movement towards a specific point. Thus, the unit length for steps represents the perceptual range of animals while traveling inside their patch habitat. This is also why the width band of edge effects was set at 1 unit from the edge. This conception of the units allows us to apply some of the quantitative predictions to other systems. A key result is that for all of these responses, the further from the tip of the shape, the smaller the response, with effective no response past 40% of the perceptual range of the animal. This result occurs over a four-fold range of shape widths (width/height 0.4 to 1.5), and edge reaction functions from strong avoidance to strong attraction. This means that one can apply these predictions to realistic situations, appropriately scaled. For example, Fender’s blue butterflies [8] turn towards edges from a distance of 10 m away. Thus one would expect that these butterflies would collect within ,4m of the tip of edge convexities, and would disperse from within ,4m of the tip of concavities. These results also generate predictions for the effects of edge tortuousity. It has been long noted that a higher perimeter:area ratio increases emigration [17,22,23], and that thus more tortuous edges should be more permeable. My results suggest that this effect can be magnified by edge shape effects. Assuming a similar number of convex and concave edges, the response to tortuous edges depends on the edge behavior. Animals that avoid edges show a symmetrical response, with similar positive and negative responses to concavities and convexities with a greater positive effect for convexities than a negative effect for concavities (Figure 5 C). Thus emigration should show no predictable response to edge tortuosity. On the other hand, animals that are attracted to edges show an asymmetrical response, with a greater positive effect for convexities than a negative effect for concavities (Figure 5 A). Thus emigration should increase with edge tortuousity when animals are attracted to edges. It would be useful for theoretical and field studies to explicitly test the effects of tortuous edges on permeability. Ecological aspects of edge shape My results showed that simply reacting to edges causes an emergent property of responding to edge geometry. This considerably broadens the scope of edge shape effects because animals need a certain level of cognition to recognize edge geometry; one would expect many more species to recognize and react to edges (for example, [24–26]) than to edge shapes. Furthermore, all edges have convexities and concavities at some scales; edge shape effects might very be common. Thus edge geometry could have important effects on local ecological communities. Edge shapes tend to either concentrate or disperse animals, simply because the animals are either attracted to or avoid edges, with an effect as great as 3 times the normal density. This effect would be felt both up and down the food chain. References 1. Pagel M, Payne RJH (1996) How migration affects estimation of the extinction threshold. Oikos 76: 323–329. 2. Zollner PA, Lima SL (1999) Search strategies for landscape-level interpatch movements. Ecology 80: 1019–1030. 3. Holtcamp EN (1997) Patch use under predation hazard - effect of the red imported fire ant on deer mouse foraging behavior. Ecology 78: 308–317. 4. Hardt RA, Forman RTT (1989) Boundary form effects on woody colonization of reclaimed surface mines. Ecology 70: 1252–1260. 5. Haddad NM (1999) Corridor use predicted from behaviors at habitat boundaries. Am Nat 153: 215–227. 6. Wolfram Research (2008) Mathematica.7th ed. ChampaignIllinois: Wolfram Research, Inc.. 7. Cain ML (1985) Random search by herbivorous insects: a simulation model. Ecology 66: 876–888. 8. Schultz CB, Crone EE (2001) Edge-mediated dispersal behavior in a prairie butterfly. Ecology 82: 1879–1892. Patch Shape Emergent Properties Here are three examples. First, many small mammals respond to edges [27]; a high proportion of seeds are eaten by small mammals [28] and many predators prey on small mammals. Second, some pollinating bee species (e.g. Bombus lapidarius L. bumblebees [29] and honey bees [30]) avoid edges while foraging for pollen inside of patches of flowering plants. Finally, many birds have been shown to respond to edges [25], and many species of plants are primarily dispersed by birds. Thus edge shape could affect pollination, seed predation and dispersal and predator abundance. It would be useful to test these prediction in the field. Another potential effect of edge shape that more directly affects humans, is on the behavior of large ungulates. Collisions between vehicles and large wildlife (e.g. white-tailed deer (Odocoileus virginianus) [31], moose (Alces alces) [32], brown bears (Ursus arctos) [33]) cause significant damage in both North America and continental Europe. This significantly affects not only vehicles, but some local populations that are in danger of extinction because of vehicle collisions (e.g. Florida panthers (Puma concolor coryi) [34] in Florida, black bears (Ursus americanus) near urban areas [35], and ocelot (Leopardus pardalis) in United States [36]). One factor that affects the likelihood of wildlife-vehicle collisions is the landscape features of the surrounding area [37,38]. Thus it may be possible to ameliorate the effects of roads on wildlife by manipulating the geometry of habitat edges near roads. Future directions This is a new area of research and my model has only been able to answer a few questions. It would be useful to test these model predictions with experimental and field work, and also to explore general questions. How do edge shapes affect animal movement, edge permeability and emigration? Which types of animals respond most to edge shape? Which properties of animals could be used to predict animal response. These types of studies have been difficult in the past because it has been difficult to track animals with a high enough resolution to identify edge behavior, and with enough data points to have enough edge shape encounters. However in the last ten years GPS devices for remotely tracking animals have increased in capability. For example GPS collars now are as light as 150 grams [39], allowing biologists to track animals as light as 1 kg. Locations can be obtained every 10 seconds as accurately as 2.5 m. This capability in animal tracking should allow us to answer questions about effects of edge geometry on animal movement. Author Contributions Conceived and designed the experiments: VON. Performed the experi- ments: VON. Analyzed the data: VON. Contributed reagents/materials/ analysis tools: VON. Wrote the paper: VON. 9. Levey DJ, Bolker BM, Tewksbury JJ, Sargent S, Haddad NM (2005) Effects of landscape corridors on seed dispersal by birds. Science 309: 146–148. 10. Stamps JA, Beuchner M, Krishnan V (1987) The effects of habitat geometry on territorial defense costs: intruder pressure in bounded habitats. Am Zool 27: 307–325. 11. Debinski DM, Ray C, Saveraid EH (2001) Species diversity and the scale of the landscape mosaic: do scales of movement and patch size affect diversity? Biol Conserv 98: 179–190. 12. Ewers RM, Didham RK (2007) The effect of fragment shape and species’ sensitivity to habitat edges on animal population size. Conserv Biol 21: 926–936. 13. Baguette M, Petit S, Queva F (2000) Population spatial structure and migration of three butterfly species within the same habitat network: consequences for conservation. J Appl Ecol 37: 100–108. 14. Wahlberg N, Klemetti T, Selonen V, Hanski I (2002) Metapopulation structure and movements in five species of checkerspot butterflies. Oecologia 130: 33– 43. PLoS ONE | www.plosone.org 7 July 2011 | Volume 6 | Issue 7 | e21886