Trisalyn A. Nelson

*Spatial Pattern Analysis and Research Laboratory, Department of Geography, University of Victoria Canada* 

#### **1. Introduction**

268 Modern Telemetry

Tomkiewicz, S. M., Fuller, M. R., Kie, J. G. & Bates, K. K. (2010). Global positioning system

Millspaugh & J. M. Marzluff (Eds.), pp. (43–75), Academic Press, San Diego Worton, B. J. (1995). Using Monte Carlo simulation to evaluate kernel-based home range

estimators. *Journal of Wildlife Management*, Vol.59, No.4, pp. 794–800 Worton, B. J. (1989). Kernel methods for estimating the utilization distribution in home-

range studies. *Ecology*, Vol.70, No.1, pp. 164–168

and associated technologies in animal behaviour and ecological research. *Philosophical Transactions of the Royal Society B*, Vol.365, No.1550, pp. 2163–2176 Withey, J. C., Bloxton, T. D. & Marzluff, J. M. (2001). Effect of tagging and location error in

wildlife radiotelemetry studies, In: *Radio tracking and animal populations*, (J. J.

In wildlife research, telemetry data are often converted to home ranges. The concept of an animal's home range can be defined as the ". . . area traversed by the individual in its normal activities of food gathering, mating and caring for young" (Burt, 1943, pg. 351). The delineation and analysis of home ranges is common in wildlife research, and several reviews of home range studies exist (Harris et al., 1990; Laver & Kelly, 2008). Site fidelity (Edwards et al., 2009), population abundance (Trewhella et al., 1988), prey-predatory abundance (Village, 1982), impacts of human disturbance (Apps et al., 2004; Berland et al., 2008; Frair et al., 2008; Rushton et al., 2000; Thiel et al., 2008), feeding strategies (Hulbert et al., 1996) and ecological correlates of critical habitat (Tufto, 1996; Fisher, 2000) are examples of topics addressed using home range as the analysis unit.

Home ranges are typically delineated with polygons. Locations within the polygon are considered part of the animal's home range, and locations outside are not. As evidenced by the large number of home range studies, such binary approaches have been useful. However, landscape use by wildlife is spatially heterogeneous (Johnson et al., 1992; Kie et al., 2002). Edges (Yahner, 1988), disturbances (i.e., roads and forest harvesting) (Berland et al., 2008), and patch size (Kie et al., 2002) are just a few landscape features that cause heterogeneity in the geographic distribution of wildlife within home ranges. To account for spatial heterogeneity within a home range, core areas, defined as those used most frequently and likely to contain homesites, along with areas of refuge and dependable food sources (Burt, 1943) are sometimes delineated to create categories of habitat use (e.g., Samuel et al., 1985). Characterizing the spatial variation in wildlife distributions should improve our understanding of habitat use, especially in conjunction with the growing spatial extents of wildlife data sets.

Arguably, the two most common approaches to demarcating a home range are the minimum convex polygon and kernel density estimation (Harris et al., 1990). The minimum convex polygon tends to overestimate home range size by including all the unused areas between outermost locations and increasing in area with large sample sizes (Börger et al., 2006a; Katajisto & Moilanen, 2006). As such, kernel density estimation is often preferred when demarcating a home range (Seaman & Powell, 1996; Marzluff et al., 2004; Börger et al., 2006a; Laver & Kelly, 2008). Although used to delineate binary home ranges, kernel density estimation generates a surface of values within the home range, which is useful for characterizing spatial variability in wildlife intensity. Kernel density surfaces are often referred to as utilization distributions as they give values that indicate higher and lower utilization of locations by individuals.

Quantifying Wildlife Home Range Changes 271

131°07'W), and northern British Columbia, east of Teslin Lake (59°59′N, 132°25′W). Data were collected using very high frequency (VHF) transmitters. In 2006, 128 telemetry locations were obtained from 27 animals. In 2007, 68 telemetry locations were obtained from

18 animals (Fig. 1).

intensity

λ

kernel density estimator

A more exact estimate, ˆ

λ

Fig. 1. Caribou telemetry data for 2006 and 2007.

λτ

**2.2 Home range delineation and standard change analysis** 

λτ

Home ranges were delineated using kernel density estimation, a nonparametric approach for generating a continuous intensity surface (Seaman & Powell, 1996). Theoretically, the

the numberof events in a neighbourhoodcentredon ˆ( ) areaof the neighbourhood

(*z*), can be calculated using

*i*

2 1 <sup>1</sup> ( ) <sup>ˆ</sup> ( ) *<sup>n</sup> <sup>i</sup>*

τ *k*

 = <sup>−</sup> <sup>=</sup> *z z z z* 

τ

where *z* and *A* are defined as above, τ is the radius or bandwidth of a circular neighbourhood centred on *z*, *k*() is the probability density function that is symmetric about

<sup>=</sup> *<sup>z</sup>*

( )*z* of observations at each location *z* in a study area *A* is estimated using the

*z* (1)

∈

 *A*, (2)

Regardless of how the home range is calculated, there are benefits to converting point-based telemetry data to polygonal home ranges. First, unless telemetry data are collected at a very high temporal frequency, almost continuously, telemetry data represent a sample of locations visited by an individual. Conversion to a polygon is an attempt to represent the complete range of possible movements. Second, conversion to a utilization distribution has the additional benefit of being useful for integrating telemetry data with environmental data sets. Often stored within a Geographic Information System (GIS), many environmental data sets are represented using raster grids. A common example is elevation data sets, which are stored in grid cells, of varying size. Kernel density estimated values are also stored as grid cells enabling efficient integration of utilization distributions with other map-based data sets.

As telemetry data sets have grown in temporal extent, it has become useful to employ home ranges to assess wildlife movement and habitat use through time. Characterizing the temporal change in home ranges has been used to study seasonal movement (Georgii, 1980), relate home range size to population abundance (Lowe et al., 2003) and land use (Viggers & Hearn, 2005), and characterize the spatial interactions of predator and prey (Village, 1982). Typically, when quantifying home range change, areal sizes are compared (e.g., Lurz et al., 1997; Lowe et al., 2003; Edwards et al., 2009) or the proportions of areal overlap enumerated (e.g., Georgii, 1980; Atwood & Weeks, 2003). In a few examples, spatial-temporal patterns of home ranges are quantified in greater detail. For instance, the multi-temporal persistence of home ranges has been related to landscape disturbance (Berland et al., 2008). Two additional approaches were identified by Kie et al. (2010) as showing potential for identifying temporal changes in home ranges. The first approach uses mixed effect models to relate temporal variation in patterns of telemetry data to climate, habitat, and age/sex variables of deer (Börger et al., 2006b). The second considers spatial variation in habitat use (represented by utilization distributions, defined below) continuous in time and representative of four dimensions (latitude, longitude, elevation, and time) (Keating & Cherry, 2009). Using a product-kernel, temporal patterns in space use were characterized using a circular time scale. Improved approaches to wildlife data collection, such as satellite and global positioning system (GPS) collars, in combination with concerns over climate change and growing anthropogenic pressures on wildlife, have increased the number of possible multi-temporal wildlife research questions. Development of new analytical approaches has begun and must continue if high temporal resolution telemetry data can be used to their full potential.

Here, I present three novel approaches to quantifying spatial-temporal change in home ranges. The first method, Spatial Temporal Analysis of Moving Polygons (STAMP), uses topological relationships of home range polygons to quantify spatial-temporal patterns of home ranges. The second method detects statistically significant change between two kernel densityestimated surfaces, and is utilized to characterize statistical change in intensity of habitat use within home ranges. The third method, an integration of methods one and two, simultaneously quantifies both the spatial-temporal pattern and change in wildlife intensities within home ranges. Described below, the new methods are demonstrated on caribou (*Rangifer tarandus* caribou) data from western Canada, and their benefits are outlined and compared to traditional approaches. To begin, home range delineation and typical approaches to change detection are presented as the basis for comparison with these novel approaches.

#### **2. Home range methods**

#### **2.1 Telemetry data**

The methods presented and compared in this chapter are applied to data on the Swan Lake woodland caribou herd, located in the southern Yukon, near Swift River (60°10'N,

Regardless of how the home range is calculated, there are benefits to converting point-based telemetry data to polygonal home ranges. First, unless telemetry data are collected at a very high temporal frequency, almost continuously, telemetry data represent a sample of locations visited by an individual. Conversion to a polygon is an attempt to represent the complete range of possible movements. Second, conversion to a utilization distribution has the additional benefit of being useful for integrating telemetry data with environmental data sets. Often stored within a Geographic Information System (GIS), many environmental data sets are represented using raster grids. A common example is elevation data sets, which are stored in grid cells, of varying size. Kernel density estimated values are also stored as grid cells enabling

As telemetry data sets have grown in temporal extent, it has become useful to employ home ranges to assess wildlife movement and habitat use through time. Characterizing the temporal change in home ranges has been used to study seasonal movement (Georgii, 1980), relate home range size to population abundance (Lowe et al., 2003) and land use (Viggers & Hearn, 2005), and characterize the spatial interactions of predator and prey (Village, 1982). Typically, when quantifying home range change, areal sizes are compared (e.g., Lurz et al., 1997; Lowe et al., 2003; Edwards et al., 2009) or the proportions of areal overlap enumerated (e.g., Georgii, 1980; Atwood & Weeks, 2003). In a few examples, spatial-temporal patterns of home ranges are quantified in greater detail. For instance, the multi-temporal persistence of home ranges has been related to landscape disturbance (Berland et al., 2008). Two additional approaches were identified by Kie et al. (2010) as showing potential for identifying temporal changes in home ranges. The first approach uses mixed effect models to relate temporal variation in patterns of telemetry data to climate, habitat, and age/sex variables of deer (Börger et al., 2006b). The second considers spatial variation in habitat use (represented by utilization distributions, defined below) continuous in time and representative of four dimensions (latitude, longitude, elevation, and time) (Keating & Cherry, 2009). Using a product-kernel, temporal patterns in space use were characterized using a circular time scale. Improved approaches to wildlife data collection, such as satellite and global positioning system (GPS) collars, in combination with concerns over climate change and growing anthropogenic pressures on wildlife, have increased the number of possible multi-temporal wildlife research questions. Development of new analytical approaches has begun and must continue if high

Here, I present three novel approaches to quantifying spatial-temporal change in home ranges. The first method, Spatial Temporal Analysis of Moving Polygons (STAMP), uses topological relationships of home range polygons to quantify spatial-temporal patterns of home ranges. The second method detects statistically significant change between two kernel densityestimated surfaces, and is utilized to characterize statistical change in intensity of habitat use within home ranges. The third method, an integration of methods one and two, simultaneously quantifies both the spatial-temporal pattern and change in wildlife intensities within home ranges. Described below, the new methods are demonstrated on caribou (*Rangifer tarandus* caribou) data from western Canada, and their benefits are outlined and compared to traditional approaches. To begin, home range delineation and typical approaches to change

The methods presented and compared in this chapter are applied to data on the Swan Lake woodland caribou herd, located in the southern Yukon, near Swift River (60°10'N,

efficient integration of utilization distributions with other map-based data sets.

temporal resolution telemetry data can be used to their full potential.

detection are presented as the basis for comparison with these novel approaches.

**2. Home range methods** 

**2.1 Telemetry data** 

131°07'W), and northern British Columbia, east of Teslin Lake (59°59′N, 132°25′W). Data were collected using very high frequency (VHF) transmitters. In 2006, 128 telemetry locations were obtained from 27 animals. In 2007, 68 telemetry locations were obtained from 18 animals (Fig. 1).

Fig. 1. Caribou telemetry data for 2006 and 2007.

#### **2.2 Home range delineation and standard change analysis**

Home ranges were delineated using kernel density estimation, a nonparametric approach for generating a continuous intensity surface (Seaman & Powell, 1996). Theoretically, the intensity λ( )*z* of observations at each location *z* in a study area *A* is estimated using the kernel density estimator

$$\hat{\lambda}(\mathbf{z}) = \frac{\text{the number of events in a neighborhood centred on } \mathbf{z}}{\text{area of the neighborhood}} \tag{1}$$

A more exact estimate, ˆ λτ(*z*), can be calculated using

$$\hat{\mathcal{A}}\_{\mathbf{r}}(\mathbf{z}) = \left\{ \sum\_{i=1}^{n} \frac{1}{\pi^2} k\left(\frac{(\mathbf{z} - \mathbf{z}\_i)}{\pi}\right) \right\} \quad \mathbf{z} \in A\_{\mathbf{r}} \tag{2}$$

where *z* and *A* are defined as above, τ is the radius or bandwidth of a circular neighbourhood centred on *z*, *k*() is the probability density function that is symmetric about

Quantifying Wildlife Home Range Changes 273

Fig. 4. Caribou home ranges for 2006 and 2007, generated using kernel density estimation.

Fig. 5. An overview of the three methods presented: STAMP, kernel density estimation (KDE) change detection, and the integration of STAMP and KDE change detection. T1 and

T2 indicate time period 1 and time period 2, respectively.

**3. Quantifying spatial-temporal change in home ranges**  An overview of the three methods presented is provided in Fig. 5.

*z*, and *zi* (i =1, …, n), are the locations of *n* events. For home range delineation, the bandwidth size is typically selected via least-square cross-validation (LSCV) and a 95% threshold used to demarcate the home range boundary (Seaman & Powell, 1996; Seaman et al., 1999).

Fig. 2. Kernel density estimated surface generated from 2006 caribou telemetry data.

For the woodland caribou data, the bandwidth was defined as the mean LSCV for 2006 and 2007 data, which is 2.18 km (Fig. 2 and 3). For kernel-based change detection, it is beneficial to have consistent bandwidths (Bowman & Azzalini, 1997, pg. 114). The annual home range size was 1999.31 km2 and 1231.28 km2 in 2006 and 2007, respectively. Home ranges overlapped by 781.48 km2 (31.91%) (Fig. 4).

Fig. 3. Kernel density estimated surface generated from 2007 caribou telemetry data.

*z*, and *zi* (i =1, …, n), are the locations of *n* events. For home range delineation, the bandwidth size is typically selected via least-square cross-validation (LSCV) and a 95% threshold used to demarcate the home range boundary (Seaman & Powell, 1996; Seaman et

Fig. 2. Kernel density estimated surface generated from 2006 caribou telemetry data.

Fig. 3. Kernel density estimated surface generated from 2007 caribou telemetry data.

overlapped by 781.48 km2 (31.91%) (Fig. 4).

For the woodland caribou data, the bandwidth was defined as the mean LSCV for 2006 and 2007 data, which is 2.18 km (Fig. 2 and 3). For kernel-based change detection, it is beneficial to have consistent bandwidths (Bowman & Azzalini, 1997, pg. 114). The annual home range size was 1999.31 km2 and 1231.28 km2 in 2006 and 2007, respectively. Home ranges

al., 1999).

Fig. 4. Caribou home ranges for 2006 and 2007, generated using kernel density estimation.
