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87 and body size, where animals with bigger bodies have bigger effects) effects on wildlife populations and on ecological brains. patterns and processes.26,30 In particular, animal movement is Here the relationships between home range size and dif- hindered as road density and traffic volume increase. Spatial ferent measures of movement ability (namely, Median linkage, accomplished by animal movement, is critical because Dispersal Distance [MedDD] and linear home range distance the arrays of resources that are essential to population viability [LHRD]) are referred to as allometric because movement are usually distributed heterogeneously across the habitat net- ability changes in proportion to home range size, which is re- work.168 Animal movement can be seasonal migrations120 that lated to the size of organisms; i.e., there are consistent scaling tend to be cyclic, dispersal events227 that are usually unidirec- properties that can be expressed by equations. Scaling prop- tional,180 or ranging behavior144,228,216 characterized by shorter erties can be translated into movement distances characteris- exploratory movement within a home range or territory. Re- tic of a species. Movements of animals over time can be gardless, the ability of animals to move has profound impacts referred to as their ecological neighborhood, i.e., a region de- on ecological phenomena and processes, including individual fined by an animal's movement pattern. Ecological neigh- fitness, population structure, life history strategies, foraging dy- borhoods for any individual species vary depending upon namics, and species diversity.3,33 Generically, dispersal has been which process is involved. For example, while foraging move- defined as the movement of organisms, their propagules, or ment distances typically are relatively short, migratory move- their genes away from the source.223,234,59,179,38 Although this ments involve larger ecological neighborhoods. Animals of study explores the patterns of dispersal distances to understand similar size tend to have similarly sized home ranges and eco- the placement of wildlife crossings, clearly the processes logical neighborhoods. When this is so, it is possible to estab- involved in dispersal underpin our ecological understanding. lish scaling domains that include a few to many species. For The phenomena of immigration and emigration, collectively the purposes of this report, a scale domain refers to a range of termed dispersal, are two of four (births and deaths being the species movement distances that are similar, so that several other two) processes that are the least understood in the fields species can be considered to belong to that particular domain. of population ecology and life history evolution,75 and repre- Domains range from small to large, typically with more sent one of the most significant gaps in how ecologists under- sedentary animals belonging to a domain characterized by stand animal ecology.22 Wiens246 has argued that dispersal is a short movement distances and highly vagile animals belong complex process that involves more than just patterns of where to a domain characterized by longer movement distances. To animals settle. According to Doerr and Doerr75 a more com- the extent that species belonging to a specific domain move prehensive view of dispersal is emerging. Clobert et al.59 have similarly, the placement of wildlife crossings of appropriate argued recently that at least three components are involved in type and configuration at appropriate (allometric) distances dispersal: (1) a decision to leave the natal area, (2) a middle will promote landscape permeability. Less vagile animals phase where new areas are searched and evaluated, and (3) a need crossings placed closer together, while for more vagile final phase that involves choosing a place to settle. This view animals wildlife crossings can be spaced further apart. The suggests that dispersal distances result from this integrated se- advantage of domains is that often, a single crossing can be ries of decisions and processes and are influenced by environ- used by many different types of species. There are obvious ad- mental and physiological factors, as well as stochastic events.75 vantages for both population viability and driver safety when Perhaps most critical to our understanding is a dearth of data species use crossings and stay off the road surface. Mitigation regarding these processes. For this report, dispersal is consid- to decrease the effects of the roaded landscape includes, ered to be at the level of individuals and populations. Although among other things, the construction of crossings of two barrier effects are not similar across roads, the effects of road general types; those that promote wildlife crossing over the geometrics (e.g., road type, width, presence of fences) present road, and those that provide passage underneath. The num- significant problems to animals, resulting in fragmented ber, type, configuration, and placement of crossings will habitats, disconnected networks, non-permeable or semi- determine whether permeability is restored to the roaded permeable landscapes26 and often isolated populations.43,240,137 landscape. The relevant hypothesis is that landscape perme- ability can be improved by the placement of crossings allo- A Brief History of Allometric Scaling in Ecology metrically scaled to organism movement characteristics. Allometric scaling in ecology has had a long history. The fol- lowing summary is intended not to cover the history Research Approach: Methods and Data exhaustively, but only to indicate the line of logic that led to The roaded landscape has both direct (e.g., roadkill) and in- these analyses. As early as 1909, Seaton209 recognized that animal direct (e.g., habitat loss, reduced habitat quality, fragmenta- size corresponded roughly with home range size. Mohr174 dis- tion, loss of connectivity and reduced permeability, and barrier cussed the same relationship specifically for mammalian species.

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88 Kleiber141 looked at the scaling relationships between basal perhaps the least well understood of ecological phenom- metabolic rate (BMR) and body mass and found that BMR = ena.227 Bowman et al.33 showed that dispersal distance is ac- aM0.75, where M is body mass, a is the allometric coefficient tually more closely related to home range size (R2 = 0.74) (y intercept), and 0.75 is the allometric scaling exponent. The than to body size (R2 = 0.60), where R2 is the proportion of general form of the allometric (power law) scaling equation is: the variance explained by home range size and body size, re- spectively. This discovery is significant because dispersal dis- Y = aXb tances, as well as ranging and migratory behavior, represent where Y is the response variable, X is the explanatory variable, animal movement across the landscape. Bowman et al.33 a is a scaling constant or coefficient (y intercept), and b is the found that when body size effects were removed, the slope of scaling exponent equal to the regression slope.141,147 McNab165 the relationship of the residuals of dispersal distance re- showed that among mammals, an almost identical power law gressed against the residuals of home range size was not sig- (scaling exponent) existed between home range size and body nificantly different from 0.50 (F = 31.6, df = 1, 32, P = 3.2 x weight, although Harestad and Bunnell112 found scaling expo- 10-6, S.E.E. = 0.54), a result with very important ramifica- nent values near 1.0 or greater when they looked at different tions. The significance is this: Dispersal distance is a linear trophic levels. They concluded that differences in weight alone measure, while home range area is a squared linear measure. accounted for a large proportion of the differences between Because X0.05 is equal to the square root of X, and because X male and female or subadult and adult home range sizes. They in the scaling equation is equal to home range area, taking suggested that inter-trophic (namely, herbivores vs. carnivores the square root of the home range area yields a linear di- vs. omnivores) scaling functions differed significantly from mension of home range, allowing dispersal distance to be re- each other. Damuth68 and Brown37 have suggested that the dif- lated to home range size by a single constant value. ference between the scaling exponents of 0.75 for energy re- Bowman et al.33 found that maximum dispersal distance quirements and approximately 1.0 for home range size may be (MaxDD) was related to home range size (HR) by the equation: explained by per capita resource requirements and greater over- MaxDD = 40 (linear dimension of HR) lap in home ranges for larger mammals. However, more recent work by Kelt and Van Vuren,139 working from a large data base and median dispersal distance (MedDD) was related to home of over 700 publications, found that the scaling relations of range size by the equation: inter-trophic home ranges did not differ and scaled with a slope MedDD = 7 (linear dimension of HR) of 1.13, greater than either the results of McNab165 or Harestad and Bunnell112. Kelt and Van Vuren139 (p. 637) admit however Because home range size is easy to measure and is readily that the relationship between home range size and body mass available in published literature, appropriate scaling functions "has been perhaps the most difficult to understand." Recently, for deciding the general ecological neighborhood of species Wolff248 and Sutherland et al.227 demonstrated that body size of would appear to be easy to obtain. If so, they provide the next mammals is linearly related to dispersal distance when both step to inform the placement of wildlife crossings. variables were expressed on a log10 scale. However, as Bowman et al.33 point out, both of these relationships are limited because: What is an Ecological Neighborhood? (1) some species disperse much further than expected from body size, and (2) some mammals have larger or smaller home The concept of ecological neighborhoods is defined by ranges than predicted for a given body size. Given these results, three properties: (1) an ecological process (e.g., inter-patch one expects that home range size and dispersal distance should movement), (2) a time scale relevant to the process, and (3) co-vary across mammalian species and this is the argument that an organism's activity during that time period.3 Additionally, Bowman et al.33 expand upon. They argue that the residual vari- no single temporal or spatial scale is appropriate to represent ance in the body size versus home range, and the body size ver- the mix of processes that influence individual and species re- sus dispersal distance relationships represent real differences in sponses through time and space; hence, several ecological vagility independent of body size and therefore the relationship neighborhoods exist, depending upon what process is between dispersal distance and home range size should co-vary involved (e.g., foraging, territory defense, migration). Char- across mammal species after the effects of body size are acteristically, for mobile organisms, the ecological neighbor- removed. hood for a given process is the region within which that organism is active, definable by its movement patterns. In- deed, Addicott et al.3 (p. 343) suggest that "for neighbor- The Dispersal Distance Connection hoods. . . . the most appropriate indicator of activity may be Dispersal is a fundamental element of demography,7 col- a measure of net movement of individuals . . . . One [such in- onization,117 and gene flow182 but dispersal movements are dicator] is the direct measurement of dispersal distances."

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89 to attempt to place crossings allometrically for each individ- % cumulative distribution of movement 95 A ual species. Some grouping of species is desirable, especially if 50 their home range sizes are similar in size and have small among versus between group differences. 0 Na Nb Domains of Scale 95 foraging To the extent that (1) similarities in home range sizes exist B for groups or guilds of species and (2) there are recognizable 50 differences between groups, it should be possible to deter- inter-patch movement mine a few effective scale domains that characterize the 0 movements of each group. Theoretically, boundaries of scale N1 N2 domains should be recognized where the differences (e.g., in spatial unit (distance) dispersal distances) increase as transitions between domains Source: Redrawn from Addicott et al.3 are approached. If possible, then the recognition of a few Figure 31. Theoretical relation- groups or guilds composed of similarly sized species with ship between the cumulative similar home range domains is an important first step in distribution of organism move- determining the spatial location for effective crossings for ment and spatial scale, i.e., eco- most species. The assumption is that similarly sized animals logical neighborhood. will use similar types and similarly spaced crossings. However, there may be inter-trophic differences (i.e., carni- vores, herbivores, and omnivores may scale differently). If so, Figure 31 shows the theoretical relationship between consideration should be given when deciding on the type and movement and two ecological neighborhoods where N1 and placement of wildlife crossing. The calculation of guild- N2 represent two different spatial units related to two distinct specific movement domains is an important step in allomet- animal activities. The horizontal and vertical dashed lines in- rically placing wildlife crossings. To the extent that these dicate different "neighborhood sizes" for the two different ac- arguments hold, the placement of appropriate types of cross- tivities (dotted lines, Figure 31A). In general, thinking about ings can be accomplished in a scale-informed and sensitive landscape permeability involves larger spatial units. In this manner, resulting in a more permeable roaded landscape that example, foraging involves a smaller ecological neighborhood effectively restores the broader habitat network. (N1), but inter-patch movements, which might include find- ing mates or additional resources, typically involves larger Wildlife Crossings and Inter-Patch Movements spatial areas (N2), i.e., larger ecological neighborhoods, and may be equated with some measure of dispersal. The intent, of course, of establishing allometrically scaled When roads cross the landscape, the larger ecological wildlife road crossings is to enhance inter-patch movements. neighborhoods that animals use (e.g., related to inter-patch Most if not all organisms live in discontinuous habitat patches movement) may be intersected. When such intersection oc- of suitable habitat within a matrix of less suitable habitat that curs, barrier effects become apparent. In Figure 31, both inter- is embedded in larger, naturally heterogeneous landscapes,34 patch interactions involving movement over large distances and the presence of roads generally increases patch isolation. and the movements related to the shorter foraging activities Ecologically, animal vagility and movement ability determine are defined by a cumulative distribution of distances moved. if populations are isolated in a naturally heterogeneous land- Each line in Figure 31B represents a cumulative distribution scape.3,34 Although important, inter-patch movement has not of movements with an associated neighborhood size (N1, N2) been extensively studied and few empirical estimates of move- for foraging and inter-patch movements. The decision crite- ment rates or effects on populations have been derived.34 It is rion is 95% of all movements related to either process,3 but is unclear what amount of inter-patch movement is needed to arbitrary; it could easily be different. Given the results from influence the dynamics of populations divided by roads. Bowman et al.,33 the problem of deciding an appropriate spac- While real problems exist in gathering inter-patch movement ing for wildlife crossings is now somewhat easier because plan- data,34 Bowne and Bowers34 conducted a database search to ners can relate ecological neighborhoods of activity required determine the extent that documented rates were available. by animals to survive to a distance measure. Usually, ecologi- From a review of 415 published articles, they found that for cal neighborhoods are defined for each individual species. 89 species-system combinations, roughly 15% of all individ- However, it is unreasonable from a management perspective uals in a population moved between habitat patches each