Evaluation of the Use and Effectiveness of Wildlife Crossings (2008)

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139 The literature description for this appendix contains stand- alone references. The literature review of all other appendices is contained in the References section. I. Wildlife-Vehicle Collision Analysis Allen, R.E., and McCullough, D.R. 1976. Deer-car accidents in south- ern Michigan. Journal of Wildlife Management 40(2):317–321. Bashore, T.L., Tzilkowski, W.M., and E.D. Bellis. 1985. Analysis of deer- vehicle collision sites in Pennsylvania. Journal of Wildlife Manage- ment 49(3): 769–774. Bellis, E.D., and H.B. Graves. 1971. Deer mortality on a Pennsylvania interstate highway. Journal of Wildlife Management 35(2):232–237. Biggs, J., Sherwood, S., Michalak, S., Hansen, L., and C. Bare. 2004. Animal-related vehicle accidents at the Los Alamos National Lab- oratory, New Mexico. The Southwestern Naturalist 49(3):384–394. Caryl, F.M. 2003. Ungulate mortality on a forested highway. University of East Anglia, Norwich. M.Sc. dissertation. 42 pp. Finder, R.A., Roseberry, J.L., and A. Woolf. 1999. Site and landscape conditions at white-tailed deer/vehicle collision locations in Illi- nois. Landscape and Urban Planning 44: 77–85. Gundersen, H., and H.P. Andreassen. 1998. The risk of moose-collision: a logistic model for moose-train accidents. Wildlife Biology 4(2): 103–110. Gundersen, H., Andreassen, H.P., and T. Storaas. 1998. Spatial and temporal correlates to Norwegian train-moose collisions. Alces 34: 385–394. Hubbard, M.W., Danielson, B.J., and R.A. Schmitz. 2000. Factors in- fluencing the location of deer-vehicle accidents in Iowa. Journal of Wildlife Management 64(3):707–713. Joyce, T.L., and S.P. Mahoney. 2001. Spatial and temporal distributions of moose-vehicle collisions in Newfoundland. Wildlife Society Bul- letin 29(1): 281–291. Kassar, C., and J.A. Bissonette. 2005. Deer-vehicle crash hotspots in Utah: data for effective mitigation. UTCFWRU Project Report No. 2005(1):1-28. Utah Cooperative Fish and Wildlife Research Unit, Utah State University, Logan Utah. Malo, J.E., Suarez, F., and A. Diez. 2004. Can we mitigate wildlife– vehicle accidents using predictive models? Journal of Applied Ecol- ogy 41: 701–710. Nielsen, C.K., Anderson, R.G., and M.D. Grund. 2003. Landscape in- fluences on deer-vehicle accident areas in an urban environment. Journal of Wildlife Management 67(1): 46–51. Nielsen, S.E., Herrero, S., Boyce, M.S., Mace, R.D., Benn, B., Gibeau, M.L., and S. Jevons. 2004. Modelling the spatial distribution of human-caused grizzly bear mortalities in the Central Rockies ecosystem of Canada. Biological Conservation 120:101–113 Premo, D.B.P., and E.I. Rogers. 2001. Town of Amherst deer-vehicle ac- cident management plan. White Water Associates, Inc., Amasa, Michigan (www.white-water-associates.com) Rogers, E. 2004. An ecological landscape study of deer-vehicle collisions in Kent County, Michigan. Report for the Michigan State Police, Office of Highway Safety and Planning. White Water Associates, Inc., Amasa, MI 49903. 56 pp. Romin, L.A. and J.A. Bissonette. 1996. Temporal and spatial distribution of highway mortality of mule deer on newly constructed roads at Jordanelle Reservoir, Utah. The Great Basin Naturalist 56(1): 1–11. Seiler, A. 2005. Predicting locations of moose-vehicle collisions in Swe- den. Journal of Applied Ecology 42: 371–382. Simek, S.L., Jonker, S.A., and Mark J. Endries. 2005. Evaluation of prin- cipal roadkill areas for Florida black bear. ICOET 2005. Singleton, P.H., and J.F. Lehmkuhl. 1999. Assessing wildlife habitat connectivity in the Interstate 90 Snoqualmie Pass Corridor, Wash- ington. ICOWET III. II. Spatial Analysis Techniques Boots., B.N. and A. Getis. 1988. Point Pattern Analysis. Sage Publica- tions, Inc. Newbury Park, California. 85 pp. Burka, J., Nulph, D., and A. Mudd. 1997. Technical approach to devel- oping a spatial crime analysis system with ArcView GIS. INDUS Corporation and U.S. Department of Justice. Lee, J., and D.W.S. Wong. 2001. Statistical Analysis with ArcView GIS. John Wiley and Sons, Inc., New York, New York. 192 pp. Levine, N., Kim, K.E., and L.H. Nitz. 1995. Spatial analysis of Honolulu motor vehicle crashes: I. Spatial Patterns. Accident Analysis and Pre- vention 27(5):663–674. Levine, N. 1996. Spatial statistics and GIS: software guides to quantify spatial patterns. Journal of the American Planning Association 62(3): 381–391. Levine, N. 1999. Quickguide to CrimeStat. Ned Levine and Associates, Annandale, VA. Levine, N. 2004. CrimeStat III: Distance analysis. Chapter 5 in: A spa- tial statistics program for the analysis of crime incident locations. Ned Levine & Associates: Houston, Texas, and the National Institute of Justice, Washington, D.C., USA. A P P E N D I X E A Literature Review of Field Studies and Spatial Analyses for Hotspot Identification of Wildlife–Vehicle Collisions

Spooner, P.G., Lunt, I.D., Okabe, A. and S. Shiode. 2004. Spatial analy- sis of roadside Acacia populations on a road network using the net- work K-function. Landscape Ecology 19:491–499. I. Wildlife–Vehicle Collision Analysis Allen, R.E., and D.R. McCullough. 1976. Deer-car accidents in south- ern Michigan. Journal of Wildlife Management 40(2): 317–321. Objective: to identify the time, place, and characteristics of traffic and deer that contribute to collisions. It was hoped that such an under- standing would suggest measures to reduce collisions Data layers: 10 counties in S. Michigan; data on DVC from accident re- ports, 1966-1967 • Variables analyzed for all accidents: date, day of week, time, speed of car, sex of deer, road type • Added to 1967 data: location within 0.16 km from a landmark; number deer seen at time of accident; fate of deer involved; whether car driven or towed away; extent of injuries • Traffic volume data from MI Dept of State Highways: average traffic volume for various time intervals (hourly, daily, monthly) Analyses: 3 areas from highest accident roads chosen for habitat analy- sis: all accidents plotted on aerial photos and roadside habitat clas- sified as cropland, forest, or unimproved field Results: most accidents occurred between 1600–0200; 2 peaks, sunrise and 1-2 hours after sunset; traffic volume and DVC correlated for evening and nighttime hours (85% of variation in DVC accounted for by traffic volume) • Number of accidents and traffic volume highest on weekends; largest number of DVC in fall and early winter • In 3 sections where habitat determined, accidents and habitat types occurred in similar proportions • % of accidents increased up to a speed of 80-95 kph, then de- clined at higher speeds Bashore, T.L., Tzilkowski, W.M., and E.D. Bellis. 1985. Analysis of deer-vehicle collision sites in Pennsylvania. Journal of Wildlife Management 49(3): 769–774. Objectives: examined roadkill locations plotted on highway maps by PA Game Protectors since 1968. A cursory exam revealed that deer kills tend to be aggregated at specific sites where accidents occur year after year. Analyzed aerial photos and highway and topo maps and conducted field studies to determine which factors characterize concentrations of collisions at particular sites. A model was devel- oped to predict probabilities that a section of highway would be a high kill site and then tested for reliability. 4 PA counties studied, used 2-lane hard-top roads, 51 paired sites (kill and control), data collected from 1 July–30 Oct 1979 and 27 June– 1 Oct 1980 Data layers: residences (number/ha); commercial buildings (num- ber/ha); other buildings (number/ha); banks (prop. of terrain ele- vated more than 1 m above road surface); gullies (more than 1 m below road surface); level (not bank or gully); wooded; non- wooded; barren; distance to woodland; increasing slope; decreas- ing slope; no slope; angular visibility; in-line visibility; shortest vis- ibility; speed limit; fencing; guardrails Data obtained by selecting a random point from within each 100m in- terval of site length and running a 100 m transect perpendicularly from each side of the road; at sites shorter than 100 m, two points were randomly selected Analysis: stepwise logistic regression used to test the importance of the variables used in the model; 5 pairs of sites randomly selected for a test of the model’s predictive ability Results: 9 of 19 variables selected for inclusion in model (residences, com- mercial buildings, other buildings, shortest visibility, in-line visibil- ity, speed limit, distance to woodland, fencing, non-wooded area); • 85% of kill locations had a prob. of 0.70 or greater of being clas- sified as kill site; 89% of control had a prob. of 0.30 or less of being classified as kill site • high correlation between speed limit and in-line visibility; be- tween residences and other buildings; removal of correlated variables did not significant change model • 9 and 7 variable models performed equally well in predicting kill and non-kill sites; 5 kill locations correctly classified, one con- trol location misclassified by both models Discussion: DVCs not random in time or space; kills aggregated Bellis, E.D., and H.B. Graves. 1971. Deer mortality on a Pennsylvania in- terstate highway. Journal of Wildlife Management 35(2): 232–237. Objective: to present the results of an analysis of data on highway mor- tality collected from November 1968 through December 1969 Data layers: data collected from an 8.03-mile section of I-80; divided into 212 contiguous sectors of 200 ft length • Kill data obtained from game protector who filled out re- searcher-supplied data sheets (date, location by sector number, highway lane, sex, age class); it was understood that many kills were probably not reported • 5 portions of each of the 212 sectors analyzed for physical and vegetation factors that might affect deer mortality: planted ROW on each side of highway; area adjacent to ROW on each side of highway; median strip • Factors used in the analyses: quality and amount of vegetation; topography; area of ROW; presence of fences or guardrails • Deer counts obtained from May 68–May 69 by spotlighting from vehicle Results: 286 reported DVC; 67.9% of sectors had at least one DVC (max of 9 in one sector); roadkills often concentrated in groups of con- tiguous sectors • 70% of deer seen through spotlighting were grazing (conserva- tive estimate); suggests presence and type of vegetation within sectors accounted for much of variation in numbers killed • Low correlation between DVC and all measured variables— demonstrated that with our technique we could not account for the variation in numbers of deer killed • Examined data in a less analytical manner by considering com- bos of sectors in relation to overall topography – High mortality: (1) where sections of road lay in troughs formed by elevated median strips with steep banks and steep inclines on ROW; (2) where troughs terminated by reduc- tions in elevation of the median strips allowing deer to easily cross road; (3) both sides of highway and median strip had good grazing and relief relatively flat – Low mortality: (1) area with low relief, abundant food on ROW and chain link fence; (2) ROW declines sharply to a stream or other lowland area, guardrails present • High correlation between number killed per month and num- ber seen per month 140

Biggs, J., Sherwood, S., Michalak, S., Hansen, L., and C. Bare. 2004. Animal-related vehicle accidents at the Los Alamos National Labo- ratory, New Mexico. The Southwestern Naturalist 49(3): 384–394. Objectives: to (1) analyze wildlife–vehicle accident data with respect to time, season, location, and species for accidents occurring on LANL internal and perimeter roads and (2) perform an analysis of site characteristics at accident locations identified as hotspots. Data layers: ~68 km of primary rd included in study; majority of traffic volume in early morning and late afternoon; WVC data from 1990–1999 • Accident data: from NMDGF, LAPD and LANL security force reports (date, time, location, species, cost of damage, injuries to humans, injuries to animals); accident locations recorded into GIS (sometimes based on approximate description of site) • Hotspot characterization data: vegetation characteristics (dom- inant tree, shrub, forbs and grass sp.), posted speed limit, road type (straight, curve, hill), presence of lighting, amount of avail- able light (high, mod, low, none), presence and length of guardrails, height of fencing, slope characteristics, motorist vis- ibility distance Analyses: Cluster analysis using GIS nearest neighbor index approach used to determine whether accidents were distributed randomly; deer and elk examined separately • Density analysis using the “simple” type calculation of the GIS program and a search radius of 100 m applied to identify acci- dent hotspots • Accident site characterization analysis: 15 hotspots selected, with 15 paired control sites; 100 m transect centered on site placed parallel to road on either side, six 15 m transects (at 25, 50, 75 m marks) placed perpendicular to 100 m transects; hotspot characterization data recorded along 15 m transects • Statistical analyses: χ2 used to test for differences in accident counts between seasons – Exact binomial tests: to determine if differences occurred be- tween the numbers of accidents in different pairs of seasons; also if significant difference occurred among hourly counts of accidents; deer and elk analyzed separately – Poisson regression: if accident count in given year significant difference from other years; also to test if association between monthly accident counts and monthly snowfall amounts sig- nificant; deer and elk analyzed separately – Logistic regression: to model status of an area as a hotspot or control as a function of measured variables – Fisher’s exact test: if diff in recoded variables between hotspots and controls were statistically significant – Univariate logistic regression: as first step to identify poten- tial predictors for a larger model; potential predictor vari- ables chosen if (1) absolute value of the Wald statistic > 1, (2) lit search revealed potential importance, or (3) authors thought important Results: seasonal peaks in DVC (fall) and E(lk)VC (winter, fall); most accidents in late afternoon and evening hours • Cluster analysis: EVC and DVC did not occur randomly • Density analysis: identified several areas with higher concentra- tions of accidents • Accident site characteristics: when considered 1 at a time, no variable measured was a statistically significant predictor of hotspot or control status; variables chosen as predictors in final model were ln(average number woody stems > 2 m in height), and maximum slope Discussion: ambiguous relationship between accidents and snowfall might derive from our pooling of snowfall and accident data by month instead of using daily snowfall measurements and accident counts • Poor results with utility of different variables could be result of small sample size • Because of small sample size, placed a higher priority on finding a well-fitting model that made sense rather than on finding one that was statistically significant Caryl, F.M. 2003. Ungulate mortality on a forested highway. University of East Anglia, Norwich. M.Sc. Dissertation (copyrighted) 42 pp. Objective: to produce a multi-species empirical model of ungulate road mortality using highly accurate spatial data from field and GIS based sources in Kootenay National Park, British Columbia, Canada. It would then be determined if the model could be repro- duced using GIS-based variables only, to provide a quick and ef- fective management guide to focus mitigation efforts at high risk locations Data layers: species included moose, mule deer, white-tailed deer, elk and bighorn sheep • Ungulate mortality data: date, number, species, sex, age, loca- tion from GPS • Control site data: randomly selected non-kill sites along high- way; ratio of control sites to kill sites larger than one desirable due to greater expected variation in control environmental attributes • Field-based environmental variables: distance to cover (> 1 m tall and continuous), % cover forest; % cover shrub; % cover herb; % cover bare ground; roadside slope; verge slope; adjacent land slope; inline visibility; angular visibility • GIS-based variables (using ArcView): elevation; distance to hy- drology; distance to human use; road sinuosity ratio; change in elevation; habitat importance for deer, moose and elk; barrier Analysis: Spearman’s rho correlations used to screen for multi- collinearity, removed one highly correlated biophysical variable be- fore model development; differences between seasons compared using χ2 tests • Model development: logistic regression, stepwise selection process using log likelihood ratio tests and a prob. value of 0.05 for entry and removal of variables to the model; selection process then repeated using only GIS-based variables; χ2 used as a goodness-of-fit test of model appropriateness; Wald stats to test the significance of independent variables; direction of pre- dictor influence verified using Mann-Whitney U tests; odds ra- tios examined to assess contribution that a unit increase in pre- dictor variable made to outcome probability • Model validation: 5 control and 5 kill sites randomly chosen to validate model’s predictive ability; 0.29 chosen as classification cut-off for predicted group memberships based number of kill sites vs control sites; predicted probabilities classified into 3 groups: low, moderate and high risk of kill Results: Kill sites highly aggregated; highly significant seasonal differ- ences (high in summer); roadkills positively associated with daily traffic volumes • 3 of 17 environmental variables shown to be reliable predictors: distance to humans, elevation, distance to cover; all had nega- tive coefficients; 67.3% kill sites, 64.3% control sites predicted correctly, giving overall success of 65.2% 141

• 2 of 9 GIS variables shown to be reliable predictors: distance to humans, elevation; both had negative coefficients; 61.5% kill sites, 65.1% control sites predicted correctly, giving overall success of 64% • Model testing: 3 of 5 control sites, 4 of 5 kill sites (70% of sites) correctly classified using GIS model • Probability surface with low moderate and high collision prob- ability created using 2 GIS variables Discussion: kill sites not located randomly in time or space; kill sites found at lower elevations than control sites and closer to human use areas; odds of a kill decreased by 96% with each additional 1000 m elevation above sea level if all other variables controlled; odds of a kill decreased by 40% with each additional 1 km distance from human disturbance sites; probability surface showed a close agree- ment with observed roadkill locations, would be useful guide for quick assessment of possible high risk locations Finder, R.A., Roseberry, J.L., and A. Woolf. 1999. Site and landscape conditions at white-tailed deer/vehicle collision locations in Illi- nois. Landscape and Urban Planning 44: 77–85. Objective: to determine if high deer/vehicle accident locations could be predicted from remotely sensed land use/land cover patterns Data layers: 98 counties in IL; 1989–1993; rd segments with high con- centrations of DVAs on state marked routes; n=86 locations with ≥ 15 reported DVAs analyzed • Plotted hotspot road segments using TIGER data files and Map and Image Processing System GIS software; road segments ad- justed to 1.3 km; random locations on same route of same length for control purposes • Landcover classification (Landsat TM): crops, forest, grass, water, developed, orchards; topographic physical features from aerial photographs and topographic maps Analyses: 0.8 km radius buffer zone around each road segment to quan- tify and compare landscape composition and pattern using FRAGSTATS • Simple correlation used to investigate relations among variables; highly correlated eliminated • t-tests to determine if variable means differed between hotspots and controls; those indices with |t| values ≥ 3.0 selected as pre- dictor variables for logistic regression • Stepwise logistic regression model selection process to obtain a preliminary equation • AIC to compare models • Stepwise selection process repeated using only landscape in- dices, satellite imagery data only • 5 paired sites used to test models’ predictive abilities Results: variables included in model 1: % distant woody cover, % adja- cent gully; natural log of area of recreational land within buffer, natural log of width of corridors crossing road; of 10 samples to test model validity, 5 control and 4 hotspots correctly predicted • Variables included in model 2: Simpson’s diversity index; natu- ral log of woods mean proximity index; of 10 samples to test model validity, 4 control and 2 hotspots correctly predicted Discussion: study demonstrated that DVA site statistics and RS habitat and highway data can be used to predict DVA locations Gundersen, H., and H.P. Andreassen. 1998. The risk of moose- collision: a logistic model for moose-train accidents. Wildlife Bi- ology 4(2): 103–110. Objective: to use a logistic model to establish the most risky train de- partures for Rørosbanen railway which has the highest risk of moose-train collisions per km in Norway (Gundersen et al. 1998). In the model we have included speed of train, type of train, time of day and lunar phase, besides climatic covariables known to be cor- related with moose-train collisions. Data layers: success (1) or failure (0) of train hitting moose; train departures; train route; train predictor variables (average speed, train type, time of day); daily average temperature; snow depth; lunar phase; data recorded from Dec-Mar 1990-1997 Analysis: a logistic model was applied incorporating the above variables; the most parsimonious model chosen using AIC; another model made containing only passenger trains running the whole distance between 2 towns, snow depth, daily average temp, lunar phase, train speed, time of day left station; used data from 1990–1996 to predict the number of train-killed moose for each train for the winter of 1996/1997 Results: most parsimonious model included route, time of day, lunar phase, snow depth, temp; according to AIC, this model is indistinguishable from one includ- ing average train speed; best model for the second analysis included all predictor variables. Problems with morning train results in second analysis due to in- troduction of logging activity in Storholmen in 1996. Second model gave good results for morning train after removing 6 collisions at Storholmen Discussion: authors introduced a new approach to study game-vehicle accidents by focusing on factors that cause vehicles to collide with game rather than focusing on the factors that cause game to be close to traffic arteries. Gundersen, H., Andreassen, H.P., and T. Storaas. 1998. Spatial and temporal correlates to Norwegian train-moose collisions. Alces 34: 385–394. Objectives: In this study we reveal how temporal variation, i.e. climatic factors and moose population density, and spatial variation, i.e. landscape pattern and changes in food availability, correlate with moose–train collisions along the railway in Norway which is most burdened by wildlife collisions. Data layers: train kills (time, location to nearest 100 m) daily average temperature, snow depth size of moose pop estimate by population model Cersim (based on observations by hunters in previous season) Analysis: 2 categories of analysis—temporal factors (climatic and pop den- sity) and spatial factors (landscape patterns and food availability) • Temporal factors: compared the freq. distribution of days w/ certain weather conditions (expected) w/ the freq. distribution of collisions at the various weather conditions (observed) by a goodness-of-fit test. GLMs used to correlate moose pop size and number of collisions • Spatial factors (regional): analyzed correlation between land- scape patterns and number of collisions per 1 km segment – Landscape patterns: (1) topography—measured as the dif- ference in height from the bottom of the valley to the highest point within 2.5 km to East and West of line and averaged; (2) distance to the nearest side valley—because assumed to channel moose migratory behavior; – Tested and corrected for autocorrelation in 1 km segments • Spatial factors (local): to explain spatial variation of collisions, compared number of collisions before and after changes in food availability due to logging activity in two areas 142

– One area had increased food availability while the second had decreased food availability – Linear model including factors that significantly correlated to yearly variation in collisions (climatic factors and population density) used to obtain estimate of expected number of col- lisions before and after change in food availability; expected vs observed compared with goodness-of-fit test Results: Temporal effects: number of collisions associated with both temp and snow depth; combined temp and snow depth into vari- able (accidental period) which started when snow depth exceeded 30 cm and lasted until temp stabilized above 0 degrees C. Number of days in new variable explained 83% of yearly variation in num- ber of moose collisions; GLM including both accidental period and pop density explained 88% of yearly variation Spatial effects: significant negatively correlated between number of col- lisions and distance to nearest side valley; no association between number of collisions and topography; changes in food availability strongly associated to number of collisions Discussion: moose usually killed in winter on days with lots of snow and low temps; influenced by migratory routes to lower elevations and availability of food; temporal variation due to climatic factors, spa- tial variation due to migratory routes and food availability. Hubbard, M.W., Danielson, B.J., and R.A. Schmitz. 2000. Factors in- fluencing the location of deer-vehicle accidents in Iowa. Journal of Wildlife Management 64(3):707–713. Objective: to examine the influence of highway and landscape variables on the number of DVAs in Iowa Data layers: number of DVAs, traffic and landcover data obtained for all milepost markers within the state (n = 9,575) • GIS maps of habitat (Landsat imagery, 1990–1992): collapsed habitat types into cropland, woody cover, grass, artificial, water and miscellaneous • White-tailed deer harvest numbers for each county from IDNR; DVAs from 1990–97 for state’s highways from IDOT; traffic vol- ume estimates linked to all accident sites • For each DVA included: distance to nearest town or city, dis- tance to nearest city with pop > 2,000, number of bridges, num- ber of lanes of traffic • Accident location often recorded to nearest 0.10 mile, but more than 33% recorded at milepost, therefore all locations collapsed to nearest milepost Analysis: dependent variable-number of accidents in each 1.61 km seg- ment from 1990–97 • Randomly selected sample sites (n = 1,284); clipped 2.59 km2 landscape section with sample site • FRAGSTATS used to characterize landscape sections; linked to number of DVAs for segments • DVAs separated into 2 categories (0-13, > 14 hits/segment) based on natural break and sample size • Logistic regression: to examine relationship of DVAs to traffic, highway characteristics, human pop centers, and landscape vari- ables; stepwise selection procedure for variable inclusion during model development • Factor classification tree (FCT) constructed to refine ability to select high DVC areas – Robust relative to a more standard cluster and discrimination analysis that might be used (Emmons et al. 1999) – Followed method described by Venables and Ripley (1994) to find the rooted subtree with a minimum AIC • Evaluated performance of logistic regression model by applying to a randomly selected set of DVA sites not included in model development (n = 245) Results: 67% of 9,575 mileposts associated with DVA; > 25% DVAs at 3.4% of mileposts (325) • Significant 6-variable model produced; 4 variables landscape features, 2 highway characteristics • FCT final classification produced a tree with 57 nodes and a mis- classification rate of 0.153%; bridge frequency was best predic- tor of high DVA sites • Model validation: correctly classified 63.3% of sites Discussion: edges not found to be important, however it is possible that the resolution of our data was too coarse to identify all edges used by deer as travel corridors. Bridges always indicate points where major edge-creating landscape features intersect roadways, and therefore may be better predictors of concentrations of DVAs than more broadly defined edge indices Joyce, T.L., and S.P. Mahoney. 2001. Spatial and temporal distribu- tions of moose-vehicle collisions in Newfoundland. Wildlife Society Bulletin 29(1): 281–291. • Objective: “we . . . relate rate & severity of human injury to time of accident, road conditions, road alignment, vehicle speed (via posted speed limits), number of vehicle occupants, and sex/age of moose struck . . . to develop measures to reduce MVCs and severity of injuries” • MVC reports from conservation officers and RCMP from 1988–1994; accidents generally reported if damage > $1000 CD ($500 CD before 1991). • Spatial analyses: N = 1690 MVCs on Trans-Canada Highway, mapped/digitized, divided 900 km of TCH into ninety 10 km sections. Category each section by – Annual average MVCs (< 1.75 = low, 1.75-3 = medium, and > 3 MVCs = high) – Moose density (< 1.0 = low, 1-2 = medium, and > 2 = high) – Traffic volume (low vs. high) – Results:  Areas of low or high moose densities experienced greater probabilities of MVCs than areas of moderate moose densities.  Higher probability of MVCs in areas with high traffic volumes, regardless of moose densities • MVCs and human injuries analyses: log linear modeling to eval- uate effects of the following variables on severity of human injuries (low vs. fatalities) – Darkness (day vs. dusk/dawn/dark) – Road condition (wet-slick vs. dry) – Road alignment (straight or curved) – Vehicle occupants (driver only vs. driver + passengers) – Posted speed limits (< 80 km/h vs. > 80 km/h) – Passenger vehicles only (made up 89.5 of all reported colli- sions and had most serious injuries/fatalities) – Determined influence of each variable on injury severity through forward model selection from main effects to sat- urated model; used log-likelihood value (G-sq) of main ef- fects model (included all variables) as baseline against which all other parameters were judged; each 2-way inter- action was then added to main effects model and tested. De- viance between baseline value and derived G2 stat measured importance of that parameter to model. Excluded parame- 143

ters with small deviation, determined at 95% confidence level. – Results:  No significant relationship between road alignment and ac- cident severity (though 79% of accidents occurred on straight vs. curved roads)  Model 1 (injury, darkness, speed): Light condition and posted speed limit related to severity, and mutually inde- pendent—risk 2.1x greater at night and 2x higher at high- way (high) vs. non-highway (low) speeds.  Model 2 (injury, road condition, occupants): more acci- dents occur than expected when passengers were in vehi- cles on dry roads, but not when there were no passengers or wet roads. Risk of severe injury or death 2x higher w/at least 1 passenger present compared to driver only. • Also looked at temporal and age/sex influence . . . – Moose calves more likely to be involved Aug–Oct, yearlings in June/July, and adults in July–Aug. – More bull moose involved than exp. – No significant relationship between diurnal patterns and sex or age. – Injury 6x more likely in collision w/ adult than calf • Discussion points of interest beyond results: – “Bashore et al. 1985 found positive relationship b/w speed limit, driver in-line site visibility along road, and number of collisions (see also Poll 1989).” – “Damas & Smith 1982 estimate night speeds have to be re- duced to 60km/hr or less under low-beam light to sufficiently expand stopping distances and prevent accidents...enforce- ment key and difficult/enormous . . . most effective measure may be with drivers” – Lavsund and Sandegren 1991. Moose vehicle collisions in Sweden, a review. Alces 27:118–126.  “Lavsund and Sandegren (1991) found 3x increase in severity of injury for vehicles moving 70–90km/hr com- pared to lesser rates” – Discussed PR programs, mentioned Terra Nova National Park in Canada—long running program (12 yrs as of 2001) involving using moose silhouettes and posting of number of MVCs/year; have found Newfoundland drivers perceive Terra Nova National Park as area with greatest number and risk of MVCs. See Hardy R.A. 1984. Resource management plan for MVCs, internal Terra Nova NP Parks Canada report. Kassar, C., and J.A. Bissonette. 2005. Deer-vehicle crash hotspots in Utah: data for effective mitigation. UTCFWRU Project Report No. 2005(1):1–28. Utah Cooperative Fish and Wildlife Research Unit, Utah State University, Logan Utah. The data originate from collision reports prepared by law enforcement officers and provided to UDOT by the Utah Department of Public Safety. A wildlife–vehicle collision is included in the database only if an animal was actually hit, if the estimated vehicle damage ex- ceeded $1,000 and/or if a person was injured. Collisions included in the database do not account for crashes that occurred as a result of swerving to miss an animal. We focus on collisions involving almost exclusively mule deer. We used the UDOT vehicle crash database to study DVC patterns and trends from 1992–2002 on 248 state routes. We evaluated all routes for frequency of deer kills and identified hotspots (at least 1 collision/ mile/year). We considered hotspots to consist of two parts: (1) a core area, the road segment where collisions per mile are most con- centrated; and (2) a mitigation zone, buffering segments on each side of the core where appropriate mitigation actions can account for animal movement and behavior and help avoid the “end of the fence” problem. Summary of results: 24,299 WVC over 11 years; 99.6% had dates and years associated with them; average of 2,202 (2,025–2,577) colli- sions per year; 12 routes had high DVC rate over entire length (≥ 10/mile); 16 with moderate (5–9.99/mile); 148 with low rates (> 0–4.99); 65 routes with no reported DVC; 7 with data unavailable; 54.6% of all collisions occurred on 10 routes Collision frequency: 0–21.27 per mile; 1/3 occurred Oct–Dec; 55.7% occurred 1800–2400 hr Hotspots: found 183 hotspots in Utah; core hotspots average 5.3 miles in length; isolated hotspots were 1 mile (1.6 km) in length; hotspot collisions were concentrated; 57.74% of all collisions occurred within a cumulative (~ 1001 km) range, or 10.5% of total analyzed highway miles (9,500 total km) Malo, J.E., Suarez, F., and A. Diez. 2004. Can we mitigate wildlife– vehicle accidents using predictive models? Journal of Applied Ecology 41: 701–710. Objective: the present study analyzed a European case and developed models of the environmental variables associated with the occur- rence of collisions with animals at two spatial scales (1.0 and 0.1 km). Provided that a few variables underlie the location of animal crossings, it should be possible to predict where accidents may occur and use this information to optimize mitigation efforts. With this aim, we (1) defined road sections with high collision rates using a clustering detection procedure; (2) analyzed the landscape vari- ables of sections with high collision rates in contrast to low colli- sion sections; and (3) used a 0.1 km scale to analyze the points where collisions occur in contrast to those where they do not. Data layers: official traffic database on WVC for Jan 88–Feb 01; n = 2,067; includes date, location (0.1 km); 63% of WVCs occurred be- tween 1998–2001; 98% involved roe deer, wild boar or red deer • Definition of high accident rd sections: determined by detecting clusters of WVC locations; contiguity analysis conducted by comparing the spatial pattern of collisions with that expected in a random situation; each km of rd with 3 or more collisions, es- pecially over consecutive km, could be defined as a high colli- sion section • 1:50,000 digital forest cover map (cover types used: riparian for- est, other forest, scrub, grassland, crops, rivers and dams, ur- banized and unproductive); processed in ArcView 3.2 • Habitat features in high collision sections: analyzed 84 loca- tions—41 high collision, 43 low collision; sampling unit = cir- cular area (radius 1000 m) around reference point; calculated proportion of each habitat type; ecotone length (meters of contact lines between habitat polygons); habitat diversity (Shannon index) • Variables associated with collision point: analyzed at 0.1 km scale: sampling points from 18 high collision sections in which WVCs had been recorded in at least 12 hectometer posts; 6 hec- tometer posts with highest number WVCs chosen from each section; a further 6 taken at random from amongst those with recorded collisions; 12 control samples w/o WVCs taken at random from each section • Evaluated 13 quantitative and 15 qualitative variables covering aspects linked to driving, general features of the road environs, features associated with animal movements; measurements 144

taken for 100 m rd stretch and evaluated 100 m on each side of road Analysis: analyzed at both regional and local scales; predictive models for the location of sections/points with and without collisions were gen- erated by binary logistic regression; validated with independent data • 2 models fitted for each analysis: 1 complete with all measured variables, 1 reduced version with only most significant explana- tory variables • Variable selection for reduced models using G2 statistic; ensured new model was not significantly more informative than previ- ous one, avoided correlated variables and those w/o predictive capacity • Significant threshold in variable comparison: P = 0.05; proba- bility threshold for model: P = 0.1 Results landscape scale: 41 high collision rd section identified; 7.7% of rd network accounting for 70.5% of all records; distributed among secondary and tertiary roads; none along A-2 fenced motorway • High collision areas had higher cover of non-riparian forest, lower crop cover, lower urbanized areas, and higher habitat di- versity than low collision areas • Simplified model included forest cover, urbanized area and habitat diversity; had same predictive capacity as full model: 87.0% correct classification for all cases, 88.5% for high and 85.7% for low collisions sections; successfully predicted 70% of 30 cases used as test data Results for local scale: low collision areas associated with crossroads, underpasses, guard rails, embankments at least 2 m high with mod- erate or steep slopes, greater distances from roads to hedgerows and forest stands, and shorter distances from roads to buildings • Reduced model included presence of crossroads, presence and continuity of guardrails, presence and continuity of embank- ments and distance to nearest forest stand; correctly predicted 61.2% of cases, 72.7% of collision points, 48.4% of non-collision points; full model results were 74.0%, 79.2% and 68.1% respec- tively; correctly classified 64.2% of test cases Discussion: results show it is possible to predict the location of WVCs at 2 scales; results should be considered cautiously; validity could be hindered by assumption of a binomial distribution of errors— bigger issue for local rather than landscape model Nielsen, C.K., Anderson, R.G., and M.D. Grund. 2003. Landscape in- fluences on deer-vehicle accident areas in an urban environment. Journal of Wildlife Management 67(1): 46–51. Objective: quantified the effect of landscape factors on DVA in 2 Min- neapolis suburbs to provide public officials and wildlife managers with recommendations for managing the landscape to reduce DVA. Data layers: digitized DVA locations from 1993–2000 using ArcView • DVA clustering to differentiate DVA areas (≥ 2 DVA) and control areas (0 or 1 DVA); overlaid 0.5 km road segments at midpoint of DVA clusters; buffered road segments for variable selection purpose with a 0.1 km perpendicular distance from edge of each side of road; repeated for control areas (n = 160 total) • Landscape variables: land cover (grassland/residential, wood- land, open water); land use (commercial/industrial, residential, public land); ArcView Patch Analyst used to calculate 60 class and landscape level variables; road curvature (straight or curved); number of buildings in buffer, speed limit; number of lanes; distance from road to nearest forest cover patch; ROW topography based on presence or absence of ditches Analysis: univariate procedure used to reduce 66 variable set to smaller group; removed variables correlated at r ≥ 0.70; left with number of buildings, number of forest cover patches, proportion of forest cover, Shannon’s diversity index for further analysis • Logistic regression analysis to determine which variables best explained difference between DVA areas and control areas; built one global model and 10 a priori models; used AIC and Akaike’s weights to rank and select best model; used relative weight of evidence to compare parameter importance; model averaging to incorporate model-selection uncertainty into final uncondi- tional parameter estimates and standard errors • 40 sites retained to validate best-fit model Results: global model was significant; areas with DVA contained fewer buildings, more patches and higher proportion of forest cover, more public land patches and higher Shannon’s diversity index of landscape; Akaike’s weights indicated number of buildings and number of public land patches most important variables • 7 models necessary to compile a 95% confidence set; best-fit model correctly classified 77.5% of test sites Discussion: study unique because assessed landscape factors influenc- ing DVA in an urban environment; pooled data over 7-year period so pop growth or land-use change may have affected data Nielsen, S.E., Herrero, S., Boyce, M.S., Mace, R.D., Benn, B., Gibeau, M.L., and S. Jevons. 2004. Modelling the spatial distribution of human-caused grizzly bear mortalities in the Central Rockies ecosystem of Canada. Biological Conservation 120:101–113 Objective: “We develop predictive models and maps that describe the distribution of human-caused grizzly bear mortalities . . . Our goal was to understand, through modeling, the relationships among bear mortality locations and landscape-level physiographic and human variables. More specifically interested in (1) examining the spatial density of grizzly bear mortalities; (2) evaluating possible differences in the physiographic attributes of mortality locations . . .; and (3) developing predictive models that estimate the relative proba- bilities of bear mortality (risk) given multivariable combinations of physiographic variables.” Data layers: mortality info from 1971–2002; included dead bears and translocated bears; location (UTM when possible), accuracy of location (accurate, reasonable, unknown), month, year, sex, age, and cause of mortality; n = 279 accurate and reasonable locations • GIS (spatial) predictor variables: land cover (Landsat TM 95-98, 5 classes); distance to edge of nearest land cover; greenness index; distance to nearest water feature; distance to nearest lin- ear human use feature; terrain ruggedness index Analyses: 3 separately scaled moving windows to calculate total density of mortality locations: 520 km2; 900 km2; 1405 km2; secure sites = pixels with 0 mortalities; high mortality zones = pixels with > 31 mortalities (≥ 1 mortality/year) • Logistic regression to assess relationship between landscape at- tributes of mortality locations and categories of demographic status, season, and mortality type • Random sample of locations generated to contrast with human- caused mortality locations • Data divided into model training (80%) and model testing (20%) data sets • Logistic regression used to contrast the location of grizzly bear mortalities with sites used by bears (through telemetry) 145

Results: mortalities concentrated within 3 regions regardless of scale examined • 900 and 1405 km2 scales: mortality densities within moving win- dows exceeded 31 mortalities for the three sites; at 520 km2 scale: only one site as high mortality zone • Total area occupied in high mortality zones: 520 km2 =1.4%, 900 km2 = 3.8%, 1405 km2 = 13.2% • Total area occupied in secure zone: 520 km2 = 23.9%, 900 km2 = 13.9%, 1405 km2 = 23.9%; 22–32% secure habitat in areas of non-habitat • Mortality locations positively associated with access, water, and edge features; negatively associated with terrain ruggedness and greenness indices • Non-harvest mortalities more likely to occur in shrub and grass- land habitats and closer to edge features and access than random points • Mortalities more likely to occur in deciduous forest and shrub habitats, nearer to edge, access, and water than radiotelemetry locations; also sig related to areas of low greenness and minimal terrain ruggedness Premo, D.B.P., and E.I. Rogers. 2001. Town of Amherst deer-vehicle accident management plan. White Water Associates, Inc., Amasa, Michigan (www.white-water-associates.com) Objective: This plan’s focus is reducing DVAs. The primary measures of concern are the numbers of DVAs and the patterns of their dis- tribution in the Amherst landscape. The DVA Management Plan establishes its initial goal at two spatial scales, whole town and hotspots. Data layers: DVAs reported to police (n = 3300) and counts of carcasses removed from road (n = 3320); Jan 1991–Dec 2000; entered into GIS; time of day, time of year, location, speed limit, landcover; deer population; management zones Analyses: density analysis in ArcView used to examine landscape pat- terns of DVAs. This allowed mapping of DVAs as density contours and identification of DVA hotspots; density calculated by circles of half-mile radius; DVA density = DVA/sq. mi.; when displayed in conjunction with other mapped features, contours could be used to determine the causes of the hotspots as well as examine tempo- ral changes Results: temporal changes in hotspots before, during and after the con- centrated lethal control period Rogers, E. 2004. An ecological landscape study of deer-vehicle colli- sions in Kent County, Michigan. Report for the Michigan State Police, Office of Highway Safety and Planning. White Water As- sociates, Inc., Amasa, MI 49903. 56 pp. Objective: an analysis of landscape patterns of DVCs in 4 townships of Kent County, Michigan Data layers: GIS database available; included spatial layers drawn from MiRIS Base Maps and Land Cover Maps; political boundaries, land survey section lines, transportation, watercourses and lakes, major veg cover types, development DVC locations from Michigan Accident Location Index (MALI) main- tained by Michigan State Police, 1992–2000; locations based on po- lice reports; uses system of unique physical reference numbers to spatially record accidents N = 3127 DVC records coded by township, year, month, time of day Half-mile grid created in ArcView and superimposed on study area for summarization of landscape data; 1⁄2 mile chosen because of assumed low precision in DVC location data; grid split into two equally sized groups of cells, 1 group for model development, 1 for validation Density function in SpatialAnalyst used for visual inspection of DVC patterns; density calculated for each cell by summing number of DVCs found within search radius (1⁄2 mile) and dividing by the area of the circle Stepwise logistic regression to identify a subset of parameters to build predictive logit model; final model had 3 parameters: linear feet of highways and roads, linear feet of roadway within 1000 ft of water- course, number of mapped land use polygons Analysis: mapping of DVC densities summed across all years; mapping in 3-year blocks; resulted in very little change in hotspots across years, only minor shift in location and density Romin, L.A., and J.A. Bissonette. 1996. Temporal and spatial distri- bution of highway mortality of mule deer on newly constructed roads at Jordanelle Reservoir, Utah. The Great Basin Naturalist 56(1): 1–11. Objectives: (1) to determine whether mule deer roadkills on newly relo- cated highways would increase, (2) to evaluate the influence of topo- graphic features and vegetation characteristics on the kill pattern Data collected from 15 Oct 1991–14 October 1993; 47.3 km total on 3 highway segments; road construction completed in 1989 Data layers: deer roadkill data collected at least once per week (date, highway identification, location to nearest 0.10 mile, age class); • 4 randomly selected pairs of kill (5 or more kills/mile) and non- kill zones of 0.10-mile road length each; for each pair, estab- lished 3 transects perpendicular to road, 100 m apart, extended 100 m beyond ROW fence to evaluate respective road alignment and associated habitat features • Distribution of kills (nearest 0.01 mile); avg traffic volume and speed for each highway; % vegetative cover; topography proxi- mal to area roads; twice monthly spotlight counts of deer (sex, age class, activity, location to nearest 0.10 mile); deer snow track counts (number of trails, orientation relative to road—parallel vs. perpendicular); observable area from highway every 0.10 mile; ROW width and slope; ROW vegetation; vegetation com- position; road type Analysis: stereoscopic aerial photography used to describe habitat fea- tures; transparent grid placed over photos to determine percent cover and topographic features at deer-highway mortality locations beginning at the road and extending 1.2 km distant; identified roadkill and live deer locations, as well as descriptive roadside fea- tures to 0.10 mile Results: 397 deer roadkills during 2 years of study; deer kills averaged < 20 before roads relocated; 19 deer kill zones identified; deer spot- light counts not significantly correlated with kill sites; kill zones had higher mean % cover Discussion: traffic volume significantly influenced deer mortality; higher kill levels occurred along drainages; ROW topography may funnel deer to the ROW and encourage movement along highway corridor Seiler, A. 2005. Predicting locations of moose-vehicle collisions in Sweden. Journal of Applied Ecology 42: 371–382. Objective: to develop MVC prediction models based on data that are readily available for road planning at strategic and project levels (Seiler and Eriksson 1997). This study used accident statistics from before 1999, remotely sensed landscape information, digital topo- 146

graphic data and official road and traffic data to identify the strongest set of environmental and road traffic parameters that can be used to foresee the risk of MVC. Data layers: Landscape, road and traffic, collisions, moose abundance and harvest • Landscape data: Swedish Terrain Type Classification maps (TTC) (based on SPOT and Landsat TM satellite images) com- bined with digital topographic maps at a scale of 1:100,000; 1994-1998, updated with aerial photographs from 1999 – 25x25 meter pixel size; 6 major land cover types; densities of landscape features measured as km per km2, number of in- tersections per km rd; distances between rd and landscape el- ements measured in meters and log(e) transformed • Road and traffic data: from digital road databases provided by the SNRA – Averaged rd density: model area—1.92 km/km2; test area— 1.76 km/km2; 75% is privately owned – National trunk roads: 2,500–20,000 vehicles/day; > 90 kph; Tertiary public roads: 80% of rd network, < 1,000 vehi- cles/day, < 70 kph; Primary roads (speed limit > 90 kph) in model area 71% fenced, in test areas 35% fenced – Average number of vehicles/day used jointly with its square to adjust for the humpbacked relationship between traffic volume and MVC frequencies observed in the data • Moose–vehicle collisions: obtained from the SNRA rd acc stats containing all police-reported accidents on public rds between 1972–1999 (type of accident, place, time) – Accuracy not evaluated, error estimated at ± 500 m (L. Savberger, pers com). – N = 2185 for model area; N = 1655 for test area (for 1990–1999) • Moose abundance and harvest: indices of moose abundance were determined from the average annual game bag per hunt- ing district during the 1990s – Model area: 21 hunting districts, avg 3.45 shot/1000 ha (1.0–5.1); Test area: 14 hunting districts, avg 4.25 shot/1000 ha (1.6–6.4) – Moose harvest and MVC correlated strongly at county and national levels over the past 30 years (Seiler 2004) – No migration between winter and summer ranges Analysis: 3 logistic regression models were developed to identify pa- rameters that significantly distinguished between observed MVC sites and non-accident control sites • Model composition: N = 2000 MVC records, N = 2000 ran- domly distributed non-accident control sites located at least 1 km away from MVC site – 500 m buffer created around each point (to account for esti- mated error) – Unpaired t-tests and univariate logistic regression models used to identify among 25 variables those that sig (P < 0.1) differed between accident and control sites (all other analyses used P < 0.05); intercorrelated variables removed, 19 variables left – 3 a priori models: (1) road-traffic (only basic road and traf- fic parameters); (2) landscape (parameters obtained from RS landscape data and digital maps); (3) combined model – Stepwise (backward) regression to identify sig parameter combos; sets compared using AIC and Akaike weights; model structure considered adequate if variance inflation factors were close to 1.0 • Model validation: N = 1300 accident sites (1km road sections) and 1300 non-accident sites (1km road sections) from new county; 500 meter radius around the center point of each road section; univariate logistic regression analyses to determine model performance in distinguishing accident from non-acci- dent sites • Counteractive measures: to illustrate and evaluate the predicted effect of different counteractive measures on accident risks, changes in MVC probabilities relative to varying traffic volume and moose abundance modeled with respect to increased forest proximity, reduced vehicle speed and road fencing. Results: Dominant factors determining MVC risks included traffic vol- ume, vehicle speed and the occurrence of fences • Model results: model ranking according to AIC weights: (1) traf- fic (classified correctly 81.2% of all observations), (2) combined (83.6%, but lower ranking because of greater number of vari- ables), (3) landscape (67.5% MVC sites and 62.2% control sites) • Validation results: combined model gave best results predicting 72.4% of all MVC sites and 79.8% of all control sites; traffic model concordance = 77.9%; landscape model concordance = 62.0%; all results are significant • Identified 72.7% of all accident sites • Other parameters were important in distinguishing between ac- cident and control sites within a given road category including amount of and distance to forest cover, density of intersections between forest edges, private roads and the main accident road, moose abundance indexed by harvest statistics • Together, road traffic and landscape parameters produced an overall concordance in 83.6% of the predicted sites and identi- fied 76.1% of all test road sections correctly • Speed reduction appeared to be most effective measure to re- duce MVC risk at any given traffic volume; modified by fencing, moose abundance and forest proximity Discussion: spatial distribution of MVC not random; collisions a prod- uct of environmental factors quantified from RS landscape info, road traffic data and estimates of animal abund.; parameters used to identify high risk roads (traffic data) different from parameters used to identify high risk road segments (landscape data) Simek, S.L., Jonker, S.A., and Mark J. Endries. 2005. Evaluation of principal roadkill areas for Florida black bear. ICOET 2005. Principal roadkill areas (PRA) defined as 3 or more roadkill bear within a distance of 1 mile (1.6 km) Data from 2001-2003 analyzed using density analysis with Spatial Analyst in ArcGIS 6 core and 2 remnant black bear populations evaluated Objectives: to establish whether previously identified “chronic” areas were still apparent or had shifted, and whether different criteria and timeframes would impact results and subsequent conservation recommendations using current and previously evaluated roadkill data Data layers: FWC bear roadkill data and the major roads shapefile (in- terstates, state highways, county highways, highway access ramps, and major local and forest roads) Density analysis: raster format with 30 m x 30 m pixel size; creates a 2D raster grid of pixels calculating the total number of points that oc- curred within the search radius divided by the search area size; pix- els within areas meeting principal roadkill definition reclassified to 1 (referred to as CRDA), all others classified as no value; 1-mile buffer created around CRDA dataset (referred to as PRBA); analy- sis repeated using criteria outlined by Gilbert and Wooding (1996) of 8 roadkill bear/7 miles (they used dataset from 1976–1995) 147

Results: With a few exceptions, most of the PRA identified by both methodologies overlapped; Gilbert methodology encompassed a much larger area which included more roads whereas the current methodology identified more specific principal roadkill road seg- ments; using similar timeframe (1976–1995), two methods again identified very similar PRA but new method identified additional areas; using complete timeframe (1976–2004) PRA identified in all 6 populations, including 2 which had not been previously identi- fied as containing PRA Discussion: illustrated that changes in locations of PRA can occur when using different methods and timeframes; different results with re- spect to scale—Gilbert’s method gives PRA on a broader scale, new method provides increased specificity on actual locations of hotspots; PRA will change with changes in habitat and land use; preferred method (Gilbert or new) will depend on goals and objectives Singleton, P.H., and J.F. Lehmkuhl. 1999. Assessing wildlife habitat connectivity in the Interstate 90 Snoqualmie Pass Corridor, Washington. ICOWET III. Objective: an assessment of wildlife habitat connectivity and barrier ef- fects of I-90 from Snoqualmie Pass to Cle Elum was initiated in Jan- uary 1998. The assessment consists of 5 components including a GIS analysis of ungulate roadkill distribution Data on ungulate roadkill locations was collected by WSDOT mainte- nance personnel from 1990 to 1998. We imported these records on species and location of roadkills into the GIS and used a moving win- dow analysis to determine the number of kills per mile along I-90 Results: 4 roadkill concentration areas were identified based on the analysis of 490 deer and 194 elk kills. Quantitative analysis of land- scape characteristics of collision locations has not yet been con- ducted. However, roadkill distribution appears to be affected by landforms that channel animal movement and by human develop- ment and disturbance patterns. II. Spatial Analysis Techniques Boots., B.N. and A. Getis. 1988. Point Pattern Analysis. Sage Publica- tions, Inc. Newbury Park, California. 85 pp. • Development of statistical analysis of point patterns originated in plant ecology over 50 yrs ago. • Point pattern map has 2 components: – Point pattern: has size (# points, n) – Study area: may be 1 or multidimensional. Roads would be rep- resented as a one-dimensional study area. Two-dimensional study areas are enclosed by a boundary, which determines the shape of the study area. Road study areas do not have a shape necessarily. – If studying the location of points relative to the study area, then examining dispersion of points; if studying locations of points relative to other points, then examining the arrangement of points. In many cases dispersion and arrangement may be highly correlated. • When analyzing pt patterns, usually use method that involves establishing a theoretical pattern that is compared to other pat- terns that are identified. That theoretical pattern chosen is for- mally called a homogeneous planar Poisson point process, and these points are generated under two conditions: – Each location has equal chance of receiving a point (uni- formity). – Points selected do not influence the selection of other loca- tions for points (independence). – These conditions imply the study area is homogeneous w/no interaction b/w points, and the resulting pattern from that point generation process could be considered to occur by chance in an undifferentiated environment, referred to as “complete spatial randomness” or CSR (cites Diggle 1983). – CSR is idealized standard which other patterns can be com- pared to—  Clustered patterns occur when points are significantly more grouped in the study area than they are in CSR.  Regular patterns occur when points in the study areas are more spread out than they would be in CSR – Opposite of uniformity condition/homogeneous model: het- erogeneous models, which imply some locations in study area are more prone to receive a point than other locations, or may be less likely to receive a point. – If independence assumption is relaxed, then there may be in- teraction among points—i.e., they may attract or repulse each other. – To analyze dispersion or arrangement characteristics, use hy- pothesis testing procedures, with the null hypothesis always that the pattern is CSR, with the simplest alternative hypoth- esis being that the pattern is not CSR.  If null not rejected, no further analysis needed.  Null (CSR) provides division between clustered and reg- ular patterns.  If null is rejected, can develop further/formulate new null hypotheses to test other theories. • Spatial autocorrelation is a measure of the correlation among neighboring points in a pattern. – No spatial autocorrelation means no correlation between neighboring values and would expect CSR • Measures of dispersion/distance methods analyze patterns using stats calculated using characteristics of distances separating in- dividual points in the pattern. – Nearest neighbor analysis (NNA):  as originally developed, several limitations—inaccuracy in interpretation in some situations and edge effects  2-D study areas (not roads): defined as distance between point a and the nearest other point in the pattern  Distances other than those between a point and its closest neighbor are referred to as second, third, or “higher order neighbor distances”  NNA in 1-D study areas (roads): same concepts, but the line is bounded by its ends, so two ways to deal with these ends (edges)  If points at ends of line  If no points at either end of the line  NN dist for any point not located at an end point is dis- tance to either the preceding or succeeding point en- countered on the line; thus nearest neighbor distances are part of the set of all interpoint distances on the line. To test, interpoint distances converted to proportions of the sum of the interpoint distances, resulting in scaled values ranked from smallest to largest, within n as the number of interpoint distances. Observed and expected values compared to normally distributed sta- tistic z; if calculated value of z is positive and larger than value of z = 1.96 (alpha 0.05) obtained from tables of normal dist, the null is rejected in favor of hypothe- sis that indicates regularity in the point pattern. 148

– Refined NNA (cites Diggle 1979 pg 79) involves comparing the complete distribution function of the observed nearest neighbor distances F(di), with the distribution function of ex- pected nearest neighbor distances for CSR P(di).  Observed nearest neighbor distances obtained by taking nearest neighbor distances and ranking smallest to largest, then determine what proportion F(di< = r) of nearest neighbor distances are less than or equal to some chosen distance ≤ r (usually selected to correspond with nearest neighbor distance values).  Cited Pielou (1969:111–112) with equation that shows that the corresponding proportion of expected nearest neighbor distances ≤ r for unbounded CSR pattern. P(r)  Diggle 1981 suggests P(r) and F(r) can be compared using dr = max | F(r)-P(r) |  Because nearest neighbor distances are not mutually in- dependent Diggle (1981:26) suggests, to evaluate the sig- nificance of dr, use Monte Carlo test procedure to gener- ate set (usually 99) of CSR patterns each with the same number of points as the empirical pattern in the study area, then calculate dr for each of the calculated simulated patterns, then examine where the value of dr for the em- pirical/observed pattern falls within the entire set of 100 values (99 simulated and 1 observed patterns). If dr for ob- served pattern were among 5 largest values of dr, the null of CSR can be rejected (at alpha 0.05). Diggle 1979 sug- gests that if for dr, F(r) > P(r), then clustered, whereas if F(r) < P(r) than indicates regular pattern of points. – Second order procedures requires distance measurements between all combinations of pairs of points. Study of in- terevent distances where events are mapped points. Focus is on the variance, or second moment, of interevent distances.  Advantages over other techniques: more info about pat- tern is potentially available; CSR model available for in- terevent distances can be used as basis for statistically sig- nificance (second order analysis); statistically defensible boundary correction technique developed for second order studies. Convenient to use to study various distance subdivisions or distance zones.  Analysis based on circle with radius d centered on each point, each of the points w/in the circle is paired with the center point of that circle and it is this number of pairs that form our data. As d increased, see increased number of pairs of points in each circle. Analysis of that data depends on expected pairs of points derived similarly to points in a Poisson process (CSR model). Ripley (1981:159–60)  Cites Haining (1982), Getis (1983, 1984), Ripley 1981 and Diggle 1983 additional background. • Measures of arrangement examine locations of points relative to other points in the pattern. Two advantages over measures of dispersion: – Advantages  “Density free”: to compare arrangement properties of CSR pattern against observed pattern, don’t need to esti- mate any values from the observed data.  Arrangement measures are concerned with the locations of points relative to each other and not relative to the study area (as is the case with dispersion methods) – Disadvantages:  Not as rigorous than measures of dispersion, sort of like how non-parametric statistics are usually less powerful than their parametric equivalents.  Measures of arrangement are insensitive to some differ- ences in some pattern characteristics so that identical val- ues may be expected for patterns that are different in some way.  Stats theory less well developed (in 1988) so greater ele- ment of subjectivity enters when interpreting results of analyses of measures of arrangement. – Reflexive nearest neighbor analysis:  When two points are the nearest neighbor of each other, said to be reflexive (reciprocal) nearest neighbors.  Test number of reflexive nearest neighbors in the pattern observed compared to expected number of reflexive near- est neighbors in CSR.  Lack of a test of significance and unanimity in interpret- ing results . . . common to extend analysis to analysis of reflexive nearest neighbors to higher orders; in interpret- ing number of observed pairs in relation to CSR values, most researchers suggest that higher order values in excess of the CSR expectations indicate a measure of regularity in the arrangement of points whereas lower empirical values imply grouping.  Dacey 1969 gives tables of probabilities that a point along a line in a random pattern is the jth neighbor of its own jth nearest neighbor for j ≤ 6. 1st order prob: 0.6667; 2nd order prob: 0.3704; 3rd order prob: 0.2716; 4th order prob: 0.2241; 5th order prob.: 0.1952; 6th order prob.: 0.1753; to get “expected,” multiply total number of points that are by the corresponding probability, and if observed number of jth pairs is less than expected, then suggests grouping  May be that the reflexive nearest neighbor observed = CSR, but when look at higher order reflexive pairs (2nd, 3rd, etc.) may see tendencies toward grouping. • Summary: No one single optimal method. – Power of most point pattern techniques (i.e., ability to elim- inate false hypothesis) varies depending on the type of pat- tern so some techniques are better than others in detecting clustering whereas others are better at detecting regularity. – Measures of dispersion better than measures of arrangement since the latter methods require more subjectivity in the in- terpretation of their results. – Measures of dispersion used in combo with arrangement techniques can provide confirmation of results and further insights into the patterns. Burka, J., Nulph, D., and A. Mudd. 1997. Technical approach to de- veloping a spatial crime analysis system with ArcView GIS. INDUS Corporation and U.S. Department of Justice. • Discusses methods used to develop and implement an ArcView- based spatial crime analysis system for geographic analysis. • Sample application functions include – Pin maps and summaries – Geocoding – Change maps that look at trends over time based on two maps of same area representing incidents at different times, which produces a third map that shows increase or decrease in incidents per polygon b/w the two time periods. – Surface-derived hotspots—many ways to do this, but they use ArcView spatial analyst to build a surface of incident density for a selected set of incident pts, using the kernel function in SpatialAnalyst, then reselect out the “peaks” depicting hotspots 149

– Standard deviation Ellipses – Temporal and spatial trend charts – Layout generation (maps) Lee, J., and D.W.S. Wong. 2001. Statistical Analysis with ArcView GIS. John Wiley and Sons, Inc., New York, New York. 192 pp. • Chapters: – Attribute Descriptors – Point Descriptors – Pattern Detectors – Line Descriptors – Pattern Descriptors Levine, N., Kim, K.E., and L.H. Nitz. 1995. Spatial analysis of Hon- olulu motor vehicle crashes: I. Spatial Patterns. Accident Analy- sis and Prevention 27(5):663–674. • Examines method for geo-ref crash locations and guides for de- scribing spatial dist of crash locations, and how types of crashes can be spatially differentiated. Study area was assumed homo- geneous planar, not a network (system of roads). • 4 general categories of analyzing spatial variations in auto crashes: – Diff types of environments—rural vs. urban, large cities vs. small cities, state comparisons, national comparisons; tend to use highly aggregated data and large geographical units. – Examines crashes as function of volume, speed, other vari- ables on roads, road types, intersections, emphasis on func- tions of the road system, how different road segments or elements create different crash likelihoods. Classic “black- spot” analysis included in this category (cites: Boyle and Wright 1984, Persaud 1987, Maher and Mountain 1988). – Crashes in particular areas, corridors, neighborhoods, em- phasis on analysis units, which are socially and ecologically integrated. – System-wide spatial variations in crashes (few studies on this) to look at variations across region, examine how crashes in a particular zone or sub-area are part of larger spatial pattern. • Developed own software to derive different indices of spatial point pattern (Hawaii Pointstat; cites Levine et al. 1994). Takes list of lat/long for each crash location and produces 4 measures of concentration – Mean center (mean lat and mean long on list, “center of gravity”) – Standard distance deviation, based on “Great Circle” dis- tance of each point from mean center (cites McDonnell 1979 chap 1; Snyder 1987 pp. 29–33). – Standard deviational ellipse, which calculates the SD along a transformed axis of maximum concentration and another SD along an axis which is orthogonal to this (cites Ebdon 1985 pp. 135–141). More concise than standard distance de- viation circle (above). – Nearest neighbor index, which measures average distance from each point to the nearest point and then compares this to a distribution that would be expected based on chance (cites Ebdon 1985 pp. 143–150; Cressie 1991 pp. 602–615). Developed by plant ecologists for describing clustering of point patterns (cites Clark and Evans 1954). For each point, distance to every other point calculated and shortest distance selected, then shortest distances are averaged and compared to a NNDist which would be expected based on chance (near- est neighbor index). Index of 1.0 is indistinguishable from chance, lower than 1.0 indicates clustering and > 1.0 indi- cates dispersion. – These measures allow description of spatial variation and de- gree of concentration (spatial autocorrelation). • Compared SD ellipses for types of crashes (fatal, serious injury, alcohol-related, single-vehicle, head-on, two-vehicle, etc.) to e/o as well as to other ellipses for residential population and employment. • Used to provide insights into how certain relationships have a spatial dimension (e.g., between alcohol and severe injuries; types of impact and injury level), can be used to compare diff types of accidents, the same type of accident for 2 diff time pe- riods, or same type for two different areas. These do not provide behavioral insights. • These methods go beyond “blackspot” analysis—blackspot analysis assumes that observation locations are spatially inde- pendent; that each observed location has its own random process, whether Poisson distributed or not. Cites Loveday and Jarrett 1992 re: spatial autocorrelation and that you can’t treat each observa- tion as independent. • Limitations to these guides: assume monocentric spatial plane but in cities often have multiple centers and these distort the re- lationships by assuming a center, but they say that there are no accepted methods for identifying multiple nodes in a spatial plane; most cluster analyses produce biased results since they don’t take spatial autocorrelation (see Anselin 1995 for devel- opments in this area). Levine, N. 1996. Spatial statistics and GIS: software guides to quantify spatial patterns. Journal of the American Planning Association 62(3): 381–391. • Reviews the following software guides: – STAC (Spatial and Temporal Analysis of Crime) – Hawaii Pointstat – S-Plus – Venables and Ripley Spatial Statistics Functions – SASP: A 2-D Spectral Analysis Package for Analyzing Spatial Data – SpaceStat: A Program for the Statistical Analysis of Spatial Data • Variables may be described spatially as either – Occurring at unique point locations (incidents, buildings, people) – Aggregated to areas (census tracts, traffic analysis zones, city boundaries) • Stats describing points or areas fall into 3 general categories – Measures of spatial distribution, which describes center, dis- persion, direction, and shape of the distribution of a variable (cites Hammond and McCullogh 1978; Ebdon 1988), e.g., get latitude/longitude locations geo-coded, then can calculate center of the distribution (“center of gravity” or mean cen- ter), dispersion (standard distance variation), direction of the dispersion (standard deviation ellipse)—then can compare to other distributions. – Measures of spatial autocorrelation describe relationship among different locations for a single variable, indicating degree of concentration or dispersion (cites Cliff and Ord 1981; Haining 1990; Cressie 1991). Indicates whether clus- tering is greater than can be expected on basis of chance. 150

– Measures of spatial association between two or more variables, describes the correlation or association between variables dis- tributed over space (Anselin 1992b spatial dependence article) • STAC, DOS-based program designed by Statistical Analysis Center of the Illinois Criminal Justice Information Authority to help police depts. identify small concentrations (called “hot spot areas”) of crime. – Two modules—TIME, SPACE. SPACE module does two things: radial search for incidents from a selected point and identification of highest concentrations of incidents within a study area. SPACE needs identification number and x, y lo- cation of each point in Euclidean coordinates (plane coordi- nates, UTMs). It must specify limits of study area (min/max x, y coordinates) as well as search radius which is a circular area that the program uses to search for points that cluster to- gether. No theoretical basis for choosing particular radii, and different search radii will produce slightly different clusters. Produces ellipses to identify areas of clustering. Doesn’t have statistic to objectively group points into unique clusters (i.e., with fixed number of clusters and each pt assigned to one and only one cluster). • Hawaii Pointstat provides summary measures of the spatial dis- tribution of points. Available in DOS and Sun Unix versions, can be obtained from the Internet. – Takes list of x,y location points, can use weights/intensities for points (i.e., if multiple WVCs occurred at same location). Distances between points calculated with 2 different metrics  Spherical geometry using “great circle” distances;  Spherical grid distances, which assume that travel occurs only in horizontal or vertical direction (not diagonally)— used in cases of grid street systems. – Program produces following outputs: mean center; standard deviation of distance of each point from mean center; stan- dard deviation of ellipse (which is 2 standard deviations, one along a transformed axis of maximum concentrations and one along an axis 90 degrees to that other axis, defining an el- lipse); nearest neighbor index; Moran’s I (Moran 1948, 1950; Ebdon 1988, Haining 1990) – Provides summary stats of point spatial distributions and can output distance files for use in other programs. Useful to de- scribe distribution of points and can be used to compare dif- ferent types of distributions. • Venables & Ripley’s Spatial Statistics Functions in S-Plus: mod- ules written in S-Plus (distributed by StatSci), available in both Unix and Windows systems. Has Ripley’s K function utilities. Ripley’s K function uses distances between all points and com- pares the observed number of neighbors within a certain dis- tance to a theoretical number based on a Poisson random process; k-fx generally considered most comprehensive of the distance measures and can be used for determining the distance scale at which randomness occurs. • SASP—two-dimensional spectral analysis package for analyzing spatial data—set of utility modules for conducting 2-D spectral analysis using a grid cell organization (Renshaw and Ford 1983; Ford and Renshaw 1984; Renshaw and Ford 1984). 2-D spectral analysis is technique for detecting patterns in a spatial distribu- tion and is direct extension of 1-D spectral analysis used in time series analysis. – Data consist of series of rectangular grid cells imposed over spatial plan with m rows and n columns. The value within each cell represents an estimate of a third variable, which could either be number of discrete points that fall within the cell or a value attributed to the entire cell. – “Distribution of grid cell structure can be decomposed into trigonometric (“cyclic”) components, called a Fourier de- composition,” resulting in discrete frequencies (p & q) that are independent of e/o and that indicate the contribution of each frequency to the overall pattern. Essentially an ANOVA splitting up the variance into sine/cosine components. – Central output is periodogram which is a plot of the sine/co- sine components and is expressed as the number of waves down the rows, p, and the number of waves across columns, q, with an origin at p = 0 and q = 0. Two summary indices: R-spectrum is average of periodogram values for semicircu- lar “distance” bands emanating from the origin (p = 0, q = 0) and a width of 1. The θ spectrum is an average of the peri- odogram values for an angular band (i.e., pie slices) from the origin; that is, it is a polar coordinate band that is 10 degrees wide, starting at -5 deg -+5 deg along the x-axis and turning clockwise until 165–175 degrees. – Also 3-D figure showing a smoothed rearranged peri- odogram. – 2-D spectral analysis seen as exploratory guide for examining repeating spatial patterns. • SpaceStat program designed to spatially analyze areal distribu- tion (Anselin 1992a), written in Gauss (matrix language). Can be applied to data collected on individual zones or areas within a larger geographical area. – Ability to create a spatial weights file, which is a series of weights, assigned to individual observations, indicating their location in relationship to e/o. Two forms of weights:  Binary (contiguity matrix that indicates which zones are adjacent to each other)  General (distance based matrix that indicates the relative distance of each zone from the others. Typically defined in terms of inverse distance raised to an integer power (e.g., 1/d, 1/d2, 1/d3); the higher the power of the distance fac- tor, the more “local” the effect. – 4 modules:  First allows data to be input and transformed  2nd involves guides for creation of spatial weights input  3rd involves exploratory analysis including descript stats correlations, and principal components. Includes a Join- Count statistic for binary variables and several measures of spatial autocorrelation and descriptive model provides a local indicator of spatial association (LISA) by applying Moran’s “I” to individual observations (Anselin 1995).  4th module has number of regression routines, with ordi- nary least squares (OLS) and robust method for estimat- ing OLS using a “jackknife” procedure, and provides di- agnostics to examine residuals. Includes tests for spatial autocorrelation, gauging whether spatial dist is affecting either the distribution of the dependent variable or the residual error terms. If no apparent spatial autocorrela- tion, then OLS is valid procedure. If there is spatial auto- correlation, then model that incorporates spatial location needs to be developed.  Most regression packages don’t incorporate spatial lo- cation and implicitly treat space as if it were random (i.e., part of the residual error term). SpaceStat only package that Levine is aware of that explicitly builds lo- cation into regression procedure. While one can apply 151

non-spatial statistics to spatial data, the error associ- ated in not considering spatial location is enormous. In effect one is assuming that each observation is inde- pendent of all others, which is clearly wrong for spa- tially affected phenomena.  Author provides info on accessing all software de- scribed in article. Levine, N. 1999. Quickguide to CrimeStat. Ned Levine and Associates, Annandale, VA. • Guide to parallel online help menus in the program. • Eight program tabs, each with lists of routines, options and parameters 1. Primary file: point file w/x-y coordinates. 2. Secondary file: optional; also point file w/ x-y cords used in comparison with primary file. 3. Reference file: “used for single and dual variable kernel den- sity estimation.” Usually though not always a grid overlaying the study area. 4. Measurement parameters a. Area: define area sing units (square miles, square meters, etc.) b. Length of street network: total length c. Type of measurement—direct (shortest distance between two points) or indirect (distance constrained by grid, called “Manhattan” metric). 5. Spatial distribution: provides statistics describing overall dis- tance (first order spatial stats). 3 routines for describing spatial distance, and 2 routines for describing spatial autocorrelation (intensity variable needed for the latter two routines, weight- ing variable can also be used)—details on these routines with descriptions are included. 6. Distance analysis: provides stats about distances between point locations, useful for identifying degree of clustering of points (second order analysis). Three routines for describing properties of the distances and two routines that output dis- tance matrices. a. m-sub:Nearest neighbor analysis b. Number of nearest neighbors c. **Linear nearest neighbor analysis d. **Number of linear nearest neighbors e. **Ripley’s K statistic f. Distance matrices g. Within file point-to-point: routine outputs distance be- tween each point in primary file to each point in second- ary file (can relate to guardrails, intersections, fencing, etc.) 7. Hotspot analysis: identifies groups of incidents clustered to- gether. Second order analysis. 3 stats: a. Nearest neighbor hierarchical spatial clustering: groups points together on basis of spatial proximity—user defines significance level associated with a threshold, minimum number of points that are required for each cluster and output size for displaying clusters with ellipses b. K-means clustering routine for partitioning all points into k-groups in which K is a number assigned by the user c. Local Moran statistics: applies to the Moran’s I statistic to individual points or zones to asses whether particular pts/zones are spatially related to nearby points or zones 8. Interpolation tab: allows estimates of point density using the kernel density smoothing method. • Chapter 6 hotspot analysis: – Pg 164 overview of types of cluster analyses methods 1. Hierarchical techniques: like inverted tree diagram in which two or more incidents are first grouped on the basis of some criteria (e.g., nearest neighbor). Then these are grouped into second order clusters, which are then grouped into third order clusters and this process is re- peated until either all incidents fall into a single cluster or else the grouping criteria fails.  Literature cited: Sneath 1957; McQuitty 1960; Sokal and Sneath 1963; King 1967; Sokal and Michener 1958; Ward 1963; Hartigan 1975 2. Partitioning techniques, or K-means technique, partition the incidents into a specified number of groupings, usu- ally defined by the user. All points are assigned to one (only one) group. Displayed as ellipses.  Literature cited: Thorndike 1953; MacQueen 1967; Ball and Hall 1970; Beale 1969 3. Density techniques identify clusters by searching for dense concentrations of incidents (next chapter of book dis- cusses one type of density search algorithm that uses the kernel density method.  Literature cited: Carmichael et al. 1968; Gitman and Levine 1970; Cattell and Coulter 1966; Wishart 1969 4. Clumping techniques involve partitioning incidents into groups or clusters but allow overlapping membership  Literature cited: Jones and Jackson 1967; Needham 1967; Jardine and Sibson 1968; Cole and Wishart 1970 5. Miscellaneous techniques: other methods less commonly used including techniques applied to zones, not incidents. Local Moran (cites Anselin 1995) 6. Also hybrids of these methods, Block and Green 1994 use a partitioning method with elements of hierarchical grouping – Optimization criteria: distinguish techniques applied to space. 1. Definition of cluster: discrete grouping or continuous variable; whether points must belong to a cluster or can be isolated; whether points can belong to multiple clusters. 2. Choice of variables: whether weighting or intensity values are used to define similarities. 3. Measurement of similarity and distance: type of geometry used; whether clusters are defined by closeness or not; types of similarity measures used. 4. Number of clusters: whether there are a fixed or variable number of clusters; whether users can define the number or not. 5. Scale: whether clusters are defined by small or larger areas; for hierarchical techniques what level of abstraction is considered optimal. 6. Initial selection of cluster locations (“seeds”): whether they are mathematically or user defined; specific rules to define initial seeds. 7. Optimization routines used to adjust initial seeds into final locations whether distance is being minimized or maxi- mized; specific algorithms used to readjust seed locations. 8. Visual display of clusters once extracted: whether drawn by hand or by geometrical object (ellipse); proportion of cases represented in visualization. – No single solution—different techniques will reveal different groupings and patterns among the groups. 152

– Chapter goes on to specifically explain Crimestat routines and criteria for 3 techniques—hierarchical clustering based on nearest neighbor analysis; partitioning technique based on K-means algorithm, and zonal technique that identifies zones which are different from their nearby environment, whether they are “peaks” or “troughs” – Discusses some advantages/limitations for some techniques:  Nearest neighbor hierarchical clustering: identify groups of incidents where groups of incidents are spa- tially closer than would be expected on basis of chance. 4 advantages 1. Can identify small geographical environments where there are concentrated incidents, useful for specific targeting of microclimates where incidents are occurring. Sizes of clusters can be adjusted to fit particular groupings of points 2. Can be applied to any entire dataset and need not be applied to smaller geographic areas, easing compar- isons between different areas 3. Linkages between several small clusters can be seen through second and higher order clusters—i.e., there are different scales (geographical levels) to the clustering of points and hierarchical clustering can identify these levels 4. Each level may imply different management strategies  Hierarchical clustering limitations 1. Size of grouping area dependent on sample size since lower limit of mean random distance is used as cri- teria—for distributions with many incidents thresh- old will be smaller than distribution with fewer inci- dents, so not consistent definition of hotspot area 2. Arbitrariness due to minimum points rule requiring user to define a meaningful cluster size so two differ- ent users may interpret the size of a hotspot differ- ently, also selection of p-value in the students t-dis- tance can allow variability between users. Almost all other clustering techniques have this property too. 3. No theory or rationale behind clusters. Same goes for many other clustering techniques that are em- pirical groupings with no theory behind them; how- ever, if one is looking for a hotspot defined by land use, activities, and targets, the technique provides no insight into why clusters are occurring or why they could be related.  K-means partitioning clustering: data are grouped into k groups defined by user, after specified number of seed locations are defined by user. Routine tries to find best positioning of K centers and assigns each point to the center that is nearest. Assigns points to one and only one cluster, but all points are assigned to cluster, thus no hierarchy (second, higher order clusters) in routine. Basically, k-means procedure will divide the data into the number of groups specified by the user.  Advantages and disadvantages: Choosing too many clusters will lead to defining patterns that don’t really exist whereas choosing too few will lead to poor dif- ferentiation among areas that are distinctly different. Given the numbers of clusters one chooses, the re- sults may or may not relate to actual “hotspots”  Local Moran statistics: aggregate data by zones, applies Moran’s I stat to individual zones allowing them to be identified as similar or different to their nearby pattern. Basic concept: LISA local indicator of spatial associa- tion, indicator of the extent to which the value of an observation is similar or different from its neighboring observations. Requires two conditions: (1) each obser- vation has a variable value that can be assigned to it in addition to its x/y coordinates; (2) the neighborhood needs to be defined—could be adjacent zones or all other zones negatively weighted by the distance from the observation zone – Some thoughts on hotspots  3 advantages to the 3 techniques discussed above  Identifies areas of high or low concentrations of events;  Systematically implements algorithms (though human decisions affect how the algorithms run); and  Lastly, these techniques are visual.  Disadvantages:  Choice of parameters in algorithms is subjective; makes this as much an art as science. Greater effect, the smaller the sample size.  Applies to volume of incidents, not underlying “risk.” It is an implicit density measure, but higher density may be a function of a higher population or risk or both.  One thing to identify a concentration of incidents, but these hotspot methods don’t explain why there is a concentration of events there. It could be ran- dom, not relate to anything inherent about the lo- cation.  Hotspot identification is merely an indication of an underlying problem, but further analyses are re- quired to identify what is contributing to the occur- rences in that area. Levine, N. 2004. CrimeStat III: Distance Analysis. Chapter 5 in: A Spa- tial Statistics Program for the Analysis of Crime Incident Loca- tions. Ned Levine & Associates: Houston, Texas, and the National Institute of Justice, Washington, D.C., USA. • First order properties are global and represent dominant pattern of distribution. • Second order (or local) properties refer to subregional patterns or neighborhood patterns within overall distribution, and tell about particular environments that may concentrate crime incidents. • NNI (nearest neighbor index): – Simple to understand, calculate ... for areas, not linear fea- tures. – Basis of many distance statistics, some of which are imple- mented in CrimeStat. – Compares distances between nearest points and distances that would be expected on basis of chance and is an index that is the ratio of two summary measures.  For each point distance to closest other point (nearest neighbor) is calculated and averaged over all points.  Expected nearest neighbor distance if CSR = the mean random distance. Mean random distance = d(ran) = 0.5 SQRT[A/N] where A is area of region and n is number of points.  NNI = d(NN)/d(ran) = ratio of observed nearest neighbor distance to mean random distance 153

 If observed distance is same as mean random distance, then ratio will be ~1; if observed average distance is smaller than the mean random distance, then the index will be < 1 indicating clustering; if observed average distance is greater than the mean random distance, then index > 1 indicating dispersion and that points are more widely distributed than would be expected based on chance.  Testing significance of NNI: Z-test to determine if signif- icant difference between observed and expected. Z = [d(NN)-d(ran)]/[SE of d(ran)]  SE of d(ran)~ = SQRT[(4-pi)A/4pi(N-sq)] where A is area of region and n is number of points.  Note: significance test for NNI is not a test for CSR, only a test of if average nearest neighbor distance is sig- nificantly different than chance, i.e., test of first order nearest neighbor randomness. There are also second, third, and so forth order distributions that may or may not be significantly different from CSR. All these are K- order effects.  Edge effects can bias NNI—a point near border of study area may actually have its nearest neighbor on the other side of the border, but program selects another point within the study area as nearest neighbor of border point, which may exaggerate the nearest neighbor distance. No consensus on how to deal with this (cites Cressie 1991 for options) and “this version” of CrimeStat has no correc- tion for edge effects. However, bias will be significantly smaller given datasets with clustering. • K-order nearest neighbors: beyond nearest neighbor distances, 2nd nearest neighbor, 3rd nearest, etc. In CrimeStat can specify number of nearest neighbor indices to be calculated. – Output includes order, starting with 1; mean nearest neigh- bor distance for each order (m); expected nearest neighbor distance for each order (m); and NNI for each order. – Kth NNI is ratio of observed Kth nearest neighbor distance to the Kth mean random distance. – CrimeStat has no test for significance (none has been devel- oped) for Kth NNI since orders aren’t independent. – No restrictions on number of nearest neighbors that can be calculated, but since average distance increases with higher order nearest neighbors, bias from edge effects will increase. Orders no greater than 2.5% of pts should be calculated (cites Cressie 1991 pg 613 for example). • Linear NNI (Lnna): applied to roads, with assumptions that in- direct distances are used following network or grid. – Theory: cites Hammond and McCullagh (1978). – CrimeStat calculates average of indirect distances between each point and its nearest neighbor = Ld(NN). – Expected linear nearest neighbor distance is Ld(ran) = 0.5(L/n-1) where L is total length of road and n is sample size. – Linear NNI = LNNI = [Ld(NN)]/[Ld(ran)] – Theoretical standard error for random linear nearest neigh- bor distance not known  Author of CrimeStat developed approx SD for observed Ld(NN) = SLd(NN) = SQRT[Σ(min(di,j) − Ld(NN))2/N-1] where min(di,j) is nnd for point I and Ld(NN) is average linear nearest neighbor distance.  SELd(NN) = [SLd(NN)]/SQRT[N]  Approx significance test = t = [Ld(NN)-Ld(ran)]/SE of Ld(NN)  Since empirical standard deviation of Ld(NN) used in- stead of theoretical value, t-test used rather than Z-test.  CrimeStat output with Lnna routine: 1) Sample size 2) Mean linear nearest neighbor distance in meters, feet, miles 3) Minimum linear dist b/w nearest neighbors 4) Maximum linear dist b/w nearest neighbors 5) Mean linear random distance 6) Linear nearest neighbor index 7) SD of linear nearest neighbor distance 8) SE of linear nearest neighbor distance 9) Significance test of NNI (t-test) • K-order linear nearest neighbors: beyond nearest neighbor dis- tances, 2nd nearest linear neighbor, 3rd nearest, etc. In Crime- Stat can specify number of nearest linear neighbor indices to be calculated. – Output includes order, starting with 1; mean linear nearest neighbor distance for each order (m); expected linear near- est neighbor distance for each order (m); and linear NNI for each order. – Kth linear NNI is ratio of observed Kth linear nearest neigh- bor distance to the Kth linear mean random distance. – Expected linear nearest neighbor distance is Ld(ran) = 0.5(L/n-1) where L is total length of road and n is sample size, only adjusting for nk which occurs as degrees of freedom are lost for each successive order. Index is really the k-order lin- ear nearest neighbor distance relative to the expected linear neighbor distance for the first order—it is not a strict NNI for orders above 1. – (*These are notes from non-linear NNI; not sure if applica- ble here, too, but there are no other notes on these issues in linear NNI section.) CrimeStat has no test for significance (none has been developed) for Kth NNI since orders aren’t independent. – (*These are notes from non-linear NNI; not sure if applica- ble here, too, but there are no other notes on these issues in linear NNI section.) No restrictions on number of nearest neighbors that can be calculated, but since average distance increases with higher order nearest neighbors, bias from edge effects will increase. Orders no greater than 2.5% of points should be calculated (cites Cressie 1991 pg 613 for example). – Example of interpreting results from higher order analyses— if one parameter shows clustering through fourth order, then tending toward more dispersed than random, then may in- dicate that there are small clusters of points, but that the clus- ters themselves are relatively dispersed; the more orders an- alyzed showing clustering, the more overall clustering across the entire study area. – Linear k-order nearest neighbor distance different than non- linear (areal). Index slightly biased as denominator (k-order expected linear neighbor distance) is only approximated. Also, index measures distance as if the streets follow a true grid, oriented E/W and N/S, hence may not be realistic for places where streets traverse in diagonal patterns—in these cases, use of indirect distance measurement will produce greater distances than what actually may occur on the street network. • Ripley’s K Statistic (not for linear features—only areas) – Index of non-randomness for different scale values (cites Ripley 1976, 1981; Bailey and Gattrell 1995; Venables and 154

Ripley 1997). “Super-order” NN statistic providing test of randomness for every distance from the smallest up to the size of the study area. Sometimes called reduced second mo- ment measure implying that it is meant to measure second order trends (i.e., local clustering vs. general pattern over re- gion); however, also subject to first order effects so is not a strictly second order measure. – Consider spatially random dist of n points. Circles of radius, ds, are drawn around each point, where s is the order of radii from smallest to largest and the number of other points that are found within the circle are counted and then summed over all the points (allowing for duplication), then the ex- pected number of points within that radius are E(number of points within distance di) = [N/A]K(ds), where N is sample size, A is total study area, and K(ds) is area of a circle defined by ds. For example, if area defined by particular radius is 1⁄4 the total study area, and if there is spatially random distribu- tion, on average approximately 1⁄4 of the cases will fall within any one circle (+/− sampling error). More formally, with CSR, expected points within distance ds is E(number under CSR) = [N/A] π ds2 And if average number of points found within a circle of a particular radius placed over each point is greater than found in above equation (expected), then clustering occurring or if average number of points found within circle of particular radius placed over each point is less than found in above equation (expected), then dispersion. – K statistic similar to NND because it provides info about av- erage distance b/w points, but more comprehensive than nearest neighbor distance stats for two reasons:  Applies to all orders cumulatively, not just a single order  Applies to all distances up to the limit of the study area be- cause the count is conducted of successively increasing radii. – Under unconstrained condition, K is defined as K(ds) = [A/N2] Σi Σj I(di,j) where I(di,j) is the number of other points, j, found within distance ds summed over all points, i. So, cir- cle of radius ds placed over each pt I, then number of other pts ij are counted. Circle is moved to next pt i and process re- peated, thus double summation points to the count of all j’s for each I, over all I’s. When done, radius of circle is increased and process is completed. Typically radii of circle are in- creased in small increments so there are 50-100 intervals by which the statistic can be counted. In CrimeStat, 100 inter- vals (radii) are used based on ds = R/100 where R is the radius of a circle for whose area is equal to the study area. – Can graph K(ds) against ds to see if there is clustering at cer- tain distances or dispersion at others, but since this plot is non linear (increasing exponentially), then transform into sq-root function L(ds) = SQRT[K(ds)/π] – ds. In practice only the L statistic is used even though the name of the statistic is based on the K derivation. – L statistic prone to edge effects, i.e., for points located near the boundary of the study area, the number enumerated by any circle for those points will (all other things =) be less than points in the center of the study area because points outside the boundary aren’t counted. The > distance between points tested (i.e., the greater the radius of the circle placed over each point), the greater the bias, thus a plot of L vs. distance will show decline as distance increases. – Ripley proposed edge adjustments  “Guard rail” within study area so points outside the guardrail but inside the study area can be counted for center points (an enumerator) inside the guardrail, but cannot have own circle placed upon them (i.e., only a re- cipient, can only be j’s and not I’s). Must be done manu- ally, must identify each point as either an enumerator and recipient or recipient only. Can be problematic if study area boundary not “regular” shape.  Venebles and Ripley 1997—weighting to account for pro- portion of circle placed over each point within the study area. Thus K(ds) = [A/N2] Σi Σj I(di,j) becomes K(ds) = [A/N2] Σi Σj Wij−1 I(di,j) where Wij−1 is inverse of proportion of circle of radius ds placed over each point which is within the total study area; thus if point is near border, it will get greater weight because smaller proportion of circle placed over it will be within the study area. Again, has to be done manually and can be problematic if study area boundary not “regular” shape.  CrimeStat only calculates the unadjusted L and tells users to anticipate the bias by only examining L stat for small distances where bias is smallest (even though one could calculate 100 distance intervals). – Comparison to spatially random distribution—because sam- pling distribution of L statistic not known, do 100 random distance simulations, then for each simulation the L statistic is calculated for each distance interval, after all simulations have been conducted, highest/lowest L-values are taken for each interval and is called an “envelope.” By comparing dis- tribution of L to random envelope, one can assess if observed is different from chance.  Note: since no formal test of significance, comparison with envelope only approximate confidence about whether distribution differs from chance or not, i.e., one can’t say likelihood of obtaining this result by chance is less than e.g., 5%. Spooner, P.G., Lunt, I.D., Okabe, A. and S. Shiode. 2004. Spatial analysis of roadside Acacia populations on a road network using the network K-function. Landscape Ecology 19:491–499. • Ripley’s K-function (Ripley 1976, 1991) not appropriate for point patterns on road networks since k-function assumes infinite ho- mogeneous environment for calculating Euclidean distances. • Network k-function for univariate analyses and network cross k-function for bivariate analyses more appropriate. • Used these methods to confirm significant clustering of Acacia populations at various scales and spatial patterns. • K-function been used to study spatial patterns of mapped point data in plant ecology (cites a list). • K-function uses all point-to-point distances not just nearest neighbor distances • When k-function used for point patterns constrained by linear road networks, can overdetect clustering patterns possibly lead- ing to Type 1 errors. • Cites Forman 1999 ICOET article says lack of spatial guides to analyze point patterns on road networks. • Credits Okabe and Yamada 2001 (The k-function method on a network and its computational implementation. Geographical Analysis 33:271–290) with developing k-function analysis of point patterns on a network. 155

• Refers to k-function to “reduced second moment measure” to measure two-dimensional distribution pattern on infinite ho- mogeneous plane where circle of radius t centered on each point and number of neighboring points within circle are counted. Can vary radius t scale, deviation of observed from expected number of points plotted against t. Null hypothesis for k-func- tion is complete spatial randomness (CSR) and if observed func- tion deviates from a randomly generated (Poisson) point process, the null is rejected. • Univariate network k-function similar process but calculates the shortest path distance from each point to all other points on a finite connected planar network, assumption of binomial point process based on hypothesis that points p (the set of points as- sumed on network) are uniformly and independently distrib- uted over finite road network, thus if hypothesis rejected, points are spatially interacting and may form non-uniform patterns. • 100 Monte Carlo simulations used to construct confidence “envelope” based on max and min values from an equivalent number of random coordinates for k(t) compared to k-hat (t) or observed. Any values of k-hat (t) that lie outside confidence envelope were considered significant deviation from CSR. If k-hat(t) > k(t), then points p are clustered; if k-hat(t) < k(t), then points p are tending toward regularity. Edge effects are taken into account with distance computations so no need for edge adjustment factor (Okabe & Yamada 2001) • Bivariate network k-function, two different kinds of points A&B are analyzed on network, with hypothesis of spatial interaction between different types of points. Statistical test for bivariate analysis similar to univariate network k-function but present version of SANET used for network cross k-function analyses does not construct a confidence envelope, but can be theoreti- cally obtained from the binomial distribution approximated by normal distribution for large number of points. To check for statistically significance of observed from CSR, approx of 95% CI constructed using standard deviation of normal distance, and max/min values of +/-1.65*SD using one-sided tests. If observed > expected and outside CI, then points A&B are significantly “attracted”; if observed < expected and outside CI, then points A&B are significantly repelled. • “Spatial point patterns were analyzed on a road network shape- file using SANET Version 1.0 – 021125 (Okabe et al. 2002, okabe.t.u-tokyo.ac.jp/okabelab/atsu/sanet/sanet-index.html), an ESRI Arcmap extension.” First preprocessed all polylines to make sure properly connected to e/o. SANET used first to cal- culate distances between all notes on road network then used to assign points to the nearest point on the road network. Network k- and cross k-function analyses were performed by SANET and output data were exported to Excel to aggregate data, calculate confidence intervals (for x-k-function analyses) and produce graphs. • Univariate addresses clustered vs. regular distributions; bivari- ate addresses if two types of sets of points are attracted or repulsed from e/o. • Combo of using graphical Kernel (for visual) and network k-function was helpful, but must be realized that kernel estima- tions do not compensate for spatial differences I road networks and their effect on point patterns observed. Final paragraph: possible applications of network k-function include animal movement patterns from survey and traffic mortality, en- vision network k-function becoming standard GIS application on networks. 156