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Keywords:

  • animal movement;
  • connectivity;
  • corridor;
  • dispersal;
  • fragmentation;
  • linkage design;
  • model validation

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

1. The need to conserve and create linkages among fragmented habitats has given rise to a range of techniques for maximizing connectivity. Methods to identify optimal habitat linkages face trade-offs between constraints on model inputs and biological relevance of model outputs. Given the popularity of these methods and their central role in landscape planning, it is critical that they be reliable and robust.

2. The most popular method used to inform habitat linkage design, least-cost path (LCP) analysis, designates a landscape resistance surface based on hypothetical ‘costs’ that landscape components impose on species movement, and identifies paths that minimize cumulative costs between locations.

3. While LCP analysis represents a valuable method for conservation planning, its current application has several weaknesses. Here, we review LCP analysis and identify shortcomings of its current application that decrease biological relevance and conservation utility. We examine trends in published LCP analyses, demonstrate the implications of methodological choices with our own LCP analysis for bighorn sheep Ovis canadensis nelsoni, and point to future directions in cost modelling.

4. Our review highlights three weaknesses common in recent LCP analyses. First, LCP models typically rely on remotely sensed habitat maps, but few studies assess whether such maps are suitable proxies for factors affecting animal movement or consider the effects of adjacent habitats. Secondly, many studies use expert opinion to assign costs associated with landscape features, yet few validate these costs with empirical data or assess model sensitivity to errors in cost assignment. Thirdly, studies that consider multiple, alternative movement paths often propose width or length requirements for linkages without justification.

5.Synthesis and applications. LCP modelling and similar approaches to linkage design guide connectivity planning, yet often lack a biological or empirical foundation. Ecologists must clarify the biological processes on which resistance values are based, explicitly justify cost schemes and scale (grain) of analysis, evaluate the effects of landscape context and sensitivity to cost schemes, and strive to optimize cost schemes with empirical data. Research relating species’ fine-grain habitat use to movement across broad extents is desperately needed, as are methods to determine biologically relevant length and width restrictions for linkages.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Habitat fragmentation and isolation have long been considered among the greatest threats to the persistence of species (Karieva 1987; Quinn & Harrison 1988). Fragmentation increases a species’ risk of extinction from inbreeding and genetic and demographic stochasticity (Wilcox & Murphy 1985; Mills & Smouse 1994), and limits the ability of populations to move in response to perturbations (e.g. harvest, habitat degradation or disturbance). The effects of fragmentation on dispersal and colonization, in particular, have received increasing attention as planners attempt to predict the response of species to climate change (e.g. Thomas et al. 2004; McLachlan, Hellmann & Schwartz 2007). Efforts to mitigate the impacts of habitat fragmentation by preventing or reversing population isolation are encompassed within the growing field of connectivity conservation (Crooks & Sanjayan 2006).

Promoting connectivity, the movement of species or genes between habitats, alleviates problems associated with habitat fragmentation (Crooks & Sanjayan 2006). Most efforts to conserve connectivity rely on the creation or protection of habitat linkages; i.e. land that promotes movement or dispersal of plants or animals between core habitats (Briers 2002; Beier, Majka & Spencer 2008; Fig. 1). However, while researchers generally agree that maintaining connectivity is essential to the persistence of fragmented subpopulations, they often disagree on the process by which linkages are designed for conservation (Rothley 2005). Although placement of linkages/corridors based on empirical observations of dispersal movement may be the most reliable method for designing connectivity networks (Hilty & Merenlender 2004; Graves et al. 2007) such data are sparse or non-existent for most species and most locations (Fagan & Calabrese 2006). As a result, conservation relies heavily on models of connectivity that may have little empirical basis. Conservation planners are faced with a critical question: will such models improve placement of linkages/corridors by explicitly incorporating habitat effects on movement, or will they result in misleading and potentially costly recommendations for conservation by concealing invalidated assumptions (Chetkiewicz, St. Clair & Boyce 2006)?

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Figure 1.  Introduction to important questions, steps and definitions for least-cost path modelling.

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In this review, we evaluate the current use, strengths and weaknesses of least-cost path (LCP) analysis (Fig. 1; see Appendix S3 in Supporting information for a discussion of current LCP terminology), the most widely used modelling approach for design of habitat linkages (LaRue & Nielsen 2008; Phillips, Williams & Midgley 2008). We focus on applications of LCP analysis in which a single path or corridor is identified for placement between pairs of source patches. A detailed description of the steps involved in LCP analysis is provided in Figure 1. In short, LCP analysis evaluates potential animal movement routes across the landscape based on the cumulative ‘cost’ of movement (Chetkiewicz & Boyce 2009). Resistance of each landscape unit (usually a grid cell on a raster map) is intended to represent the sum of hypothetical energetic expenditures, mortality risks, or other facilitating or hindering effects of landscape elements on movement within the cell (Adriaensen et al. 2003; Fig. 1). In practice, resistance values in LCP models are usually assigned on an arbitrary scale meant to reflect ‘high’ or ‘low’ suitability (with respect to movement) of different landscape factors (e.g. land cover, human activity, etc.). Resistance values for each factor are weighted according to their perceived importance and combined (e.g. by geometric mean) to produce a single resistance value. We call this series of choices the ‘cost scheme’. The ‘effective distance’, or cost of a path between habitat patches for a species, is the Euclidian distance weighted by the cumulative resistance values of all cells traversed (Adriaensen et al. 2003; Beier, Majka & Spencer 2008; Fig. 1). The LCP is the combination of cells that minimizes effective distance between two patches (Verbeylen et al. 2003) and is used to inform optimal placement of a linkage (Fig. 1).

Least-cost path analysis is an attractive technique for analysing and designing habitat corridors because it: (i) allows quantitative comparisons of potential movement routes over large study areas, (ii) can incorporate simple or complex models of habitat effects on movement and (iii) offers the potential to escape the limitations of analyses based solely on structural connectivity (i.e. designating areas simply as ‘patch’, ‘matrix’ or ‘corridor’) by modelling connectivity as it might be perceived by a species on a landscape (‘functional connectivity’; Taylor, Fahrig & With 2006). However, as with any modelling approach, the effectiveness of LCP analysis is limited by the quality of input data. For instance, modellers often use expert opinion to assign resistance values to remotely sensed landscape traits (e.g. Adriaensen et al. 2003; see Fig. 1 & Table 1). Thus, the accuracy and value of these models depends on how strongly these coarse-grain habitat proxies and their assumed resistances correlate with actual habitat use/movement by focal species (Calabrese & Fagan 2004; Beier, Majka & Spencer 2008). Methods for defining habitat patches are often unclear or based largely on human rather than animal perception of habitats (Theobald 2006). In worst-case scenarios, LCP analyses are little more than subjective interpretations of coarse habitat maps, but the method has potential for much more. For example, ideal applications of LCP analysis would employ organism-centric approaches in which practitioners use species- and landscape-specific empirical data to quantify behavioural responses to finer-grain habitat elements (e.g. distribution of critical resources, escape cover and threats), to: (i) consider attributes of surrounding cells when assessing resistance of a cell and (ii) assess the likelihood of use for a path of known width and length (Adriaensen et al. 2003; Theobald 2006; Graves et al. 2007). While a challenging standard, such organism-centric approaches have the potential to reduce researcher bias and increase the replicability, defensibility and transparency of LCP and related analyses (Chetkiewicz & Boyce 2009).

Table 1.   Summary of recent studies that used least-cost path (LCP) modelling for habitat connectivity design (see Table S1 in Supporting Information for a more complete summary)
StudyVariables included1Source of cost scheme2Source patches3Adjacent habitat4Cost value rangesValidationSensitivity analysisPath to corridor5
  1. 1LCT, land cover type; LUT, land use type; HT, habitat type; VT, vegetation type; NDVI, Normalized Difference Vegetation Index. Number of cover/type categories is indicated in parentheses.

  2. 2L, literature; EO, expert opinion; RT, radiotelemetry; G, genetics; S, species presence locations; PS, previous studies HSI, habitat Suitability Index; RSF, resource selection function.

  3. 3HR, home range; MCP, minimum convex polygon.

  4. 4Did study consider adjacent habitat characteristics when determining resistance of cell?

  5. 5Did study go beyond least-cost path (LCP) to make a more biologically relevant recommendation, or least-cost corridor (LCC)?

Beazley et al. 2005Forest cover (3); road densityEO; L; HSI; SAll ‘suitable’ habitat patches (HSI)NoUnknownPresence/absence of dungNoMinimum width
Chetkiewicz & Boyce 2009LCT (5); subregion; food resources; terrain; road densityRSF; RTHigh RSF value polygonsNoInverse of RSF coefficientsTelemetry locations;NoBuffered: 350 m
Cushman, McKelvey & Schwartz 2008LCT (26); elevation; slope; roadsEO; L; GIndividual locations;No1–10Genetic distanceNoSmoothed: 2500 m radius parabolic kernel
Driezen et al. 2007LCT (12); roads; waterL; PSUnknownNo1–1000Experimental dispersal dataCompared 12 sets of costsNo
Epps et al. 2007Slope (2); distance; barriersG; RTMCP; suitable habitat; EONo0·1–1·0Radio- telemetry dataCompared multiple gene flow measuresNo
Hepcan et al. 2009VT (12); road densityEO; L‘Key Biodiversity Areas’NoUnknownNoNoMinimum width: 1 km
Joly, Morand & Cohas 2003HT (7); roads; riversEO; LUnknownNoHT: 5–80; roads: 0–1NoNoNo
Kautz et al. 2006LCT (16)RTHR and potential habitats (HSI)NoLCT: 1–11; water: 15; road: 20NoPartial: road and waterPost-analysis buffer
Kindall & Van Manen 2005Forest cohesion, diversity, forest-agriculture edge densityProblem of occurrence model50% fixed kernel HRNo1–8NoNoNo
Kong et al. 2010LUT (12)EOUrban green space >12 ha connected to areas outside cityNo0·1–50 000NoNoNo
Larkin et al. 2004HT (5) based on suitability modelEO; L‘Suitable’ habitat (EO)No1; 10; 50; 100NoTwo cost schemesNo
LaRue & Nielsen 2008LCT (8); distance to road and water; slope, human population densityEOAreas where cougar may be living (EO)Distance to road and water0·19–1·92NoNoBuffered LCP by 1 km
Li et al. 2010LCT (9), slope; dist to water and human activities (3)EOPanda occurrence or suitable habitatDistance to human activitiesReciprocal suitability: 0·002–0·098NoNoSmoothed: 90 m cumulative kernel
Meegan & Maehr 2002HT (2); roadsEO; L; RTforest patches ≥500 haNo1,2 or 3presence locationsNoNo
Osborn & Parker 2003HSI (2); distance to river, roads, and settlementsEOIndividual locationsDistance to settlement and roadUnknownNoNoNo
Rabinowitz & Zeller 2010LCT; % tree/shrub cover; elevation; distance to road and settlement; human population densityEOJaguar conservation unitsDistance to road and settlementIntegers 0–10field interviews on-goingNoSelected lowest 0·1% of grid cell values
Rouget et al. 2006‘Suitability’ (foraging model)UnknownUnknownNo0; 300; 600; 900NoNoBuffered to 1 km
Schadt et al. 2002LCT (5); roadsEO; L‘Suitable’ habitat: size, isolation, and forest coverNo1–1000NoPartial: ‘matrix’No
Shen et al. 2008LC; bamboo cover; slope, elevation; aspect; distance to road and residential areasEO‘Core’ habitats based on LCTDistance to residential area and road1–50NoPartial: land and bamboo coverNo
Singleton, Gaines & Lehmkuhl 2004LCT (13); road density; human population density; slopeEO; LLargest areas of low human influence with suitable LCTNo0·1–1·0NoNoSelected lowest 10% of cost surface
Stevens et al. 2006LCT (6); waterMovement behaviourPopulation MCPNo3 Models: 1–10 000Genetic dispersal ratesCompared multiple gene flow measuresNo
Wang et al. 2008NDVI; slope; aspect; distance to LCTHSI on SIndividual locationsDistance to LUT1–1 000Presence; Gene flowNoNo
Wang, Savage & Shaffer 2009VT (3)EO; SBreeding pair locationsNo1–10Gene flow estimatesNoNo
Wikramanayake et al. 2004HT (3); elev.; LCT in buffer (5); patch sizeEO; PSUnknownDistance to agriculture or population centre1–25NoNoSelected 10, 20 and 30% of lowest cost cells

In reviewing the use and application of LCP approaches we set out to address the following questions: (i) do recent studies employing LCP analysis shift emphasis from structural towards functional connectivity by considering species-specific behaviours and do they provide explicit, empirically derived justification for their choices? (ii) do researchers using LCP analysis attempt sensitivity analysis, model validation or compare multiple model outputs to assess the robustness of their projections? and (iii) how have researchers translated LCP model outputs into optimal linkage or corridor placement for their study areas?

Finally, to demonstrate the challenges of LCP analyses and highlight the sensitivity of LCP model outputs to input data, we present a case study in which we conduct an LCP analysis for desert bighorn sheep Ovis canadensis nelsoni (Merriam 1897) in southern California. We use our LCP analysis between two bighorn populations to examine congruence of outputs from two commonly used techniques for assigning cost schemes (expert opinion and gene flow optimization; see Figs. 1 and 2) and two scales of habitat suitability assessment (regionally-significant topographic/anthropogenic variables and locally-specific habitat traits).

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Figure 2.  A comparison of four least-cost path models between two bighorn sheep populations in southern California highlights the sensitivity of results to model inputs. Cost surfaces used to produce the four paths incorporate the following landscape characteristics: topography alone (Optimized model); wooded habitat alone (Incomplete model); topography, habitat and road density (Expert model); or topography, wooded habitat and urban areas (Optimized Local model). Total least-cost path length overlapped less than 2%; least-cost corridors based on the lowest 10% of the resistance surface overlapped from 0 to 44%.

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Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Selection of papers

We limited our analytical review to studies with the stated aim of designing optimal connectivity strategies for focal species. We performed a search in ISI Web of Knowledge (ISI 2010) using the following search terms: least-cost OR cost-distance OR least-cost path OR least-cost-path AND connectivity OR corridor OR linkage OR conservation. To reflect current trends in the peer reviewed literature, we restricted our search to 373 studies published between 2002 and 2010. We then refined the list to the subject areas Biodiversity and Conservation, Environmental Sciences and Ecology, and Genetics and Heredity, which reduced our pool to 135 results. We then further restricted our review to publications with the following keywords in the study abstract: identify OR predict OR model OR delineate OR place OR validate OR draw AND linkage OR corridor OR optimal connection OR key connectivity area OR migration zone. We excluded studies that used LCP analysis solely to predict occupancy, model species distributions (e.g. Verbeylen et al. 2003; Magle, Theobald & Crooks 2009), explain gene flow (e.g. Vignieri 2005) or predict how landscape changes might affect focal species (e.g. Graham 2001) if they did not explicitly aim to design or evaluate linkages. Finally, for each study that met our criteria for inclusion, we evaluated the following methodological choices: type of habitat data, choice of grain (cell size) and study extent, determination of cost schemes and source patches, consideration of effects of adjacent habitat, exploration of different resistance values, sensitivity analysis for other modelling choices and conversion of a ‘path’ to a ‘corridor’.

Bighorn sheep case study

To test the sensitivity of LCP model outputs to input data, we compared two LCP models published for bighorn sheep populations in the Mojave Desert of California (Epps et al. 2007; Penrod et al. 2008), and two additional LCP models based on modifications of those published models. We chose two populations, San Gorgonio and Cushenbury, that exhibit clear evidence of connectivity in the recent past (Epps et al. 2010).

The ‘Expert’ model (Penrod et al. 2008) was based on a linkage design for nearby Joshua Tree National Park. The Expert model estimated resistance values using expert opinion and included dense woody vegetation as determined from the California Wildlife Habitat Relationship vegetation type (Mayer & Laudenslayer 1988). Areas of flat topography, urban areas and areas with high road density were all defined as highly resistant (up to 10 times more than the best habitat). The final combined model was calculated as:

  • image

where topography, habitat and road density were assigned resistances between 1 and 10, as specified by Penrod et al. (2008, pp. 7–10).

The ‘Optimized’ model (Epps et al. 2007; Appendix S1 Supporting information) considered only topography and optimized resistance values using observed gene flow among populations over the entire study area, including those in our case study:

  • image

where areas with >15% slope and <15% slope were assigned resistances of 1 and 10 respectively.

Epps et al. (2007) recognized that their model was optimized for the southern California population as a whole, and would not account for locally specific habitat variables, such as the large amount of wooded habitat in the vicinity of the San Gorgonio and Cushenbury populations. Bighorn sheep typically avoid wooded habitat, presumably because of higher predation risk (e.g. DeCesare & Pletscher 2006). Therefore, we developed a third model (‘Optimized Local’) that added high resistance for any urban area (10 times higher) or wooded area (10 times higher) and calculated the final model as:

  • image

where areas with >15% and <15% slopes were assigned resistances of 1 and 10, respectively, wooded habitat was assigned a cost of 10, and urban habitat was assigned a cost of 10. Non-wooded and non-urban areas were assigned a cost of 1.

Finally, to simulate the common situation where little is known about dispersal, we constructed a fourth model (‘Incomplete’) that was biologically relevant but omitted several important factors:

  • image

where areas with and without tree cover were assigned a cost of 10 and 1 respectively.

All input grids were re-sampled to 100 m resolution before combining into final cost grids. We calculated a single LCP for each model using Pathmatrix (Ray 2005). We used ArcMap and CorridorDesigner (http://www.corridordesign.org/) to generate ‘least-cost corridors’ (Beier, Majka & Newell 2009; Fig. 1) representing the lowest 10% of possible least-cost paths for each model and estimated the area of overlap of those least-cost corridors.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Literature review

Twenty-four studies met our criteria for review. Each of the 24 used remotely-sensed land cover or habitat type as a proxy for habitat suitability and movement of focal species (Table 1). Study extent ranged from 10 to 4 000 000 km2; and study grain (cell size) varied from 1 to 1 km2 but most commonly corresponded with the grain of freely available Landsat imagery (900 m2; see Table S1 in Supporting information for a complete summary of reviewed studies’ methodological choices). Two studies distinguished only two types of habitat while all others included at least three habitat categories (Table 1). None of the 24 studies directly considered more organism-centric measures of microhabitat suitability, including those identified by authors as affecting animal habitat selection/movement, such as percentage habitat cover or distribution of food (Binzenhofer et al. 2005), presence of nutrient sources such as salt licks (Beazley et al. 2005), denning/nesting habitats (Singleton, Gaines & Lehmkuhl 2004), prey availability (Rabinowitz & Zeller 2010) or cover or escape terrain for predator avoidance (Wang et al. 2008). While some studies stated that habitat types serve as reliable proxies for predator presence and/or abundance of preferred foods (e.g. Driezen et al. 2007; Shen et al. 2008), no studies validated this assumption or included habitat distribution models of either predator or prey species.

Fourteen of the 24 studies evaluated in our review based their LCP analysis cost schemes (Fig. 1) on expert opinion, published literature, or both, although explanations of cost surface derivation were often lacking in sufficient detail to replicate analyses (Table 1). Of those, only three attempted to systematically and objectively translate expert opinion into cost schemes [e.g. using analytic hierarchy process or similar approaches (Banaikashani 1989; see Table S1 Supporting information)]. Six studies used telemetry or trapping (presence) data to designate costs. Three studies used relative gene flow, or combined gene flow and telemetry data, and two studies assigned resistance values using behavioural data from focal species. Across the surveyed studies, source habitat patches were variably defined as ‘known population/individual locations’ (10 studies), habitat deemed most ‘suitable’ by size, habitat type, or both (nine studies), or ‘key conservation areas’ (one study). Four studies did not define their source patches (Table 1). Eight studies included some effect of surrounding habitat in their cost designation (Table 1). Six studies partially based pixel cost on distance to particular habitat types or human activities. Kindall & Van Manen (2005) included forest/agriculture edge density in their cost measures while Wikramanayake et al. (2004) considered all areas within 1 km of agriculture or population centres to be ‘poor habitat’, regardless of habitat type.

Only four studies (17%) quantitatively assessed sensitivity of model-selected paths to different cost schemes for all variables, and these four consistently found their model outputs to be highly sensitive to input decisions (Table 1). Larkin et al. (2004) found overlap of only 0–51% among paths generated using different cost schemes. Stevens et al. (2006) and Epps et al. (2007) used multiple measures of gene flow to test LCP models and discovered that models were highly sensitive to different resistance values. Driezen et al. (2007) showed that the measurement of a species’ ability to find low-cost sites depends heavily on the cost scheme used. Three other studies conducted partial sensitivity analysis: Schadt et al. (2002) found that changing resistance values of the matrix led to significantly different LCPs while Shen et al. (2008) discovered high model sensitivity to costs of bamboo and land cover. Kautz et al. (2006) did not detect model sensitivity to costs of roads and water. Only nine of the 24 studies attempted some form of model validation in the published results (Table 1). Four studies examined relative support for cost schemes based on gene flow. Four studies used presence data (telemetry or trapping) to validate their models, while one used presence and absence data (Beazley et al. 2005).

Only 10 of the 24 studies we evaluated attempted to move beyond a single-pixel wide path to consider more biologically relevant (Majka, Jenness & Beier 2007) least-cost corridors (LCC; see Fig. 1) either by including minimum acceptable widths, buffering paths or selecting a percentage of least-cost cells (Table 1). Two studies included a minimum acceptable width cut-off. Kautz et al. (2006) found that one-pixel wide paths can go through extremely unsuitable habitat, and therefore buffered LCPs and rejected paths that passed through poor-quality habitat types. Four additional studies buffered their LCPs to make them wider. Three studies took a percentage of lowest grid cell values to make a least-cost corridor. However, empirical justifications for most of these analytical choices, such as buffer width, were not presented when defining LCCs.

Case study: LCP analysis of bighorn sheep

The four LCP models compared in our analysis of two populations of desert bighorn sheep produced LCPs that varied widely in location and length (Fig. 2). Along-path distances for the four paths were 34·6 km (Expert), 21·6 km (Optimized), 31·7 km (Optimized Local) and 28·5 km (Incomplete); those paths overlapped <2% of total length (Fig. 2). Least-cost corridors overlapped from 0 to 44% (average 13%; Table 2).

Table 2.   Percentage overlap of least-cost corridors based on four connectivity models between two bighorn sheep populations
ModelIncomplete (%)Expert (%)Optimized (%)
Expert0
Optimized544
Optimized Local3000

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Literature review

Although LCP modelling has been touted as combining detailed geographical information with animal behaviour to move beyond structural towards functional connectivity analysis (Adriaensen et al. 2003; Theobald 2006), our review suggests current LCP model implementation often ignores factors that affect how animals utilize landscapes. Nearly, all recent LCP analysis-based studies employed coarse-grain environmental data layers to determine habitat connectivity, an approach that is often biased by researcher-perceived structural connectivity and runs the risk of missing important biological aspects of species’ connectivity (Mortelliti & Boitani 2008). For instance, although scale of analysis has been shown to greatly impact strength of detected relationships, study grain was typically dictated by freely available remotely sensed data (see Table S1 Supporting information) rather than species perceptions of landscape features (Cushman & Lewis 2010; see Appendix S2 in Supporting information for recommendations on improving application of LCP analysis).

Overall, the strength of the correlation between remotely-sensed habitat layers and species’ movement is relatively unknown and poorly validated (Chetkiewicz, St. Clair & Boyce 2006; Beier, Majka & Spencer 2008). Our analysis in no way rejects the utility of coarse proxy data, especially given the need to model movement over large landscapes, but illustrates the need to explore effects of scale, explicitly justify choice of scale, and conduct model sensitivity and validation (see Appendix S2 Supporting information). In many cases, remotely-sensed proxies may provide adequate coverage at limited cost, and may prove to be efficient for conservation planning in the face of limited time and funding [e.g. fishers (Martes pennanti): Caroll, Zielinski & Noss 1999; large carnivores: Schadt et al. 2002; bighorn sheep: Epps et al. 2007]. However, animals frequently select high-quality microhabitats in areas that appear unsuitable at a macro-level (Mortelliti & Boitani 2008). Animals often select against low quality habitat within largely suitable areas as well, and accounting for the presence of low quality habitat within otherwise high-quality habitat patches may significantly improve model predictions (e.g. Wang et al. 2008).

We suggest that those using LCP analysis should strive to evaluate the predictive power of coarse-grain proxies for focal species movement over a portion of the study range before constructing analytical models (see Appendix S2 Supporting information). For species and linkages above the scale of rapid dispersal movements, using resource selection function models (RSF) with LCP analysis appears to be a step forward from more arbitrary methods (e.g. Chetkiewicz & Boyce 2009). Hypothesis testing and model selection that compares critical scales of habitat use or movement for taxa will help to build a stronger foundation for linkage-design methodology. Better understanding of a species’ perception of its environment will help modellers to identify appropriate scales of analysis and, thus, provide more reliable and accurate model outputs for practitioners (With, Gardner & Turner 1997; Uezu, Metzger & Vielliard 2005; Cushman & Lewis 2010).

LCP analysis of bighorn sheep

Our LCP analysis of bighorn sheep in California demonstrated many of the challenges and uncertainties we highlight above. The four models used to identify LPCs for desert bighorn sheep were derived at different scales (e.g. metapopulation vs. population level) and yielded very different paths (Fig. 2). Use of 10% least-cost corridors for each scheme did little to reduce differences between the models (Fig. 2, Table 2). For instance, the corridor suggested by the Optimized model (developed over a much larger geographic area) did not overlap with the Optimized Local model, which included wooded and urban habitat (Fig. 2). The Optimized model only partly overlapped the Expert model corridor, which was based only on coarse habitat maps and expert opinion (Fig. 2). This case study makes clear that reasonable alternative models can lead to strikingly different conclusions regarding prioritization of land acquisition, easements or other management actions for linkage conservation.

How can we improve LCP modelling?

Organisms respond differently to landscape elements depending on their perceptive range and characteristics of surrounding areas (Coulon et al. 2008; Richard & Armstrong 2010). Species’ movements in one habitat type will often be affected by nearby disturbances such as man-made structures and light pollution (Beier 1995; Coulon et al. 2008), width of habitats (Laurance & Laurance 1999; Hilty & Merenlender 2004), traits of and distance to adjacent habitat (Binzenhofer et al. 2005; Anderson, Rowcliffe & Cowlishaw 2007; Richard & Armstrong 2010), and level of perceived cover and safety (Rizkalla & Swihart 2007; Beier, Majka & Spencer 2008). However, only 2 of 24 studies in this review were able to validate their model with behavioural data (Stevens et al. 2006; Driezen et al. 2007). Given the sensitivity of least-cost models to incorrect resistance specification, the best way to evaluate model performance would be comparison of predictions based on multiple methods and independent data sets (e.g. radiotelemetry movement data and landscape genetics: Cushman & Lewis 2010). Testing the role of individual behaviour, preference and perceptual range in habitat selection or movement decisions (e.g. radio or global positioning system tracking: Beier 1995; Cushman, Chase & Griffin 2010; Driezen et al. 2007; Richard & Armstrong 2010; experimental data: Stevens et al. 2006; Hadley & Betts 2010) and using model selection to better integrate these behavioural with ecological and landscape data will greatly improve connectivity design (see Appendix S2 Supporting information).

Determining the relationship between movement or gene flow and effective distance under a given cost scheme, and thus the maximum effective distance at which a corridor is useable by a given species, may be the most biologically important and widely ignored aspect of LCP and other connectivity analyses. Even the best-supported paths will not function as planned if their lengths exceed the movement capability of a focal species. For example, gene flow estimates (Epps et al. 2005, 2007) suggest that in our bighorn sheep example, only the corridors produced by the Optimized and Incomplete models would serve a connective function (21·6 and 28·5 km along-path lengths respectively) while the Expert and Optimized Local models would result in corridors too long to promote connectivity (35 and 31·7 km respectively). Yet, only two studies reviewed here (Schadt et al. 2002; Singleton, Gaines & Lehmkuhl 2004) considered cut-offs for maximum useable effective distance (the greatest effective distance a species can travel between patches) based on knowledge of species dispersal. One study used gene flow estimates to determine maximum effective distance (Epps et al. 2007; Appendix S1 Supporting information). We recommend that wherever possible, defensible estimates of maximum useable effective distance should be developed by analysing genetic or movement data as functions of effective distance (see Appendix S2 Supporting information). An alternative approach is to define resistance more explicitly in terms of biological parameters, such as mortality risk or energy expenditure based on demographic, diet or metabolic data, and use movement models based on those parameters to explore modelling choices (see Chetkiewicz, St. Clair & Boyce 2006). In general, a more explicit discussion of resistance in each study would improve linkage design and interpretation. For instance, does the resistance value used in an LCP analysis reflect the physical costs of moving through a cell, its mortality risk, or habitat value? Each definition may be defensible depending on the goals and scale of analysis, but each will have different implications, especially when considering maximum path lengths.

Individual animals rarely use a single optimum route, and single-pixel-wide LCPs are of limited biological value (Majka, Jenness & Beier 2007; McRae & Beier 2007; McRae et al. 2008; Pinto & Keitt 2009). Although alternative paths with comparable costs may exist on a landscape, studies regularly failed to consider larger swaths of low-cost grid cells (i.e. a least-cost corridor). Recently, circuit theory has been used to incorporate multiple pathways and patch characteristics when evaluating connectivity designs (McRae & Beier 2007; McRae et al. 2008). This method allows modelling alternative linkages, ranking potential corridors and reassigning values as pathways are removed (Fig. 1; see Appendix S2 Supporting information), but it is equally reliant on a biologically realistic resistance surface. Alternatively, researchers can select lowest percentiles of cost surfaces (Beier, Majka & Newell 2009; this study Fig. 2) or combine multiple low-cost routes in an LCP analysis to delineate ‘probable movement zones’ (Rayfield, Fortin & Fall 2010; see Appendix S2). While these alternatives may increase robustness to uncertainty in model parameters, selection of a percentile cut-off (e.g. lowest 10%) or combining a number of low-cost routes is still a subjective decision with unclear biological justification. Some of the techniques we describe above for optimizing or validating models of effective distance should also be applied to this problem.

Few studies examined in this review conducted sensitivity or uncertainty analyses, which are essential to the landscape planning process and should be a requirement of any LCP or related connectivity model (Beier, Majka & Newell 2009; Rayfield, Fortin & Fall 2010). Studies that conducted sensitivity analyses (Table 1) found that different cost schemes (both choice of factors incorporated in the resistance surface, as well as the weights and resistance values assigned) produced very different LCPs, although Beier, Majka & Newell (2009) found their models robust to uncertainty. Indeed, Beier, Majka & Newell (2009) methods for evaluating uncertainty should prove useful where data for optimizing cost schemes are sparse (see Appendix S2 Supporting information). Sensitivity to the choice of habitat factors, factor weights, resistance values, grain and definitions of least-cost corridors should all be considered (see Appendix S2 Supporting information). Our LCP analysis for desert bighorn sheep highlights the disparity of LCPs based on expert opinion, gene flow optimization models, and other reasonable combinations, as well as the point that models optimized over large areas may still need local modifications. Researchers should strive for replicability, objectivity and organism-centred methodology to improve efficacy of LCP and other models in connectivity conservation planning (see Appendix S2 Supporting information). To avoid accusations of ‘black-box’ modelling (e.g. Shrader-Frechette 2004), studies must clearly address details of model construction, assumptions and uncertainties. Through these improvements, connectivity science will more ably inform landscape planning.

Least-cost path analysis and other connectivity conservation approaches should be viewed as one piece of a larger landscape conservation puzzle. Least-cost modelling cannot fully incorporate quality, size or importance of individual source patches, thus, it is best applied as part of a wider conservation strategy for focal species. A current debate questions whether connectivity conservation strategies like LCP analysis bear consideration in conservation planning, or simply detract focus from more certain measures to protect high-quality breeding habitats (Doerr, Barrett & Doerr 2011; Hodgson et al. 2011). This debate promotes a dichotomy between high-quality breeding habitat and habitats designated for connectivity that may represent an overly simplistic view of connective habitats. Regardless, recent summaries (e.g. McLachlan, Hellmann & Schwartz 2007; Hodgson et al. 2011) emphasise that conservation of diverse and connected habitat mosaics is likely to be the safest approach for sustaining species on our rapidly changing planet.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

We thank C. Kremen, P. Beier, T. Bean, three anonymous referees and students of ESPM 277 for helping to inspire and improve the original concept for this review. This work was supported in part by NSF-IOS 0818185 to JSB. SS also was supported by a Chancellor’s Fellowship from the University of California Berkeley.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Appendix S1. Background information for the desert bighorn sheep case study on LCP methods.

Appendix S2. Recommendations for effective LCP analysis.

Appendix S3. A note on variation in least cost terminology.

Table S1. Complete summary of recent studies that used least-cost path (LCP) modelling for habitat connectivity design.

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