Effects of Sample Size on Kernel Home Range Estimates

“Suggested sample sizes required for obtaining a reasonable estimate of home-range size vary from 30 to 50 observations (Seaman et al. 1999) to 200 observations (Garton et al. 2001).”

“Other problems associated with the number of locations and the patterns of space use by individuals can also lead to variable estimates of home-range sizes when using kernels (Seaman et al., 1999; Blundell et al., 2001; Hemson et al., 2005).”

“Therefore, it is important to investigate alternative methods for choosing h (Seaman et al. 1999).”

“Allowing the bandwidth to vary so that smoothing is greater in the tails of the distribution, where uncertainty is higher, is intuitively appealing (Silverman Millspaugh et al. Resource Selection and Utilization Distributions 385 1986:100) because greater smoothing inherently considers uncertainty…”

“We assumed individuals with P30 point locations as ‘adequately sampled’during the breeding season (Seaman et al., 1999).”

“Small sample sizes may be insufficient to capture the variability among individuals in space use (Lindberg & Walker, 2007) and debate continues over the appropriate sample size required to account for variability in behaviour and distribution of the wider population (Seaman et al., 1999; Soanes et al., 2013; Delord et…”

“In the absence of the latter, researchers have been encouraged to obtain a threshold number of locations (Seaman et al. 1999, Girard et al. 2002) or days (e.g., B€orger et al. 2006, Signer et al. 2015), but the precise conditions under which autocorrelation and movement behavior can a priori be…”

“Utilization distributions are most often computed using the kernel density estimation method, which outperforms previously available estimation tools (Worton 1989, 1995; Seaman and Powell 1996).”

“…kernel estimators have limitations, and home range estimates can be sensitive to sample size [Boulanger and White, 1990; Seaman and Powell, 1996; Seaman et al., 1999; Girard et al., 2002], time scales [Gautestad and Mysterud, 1993] and seasonal and behavioral variations [Harris et al., 1990;…”

“[18] reported that global use of hlscv resulted in little bias in home-range estimates, but that local-bandwidth approaches overestimated areas of distribution, and thus should not be used.”

“, mixtures of multivariate normal distributions [Seaman et al. 1999]), which do not capture the temporal nature of animal location data.”

“All kernels were calculated using a least-squares cross-validation smoothing function (LSCV)—an iterative process that estimates the least-biased smoothing factor (Worton, 1989; Seaman and Powell, 1996; Seaman et al., 1999; Gitzen and Millspaugh, 2003).”

“tions (Seaman et al. 1999).”

“Home ranges were estimated from a mean SD of 202.9 36.4 coordinates per group (range 160e260), which is sufficient for kernel analysis (Seaman et al. 1999).”

“50 positions would be adequate to avoid this problem [37].”

“, 50% and 95% isopleths (Seaman et al. 1999).”

“This approach provides greater accuracy than other methods when basing range estimates on more than 30 locations (Seaman et al., 1999).”

“Home ranges were found to reach an area asymptote with a minimum of 30 locations and this constituted our minimum for inclusion in home range analysis (Seaman et al., 1999).”

“There is still much dispute concerning how best to measure home ranges (Seaman et al. 1999; Calenge 2006; Horne & Garton 2006; Row & Blouin-Demers 2006).”

“A reduced dataset (maximum of two randomly selected locations per calendar day) was used for method c as kernel smoothing is strongly influenced by sampling frequency (Seaman et al. 1999).”

“Kernels were estimated using the reference bandwidth method [34] because the least-squares cross-validation method failed to converge for six animals with large sample sizes [35].”

“…density estimator in Hawth's Tools (Beyer 2004), available for ArcMap 9.3 (ESRI 2008) to estimate a home range (Worton 1989, Seaman and Powell 1996, Kernohan et al. 2001) for each cougar with more than 30 GPS or VHF relocations within a calendar year (January-December; Seaman et al. 1999).”

“We adopted the traditional HR definition as the area an individual traverses in its normal activities (53) and estimated HRs for all children who placed ≥30 dots (n = 178, 9 children were excluded for not reaching this number) using the 100%minimum convex polygon (MCP) (54), wherein 30 points is the minimum number rec…”

“The minimum convex polygon method (MCP) is criticized because of high sensitivity to outliers, sample size and sampling strategy (Seaman et al. 1999; Börger et al. 2006a).”

“The widespread use of GPS and satellite-tracking devices has led to the publication of studies that reveal the importance of the effect of sampling regime (Seaman et al. 1999; Girard et al. 2002; Taylor, Terauds & Nicholls 2004; Nicholls, Robertson & Naef-Daenzer 2005; Borger et al. 2006) and to warnings that tracking…”

“The criterion for minimum number of locations follows the recommendation of Seaman et al. (1999) to reduce effects of small sample sizes on the kernel estimator.”

“We determined their spatial distributions by 95% kernel analysis, choosing band width using the least-squares cross-validation method (Seaman et al. 1999; Kernohan et al. 2001), using the ADEHABITATHR package for R (Calenge 2006) and mapped them using ARCGIS 10.”

“This method can be unreliable when used on multimodal E-space distributions, as it often results in over-smoothing (Worton 1995, Seaman et al. 1999).”

“We standardized the number of points used within individual to control for a potential correlation between home range size and the number of points used to estimate home range size (Seaman et al. 1999), although preliminary analyses suggested that there was no such correlation in our data.”

“For calculating kernel home ranges, we used fixed kernel method with smoothing factor (bandwidth) calculated by least square cross validation (LSCV) of wolf locations (Seaman et al. 1999).”

“Home range size and habitat selection We included raccoons with ≥30 locations (Seaman et al. 1999) during the summer season in home range analyses, and used the fixed-kernel model (Worton 1989) in the Animal Movement extension (Hooge and Eichenlaub 1997) for ArcView to generate 95% (home range) and…”

“Annual range and core area was calculated for cats with .25 locations (Seaman et al. 1999).”

“…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.,…”

“Further, some methods for delimiting home-range boundaries, including adaptive kernels, overestimate home-range size when sample size is small (,30; Seaman et al. 1999).”

“Fixed kernel home ranges derived from smaller sample sizes typically yield larger home range size estimates (Seaman et al. 1999, Powell 2000, Kernohan et al. 2001), which for habitat selection analysis should minimize the differences between wolf used and unused areas and thus create a more…”

“We determined their spatial distributions by 95% kernel analysis, choosing band width using the least-squares cross-validation method (Kernohan et al., 2001; Seaman et al., 1999), using the ADEHABITATHR package for R (Calenge, 2006) and mapped them using ARCGIS 10.0.”

“Home range estimates are susceptible to relocation sample size (Seaman et al. 1999, Borger et al. 2006).”

“, 2001) and a complex technique (fixed kernel) generally regarded as the best home range estimator currently available (Kernohan et al., 2001; Seaman et al., 1999; Worton, 1989).”

“We estimated utilization distributions using the fixedKDE method because fixed kernel was considered most accurate compared with adaptive kernel [17,24].”

“Latitude and longitude recordings were used to calculate 95% minimum convex polygon (MCP) home ranges (White & Garrott, 1990), as well as 95 and 50% adaptive kernel homerange estimates (Worton, 1989; Seaman et al., 1999).”

“To assess model fit, several authors have used computer simulations to generate known home ranges and then have compared the fit of various home range models to the simulated distribution (e.g., Boulanger and White 1990, Seaman et al. 1999, Worton 1995).”

“Although some authors have previously warned against the use of kernel estimates when 30 locations are available (e.g. Seaman et al., 1999), it was found that 17 locations provided reliable monthly estimates of home-range size in roe deer at Chizé.”

“Results for REF in our simulations varied, but it rarely outperformed other bandwidth selectors, and other studies have generally found that REF provides inferior fits for complex UDs (Seaman and Powell 1996, Seaman et al. 1999, Gitzen et al. 2006).”

“Because estimates of home-range size can be affected by the intensity of location sampling (Seaman et al. 1999), the number of locations was included as a covariate in the analysis.”

“Monthly and annual home range sizes were estimated for each sloth using 95% fixed-kernel home-range areas with least squares cross-validation (Seaman et al. 1999) using the ArcView 3.3 (Environmental Systems Research Institute, Inc., Redlands, California); the “animal movement” and “home range”…”

“Since the kernel method is sensitive to sample size (Seaman et al. 1999), we standardised the calculations using almost 125 fixes for annual HR, 83 fixes for spring-summer HR, and 39 for spring HR.”

“…the area expected to include 99% of locations of all animals in the target population, all else held equal) with least-squares-cross-validated fixed kernels (Seaman and Powell 1996; Seaman et al. 1998, 1999), overlaid all these daily contours, and obtained the outer perimeter of all daily 99% UDs.”

“Generally, a minimum of 30 locations is recommended for kernel density home range estimation (Seaman et al. 1999), and use of fewer locations may overestimate home range size (Seaman and Powell 1996).”

“In accordance with Seaman and Powell (1996) and Seaman et al. (1999), we considered the 95% fixed-kernel estimates to best represent the home range of the groups of peccaries we tracked (Fig.”

“We estimated home ranges based on point locations in ArcGIS 9.2 using the Home Range Tools (HRT) for ArcGIS 9.x (Rodgers et al. 2005) by implementing a 99% fixed kernel estimator (Seaman et al. 1999).”

“Poor overlap of true animal habitats was only observed for small sample sizes, which confirms that kernel computation requires a minimum number of observations [70,71].”

“For each deer, we attempted to obtain 50 locations per season (Seaman et al. 1999).”

“All species recorded adequate fixes to exceed the minimum of 50 fixes required for kernel home range estimation (Seaman et al. 1999).”

“We examined the sampling distribution of UDs by randomly selecting 15– 50 locations from each bobcat data set at intervals of 5, and then we calculated a home range from those randomly selected locations (Seaman et al. 1999).”

“Seaman and Powell (1996) and Seaman et al. (1999) have suggested that adaptive kernels tend to overestimate home range boundaries.”

“2001) and is considered more accurate and precise than the adaptive method (Seaman et al. 1999).”

“We used the fixed kernel least squares cross-validation estimate because it is best at defining interior contours (Seaman et al. 1999; Blundell et al. 2001).”

“Seaman et al. (1999) recommended a minimum of 30-50 locations for this technique.”

“It is important to assess the number of locations at which home-range size estimates stabilize (Harris et al. 1990; Seaman et al. 1999).”

“analysis (Seaman et al., 1999).”

“LSCVh generally performs better than the optimal h for a standard multivariate normal distribution (Seaman and Powell 1996; Seaman et al. 1999) but has very poor performances at small sample size (Horne and Garton 2006; Seaman et al. 1999).”

“KDE is sensitive to the various bandwidth values (Seaman et al. 1999; Silverman 1986), the objective algorithms applied to determine both the distance between the kernel and an evaluation point in the environment, and the contribution of the kernel to the overall density estimate at a location.”

“Lamb survival in desert bighorn sheep is greatly influenced by precipitation during autumn of the previous year, likely through its influence on forage quality and quantity (Douglas and Leslie 1986, Wehausen et al. 1987, Krausman et al. 1999).”

“We chose the fixed-kernel method with the smoothing parameter selected by least-squares cross-validation (LCSV) because this approach generally produces the most accurate and precise estimates (Kernohan et al. 2001; Powell 2000; Seaman et al. 1999).”