Multipurpose habitat networks for short-range and long-range connectivity: a new method combining graph and circuit connectivity
Summary
- Biodiversity conservation in landscapes undergoing climate and land-use changes requires designing multipurpose habitat networks that connect the movements of organisms at multiple spatial scales. Short-range connectivity within habitat networks provides organisms access to spatially distributed resources, reduces local extinctions and increases recolonization of habitat fragments. Long-range connectivity across habitat networks facilitates annual migrations and climate-driven range shifts.
- We present a method for identifying a multipurpose network of forest patches that promotes both short- and long-range connectivity. Our method uses both graph-theoretic analyses that quantify network connectedness and circuit-based analyses that quantify network traversability as the basis for identifying spatial conservation priorities on the landscape.
- We illustrate our approach in the agroecosystem, bordered by the Laurentian and Appalachian mountain ranges, that surrounds the metropolis of Montreal, Canada. We established forest conservation priorities for the ovenbird, a Neotropical migrant, sensitive to habitat fragmentation that breeds in our study area. All connectivity analyses were based on the same empirically informed resistance surface for ovenbird, but habitat pixels that facilitated short- and long-range connectivity requirements had low spatial correlation. The trade-off between connectivity requirements in the final ranking of conservation priorities showed a pattern of diminishing returns such that beyond a threshold, additional conservation of long-range connectivity had decreased effectiveness on the conservation of short-range connectivity. Highest conservation priority was assigned to a series of stepping stone forest patches across the study area that promote traversability between the bordering mountain ranges and to a collection of small forest fragments scattered throughout the study area that provide connectivity within the agroecosystem.
- Landscape connectivity is important for the ecology and genetics of populations threatened by climate change and habitat fragmentation. Our method has been illustrated as a means to conserve two critical dimensions of connectivity for a single species, but it is designed to incorporate a variety of connectivity requirements for many species. Our approach can be tailored to local, regional and continental conservation initiatives to protect essential species movements that will allow biodiversity to persist in a changing climate.
Introduction
Hundreds of habitat network initiatives are underway around the world (Bennett & Mulongoy 2006) as a means to implement the 21st-century paradigm of connectivity conservation (Crooks & Sanjayan 2006; Worboys, Francis & Lockwood 2010). This conservation model focuses on the spatial arrangement and connections among patches of habitat in order to enhance the long-term viability of populations living in and moving through fragmented landscapes (Chisholm, Lindo & Gonzalez 2010; Doerr, Barrett & Doerr 2011). The global pace and extent of habitat fragmentation make connectivity conservation an imperative, but the science is challenging because changing patch area, isolation, shape and quality (Ewers & Didham 2006) disrupt connectivity at multiple spatial and temporal scales. To date, habitat networks have generally been conceived to protect a single scale of connectivity relevant to either the persistence of metapopulations within networks (e.g. Urban et al. 2009), the traversability of networks for seasonal migrations (e.g. Taylor & Norris 2010) or longer-term range shifts under climate change (e.g. Phillips et al. 2008). There is a pressing need for methods that guide the design of networks that facilitate the movements of organisms at multiple spatial scales.
Landscape connectivity (Taylor et al. 1993) mediates movement at multiple scales and so affects the spatial distribution of ecological and evolutionary processes (Staddon et al. 2010; Gonzalez, Rayfield & Lindo 2011). Short-range connectivity within habitat networks plays a vital role in allowing species to colonize empty habitat patches to maintain source–sink dynamics (Hanski & Gaggiotti 2004) and buffers genetic diversity in the face of demographic declines (Ramírez et al. 2013). Long-range connectivity across habitat networks may enable long-distance movements by migrating individuals (e.g. Marra et al. 2006; Iwamura et al. 2013), which in turn may affect ecological processes such as nutrient redistribution and cycling (e.g. Knapp et al. 1999). Furthermore, long-range connectivity between habitat patches that are climatically suitable at present and those that will be suitable in future is also important to allow species to expand or shift their ranges in response to climatic changes (Schloss, Nuñez & Lawler 2012).
Incorporating connectivity criteria in spatial conservation planning is an ongoing challenge (Kool, Moilanen & Treml 2013). Most approaches focus on either selecting protected areas or designing corridors (Alagador et al. 2012; but see Pouzols & Moilanen 2014). When selecting protected areas, the primary goal is to efficiently meet habitat targets for all species within the protected area system. Connectivity can be accounted for implicitly by including spatial selection criteria (e.g. proximity, Önal & Briers 2002; compactness, Önal & Briers 2003; contiguity, Önal & Briers 2005) or explicitly by including species-specific connectivity requirements (e.g. Moilanen & Wintle 2007). When designing corridors, the emphasis has been placed on connecting two or more existing protected areas and has typically involved mapping linkages (Cushman et al. 2013). Least-cost paths and corridors (Cushman, McKelvey & Schwartz 2008) have been the most common analyses used to map connections between a single pair of areas. These analyses identify the building blocks for either discrete models of landscape connectivity such as habitat networks (derived by factorial approaches, Cushman, McKelvey & Schwartz 2008; or by graph-theoretic methods, Urban et al. 2009; Alagador et al. 2012) or continuous connectivity models such as ecological circuits (McRae et al. 2008). These different models are able to capture different scales and types of connectivity but are rarely combined into a single analysis. Moreover, the most recent advances in connectivity modelling (specifically circuit theory, landscape networks and centrailty analysis; reviewed in Cushman et al. 2013) have been implemented in specialized software (reviewed in Brás et al. 2013) and have not been integrated with protected area selection. The spatial planning software, zonation (Moilanen et al. 2005), has functionality to incorporate other connectivity analyses into protected area selection including structural corridors (Pouzols & Moilanen 2014) and connectivity modelled with species-specific dispersal kernels (Lehtomäki & Moilanen 2013). The combination of different types and scales of connectivity within zonation is possible in principle, but further research is needed to assess its use as a tool for the design of multipurpose networks.
In this study, we propose the design of multipurpose habitat networks that promote the persistence of metapopulations within a habitat network but also allow for traversability of the network to promote seasonal migrations or range shifts in response to climate-induced changes in habitat distribution (Fig. 1). We combine habitat patch network analysis with circuit-based movement models to attain two conservation objectives: (i) the long-term maintenance of populations within habitat networks and (ii) the persistence of large-scale migrations and potential for distributional changes across the habitat network in response to climate. The spatial distribution of conservation priorities emerges from a multi-objective analysis implemented with the zonation algorithm (Moilanen et al. 2005) and allows us to explore trade-offs among the different scales of connectivity (Fig. 1).
Methods
Study Area
The analysis was conducted in the southernmost region of Quebec, Canada, along both shores of the St. Lawrence River surrounding Montreal (centred on 45°40′N, 73°15′W). The extent of the study area was approximately 27 500 km2, extending north and east of the Montérégie administrative region (Fig. 2). The study area overlapped three ecoprovinces representing distinct combinations of climate, geology, topology, faunal realms and vegetation zones as classified by the Quebec Ecological Reference Framework (Marshall, Smith & Selby 1996; Li & Ducruc 1999). The central ecoprovince, covering 69% of the study area, comprises primarily fertile agricultural lands along the St. Lawrence River Valley and houses the vast majority of the population of Quebec (Fig. 2). This study area allowed us to examine multiple types of connectivity in forested ecosystems: (i) connectivity within the highly fragmented forest habitat network of the St. Lawrence Central Lowlands and (ii) traversability across the St. Lawrence Central Lowlands forest habitat network between the Appalachian Mountains along the southern edge and the foothills of the Laurentian Mountains at the northern edge.
Land cover was aggregated into two categories (details in Appendix S1, Supporting information): forest and open areas (Desrochers et al. 2011). Forest areas covered 37% of the study area (Fig. 2) and comprised all deciduous, mixed and coniferous forest stands. Open areas were classified as either vegetated (47% of the study area) or non-vegetated (16% of the study area). Open, vegetated areas were dominated by agricultural fields (85% of open, vegetated areas), while non-vegetated areas comprised primarily urban agglomerations and road systems (47% of open, non-vegetated areas) and water (40% of open, non-vegetated areas).
Study Species
We demonstrate our method by focusing on the ovenbird (Seiurus aurocapilla), a representative Neotropical migrant species sensitive to forest fragmentation on its breeding grounds (Robinson et al. 1995). Eastern populations of ovenbirds migrate through eastern North America during spring migration along flyways that are different and non-overlapping from western populations (Hallworth et al. 2015). Landscape structure along these flyways is thought to affect migratory movements over land (Marra et al. 2006); however, the extent to which landscape structure affects movement dynamics during migration is still largely unknown for songbirds. Habitat network structure that allows for intrapatch and interpatch movements may reduce negative effects of habitat loss for ovenbirds (Betts et al. 2006). Interpatch movements can contribute to ovenbird population persistence in fragmented landscapes in several ways: by gaining access to multiple patches to supplement resources (Betts et al. 2006), by increasing pairing success of males (Bayne & Hobson 2001) and by facilitating extrapair copulations (Norris & Stutchbury 2001). Habitat networks within breeding grounds may also enable settlements of new breeding sites (Desrochers & Hannon 1997) and facilitate potential range shifts in response to climate-induced changes in habitat distribution (McKenney et al. 2011) and food resources (Strode 2003). The sensitivity of Ovenbirds to the structure of their forest habitat network may be attributed to their specialization on forest-interior habitat (Gibbs & Faaborg 1990) in combination with their preference to use forested movement corridors (Robichaud, Villard & Machtans 2002) and avoid crossing open areas (St-Louis et al. 2014).
Study Species Habitat Data
We modelled connectivity of forest habitat for ovenbirds based on the quality of forest habitat and the degree of landscape resistance to ovenbird movement. Habitat quality was estimated in each map pixel based on forest composition and density data measured at the stand level (Appendix S2). Higher-quality pixels were those dominated by deciduous tree species where ovenbirds are more abundant (Smith & Shugart 1987).
The landscape resistance map for the ovenbird quantifies the relative ease with which an individual can move through each pixel in the study area. Resistance values were informed by field data from ovenbird translocations (Desrochers et al. 2011) and gap-crossing experiments (Bélisle & Desrochers 2002). Desrochers et al. (2011) measured homing times of translocated ovenbirds and calculated least-cost paths among forest patches based on different resistance scenarios to determine that resistance increased from forest to non-vegetated areas: forest had a resistance of 1; open, vegetated areas within 30 m of forest had a resistance of 14; and remaining open, vegetated areas had a resistance of 27 (Fig. S5.1). We added a resistance class for open, non-vegetated areas with a resistance of 100 to account for the higher human population density and larger water bodies in our study area.
Graph-Based Connectivity Analysis
Intrapatch connectivity and interpatch connectivity were assessed using spatial graph analysis in which forest habitat patches (represented as graph nodes) are connected from edge-to-edge via least-cost links to form a habitat network (Fall et al. 2007). We constructed the minimum planar graph of forest habitat patches for the entire study area based on the ovenbird resistance surface (Appendix S5), hereafter simply referred to as the habitat network. We restricted our network analysis and node prioritization to the fragmented, agricultural landscape of the St. Lawrence Central Lowlands (Fig. 2). Only those forest patches that had at least 80% of their area within this ecoprovince were considered nodes during the network analysis. Forest is more continuous in the other ecoprovinces within our study area; therefore, by restricting our focus to the portion of the forest that is embedded in the agricultural matrix, we concentrated on the viability of ovenbirds spread across discrete habitat fragments. Due to the size of the landscape (27 × 106 pixels), the minimum planar graph was constructed in 11 overlapping subsections of the landscape and then stitched together to produce the final habitat network. Network extraction was performed in r 2.15.2 (R Development Core Team 2012) using the ‘grainscape’ package (available at http://grainscape.r-forge.r-project.org) which implements the spatial graphs model (Fall et al. 2007) originally distributed with seles v.3.4 software (Fall & Fall 2001).
We calculated the equivalent connectivity (EC; Saura et al. 2011) of the habitat network for ovenbirds which provides a measure of the quality-weighted area of a single patch that would have the same probability of connectivity (Saura & Pascual-Hortal 2007) as the habitat network (details provided in Appendix S3). This measure captures both intrapatch and interpatch connectivity. We set alpha (a distance-decay constant that characterizes the rate of dispersal) to −0·01 to obtain a 0·05 probability of dispersing farther than the 300-m gap-crossing ability of ovenbirds (Bayne & Hobson 2001). We assessed the importance of each habitat patch (dEC) to the maintenance of the overall EC of the metapopulation by systematically removing each patch and evaluating its individual impact on the calculated value of EC (Urban & Keitt 2001; Saura & Pascual-Hortal 2007).
(eqn 1)Circuit-Based Connectivity Analysis
Traversability across the entire study area was assessed through the application of circuit theory, which predicts movement pathways between regions based on the conductance of the intervening landscape (McRae 2006; McRae et al. 2008). A conductance map was calculated as the inverse of the empirically based resistance map for ovenbirds and was used as the basis for the circuit analysis to determine the pattern of current density (i.e. flow) across the landscape. Current density patterns were assessed using the tiling approach described in Pelletier et al. (2014) which produces an omnidirectional current density map quantifying current flow in multiple directions (details provided in Appendix S6). The current density map was clipped to the St. Lawrence Central Lowlands ecoregion to produce a spatial, pixel-level description of traversability based on a pixel's contribution towards maintaining connectivity across rather than within the habitat network. Circuit analyses were conducted using circuitscape version 3.5 (McRae 2006).
Multi-Objective Conservation Prioritization Using zonation
We used the spatial prioritization software zonation v3.1 (Moilanen et al. 2005) to explore trade-offs between these three complementary measures of connectivity: dEC, betweenness and current density (Fig. 1). zonation has been widely applied to identify spatial conservation priorities using the distribution of multiple conservation features such as species, habitats and ecosystem services (Moilanen 2007; Moilanen, Leathwick & Quinn 2011; Moilanen 2013). We used the spatial, node-level descriptions of patch connectivity (based on dEC and betweenness) as two of the conservation feature layers for zonation analyses (Fig. 3). These input layers allowed us to explicitly prioritize intrapatch and interpatch connectivity (see Lehtomäki & Moilanen 2013 for other connectivity criteria currently implemented in zonation). We complemented these patch-level descriptions with stand-level habitat quality and pixel-level current density maps, which were also used as conservation feature layers in zonation analyses, to allow for a finer grained prioritization of the landscape that emphasized traversability both within- and between-habitat patches.
zonation produces a priority-rank map and set of performance curves that quantify the fraction of the conservation features remaining at any stage of the priority ranking. The priority ranking proceeds by iteratively discarding the pixel with the lowest conservation value and recalculating the conservation value for each remaining pixel, accounting for the occurrences of each conservation feature in the pixel and in the remaining landscape. The order of pixel removal therefore provides the priority ranking such that the lowest priority pixels are removed first. The calculation of the conservation value of each pixel is determined by the pixel-removal rule, which we selected to be additive across features so that the priority would be given to pixels of high quality that contributed to all types of connectivity (additive benefit function with z = 1; Moilanen 2007). Habitat quality and connectivity layers were all given equal weight in the analysis.
We compared this multipurpose conservation prioritization to three single-purpose prioritizations that were each based on a single criterion for connectivity. The input layers of the single-purpose priority rankings were habitat quality and one connectivity layer (dEC, betweenness or current density). Comparisons of these priority rankings assessed the spatial overlap of the highest priority areas (Moilanen et al. 2012).
Results
The zonation priority ranking was based on four input layers derived from habitat quality (Fig. 3 Panel C), spatial graph (Fig. 3 panels A and B) and circuit analyses (Fig. 3 Panel D). Habitat pixels in the four input layers were not strongly correlated (max Spearman's correlation was 0·26 between dEC and betweenness, Fig. S7.1). The spatial ranking of conservation priorities derived from these input layers (Fig. 3) highlights the most important areas for simultaneous conservation of these different types of connectivity (Fig. 4). It represents a hierarchy of solutions depending on what fraction of the landscape can be protected. For example, the top 12% of pixels in the landscape could be protected which would correspond to protecting 57% of the ovenbird habitat (Fig. 4). Highest conservation priority is given to a series of large stepping stone patches along a north-east/centre-west orientation. In the north-east corner, many small forest fragments are in close proximity to one another and the conservation value of this entire region is relatively high (comprising red, orange, yellow and light grey pixels; Fig. 4). The south-west region of the lowlands shows a similar pattern of conservation importance. These two regions are largely separated by an intensive agricultural zone with low conservation value (dark grey pixels; Fig. 4). However, many core areas of small forest fragments in this agriculturally intensive zone are of high conservation value (red and orange pixels) and some higher-ranked, non-habitat pixels are present (light grey pixels) in the form of distinct corridors between forest fragments or partial buffers oriented along entry and exit routes.
This ranking of map pixels in terms of their conservation priority represents spatial trade-offs between the different types of connectivity criteria for the study region. These trade-off curves show a pattern of diminishing returns (Fig. 5). Increased conservation of the traversability of the St. Lawrence Lowlands (measured by current density) results in increased intrapatch and interpatch connectivity (measured by dEC and betweenness), but beyond 35% (dEC) and 60% (betweenness), additional conservation of traversability only marginally increases dEC and betweenness. To conserve 35% of the traversability (current density) would require protecting 5% of the study area (24% of the ovenbird habitat) and would result in 83% and 60% of total dEC and betweenness being conserved, respectively (Fig. S8.1).
Comparisons among conservation priority rankings based on either one or all of the connectivity criteria show that the degree of agreement depends on what fraction of the ranking is considered (Figs 6 and S9.1). Relatively little overlap exists among the top ranked 1% and 5% of pixels (ALL < 15%; Fig. 6 Panels A and B); however, the majority of the priority areas overlap when considering the top ranked 12% of pixels (ALL > 50%; Fig. 6 Panel C). This indicates that the three types of connectivity rely on some of the same areas of the landscape but that the very best areas for maintaining each type are different. The priority ranking based on multiple connectivity criteria best aligns with the highest 1% of priorities for the dEC ranking and the highest 5% of priorities for the betweenness ranking. Alignment with the current density ranking was slightly lower because only the current density input layer had values in non-habitat pixels.
Discussion
Habitat networks have been useful in previous attempts to quantify multiple connectivity properties at several structural levels, from individual nodes up to whole-network properties (Rayfield, Fortin & Fall 2011). The innovation of our method is that it combines connectivity conservation approaches focused on interpatch connectivity within habitat networks and long-distance movements across habitat networks. We identify key patches for conservation where these conservation priorities intersect. The resulting multifunctional habitat networks will better integrate the needs of organisms residing within the network and those that rely on the network to displace and track changing environments.
Multiple dimensions of connectivity need to be included in conservation planning given the multifaceted (Ewers & Didham 2006) and multiscale (Reino et al. 2013) effects of habitat fragmentation on biodiversity (Haddad et al. 2015). We have demonstrated our conservation prioritization method based on a network model of short-range (intrapatch and interpatch) connectivity and a circuit model of long-range (traversability) connectivity, but other connectivity models could also be used. Indeed, any model that produces a raster of relative connectivity across the study area could be included in the conservation prioritization. The method is therefore able to incorporate future advances in connectivity modelling at different scales. For example, recent work has shown that simple individual-based models (Palmer, Coulon & Travis 2011) can predict genetic connectivity between pairs of habitat patches better than least-cost paths or circuit models (Coulon et al. 2015). Network-based estimates of short-range connectivity could be refined by using such individual-based models to calculate the strength of links (e.g. to replace the term 
in the calculation of EC; eq. 1 in Appendix S3). Prior to integrating individual-based and network models, however, it will be important to assess the sensitivity of network connectivity metrics, such as EC, to the underlying measure of link strength (Coulon et al. 2015). This will be especially important in a conservation planning context in order to justify additional resources required to parameterize the individual based model.
Our method can also be applied to conserve many other types of connectivity that can be represented in raster format (e.g. broadscale linkages between wild lands, connectivity between current and future suitable habitat, and connectivity between consumer and resource distributions). Different types of connectivity have been inherently defined in recent reviews of the many techniques available to model connectivity (Cushman et al. 2013; Kool, Moilanen & Treml 2013). By contrast, defining different types of movement has been an explicit and thorough undertaking that has resulted in key distinctions with regard to fitness and conservation implications (Clobert et al. 2001). For example, Jacobson & Peres-Neto (2010) differentiate among movement (home-range-scale relocations such as foraging), migration (population-scale, round-trip relocation) and dispersal (landscape-scale, unidirectional displacement) in terms of their effects on metacommunity dynamics. Further refinements of dispersal include natal dispersal (dispersal to the first breeding site), breeding dispersal (dispersal between subsequent breeding sites) and dispersal of sexually immature juveniles (i.e. post-fledging dispersal in birds; Desrochers & Hannon 1997). Connectivity patterns are also sensitive to the spatial scale of analysis (Urban & Keitt 2001). Multiscale connectivity analysis of landscape networks involves computing a connectivity metric over different spatial extents by constraining network distances (e.g. Van Looy et al. 2013). Scale-specific contributions of each habitat patch (or pixel) in the landscape can also be included in conservation priority rankings. Rayfield, Moilanen & Fortin (2009) provide an example of combining home-range- and juvenile-dispersal-scale connectivity with consumer–resource connectivity to identify spatial conservation priorities for American marten.
Multipurpose habitat networks help to avoid protecting one type or scale of connectivity at the expense of another. We found that 12% of the landscape needed to be protected in order for the majority of priority areas in the multipurpose priority ranking to overlap with priority rankings based on single types of connectivity. The degree of overlap will depend in part on the relative weights assigned to the connectivity input layers in the multi-objective conservation prioritization. We used equal weights for all input layers, but the method is flexible, allowing users to implement a different balance between them depending on the species and conservation goals. Further research into the population-level consequences of unequal weighting of short-range and long-range connectivity in conservation plans would complement recent efforts to determine optimal conservation strategies of migratory species (Martin et al. 2007). More broadly, exploring the sensitivity of the conservation prioritization to different weighting schemes would highlight which landscape elements are ranked with highest priority across weighting schemes.
We selected the ovenbird as a study species because its habitat preferences and dispersal abilities have been well-studied, a requirement of any scientifically sound connectivity analysis (Baguette et al. 2013). However, even in relatively well-studied species, the parameterization of detailed connectivity models is challenging. For example, while the resistance surface we used was based on field studies that controlled for dispersal motivation by translocating male ovenbirds from their territories during the breeding period (Desrochers et al. 2011), the gap-crossing estimate we used was based on radiotelemetry data from ovenbirds during the post-breeding period that may have been affected by different motivational factors (Bayne & Hobson 2001). Furthermore, the connectivity input layers used in our conservation prioritization were derived from two different connectivity models that were based on the same resistance surface: a landscape network model characterizing intrapatch and interpatch dispersal and a circuit model characterizing traversability across the landscape. In general, the same resistance surface, characterizing potential dispersal at a given point, can be used to generate multiple connectivity surfaces, characterizing potential dispersal along routes (Cushman, McKelvey & Schwartz 2008). However, species habitat preferences may not be the same during short- and long-range movements. For example, species may not select patches of breeding habitat when traversing a landscape during migration due to extrinsic factors such as weather patterns (Moore et al. 1995). If the contrasts between forest, edge and open areas had been decreased for the circuit model, as suggested by St-Louis et al. (2014), it may have resulted in even less congruence between pixels identified to be important by circuit and network connectivity models.
Our method focuses on identifying habitat fragments that maintain multiple connectivity features for conservation. We chose a single species approach here, but comprehensive biodiversity conservation necessitates simultaneously maintaining the requirements of multiple species (Nicholson & Possingham 2006). Developing spatial conservation priorities based on the connectivity requirements of multiple species (Breckheimer et al. 2014) is an obvious application of our method. Indeed, our prioritization of habitat patches for conservation could be extended to a prioritization of the intervening matrix if the traversability requirements of multiple forest-dwelling species were included. In the ovenbird example, only the current density map had coverage in non-forest pixels. While the current density map can guide conservation (Pelletier et al. 2014) and restoration (McRae et al. 2012) priorities on its own, the strength of our method is that it combines graph-based connectivity models with spatial conservation prioritization (Kukkala & Moilanen 2013). This allows us to go beyond conservation recommendations based on single descriptors of connectivity patterns (Carroll, McRae & Brookes 2012) or superpositions of individual species’ networks and linkages (Cushman & Landguth 2012; Baguette et al. 2013). Our spatial ranking of conservation priorities across the landscape could be used to simultaneously maximize the retention of connectivity criteria aggregated across all species. Using the outputs of graph-based connectivity models as inputs of spatial conservation prioritization provides a means to identify and optimize trade-offs among connectivity objectives and other conservation and socio-economic objectives. The computational power of zonation allows for prioritizations for tens of thousands of input layers (e.g. species distributions and connectivity layers) across landscapes with tens of millions of pixels (Arponen et al. 2012).
Conclusion
We addressed the need for simultaneously conserving multiple types of connectivity by bringing together the most recent methods in connectivity science and spatial conservation planning. Our approach identifies spatial conservation priorities that balance the requirements for short-range and long-range connectivity through spatially complex landscapes. The generality of our approach allows for the inclusion of different connectivity requirements for multiple focal species at a regional scale for networks with thousands of nodes and rasters with millions of pixels. Conserving the ability for species to move among habitat patches is increasingly important as climatic and land-use changes are forcing species to relocate or adapt to fragmented landscapes (Doerr, Barrett & Doerr 2011). Our method can provide a starting point for an integrated approach to connectivity conservation that can mitigate the consequences of poor landscape connectivity that translate into losses of biodiversity and an erosion of the ecosystem services that are essential for human well-being (Balvanera et al. 2014).
Acknowledgements
Our sincere thanks to Cécile Albert, Alan Dabrowski and Tyler Rudolph for stimulating discussions. This work was financially supported by the Ouranos Consortium, the Natural Science and Engineering Research Council of Canada (NSERC) and the Canada Research Chair in Biodiversity Science. Computations were made on the supercomputer Mammouth-série 2, Université de Sherbrooke, managed by Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI) and the Fonds de recherche du Québec – Nature et technologies (FRQ-NT).
Data accessibility
r scripts: uploaded as online supporting information (Appendix S4). Ovenbird landscape resistance raster, ovenbird habitat quality raster and St. Lawrence Lowlands Ecoregion raster: DRYAD entry doi: 10.5061/dryad.tc45g (Rayfield et al. 2015).
