Patch Shape Emergent Properties Figure 6. Edge-following, where 1 means completely parallel to the edge and -1 means completely perpendicular. A: Overall effects for different edge behaviors and edge shapes. Bars are grouped by behavior to edge, and within each group, bars show animals’ behaviors to the edge: straight, in and out. The main differences are in the type of avoidance behavior, not in edge shapes. B: For the Out shape only, edge-following vs. width of shape. Each color represents different edge behaviors. With attraction (brown lines), animals lose directionality close to the tips of the shapes. With avoidance (green lines), animals orient perpendicular near the point, but then more parallel right at the point. With neutrality (black lines), animals orient parallel to the edge near the tips of the edge shapes. doi:10.1371/journal.pone.0021886.g006 measured the proportion of Regal fritillaries (Speyeria idalia Drury) and monarch (Danaus plexippus L.) butterflies turning away from habitat edges for 4 types of habitat edges. Six out of those eight combinations show a smaller edge avoidance than I observed (Figure 3). Ross et al. [20] measured the tendency for Rocky Mountain parnassian (Parnassius smintheus) butterflies to fly towards vs. away from forest edges at different distances from the edge. My measure of this tendency (variable To-inside, Figure 8 A) showed an overall directionality towards the edge, averaged over all distances, which is reached by parnassian butterflies only within 0.3 units of the edge (Figure 4 [20]). Thus the parameters I used for avoidance vs. attraction bounded the expected biological range. Predictions Although my model only predicts edge shape effects when animals just respond to edges, in some situations we can use these predictions to test whether animals do recognize edge shapes. For example, Hardt and Forman [4] found that woody colonizers were more abundant in grassland areas adjacent to edges that were Figure 5. Density of animal locations vs. widths of edge shapes. Densities are in proportion to the mean density in the whole patch - thus, 1 means no effect of the edge. The three plots show different types of behaviors to the edge: A - attraction, B - neutral, C - avoidance. Within each graph, the different colors lines represent the different types of edge shapes. The different lines of each color represent different narrownesses. The tight clustering of the colored lines as compared to the change along the x-axis shows that most of the effects on density are due to point width, not point narrowness. doi:10.1371/journal.pone.0021886.g005 bias of 0.74 [9]. For edge avoidance, no studies have measured the amount of edge bias. However two studies report general results which can be compared with mine. Ries and Debinski [19] PLoS ONE | www.plosone.org 5 July 2011 | Volume 6 | Issue 7 | e21886