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90 generation. More importantly, population rates (i.e., birth was used because it is one of the simplest measures and is rates, death rates, recruitment, survival) were either positive roughly equivalent to the linear distance between any two (n = 28) or neutral (n = 14) over 95% of the time, but nega- measures. The shorter the distance, the more similar the meas- tive in only two instances (<5%). This finding underscores ures and the more likely the species involved will be included the necessity of restoring functional connectivity to the in a group. Ward's method is based on minimizing the sum of roaded landscape. Inter-patch movements may involve the squares of distances from each individual species to the relative short distances or long-distance dispersal. Shorter centroid of its group.161 The method produces a clustering movements are more frequent, while longer dispersal matrix and a dendrogram of the species groups. The research distances are typically rare.232 team chose to represent the data to the sixth cluster (i.e., to the 0.16-mi level). After the natural breaks were detected, frequency distribu- Description of Methods tions for the species home range areas that had been converted Bowman et al.33 developed their home range dispersal re- to the median dispersal distances and to the linear home range lationships for mammals from data given in Harestad and distances were calculated. The frequency distributions are Bunnel.112 For this study, the Harestad and Bunnell112 data equivalent to scale domains that represent similar scaling by was augmented with the species home range list given in groups of species. The research team also compared trophic Holling122 Appendix 7 to amass a total of 103 mammalian level (i.e., carnivore, herbivore, and omnivore) median disper- species from around the world (Appendix G). Other sources sal distances to determine if differences existed. The research of home range information are available, but the Harestad team looked at a sample of 10 papers that provided daily move- and Bunnell112 data are well known, are accepted by ecolo- ment data and examined if a consistent relationship existed gists, and have been used to advance the allometric scaling of between daily movement distances and median dispersal dis- mammals.139 The Holling122 paper increased the number of tance. Because median dispersal distance and linear home species for which reliable home range data are available. Only range distances are derived from home range area, if there was data for species with at least five replicates were used in the a relationship, it should apply to any of these measures. Holling paper. Some species do not occur in North America, Finally, the research team compared the options for spac- but were included because (1) their home range area infor- ing wildlife crossings and presented the most feasible scaling mation was reliable and (2) they provided a reasonable domains for large mammals that are most likely to be in- sample size from which to develop reliable dispersal distance volved in serious animalvehicle collisions. domains. Elimination of duplicate entries left 103 species. A caveat is necessary here. Home range size varies over time for individuals and for populations. The values used in this Findings and Results study are the best representative values available for the Mammalian Species Scaling: species. Individual home ranges will no doubt vary around Median Dispersal Distance these mean values. The Bowman et al.33 equations were then used to calculate When the median dispersal distance equation (7 * Home MedDD (i.e., 7* HR) and LHRD (i.e., HR) from these home Range) was used, mammalian species dispersal distances range data and from data in 10 papers that listed daily move- ranged from 0.06 mi for the northern pocket gopher (Tho- ment distances (DMD) to explore if a consistent relationship momys talpoides) to 168.46 mi for the wolverine (Gulo gulo). existed between DMD and the MedDD. If a consistent rela- Of 103 species, 50% scaled to less than 4 mi (Figure 32, Table tionship exists, then three different scaling domains could be 34). More than 70% of species had median dispersal distances developed to inform the placement of crossings. All three of 8 mi or less. When median dispersal distances were transformations (MedDD, LHRD, and DMD) represent grouped by a hierarchical polythetic agglomerative clustering different ecological neighborhoods for individual species. technique,162 55.4% scaled longer than 3.05 mi (Figure 33). After the distance conversions were calculated, the research Not all trophic levels (i.e., carnivores, herbivores, and om- team applied a hierarchical monothetic agglomerative cluster- nivores) scale similarly. One expects that carnivores, whose ing technique using Ward's linkage method with a Euclidean prey is the herbivore component of the community, would distance measure as the sorting strategy162 to detect natural travel greater distances and have larger home ranges. Simi- breaks in the data. Monothetic refers to the clustering of one larly, herbivores, whose primary food resource includes variable (i.e., the measure of home range); agglomerative refers plants, would be expected to scale differently and indeed that to the procedure of clustering groups of species and means is the case. Indeed, MedDD for omnivores ranged from 0.39 such that each group starts as a single species and is clustered to 50.05 mi, herbivores ranged from 0.06 to 16.47 mi, and (agglomerated) by some linkage method. Euclidean distance carnivores from 0.14 to 168.46 mi (Figures 34 and 35). It is

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91 MEDIAN DISPERSAL DISTANCE DOMAINS 1.0 1.00 0.9 0.90 0.85 CUMULATIVE PERCENT SPECIES 0.8 0.73 0.7 0.6 0.53 0.5 0.50 0.45 0.4 0.41 0.35 0.3 0.23 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 MEDIAN DISPERSAL DISTANCE (miles) Figure 32. Median dispersal distances of 103 mammalian species with no clustering. Table 34. Cumulative percentage of mammalian species that scale at distances from 0.5 to more than 35 mi. MedDD (mi)* 0.5 1.0 2.0 3.0 4.0 6.0 8.0 20.0 35.0 >35.0 Cumulative% 28.2 35.0 40.8 44.7 50.5 63.2 70.9 85.4 90.3 100 * mile value given is upper limit for that distance domain MEDIAN DISPERSAL DOMAINS BY SPECIES GROUPS FOR 103 MAMMALIAN SPECIES 30.0 28.2 27.2 25.0 23.3 PERCENT OF SPECIES 20.0 15.0 10.0 8.7 7.8 4.9 5.0 0.0 0.16 1.07 3.05 7.15 10.71 >11.00 MEDIAL DISPERSAL DISTANCE (miles) Note: X-axis values represent the upper boundary of the particular domain. Figure 33. Median dispersal (7 * Home Range) domains for 103 mammalian species based on a hierarchical polythetic agglomerative clustering.

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92 Figure 34. Carnivores, herbivores, and omnivores show different median dispersal distances. clear that wildlife crossings placed 6 mi or more apart will not crossings according to a mile-marker spacing, approximately provide either permeability or adequate crossing opportuni- 12% of species would be likely to cross at a distance of 7 mi, ties for approximately 63% of the mammalian species likely approximately 30% at 3.0 mi, and approximately 64% at to be found on the landscape. Clearly median dispersal crossing distances of 1 mi. All species would likely cross at a distances provide only the extreme limit and by themselves spacing distance of 0.16 mi (Figure 36). Consequently, maxi- cannot fully inform the placement of wildlife crossings. mum landscape permeability is more likely when placing wildlife crossings based on the linear scale domains. Mammalian Species Scaling: Linear Dimension Distance Mammalian Species Scaling: Daily Movement Distance At the other end of the spectrum, the linear dimension of the home range (HR) provides a scaling that more closely ap- It is possible that daily dispersal distances may provide an proximates the majority of movements made by mammalian alternative scenario for placing wildlife crossings; however, species, which typically move within their home range for daily movement distances are difficult to collect and often not most of the year. During spring and fall of course, juvenile an- uniformly collected. For example, Krausman et al. (unpub- imalsusually make longer migratory movements.227 When lin- lished data) collected movement data on 46 mule deer ear movement domains were used to place multiple wildlife (Odocoileus hemionus) whose movements were followed COMPARISON OF TROPHIC MEDIAN DISPERSAL DISTANCES 60.00 53.7 CARNIVORES HERBIVORES OMNIVORES TOTAL SPECIES 50.00 42.9 43.9 PERCENT OF SPECIES 40.00 30.00 28.2 27.2 24.4 23.3 23.8 19.0 20.00 14.6 12.2 12.2 12.2 9.5 8.7 10.00 7.8 7.3 7.3 4.9 4.9 4.8 4.9 2.4 0.0 0.00 0.16 1.07 3.05 7.15 10.71 >11 DISTANCE (miles) Figure 35. Comparison of the median dispersal distance domains of carnivores, herbivores, and omnivores.