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Kernel Home Range Estimation for ArcGIS, using VBA and

1. unchecked Close the Visual Basic Editor References Project Available References OK _ ESRI ReportWriter Localization Resource Library Cancel ESRI SceneVviewer Control 1 0 _JESRI Schema Creation Wizard CASE _ ESRI Schema Creation Wizard Resource Library E Browse _ ESRI Semantics Checker Resource Library ESRI Spatial Analyst Extension Object Library WE SEI Spatial Analyst Shared Object Library lt lt _JESRI StreetMap Europe Extension Object Library Priority t el ESRI StreetMap USA Extension Object Library Help ESRI Survey Analyst ArcCatalogEx 4 ESRI Survey Analyst ArcMapEx ESRI Survey Analyst 4rcMapEx _ ESRI Survey Analyst COGOObjecks FSET Survey Anales COGOPackane Ohiert ae F ESRI Spatial Analyst Shared Object Library Location Carcgislarcexe8s binesrispatialshared olb Language Standard Figure 8 1 2 12 Referencing object libraries in ArcMAP 8x 8 1 3 The easy start up for ABODE ABODE has already been loaded into a map document and a map template called abode mxd and abode mxt respectively Referencing of Object Libraries still has to be performed Figure 8 1 2 11 and its supporting text in Section 8 1 2 explain how this can be done The map 45 document or map template may be saved with other names Data should be loaded into the document in the form of a shapefile It is recommended that the data are projected in UTM met
2. A spike in the graph shows fandomly this will not be possible Figure 2 1 6 Since kernel density estimates should be more robust towards outliers in the dataset the detail required for analyzing individual behaviors is lost The kernel asymptote analysis will however provide a better estimate for home range asymptotes using either consecutive locations Figure 5 2 2 a or randomly added locations Figure 5 2 2 b 1200 1200 1000 1000 o B00 B00 peee nil Area km 600 4 Area km 600 oe a ania 400 4 a oo P 200 f 2004 J er j g a r 20 40 60 B 100 120 140 0 20 40 60 80 100 120 140 Locations n Locations n a b Figure 5 2 1 MCP asymptote analyses for one female cheetah using consecutively a and ease added locations z n in the graph B00 1000 Se T aedi s00 rot 4 ae 1 i aan fms P a00 vy wt een 600 EONA p b ins a MN meeen Fad m rood oy MA inf i 7 500 tae 600 Area km 400 4 F Area km 500 1 300 4 400 200 200 4 200 100 ams 100 o H 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Locations n Locations n a b Figure 5 2 2 Kernel density asymptote analyses for one female cheetah using consecutively a and randomly added locations b Kernel estimation is stvely ne xara E a and probably provides a better asymptote estimate if enough data are available 32 6 Core Home Ranges 6 1 Does a core really exist Harris et al
3. Wh Options Contouri nrc Kernel Contour Grid cell Asymptote Core f die Locations Smoothing Factor Smoothing Function i Smoothing a baits Operation E Output il wee Pes a Allow Debug units units Grid a Asymptote Refresh Contour Show Destination a Union Errors For results z F Kernel Quit Figure 8 2 3 1 Subset Field dincted Featijes Subset CheckBox ListBox CheckBox cbSubset IstField X Coordinate Source Layer Temporal Metadata cbSelected Discretization Discretization Field ListBox ListBox CheckBox CheckBox Error ComboBox IstX IstLayer cbTemporal cbDiscretization cboError Input Selected features only Subset Temporal Coordinate Metadata Data are discretized 7 Y Coordinate Y Coordinate Temporal Metadata Day Field Month Field ListBox Year Field ListBox Field ListBox Frame frTemporal ListBox IstMonth IstYear IstY IstDay Figure 8 2 3 2 As with the Minimum Convex Polygon Page ABODE will search the ArcMap Table of Contents for point layers It will then display these in the Source Layer ListBox Figure 8 2 3 2 For this analysis the user must indicate which fields contain the coordinate data Fields that contain data 53 in a number format will be listed for the selected Source Layer in the X and Y Coordinate Field
4. 4 3 2 Statistical methods Two statistical methods that are commonly used for automatically choosing a smoothing parameter are the reference smoothing method and the least squares cross validation method 16 Silverman 1986 suggested that an optimum bandwidth could be chosen for a standard distribution the bivariate normal distribution Though this method is known to oversmooth data that are multimodal and non normal it does provide an easy and automatic starting point with which to analyze datasets 3 Worton 1995 referred to this optimum bandwidth as A nis the sample size The standard deviation term is calculated as Worton 1995 o to gaa ee 4 2 ox and g are the variance estimates for the data in the x and y directions Since most animal of home range size and will generally overestimate In ABODE a biweight kernel is used and the reference smoothing factor should be adjusted using a constant A K see Equation 13 and supporting text Least squares cross validation LSCV was proposed by Rudemo 1982 and Bowman 1984 as another automatic method for selecting the optimum bandwidth or smoothing parameter based on the unknown density of the given distribution of points This method involves the minimization of those that deviated from normality Bowman 1985 showed that this squared error cross validation technique performed consistently better than several other loss
5. Figure 4 1 6 c where the darker cells for points 1 and 2 indicate a higher density where the pixel values were summed In this sequence the final contour shows the 95 volume home range for a user defined 300m grid and a user defined smoothing factor of h 1000m Using a fixed biweight kernel and no standardization in ABODE Figure 4 1 6 standardization is explained in Section 4 5 d e f Figure 4 1 6 Progression of kernel density estimation for a real dataset serves the same purpose as the more lengthy analysis at each and every pixel benefit of this procedure is that outliers in the dataset are effectively eliminated from the analysis before the time consuming pixel to point analysis begins Using a biweight kernel satisfies one of the tenets espoused by Burt 1943 in his home range definition In this case the occasional sallies are essentially removed from the dataset though it must be understood that this discrimination is based solely on the spatial qualities of the distribution and not on verified dispersal or exploratory movements It is important that the user understands how these outliers are treated in different software packages In one of the most commonly used packages available at the moment Figure 4 1 7 a pixels surrounding outliers are giving a density value Rot be a problem since the outliers will probably not be picked Up No testing has been done to see what the likelihood is of
6. f i asymptote Refresh ee Mocs oh Kernel Quit f a None MousePointer 0 fraMousePc Picture None PictureAlignmen 2 frnPictureAl PictureSizeMode 0 froPictureSi PictureTiling False RinhtTal eft Figure 8 1 2 9 False 4g Microsoft Visual Basic YourProjectHame mxd Eile Edit view Insert Format Debug Run Tools Add Ins Window Help aa Gs Ge teat s Project Project i YourProjectName n Joc ent Code Normal NormaLmut 4 YourProjectName mxd ThisDocument Code g Project YourProjectNan 2 ArcMap Objects Se a ThisGiocument Private sub Abode Click oS Forms Load frmHR me Fal FrmHRF frmHAR Show H E References End sub Figure 8 1 2 10 44 One more step is required to start ABODE On the menu bar left click on Tools Left click on References Figure 8 1 2 11 4g Microsoft Visual Basic YourProjectName mxd File Edit View Insert Format Debug Bun ITa Add Ins Window Help Project Project Ey Eisen a Macros 4 Normal Normal mxt H i Project fourProjectNan H E ArcMap Objects eat ThisDocurment Options Project Properties Digital Signature Figure 8 1 2 11 Scroll through Available References If you are using ArcMAP 8x Check ESRI Spatial Analyst Figure 8 1 2 12 If you are using ArcMAP 9 these references will be denoted as missing and they should be
7. 2 2 Minimum Convex Polygons MCPs To begin a home range analysis a point layer must be present in the Table of Contents in ArcMap Start the analysis by left clicking on the toolbar on the tool called ABODE If no point layer is present in the Table of Contents then ABODE will not open the user form Instead a Message Box will appear notifying you that a point layer must be added ABODE can analyze point shapefiles that have points projected in UTM In the attribute table of the shapefile there must be a field each for the x and y coordinates The user form for ABODE consists of two pages One is for Minimum Convex Polygons Figure 8 2 2 1 The other is for Kernel Density Estimation this will be dealt with in section 8 2 3 This page is divided into two distinct sections The top section is for regular Minimum Convex Polygon analyses Figure 8 2 2 2 The bottom section is for analyzing home range asymptotes Please note that on the Kernel Density Estimation page all analyses are included in one section and asymptotic analyses are not set apart 48 ABODE beta v 2 Pete Laver 2005 Minimum Convex Polygon Kernel Density Estimation MCP MCP Input Allow Debug ince Selected features only I Show Errors V Subset M Refresh MCP Output 4rea Units ME Destination oOo O z f for results v G Linear Units Quit Asymptote Asymptote Input Selected features only I Subset P Temporal Metadat
8. ABODE If no areal or linear units are selected ABODE will default to using the projected units from the Map Left clicking on the Quit Button cmdQuitMCP will remove the form from sight The Refresh Button cmdRefreshMCP will clear the input selections and leave a fresh form for the user Home range asymptote analyses are commonly done using Minimum Convex Polygons Please read Section 5 for justification for performing this analysis and for more detail on the theory behind home range asymptotes The bottom section of the Minimum Convex Polygon Page deals with this analysis Figure 8 2 2 3 50 Date Field CheckBox Day Field ListBox Month Field ListBox Temporal Metadata cbDateFieldAsymptote IstDayAsymptote IstMonthAsymptote CheckBox cbTemporalAsymptote Asymptote Asymptota Input Laver Selected eatures only a Subset f Year Field ListBox IstYearAsymptote Allow Debug Show Errors Iv Refresh 4rea Units i BRA te Spon AG Linear Units Tempcyal Metadata Asymptote Z Asymptote Shapefile Output Locations Destination for Destination Folder Command Buttons lpp Method ListBox Shapefile Output i i cb sg ox aaa ote IstAsymptoteLocationsA CheckBox p ia y eaa a k 7 cbOutputAsymptote cmdQuitAsymptote Figure 8 2 2 3 This analysis runs in the same manner as the regu
9. ListBoxes Figure 8 2 3 2 The use of selected features and subsetting follows as for the Minimum Convex Polygon analysis please see above lf coordinate data are discretized i e rounded and if the user has an estimate of the maximum rounding error associated with individual points then the Discretization CheckBox should be checked Figure 8 2 3 2 This option enables the Discretization Error ComboBox in which the error distance in map units should be entered Please see Section 4 4 for a discussion of this problem Discretization may result in poor estimation of the required smoothing factor when using Least Squares Cross Validation as a method for choosing the smoothing factor Silverman 1986 Chiu 1991 Seaman and Powell 1996 Kernohan et al 2001 If the Discretization CheckBox is checked then ABODE will correct for this problem while estimating the smoothing factor using Least Squares Cross Validation If the distance between two points is calculated as zero map units i e they are at the same place then the distance will be automatically adjusted to a value selected at random by ArcMap from an even distribution between 1 and the value entered into the Discretization Error ComboBox Figure 8 2 3 2 see Section 4 4 When the actual probability density function is being calculated then the distances between points will not be adjusted according to this distribution Checking the Temporal Metadata CheckBox will enable the T
10. case it is the area difference but in home range estimation with bivariate data the loss function would be the difference in volume between the two surfaces In reality this loss function is the integrated square error integrated since we are dealing with a density and Square error since we want to incorporate error in both over and under estimation It is intuitive on the curve At this point we find the associated smoothing parameter which becomes our estimate of the optimum smoothing parameter 18 Density 0 factor h Figure 4 3 2 2 Generation of a loss function from LSCV the definitions of X and X follow from Equation 1 Silverman 1986 gt K E x l h 2K 0 M h 5 i n h nh K is defined by K t K t 2K t 6 Silverman 1986 This is demonstrated by multiplying two bivariate normal densities fand g in equations 7 and 8 respectively to give f g in equation 9 t u Y here e 8 8 sae 8 juat F Ilo 05 os J 8 9 2m o 0 The multivariate normal density function as described by Silverman 1986 is 19 e K x 10 Where xx is the distance between the evaluation point and another point in the distribution divided by the smoothing parameter x x distance h Given equation 9 the convolution of the multivariate normal density function Ke becomes K x 11 AOO Ss st 12
11. density in black to low density in grey white indicates zero density Overlaying a grid is the next step towards building a density surface 12 a b C Figure 4 1 4 Assigning pixel density Pixels or grid cells are given density values based on their proximity to an evaluation point This happens for each location in the set calculated cumulatively Figure 4 1 5 a This is the same as summing the value for the kernel at every point on the surface Finally a surface is created that contains pixel values of the kernel density estimate of the distribution Figure 4 1 5 b The surface is then contoured at specified volumes to give percentage home ranges i e a 95 home range is contoured at 95 of the volume of the density surface not at 95 of the area of the home range Figures 4 1 5 c Pr a b C Figure 4 1 5 Pixel density accumulation values assigned to pixels from different evaluation points are summed and volume contouring defining the 2 dimensional area that contains a specified percentage volume of the density surface To see this process in effect for a real dataset Figure 4 1 6 shows the progression of pixel evaluation for the locations of a female cheetah in the Serengeti National Park Tanzania The second point in the dataset was at the same location as the first point The evaluation for this second point was omitted from the sequence but the result can be seen in the evaluation for point 3
12. functions Usually this process would require integration but by using a normal kernel the evaluation may be done analytically Bowman 1984 The normal kernel is computationally simpler to use in least squares cross validation but is not necessarily used in the actual density estimation The N biweight kernel this is an unexplained discrepancy between Seaman and Powell 1996 and Silverman 1986 Given a true density function for some distribution of data Figure 4 3 2 1 a various values of h the smoothing parameter are used to obtain density estimates For example Figure 4 3 2 1 b shows the density estimate given a smoothing parameter smaller than the optimum or true value The difference between the estimated and true density is evaluated as the sum of the area of deviation of the estimate from the true density Figure 4 3 2 1 c shows that difference given a Density Density Den sity space x Space x Space x Figure 4 3 2 1 Least Squares Cross Validation with the true density black line a and an over yellow line b and under estimate blue line c of the smoothing parameter Finally with highly oversmoothed data as with a smoothing parameter that is considerably larger than optimum Figure 4 3 2 2 a the difference between the density estimate and the true density is large The loss function can be considered to be the difference in area between the estimate and the truth In this
13. seeing significant differences at different percentage home ranges volume contouring In the example shown the commonly used estimator AMAE evaluates pixels up to 4200m away when the smoothing factor selected was 3000m The contours begin at 3000m from the points In Figure 4 1 7 b ABODE evaluates only pixels for which their center is within 3000m from the points and only for those points that have other points within the search radius In this case contours depend on the volume of the density surface and may begin for 14 example at only 1750m from the points Both Figure 4 1 7 a and Figure 4 1 7 b are at the same scale the difference in size of the bounding box shows the extent of the grid used in each with blue pixels showing a density value of 0 Both analyses used fixed kernels with a user defined smoothing factor of 3000m and 1000m grid cells Data were not standardized in ABODE and a biweight kernel was used In AMAE no standardization was used and a normal kernel was used instead of the biweight kernel 3000 a b Comparison of two kernel packages AMAE and ABODE using the same user inputs of a 3000m smoothing factor h with 1000m grid cells The only apparent difference in analysis is the use of a normal kernel in AMAE a and the use of a biweight kernel in ABODE b though this should not result in the differences obtained see Section 4 2 4 2 What to make of all these user inputs Running a ke
14. side of the given interval that ABODE will use when searching for displacement data pairs Interval Daves Tolerance Davs J OO e E ee O a 150 179 180 359 Oo 0 O e as 20 149 a aa a ea ABODE is a Home Range tool developed for ArcGIS using ArcObjects and Visual Basic for Applications VBA To use ABODE you will need ArcGIS 8x or higher The code and VBA form provided will not work in ArcView The functionality of ABODE is limited by the user s understanding of home range analysis therefore it is suggested that the first part of this user manual be understood The use of ABODE also requires that users have a basic understanding of and proficiency in ArcGIS much of the terminology relating to this software package has been left undefined in this user manual Default settings were purposefully omitted from the program in an attempt to force users to make well informed decisions about their analyses This user manual is designed to give a very basic understanding of home range analysis such that a user will be able to decide upon the best inputs and constraints for the analysis ABODE can be used as a Visual Basic for Applications VBA user form that can be added to an existing map document mxd or it can be used in a map document or map template mxt to which the form has already been added Both formats are provided and explained in the following sections The easiest method would be to use the map d
15. that in the y direction 28 4 5 3 Covariance Bias Seaman and Powell 1996 standardized their data to obtain an estimate of the required smoothing factor using the Least Squares Cross Validation technique They then rescaled the smoothing factor to represent the variance in X and Y This issue is dealt with in depth by Gitzen and Millspaugh 2003 ABODE provides an analog to the method used by Seaman and Powell 1996 Given a distribution of location estimates Figure 4 5 3 1 a an evaluation point red is any point for which the kernel density is being estimated The smoothing factor h4 Figure 4 5 3 1 b represents the smaller of the variances x in this case Grey points would be excluded in the evaluation of the red point Black points would be included A second smoothing factor h2 represents the larger of the variances y in this case Figure 4 5 3 1 c The single grey point would be excluded in the evaluation of the red point Figure 4 5 3 2 a shows the adjusted smoothing factors together The actual search area is determined by a combination of this case Figure 4 5 3 2 c Once the candidate points black have been obtained for the evaluation of the red point Figure 4 5 3 3 a the larger of the smoothing factors is used in the weighting function applied Equations 1 and 2 Distances of candidate points to the evaluation point are calculated figure 4 5 3 3 b Forthe case Of x variance greater than
16. their analysis In most cases the form will not allow procedures that may cause the program to crash This often occurs when the user has not chosen a required input When the form fails to catch these potential errors however and error message will occur that asks the user if they wish to debug Figure 8 2 1 1 if the Allow Debug checkbox is checked ABODE Pete Laver 2004 Microsoft Visual Basic Minimum Convex Polygon Kernel Input Run time error 13 1012 Layer a Type mismatch x Coordinate Coordinate ier comme f a a AA Metadata Options Standardize Unit variance Contouring volume Biweight o Data x Variance 3 method Density Kernel Biased K2 Contour i Covarianc Grid cell bias a Asymptote Random Core ms Locations Consecutive Smoothing Factor Smoothing User Smoothing Fixed e Function HRef Operation Adaptive Area sqm n Linear m a Grid T units sq km gt units km Eo T Asymptote Refresh Destination Union f For results Kernel Quit Output Figure 8 2 1 1 The user may choose to debug this is not recommended or may choose end recommended and determine based on the attempted inputs why the procedure was not allowed Choosing to debug will open the Visual Basic Editor If the user wishes to exit at this stage they may close the editor At this point they will be prompted with stopping the debugger Figure 8 2 1 2 Choos
17. to move out of the area before being sampled again This is depicted in Figures 7 1 b e where an animal s walk dotted line is traced after having left the evaluation point red The subsequent a b C d e Figure 7 1 Inappropriate choice of smoothing parameter allowing the inclusion of points from subsequent days as an artifact of the daily distance traveled equal to or smaller than the distance typically traveled in the given sampling interval displacement distance Figure 7 2 2 then in theory the animal would have left the rea by the chose to stay in the area instead of moving its typical interval distance or if it subsequently returned to the area Figures 7 2 c e In both cases it is fair to assume that a high density of location estimates may reflect biological importance to the animal a b C d e Figure 7 2 Appropriate choice of smoothing parameter based on the structure of the location data sampling schedule and the movement behavior of the species displacement distance parameter for the dataset In reality not all studies will have the luxury of a generally consistent sampling interval Many data are collected opportunistically and will thus have an irregular sampling schedule In such cases ABODE can look for a sampling interval that best represents the data The user should decide which measure of central tendency would best represent the data ABODE can look for the median mean and mod
18. will not be removed on the refresh function Asymptote will run the kernel asymptote function and requires that the user select either Random or Consecutive in the Asymptote Method Listbox in the Options section To run either a normal kernel analysis or the core home range analysis the 58 Kernel button should be used Asymptote options will be ignored if the Kernel option is chosen Likewise the core option will be ignored if the Asymptote option is chosen 9 Conclusion Be faithful to your data and to the natural history of your animal Choose a home range estimator or inputs that will best reflect the objective of your study that will match the underlying data structure and that will be biologically meaningful considering the movement behavior of the animal Always report all user inputs and methodology for the sake of defensibility and replicability 10 Acknowledgements Marcella Kelly and the Department of Fisheries and Wildlife Sciences Virginia Tech provided financial and logistical support for this project Marcella helped with the development of theory for alternative deterministic smoothing factor choices Steve Prisley helped throughout the project both with intellectual contributions and with code improvements Roger Powell provided the impetus for undertaking this project after many discussions of discrepancies in available software packages and the inadequacies of current me
19. y variance the kernel would be oriented in a perpendicular fashion Figure 4 5 3 3 c e a n a Ss bad a b C Figure 4 5 3 1 Generation of two smoothing parameters based on either the x or y variance a b C Figure 4 5 3 2 Truncation of the search area based on the smaller of the variances in either the x or y direction 29 a b C Figure 4 5 3 3 Inclusion of points in a density estimate based on the truncated search area when using the covariance bias method of standardization should the user wish to make comparisons between home range estimators that may only provide this method of standardization This method is heavily biased by not incorporating the 5 Home Range Asymptotes 5 1 Why we should look at them Harris et al 1990 suggested that a home range analysis should be done using data that encompass the full range of variation in movement behavior attributable to sex and age differences This is only possible if a representative sample generally evenly spaced in time is obtained for the entire sampling duration To ensure that the sampling duration covers the full range of behavior exhibited by the animal home range asymptotes are necessary This should typically be done using a preliminary dataset before the majority of the data are collected The point in time conversely the number of locations required where the home range reaches an asymptote will indica
20. 1990 concluded that core areas if they exist in an animal s home range may be useful in understanding the behavior of the animal by providing a clearer interpretation of shifting patterns of use within a home range and allowing better insight into intraspecific and interspecific patterns of area use They suggested that in some cases total home ranges might overlap while higher concentrations of important resources and are thus more important to us in understanding an animal s life requisites than are peripheral areas Not all animals will necessarily have a core in the range Powell 2000 and this could be due to an even or a random use of space by the animal Cores should reflect biologically important areas in a range rather than arbitrary probability cut offs In home range analyses core areas are often reported simply as percentage use areas at some arbitrarily defined probability Powell 2000 This type of analysis should not be done Rather each home range should be tested to see if a biologically meaningful core area does exist 6 2 How do we test for this Harris et al 1990 proposed that core areas could be defined by plotting the area y axis against the harmonic mean isopleth x axis for harmonic mean analyses The core area would be at the point of inflection on the graph For kernel analyses Powell 2000 and Horner and Powell 1990 suggested the use of a plot of the percentage area home range against the pr
21. 2 Minimum Convex Polygons MCPs 8 2 3 Kernel Density Estimation 9 Conclusion 10 Acknowledgements 11 References O O O N NO DG FP OOHO 1 Preface Home range analysis is an important part of our study of animals and it is fraught with problems from data collection to final management implementation ABODE is user friendly freeware that can be used in ArcGIS to do both MCP and kernel analyses Both batch and single processing are available as well as automatic functions for asymptote analyses and core home range analyses The code for this package is open and can be manipulated to suit the needs of the user with minimal VBA and or ArcObjects experience The functionality in and the detailed documentation provided with ABODE are aimed to address some of the more contentious issues in home range analysis Beyond providing documentation for ABODE this user manual is also aimed at giving the user background in home range theory and home range analyses Should the user feel comfortable with the theory they should skip to the documentation for ABODE towards the end of the manual 2 Introduction 2 1 Home Range Analysis One of the basic requirements in the study of animals is an understanding of the relationship between the animal and its environment Ata grossly simplified level this requirement is sufficed with home range analyses Home range is a concept that attempts to describe the spatial context of an animal s
22. 2 1 b In both figures the user defined fixed smoothing factor was 32m and both had a grid cell size of 15m In ABODE a biweight kernel was used with a normal kernel being used in the other package Standardization was not implemented in either package Both figures are displayed at the same scale and clearly there are not only differences in the extent of smoothing given the same inputs but also in the ability to distinguish probability differences at a fine resolution a b Figure 2 2 1 95 Volume fixed kernel home ranges using no standardization a normal AMAE or biweight ABODE kernel h 32m and 15m grid in software AMAE red line and ABODE blue line Orange points are a hypothetical set of location estimates Blue cells in the grid indicate 100 probability no density value while dark cells indicate higher density than lighter cells The difference in software packages due to the contribution of outliers in a dataset is dealt with further in Section 4 1 Very briefly a commonly used estimator assigns a density value to pixels that surround even outlying data The effect is best observed when comparing Figures 2 2 2 a and b in which the former is the commonly used estimator and the latter is the product of ABODE for the same dataset Both analyses had the same user inputs which are discussed in Section 4 1 differences in home range size using kernel estimation a b Figure 2 2 2 Single female cheet
23. 2000 and the Home Range Extension HRE Rodgers and Carr 1998 Unfortunately no detailed review has been done for these kernel estimators Several Minimum Convex Polygon MCP estimators are available but it is hoped that different packages would provide identical results for a deterministic measure such as MCP They are both extensions that can be added easily to ArcView a software package that has previously been the most commonly used package for ecological Geographic Information systems Many studies have reported the use of one or the other Since ArcGIS 8x became available many research and academic institutions have started to use this software as a replacement for ArcView It was my goal to provide home range freeware that could be used in ArcGIS which fully documented the algorithms and techniques used in analyses and which would use the elements from the available ArcView extensions that were most helpful aimed to improve on certain analyses that I felt were not implemented optimally Though many software discrepancies do exist and no estimator certainly not ABODE will be perfect it is suggested that the user read some of the following points highlighting differences that could have a considerable effect on a home range analysis uninhabitable areas within the range In Figure 2 2 1 0 a commonly used estimator is not able to eliminate areas of low probability within the distribution as does ABODE Figure 2
24. A 1990 Analysis of wildlife radio tracking data Academic Press San Diego Woodroffe R and Ginsberg J R 1998 Edge effects and extinction of populations inside protected areas Science 280 5372 2126 2128 Worton B J 1995 Using Monte Carlo simulation to evaluate kernel based home range estimates Journal of Wildlife Management 59 794 800 Worton B J 1989 Kernel Methods for Estimating the Utilization Distribution in Home Range Studies Ecology 70 1 164 168 Worton B J 1987 A review of models of home range for animal movement Ecological Modeling 38 277 298 62
25. ABODE Kernel Home Range Estimation for ArcGIS using VBA and ArcObjects By Pete Laver User Manual Beta v 2 7 February 2005 DEPARTMENT OF AND PETEN LAVER Department of Fisheries and Wildlife Sciences Virginia Tech 149 Cheatham Hall Blacksburg 24061 0321 540 231 5320 plaver vt edu Table of Contents 1 Preface 2 Introduction 2 1 Home Range Analysis 2 2 Software discrepancies 3 Minimum Convex Polygons 3 1 The first home ranges 3 2 Problems with polygons 3 3 Benefits of polygons Simple can be good 3 4 A final note on comparability 4 Kernel Density Estimation 4 1 The move from deterministic to probabilistic techniques 4 2 What to make of all these user inputs 4 3 Selecting a smoothing factor 4 3 1 Non statistical methods 4 3 2 Statistical methods 4 4 Discretization and the effect of rounding error 4 5 Standardization 4 5 1 Unit Variance Standardization 4 5 2 X Variance Standardization 4 5 3 Covariance Bias 5 Home Range Asymptotes 5 1 Why we should look at them 5 2 How we should analyze them 6 Core Home Ranges 6 1 Does a core really exist 6 2 How do we test for this 7 Data driven and Biologically meaningful methods 8 Using ABODE 8 1 How to start using ABODE 8 1 1 Loading the form into the VBEditor 8 1 2 The VBA realm 8 1 3 The easy start up for ABODE 8 2 Using ABODE for home range analysis 8 2 1 The Visual Basic form and error trapping 8 2
26. Document code source It will read Normal mxt or the name of your document depending on the option chose above Figure 8 1 2 4 Without clicking anywhere you may begin typing to have the code inserted between the wrappers Wrappers contain the code for calling the form you are about add whenever the tool button is left clicked Between Private Sub _ your tool name_click and End Sub where the cursor currently rests type the following Figure 8 1 2 5 load frmhr frmhr show Microsoft Visual Basic YourProjectName mxd Eile Edit View Insert Format Debug Run Tools Add Ins Window Help le ea ee yl eee TETEE a An Wiona noco gt naX BKB B inca Project Project x ogo 4 YourProjectName mxd ThisDocument Code Abode YourProjectName mxd ThisDocument Code Normal Normal mxt BE Project YourProjectNan abode S lt lt lt Private sub dbode Click 3 ArcMap Objects e E hode trie Load frmhr rivate ode Clic p Q ThisDocument frrhr Show 59 References E End Sub Figure 8 1 2 4 Figure 8 1 2 5 Now right click in the Project explorer window and left click on the Import File option Figure 8 1 2 6 Navigate to where you saved the form ABODE frm and open this file Figure 8 1 2 7 Expand the folder for Forms and you will see that frmHR is registered Figure 8 1 2 8 Mic
27. Northing i Northing ry O MY xn O KY Original Original Data Data xv Ox xv X 3 Y s O aY standardized XY Data POP Origin x Origin x 0 0 UTM Easting 0 0 UTM Easting b a Figure 4 5 1 1 Unit Variance Standardization Original a and standardized datasets b Y Y UTM UTM sigs Northing Northing XY XY O C Original Data Original _ o Data Ca Y a XY amp Xo o o fe e xy te a Standardized Standardized Data Data onan x Origin 7 0 0 UTM Easting 0 0 UTM Easting b a Figure 4 5 1 2 Spatial relationships maintained with original datasets that have equal variance in the X and Y directions a Original data with unequal X and Y variances are transformed in a non uniform fashion b Y nanan Y ahem UTM 2777n UTM a gaint Te Northing r x Ls y Pi O i Northing i N 4 F Original 1 Original i 1 Data 1 Data 1 i r Standardized p i amp Qa Data D amp pi eo Sei 0o E e e f Standardized a Data Origin x Origin x 0 0 UTM Easting 0 0 UTM Easting b a Figure 4 5 1 3 Re projection of home ranges dotted lines from standardized to original datasets using unit variance standardization 27 4 5 2 X Variance Standardization Another method for equalizing the variance is to apply X Variance Standardization Rodgers and Carr 1998 Kenward and Hodder 1996 the variance
28. Without having saved the map document yet the other option 40 in the drop down menu reads Untitled Figure 8 1 1 5 If you have saved your document the option will show your document s name Figure 8 1 1 6 Left click New UlControl From the options given leave the radio button for UlButtonControl activated Figure 8 1 1 7 a Save in Untitled Keyboard SERB Normal met UlCortrols Mew U Control MHormal mst gave ini ette ee Figure 8 1 1 4 Figure 8 1 1 5 Pea Ar m Hew UlControl x Sr M UlControl Type gt i f U ButtonContral UIEditboxControl a E E UlToolContral f UlComboboxControl New UlContral Di f Save in Mormal rnst keyboard ly 1 Create and Edi i Cancel fourProjecth ame m New UlConitrol Delete U Contral Figure 8 1 1 6 Figure 8 1 1 7 Left click Create In the Commands window Normal U IButtonControl1 is displayed if you have chosen the template option Project UIButtonControl1 is displayed if you have chosen to save as part of a unique document Change the extension UIButtonControl to ABODE Figure 8 1 1 8 Drag the newly created button to a tool bar Figure 8 1 1 9 Right click on the new button Check Text Only Figure 8 1 1 10 This should display the tool as the name entered for the extension ae SSS pa Abode Ch
29. a M M pa Monti A lf J Refresh Asymptote Output Asymptote Shapefile Output P Locations 4rea Units Destination p00 z for results vj Gr Linear Units Allow Debug Layer Show Errors V Whe Figure 8 2 2 1 tipigi aiteis nietos Ube Fe IstLayerMCP cbSelecteamcp cbSubsetMICP IstFieldMCP ABODE beta v 2 Vete Laver 2005 Minimum Convex Palyg n Kernel Density Estimation MCP MCP Input Allow Debug Selected features only Show Errors V Layer Subset Refresh MCP Output Area Units mE Destination i Quit for results Cae Linear Units Destination F Command Buttons Output Units i Shar a e p eei p sie cmdQuitMCP Figure 8 2 2 2 The code used to run the Minimum Convex Polygon section of this form was adapted with permission from Dr M Sawada from the University of Ottawa Convex Hull ABODE will automatically register point shapefiles in the table of contents and display the available layers in the Source Layer ListBox Figure 8 2 2 2 As soon as the user selects one of the point layers the form will automatically be primed for that layer This means that when the user then selects for example to subset the dataset Subset CheckBox Figure 8 2 2 2 the available fields from 49 the selected layer Source Layer become activated in the Subset Field ListBox Once a layer is selected there is
30. ah dataset analyzed using identical user inputs in AMAE red line and ABODE blue line AMAE appears to assign values to outliers in the dataset and appears to assign value to cells further than the chosen smoothing parameter distance from orange points to white grid cells This is one example of software discrepancies that result in different home range sizes and area use patterns The are numerous others that the user should be aware of 3 Minimum Convex Polygons 3 1 The first home ranges minimum convex polygon MCP to delineate a home range boundary Since then MCPs have been the most widely used home range estimation tool Beyond the minimum convex polygon the other major deterministic technique used in home range analysis is the grid cell count Siniff and Tester 1965 3 2 Problems with polygons The definitional and analytical flaws associated with the MCP estimator are reviewed elsewhere Use of the minimum convex polygon encourages the notion of home range as a 2 dimensional entity with even space use Powell 2000 This is contrary to the cognitive map of variable resource and landscape value Peters 1978 that is manifested as a 3 dimensional entity of variable and potentially clumped use with a diffuse and general boundary Stickel 1954 Gautestad and Mysterud 1993 Gautestad and Mysterud 1995 Powell 2000 The MCP method has been shown to be highly sensitive to sample size number of loca
31. aive estimator is a histogram constructed such that each point falls in the centre of a sampling interval bin Figure 4 1 1 b In this method the sampling intervals overlap and the points that are included in any interval are weighted according to a uniform distribution The kernel estimator is an improvement of this naive estimator in that it replaces the uniform weighting function with a kernel function This kernel function is a probability density function with a specified distribution Figure 4 1 1 c Equation 1 defines the kernel density estimator F X m AX Relative Density Density Frequency 0 Figure 4 1 1 Progression of density estimation from simple histogram techniques to smooth kernel estimation Adapted from Silverman 1986 In these examples the abcissa x axis could be x coordinate for a set of locations that in the animal spends more time or is seen more in the center of the distribution in the x direction v x ona s Kis the kernel that determines the shape of the distribution that is placed over each of the points which controls the search radius or width or the kernel nis the number of location estimates points used in the analysis x and X refer to the vectors of the coordinates of the evaluation point and all other points respectively Various kernels have been described Silverman 1986 1986 Seaman and Powell 1996 use as an example the Biweight Kernel Kz from Silver
32. analyses Rodgers and Carr 1998 This means that when the user wishes to contour at a certain percentage of the home range e g 95 contouring takes place at that percentage volume of the probability density function and not percentage of the total home range area In the Kernel Function ListBox the user can select the form of the kernel used in the density calculation Silverman 1986 provided the Biweight Kernel K2 as an option This was used by Seaman and Powell 1996 and is the only option in ABODE In the Percentage Home Range Contour ComboBox the user can set the required contour level If the Home Range Core CheckBox is checked then the options for the percentage contour will be disabled If this option is chosen ABODE calculates home ranges for 1 5 to 95 in 5 increments and 99 9 home ranges If a core area exists then ABODE will find the 5 range in which it occurs and calculate home ranges in 1 percent increments If a core area exists it will be output as a shapefile contoured to the nearest percentage of home range volume A table will also be created which contains for each percentage home range the percent maximum probability and the percent home range area These values should be graphed in a graphing package such as MS Excel to check that a concave curve clumped use is displayed see Section 6 Grid cell size may be set in the GridSize ComboBox Setting this parameter should be determined by the tradeoff b
33. ange Button Image P E Comme Image and Text Image Only Toolbars Commands Option Begin 4 Group eS Categories Commands sp Spatial Analyst a Amail E Surface o a Figure 8 1 1 8 Figure 8 1 1 9 Figure 8 1 1 10 41 8 1 2 The VBA realm With the Customize window open you can right click on the tool ABODE button and choose the View Source option to enter the Visual Basic Editor Figure 8 1 2 1 Alternatively with the Customize window closed you can right click on the tool whenever the ABODE window is closed and scroll down to choose the View Source option Figure 8 1 2 2 A left click on View Source will open the Visual Basic Editor Figure 8 1 2 3 nf heave AR Abode Reset en Main Menu Delete ve Standard Abode E Tools Change Button Image d 4 Draw PENA E Survey Editor Toolbars Eommar le Text Only Categories Image Only Spatial Analyst Image and Text Editor Surface aE Survey Analyst Begin a Sroup Tracking Analyst Survey Data Esch Customize Survey Editor View Source Survey Explorer Sure Feature Tanla Figure 8 1 2 1 Figure 8 1 2 2 Ce G sha s oe aot we g na GFTP Private Sub Abode Click End Jub furl G aaae Figure 8 1 2 3 Dp abada Ea arua Marccatalog Mabodw dos IF Micra H viewnw t A Microsatt DE 42 The active window is the This
34. bandwidth may be set in the Smoothing Factor Frame Firstly the smoothing Function may be set in the Smoothing Function Listbox This determines how the smoothing factor is selected If LSCV Least Squares Cross Validation is chosen then ABODE will determine the optimal smoothing factor for the given dataset Section 4 3 2 This method involves minimization of the mean integrated square error for the density over various values for the smoothing factor h Silverman 1986 This is achieved through the use of minimizing function GOLDEN Sprott 1991 LSCV will in most cases provide the optimal choice of smoothing factor Seaman and Powell 1996 Selecting HRef Reference smoothing will provide the smoothing factor based on the assumption that the given data fit a bivariate normal distribution With most animal movement distributions this assumption is violated and this option will thus produce an overestimate of the required smoothing factor and subsequently an overestimate of the home range size As noted by Silverman 1986 this option may be a good choice for exploratory analyses Choosing the User option will enable the Smoothing Factor ComboBox and allow the user to enter or select a smoothing factor This choice may be based on prior knowledge of the underlying data structure or on the knowledge of the behavior of the animal in question Finally choosing Displacement will provide a smoothing factor that is ca
35. behavior Home Range was formally defined by Burt 1943 that area of the home range From the outset home range has been measured in terms of the hard boundary defining the edge of polygon containing the area used by an animal Home ranges have been analyzed since the earliest of hunting cultures first started to track their quarry Today techniques and uses of home range analysis have become more sophisticated Home range theory is now used in conservation and management strategies It is used to delineate protected area boundaries As legal mandates for the protection of imperiled species have become more common e g Endangered Species Act of 1973 USA understanding the spatial requirements of an individual and then collectively for a minimum viable population has become more important The spatial context of animal behavior is important not only in the management of threatened species that we aim to preserve but also in the management of threats e g invasive species With the improvement in our conceptual grasp of home range and our improvements in home range analysis the concept of home range has been used for Mitchell and Powell 2003 Home range theory can be used for many conservation and management ends Three things should dictate the methods used for doing this the objective of the study the potential of the data and the life history of the animal Unfortunately there is no perfect home range estima
36. cases analyses should not be reported as home range estimates but rather as total range estimates These are often as important to managers and conservationists as are home range estimates They could indicate sensitivity to external threats that may only be contacted once in a lifetime but that could be deleterious to the animal A common threat of this sort would be becoming a pathogen vector or invasive species vector An example of this could be the contraction of an infectious disease at the edge of a range or perhaps persecution upon leaving a protected area e g Lycaon pictus Woodroffe and Ginsberg 1998 MCPs might highlight this sort of high risk but infrequent movement behavior Very often the data used in home range analyses are so poor that MCP sizes number of locations per animal are required for kernel analyses In cases where sample sizes are insufficient an MCP estimate of area used though not necessarily a home range will be better than nothing Occasionally the movement behavior of an animal is such that the uniform area use suggestive of MCPs may in fact be valid This would be the case if the animal s much more detail than an MCP since the density of locations will be equal everywhere in the interior of the area of use The sensitivity of MCP estimates to sample size and sampling duration when points are added sequentially and outliers may be understood in the simplified sequence of Figure 3 3 1 and i
37. duration was appropriate then the fact that the home range does not reach an asymptote probably indicates a biologically important movement behavior One home range that does not asymptote should not affect the estimate of required sample size If many home ranges follow this pattern then perhaps the behavior of the animal does not lend itself to a stabilization of home range size The animal does not have what can be considered a true home range but is instead migratory continuously dispersing or simply transient If the user chooses to do a kernel asymptote analysis the option to output grids for each increment of locations will not be available Outputting all the grids would take up too much Space on most systems The user will be able to output the shapefiles at the specified contour For both kernel and MCP analyses the most useful output from ABODE is the table that contains bkd the area values for each subset of the data These tables are labeled _your shapefile name _ and then a suffix KACons dbf for the kernel asymptote using consecutive locations estimate on the y axis and the number of locations in the analysis on the x axis This can be done by opening the database file dbf in a graphing package such as MSExcel Graphically the 31 By using MCPs in the asymptote analysis the user will be able to pick out dispersal events or significant sallies if the data are added sequentially Figure 5 2 1 a
38. e options in ABODE are date sensitive they require day month and year fields it is suggested that a date field if available be converted to separate fields for day month and year This can be done in MS Excel using the functions day month and year 8 2 1 The Visual Basic form and error trapping ABODE was designed to be a relatively simple program with open code The benefit of this feature is customization The field of home range analysis is progressing fairly rapidly No estimation techniques are or should be taken as irrefutable truths Thus it is anticipated that the technology and theory behind home range estimation will change In addition to this no technique will fit all data Instead of massaging data to fit a technique techniques should be developed and changed such that we are faithful to our data and their capabilities Written in Visual Basic for Applications and ArcObjects you as a user have the ability to change the code The user interface is a simple form in which you enter or select parameters to be used in the analysis 46 ABODE has been tested but as with most software it has not been tested enough The form is designed in such a way that it traps potential errors before the code runs This prevents the user having to debug code line by line a tedious and difficult procedure The drawback is that the form may be a source of frustration to many users who are trying to customize
39. e sampling interval Before making a selection the user should understand the implications that outliers in the data will have on each estimate It may be best to run all three analyses and choose a method that seems most appropriate Sample size considerations dictate that ABODE uses a range of values for its search criteria The mean sampling interval may not even be represented in the dataset or may at best be represented by only a few actual data pairs To base a travel distance on such a small sample size may produce undesirable results Similarly the median sampling interval may only be represented once in a dataset and the mode at least twice ABODE will search for sampling intervals within a range that operates on an increasing Scale Table 4 If the interval ABODE is searching for is less than 7 days then the tolerance on either side is O days If the interval is less than two weeks 14 days then the tolerance is 1 day on either side This means that if the interval is one week ABODE will search for data pairs that are 6 7 or 8 days apart and then calculate the displacement from the new set These values were chosen subjectively by the author and could be adjusted very easily in the code for the program Table 1 Tolerances used to guide search criteria in the Displacement Smoothing Function option in ABODE The interval that the search is based on is given in days and the tolerance is the number days on either
40. ects the density at that particular point Where the point being evaluated is isolated the kernel value is zero if a biweight kernel is used Ideally a grid of infinitesimal resolution is placed over the distribution of points AE aGh grid intersection or from the Genter Of each Grid Cell the values Of Gach Of the function In reality this analysis would take an almost infinite amount of time We thus select a grid size to represent the most favorable tradeoff between resolution and hence smoothness of the pdf and time course grids taking less time to analyze Even with a reduced number of pixels to evaluate the process is still time consuming A short cut can be taken by selecting only the pixels that have a chance of having a value greater than zero i e only those within the search radius of those points that have not effectively been eliminated by the biweight kernel In kernel estimation each point in a given distribution Figure 4 1 2 a is evaluated Each evaluation point red in Figure 4 1 2 b is in turn evaluated based on the points that surround it A point that is surrounded by many other points will have a high density value To determine which surrounding points will contribute to the estimation of the density at the evaluation point a smoothing factor bandwidth h is used to describe the search radius about the evaluation point 11 green radius of the blue search area in Figure 4 1 2 b The dis
41. emporal Metadata Frame Figure 8 2 3 2 Again the Day Month and Year Field ListBoxes will register all the fields in the selected Source Layer that have numeric fields From these options choose the fields that correspond to the time interval A kernel analysis may be run without temporal metadata In order to get the kernel asymptote analysis for random locations or consecutive where the points are not tabulated in chronological order and for any analysis involving the Displacement smoothing choice Section 7 these data must be available Future versions of ABODE will allow the user to select a date field that contains these temporal data For the present individual fields are needed for all three For the use of the Displacement smoothing method the user must indicate what Sampling interval was used for data collection i e the time between consecutive locations If the data were collected using a regular or close to regular schedule or if the user wishes to manually set the minimum sampling interval then this value should be entered into or selected from the Minimum Sampling Interval ComboBox If the interval is not known or is highly irregular then the user should check the Irregular Displacement CheckBox Selecting this option will result in analysis of consecutive points For each pairing of consecutive points the time interval in number of days is calculated The arithmetic mean or the median or the mode interval is then e
42. eported for comparison s sake then the sample size sampling duration and treatment of outliers should be explicitly stated and hence matched for each individual analyzed 4 Kernel Density Estimation 4 1 The move from deterministic to probabilistic techniques We rarely have complete information about an animal s movement behavior The result of this is that deterministic techniques will be heavily biased by our sampling methods This may also be true for probabilistic techniques The latter use interpolation and extrapolation based on the distribution of the data They provide a more robust analysis that acknowledges the importance of the distribution of the data as a whole rather than evaluating each point in isolation The first Powell 2000 Nonparametric estimators in this group include Fourier series Anderson 1982 harmonic mean distribution Dixon and Chapman 1980 and kernel estimators Worton 1987 Worton 1989 Kernel estimation is currently the most widely used home range technique Silverman 1986 first described kernel density estimation for the layperson As a result much of the subsequent kernel home range literature rests heavily on this work Silverman describes kernel estimation as follows Figure 4 1 1 adapted from Silverman 1986 Density estimation in its simplest form is a histogram representation of the variable in question i e the x or y coordinate of a set of locations Figure 4 1 1 a The n
43. ers ABODE has not been tested with other projections systems yet 8 2 Using ABODE for home range analysis In order to facilitate the automation of tedious home range analyses ABODE provides options for subsetting datasets This is equivalent to running batch mode This allows users to load their data as a single shapefile into ArcMAP As an example one shapefile may have the location data x and y coordinates day month year and ID for all the animals in a population When subsetting the user chooses the field on which to subset i e the ID field and ABODE will then run the anaylsis for the data that have the same value in that field before starting new analysis for the next value Thus if a dataset has 5 individuals with IDs 1 2 3 4 and 8 and if the 1 then for individual 2 etc and then provide a single table as output containing the results from the 5 analyses ABODE can only handle subsetting at one level but if separate analyses are desired for multiple fields then the fields in the dataset should be manipulated in either ArcMAP in the attribute table or in a software package such as MS Excel MS Access or SAS before being imported back into ArcMAP In this manner a yearly analysis by individual is possible by generated a field i e IDyear in which the ID and year are concatenated individual 1 in year 83 would be 183 and year 84 would be 184 etc Since some of th
44. etween speed or efficiency of the analysis and its resolution The choice should reflect the scale of the data such that the spread in X and Y direction would be covered by an adequate number of cells A cell size that is very small relative to the scale of the 56 data will produce a fine resolution for the home range contour Contours will look smooth and show fine detail Such analyses will take longer and the resultant grids will require more disk space if kept Choosing a cell size that is large relative to the scale of the data will result in a quicker analysis but will be coarse and may not show the detail necessary At such a scale the shape and smoothness of the contours is largely governed by the contouring smoothing function in ArcMap This is the method that ArcMap uses to interpolate between the center point of each cell ABODE contains options that allow for relative grid sizes for example Resolution 25 would produce a grid cell size based on the size required to fit 25 cells into the smaller of the two ranges for X and Y data Such options will optimize the tradeoff between resolution and speed If you wish to run an asymptote analysis then the asymptote method consecutive or random must be selected in the Asymptote Method Listbox The procedure for sorting and randomizing the points is equivalent to that used in the MCP asymptote technique see Section 8 2 2 Specific parameters for the smoothing factor window or
45. he smoothing parameter It is suggested that discretization be dealt with in the same manner as depicted in Figure 4 4 5 to be moved and the original dataset may be preserved unlike the theoretical depiction in Figure 4 4 5 Instead if distances are zero i e points are overlapping then the distance may be manipulated artificially in the LSCV estimation this process goes on behind the scenes propose that the rounding error be used as the basis for this manipulation such that the rounding error forms the upper bound for a uniform distribution of numbers from which a manipulation distance is randomly selected This is tantamount to shifting overlapping points within the area described by a radius equal to the rounding error This does not allow for the opportunity of shifting points in the corners of grid cells and this may in some cases be a problem Sensitivity to this effect still needs to be evaluated used an initial dataset of 50 random points with x and y coordinates rounded to the nearest 10m i e 5m rounding error and then randomly selected 10 points to be repeated in subsequent analyses Once the ratio of overlapping points to the total number of points reaches a certain threshold Silverman 1986 the smoothing factor h selected by LSCV will tend towards 0 red data points Figure 4 4 8 a This subsequently results in area estimates that also degenerate Figure 4 4 8 b In both of these figures it can be see
46. her on sequential or temporally random points If no temporal metadata exist ABODE will assume that the data points are in identifier an OID is given to each record in the dataset automatically by ArcMAP when data are loaded as a shapefile these IDs are numbered in order of the records in the table Metadata should they be available are required in the form of separate fields for the day month and year Manipulation of a date field in order to obtain this format can be done in MS Excel or MS Access before importing the point data into ArcMap Once the user checks the Temporal Metadata CheckBox the Day Month and Year Field ListBoxes will be activated Figure 8 2 2 3 Choose the correct field for each of these temporal categories ABODE adds consecutive points by looping through the attribute table ordered according to the temporal metadata fields selected as inputs If these are not available ABODE will loop through the table of the points in the order that they appear in the attribute table i e ordered by the OID such that the table becomes randomized The new randomized table is then used in the analysis where ABODE again loops through the table Given that no seed value is set for ArcMap s randomization procedure each time this analysis is run a new starting subset and new subsequent subsets will be generated Thus the graph depicting the home range asymptote is no Please note that if an analysis is comp
47. in the x direction This is achieved by dividing the y coordinates by the standard deviation in Y and then multiplying them by the standard deviation in X Figure 4 5 2 1 a Using this method the variance in x is preserved The home range obtained using the standardized data can then be re projected using the factor of 0 for the x direction and o for the y direction Figure 4 5 2 1 b If the variance in y is greater than the variance in x then the scale will be reduced in the standardized data Figures 4 5 2 1 whereas the scale will be expanded if the opposite is true Figures 4 5 2 2 Y Y UTM UTM a Northing XY Northing eo Original O XaYa Original Data Data xY e x Y y 3 3 xy as Standardized O X Y Standardized Data Xa Y a Data bt 2 xY oe Origin x Origin x 0 0 UTM Easting 0 0 UTM Easting a b Figure 4 5 2 1 X Variance standardization where the original variance in the y direction far exceeds that in the x direction Y j A 3 UTM X3 3 Ly Northing O XY TM TE l Standardized Northing t d a Data _ Standardized O Data O 9 Xa Y3 AN E B E Pe ai O XY Original ata i Data XY ata Origin X Origin X 7 a k ee 0 0 UTM Easting 0 0 UTM Easting a b Figure 4 5 2 2 X Variance standardization where the original variance in the x direction far exceeds
48. indow Help aa B t 2e8 aN SESO Hao Normal Normal mxt El z Project YourProjectNan ArcMap Objects ThisDocument Private Sub Abode Click EN Forms Load frmHR FrmHR s20 YourProjectName mxd frmHR UserForm References K Cu gt u YourProjectName mxd ThisDocument Code m 0 BODE Pete Laver 2004 paa R AA E REE REESE r E BEEN Geer ON A A A A eee 2 to subset meters Tae peppers weer gt EREA pee ead Properties frmHR x 6 EE aR Zar ere eee a LR aaa CLT LEER eRe ORC aL Sa eT OTe SARA Temporal E i a Men Pe Pen A K Date See Irregular ESOS Minimum gt EE frmHR UserForm z ee Meda e ed E E UE LET EES RIT a E Alphabetic Categorized pba eS 5 re oE e re a EE oe E aE E iE aE E ae P SA Se S ae S SA ae Sd oae Sd bd de pd ad ade yd ade pS ade ade ade ade ade ade ade ode de o rde ade ode ede ode ede de de de od ode od S d ode ie de e d d i e e d ade ed ede e e d d d a d i d i e gt 3 Standardize par con Becca ens V Y m a Eee EEES E E ANEO E EE vl Pee a E A E OA ee a STOO ETI DEE E ESETT EA E I O T I I I E I T A A I I N E E A N I N N A oe Smoothing Smoothing Fetes Smoothing Bi et Function factor gt Operation Be peal WB eHso00001 0 FmBorderSt ABODE Pete D FrnCycleallr 32000 True Tahoma BB sxs000001 386 25 o ot units vit Gid
49. ing Cancel will return the user to the visual Basic Editor Choosing OK will close the editor and return the user to ArcMap closing the failed ABODE procedure If you forgot to check the ESRI Spatial Analyst Extension Object Library and ESRI Spatial Analyst Shared Object Library Figure 8 1 2 12 you will get an error when you first run a kernel analysis Figure 8 2 1 3 In this situation click OK Go through the steps outlined above Section 8 1 2 for setting the required references Then close the Visual Basic Editor Go to the folder you chose for saving 47 the outputs from the analysis Delete any new table that has been created Begin your analysis again niu u Do While dblCutoOttVolume gt dblVolumeSubTotal niO niO 1 lPixelCount 1PixelCount 1 Microsoft Visual Basic ai z aiiai dblVolumesSubTotal dbl3aarray Microsoft Visual Baste x Loop wan A This command will stop the debugger si a a AN Compile error es contour method User defined type not defined coc mob reo 2A AS TELING ErcmHE LletLayer Value Figure 8 2 1 2 Figure 8 2 1 3 If the Show errors checkbox is left checked a message box will pop up on every error with a description This may be left unchecked if multiple analyses are performed using the Subset option i e the code will not be interrupted and the analysis will run to completion without notifying the user of the errors 8
50. ing factor when comparison of home ranges is desired In many cases our data and the 36 behavior of our study species will give us clues as to what our smoothing parameter should be When obtaining the kernel density estimate the smoothing parameter h determines which points will contribute to the density at any particular point in space since it defines the search radius around each point It makes intuitive sense that areas that are biologically important cause the algorithm searched too far to find points that would contribute to density The distribution of data for an animal s home range will usually be determined by a combination of the sampling interval and sampling duration and the behavior or natural history of the animal Some data are collected on a regular sampling schedule with a generally constant sampling interval Given this type of schedule the next location estimate for would be found somewhere within this radius Some other behavioral phenomenon may determine the shape of the search area which might not be a circle If a smoothing parameter is chosen that far exceeds this hypothesized radius Figure 7 1 a then subsequent location estimates for that animal may be included in the density estimate of a point even though the animal was only passing through the area In other words location estimates at subsequent sampling efforts are included only because the animal would not have had enough time
51. istBox CheckBox Displacement ComboBox IstSmoothing IstStandardization cbCovBias CheckBox cbhoSmoothing cbirregular Smoothing Method Central Tendency Zero Displacement Minimum Sampling ComboBox ListBox IstCT CheckBox Interval ComboBox IstFixedAdaptive cbZero cbolnterval Figure 8 2 3 3 This section is vital for setting all the required parameters for the kernel analysis The selections on this part of the page are all required to qualify the result of the analysis when publishing results The first selection a user should make is whether or not to standardize the data Data should in most cases be standardized Silverman 1986 Worton 1989 Seaman and Powell 1996 Rodgers and Carr 1998 see Section 4 5 Currently standardization is only available for the Least Squares Cross Validation procedure When running the analysis using the reference smoothing factor HRef then data should be left at their original scale since the smoothing factor is calculated for the data assuming that the distribution is already bivariate normal i e theoretically standardization of the data would result in exactly the same distribution as the original data For user defined smoothing the smoothing factor is set either arbitrarily or based on some prior knowledge about the data structure or biological movement behavior of the animal Thus it is set disregarding the distributio
52. istribution that has truly random or even use only because the probability of use increases significantly just inside the edge of the distribution Figure 6 2 2 a is a cross section of a kernel density estimate for random use where A and B are two points at the edge of the distribution Plotted using Powell s 2000 method the area contoured for a low probability of use will be large high value on y axis but low value on the x axis while that contoured for a large probability of use will be much greater Figure 6 2 2 b In Figure 6 2 2 b the kernel density cross section is inverted and rotated so that the axes of the probability plot and that of the kernel plot will roughly match up In theory an even distribution should produce a graph that is flat equal area value for all probability of use values There should only be one value for probability of use since it is everywhere equal In reality at the edge of the distribution probability of use will be lower than the middle but will increase slightly before remaining constant moving inwards from the edge Figure 6 2 3 a The result of this kernel density cross section can be seen in Figure 6 2 3 b where there will be a core estimated at a very low probability of use near the boundary of the used area Finally in a clumped distribution as with normally distributed locations Figure 6 2 4 a a true concave pattern is evident in the probability plot Figure 6 2 4 b He
53. lar Minimum Convex Polygon analysis see above The difference in this case however is the number of points used each time a polygon that contains the number of points and the area for each polygon This table can then be graphed in a software package such as MS Excel In ABODE only the polygons that show an norease in area from the previous polygon SUBSet are displayed All polygons for which the addition of a point did not increase the polygon size i e these points fell within the perimeter of the previous polygon are not kept in the destination folder This reduces the number of superfluous shapefiles stored by ABODE The user has the option of keeping the shapefile output from the analysis which will be displayed in the Table of Contents and in the Map To do this check the Shapefile Output CheckBox Figure 8 2 2 3 Given a sample size of n points this analysis could potentially produce n 2 shapefiles this would occur if every subsequent point occurred outside of the previous polygon boundary For this reason the user may wish to leave this checkbox clear Two methods are available for running the asymptote analysis The choice of method depends upon the sampling protocol used to collect the data If the data are discontinuous then the points should be added 51 An asymptote analysis requires temporal metadata data such as day Month and year associated with each location in the dataset since it runs eit
54. lculated by ABODE based on the data provided ABODE takes either the given minimum sampling interval or the calculated mean median or mode sampling interval and estimates the mean distance traveled crow flight distance for that time interval This distance is then used as the smoothing factor This option will not be robust in all data sets and is especially sensitive to the sample size such that enough samples for the selected or estimated time interval are needed to provide a good estimate for the smoothing factor The theory behind this method suggests that it is both data driven and biologically 57 motivated It does however need to be tested extensively and should be used with caution and a healthy dose of pragmatism Finally in the Smoothing Function Listbox the method for smoothing may be chosen Currently only Fixed smoothing is available as an option following the recommendations of Seaman and Powell 1996 Future versions of ABODE will allow for Adaptive smoothing The lower section of the Kernel Density Estimation Page allows the user to customize the output provided by ABODE Figure 8 2 3 4 Shapefile Output Output Units IstArea Grid Output CheckBox CheckBox and IstLinear cbGridOutput cbContourOutput Asymptote cunt Allow Defiug Area Line Grid units units Contour Show Refresh Destination ox Union Errors for results lv Destination Folder Polygo
55. ler B L 1984 Home range of coyotes a critical review Journal of Wildlife Management 48 127 139 Lawson E J G and Rodgers A R 1997 Diffreneces in home range size computed in commonly used software programs Wildlife Society Bulletin 25 3 721 729 Mitchell M S and Powell R A 2003 Linking fitness landscapes with the behavior and distribution of animals In Bissonette J A and Storch Eds Landscape Ecology and Resource Management Linking Theory with Practice Island Press Washington DC USA pp 93 124 Mohr C O 1947 Table of equivalent populations of North American small mammals American Midland Naturalist 37 223 249 Otis D L and White G C 1999 Autocorrelation of Location Estimates and the Analysis of Radiotracking Data The Journal of Wildlife Management 63 3 1039 1044 Peters R 1978 Communication cognitive mapping and strategy in wolves and hominids In Hall R L and Sharp H S Eds Wolf and Man Evolution in parallel Academic press New York pp 95 108 Powell R A Zimmerman J W and Seaman D E 1997 Ecology and behavior of North American black bears home ranges habitat and social organization Chapman amp Hall London In Boitant L and Fuller T Eds Research Techniques in Animal Ecology Controversies and Consequences Columbia University Press New York pp 65 110 Rodgers A R and Carr A P 1998 HRE The Home Range Extension for Arcview User s Manual Cent
56. leted successfully the user form will be closed automatically If you were to run another analysis however the choices and values entered on the form will be retained If you fill in the inputs for the form and then left click Quit these inputs will also be retained However if your analysis does not run successfully then the form will be cleared Likewise when the user closes the user form manually the form will be cleared Ifa point layer is added to or removed from the ArcMap Table of Contents and no change has been made to the form since it last ran successfully or since the user clicked Quit then the Source Layer ListBox will not register the change If you left click on Refresh or close the form manually or if the last analysis was unsuccessful then the change should register in the Source Layer ListBox 52 8 2 3 Kernel Density Estimation The Kernel Density Estimation Page consists of three sections Figure 8 2 3 1 All three sections are required to run a kernel analysis These sections group user inputs into the categories of input data user defined options and output data The top section of the Kernel Density Estimation Page is the Input section Figure 8 2 3 2 ABODE beta v 2 Pete Laver 2005 x Minimum Convex Polygon Kernel Density Estimation Input Una Selected features only T j f ti Subset T cca B Data are discretized CO TT o x Coordinate Coordinate Wt
57. man 1986 Equation 2 defines the biweight kernel 10 K x 370 1 x x if xx lt l 2 i otherwise X X is the distance from the evaluation point to any other point in the set divided by the smoothing factor h Thus if Xx lt 1 then the point in question is within the search radius h of the evaluation point and is used in estimating the density at the evaluation point If xXx gt 1 then the point is too far away from the evaluation point to be considered Once a point is included in the kernel This makes intuitive sense since a point that is near the periphery of the search area will have a large distance x x tends towards 1 and should consequently contribute less to the density estimate than a point close to the evaluation point This kernel is calculated more quickly than the normal kernel and has higher differentiability properties than the Epanechnikov kernel two of the other commonly used kernel options that are available Silverman 1986 The final In the following paragraphs hope to provide a functional description of how kernel estimation may be done ABODE uses the following methodology in its kemel estimation This process is a simplification of a true kernel density estimate but provides a reasonable proxy Ideally a kernel function is placed over each point in the dataset Where there are other points in the vicinity within the search radius or h then the kernel has a value that refl
58. n Union Command Buttons cmdRefresh ComboBox cboFolder CheckBox cbMerge cmdKernelAsymptote cmdKernel and cmdQuit Figure 8 2 3 4 In the Area and Linear Output ListBoxes the units of output in the attribute tables and generated summary tables can be converted from the map units to the required units These units will be displayed in the tables and all values following this will be in the stated units Checking the Grid and Shapefile Output CheckBoxes will keep the raster and shapefiles generated by analyses If an asymptote or core home range analysis is performed then the user is not given the option of keeping the grids This is to reduce the amount of data stored to the hard drive The user may however keep the shapefile output for these analyses This will allow the user in the case of the asymptote analysis to see how the home range size increases as points are added For the core home range analysis only the core home range will be kept and displayed If no core exists no shapefile will be displayed The Destination Folder ComboBox allows the user to enter or select the folder in which to store the results Command buttons work as for the Minimum Convex Polygon Page Quit will remove the form from view but will retain the selections until the application is closed Refresh will provide a fresh page on which to start a new analysis Values that are typed into ComboBoxes
59. n of the underlying data and should be applied at the 55 original scale For Displacement smoothing the smoothing factor is as with user defined a biologically meaningful and data driven value and should be applied as such to the original dataset and not to standardized data Should Least Squares Cross Validation be chosen as a method for generating a smoothing factor then the options to use either Unit Variance standardization or X Variance standardization become available Both methods should provide equivalent results Rodgers and Carr 1998 though the detail in the contouring may be slightly different For the other smoothing function options the user will not be allowed to choose a standardization option and the option None should be chosen By checking the Covariance Bias CheckBox the user is able to standardize according to the method for standardization used by Seaman and Powell 1996 This method introduces bias since it is unable to account for covariance in the dataset Leaving the Box unchecked will allow for standardization to occur in a manner that accounts suitably for covariance Silverman 1986 77 The user then needs to decide on the method for contouring in the Contouring Method ListBox Figure 8 2 3 3 Two options are possible for contouring by density or by volume Rodgers and Carr 1998 In ABODE only the volume contouring option is currently available This option is used widely for home range
60. n shows overlap from 1 to 38 points 25 4 5 Standardization Not all datasets are created equal itis offen the case that data will have greater variance in a particular direction This may be caused by the behavior of the animal or it may be a result ofa estimate for an evaluation point Complex kernels are one method of overcoming this bias in the data and an alternative technique is described in section 4 5 2 A better solution would be to ABODE allows the user to incorporate standardization in the analysis using the aforementioned methods and a thrid option Covariance Bias Section 4 5 3 4 5 1 Unit Variance Standardization Standardizing data to have a unit covariance matrix was proposed by Silverman 1986 The original data Figure 4 5 1 1 a are standardized using the variance measures in the x and y directions The x coordinate for each point is divided by the standard deviation in X 0x Similarly y is scaled by oy This results in a set of standardized data Figure 4 5 1 1 b In this simple example the relationship between points is preserved since the variance is equal in both X and Y Figure 4 5 1 2 a In cases where the variance in X and Y is not equal Figure 4 5 1 2 b the relationship between the points is altered such that the variance in each direction is equal The kernel density estimation would typically be done on the standardized data to 26 Y Y UTM UTM
61. n that the manipulation of distances relative to the known rounding error will result in robust estimates of the smoothing parameter blue data points 45 With Discretization Manipulation Without Discretization Manipulation h m 0 20 40 60 80 100 Percentage overlapping points 16000 With Discretization Manipulation i Without Discretization om Manipulation 12000 10000 Area 8000 m 0 20 40 60 80 100 Percentage overlapping points Figure 4 4 8 Degradation of h using LSCV with data that are discretized 10 separate locations show overlap from 1 to 8 points per location When only one point is repeated in the dataset the breakdown of the LSCV estimate occurs much sooner Figure 4 4 9 It would seem from this cursory analysis that number of repitition ata single point may be more important than the number of points with repititions Manipulation will suffice only up to a certain point but ultimately with enough discretization the least squares estimate will degenerate It has been suggested that overlapping points should simply be 45 With Discretization Manipulation 40 Without Discretization Manipulation h m 0 10 20 30 40 Percentage overlapping points 14000 e h Treia 12000 ge en 10000 Area 8000 my 6000 4000 2000 0 10 20 30 40 Percentage overlapping points Figure 4 4 9 Degradation of h using LSCV with data that are discretized 1 locatio
62. nappropriate for analyses may indicate important biological events such as dispersal events that are important to our understanding of an animal s natural history and to its conservation Woodroffe and Ginsberg 1998 The simplest polygon is a triangle of three points Figure 3 3 1 a As the animal moves around points may be added within the boundary formed by that triangle Figure 3 3 1 b Eventually the animal will extend the estimate of area used by moving outside of the perceived boundary Figure 3 3 1 c a b C Figure 3 3 1 Sequence of hypothetical location estimates added sequentially with resultant increases in MCP home range estimates polygons As this continues and as sample size increases the estimate of area use increases Figure 3 3 2 a Eventually certain exploratory movements sallies or directed dispersal events will a b C d Figure 3 3 2 As exploratory movements are added to the dataset the polygon defining the home range boundary increases The addition of a few can greatly increase the area of the polygon The decrease in the number of points defining the polygon boundary red points may indicate the addition of exploratory movements 3 4 A final note on comparability While there is still a place for MCPs in home range analyses usually the polygon will not define information in its own right but should not be compared across studies as is so often the case in literature If the MCP is r
63. nature of the data and of the behavior of the animal Seaman and Powell 1996 suggested the use of fixed kernels with 4 3 1 Non statistical methods Non statistical methods are usually not as robust as statistical methods in the sense that they are more subjective and are not necessarily always reproducible The starting point for any kernel the nature of location data An example of a method that incorporates these two concepts is detailed later in section 7 If there are no insights available to guide the choice of smoothing parameter then the user is left with two options The user can subjectively choose the appropriate smoothing factor based on a candidate set of curves i e run the the analysis using various smoothing factors and choose the option the resulted in the best fit The smoothing parameter used to obtain the curve that best suits the objectives of the analysis should then be used While this is not a statistically defensible choice of h it may allow for a greater range of objectives in the analysis This type of method may allow the user to elucidate fine scale detail in the distribution or to get a very general description of the overall pattern of density and any level of detail necessary within this range The second option would be to use a more statistically defensible and repeatable method thus automatic methods for choosing the smoothing parameters may be favored These are described in the next section
64. obability of use T he probability of use is plotted on the x axis scaled by the maximum probability of use the highest probability of use occurs at 100 The percentage area of the home range ata specified probability of use is plotted on the y axis scaled by the maximum area In theory curve 6 2 1 c The core should be contoured at the probability of use where the curve has a slope equal to that for random use m 1 this is equivalent to the point on the graph farthest in vertical distance from the slope m 1 33 100 100 100 h of Home Of Home of Home Range Area Range Area Range Area with with with probability probability probability of use gt X of use gt X of use gt X 100 of Maximum 100 5 of Maximum 100 probability of use 0 probability of use of Maximum 0 probability of use a b C Core area determination following Powell 2000 and Horner and Powell 1990 with random a even b and clumped c use of space Adapted from Powell 2000 Powell 2000 At very high probabilities of use there may be a concave shape in the graph In addition to this the distribution with random use will not be everywhere random since the location estimates fall off at the periphery So at the edges of the distribution the probability of use will be significantly lower than everywhere else within the middle of the distribution Thus a core area will be indicated for every d
65. ocument supplied and users wishing to do so should skip Section 8 1 1 and Section 8 1 2 39 8 1 How to start using ABODE 8 1 1 Loading the form into the VBEditor You have two choices in applying this program You can either save ABODE as part of a template document or you can save ABODE independently as part of a unique and saved map document mxd Be warned that if you save ABODE as a template it will appear as an available tool every time you open a new empty map Right click on the menu bar Figure 8 1 1 1 Scroll down to the Customize option and left click on it Figure 8 1 1 2 Left click on the Commands tab scroll under Categories and left click on UIControls Figure 8 1 1 3 Untitled ArcMap Arcinfo File Edit View Insert Selection Tools Window Help Ome S eX lo sor Figure 8 1 1 1 Customize 3 x Toolbars Commands Options Sa Categories Command Spatial Analyst Main Menu Standard New UlContral Deli Save ir Normalmst Keyboard Add from file Close Tracking Analyst Figure 8 1 1 2 Figure 8 1 1 3 You will notice that the Save in option reads Normal mxt if you have not saved the map document yet Figure 8 1 1 4 Use this option if you wish to have ABODE appear every time you open a new and empty map This is the normal template to which the code and form will be saved and subsequently applied
66. ollard T and Wray S 1990 Home range analysis using radio tracking data a review of problems and techniques particularly as applied to the study of mammals Mammal Review 20 2 3 97 123 Hawes M L 1977 Home range territoriality and ecological separation in sympatric shrews Sorex vagrans and Sorex obscurus Journal of Mammalogy 58 354 367 Hayne D W 1949 Calculation of size of home range Journal of Mammalogy 30 1 18 Hooge P N and Eichenlaub B 2000 Animal movement extension to Arcview ver 2 0 Alaska Science Center Biological Science Office U S Geological Survey Anchorage AK USA Horner M A and Powell R A 1990 Internal structure of home ranges of black bears and analyses of home range overlap Journal of Mammalogy 71 402 410 60 Jenrich R I and Turner F B 1969 Measurement of noncircular home range Journal of Theoretical Biology 22 227 237 Kenward R E and Hodder K H 1996 Ranges V an analysis system for biological location data Institute of Terrestrial Ecology Furzebrook Research Station Wareham UK Kernohan B J Gitzen R A and Millspaugh J J 2001 Analysis of Animal Space Use and Movements In Millspaugh J J and Marzluff J M Eds Radio Tracking and Animal Populations Academic Press San Diego pp 126 166 Larkin R P and Halkin D 1994 A review of software packages for estimating animal home ranges Wildlife Society Bulletin 22 2 274 287 Laundre J W and Kel
67. one more required input the destination for the files that are created This can be selected from or entered into the Destination Folder ComboBox Choosing to run the analysis on only selected features is an option Selected Features CheckBox features can be selected in ArcMAP using either the Attribute Table or the Select features tool features are selcted if they are highlighted i e in the light blue default color Please note that if no features in the layer chosen are selected ABODE will default to using all of the features in the layer Conversely if features are selected in ArcMap in the layer but the Selected Features CheckBox is not checked then ABODE will again default to using all of the features in the layer To reiterate ABODE will run an analysis on a selected feature only if features are in fact selected in a point layer and if the Selected Features CheckBox is checked Subsetting on a particular field will provide individual Minimum Convex Polygons for all the unique values contained in that field This means that all the features that have a common value for that particular field will be grouped together for the analysis One shapefile for each subset will be created Choosing selected features works within the subsetting function and the same rules apply concerning selection requirements see above Finally you can set the output units for the Attribute Tables of the polygons and for any summary tables that may be created by
68. or This rounding error is roughly half of the diameter of the grid cell Figure 4 4 5 a though greater error would occur if the initial location estimate was in the corner of a cell By the density of the distribution Figure 4 4 5 b may be better visualized Figure 4 4 5 c _In this case depiction in 3 dimensions Figure 4 4 6 would not be necessary for density interpretation 22 a b C Figure 4 4 5 Visualization of density estimates produced by shifting location estimates when overlap occurs Figure 4 4 6 With shifting of overlapping points 2D depiction is sufficient for interpreting density smoothing parameter that tends to zero Where discretization is severe and overlap between points is extensive LSCV may choose h 0 for the smoothing factor Since LSCV is the currently preferred automatic method for an objective choice of smoothing parameter this may pose a problem in many analyses Depending on the magnitude of the discretization and the extent of overlap LSCV may underestimate the smoothing parameter to varying degrees and Discretization effects may be borne out in contours that contract to form small islands throughout the distribution Figure 4 4 7 lt gt BE 28 g Re a aS lt gt E Figure 4 4 7 Effect of discretization and overlap in a female cheetah dataset using HRE Home Range Extension Rodgers and Carr 1998 LSCV was used to automatically choose t
69. phs for every core area analysis A decision based on the general shape of the graph should guide the interpretation of core areas In other words where the graph appears to be generally straight with a slope of m 1 until very high probability of use then the animal is probably using space randomly In ABODE core areas will be contoured based on the above probabilities It is called _your shapefile name_ and a suffix of CoreGraph dbf and can be opened in a graphing package such as MSExcel Figure 6 2 5 b This post hoc visualization is recommended for every analysis It should be noted that the x axis in such a plot is not the percentage home range but rather the percentage of the greatest probability value in the density grid 100 30 BO 4 Area of Home Range 0 40 40 60 g 100 Of Maximum Probability of use a b Figure 6 2 5 95 kernel home range red line and core home range contoured in blue at 70 of the volume of the density surface for a single female cheetah Both estimates used LSCV fixed kernels unit variance standardization and 1000m grids The core area probability plot used to determine the core area shows a concave form 7 Data driven and Biologically meaningful methods It has been shown that LSCV will not always be a suitable method for selecting a smoothing parameter automatically Silverman 1986 It is also inappropriate to use a subjectively chosen smooth
70. re for Northern Forest Ecosystem Research Ontario Ministry of Natural Resources Rudemo M 1982 Empirical choice of histograms and kernel density estimators Scandinavian Journal of Statistics 9 65 78 Seaman D E 1993 Home range and male reproductive optimization in black bears Ph D thesis North Carolina State University Raleigh Seaman D E Millspaugh J J Kernohan B J Brundige G C Raedeke K J and R A Gitzen 1999 Effects of Sample Size on Kernel Home Range Estimates Journal of Wildlife Management 63 2 739 747 61 Seaman D E and Powell R A 1996 An Evaluation of the Accuracy of Kernel Density Estimators for Home Range Analysis Ecology 77 7 2075 2085 Silverman B W 1986 Density estimation for statistics and data analysis Chapman and Hall London Siniff D B and Tester J R 1965 Computer analysis of animal movement data obtained by telemetry Bioscience 15 104 108 Sprott J C 1991 Numerical Recipes Routines And Examples in BASIC Cambridge University Press Cambridge England Stickel L F 1954 A comparison of certain methods of measuring ranges of small mammals Journal of Mammalogy 35 1 15 Swihart R K and Slade N A 1985 Influence of sampling interval on estimates of home range size Journal of Wildlife Management 49 1019 1025 van Winkle W 1975 Comparison of several probabilistic home range models Journal of Wildlife Management 39 118 123 White G C and Garrot R
71. re the point where the core should be contoured is where the probability of use increases significantly indicated by a slope m 1 34 100 of Home Range Area Eai with Probability probability of use of use gt X 0 0 of Maximum 100 A B 0 probability of use a b Figure 6 2 2 Methodology for generating a core area probability plot with a random distribution of locations t 100 r T 100 of Home E Range Area Probabilit with s of use y probability Fh of use gt X 0 0 A B of Maximum 100 0 probability of use a b Figure 6 2 3 Core area probability plot with an even distribution of locations mee ea 100 A A E Si Bie OA f jl t i 100 of Home Hi Range Area Pt aien i a Probability with probability of use ofusea gt nite 3 of Maximum 100 A B o probability of use a b Figure 6 2 4 Core area probability plot with a clumped distribution of locations 35 It is evident that all distributions will exhibit home range cores using this method Random and even distributions of use will show core areas according to the definition even if these appear within but near the periphery of the distribution In such cases this could be used as the definition of the total home range instead of the arbitrarily defined 95 volume cut off For areas These Cores are probably not biologically meaningful In all cases it is suggested that the user plot these gra
72. rnel analysis can be a daunting task considering all the user inputs that are required To date there is no industry standard for the protocol to be followed when estimating a kernel density This can be both good and bad It is good since no single protocol will be suitable or desirable in all situations It is bad since the estimates produced for a kernel analysis will only strictly be comparable if the same protocol is followed i e the inputs are the same It is evident from various sources Epanechnikov 1969 Silverman 1986 Worton 1987 that the kernel used i e biweight or normal will have little effect on the outcome of the analysis but the nature of the Silverman 1986 A fixed kernel uses a single smoothing factor h for evaluation of the entire dataset whereas an adaptive kernel evaluates a new smoothing factor for areas of the dataset with different densities It is unlikely that a consensus will be reached in the near future about which inputs should be used For this reason the user should always state all user inputs when reporting kernel results If these are reported then studies with the objective of comparison may be tailored to use the same estimator inputs ensuring that the studies are comparable 4 3 Selecting a smoothing factor As stated above the most important input when doing kernel density estimates is the smoothing factor Silverman 1986 This decision requires some consideration of the
73. rosoft Visual Basic YourProjectName n File Edit View Insert Format Debug Run Tools Ac a B s SRBA HO a gt Il E Normal Normal mxt Project YourProjectNan Abode Privati Import File x frmhr A i abode vi End Sy Okin o 7 e 2 63 ArcMap Objects 8 FThisDocument References view Code view Object Project Properties Insert Import File Export File re This Document g Print File name xvarbias Frm Abode Fri qa Microsoft Visual Basic Yo Eile Edit View Insert Format Lu Project Z Project paje Hl El Normal Normal mxt 8 Project YourProjectNan ArcMap Object fmm SO aoe ThisDocument Stoperties TO Dockable Files of type ve Files frm bas cls Cancel aj i a dig Thi D I MxD i ee rm is salad x Hide Help H References Alphabetic Categorized LEN LE E Figure 8 1 2 6 Figure 8 1 2 7 Figure 8 1 2 8 43 If you double left click on this option the form that runs ABODE will be displayed Figure 8 1 2 9 If you then go back to the ThisDocument code with a double click you will see that capitalization of the form name has occurred and it will now read as Load frmHR frmHR show indicating that the form has been recognized Figure 8 1 2 10 4g Microsoft Visual Basic YourProjectName mxd Eile Edit view Insert Format Debug Run Tools Add Ins W
74. s and camera trapping grids Here location estimates show the actual location but may still result in considerable overlap since the sampling effort is concentrated in those specific places a Ja 5 Ld Ci C C C C a b Figure 4 4 2 Density evaluation without taking into account overlapping points 21 One could consider the same evaluation area in 3 dimensions such that the x and y coordinates are plotted in the horizontal plane Figure 4 4 3 a and the number of points is plotted on the vertical axis Figure 4 4 3 b The number of points could very simplistically be a proxy fora density estimate Figure 4 4 3 c When the overlapping points are displayed on the vertical axis Figure 4 4 3 d the original density Figure 4 4 3 e changes to reflect the clumping of points Figure 4 4 3 f The final density estimate is not intuitive when compared to the 2 dimensional depiction of the distribution as is most common with our data Figure 4 4 4 a b p D d 5 ah a e k zi Se d m Figure 4 4 3 Demonstration of the effect overlapping points may have on density estimates using simple grid cell counts Figure 4 4 4 Comparison of 2D and 3D depictions of discretized data One method for depicting the overlapping distribution in 2 dimensions that would allow for improved interpretation would be to shift the overlapping points such that they would reflect the rounding err
75. sity estimates Biometrika 71 2 353 360 Burt W H 1943 Territoriality and home range concepts as applied to mammals Journal of Mammalogy 24 346 352 Chiu S T 1991 The effect of discretization error on bandwidth selection for kernel density estimation Biometrika 78 436 441 Dixon K R and Chapman J A 1980 Harmonic mean measure of animal activity areas Ecology 61 1040 1044 Dunn J and Gipson P 1977 Analysis of radiotelemetry data in studies of home range Biometrics 33 85 101 Epanechnikov V A 1969 Nonparametric estimation of a multidimensional probability density Theory of Probability and its Applications 14 152 158 Forde P 1989 Comparative ecology of muntjac Muntiacus reevesi and roe deer Capreolus capreolus in a commercial coniferous forest Ph D thesis University of Bristol Gautestad A O and Mysterud 1995 The home range ghost Oikos 74 195 204 Gautestad A O and Mysterud 1993 Physical and biological mechanisms in animal movement processes Journal of Applied Ecology 30 523 535 Gitzen R A and Millsoaugh J J 2003 Comparison of least squares cross validation bandwidth options for kernel home range estimation Wildlife Society Bulletin 31 3 823 831 Hansteen T L Andreassen H P and Ims R A 1997 Effects of spatiotemporal scale on autocorrelation and home range estimators Journal of Wildlife Management 61 280 290 Harris S Cresswell W J Forde P G Trewhella W J Wo
76. stimated Using either the estimated irregular displacement or the user defined minimum displacement ABODE will find all pairs of consecutive points that fall into an interval class that 54 contains the value For all of the pairings the distance between points in map units is calculated Again an arithmetic mean is generated This is the mean displacement in distance units per mean sampling interval This is the displacement distance that will subsequently be used as the smoothing factor It should be understood that the user has a choice of the mean median or mode interval between locations but the distance representing this interval is estimated as only the mean value The middle section of the Kernel Density Estimation Page deals with the options that users can select to customize their analysis Figure 8 2 3 3 Asymptote Method ListBox IstFixedAdaptive Percentage Home Home Range Core Range Contour GridSize CheckBox ComboBox ComboBox cbCore cboContour cbhoGidSize Contouring Method ListBox IstContour Kerel Function ListBox IstKernel Options Biweight Biased K2 Asymptote Random Locations Consecutive Kernel Contour Grid cell Core ae Smoothing Factor Smoothing ke Unit Variance _ Function HRef bd x Variance a Smoothing Standardization Covariance Bias Irregular Smoothing Factor Function ListBox Method L
77. tance from each point within the search radius to the evaluation point is then calculated Figure 4 1 2 c Based on these distances a cumulative value is assigned to the evaluation point Next another evaluation point is selected Figure 4 1 3 a This procedure continues until all the points in the distribution have been evaluated They are all scored and assigned density values denoted by classified symbology in Figure 4 1 3 b A grid of specified size is then overlaid on the distribution Figure 4 1 3 c Starting again with each evaluation point red the pixels within the search radius are populated with assigned their respective density values Figures 4 1 4 a and 4 1 4 b Each subsequent point is evaluated in the distribution Figure 4 1 4 c Thus two processes are occuring first a point to point evaluation and then a pixel to point evaluation 8 5 G 2 E K 5 li f j i mme gt o amp amp a d E a _ B a amp a a b C Figure 4 1 2 Process of finding points in a distribution yellow points that will contribute to the density estimate at an evaluation point red point The area searched blue circle is determined by the smoothing parameter h green line a b C Figure 4 1 3 The procedure for generating density estimates continues from point to point in the distribution yellow points until all locations have a density value high
78. te what the sampling duration Sample size requirement should be If home Gautestad and Mysterud 1993 Harris et al 1990 suggested the use of area observation plots Otis and White 1999 to determine the number of locations required to obtain a stable estimate of home range size Stickel 1954 Hawes 1977 Gautestad and Mysterud 1995 power law square root ofthe number of locations This may be true for MCP analyses but kernel estimators are relatively robust towards sample size issues Seaman et al 1999 Using 30 locations for LSCV They showed that kernel techniques actually overestimated home range size at lower sample sizes They admitted that these results were obtained from simulated datasets and it is unclear how real data will behave Few analyses have used kernels in an asymptote analysis mainly because of the tedium involved in doing them ABODE provides an automated method for doing both MCP and kernel asympitotes 5 2 How we should analyze them sample sizes This can be done by adding locations either randomly or sequentially Harris et al 1990 if the data are continuous i e they are collected at a constant sampling interval then the locations should be added sequentially if the data are discontinuous irregular sampling interval then the locations should be added randomly Forde 1989 used regression equations to correct non asymptotic home ranges If the sampling
79. the lower bound of the search values For unit variance standardization his calculated from value is adjusted for the biweight kernel A k is the constant used to make the adjustment For conversion to a biweight kernel A K 2 04 Silverman 1986 As stated earlier this discrepancy is unexplained _ A K o opt sfn h 13 Once an h has been estimated from LSCV this value is adjusted for the biweight kernel by multiplying by the constant A K 2 04 for use as a biweight kernel in the actual density estimation Seaman and Powell 1996 Silverman 1986 87 It should be noted that ABODE 4 4 Discretization and the effect of rounding error In many cases location data for study animals are discretized or rounded One example of how this may occur is when data are recorded using a map with a grid such that location estimates are placed in grid cells Figure 4 4 1 a In this case many locations that fall within a cell may be rounded to the same point within that cell resulting in considerable overlap of points Datasets that display a regular pattern may fall into such a category Figure 4 4 1 6 and Figure 4 4 1 c a Figure 4 4 1 Discretization in a dataset This form of discretization is an artifact of data recording Sometimes the data collection scheme will also lead to this phenomenon as with the use of a regular trapping grid This is the case in small mammal trapping regular line transect
80. thods in dealing with animal movement George Terrell provided invaluable help in explaining the intricacies of Kernel Density Estimation Terrell also provided suggestions for improving the speed of the estimation procedures Bill Cartstensen provided much ArcObjects VBA assistance Dean Stauffer provided intellectual help with ideas about smoothing factors and provided support in elucidating differences between the available software packages throughout the development process Jay McGhee was a sounding board for the many intellectual and code problems faced during development Art Rodgers and Angus Carr were helpful in describing methodology for Home Range Extension after which much of ABODE s functionality was modeled Finally most of the code was adapted from snippets and samples provided by ESRI and especially by ESRI users in the User Forums on www esri com including code that integrated for generating Minimum Convex Polygons from Dr M Sawada from the University of Ottawa Without the availability of code this project would not have been possible 59 11 References Anderson D J 1982 The home range A new nonparametric estimation technique Ecology 63 103 112 Bekoff M and Mech L D 1984 Simulation analyses of space use home range estimates variability and sample size Behavior Research Methods Instruments and Computers 16 32 37 Bowman A W 1984 An alternative method of cross validation for the smoothing of den
81. tions Seaman et al 1999 Bekoff and Mech 1984 Laundre and Keller 1984 Harris et al 1990 White and Garrott 1990 Kernohan et a 2001 This issue is dealt with in the next section 3 3 as well as in the discussion pertaining to home range asymptote analyses Section 5 The sample size issue is also related to the inability of MCP s to objectively treat outliers Seaman et al 1999 Further problems include the sensitivity of the estimator to spatial resolution Hansteen et al 1997 and sampling duration Swihart and Slade 1985a Powell 2000 engenders inappropriate comparison because of the sample size issues Only the most meticulously matched studies should use MCPs as a form of comparison if the sample sizes are equivalent along with equal sampling durations and similar treatment of outliers Having stated this MCPs do have a place in home range analysis 3 3 Benefits of polygons Simple can be good Choice of home range estimator should depend on three factors see above namely the objective of the study the nature of the data and the movement behavior of the animal in question Minimum convex polygons do have a place in home range estimation where these three factors are satisfactorily incorporated into the choice of MCP Sometimes the objective of the study is only to find the entire area used by an animal even if this does not meet the commonly held definition a home range given by Burt 1943 In such
82. tor and certainly no estimator should be used indiscriminately of the concerns listed above Home range estimators should not be used as a black box but should be used as they are intended as tools to aid our improved understanding of animal behavior The workmanship of the user rather than the tool will determine the quality of the final product This document is intended to give some general background concerning home range theory as well as to describe one of the tools available for home range analysis ABODE 2 2 Software discrepancies What software should use to analyze home range Larkin and Halkin 1994 reviewed several software packages used in estimating animal home ranges At that point in time few options were available for kernel estimation and no comparison was possible Lawson and Rodgers TRACKER The differences in kernel estimation were attributed to algorithms used in the programs For this reason it is recommended that algorithms be clearly stated in program documentation They also noted that there were differences in the options that users were given in terms of the type of smoothing fixed and adaptive and the actual kernel used in the analysis In the time since those publications several other packages have become available Most notably two extensions for ArcView 3x have come into popular use These are the Animal Movements Extension to ArcView v2 0 AMAE Hooge and Eichenlaub

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