Patch Shape Emergent Properties Figure 2. Three types of modeled behaviors to edges. The top row of figures represents how animals reflected from the edge and the bottom row represents how animals turned while within detecting distance of the edge. doi:10.1371/journal.pone.0021886.g002 Results Density Animal densities were obviously affected by edge shape (e.g. Figure 4). Densities were affected by the edge up to ,1 unit away (Figure 3), so all of the rest of the results are presented for only 1 unit away from the edge. In order to compare the relative importance of absolute width vs. narrowness of the edge shapes, I combined all results into one plot (Figure 5), and plotted them vs. width. Each line joins all results from one narrowness. If animal effects chiefly varied according to narrowness of the shape, and not the absolute width, Figure 3. Density of animal locations vs. distance from edge of patch, for three different types of behaviors to the edge, for straight edges. Note the log scale for density. Densities are in proportion to the mean density in the whole patch - thus, 1 means no effect of the edge. Attraction and avoidance give proportionally similar effects, with most effects within 1 unit from the edge. doi:10.1371/journal.pone.0021886.g003 then we would expect that the lines would differ widely in their relationship to width. However if the opposite happened, that animal effects chiefly varied according to width, then we would expect that the lines would be quite similar in their relationship to width. Density effects are minimal for widths greater than ,0.3– 0.4 units for all measures of narrowness - even though narrowness varied 4-fold, from 0.4 to 1.5. Thus the absolute width of the shape is much more important than the narrowness, in the effects on density. Comparing types of shapes, we see that animals were much more affected by the Out than the In shapes. For example, densities in the Out shape varied by a range of 100-fold when comparing Attraction to Avoidance (red lines in Figure 5 A vs. C), whereas in the In shape they only varied by a range of 3-fold (blue lines in Figure 5 A vs. C). Comparing animal edge behaviors, we see that the type of response depends on both shape and edge behavior. When animals are attracted to edges, then they collect more in Out and less in In than expected (red vs. blue in Figure 5 A). The opposite happens when animals avoid edges (red vs. blue in Figure 5 C). However, although they collect more in In shapes than Straight one when they avoid edges, they do still avoid In shapes overall (e.g. the maximum values are still ,1). Directionality For edge-following, the main differences are in the type of avoidance behavior, not in edge shapes (Figure 6 A). When animals are attracted to the edge they tend to follow the edge, but when they are either neutral or avoid the edge, there is no clear parallel directionality. However, for the Out shapes, width has an effect on this relationships (Figure 6 B). When animals are attracted to edges then they lose directionality close to the tips of the shapes. When animals are neutral or avoid edges, they travel quite parallel to the edge then near the tips of the shapes, but then this directionality drops off with edge width - and for avoidance, it goes to completely perpendicular at intermediate distances. Unlike edge-following, directionality towards the point shows a large difference within types of avoidance behaviors (Figure 7 A). For all combinations there is no directionality, except that when animals are attracted to edges, they orient towards the point of In PLoS ONE | www.plosone.org 3 July 2011 | Volume 6 | Issue 7 | e21886