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)?
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).
|Study||Variables included1||Source of cost scheme2||Source patches3||Adjacent habitat4||Cost value ranges||Validation||Sensitivity analysis||Path to corridor5|
|Beazley et al. 2005||Forest cover (3); road density||EO; L; HSI; S||All ‘suitable’ habitat patches (HSI)||No||Unknown||Presence/absence of dung||No||Minimum width|
|Chetkiewicz & Boyce 2009||LCT (5); subregion; food resources; terrain; road density||RSF; RT||High RSF value polygons||No||Inverse of RSF coefficients||Telemetry locations;||No||Buffered: 350 m|
|Cushman, McKelvey & Schwartz 2008||LCT (26); elevation; slope; roads||EO; L; G||Individual locations;||No||1–10||Genetic distance||No||Smoothed: 2500 m radius parabolic kernel|
|Driezen et al. 2007||LCT (12); roads; water||L; PS||Unknown||No||1–1000||Experimental dispersal data||Compared 12 sets of costs||No|
|Epps et al. 2007||Slope (2); distance; barriers||G; RT||MCP; suitable habitat; EO||No||0·1–1·0||Radio- telemetry data||Compared multiple gene flow measures||No|
|Hepcan et al. 2009||VT (12); road density||EO; L||‘Key Biodiversity Areas’||No||Unknown||No||No||Minimum width: 1 km|
|Joly, Morand & Cohas 2003||HT (7); roads; rivers||EO; L||Unknown||No||HT: 5–80; roads: 0–1||No||No||No|
|Kautz et al. 2006||LCT (16)||RT||HR and potential habitats (HSI)||No||LCT: 1–11; water: 15; road: 20||No||Partial: road and water||Post-analysis buffer|
|Kindall & Van Manen 2005||Forest cohesion, diversity, forest-agriculture edge density||Problem of occurrence model||50% fixed kernel HR||No||1–8||No||No||No|
|Kong et al. 2010||LUT (12)||EO||Urban green space >12 ha connected to areas outside city||No||0·1–50 000||No||No||No|
|Larkin et al. 2004||HT (5) based on suitability model||EO; L||‘Suitable’ habitat (EO)||No||1; 10; 50; 100||No||Two cost schemes||No|
|LaRue & Nielsen 2008||LCT (8); distance to road and water; slope, human population density||EO||Areas where cougar may be living (EO)||Distance to road and water||0·19–1·92||No||No||Buffered LCP by 1 km|
|Li et al. 2010||LCT (9), slope; dist to water and human activities (3)||EO||Panda occurrence or suitable habitat||Distance to human activities||Reciprocal suitability: 0·002–0·098||No||No||Smoothed: 90 m cumulative kernel|
|Meegan & Maehr 2002||HT (2); roads||EO; L; RT||forest patches ≥500 ha||No||1,2 or 3||presence locations||No||No|
|Osborn & Parker 2003||HSI (2); distance to river, roads, and settlements||EO||Individual locations||Distance to settlement and road||Unknown||No||No||No|
|Rabinowitz & Zeller 2010||LCT; % tree/shrub cover; elevation; distance to road and settlement; human population density||EO||Jaguar conservation units||Distance to road and settlement||Integers 0–10||field interviews on-going||No||Selected lowest 0·1% of grid cell values|
|Rouget et al. 2006||‘Suitability’ (foraging model)||Unknown||Unknown||No||0; 300; 600; 900||No||No||Buffered to 1 km|
|Schadt et al. 2002||LCT (5); roads||EO; L||‘Suitable’ habitat: size, isolation, and forest cover||No||1–1000||No||Partial: ‘matrix’||No|
|Shen et al. 2008||LC; bamboo cover; slope, elevation; aspect; distance to road and residential areas||EO||‘Core’ habitats based on LCT||Distance to residential area and road||1–50||No||Partial: land and bamboo cover||No|
|Singleton, Gaines & Lehmkuhl 2004||LCT (13); road density; human population density; slope||EO; L||Largest areas of low human influence with suitable LCT||No||0·1–1·0||No||No||Selected lowest 10% of cost surface|
|Stevens et al. 2006||LCT (6); water||Movement behaviour||Population MCP||No||3 Models: 1–10 000||Genetic dispersal rates||Compared multiple gene flow measures||No|
|Wang et al. 2008||NDVI; slope; aspect; distance to LCT||HSI on S||Individual locations||Distance to LUT||1–1 000||Presence; Gene flow||No||No|
|Wang, Savage & Shaffer 2009||VT (3)||EO; S||Breeding pair locations||No||1–10||Gene flow estimates||No||No|
|Wikramanayake et al. 2004||HT (3); elev.; LCT in buffer (5); patch size||EO; PS||Unknown||Distance to agriculture or population centre||1–25||No||No||Selected 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).