The ability to identify regions of high functional connectivity for multiple wildlife species is of conservation interest with respect to habitat management and corridor planning. We present a method that does not require independent, field-collected data, is insensitive to the placement of source and destination sites (nodes) for modeling connectivity, and does not require the selection of a focal species.
In the first step of our approach, we created a cost surface that represented permeability of the landscape to movement for a suite of species. We randomly selected nodes around the perimeter of the buffered study area and used circuit theory to connect pairs of nodes. When the buffer was removed, the resulting current density map represented, for each grid cell, the probability of use by moving animals.
We found that using nodes that were randomly located around the perimeter of the buffered study area was less biased by node placement than randomly selecting nodes within the study area. We also found that a buffer of ≥ 20% of the study area width was sufficient to remove the effects of node placement on current density. We tested our method by creating a map of connectivity in the Algonquin to Adirondack region in eastern North America, and we validated the map with independently collected data. We found that amphibians and reptiles were more likely to cross roads in areas of high current density, and fishers (Pekania [Martes] pennanti) used areas with high current density within their home ranges.
Our approach provides an efficient and cost effective method of predicting areas with relatively high landscape connectivity for multiple species..
Habitat loss and fragmentation are significant threats to the persistence of wildlife populations because they can reduce functional connectivity of the landscape (Goodwin & Fahrig 2002). Functional connectivity is the degree to which landscape structure facilitates or impedes the movement of organisms among habitat patches (Taylor et al. 1993; Tischendorf & Fahrig 2000). Low functional connectivity can result in small, isolated populations that have an increased risk of extinction because of inbreeding depression, demographic stochasticity and reduced opportunity for rescue (Beier 1993; Keller & Waller 2002; O'Grady et al. 2006). Thus, identifying and protecting landscapes with high functional connectivity could have substantial conservation benefits. Habitat corridors, swaths of land allowing the passage of individuals between two otherwise unconnected habitat patches (Tischendorf & Fahrig 2000; Beier, Majka & Spencer 2008), have long been thought to enhance functional connectivity (Tewksbury et al. 2002).
Recently, attention has shifted from narrow, single corridor identification to modelling functional connectivity across the landscape as a whole (Kool, Moilanen & Treml 2013). Cushman, McKelvey & Schwartz (2009) and Schwartz et al. (2009) extended simple least cost path models of connectivity by merging paths from several source and destination sites (hereafter termed nodes). Similarly, McRae et al. (2008) modelled functional connectivity based on electrical circuit theory, which models connectivity across a resistance surface as electric current moving through a circuit. The benefits of this model include the ability of users to predict multiple pathways that account for the shape and structure of habitat swaths. Walpole et al. (2012) and Pelletier et al. (2014) extended the circuit theory model to be independent of point-based nodes.
Functional connectivity is generally a species-specific estimate. With respect to efficient forest management and conservation planning, there is value in a measure that incorporates functional connectivity for a suite of species (Beier, Majka & Spencer 2008). Beier, Majka and Spencer (2008) used the term linkage to describe connective land that supports the movement of multiple species. Many of the methods used to identify wildlife linkages depend on the identification of focal or umbrella species (Beier et al. 2006; Cushman & Landguth 2012). This can pose a challenge, however, because favourable dispersal habitat for one species might be impermeable to others. Indeed, several studies have found that corridors identified for one species are not necessarily used by other species (Beier, Majka & Newell 2009; Cushman & Landguth 2012; Cushman, Landguth & Flather 2013; LaPoint et al. 2013). Thus, the development of an approach that can accommodate functional connectivity requirements for multiple species would be a valuable contribution to conservation research.
There are numerous methods and software for delineating corridors (Theobald, Norman & Sherburne 2006; Compton et al. 2007; Majka, Jenness & Beier 2007; McRae et al. 2008; Cushman, McKelvey & Schwartz 2009; Saura & Torné 2009; Landguth et al. 2012; Brás et al. 2013; Carroll 2013; Pelletier et al. 2014). One concern with current methods of mapping functional connectivity is that some algorithms require independent, field-collected data, such as species distribution data, occurrence data or movement paths (Cushman, Landguth & Flather 2013; LaPoint et al. 2013). This can be problematic because these independent data sets can be prohibitively expensive to collect and estimates of connectivity may be sensitive to biases and variation in these empirical data. A second concern is that some current methods of mapping functional connectivity require the identification of one or a few focal species (Beier et al. 2006; Cushman & Landguth 2012), and estimates of connectivity may be sensitive to this choice of species (Beier, Majka & Newell 2009; Cushman, Landguth & Flather 2013). Finally, some methods work by connecting source and destination sites (McRae et al. 2008; Schwartz et al. 2009), which may not be appropriate for all types of questions (Ferrarini 2013). An ideal method of estimating multispecies functional connectivity is one that does not require independent, field-collected data, is not sensitive to the selection of a focal species or the placement of nodes and has been validated with independent data for multiple species.
We relax the definition of functional connectivity such that it includes connectivity for a suite of species, and we describe a method using circuit theory that predicts multispecies functional connectivity across large regions. We focused on circuit theory because of its success in modelling both animal movement (Walpole et al. 2012) and gene flow (McRae & Beier 2007) and because of its ability to integrate variable probabilities of connectivity across an entire surface. Circuit theory takes advantage of analogous properties of a random walk and electricity moving through a circuit (Doyle & Snell 1984) to model animal movement and gene flow across a resistance surface. Multiple or wider swaths of suitable habitat are more likely conduits of animal movement than are narrow pathways (McRae & Beier 2007). Circuit theory simultaneously considers all possible pathways connecting population pairs, producing a map where current density varies across pixels and is analogous to the probability of use by random walkers (Doyle & Snell 1984). Therefore, the cumulative current density map is meant to represent a prediction of functional connectivity. Circuitscape has largely been used to model single-species functional connectivity between defined population pairs; in our application, we extend it to model multispecies functional connectivity independent of source and destination points. First, we demonstrated our approach using a simulated cost surface with a buffer, comparing the random placement of nodes around the perimeter of the buffered study area to placing nodes within the study area, which is more typical of recent circuit theory applications (Rabinowitz & Zeller 2010; Gimona et al. 2012). We then validated our method using a cost surface developed from land-use maps in the Algonquin to Adirondack (A2A) region, a landscape of conservation importance in eastern North America. We created a cost surface that represented the general permeability of the landscape for animals that avoid unnatural landscape features such as roads and developed land. We used our method to create a map predicting functional connectivity for forest- and wetland-dwelling wildlife in all directions across and within our study area. Finally, we used road mortality data of several species of reptiles and amphibians (herptiles), and space-use data of fishers (Pekania [Martes] pennanti) in our eastern Ontario, Canada, study area to validate our connectivity map.
Materials and Methods
Development of our wildlife connectivity mapping technique
We simulated a simple cost surface by building a binary grid consisting of an interior area (30 × 30 pixels), surrounded by a 70-pixel-wide buffer (100 × 100 pixels total). We randomly labelled 10% of the 10 000 pixels as good habitat by weighting them with a cost of 10 and weighting the remaining pixels as poor habitat with a cost of 10 000 (i.e. a resistance surface; Koen, Bowman & Walpole 2012). We used circuit theory (McRae & Beier 2007; McRae et al. 2008) and Circuitscape software (version 3.5.8, McRae & Shah 2009) to highlight areas with a relatively high probability of use as movement corridors (i.e. high current density). In Circuitscape, we connected the eight neighbouring cells as an average cost using the pairwise mode.
We demonstrated the bias in current density estimates that can result from placing nodes (source and destination sites used to estimate current) within the study area. We randomly selected 50 nodes (producing 1225 unique node pairs) within the core area of the grid and connected between 2 and 50 node pairs with current using Circuitscape, with a completely new set of random node pairs at each iteration. Following each iteration, we removed the buffer and analysed the current density map of the interior area only. We did this because map edges can cause estimates of landscape resistance to be biased high, and a buffer can reduce the bias (Koen et al. 2010). If our estimates of connectivity (i.e. areas of high current density) were independent of where the nodes were randomly placed, we expected there to be little variation in the spatial pattern of current density as we increased the number of node pairs. We considered the cumulative current density map based on all possible pairs of nodes (in this case, 1225 pairs), hereafter termed the full pairwise map, to be a ‘true’ estimate of landscape connectivity that we could compare to current density maps estimated from fewer node pairs. Two current density maps that were highly correlated implied that the spatial position of relatively high and low current was similar. Thus, we compared Pearson correlation coefficients between the full pairwise current density map and current density maps, with the buffer removed, as we increased the number of node pairs.
We designed a technique to identify movement corridors that should not suffer from biases induced by node placement. We randomly selected 50 nodes along the outside edge of the cost surface buffer and connected between 2 and 50 node pairs with current using Circuitscape, with a new set of random node pairs at each iteration. We then removed the buffer and compared the cumulative current density map of the interior study area to our full pairwise current density map using Pearson correlation. If our technique produced a current density map that was independent of node placement, we should observe little variation in the spatial pattern of current density as we increased the number of node pairs.
Determination of the appropriate buffer size
One feature of current density maps produced by Circuitscape is that relatively high current is produced near the nodes. This is an undesirable feature when there is no a priori reason to place nodes in particular locations. To eliminate the bias, we placed a buffer around the study area such that the current associated with each node could be removed with the buffer, resulting in a current density map that was independent of node placement. We used a simulated cost surface to determine the buffer width that would remove the bias in current density produced by the nodes. Our simulated cost surface was square (100 × 100 cells; 10 000 cells total), and we evaluated 14 different buffer widths (0–50 cells wide in 5-cell increments, as well as 100, 150 and 200 cells wide; Fig. S1a). We labelled 25% of cells as good habitat (cost of 10) at random and the remaining cells as poor habitat (cost of 10 000). We randomly selected 50 nodes around the perimeter of each buffer and connected all node pairs with current using Circuitscape. We then removed the buffered area and used Pearson correlation coefficients to compare the resulting current density maps as the buffer size increased. We repeated this analysis using two additional cost surfaces: with randomly distributed ‘good’ habitat comprising 50% or 75% of the study area. We considered that the buffer was wide enough to remove the bias when, after buffer removal, the correlation of current density maps did not change as buffer size increased (i.e. the slope of the relationship between buffer size and correlation coefficient was zero).
We wanted to assess how the shape of the study area influenced and how wide the buffer should be to remove bias caused by node placement. We simulated a rectangular cost surface (50 × 200 cells; 10 000 cells total; Fig. S1b) and repeated the same steps we took to evaluate the square study area. We chose square and rectangular shapes to represent study areas with different edge to area ratios.
Validation of our wildlife connectivity mapping technique
Our goal was to create a current density map across our 11 225-km2 study area in eastern Ontario, Canada, within the A2A region. We added a 17-km-wide buffer to our study area, roughly 10% of the length and 30% of the width of the study area. The buffered area extended over two provinces (Ontario and Quebec, Canada) and one state (New York, USA). Thus, we merged four land cover data bases to create a continuous land cover surface (Ministére des Ressources Naturelles du Québec 2000; Ontario Ministry of Natural Resources 2004, 2007; Fry et al. 2011). We used the land cover data to create a cost surface with 100 × 100 m pixels that represented the permeability of the landscape for a suite of native, forest- and wetland-dwelling species. We assigned a high cost (1000) to land cover features that we assumed to be unnatural and impermeable to movement (e.g. primary roads, aggregate pits and quarries, developed land, large water bodies), a medium cost (100) to land cover features that we assumed to be unnatural, but permeable to movement (e.g. secondary and tertiary roads, agriculture, plantations, disturbed natural cover), and a low cost (10) to land cover features that we assumed would provide natural cover and would represent relatively high permeability to movement [e.g. forest, wetland (fen, bog, swamp, marsh) and natural vegetation communities (savanna, prairie, sand barrens, alvar, shoreline and tall grass woodland)].
We used the cost surface to create a current density map with the technique described in our simulation study. We selected 50 nodes at random locations around the perimeter of the buffered study area, resulting in 1225 unique node pairs, and connected them with current. We were uncertain about how many pairs of nodes were required to adequately characterize our mean current density map. We assessed this by randomly selecting node pairs (ranging between 2 and 50) and connecting them with current, removing the buffer and summing the resulting current maps. Following each iteration, we used a Pearson correlation to compare current density to the full pairwise current density map at 10 000 randomly selected cells. We considered that our modelling was sufficient when the curve comparing correlation coefficients to the number of node pairs reached a slope of zero (i.e. an asymptote).
We used two empirical data sets collected in eastern Ontario to validate our current density map. We obtained the locations of 725 herptiles (20 species; Table S1) that were killed along roadways in eastern Ontario between 1971 and 2001 from Ontario's Natural Heritage Information Centre (NHIC Herptile Road Atlas, unpublished data). We used road mortality locations to estimate movement routes across roads for herptiles. We added a circular buffer with a 200-m radius to each location and calculated the average current density within each circular buffer (Fig. S2a). We created a data set of random locations by randomly selecting 725 points along the same road network and calculated the mean current density within a 200-m circular buffer around each random location. We used a t-test and Cohen's effect size d (d = 0·2 is a small effect, d = 0·5 is a medium effect, and d = 0·8 is a large effect; Cohen 1988) to compare mean current density between road mortality locations and random locations. If our current density map represented functional connectivity, then we expected to observe higher current density at the road mortality locations. We also compared the performance of our current density map (a prediction of functional connectivity) to that of our cost surface (a prediction of habitat suitability) by comparing the average habitat suitability at road mortality locations and random locations.
In addition, we attempted to validate our current density map of eastern Ontario with published radiotelemetry data for fishers (Koen et al. 2007). The data set consisted of ≥25 locations obtained by triangulation for 26 adult fishers (10 M, 16 F) in 2003 and 2004. We estimated annual 95% and 50% fixed kernel home ranges (Worton 1989) with the bandwidth estimated using least-squares cross-validation (Silverman 1986). We compared the mean current density within four hierarchical levels of fisher space use: (i) the fisher study area (a 95% minimum convex polygon around pooled fisher locations); (ii) fisher home ranges (a 95% kernel home range polygon); (iii) fisher core use areas (50% kernel home range polygons); and (iv) fisher occurrences (Fig. S2b). If fisher space use was related to connectivity of the landscape, then we expected that current density would be higher at the level of home range, core use areas and fisher occurrences compared with the study area; the latter presumably encompassed areas not used as intensively by the animals. We expected fishers to occur more frequently in areas of high habitat connectivity because these areas should facilitate movement within the home range (Rosenberg, Noon & Meslow 1997). We compared both mean current density and mean habitat suitability between fisher use areas and the study area with sequential Bonferroni-corrected (Holm 1979) one-sample t-tests and Cohen's effect size d (Cohen 1988).
Results
A modest number of node pairs were sufficient to approximate the full pairwise current density map when we placed nodes around the perimeter of the buffer (Pearson r = 0·99 at 18 node pairs; Figs 1a, S3). When we placed nodes randomly within the study area, we found that current density in the interior study area was less correlated with the full pairwise current density map (Pearson r = 0·90 at 36 node pairs), and thus more dependent on the placement of nodes (Figs 1a, S4). Mean current density in the interior study area was higher when nodes were placed within the study area (Fig. 1b), demonstrating that the interior area became nearly saturated with current (Fig. S4). To summarize, placing nodes within the study area led to a current density map that was dependent on where the nodes were placed and was saturated with current. Placing nodes around the perimeter of the buffer led to a current density map that was independent of node placement and highlighted areas of high and low connectivity once the buffer was removed.
(a) Pearson correlation coefficients comparing a current density map based on all possible node pairings to current density maps created with fewer nodes, and (b) mean current density (95% confidence interval), as the number of node pairs that are connected by current increases. Current density maps were based on simulated cost surfaces with the buffer removed, for nodes located in the interior grid (closed symbols) or around the perimeter of the buffer (open symbols); in both cases, we analysed current density in the interior study area with the buffer removed.
A buffer of at least 20% of the length of a square study area was sufficient to remove bias in current density caused by nodes placed around the perimeter of the buffer (Fig. 2). This was true for cost surfaces that varied in the proportion of good and poor habitat (Fig. 2a) and that varied in shape (square vs. rectangular study area; Fig. 2b). We found a relatively low correlation between current density maps with no buffer and a buffer with a width that was 5% of the study area width (Fig. 2), demonstrating that even a narrow buffer can improve current density estimates by removing bias caused by node placement.
Pearson correlation coefficients comparing current density maps at different buffer widths. For example, the point located at a buffer width of 0 represents the correlation between the current density maps with 0 and 5 cell wide buffers. We connected 50 node pairs randomly located around the perimeter of each buffer and removed the buffer before calculating the correlation between maps. In a), we simulated a square-shaped cost surface (100 × 100 cells) with 25% (black), 50% (red) and 75% (blue) of the cells labelled at random as ‘good’ habitat. In b), we simulated a square cost surface (100 × 100 cells; solid line, unfilled symbol) and a rectangular cost surface (50 × 200 cells; dashed line, + symbol). See Fig. S1.
For our A2A study area (Fig. 3a), at least 15 node pairs were necessary to characterize connectivity in the interior of the study area; this is where cumulative current density became independent of the number of nodes (i.e. the asymptote), and maps were highly correlated with the full pairwise current density map (Pearson r > 0·98; Fig. 3b). However, we used the cumulative current density map obtained from 1225 random node pairs for our validation exercises. Compared to random, we found that herptiles moved through areas with high current density (t = 8·87, P < 0·001, Cohen's effect size d = 0·466; Fig. 4a) and high habitat suitability (i.e. low cost; t = −2·71, P = 0·007, d = 0·143; Fig. 4b). We found that fishers moved within their home range through areas with high current density and high habitat suitability: mean current density was higher within the home range (t = 2·284, P = 0·031, Cohen's effect size d = 0·195), within the core use area (t = 4·502, P < 0·001, d = 0·448), and at fisher locations (t = 12·651, P < 0·001, d = 0·341) compared with the study area (Fig. 5a). Mean habitat suitability was also higher within the core use area (t = −8·936, P < 0·001, Cohen's effect size d = 0·365) and at fisher locations (t = −8·114, P < 0·001, d = 0·214) compared with the study area, but there was no difference in mean habitat suitability between the home range and the study area (t = −0·963, P = 0·345, d = 0·065; Fig. 5b).
(a) Mean current density map of the study area (black outline separates the interior study area from the buffer) derived from a cost surface using Circuitscape software (McRae & Shah 2009); inset map shows the location of the eastern Ontario study area within the province of Ontario, and Ontario's position within Canada. (b) Correlation coefficients comparing a current density map of the study area (buffer removed) based on 1225 node pairs, to current density maps based on fewer nodes as the number of randomly selected node pairs increases. Correlations are based on 10 000 randomly selected cells within the interior study area.
(a) Mean current density (amperes) ±SE and (b) mean cost value ±SE within 200 m circular buffers at 725 random and 725 reptile and amphibian road mortality locations in eastern Ontario, Canada.
(a) Mean current density (amperes) ±SE and (b) mean cost value ±SE within different hierarchical levels of fisher [Pekania (Martes) pennanti] space use in eastern Ontario, Canada (N = 26). We considered the study area to represent available habitat, represented by the dashed line.
Discussion
Our approach for creating a predictive map of multispecies functional connectivity did not require independent, field-collected data, was not sensitive to the placement of nodes for connectivity estimation and was not based on a focal species. Our method is most appropriate for situations with no a priori reason to place nodes in any particular location. For example, for some land-use planning purposes, one might be interested in estimating the connectivity across the entire surface, or at any point on the surface, rather than between pairs of pre-defined points.
We used road mortality locations for 20 herptile species to show that multiple species move through areas that we predicted to have high connectivity. We assumed that if herptiles were killed on roads, they were in the act of moving from one location to another. Thus, we expected to find road-killed animals proximate to areas of high current density, and this is what we found. We also found that road-killed herptiles were more likely to be found in areas with high habitat suitability (or conversely, low cost). Effect size was larger for current density than for habitat suitability, indicating that our index of connectivity was a better predictor of herptile movement. Langen, Ogden and Schwarting (2009) found wetland configuration to be a strong predictor of herptile road mortality. Similarly, studies of wildlife ranging from stone marten (Martes foina; Grilo et al. 2011) to squirrel gliders (Petaurus norfolcensis; van der Ree et al. 2010) have also found a positive relationship between landscape connectivity and road crossing by animals. We found that herptiles were moving through areas that we predicted to have relatively high functional connectivity.
We used independent data for fishers to validate our multispecies connectivity map. Territorial animals move within their home range, and we assumed that independent locations and core use areas represented areas that an individual animal spends more time moving within. We expected that fishers would be found more often in areas with high connectivity (Rosenberg, Noon & Meslow 1997), and this is what we observed: current density within core use areas was higher than what was available. Fishers also used areas with low cost relative to what was available, however, making it difficult to determine whether fisher space use was related to habitat suitability, connectivity or both. The effect size using the current density map was only slightly larger than when we used the habitat suitability map; thus, we interpret these results as validation of both our cost surface and our connectivity map to predict space use of fishers at the level of the home range. Walter et al. (2009) found that white-tailed deer (Odocoileus virginianus) home ranges were located in areas of high habitat connectivity. Similarly, Wilson, Marsh and Winter (2007) found that home ranges of lemuroid ring-tail possums (Hemibelideus lemuroides) did not include areas with low canopy connectivity.
Our multispecies connectivity approach differs from approaches described by Beier, Majka & Newell (2009) and Cushman & Landguth (2012) with respect to how the cost surface is parameterized. Beier, Majka and Newell (2009) used expert opinion to parameterize a unique cost surface for each focal species and then overlayed the resulting least cost corridor maps. Similarly, Cushman and Landguth (2012) mapped the intersection of connectivity maps for several focal species. We parameterized one cost surface that was meant to coarsely represent ease of movement for general forest- or wetland-dwelling species, and we estimated connectivity between random locations placed along the perimeter of a buffer. Beier, Majka and Newell (2009)'s technique works well for predicting corridors between defined habitat blocks that act as obvious source and destination points, whereas our approach has the ability to also estimate connectivity in regions that do not have distinct habitat blocks that one might wish to estimate connectivity between. We can envision future studies that merge components of Beier, Majka and Newell (2009)'s methods (i.e. species-specific cost surfaces) with ours (i.e. randomly placing nodes around the perimeter of the buffer and evoking Circuitscape).
We recommend randomly placing nodes for connecting current around the perimeter of a buffered cost surface and then removing the buffer from the resulting current density map. A consequence of the Circuitscape algorithm is that the highest estimates of current density are near the nodes. There may be an a priori reason to locate nodes in a particular place, for example, if one is interested in comparing estimates of gene flow to predictions of landscape connectivity between two sampling sites. Schwartz et al. (2009) placed nodes within wolverine (Gulo gulo) breeding habitat and merged multiple least cost paths. However, if one is interested in predicting functional connectivity across a region in general, then the relatively high current at randomly located nodes will result in a biased current density map. We demonstrated this on a simulated cost surface: when we randomly placed nodes within the study area, current density estimates were more sensitive to the placement and number of nodes than when nodes were placed around the perimeter of the buffer that was later removed. Nodes placed within the study area resulted in a saturation of current, making it difficult to discern areas of high and low current caused by landscape patterns rather than node placement. Cushman, McKelvey & Schwartz (2009) and Walpole et al. (2012) also placed nodes around the perimeter of the study area.
There is a question of how many nodes are necessary to adequately depict connectivity, and the answer will likely vary by study. We plotted Pearson correlation coefficients calculated by comparing a full pairwise current density estimate to maps with an increasing number of nodes; we considered that our estimate of connectivity was adequate when the curve reached an asymptote, which occurred at 15–20 node pairs in our examples. Users should undertake this simple sensitivity analysis with their own data to ensure that they have sufficient sampling. Other than computation time, there is likely no penalty to including too many nodes around the buffer perimeter.
A second question that may arise is how wide the buffer should be. We found that a buffer width of ≥20% of the study area width was sufficient to remove the effect of node placement, and this width was sufficient for study areas with varying proportions of good habitat and different shapes (square and rectangular). The spatial pattern of habitat may also influence the required buffer size in some circumstances; therefore, users may want to experiment with different buffer sizes in their study systems. Users might face a trade-off between buffer size and number of pixels. Because of computer memory limitations, Circuitscape software is often unable to compute grids larger than 6 million cells (Shah & McRae 2008), ultimately restricting the size of the buffer. McRae & Beier (2007), however, showed Circuitscape software to be relatively insensitive to cell size. It is possible to map even larger areas using a tiling approach (Pelletier et al. 2014).
Many conservation-oriented government and non-government organizations view as important the establishment of networks of landscape connectivity. For example, within the A2A region, identifying important connective landscape elements for conservation is a priority. Another example is the Natural Heritage System in Ontario, a goal of which is to establish a network of linked areas that maintain biodiversity at a landscape scale. We presented an approach to predict areas of relatively high multispecies functional connectivity that is both cost-effective and efficient. We used empirical data to show that multiple species move through areas that we predicted to have high functional connectivity, supporting the work of Beier & Noss (1998) who advocated that connectivity is a necessary component of population viability.
Acknowledgements
We thank Steve Voros and Dave Tellier for providing land cover data and for useful discussions about applying our methods to natural heritage system design. We thank C. Scott Findlay and the Ontario Ministry of Natural Resources (OMNR) in Kemptville, ON, for their assistance in acquiring the fisher data set. We thank Ontario's Natural Heritage Information Centre for providing access to herpetofaunal road kill data. We thank Hance Ellington for discussion. Our manuscript benefited from the comments of 3 thorough reviewers. Funding was provided by the OMNR and an Ontario Graduate Scholarship to ELK.
Data accessibility
The eastern Ontario current density map has been deposited in the Dryad repository doi:10.5061/dryad.vr184.
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