Patch Shape Emergent Properties Figure 4. Example of densities of animals at different types of edge shapes, for width of shapes = 10. doi:10.1371/journal.pone.0021886.g004 shapes, and with a decreasing directionality the further from the tip (Figure 7 B). For all edge behaviors, the animals orient more towards the tips of Out shapes when closer to the tip (Figure 7 C). Similarly to edge-following, for directionality towards the inside of the patch the main differences are in the type of avoidance behavior, not in edge shapes (Figure 8 A). When animals are attracted to the edge then they tend orient to the outside, and when they avoid the edge then they orient to the inside. However this response decreases closer to the tips of the Out shapes (Figure 8 B). Discussion There are various assumptions this model makes which affect its application. The first assumption is that emigration rate depends on rates of encounters with patch boundaries - that organisms decide whether to emigrate or not, when they encounter the boundary. While this is also assumed by most theoretical models of metapopulation dynamics [10–12] it has never been explicitly tested. However there are some predictions of it that are supported. If emigration rate does depend on rates of encounters with patch boundaries, then we would expect that animals would emigrate more readily from patches with a greater perimeter:area ratio. This is seen with various butterfly species who immigrate out of small patches more (per area) than larger ones [13,14], and ladybird beetles who emigrate from rectangular patches faster than square patches [15]. In fact, much of the observed variation in a series of published studies on emigration rate could be explained by the scaled effect of patch size [16]. On the other hand, this assumption is not globally valid, because a few studies have not found a relationship between emigration and patch shape [17]. Thus, the relation between edge encounter rate and emigration rate likely depends on the species. The second assumption is about the realism of the algorithm of animal behavior at edges. It is difficult to assess this because little research has been done on how animals change movement in response to habitat edges. However, those few studies that measured relevant parameters do support my model. There are two important aspects to the edge-reaction model: the general structure and the specific parameters used. The general structure has two parts to it - the reaction upon detecting the edge, and then after actually encountering it. In the first part, when my modeled animals detected an edge, they changed mean turning angle either towards or away from the edge by a specific bias value. A bias of 0 means a zero mean turning angle, a bias of 1 means the animal always turns directly towards the edge, and a bias of -1 means the animal always turns directly away from the edge. This type of behavior structure has been shown in the only two studies that have specifically measured turning angles near edges. Fender’s blue butterflies (Icaricia icarioides fenderi) [8] and Eastern Bluebirds (Sialia sialis) [9] both are attracted to habitat edges and change their movement near edges by adding a bias to their turning angles. In the second part of my edge reaction model, animals reflected from the edge with a variable angle. Here a bias of 0 means complete reflection, a bias of 1 means always parallel, and a bias of 21 means always perpendicular. No study has measured specific angles of reflection at edges, however, some have reported general agreement: chickadees (Poecile atricapillus) tend to travel parallel to edges [18] and that Eastern Bluebirds tend to travel either parallel or perpendicular to them [9]. Thus there is support for the biological realism of the structure of my edge-reaction model. However it would be useful for future theoretical models to test other aspects of edge behavior, such as the effects of animal behavior after it crosses the edge. The specific parameters in my model for avoidance vs. attraction were chosen so that (1) attraction and avoidance gave proportionally similar, but opposite directions, responses to each other (e.g. Figure 3), and (2) that these would be extremes - that most species might be expected to show reactions within these ranges. For edge attraction, all published studies show bias effects less than the 0.75 used in my model. Fender’s blue butterflies were attracted to edges with a bias of 0.09–0.61 for females and 0.22– 0.38 for males [8], and Eastern Bluebirds were attracted with a PLoS ONE | www.plosone.org 4 July 2011 | Volume 6 | Issue 7 | e21886