduce survey costs substantially without compromising estimation. Our example decreased hypothetical sampling effort by 27% for the Seward Peninsula subarea, with no evidence of bias and only a modest impact on precision. Similar reductions in effort would be feasible in the remaining subareas, although the best elevation cutoff values would differ. For example, undersampling some proportion of the pixels at the highest elevations in lower Noatak and Gates of the Arctic would be preferable given that those are the areas with the lowest predicted occurrence probability (i.e. Figure 2). Our finding that undersampling can be done without causing bias in the estimators agrees with other work that has explored targeted sampling schemes that are then analysed using a spatially explicit model-based framework (Johnson et al., 2010; Murphy et al., 2019; Schmidt & Deacy, 2021; Whittington et al., 2018). Targeted designs can substantially reduce overall survey cost when good predictors of animal distribution are available. We mention these concepts here to encourage flexible thought regarding survey design and sampling effort for future surveys.

Going forward, we expect that further extension of our mark–resight model into an open population framework may prove helpful for ongoing monitoring and management of brown bears (Efford & Schofield, 2020; Gardner et al., 2018; Glennie et al., 2019; Royle et al., 2014). Once multiple surveys of each subarea have been conducted, an open population framework would be useful in identifying the potential mechanisms behind changes in spatial patterns of bear occurrence on the landscape. For example, spatially concentrated mortality risk (e.g. near human structures or roads) may lead to localized differences in density (Boulanger et al., 2018), and such information could be useful for determining effective management actions. Over longer time spans, it may also be possible to begin to ask questions about changes in distribution relative to variation in weather and climate.

5 CONCLUSIONS

Cost remains one of the primary factors limiting the implementation of non-invasive mark–resight surveys for brown bears. Our findings suggest that the cost of future surveys could be reduced by perhaps 20%–30% (approximately $40,000–$60,000 cost savings at current rates) with little impact on bias and precision. While the optimal sampling design would be subarea specific, we encourage practitioners to consider how existing knowledge about bear distribution could be used to design a targeted sampling approach. Alternatively, reallocating sampling to focus more effort on those areas more likely to contain bears is a sound strategy in cases where increased estimator precision is a primary objective. We expect the spatial approach would also be useful for managers by providing more detailed information on brown bear abundance and distribution in relation to changes in harvest regimes or other management actions. Going forward, we suggest that researchers continue to explore possible predictors of variation in detection probability to more directly address unmodeled heterogeneity. In our experience, incomplete snow cover has an apparent impact on detection probability, suggesting that deriving some measure of snow cover relevant to the timing of the survey may prove useful.

AUTHOR CONTRIBUTIONS

Joshua H. Schmidt and William W. Deacy conceived the ideas for this manuscript; Joshua H. Schmidt designed the methodology, analysed the data and led the writing of the manuscript. All authors participated in data collection, contributed critically to the drafts, and gave final approval for publication.

ACKNOWLEDGEMENTS

Any mention of product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. We thank all the pilots for hundreds of hours of safe flying over the years, as well as the many dedicated observers. We also thank E.J. Wald, J.D. Mizel, J.T. Rasic and two anonymous reviewers for helpful comments on an earlier draft, and T.S. Gorn for long-term collaboration and ongoing support for these surveys in northwestern Alaska. Funding for this project was provided by the Arctic Network as part of the National Park Service's Inventory and Monitoring Program, Western Arctic Parklands, Gates of the Arctic National Park and Preserve, Bering Land Bridge National Preserve, and the Alaska Department of Fish and Game. We thank the Bureau of Land Management, US Fish and Wildlife Service and the Wildlife Conservation Society for logistical and administrative support.

CONFLICT OF INTEREST STATEMENT

The authors have no conflict of interest to disclose.

Open Research

PEER REVIEW

The peer review history for this article is available at https://www.webofscience.com/api/gateway/wos/peer-review/10.1002/2688-8319.12288.

DATA AVAILABILITY STATEMENT

The bear survey data and the relevant covariate values for each survey unit are available at the IRMA DataStore: https://doi.org/10.57830/2301104 (Schmidt et al., 2023).