Land cover change is the main cause of extinction in terrestrial habitats (Millennium Ecosystem Assessment 2005), raising the need for a theoretical framework to model the impacts of habitat fragmentation on natural populations. One central question refers to the ability of individuals to disperse in the landscape matrix between habitat patches. Here, we present a new software package (LORACS: Landscape Organization And Connectivity Survey) that integrates GIS maps of land use/land cover and habitat preferences to predict dispersal routes across the landscape matrix. Matrix permeability has been shown to impact animal dispersal with consequences for abundance (Ricketts 2001), genetic structure (McRae and Beier 2007, Braunisch et al. 2010), and diversity patterns (Lees and Peres 2009).
The availability of GIS tools and remote sensing products has allowed the application of least-cost paths (Adriaensen et al. 2003) to model animal movement in heterogeneous landscapes. This is implemented by representing study sites as a graph (Urban and Keitt 2001) and applying search algorithms (Dijkstra 1959) to identify optimum routes between two points. The least-cost path between two nodes s and t is defined as a unique set of nodes such that the sum of edge weights is minimized. Biologically, if edge weights correlate with relative movement costs (by capturing predation risk, foraging quality, or energy expenditure), the least-cost path comprises the collection of stepping stones most likely to be used by surviving individuals moving between s and t (Pinto and Keitt 2009).
Calibrating least-cost path models requires quantifying their sensitivity to assumptions about habitat preferences (‘subjective translation problem’, Beier et al. 2008) and land cover classification (or land cover change). Ultimately, model predictions also need to be validated with field data. However, the least-cost path algorithm in its original form does not lend itself to addressing these issues. Since only a single path is output, the researcher gets no uncertainty estimates associated with the paths’ cumulative cost or spatial distribution. Here, we tackled this problem by modifying Dijkstra's breath-first search algorithm (Cormen et al. 2001) to model multiple potential movement routes using the same basic assumptions of least-cost path models (Pinto and Keitt 2009). Our modified algorithm produces two maps: Multiple Shortest Paths (MSPs) and Cumulative Minimum Transit Cost (CMTC) maps. MSPs are obtained by making edge placement a probabilistic function that generates multiple realizations of the least-cost path. The CMTC for a given pixel p between two nodes s and t is defined as the cost-weighted distance to move from s to t, conditional on the route forming the shortest passage between s and t while passing through p (Pinto and Keitt 2009). CMTC maps have been employed to model potential dispersal corridors (Majka et al. 2007). Both algorithms have been implemented in LORACS, as described below.
LORACS is free, platform-independent JAVA software. The source code as well as executable binaries are distributed under the GNU license and downloadable from the website < http://purl.oclc.org/loracs >. The package includes a GUI interface (Fig. 1A), a documentation file, sample input files, and a complete API allowing for easy extension of the functions. User input is in the form of two simple ascii rasters: 1) a cost raster where the value at each pixel represents the relative cost to cross it in any direction; and 2) an st raster with the same dimension and resolution of the cost raster and marking the location of the source and target patches between which connectivity patterns are modeled. After selecting the input rasters, the next step is to choose the number of shortest paths (1–1000) and the percent corridor width (1–100) to be calculated.
LORACS outputs two ascii rasters (‘CMTC.asc’ and ‘MSPs.asc’) with the same dimension and resolution of the input cost raster. The program also prints a comma- delimited file (‘stats.csv’) containing the cumulative cost and the total length of each shortest path. Path length is output in the same distance unit input by the user, that is, the attribute ‘cell size’ in the header of the ascii file. To demonstrate the software, we use LORACS to model movement between pairs of conservation units in the Brazilian Atlantic Forest. We show how the distribution of cumulative costs associated with MSPs can be used to statistically compare matrix permeability before and after a fire event. The spatial uncertainty of predicted movement routes is examined as follows: 1) the CMTC map depicts a cost surface as opposed to a single path; 2) the MSPs map shows the number of times each pixel is selected as part of the least- cost path, thus revealing potential dispersal bottlenecks. Last, 3) the stats.csv file has the cumulative cost and length for each MSP path. Collectively, these represent an empirical distribution of least-cost paths that can be used to statistically compare landscape connectivity under different assumptions about matrix composition, habitat quality, and distribution.
We identified conservation units in Northern Minas Gerais (Fig. 1B) based on the World Database on Protected Areas (UNEP-WCMC 2009). The pre-fire cost raster for year 2005 was built to approximate the habitat preferences of a forest specialist: each pixel value was calculated as 100 minus percent tree cover (MODIS VCF, Hansen et al. 2006). Fires occurring during the 2006–2007 fire season were mapped using the MODIS Burned Areas product (Justice et al. 2002). The post-fire cost raster was built by assigning a value of 100 to all pixels identified as burned. We modeled the connectivity between two pairs of conservation units: Itambe-Sempre Vivas and Itambe-Mata Escura. For each st pair, we ran LORACS with the pre-fire and the post-fire cost rasters. We chose to obtain 100 MSPs and 20% corridor width.
The resulting maps were displayed in ArcGIS (ESRI, CA, USA). The CMTC maps for the pair Itambe-Sempre Vivas show potential corridors with high trasversability (= low CMTC values, shown in blue) in the center (Fig. 2A, B). The post-fire corridor (Fig. 2B) covers 12% fewer pixels because the burned area in the south increases the CMTC cost beyond the 20% threshold. The CMTC maps for the pair Itambe-Mata Escura illustrates how the route of least resistance can depart from a straight line (Fig. 3A, B). The post-fire corridor (Fig. 3B) covers 8% fewer pixels than the pre-fire corridor.
MSP maps for Itambe-Sempre vivas show two possible dispersal routes next to Itambe that merge into a single bottleneck in blue (Fig. 2C, D). The list of 100 values of path cost/length output by LORACS represents an empirical distribution of least-cost paths. The pre-fire and post-fire scenarios were compared with a t-test in R (R Development Core Team 2012) for each pair of conservation units. Forest fires led to significant differences in path cumulative cost and length for the pair Itambe-Mata Escura (p < 0.05; Fig. 3E) but not for Itambe-Sempre Vivas (p > 0.05; Fig. 2E).
Least-cost paths are widely applied in conservation initiatives (Larkin et al. 2004), but evaluating their usefulness as estimates of animal movement remains a challenge. Next, we list a few scenarios where LORACS could be used to address this issue.