**3.1 Default (reference) bandwidth estimation**

Datasets for avian and mammalian species can include as many as 10,000 locations and only the reference or default bandwidth (href) was able to produce KDE in both Home Range Tools and adehabitat. Estimation with href typically is not reliable for use on multimodal datasets because it results in over-smoothing of home ranges and multimodal distribution of locations is typical for most species (Worton 1995; Seaman et al., 1999). An important point to consider with previous investigations on bandwidth selection is that analyses used simulated data on only 10–1,000 locations for assessing reliability of href (Seaman et al., 1999; Lichti & Swihart 2011). Still, results from simulated datasets and real-world examples concluded that href should not be used on multimodal data typical for most mobile species (Worton 1995; Seaman & Powell 1996; Hemson et al., 2005). Our results confirmed that oversmoothing is considerable, especially for migratory avian species that migrate across vast geographic areas. For example, a turkey vulture that traversed from South Carolina to

Because GPS data are autocorrelated, they can pose difficulties in estimating the bandwidth (Gitzen et al., 2006) and violate the assumption of independence of locations that is inherent to KDE (Worton 1989). Therefore, although previous research on principles of bandwidth selection and selection of software is suitable for some datasets (e.g. VHF sampling protocols; Seaman et al., 1999; Gitzen et al., 2006; Kie et al., 2010), GPS datasets present additional challenges that need to be addressed (Amstrup et al., 2004; Hemson et al., 2005;

Fig. 2. Multiple Universal Transverse Mercator zones traversed by a migratory American

Datasets for avian and mammalian species can include as many as 10,000 locations and only the reference or default bandwidth (href) was able to produce KDE in both Home Range Tools and adehabitat. Estimation with href typically is not reliable for use on multimodal datasets because it results in over-smoothing of home ranges and multimodal distribution of locations is typical for most species (Worton 1995; Seaman et al., 1999). An important point to consider with previous investigations on bandwidth selection is that analyses used simulated data on only 10–1,000 locations for assessing reliability of href (Seaman et al., 1999; Lichti & Swihart 2011). Still, results from simulated datasets and real-world examples concluded that href should not be used on multimodal data typical for most mobile species (Worton 1995; Seaman & Powell 1996; Hemson et al., 2005). Our results confirmed that oversmoothing is considerable, especially for migratory avian species that migrate across vast geographic areas. For example, a turkey vulture that traversed from South Carolina to

Getz et al., 2007).

White Pelican in the U.S.

**3.1 Default (reference) bandwidth estimation** 

Florida, USA, had a 95% home range calculated with href that extended inland and into the Atlantic Ocean to areas locations were not even identified (J.W. Fischer, National Wildlife Research Center, unpublished data; Fig. 3).

Fig. 3. Home range (yellow polygon) of a migratory turkey vulture from South Carolina to Florida, USA as estimated using KDE with href bandwidth selection over-layed on actual GPS locations. Note that KDE occurs inland and into Atlantic Ocean where no GPS locations were collected.

An additional practical problem we encountered with href in adehabitat is that the extent of the generated home range polygon was truncated or not generated at all because a greater extent for evaluation points needed to be specified. To work around this issue, we created an evaluation grid of increased extent and iteratively re-estimated the home range until a large enough extent was specified and all isopleth (i.e. probability contour) polygons were successfully created.

#### **3.2 Least squares cross-validation bandwidth estimation**

Both the least squares cross-validation (hlscv) and bias crossed validation (hbcv) have been suggested instead of href in attempts to prevent over-smoothing of KDE (Rodgers & Kie 2010). However, hlscv and hbcv have been minimally evaluated on GPS datasets because previous literature only evaluated datasets collected on VHF sampling protocols or simulated data that included at most 1,000 locations and did not represent actual animal distributions (Worton 1995; Gitzen et al., 2006; Lichti & Swihart 2011). Least-squares cross

What Is the Proper Method to Delineate Home Range of an

Research Center, unpublished data).

**4.1 Time interval between locations** 

Animal Using Today's Advanced GPS Telemetry Systems: The Initial Step 257

conditioned only on the time duration between the beginning and ending locations for each pair of locations and GPS location error. As such, BBMM is able to predict movement paths that otherwise would not be observed with KDE methods. While some authors have suggested using ≤90% home range contours (Borger et al., 2006; Getz et al., 2007) to remove outliers or exploratory movements for KDE, increasing size of home range from 95% to 99% for BBMM does not over-smooth the utilization distribution but rather serves to more accurately define the area of use for some species (e.g. Fig. 4; Lewis 2007). Therefore, BBMM intuitively appears better suited for mammalian and avian species that migrate or travel long distances (Sawyer et al., 2009; Takekawa et al., 2010; J.W. Fischer, National Wildlife

Fig. 4. Home range of an American White Pelican using 95% BBMM (outset) with 99% BBMM connecting potential used habitats in some areas of the home range (inset).

Although equal time intervals between successive relocations are not, in theory, a requirement of BBMM, the method uses a Brownian bridge to estimate the probability density that the animal used any particular pixel, given its relocations. The "shape" of the

validation, suggested as the most reliable bandwidth for KDE (Worton 1989), was considered better than plug-in bandwidth selection (for description see 3.3) at identifying distributions with tight clumps of points but risk of failure increases with hlscv when a distribution has a "very tight cluster of points" (Gitzen et al., 2006; Pellerin et al., 2008). Several of our species could be classified as having "very tight cluster of points" because American White Pelican locations were truncated to a grid with multiple overlapping points, vultures occupied the same roosts at dusk and dawn, or black bears rested in day beds. Considering that none of our datasets resulted in converged hlscv or hbcv estimates for home range calculation, our results on several species further supported the contention that hlscv and hbcv bandwidths are not suitable for GPS-derived datasets, unless convergence issues at sample sizes >1,000 locations and with clumped distributions can be resolved (Amstrup et al., 2004; Hemson et al., 2005). One way to address lack of convergence due to large datasets is subsampling (Avery et al., 2011) that can be used for crude estimates of home range using KDE with hlscv. We conclude with others in cautioning against subsampling as it only serves to potentially remove important movement parameters or habitats used and will not result in the same estimate of home range size as the complete GPS dataset (Blundell et al., 2001; Pellerin et al., 2008; Rodgers & Kie 2010).

#### **3.3 Plug-in bandwidth selection**

Most first generation methods of bandwidth selection for density estimation (i.e. hlscv, hbcv) were developed before 1990 but advances in theory and technological capabilities has opened the door for second generation methods (Jones et al., 1996). Second generation methods, such as the smoothed bootstrap and plug-in methods (often combined into the solve-the-equation plug-in method; Jones et al., 1996), appear to be an improved alternative because of better convergence and reasonable tradeoffs between bias and variance compared to first generation methods (Jones et al., 1996; Duong & Hazelton 2003, but see Loader 1999). Debate about the appropriateness of second generation methods still exists with some claiming the estimates obtained with bivariate plug-in bandwidth selection (hplug-in) performs poorly compared to first-generation methods (Loader 1999) while others showed it performed well even when analyzing dependent data (Hall et al., 1995).

Using hplug-in in ks, we were able to calculate KDEs for the sample GPS datasets on 3 avian species and 2 mammalian species where first generation methods (hlscv) failed or generated a considerably over-smoothed KDE (href). While home range polygons generated with hplug-in appeared fragmented, they may be appropriate when studying a species in highly fragmented landscapes such as urban areas. Based on our results and previous research, conclusions presented in Loader (1999) should be re-evaluated for analyses of large GPS dataset because sample size and clumping of locations has consistently failed using hlscv, while hplug-in estimates converged for large multimodal datasets and resulted in reasonable estimates (Girard et al., 2002; Amstrup et al., 2004; Gitzen et al., 2006).

#### **4. Brownian bridge movement models**

The concept of BBMM is based on a Brownian bridge with the probability of being in an area dependent upon the elapsed time between the starting and ending locations (Bullard 1999; Horne et al., 2007). The BBMM "fills in" the space between sequential locations irrespective of the density of locations where the width of the Brownian bridge is

validation, suggested as the most reliable bandwidth for KDE (Worton 1989), was considered better than plug-in bandwidth selection (for description see 3.3) at identifying distributions with tight clumps of points but risk of failure increases with hlscv when a distribution has a "very tight cluster of points" (Gitzen et al., 2006; Pellerin et al., 2008). Several of our species could be classified as having "very tight cluster of points" because American White Pelican locations were truncated to a grid with multiple overlapping points, vultures occupied the same roosts at dusk and dawn, or black bears rested in day beds. Considering that none of our datasets resulted in converged hlscv or hbcv estimates for home range calculation, our results on several species further supported the contention that hlscv and hbcv bandwidths are not suitable for GPS-derived datasets, unless convergence issues at sample sizes >1,000 locations and with clumped distributions can be resolved (Amstrup et al., 2004; Hemson et al., 2005). One way to address lack of convergence due to large datasets is subsampling (Avery et al., 2011) that can be used for crude estimates of home range using KDE with hlscv. We conclude with others in cautioning against subsampling as it only serves to potentially remove important movement parameters or habitats used and will not result in the same estimate of home range size as the complete

GPS dataset (Blundell et al., 2001; Pellerin et al., 2008; Rodgers & Kie 2010).

estimates (Girard et al., 2002; Amstrup et al., 2004; Gitzen et al., 2006).

**4. Brownian bridge movement models** 

Most first generation methods of bandwidth selection for density estimation (i.e. hlscv, hbcv) were developed before 1990 but advances in theory and technological capabilities has opened the door for second generation methods (Jones et al., 1996). Second generation methods, such as the smoothed bootstrap and plug-in methods (often combined into the solve-the-equation plug-in method; Jones et al., 1996), appear to be an improved alternative because of better convergence and reasonable tradeoffs between bias and variance compared to first generation methods (Jones et al., 1996; Duong & Hazelton 2003, but see Loader 1999). Debate about the appropriateness of second generation methods still exists with some claiming the estimates obtained with bivariate plug-in bandwidth selection (hplug-in) performs poorly compared to first-generation methods (Loader 1999) while others showed it performed well even when analyzing dependent

Using hplug-in in ks, we were able to calculate KDEs for the sample GPS datasets on 3 avian species and 2 mammalian species where first generation methods (hlscv) failed or generated a considerably over-smoothed KDE (href). While home range polygons generated with hplug-in appeared fragmented, they may be appropriate when studying a species in highly fragmented landscapes such as urban areas. Based on our results and previous research, conclusions presented in Loader (1999) should be re-evaluated for analyses of large GPS dataset because sample size and clumping of locations has consistently failed using hlscv, while hplug-in estimates converged for large multimodal datasets and resulted in reasonable

The concept of BBMM is based on a Brownian bridge with the probability of being in an area dependent upon the elapsed time between the starting and ending locations (Bullard 1999; Horne et al., 2007). The BBMM "fills in" the space between sequential locations irrespective of the density of locations where the width of the Brownian bridge is

**3.3 Plug-in bandwidth selection** 

data (Hall et al., 1995).

conditioned only on the time duration between the beginning and ending locations for each pair of locations and GPS location error. As such, BBMM is able to predict movement paths that otherwise would not be observed with KDE methods. While some authors have suggested using ≤90% home range contours (Borger et al., 2006; Getz et al., 2007) to remove outliers or exploratory movements for KDE, increasing size of home range from 95% to 99% for BBMM does not over-smooth the utilization distribution but rather serves to more accurately define the area of use for some species (e.g. Fig. 4; Lewis 2007). Therefore, BBMM intuitively appears better suited for mammalian and avian species that migrate or travel long distances (Sawyer et al., 2009; Takekawa et al., 2010; J.W. Fischer, National Wildlife Research Center, unpublished data).

Fig. 4. Home range of an American White Pelican using 95% BBMM (outset) with 99% BBMM connecting potential used habitats in some areas of the home range (inset).

### **4.1 Time interval between locations**

Although equal time intervals between successive relocations are not, in theory, a requirement of BBMM, the method uses a Brownian bridge to estimate the probability density that the animal used any particular pixel, given its relocations. The "shape" of the

What Is the Proper Method to Delineate Home Range of an

Animal Using Today's Advanced GPS Telemetry Systems: The Initial Step 259

Fig. 5. Example of Brownian bridge movement models with full dataset for an individual a) black bear and b) American White Pelican resulting in a bolus in home range that was removed by excluding the top 1% of time interval for both c) black bear (time interval ≤182

min) and d) American White Pelican (time interval ≤69 hours).

Brownian bridge characterizing two successive relocations is adjusted as a function of the time lag separating these two relocations: if the time lag is short, the bridge will be narrower than if the time lag is long. Even though this approximation may be useful to account for movement constraints (e.g. an animal cannot move 20 km in two minutes), its implications may be problematic if the time lag between successive relocations is highly variable such as with relocations separated by time lags distributed over several orders of magnitude (e.g. days to weeks).

The variability in time lag between successive locations was important to consider for several of our species and resulted in size of home range 1.5 to 2 times larger when not accounting for time lag (Fig. 5). The GPS collars deployed on vultures were programmed to only turn on during the local dawn-dusk period, thus time lags occurred for black vultures (mean = 114 min ± 229 SD) and turkey vultures (mean = 103 min ± 162 SD) while on roost during nocturnal hours (Beason et al., 2010). Time lag was important for black bears (mean = 49 min ± 199 SD; Fig. 5a) due to screening and removal of position dilution of precision of GPS fixes and lack of GPS fixes for Florida panther (mean = 214 min ± 152 SD) in upland forest and cypress swamps. American White Pelican (mean = 359 min ± 1,633 SD; Fig. 5b) covered up solar panels of the GPS harness or occupied habitats that prevented the battery from maintaining a full charge thereby not allowing GPS data logging upon fix attempt (Cappelle et al., 2011). To improve results, we chose a crude approach to eliminate the top 1% of outliers of time difference such that 99% of the original data were included (OREM). We estimated OREM for each individual animal so inclusion criterion varied across individual for each species. After implementing OREM that resulted in removal of locations, we re-calculated BBMM for black bear (Fig. 5c) and American White Pelican (Fig. 5d), that represented more realistic home ranges by only including time intervals ≤182 min and ≤69 hours for an individual black bear and American White Pelican, respectively.

We followed this method for all species and present the ratio of sizes of home range for the full dataset with all locations to a limited dataset after implementing OREM (Table 2). An alternative approach could be to use the median distance between successive locations as suggested by Benhamou (2011). While OREM may seem reasonable for some species and studies in eliminating large time differences and resulting in tighter home ranges, we caution researchers from using such an approach without considering its implications to the ecological questions at hand and prior to determining distribution of time differences with locations from each study animal.


Table 2. Mean (SD) ratio (full/limited) of average 50%, 95%, and 99% home range areas calculated for each species using Brownian bridge movement models with full and limited datasets, where for the latter the top 1% outlier time intervals were removed.

Brownian bridge characterizing two successive relocations is adjusted as a function of the time lag separating these two relocations: if the time lag is short, the bridge will be narrower than if the time lag is long. Even though this approximation may be useful to account for movement constraints (e.g. an animal cannot move 20 km in two minutes), its implications may be problematic if the time lag between successive relocations is highly variable such as with relocations separated by time lags distributed over several orders of magnitude (e.g.

The variability in time lag between successive locations was important to consider for several of our species and resulted in size of home range 1.5 to 2 times larger when not accounting for time lag (Fig. 5). The GPS collars deployed on vultures were programmed to only turn on during the local dawn-dusk period, thus time lags occurred for black vultures (mean = 114 min ± 229 SD) and turkey vultures (mean = 103 min ± 162 SD) while on roost during nocturnal hours (Beason et al., 2010). Time lag was important for black bears (mean = 49 min ± 199 SD; Fig. 5a) due to screening and removal of position dilution of precision of GPS fixes and lack of GPS fixes for Florida panther (mean = 214 min ± 152 SD) in upland forest and cypress swamps. American White Pelican (mean = 359 min ± 1,633 SD; Fig. 5b) covered up solar panels of the GPS harness or occupied habitats that prevented the battery from maintaining a full charge thereby not allowing GPS data logging upon fix attempt (Cappelle et al., 2011). To improve results, we chose a crude approach to eliminate the top 1% of outliers of time difference such that 99% of the original data were included (OREM). We estimated OREM for each individual animal so inclusion criterion varied across individual for each species. After implementing OREM that resulted in removal of locations, we re-calculated BBMM for black bear (Fig. 5c) and American White Pelican (Fig. 5d), that represented more realistic home ranges by only including time intervals ≤182 min and ≤69 hours for an individual black bear and

We followed this method for all species and present the ratio of sizes of home range for the full dataset with all locations to a limited dataset after implementing OREM (Table 2). An alternative approach could be to use the median distance between successive locations as suggested by Benhamou (2011). While OREM may seem reasonable for some species and studies in eliminating large time differences and resulting in tighter home ranges, we caution researchers from using such an approach without considering its implications to the ecological questions at hand and prior to determining distribution of time differences with

panther Pelican Black

50% 2.5 (1.3) 1.0 (0.04) 2.3 (2.3) 1.4 (0.4) 1.3 (0.5) 95% 2.2 (1.6) 1.0 (0.02) 1.6 (0.8) 1.3 (0.5) 1.1 (0.1) 99% 2.3 (1.7) 1.0 (0.04) 1.5 (0.8) 1.3 (0.4) 1.1 (0.2)

Table 2. Mean (SD) ratio (full/limited) of average 50%, 95%, and 99% home range areas calculated for each species using Brownian bridge movement models with full and limited

datasets, where for the latter the top 1% outlier time intervals were removed.

vulture

Turkey vulture

Florida

days to weeks).

American White Pelican, respectively.

locations from each study animal.

Black bear

Home range

Fig. 5. Example of Brownian bridge movement models with full dataset for an individual a) black bear and b) American White Pelican resulting in a bolus in home range that was removed by excluding the top 1% of time interval for both c) black bear (time interval ≤182 min) and d) American White Pelican (time interval ≤69 hours).

What Is the Proper Method to Delineate Home Range of an

compared to hplug-in (Table 3).

KDE in size of home range.

are not necessary to an animal's fitness.

territories (Fig. 7c).

Animal Using Today's Advanced GPS Telemetry Systems: The Initial Step 261

the linear movement patterns generated by migratory American White Pelicans and black and turkey vultures, regardless of isopleth. Size of home range using KDE with href would likely lead to over-smoothing between migratory locations (but see Blundell et al., 2001). Although we did not separate migratory and resident avian, differences in estimates likely would not be as considerable for avian species with minimal migratory movements. Conversely, we would expect greater differences in estimates for mammalian species that exhibit greater migratory movements such as seasonal migrations in mule deer (*Odocoileus hemionus*; Sawyer et al., 2009) and caribou (*Rangifer tarandus*; Bergman et al., 2000) that are not restricted by considerable roadways and development (i.e. Florida panther) or that occupy urban areas (i.e. black bears) that we assessed in our study. Our results support previous research on smaller datasets that even with serially correlated GPS locations, KDE with href over-estimates size of home range

All isopleths of home ranges were only 1 to 16 times larger for KDE with href than BBMM. The smaller difference in size of home range between KDE with href and BBMM than KDE with href and hplug-in is likely from the inherent nature of BBMM to identify pathways with Brownian bridges. Creating Brownian bridges across sequential GPS locations would be expected to result in larger size of home range than KDE with hplug-in that conservatively predicts a utilization distribution based on density of locations. Being that KDE has been known to over-smooth utilization distributions with href and under-smooth with hplug-in (Gitzen et al., 2006), we expected BBMM to be in between the 2 bandwidth selections for

Estimates of home range were more comparable for all species and isopleths between KDE with hplug-in and BBMM but hplug-in estimates were always smaller than BBMM with only one exception (Table 3). The minimal differences in size of home range between KDE with hplug-in and BBMM is likely only a reflection of identification of exploratory movements with BBMM. Similar to KDE with hplug-in, BBMM conservatively creates a utilization distribution around areas of concentrated use but, unlike KDE with hplug-in, also connects multiple areas of concentrated use. For example, a yearling black bear in an urban area of central Colorado, USA, exhibited exploratory movements that were identified with BBMM but not with KDE with hplug-in (Fig. 6). Actual size of home range for defining available habitats for analysis of resource selection may be more accurately depicted using KDE with hplug-in because it identified concentrated areas of use and not exploratory pathways that were not visited and

Across several avian and mammalian species, we identified similar general patterns of size and shape of home range for KDE with href and hplug-in and BBMM. For example, 95% KDEs with href (Fig. 7a) and KDE with hplug-in (Fig. 7b) bandwidths either over-smoothed or undersmoothed, respectively, size of home range of a Florida panther around agricultural habitats while BBMM (Fig 7c) identified a path around agricultural patches. Regardless of estimation method used, tradeoffs between depicting areas traversed or habitats occupied need to be considered in choosing KDE or BBMM. Use of KDE with href or hplug-in may be alternatives to minimum convex polygon for resource selection studies to determine available resources under Type II or Type III study designs (Manly et al., 2002). Assessment of migration routes or commonly used travel corridors would be better represented by BBMM because bridges identify the pathways used by animals as they traverse their home range or explore new

Wildlife derived GPS datasets require dedicated software and analysis tools for researchers to understand an animal's movements, behavior, and habitat use. The most well known program

#### **5. Comparison of home range estimators**

Use of BBMM or KDE is dependent on study objectives and should not be considered a similar method to an end result as previously suggested (Kie et al., 2010). Brownian bridge movement models were intended for data correlated in space and time to document the path followed and used by animals (Bullard 1999). Conversely, researchers have stressed the importance of using independent locations to accurately determine areas of use with KDE (Swihart & Slade 1985a; Worton 1989, but see Blundell et al., 2001). Animals that migrate several kilometers or avian species that cover large areas simply are not properly represented using traditional KDE and bandwidth selection common in available home range estimation software. Conversely, KDE with hplug-in would be better suited for less mobile species occupying patchy environments or small geographic areas because hplug-in is more conservative resulting in less smoothing than hlscv (Gitzen et al., 2006). Use of hplug-in may also be an appropriate method compared to BBMM when the study focus is on resident or seasonal animal habitat use and exploratory movements are not of interest and should be excluded.


Table 3. Mean (SD) ratio of 50%, 95%, and 99% isopleth home range areas calculated using fixed-kernel home range with default bandwidth (href), fixed-kernel home range with plugin bandwidth selection (hplug-in), and the limited dataset for Brownian bridge movement models (BBMM) for black bears (*n* = 10), Florida panthers (*n* = 10), pelicans (*n* = 10), and black (*n* = 5) and turkey (*n* = 5) vultures equipped with GPS technology.

Ratios of home range areas varied considerably depending on size of home range estimated (50%, 95%, 99%), species studied, and method of home range analysis (Table 3). For all species, all KDE home ranges calculated with href were from 2 to 40 times larger than hplug-in regardless of isopleth (Table 3). These differences were especially pronounced for avian species, and are likely a reflection of the challenges of the univariate kernel bandwidth estimator href to capture

Use of BBMM or KDE is dependent on study objectives and should not be considered a similar method to an end result as previously suggested (Kie et al., 2010). Brownian bridge movement models were intended for data correlated in space and time to document the path followed and used by animals (Bullard 1999). Conversely, researchers have stressed the importance of using independent locations to accurately determine areas of use with KDE (Swihart & Slade 1985a; Worton 1989, but see Blundell et al., 2001). Animals that migrate several kilometers or avian species that cover large areas simply are not properly represented using traditional KDE and bandwidth selection common in available home range estimation software. Conversely, KDE with hplug-in would be better suited for less mobile species occupying patchy environments or small geographic areas because hplug-in is more conservative resulting in less smoothing than hlscv (Gitzen et al., 2006). Use of hplug-in may also be an appropriate method compared to BBMM when the study focus is on resident or seasonal animal habitat use and

Species KDEhref/KDEplug-in KDEhref/BBMM KDEplug-in/BBMM

Black bear 7.4 (6.9) 5.0 (7.7) 0.5 (0.3) Florida panther 2.7 (0.5) 1.0 (0.5) 0.4 (0.1) White pelican 39.6 (26.0) 15.6 (22.3) 0.3 (0.3) Black vulture 26.4 (15.4) 2.1 (2.4) 0.1 (0.05) Turkey vulture 14.9 (17.3) 1.4 (0.9) 0.1 (0.1)

Black bear 4.5 (2.9) 4.5 (6.4) 0.8 (0.6) Florida panther 2.0 (0.4) 1.3 (0.4) 0.7 (0.1) White pelican 13.5 (9.5) 10.4 (15.3) 0.5 (0.5) Black vulture 6.8 (3.6) 1.7 (1.7) 0.2 (0.1) Turkey vulture 6.9 (3.8) 1.9 (1.2) 0.3 (0.1)

Black bear 3.6 (1.8) 4.6 (6.1) 1.1 (0.9) Florida panther 1.9 (0.4) 1.5 (0.5) 0.8 (0.2) White pelican 8.8 (4.9) 9.1 (12.9) 0.7 (0.6) Black vulture 5.4 (1.9) 1.7 (1.6) 0.3 (0.2) Turkey vulture 5.7 (2.9) 2.4 (1.6) 0.4 (0.2) Table 3. Mean (SD) ratio of 50%, 95%, and 99% isopleth home range areas calculated using fixed-kernel home range with default bandwidth (href), fixed-kernel home range with plugin bandwidth selection (hplug-in), and the limited dataset for Brownian bridge movement models (BBMM) for black bears (*n* = 10), Florida panthers (*n* = 10), pelicans (*n* = 10), and

Ratios of home range areas varied considerably depending on size of home range estimated (50%, 95%, 99%), species studied, and method of home range analysis (Table 3). For all species, all KDE home ranges calculated with href were from 2 to 40 times larger than hplug-in regardless of isopleth (Table 3). These differences were especially pronounced for avian species, and are likely a reflection of the challenges of the univariate kernel bandwidth estimator href to capture

black (*n* = 5) and turkey (*n* = 5) vultures equipped with GPS technology.

**5. Comparison of home range estimators** 

*50% contours* 

*95% contours* 

*99% contours* 

exploratory movements are not of interest and should be excluded.

the linear movement patterns generated by migratory American White Pelicans and black and turkey vultures, regardless of isopleth. Size of home range using KDE with href would likely lead to over-smoothing between migratory locations (but see Blundell et al., 2001). Although we did not separate migratory and resident avian, differences in estimates likely would not be as considerable for avian species with minimal migratory movements. Conversely, we would expect greater differences in estimates for mammalian species that exhibit greater migratory movements such as seasonal migrations in mule deer (*Odocoileus hemionus*; Sawyer et al., 2009) and caribou (*Rangifer tarandus*; Bergman et al., 2000) that are not restricted by considerable roadways and development (i.e. Florida panther) or that occupy urban areas (i.e. black bears) that we assessed in our study. Our results support previous research on smaller datasets that even with serially correlated GPS locations, KDE with href over-estimates size of home range compared to hplug-in (Table 3).

All isopleths of home ranges were only 1 to 16 times larger for KDE with href than BBMM. The smaller difference in size of home range between KDE with href and BBMM than KDE with href and hplug-in is likely from the inherent nature of BBMM to identify pathways with Brownian bridges. Creating Brownian bridges across sequential GPS locations would be expected to result in larger size of home range than KDE with hplug-in that conservatively predicts a utilization distribution based on density of locations. Being that KDE has been known to over-smooth utilization distributions with href and under-smooth with hplug-in (Gitzen et al., 2006), we expected BBMM to be in between the 2 bandwidth selections for KDE in size of home range.

Estimates of home range were more comparable for all species and isopleths between KDE with hplug-in and BBMM but hplug-in estimates were always smaller than BBMM with only one exception (Table 3). The minimal differences in size of home range between KDE with hplug-in and BBMM is likely only a reflection of identification of exploratory movements with BBMM. Similar to KDE with hplug-in, BBMM conservatively creates a utilization distribution around areas of concentrated use but, unlike KDE with hplug-in, also connects multiple areas of concentrated use. For example, a yearling black bear in an urban area of central Colorado, USA, exhibited exploratory movements that were identified with BBMM but not with KDE with hplug-in (Fig. 6). Actual size of home range for defining available habitats for analysis of resource selection may be more accurately depicted using KDE with hplug-in because it identified concentrated areas of use and not exploratory pathways that were not visited and are not necessary to an animal's fitness.

Across several avian and mammalian species, we identified similar general patterns of size and shape of home range for KDE with href and hplug-in and BBMM. For example, 95% KDEs with href (Fig. 7a) and KDE with hplug-in (Fig. 7b) bandwidths either over-smoothed or undersmoothed, respectively, size of home range of a Florida panther around agricultural habitats while BBMM (Fig 7c) identified a path around agricultural patches. Regardless of estimation method used, tradeoffs between depicting areas traversed or habitats occupied need to be considered in choosing KDE or BBMM. Use of KDE with href or hplug-in may be alternatives to minimum convex polygon for resource selection studies to determine available resources under Type II or Type III study designs (Manly et al., 2002). Assessment of migration routes or commonly used travel corridors would be better represented by BBMM because bridges identify the pathways used by animals as they traverse their home range or explore new territories (Fig. 7c).

Wildlife derived GPS datasets require dedicated software and analysis tools for researchers to understand an animal's movements, behavior, and habitat use. The most well known program

What Is the Proper Method to Delineate Home Range of an

Animal Using Today's Advanced GPS Telemetry Systems: The Initial Step 263

Fig. 7. Comparison of 95% estimates of panther home range derived from kernel density estimation with a) href bandwidth selection and b) hplug-in bandwidth selection as well as

Our goal was to assist researchers in determining the appropriate methods to assess size and shape of home range with a variety of species and movement vectors. Although we did not set out to assess the accuracy of methods, our results suggested that BBMM and hplug-in are

c) a Brownian bridge movement model with GPS locations () in background.

**6. Conclusions** 

to calculate KDE (ArcView version 3.x) is not directly compatible with 64-bit computer operating systems and current extensions in the newer versions of ArcMap 9.x do not offer the flexibility in several components (i.e. batch-processing, bandwidth selection) afforded by earlier versions of ArcView 3.x, are unable to handle thousands of locations and overlapping coordinates (e.g. Home Range Tools), or were incorporated into the Geospatial Modelling Environment that requires ArcMap 10.x (i.e. Animal Movement Extension, Hawth's Tools; www.spatialecology.com). Furthermore, several studies have indicated that size of home range calculated with KDE differed with each program by as much as 20% for 95% contours (Lawson & Rodgers 1997; Mitchell 2006). Most home range programs require various input parameters or are programmed with defaults that should be considered prior to selecting the program that best suits the needs of the researcher (Lawson & Rodgers 1997; Mitchell 2006; Gitzen et al., 2006). Many new programs to estimate home range are comparable to the graphical user interface of ArcMap (e.g. Quantum GIS, www.qgis.org), require ArcMap and R (e.g. Geospatial Modelling Environment, www.spatialecology.com/gme), or considerably under-estimate home range and require further evaluation (BIOTA, www.ecostats.com; Mitchell 2006). To evaluate every program available would have been beyond the scope of our objectives, so we presented home range estimators in R that is freely available to all researchers.

Fig. 6. Home range of a yearling black bear using 95% plug-in with kernel density estimation (thick line) and exploratory movements with 95% BBMM (thin line) prior to dispersal in year 2.

to calculate KDE (ArcView version 3.x) is not directly compatible with 64-bit computer operating systems and current extensions in the newer versions of ArcMap 9.x do not offer the flexibility in several components (i.e. batch-processing, bandwidth selection) afforded by earlier versions of ArcView 3.x, are unable to handle thousands of locations and overlapping coordinates (e.g. Home Range Tools), or were incorporated into the Geospatial Modelling Environment that requires ArcMap 10.x (i.e. Animal Movement Extension, Hawth's Tools; www.spatialecology.com). Furthermore, several studies have indicated that size of home range calculated with KDE differed with each program by as much as 20% for 95% contours (Lawson & Rodgers 1997; Mitchell 2006). Most home range programs require various input parameters or are programmed with defaults that should be considered prior to selecting the program that best suits the needs of the researcher (Lawson & Rodgers 1997; Mitchell 2006; Gitzen et al., 2006). Many new programs to estimate home range are comparable to the graphical user interface of ArcMap (e.g. Quantum GIS, www.qgis.org), require ArcMap and R (e.g. Geospatial Modelling Environment, www.spatialecology.com/gme), or considerably under-estimate home range and require further evaluation (BIOTA, www.ecostats.com; Mitchell 2006). To evaluate every program available would have been beyond the scope of our objectives, so we presented home range estimators in R that is freely available to all

Fig. 6. Home range of a yearling black bear using 95% plug-in with kernel density estimation (thick line) and exploratory movements with 95% BBMM (thin line) prior to

researchers.

dispersal in year 2.

Fig. 7. Comparison of 95% estimates of panther home range derived from kernel density estimation with a) href bandwidth selection and b) hplug-in bandwidth selection as well as c) a Brownian bridge movement model with GPS locations () in background.
