Movement cost surface

Analyzing connectivity requires an input movement cost (also called resistance) layer representing an estimation of the degree to which different land cover types affect the movement of individual animals or propagules [30, 31]. A land cover that physically slows movement, is avoided, or imparts a physiological cost is assigned a high cost (resistance) value; land cover types that are more likely to be used and crossed successfully are assigned a low cost. Cost surfaces can be constructed using expert opinion or empirical data [31]. Much like Koen et al. [22], we modelled connectivity for terrestrial, non-volant fauna that use and move across natural land cover more successfully than anthropogenic land cover types by assigning higher costs to landscape elements with higher degrees of anthropogenic disturbance. We ranked and assigned cost values to the anthropogenic layers using our own knowledge but in consultation with experts (see Supporting Information) and consistent with previously published studies [6, 17–20, 22, 26, 32–35].

We constructed our cost surface by combining land cover layers from 23 sources. Eight of those layers were from the Canadian Human Footprint (CHF) [36] and included built environments, nighttime lights, croplands, pasturelands, dams and reservoirs, mining, oil and gas, and forestry areas. We used a recently developed national road layer for Canada [37] that includes resource-access roads, along with a national railway layer. For the buffer area outside of Canada, we used six layers from the Global Human Footprint [38] (GHF): built environments, nighttime lights, croplands, pasturelands, railways, and roads. In addition to human modified land cover features, we included natural features considered to affect the movement of terrestrial, non-volant fauna, namely elevation and slope, glaciers, permanent sea ice, as well as large lakes and rivers [6, 39–42] for within both Canada and the buffer areas in the United States of America (hereafter, U.S.). Vector layers (e.g., roads, railways, rivers) were rasterized and all input layers were resampled to a resolution of 300 x 300 m, where necessary, to match the resolution of layers from the CHF. Further details, including data sources, are available in the S1 Table.

We were interested in using current density maps from circuit theory as our main model output to predict functional connectivity for multiple taxa. Current density is proportional to the probability of use during a random walk [29]. Our model produced an estimate of current density between all possible pairs of nodes while accounting for movement costs. Current density maps have low sensitivity to the absolute value of the costs assigned to land cover types so long as the rank of the types is maintained [43]. For example, if crossing a freeway is more costly than crossing a field, current density will be similar among resulting maps regardless of the absolute costs applied to the freeway and field, provided that the freeway is always assigned a higher cost. However, the range of cost values (e.g., 1 to 3 versus 1 to 1000) does appear to have a small effect on the pattern of current densities [43, 44]. To determine whether these relationships remained true for our large, real-world study area, we tested the sensitivity of current density outputs with ten cost scenarios (S2 Table) using two regions of Canada (southern British Columbia–B.C., and the Maritime provinces of New Brunswick, Prince Edward Island, and Nova Scotia). For each region, we used Spearman rank correlations to compare the generated current density values for the same 1000 randomly selected cells between pairs of scenarios. We then selected the cost scenario that was most strongly correlated with all the others for use in the subsequent analyses.

We assigned a high movement cost to human-dominated land cover types (e.g., cities, major highways), a medium-high cost to human-impacted features (e.g., agricultural lands, minor highways), and a medium-low cost to more permeable human-modified land cover types (e.g., pasture lands, resource roads, harvested forests). High movement costs were also assigned to natural features known to inhibit the movement of terrestrial, non-volant fauna based on data from published studies and consultations with experts (S1 Table). These included areas with high elevations (> 2300 m [40, 41, 45]), steep slopes (> 30 degrees [39, 42, 45–47]), large lakes (> = 10 ha) and rivers with large flow (> 28 m³/sec [6, 34, 48]). Conversely, because some mammal species are known to travel across permanent sea ice among islands in the Canadian Arctic Archipelago, we assigned a medium-low cost to that layer [49]. A single Canada-wide, cost surface raster was constructed by using the highest cost for a given pixel from among the 23 layers. Pixels that had no data (i.e., did not have any of the 23 land cover types) were assigned the low movement cost.

Circuit theory

Over the last decade, circuit theory has become one of the more commonly used approaches to assess and map connectivity [50–52]. Most applications of circuit theory have tended to connect source and destination locations (i.e., ‘nodes’, as previously mentioned), to map all probable paths of movement between those nodes, measured as electrical current density (hereafter referred to as current density). However, because node placement can affect the resulting patterns of connectivity [22, 53], omnidirectional connectivity methods are being explored more frequently when the objective is to predict connectivity across landscapes in general as opposed to among specific locations [54]. This can be done using an omnidirectional connectivity approach, which is particularly valuable when the source and destination of all movement is unknown and is highly relevant for generalized land use planning activities [6, 22, 55, 56]. The three main omnidirectional methods (wall-to-wall, point-based, Omniscape) have been described by Phillips et al. [54], who found that all three produced very similar current density patterns, while the wall-to-wall method was the fastest for computer processing.

We used the wall-to-wall omnidirectional, Julia implementation, advanced mode of Circuitscape [57] to run the circuit theory models on each tile following methods outlined by Phillips et al. [54]. The wall-to-wall method uses thin, one-pixel wide source and ground strips placed along opposite sides of a tile. Circuitscape was run in each of the four cardinal directions (east to west, west to east, north to south, and south to north) for a total of four runs per tile. The four directional runs were then combined by taking the mean of all four to produce an omnidirectional current density map for a given tile.

To increase computational efficiency, we divided Canada into a series of large tiles that were analysed individually and then stitched together to produce a national current density map. Knowing that we would likely be using tiles of different sizes because of the shape of the country, and knowing that tile size can affect current density estimates [24], we conducted a sensitivity analysis comparing current density across tiles of varying sizes. We tested ten tiles of sizes ranging from 25 x 25 to 1500 x 1500 cells. To control for effects related to the composition and spatial distribution of cost values, we simulated simplistic landscapes in which all tiles were split in two, with 50% of the cells assigned a high cost and 50% assigned a low cost. We then calculated and compared the minimum, maximum, mean and standard deviation of the current densities for each tile size to identify the size above which variation in current density estimates was minimal. We used the results from the sensitivity analyses to divide our study area into tile sizes above that threshold but that would still allow reasonably efficient run times with our computing resources. Tiles were centred on provinces and territories where possible, but some jurisdictions required multiple tiles because of their large sizes (S1 Fig). Tiles included a buffer on each side to reduce the effects of node placement and artificial map boundaries on current density patterns [22, 53]. Following Koen et al. [22], we used a buffer width equivalent to 20% of the average length of the sides of the tile of interest. This included buffers into the U.S. and surrounding oceans.

All current density maps were stitched together into a single map after their buffers and overlapping areas were removed. For the few cases where adjacent tiles overlapped within a single province or territory (e.g., Ontario; S1 Fig), we computed the mean of the overlapping areas. In two regions, however, taking the mean of the overlapping tiles still resulted in noticeable seams. To address those anomalies, we reran Circuitscape on additional tiles centred over those seams to produce new current density maps. We then computed the mean of all maps (the new maps and the originals) to create a single, seamless, national current density map. Our resulting model output was a seamless estimate of the probability of movement during a random walk for a set of terrestrial species that use natural cover across Canada.

Independent movement data

We used independent wildlife datasets from across Canada to test for a relationship between current density and animal movement. We sought datasets for animal species that we considered would use natural cover and be limited in anthropogenic habitats. Consequently, we did not include data for peri-urban species (e.g., raccoons, skunks, coyotes) [58–60]. We were also interested in selecting species from a range of environments and geographical locations. We used GPS-collar data accessed through Movebank.org for moose (Alces alces; N_id = 19; N_obs = 55,181) [61, 62], grey wolf (Canis lupus; N_id = 68; N_obs = 174,441) [63], Rocky Mountain elk (Cervus canadensis; N_id = 175; N_obs = 1,585,428) [64, 65], and mountain caribou (Rangifer tarandus; N_id = 186; N_obs = 245,449) [66] located in British Columbia and Alberta, as well as roadkill data for herpetofauna in southern Ontario and moose in New Brunswick (see S2 Fig for general locations).

For the GPS-collar data from western Canada, we compared current density values extracted from observed locations (i.e., locations used by collared individuals) to current density values extracted from randomly selected available, but unused locations (hereafter referred to as available locations). For the observed locations, we randomly selected 10 percent of each individual’s GPS data, as this is a common testing ratio used in habitat model validations [67] and can reduce the effects of autocorrelation. To obtain equal numbers of available locations we used the adehabitatHR package [68] in the R statistical computing environment [69] version 3.6.3 to first estimate each individual’s home range using a 95% utilization distribution (UD) from the individual’s full GPS dataset. We used the 95% UD to exclude areas with the lowest probability of use and thus strengthen the contrast between used and available locations. Next, we calculated each individual’s maximum displacement distance, as the greatest straight-line distance (km) from any observed location to the earliest observed location. We then buffered each individual’s UD by their maximum displacement distance and randomly selected available locations within this buffered area. We used boxplots to compare overall current density values between observed and available locations. We also examined current density between observed and available locations using species-specific linear mixed effect models with current density as the response variable, case (i.e., observed location = 1; available location = 0) as the categorical predictor and individual as the random effect, to account for possible correlation in current density values among each individual’s observations. Linear mixed effects models were conducted in R using the lmer package [70].

After initial examination of these results, we questioned whether the difference in current density between observed and available locations was influenced by displacement distance; specifically, whether those current density differences became greater with increasing maximum displacement distance. We hypothesized that individuals who travel farther have to contend with more anthropogenic factors and barriers, thus traveling through more areas of concentrated current density (i.e., pinch points). To test this hypothesis post hoc, we used the same species-specific models previously described, with the addition of an interaction between case and individual maximum displacement distance (as described above). To clarify our discussion of these results, we binned individuals into two groups: short-distance movers identified as those having maximum displacement distances in the lower quartile bin (values in the 0–0.25 quantile range), and long-distance movers as those having maximum displacement distances in the upper quartile bin (values in the 0.75–1.0 quantile range).

The herpetofauna roadkill data from Ontario contained 4496 locations of 17 species killed along roadways in southern Ontario (south of the French River) between 2010 and 2019. We used t-tests and Cohen’s Effect Size d to compare the mean current densities of the roadkill locations to densities found within an equal number of random locations along the same roads. For each location, we used the mean of the current densities of the focal pixel and within a 300 m buffer around the point data to capture current density adjacent to the roads.

We also assessed roadkill of moose in New Brunswick between 2001 and 2020, but only from highways with no wildlife fencing or passages to avoid biasing the analysis. Even so, moose roadkills were numerous, often with several observations in a given location. Moose are very large and not likely to be missed when dead on the side of the road and so we assumed that we had an accurate count of moose roadkills. Consequently, we divided roads into 900 m sections and used a Spearman rank correlation to compare the frequency of moose roadkills to the mean current densities within sections and immediately adjacent to the roads.

Independent movement data

In our initial species-specific linear mixed effects models of current density, we found the current densities among observed locations to be greater on average than current densities among available locations for grey wolf (0.81, 95% CI = 0.77, 0.86), moose (0.7, 95% CI = 0.65, 0.77, and mountain caribou (0.2, 95% CI = 0.20, 0.22, but not elk (-0.06, 95% CI = -0.08, -0.05). Similar findings are illustrated in the simple boxplots comparing current densities (Fig 5). However, after including an interaction with displacement distance, we found that for all of the species’ long-distance movers, current density values were significantly higher in the observed locations compared to the available locations. Also, as we suspected, this effect increased with increasing distance moved (Fig 6 and S3 Table; and see S5 Fig for histograms of individual maximum displacement distances and their respective binning as short or long-distance movers). Herpetofauna roadkill were not found more often in locations with higher current densities, compared to random locations along the same roads (Fig 5; n = 4496, t = -2.02, P = 0.98, d = 0.04). There was a positive, albeit weak correlation between the frequency of moose roadkills in New Brunswick and current densities in the immediate area (Fig 7; n = 1216, ρ = 0.13, P < 0.001).

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Fig 5. Comparison of current densities at observed GPS locations versus available, but unused locations.

Boxplots depict median current density (thick horizontal line) and the central 50% of current density values (boxes) for observed wildlife locations and available, but unused locations. Extreme values were omitted from the figure for visualization purposes. GPS = data collected from GPS collars; RK = roadkill data.

https://doi.org/10.1371/journal.pone.0281980.g005

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Fig 6. Predicted interactions from the species-specific linear mixed effects models of current density.

Solid lines depict predicted mean current density for observed and available locations across the range of individual maximum displacement distances. Predictions were generated from a linear mixed effects model of current density with individual as a random effect and a fixed effect interaction between case (observed or available location) and individual maximum displacement distance. Dotted lines depict 95% confidence intervals; solid black lines indicate the max displacement distances in the upper quartile bin (i.e., the long-distance movers). Preference for areas with higher current density is suggested when current density values at observed locations are greater than at available locations.

https://doi.org/10.1371/journal.pone.0281980.g006

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Fig 7. Relationship between number of moose killed and mean current densities along roads in New Brunswick, Canada.

There was a small, positive correlation between the frequency of roadkills on and the current densities within 900x900m windows along roads.

https://doi.org/10.1371/journal.pone.0281980.g007

Comparison to previous studies

Previous studies that analyzed connectivity throughout all of Canada used either large, protected areas as nodes [20, 26] or climate analogs [25, 35]. The former approach is important for helping to address the goal set by parties to the Convention on Biological Diversity to establish well connected systems of protected areas. However, given that only 12.5% of Canada’s terrestrial areas are currently protected [28], their approaches could overlook areas important for connectivity in regions with few existing protected areas, including much of southern Canada where most of the country’s species at risk reside [72]. Indeed, this is particularly apparent in southern Ontario where our analysis identifies many areas with high probabilities of movement, while the other studies do not. Interestingly, despite the differences in methods, there are many similarities among our results and the findings of the three previous studies. In particular, all three studies identified the Rocky Mountain range in the west as being important for connectivity, as well as around the southern tip of James Bay. In contrast, only our study identified the Chignecto Isthmus as an important area, which is the only terrestrial connection between Nova Scotia and the rest of Canada. Our results are also very similar to those from a study focused on the province of Alberta [6], which used a higher resolution cost surface (100 m) for their smaller study area.

Areas of high current density on our national map also correspond to regions where connectivity conservation initiatives have been established, including Yellowstone to Yukon Conservation Initiative, Algonquin to Adirondacks Collaborative, and the Chignecto Isthmus (Fig 3). This suggests that our map can be used to help support functional connectivity nationally by identifying national priorities and supporting programs such as Canada’s national Ecological Corridor Program. We believe the current density map can also be used to identify areas important for functional connectivity within regional initiatives, but we recognize the spatial resolution is likely not fine enough to make decisions on specific land parcels.

Circuit theory maps tend to highlight ‘pinch points’, or bottlenecks to movement where connectivity is tenuous with few alternative options [30]. This is particularly helpful for identifying areas that should be conserved or restored to maintain connectivity, especially in human-dominated landscapes. Notably, many high current density areas occur in close proximity to areas of high cost, where natural habitat availability is limited [81]. High current density can also occur in high-cost areas that bridge between neighbouring low-cost regions. For these reasons, current density should reflect movement patterns better than the underlying cost maps [82]. For example, Koen et al. [22] found that current density estimates from an omnidirectional circuit theory model were a better fit to movement data for a variety of taxa than a simple cost surface (input) map, demonstrating that a connectivity map is more than just a habitat map.

Areas with moderate current density do not necessarily illustrate poor connectivity. Indeed, some areas with large swaths of natural habitat (e.g., the Yukon Territory) have many potential pathways where current density is dispersed, and these can make important contributions to overall connectivity even while having lower probabilities of movement per unit area. Regions fortunate to have such areas as options should consider conserving them sooner rather than later, to avoid the creation of pinch points in the future.

Methodological advances

Our analysis combined and built on several methodological advances in the application of circuit theory to measure connectivity. We applied sensitivity analyses to much larger study areas than had been done before and confirmed that patterns of current density were relatively insensitive to the absolute cost values assigned to land cover types so long as their rank order was maintained [43]. Similarly, our results support previous studies that found that the range of cost values used had an effect on current densities, with broader ranges amplifying ‘pinch points’, which could help with prioritizing areas important for connectivity [43, 48] (S3C & S3F Fig). We also found that current densities become relatively insensitive to tile sizes above > 1.7 million pixels. Those findings, along with advances in computing power and the Julia implementation of Circuitscape, reinforce the ability to assess connectivity across large study areas. One issue we encountered was that even though we used a buffer width equivalent to 20% of the length of the sides of the tiles, as recommended by Koen et al. (2014), it was not sufficient to eliminate the effects of node placement on current density patterns in two regions. It appears that issue resulted from tile borders being too close to large geographic features (e.g., Great Slave Lake in the Northwest Territories and James Bay in Ontario and Quebec). Fortunately, the issue was easily rectified by using additional tiles centred over the regions with the anomalies.

Potential limitations

We acknowledge that decisions made during the course our analysis could have affected the results. We classified large lakes as high cost in contrast to Marrec et al. [6], who used a medium cost for their analysis that was restricted to the province of Alberta. We chose the high cost because much of the rest of the country includes many very large lakes, which we believe affect the movement of wildlife most of the year. We recognize that this may not be the case in winter once the lakes have frozen. Similarly, we assigned a high cost to rivers with high flow rates, some of which can freeze in very cold winters. Consequently, patterns of connectivity in winter may differ from our model, suggesting that connectivity may vary seasonally in Canada. We encourage more research on the implications of this idea for land use planning and conservation in Canada.

Although we used the most current land cover data available, we evaluated a snapshot in time and so our analysis does not take into consideration the inevitable continued expansion of the human footprint nor the effects of climate change. More studies like those done by Carroll et al. [25] and Huang et al. [83] are needed to predict connectivity under potential future development and climate scenarios.

When validating our current density map using the roadkill data, we measured the mean current density within a 300 m radius buffer around the road to assess connectivity at the finest resolution (i.e., immediately proximate to the road) [84, 85]. The buffer size used in such analyses can influence the strength of correlation and hence validation [52]. Further research is required to determine the most appropriate scale to use when comparing current density maps with roadkill data.

At the time of this study, we were unable to obtain wildlife data for the prairies and the far north, which would have strengthened the validation of our current density map. We also recognize that the upstream approach we used undoubtedly does not capture the connectivity needs for all species, nor all complex movement patterns or population processes [10, 86, 87]. In the future, we hope to collaborate with other researchers to compare our omnidirectional, multispecies results to results from species-specific and park-to-park connectivity analyses. In the meantime, we consider that our current density map, which factors in both natural and human-caused restrictions to movement, can be used to accurately identify existing areas important for functional connectivity that should be conserved to help mitigate the negative effects of continued development and climate change on biodiversity.