Examining local and regional ecological connectivity throughout North America

recommend maintaining to in the face of land-use and Alternative connectivity assessments conducted multiple for conservation plans. Notably, our outputs highlight the importance of small and isolated fragments of relatively natural land while simultaneously identifying broad regions important for maintaining connectivity across natural areas of North America.


Introduction
Human modification of natural landscapes results in loss and fragmentation of habitat and disruption of ecological processes (Haddad et al. 2015;Venter et al. 2016). Humans modify ecosystems by converting land to agricultural, residential, or commercial uses, building roads, railways, transmission lines, or by otherwise altering natural lands (Kennedy et al. 2019;Theobald et al. 2020). In response to habitat loss and fragmentation, conservation scientists have repeatedly recommended that we (1) stop eliminating habitat (Fahrig 1997;Wilcove et al. 1998) and (2) ensure that habitat fragments remain connected (Hilty et al. 2006;Beier 2012). How to maintain or restore connectivity between core habitats, population sources, and protected areas remains a critical conservation challenge, especially in the face of climate change (McGuire et al. 2016;Littlefield et al. 2017;Parks et al. 2020).
Various methods for identifying priority locations for maintaining or restoring connectivity between core areas have been developed in the last few decades (Rudnick et al. 2012;Correa Ayram et al. 2016). Least-cost paths, least-cost corridors, resistant kernels, and methods applying circuit theory are among the most popular (Compton et al. 2007;Carroll et al. 2011;Dickson et al. 2019;Phillips et al. 2021). Each of these methods require (1) gridded data of pixels estimating landscape resistance to movement and (2) locations of core areas or source points to connect (e.g., habitat patches, population sources, or protected areas). Developing resistance surfaces that best predict movement of species is an active area of research (Zeller et al. 2012(Zeller et al. , 2018Keeley et al. 2016;Carroll et al. 2020). Other research seeks to develop resistance surfaces that are "species-agnostic" so that they represent assumptions of how multiple species move in response to landscape conditions (Krosby et al. 2015). Species-agnostic connectivity assessments range from mapping corridors between protected areas (e.g., Barnett and Belote 2021) to identifying potential flows of ecological processes and movements of myriad species (Littlefield et al. 2017;Carroll et al. 2018).
Maps of landscape resistance are often based on assumptions that certain landscape features, like areas of high human modification or unsuitable habitat, will be avoided by individuals, require a high physiological cost to traverse, or constitute high mortality risk (Compton et al. 2007;Cushman and Landguth 2012;Tucker et al. 2018). Resistance surfaces are created using a combination of geospatial layers representing human modification, topography, and vegetation (Zeller et al. 2012). For species-agnostic approaches, maps of human modification often serve as the basis of resistance under the assumption that maintaining connectivity through the most "natural" lands will provide the best opportunities for successful movement for the greatest number of species (Lawler et al. 2013;Belote et al. 2016;Parks et al. 2020; Barnett and Belote 2021). The precise relationship between human modification and landscape resistance to movement is usually poorly quantified (Tucker et al. 2018;Brennan et al. 2022). Identifying connectivity priorities for "human-tolerant" species compared to "human-sensitive" species can be done using different transformations of human modification data to create maps of landscape resistance (Keeley et al. 2016;Belote et al. 2016;Belote and Wilson 2020).
While developing resistance surfaces that accurately predict wildlife movement and ecological flows is important, connectivity models have been shown to be sensitive to the number and locations of areas to connect (Koen et al. 2014;Belote et al. 2016). Therefore, the decision of where to place source locations or core areas is not trivial. When known, locations of source populations can be used as core areas in a connectivity model (Peck et al. 2017). In other cases, researchers have distributed source points or core areas in connectivity models based on estimated population densities or habitat suitability (Cushman and Landguth 2012;Keeley et al. 2016;McClure et al. 2016;Carroll et al. 2020). In species-agnostic cases, researchers have modeled connectivity among protected areas (Belote et al. 2016;Ward et al. 2020;Barnett and Belote 2021). Given model sensitivity to the number and location of core areas, and because sources and/or destinations may be unknown, researchers have developed 'coreless' connectivity model approaches Pelletier et al. 2017;Koen et al. 2019). These models use either resistant kernels to estimate a density of movement (Compton et al. 2007) or 'wall-to-wall' or 'omnidirectional' current flows using circuit theory (McRae et al. 2016Koen et al. 2019;Phillips et al. 2021).
Conservation scientists are evaluating connectivity priorities at local (Compton et al. 2007), regional (Leonard et al. 2017;Schloss et al. 2022), continental (Carroll et al. 2018;Barnett and Belote 2021), and global (Ward et al. 2020;Brennan et al. 2022) extents. Providing organisms opportunities to adapt to increasing human pressure and the effects of climate change via long-distance dispersal -over multiple generations and long time periods -is increasingly recognized as an important long-term adaptation strategy in conservation planning (Lawler et al. 2009;Carroll et al. 2018;Parks et al. 2020). At the same time, conservation scientists are recognizing the importance of relatively small, isolated habitat patches (i.e., "fragments") for maintaining biodiversity, supplying myriad ecosystem services, and functioning as steppingstones in local habitat networks (Hannah et al. 2014;Belote et al. 2016;Peck et al. 2017;Fahrig 2019;Riva and Fahrig 2022). Broad-scale connectivity models (e.g., those conducted across the continent) may fail to identify the importance of small habitat fragments despite their role for maintaining local connectivity (Koen et al. 2019). Many large landscape connectivity models are coarse in scale and in assumptions of dispersal ability and are therefore limited in their ability to identify the importance of smaller habitat fragments for maintaining local connectivity. Multiscale connectivity assessments based on alternative assumptions of how human modification may affect movement are needed.
Here, we conducted a factorial experiment to evaluate how spatial scale and resistance surfaces affect the identification of lands important for maintaining connectivity. Specifically, we modeled omnidirectional connectivity at various spatial scales across North America using three alternative maps of landscape resistance representing different sensitivities of species to human modification ). We took advantage of new Omniscape software Hall et al. 2021) which allowed us to assess lands important for maintaining connectivity at multiple spatial scales without deciding which core areas or sources/destinations to include in an analysis. We based our analysis on the premise that lands with minimal human modification will likely facilitate movement of species better than lands with more intense human modification. As in many conservation-planning exercises there is a tradeoff between focusing on species-agnostic, coarse filter versus species-specific, fine filter approaches. Our approach is species agnostic, does not depend on locations of core areas, is focused on multiple spatial scales, and is not constrained to a national border. We asked three primary questions: (1) Which areas are important for ecological connectivity across North America?
(2) Do areas identified as important for connectivity vary among scenarios using different resistance surfaces representing alternative sensitivities of organisms to gradients in human modification?
(3) How do areas identified as important for connectivity vary among scenarios using moving windows of different sizes, which represent multiple scales of connectivity importance?

Omniscape overview
We used Omniscape v0.5.8 to run connectivity models in Julia Hall et al. 2021) on an Amazon Web Service (AWS) instance (machine type r5a.12xlarge with 48 VCPUs and 384 GB of RAM). We used an estimate of human modification as the basis of landscape resistance (Theobald et al. 2020). Omniscape implements omnidirectional connectivity models using circuit theory (McRae et al. 2007 and gridded data representing maps of landscape resistance. Omnidirectional connectivity is assessed within moving windows where the center pixels constitute targets and are set to "ground". Pixels within the moving window serve as sources of current flow injected into the map of landscape resistance (see Source strength and blocking below). Like other circuit theory models, movement of electrical current serves as a model metaphor for random-walking organisms moving through a landscape (Dickson et al. 2019).
We produced 12 maps of omnidirectional normalized current flow using three resistance surfaces crossed with four moving window extents across North America. Omniscape outputs three representations of landscape connectivity: potential current flow, cumulative current flow, and normalized current flow. Potential current flow is assessed based on model runs where current is injected into sources but where resistance of every pixel is constant and set to 1. Cumulative current flow is calculated as the sum of current flow output from overlapping moving windows. Normalized current flow is calculated by dividing current flow by potential current flow  and is used to highlight areas of concentrated (high values) and impeded (low values) current flow (Brennan et al. 2020;Schloss et al. 2022). We focus attention and interpretation of concentrations of high values which represent channelized flow (i.e., areas of relatively high normalized current density, sensu McRae et al. 2016).

Landscape resistance
The 2015 map of human modification is a 1-km resolution (with Lambert azimuthal equal area projection) global composite of variables that represent human impacts to natural ecosystem structure and processes such as roads and transmission lines, modified land cover (e.g., urban areas, agriculture, mines), and density of human population (Theobald et al. 2020). We assume that movement of wildlife species, dispersal of organisms, and flows of other terrestrial processes are least disrupted on lands with lower human modifications. However, the degree of resistance to movement, dispersal, and flow along gradients of human modification are typically unknown. For some species (e.g., human-tolerant species like coyotes, Canis latrans), low and moderate levels of human modification may have little effect on movement or flows (Ellington and Gehrt 2019). In these cases, only moderate to high levels of human modification may impede movement. For other species or processes (e.g., human-sensitive species like grizzly bears, Ursus arctos), low levels of human modification may have a relatively large effect on movement or flows. And, in other cases, movement may be resisted in a way that is proportional to the degree of human modification. These alternative ways that human modification may influence resistance can be represented spatially through alternative mathematical transformations of the human modification data. Here, we used three transformations introduced in Keeley et al. (2016), who represented landscape resistance as a function of habitat suitability for species-specific connectivity models. In our cases, we used the map of human modification as the basis of species-agnostic resistance in lieu of species-specific habitat suitability. We used the function: To create three maps of resistance where hm2015 is the human modification and c is equal to − 8, 0.25, or 8 representing resistance for human-sensitive species or processes, resistance that varies linearly with human modification, and resistance for human-tolerant species or processes, respectively ( Fig. 1).
The human modification data assigns natural lakes and rivers no values (i.e., NA), but reservoirs or other impounded waters are assigned values relative to surrounding human modification. In our connectivity models, water assigned as NA functions as complete barriers to movement. While this treatment may represent the way water impedes some movements and spatial processes, we chose to assign all water -irrespective of reservoir or natural lake or river -the maximum value of resistance. We chose to use an eight-neighbor rule which considers corner-adjacent pixels connected in Omniscape. Lacking alternative pathways due to the barrier of water, these corneradjacent pixels near river oxbows resulted in conspicuously high concentrations of current flow. Assigning the maximum value of resistance to water eliminated these artifacts without changing other nearby patterns of current flow (Supplement 1). We also chose this approach because natural and human-caused water bodies likely do not represent complete barriers of movement for many species. Rather, water may represent areas of high resistance to movement, thus our decision to assign the maximum resistance value to water.

Source strength and blocking
Source strength of pixels constitutes the amount of current injected into a pixel and can represent locations of core habitat or known populations. Because our models are species-and population-agnostic, we did not use predetermined locations to represent variability in the sources of dispersing organisms. For our models, we used the inverse of the resistance surface as a source strength layer Landau et al. 2021;Schloss et al. 2022). This follows from the assumption that more natural lands with lower human modification will tend to represent greater sources of dispersers. It is important to note that transformations of the human modification data into resistance surfaces likely also influence intensity of movement emanating from a given area. In other words, our "treatments" of resistance surfaces also may influence source strength.
To speed processing, Omniscape allows users to reduce computations by coarsening the source strength layer using a "block size" option . In preliminary trials, we evaluated processing time and sensitivity of spatial results by varying block sizes and moving windows. Output from model runs using various block sizes were all highly correlated. For all model runs presented here, we chose to use a block size that is 10% of the size of the radius of the moving window. This choice reduced processing time with minimal conspicuous spatial artifacts associated with larger blocking sizes (Supplement 2). Fig. 1 The way that human modification influences landscape resistance may vary depending on species' sensitivity to gradients in human impacts. We created three maps of resistance based on three alternatives varying the 'c' parameter in Eq. 1. When c = 0.25 (black line), resistance scales linearly with human modification. Species movements that are more sensitive to lower levels of human modification were modeled using c = − 8 (red line), whereas species movement that are more tolerant to lower levels of human modification were modeled using c = + 8 (blue line)

Moving window sizes
We chose to vary the size of the radius of circular moving windows to identify current flow at different spatial scales. Using each of the three resistance surfaces, we ran Omniscape using one of four different moving window sizes with radii of 30-km, 150-km, 300-km, or 700-km (Table 1). The smallest moving window was intended to represent short-range dispersals or connectivity within relatively small areas. The largest moving window was intended to represent the size of broadscale conservation planning aimed at maintaining connectivity across large regions over potentially many generations of migrating or dispersing organisms. The two medium-sized moving windows were intended to represent intermediate-range (150-km) and long-range (300-km) dispersing individuals or propagules, which have been used in other national connectivity modeling efforts (Belote et al. 2016) corresponding to large-bodied terrestrial vertebrates (Bowman et al. 2002).

Mapping agreement among scenario outputs
After completing the 12 Omniscape model runs (i.e., representing alternative scenarios using three resistance surfaces × four moving window sizes), we classified values of normalized current flow into percentiles using the ntile function in the R package dplyr (Wickham et al. 2018) so that each map consisted of integer values ranging from 1 to 100. We then created composite normalized current flow maps by summing all 12 maps together. We also summed the four maps produced from output of different window sizes within each of the three resistance treatments.
We assessed areas of agreement between model runs using different moving window sizes to identify lands important for both local and regional connectivity, local but not regional connectivity, and regional but not local connectivity, etc. Specifically, we classified each of the 12 maps of normalized current flow into terciles (three classes with equal number of pixels) to create pairwise combinations of connectivity values from output among each moving window size within the three resistance surfaces. For all bivariate maps combining output from the pairwise combinations of output using different moving windows, we calculated the total area (represented as % of North America) within each of the nine bivariate classes. We also calculated the mean and range of area within these bivariate classes among all 18 pairwise combinations (six bivariate maps × three resistance surfaces) to summarize agreement among outputs using different moving window sizes.

Results
Spatial patterns of normalized current flow varied with moving window size and maps of landscape resistance (Fig. 2). In general, spatial patterns of high normalized current flow from smaller moving window sizes were more mottled than those produced with larger sizes (Fig. 2 and 3). Larger moving windows resulted in more concentrated current flows, especially in the Rocky Mountains, boreal forests, and broader Appalachian region. Omnidirectional connectivity models run with "human-sensitive" landscape resistance (c = − 8) and linearly transformed resistance (c = 0.25) resulted in concentrated current flows in northern latitudes of Alaska and Canada, where models run with "humantolerant" landscape resistance (c = 8) resulted in large areas of moderate current flow in these lands.
The composite maps of normalized current flows highlight the patterns of agreement among all models (Fig. 4). The boreal forests and arctic tundra of Canada and Alaska, the Coast Range of British Columbia in Canada, the Rocky Mountains from Canada to Mexico, the Great Basin in the western US, the Sierra Madre to the Yucatan Peninsula in Mexico, and other areas in the eastern US 1,539,379 Similar in size to Yellowstone to Yukon for regional conservation connectivity planning all possess conspicuous concentrations of current flow in the composite maps. The lowest normalized current flow in the composite map occurs in areas where relatively high development is adjacent to relatively natural lands (e.g., at the interface of the Great Plains and Rocky Mountains of Canada), not in the lands with the absolute highest resistance. While spatial patterns varied among outputs produced with different moving window sizes, on average 64% of pixels were classified into the same tercile of normalized current flow across all pairwise combinations of outputs (Table 2). Areas where outputs from smaller moving windows produced high normalized current flow but larger window runs produced low current flow only made up 1.76% (ranging from 0.13 to 5.3%) of the area across all pairwise comparisons. These areas shown in orange in Fig. 5 and Supplement 3 represent places important for local connectivity, even though they may be considered of low importance for regional connectivity planning. These areas are most common in the lands dominated by agriculture in the Midwest and central Canada.

Discussion
Our results highlight important areas for multi-scale, species-agnostic connectivity planning throughout North America while demonstrating the consequences of several key decisions when implementing omnidirectional connectivity models. Both the moving window size and alternative maps of resistance influenced spatial patterns of high normalized current flow. Varying these two factors may represent alternative methods for mapping important connectivity areas based on dispersal distances of species, the extent of connectivity planning, and the sensitivity of species' movements to human-modified lands. Our composite maps highlight areas where all models resulted in high current flow, but differences among models may provide alternative hypotheses on how movement of organisms varies with human impacts to landscapes.
Outputs from models based on the smallest moving window were characterized by a mottled pattern of high current flow without clear swaths occurring throughout North America. Concentrations of Fig. 2 Maps of normalized current flow from omnidirectional connectivity models using three different resistance surfaces (varying the c value from Eq. 1) and using four different radii of moving windows. Outputs produced where c-values equaled − 8 represent conditions for human-sensitive species, while outputs produced with c-value of + 8 represent conditions of human-tolerant species normalized current flow from the output conducted using the smallest moving window extent could highlight important areas of relatively natural conditions that may support local connectivity. These concentrations of current flow can occur in natural lands embedded within highly developed areas (Fig. 3) and seem to be identified as high normalized current flow when they represent the relatively most natural (i.e., least human modified) lands within a small moving window. Fahrig (2019) suggested that prioritizing large patches of connected habitat over small fragments can undermine local efforts for conserving biodiversity. Conducting a continental assessment of connectivity priorities could easily lead to prioritizing large regions of unfragmented natural areas over small patches of natural lands. We attempted to overcome this concern by conducting our continental assessment of connectivity using small moving window sizes across the continent and displaying our results as separate maps, as a multi-model composite, and in pairwise bivariate maps. The mottled current flow results from the small moving window may allow local conservation planners to map small fragments of natural areas onto continental connectivity priorities (e.g., Fig. 3).
While proportionally little area was identified as the highest tercile from models produced using smaller moving windows and the lowest tercile from larger moving windows, these lands shown as orange areas in bivariate maps of Fig. 5 constitute areas important for local connectivity that would be "overlooked" from broad-scale models (cf., Koen Researchers and practitioners conducting broadscale analyses should be aware of the potential to miss locally important areas. This pattern is highlighted in Fig. 3 and shows differences between output from two moving window sizes in lands identified by high normalized current flow. The smaller moving window (30-km radius) identified patches of forest and woody wetlands in an agriculturally dominated landscape as high connectivity importance, while the larger moving window (300-km) model output identified only the relatively contiguous forests as large swaths of connectivity importance, missing all potential conservation priorities within the agricultural landscape.
In general, as we increased the size of the moving window, clear concentrations of current flow were revealed throughout the broader Rocky Mountain region of Mexico, the US, and Canada. Mountainous areas and some riparian zones of the southeastern US Fig. 4 Composite normalized current flow maps that combine all 12 outputs (large map, top) and composite maps combining the four-moving window-size outputs within three resistance factors (bottom maps) Table 2 Mean (range) percent area of North America within bivariate classes where terciles of normalized current flow were combined using all pairwise combinations of smallerand larger-size moving window model runs. The table is arranged the same as the legends in Fig. 5 and shows the mean and range of all bivariate maps. About 64% percent of the total area was classified as the same tercile irrespective of moving window size. However, over 3.5% of North America was classified as the lower third current flow using smaller moving windows but high tercile of current flow using larger moving windows (blue color in Fig. 5). These are places that are important regionally, but not locally. Alternatively, on average 1.76% was the opposite situation (orange color in Fig. 5; high current flow using smaller moving windows and low current flow using larger sizes). These are places that are important for local connectivity but not identified as important in the regional models. For context, 1% area of our North American study area is 213,600 km 2 Tercile of normalized current flow from smaller moving window were also identified by high concentrations of normalized current flow. Our maps based on outputs using the large moving windows identified broad swaths of current flow that could inform connectivity planning like the vision identified by the Yellowstone-to-Yukon (Y2Y) Initiative. Other programs like Y2Y could be developed throughout the Rocky Mountains of Canada, the US, and Mexico, as well as regional linkages of natural lands in the southeastern US. Many of these regional linkages align with the findings of Barnett and Belote (2020) and Brennan et al. (2022) who modeled connectivity between protected areas across North America using a linear-transformed resistance surface based on human modification. At large spatial extents, connectivity models run with cores (protected areas) and omnidirectional coreless models described here could converge and reveal similar areas to be important for connectivity. Connectivity models conducted at large spatial extents typically rely on data quantifying human modification (Theobald et al. 2020) or human footprint (Venter et al. 2016) as the basis of mapping landscape resistance. The shared assumption among models conducted at large extents that human modification affects landscape resistance likely explains the similarities in patterns. Interestingly, results varied the most conspicuously among alternative resistance surfaces within northern latitudes on lands with generally low human modification (Alaska and Canada's tundra and boreal forests). In these areas, models run with resistance transformed for "human-sensitive" (c = − 8) and the linear alternative (c = 0.25) revealed maps with concentrations of current flow, while resistance scaled for "human-tolerant" species (c = 8) revealed relatively homogenous current flow. These results reflect how gradients in resistance vary at low levels of human modification with the different methods of transformation. In wildlands where little human modification creates variation in landscape resistance, alternative and redundant pathways result in low normalized current flow (i.e., no concentrations of current flow). While Bowman et al. (2020) found that current flow outputs from Circuitscape produced with different ranges of resistance values varied little as long as the rank order of resistance values was maintained, we found that -at least in some areas -patterns of current flow varied among our resistance "treatments".
Patterns of normalized current flow across North America may be used to develop connectivity targets and objectives. For instance, McRae et al. (2016), Schloss et al. (2021), and Cameron et al. (2022) classified omnidirectional model output using thresholds of normalized current flow to identify areas of impeded, diffuse, intensified, and channelized flow. This classification scheme acknowledges that low normalized current flow can occur in areas of either high resistance or very low resistance and can help tailor connectivity objectives to connectivity outputs (sensu . For instance, wildlands with diffuse flow represent lands where actions that prevent fragmentation of large patches would be implemented, while lands with impeded flow may require restoration of natural habitat to restore connectivity. We used classification thresholds proposed by McRae et al. (2016) and recently adopted by Schloss et al. (2022) and Cameron et al. (2022) with our output with mixed results which depended on the moving window size and resistance used (Supplement 4). In general, the classification thresholds used in earlier efforts seemed most reasonable for our output based on models run with the resistance surfaces developed using the "human-tolerant" (i.e., c = 8) transformation. Using these outputs, impeded flows occurred in agriculturally dominated lands, diffuse flows occurred in large areas of minimal human modification, and concentrated flows occurred in lands with a mix of wild and agricultural lands. For most of our output, we recommend interpreting the highest values to be of highest connectivity importance. Except for our output conducted using the humantolerant resistance (c = 8), it is difficult to distinguish between impeded and diffuse flow based on proposed classification thresholds (Supplement 4). We recommend evaluating normalized current flow alongside maps of resistance to aid interpretation of output.
Our models represent alternative hypotheses for how different organisms move through lands of various degrees of human modification, and our outputs may represent different predictions of movement. After comparing connectivity models with movement data of elk (Cervus canadensis) and desert bighorn sheep (Ovis canadensis nelsoni), Keeley et al. (2016) concluded that a negative exponential function of habitat suitability results in connectivity models most accurately reflecting movement of these species. Results from Carroll et al. (2020) also suggest that wolverine (Gulo gulo) movement was best predicted from a resistance surface created from negative exponential transformation of habitat suitability. These studies suggest that some species may be capable of moving through suboptimal habitat but avoid very poor habitat quality. For their species-specific connectivity models, Keeley et al. (2016) and Carroll et al. (2020) include developed lands and human modification in their creation of habitat suitability and resistance surfaces. Our models are speciesagnostic and based on assumptions that organisms will avoid lands with high human modification or will experience higher risks of mortality in lands dominated by human modification. However, our models also may be unrealistic in some areas with very low productivity (i.e., deserts). In these areas, species may experience high cost of movement even when human modification is low but where extreme temperature, low water availability, and low vegetation cover may limit successful dispersal (sensu Dobrowski and Parks 2016). Additional research into the relationship between species movement, human modification, and climate could reveal important insights that may inform future work. Our output could be used for comparing species-specific connectivity models or observations of movement to determine which of our model assumptions best align with different speciesspecific model predictions or observed movements.
Our work here may also be useful to future users of Omniscape. Our preliminary tests helped us decide on a blocking size of 10% that of the moving window and clearly demonstrated that blocking size had little effect on mapped outputs, at least for the scenarios we evaluated. Using AWS, our scenario runs in Omniscape took between ~ 6.5 to over 56 h with larger moving window scenarios taking longer to run. The largest moving window scenarios (700-km) took -on average -nearly 6 times longer than the smallest moving window scenarios (30-km). To facilitate future work, we share all INI files for our scenarios, including the processing time for all model runs, as supplemental files, and shared all output publicly (see Data Availability).
Our results highlight challenges with interpreting maps of connectivity importance based on circuit theory. Areas of low normalized current flow may be difficult to distinguish from areas of impeded flow. If output maps are used to prioritize conservation actions, areas with relatively low to moderate normalized current flow may be regarded as low importance for connectivity. While the lowest values may indeed represent areas unimportant for connectivity, other areas with moderately low values may represent some of the most unfragmented lands in a study area. Connectivity objectives in large contiguous areas of low resistance (e.g., diffuse flow) will likely be very different from those of the highest values (concentrated flows classified as "channelized"). Care should be taken in interpreting Omniscape output, especially when considering priorities and conservation actions needed to sustain connectivity ). Here, we found that interpreting the highest normalized current flow (which could be classified as "channelized") to be the least ambiguous values produced from the models. Therefore, we focused attention on those areas as important for connectivity through our composite and bivariate maps.
While researchers and practitioners should continue to scrutinize the costs and benefits of implementing actions to maintain or restore connectivity (Simberloff et al. 1992), connectivity modeling is increasingly becoming a key component of conservation planning at multiple spatial scales. Sometimes connectivity models are based on observations of individual organisms moving through a landscape or habitat suitability of potential movements. Other times, connectivity modeling is based on identifying landscape features that may provide opportunities for multiple species to move between conservation reserves or habitat patches. These different approaches are sometimes classified as functional versus structural connectivity models (Rudnick et al. 2012). Our work sought to identify lands that may allow organisms to move across landscapes of varying sizes or with varying dispersal distances. Ultimately, these models are based on predictions of how organisms use, avoid, or experience risk depending on the degree of human modification. These predictions vary with assumptions that we hope will be tested and compared with species-specific models and observations. Author contributions RTB and KB conceived of the study. RTB, KB, KZ, and AB developed and co-wrote the paper. JG performed model runs, analyzed preliminary data, and edited the final drafts.
Funding The Wilderness Society funded the work.

Data availability
The datasets generated during and/or analyzed during the current study are available at https:// doi. org/ 10. 5281/ zenodo. 70581 99. While we focus our assessment on