Cost distance of each pixel is the lowest possible cumulative resistance from that pixel to terminuses in each habitat block. A map of cost-distance always produces continuous swaths of permeable pixels; these swaths have been used as the basis for all published corridor designs. The most difficult issue is selecting a corridor width ('slice') wide enough to facilitate movement, but narrow enough to minimize monetary costs of conservation. We recommend a corridor slice wider than the home range width for corridor-dwellers, and various ad-hoc procedures for passage species.
As illustrated in the figure below, low resistance pixels may not form a continuous swath. To identify well-connected low-resistance pixels, all published corridor designs calculated each pixel's accumulative cost-distance as the lowest possible cumulative resistance from that pixel to terminuses in each habitat block. These cost-distance values do form continuous swaths, as illustrated in the next figure. In this figure, the pixels with the lowest cost-distance are shown in black, and progressively lighter colors represent progressively higher thresholds of cost-distance.
As the maximum cost-distance increases, the pixels with lowest cost-distance define a nested set of increasingly broad “slices” of the landscape. As the cost threshold increases from slice 1 to slice 3 to achieve minimum width, w, the modeled corridor becomes very wide in areas outside the bottleneck. As the cost threshold increases even more (slice 4) the modeled corridor gains additional strands.
Note that resistance or travel cost is an attribute of a pixel resulting from the pixel's internal characteristics, and is simply the inverse of the pixel's permeability or habitat suitability. In contrast, cost-distance (sometimes called effective distance or cost-weighted distance) is a pixel attribute resulting from the pixel's resistance plus the resistance of a chain of pixels reaching to each terminus. Thus in moving from resistance to cost-distance, you are moving from a single pixel's content to its landscape context.
The previous analytic steps produce a map of increasingly wide corridors displayed as nested polygons, each defined by the largest cost allowed in the polygon. Although a wider corridor is better in the sense that broad swaths include narrower ones, financial constraints favor smaller corridors. In multiple-species linkage designs, partial overlap among species corridors will tend to widen each single-species corridor, so the width needs only to be “about right” at this state. But still, you need a stopping rule to map each single-species corridor.
For a corridor dweller, one suggestion is that the corridor should be as wide as the species' typical home range. However, if the focal species is strongly territorial, this could result in corridors fully occupied by home ranges where social interactions impede movement through the corridor. Such social interactions probably led to the disturbing case of an occupied but non-functional corridor previously described. Overview of habitat modeling. Therefore we suggest that minimum width for a corridor dweller should be at least two home range widths along all or most of the length of the corridor.
Species able to move through a corridor in one or several days can doubtless pass through areas narrower than their typical home range. Like other corridor designers, we consider the biology of the focal species to recommend a reasonable minimum width. But a cost threshold that achieves a minimum width in a bottlenecked area may cause impractically broad swaths elsewhere (e.g. swath 4 in the figure above). Reasonable procedures include:
No matter what approach you adopt, choosing the right corridor slice is an iterative process of examining a series of slices and evaluating the advantages and disadvantages of moving to the next larger or smaller slice. An objective set of decision rules, and an automated way to run them, would be significant advances. However, given the myriad of possible landscape configurations and reasonable differences of opinion about when a corridor is “big enough,” this may be an impossible goal.
We see no excuse for using least cost paths instead of corridor swaths to define wildlife corridors. A least-cost path is only one pixel wide. Because it is easy to identify in GIS software, it is popular. But a pixel-wide path surrounded by otherwise inappropriate habitat is unlikely to be used, and would be biologically irrelevant. Furthermore, the location of a least cost path is highly sensitive to pixel size and errors in classifying single pixels. Finally, you would never recommend conservation of a pixel-wide path.