Finding Analytical Corridors in Artificial Landscapes using "Walkers" - Preliminary Results
William W. Hargrove and Forrest M. Hoffman
Two simple patches of habitat, separated by a homogeneous matrix. Top image shows that a vertical corridor connects them. Below that, image B shows that both habitat patches are equal in terms of source importance (B) and sink importance (C). Image D shows collective footprints of walkers dispersing from the patch at the top of the map, while image E shows footprints of walkers dispersing from the bottom patch. Images F through K show the footprint tracks of individual successfully dispersing walkers.
If we add a sort of backstop or wing behind the bottom habitat patch which acts as a barrier to walkers, it broadens the corridor at the bottom. Both patches are still equivalent in terms of source importance and sink importance.
Adding concentrator wings behind both top and bottom habitat patches broadens the corridor between them even more, without altering relative source or sink importance. Because the back sides of the habitat patches are open, walkers can still arrive by going behind the wings. This is reflected in the blue and violet lateral bulges past the tips of the wings.
If we move the backstops in front of the habitat patches, they become shields, forcing walkers to go around them to successfully disperse. The corridors which are found reflect this shielding by the intervening millieu. Because the shields are symmetrical, there are still no changes in relative source or sink importance between the patches.
If we remove the top shield, walkers traveling upward can take a more diffuse path, once they successfully get past the first set of wings. This is manifest as a more diffuse corridor. Now the bottom patch becomes a more important source than the top patch (Image B), since its sending ability is now superior to that of the top patch, whose walkers tend to become trapped within the arms of the shield. Relative sink importance remains equal (as it is ith all 2-patch maps), since all dispersing walkers leaving one patch must arrive at the other.
If we reduce the thickness of the bottom shield, walkers can squeeze through at the thinnest points. Thus, it becomes a semi-permeable filter. Mini-corridors can be seen diagonally through these thinnest points, where walkers have passed through the filter. Even when shielded with reduced effectiveness, the lower patch is more important as a source than the upper patch.
These images result from five habitat patches arranged like the five spots on a die. Corridors are detected mostly as diagonals, but movement between the corner habitats is also shown as a blue halo. In this configuration, the center habitat is the most important source (Image B), and is also the most important sink (Image C). The edge option is set so that walkers die whenever they step off of any edge of the map. The footprints of any walker not successfully dispersing to another habitat patch dissappear, and do not contribute to the formation of corridors.
We can change the edge option so that, instead of dying, walkers stepping off of any edge of the map wrap around to appear again on the opposite side of the map. While the diagonal corridors remain, they are weaker, since the strongest corridors are around the corners of the map to the now-adjacent other corner patches. The vertically wrapping corridors (like the routes taken by the walker in Image H and Image I) are the strongest, since the corner patches are slightly closer together than the laterally wrapping corridors (like the route taken by the walker in Image K). In contrast to the last example, the corner patches now surpass the center patch in terms of both source importance (Image B) and sink importance (Image C).
If we remove the center patch of habitat and restore the edge die option, the corridors shift to favor the vertical and horizontal exchange routes. Because the patches are slightly closer horizontally, these corridors dominate. The slightly farther diagonal connections are still present, but are weaker yet (note the lighter hole in the middle of Image A). All patches are again equivalent sources and sinks.
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