Effects of Sample Size on Kernel Home Range Estimates

“We used Hawth’s Tools (Beyer 2004) in ArcGIS 9.3 (Environmental Systems Research Institute, Redlands, CA) to delineate 95% fixed-kernel home-range and 50% core areas (Worton 1989) using least-squares-cross validation to select the smoothing parameter (Seaman and Powell 1996, Seaman et al. 1999).”

“[41], analysing a 95%kernel home range using a raster cell size of 12m [42, 43].”

“We estimated 95% fixed kernel utilization distributions (UD; Millspaugh et al., 2006) with 30 3 30 m pixels for badgers with $30 radiolocations (Seaman et al., 1999) during annual periods using program R 2.15.1 (R Core Development Team, 2012) and a plug-in bandwidth estimator (Millspaugh and…”

“Fixed kernel estimates (50, 90, and 95% contours; Kernohan et al. 2001, Seaman and Powell 1996, Seaman et al. 1999) were calculated using the ad hoc bandwidth method (Schroeder 2007) utilizing Home Range Tools for ArcGIS (Rodgers et al. 2007).”

“…the number of relocations per individual and the autocorrelation between successive points, several authors have argued that increased sample size is more important than eliminating autocorrelation between points (McNay et al. 1994, De Solla et al. 1999, Seaman et al. 1999, Marzluff et al. 2004).”

“Because sizes of both MCP and FKC home ranges are affected by sample sizes (Powell 2000; Seaman et al. 1999), we consider these size estimates to be relative indices of space use rather than absolute estimates of homerange size.”

“…contours (95% home range and 50% core area) utilizing the least-squares cross-validation method in Ranges6 for those animals with 30 locations (Millspaugh et al. 2006; Seaman et al. 1999); application of this criterion resulted in the exclusion of 17 additional individuals for FK analyses.”

“We calculated both 50% and 95% UDs for stilts with ≥ 30 observations (Seaman et al. 1999).”

“Most recent research suggests that KDE is an appropriate method for home range analysis when sample sizes are adequate, locations are not temporally autocorrelated, and spatial autocorrelation is not eliminated [7, 8, 14, 19, 20, 22, 25-27].”

“To ensure an accurate UD estimation, only individuals with a minimum of 40 telemetry points were included in this analysis (Kauhala et al. 2010; Seaman et al. 1999), resulting in a total of 129 individuals with the mean number of telemetry points per individual being 1,900, the minimum being 41 and…”

“The KDE bounds of the innermost 95% of the presence data points were used to estimate the size and created the map of the area of use [53] of the reintroduced banteng.”

“Unfortunately, we could not obtain sufficient points ( n 50; ( Seaman et al. 1999 ) for an unbiased estimate of stable ome-range; hence, our results may overestimate the area used y translocated bilbies and should be interpreted as the potential ost-translocation movement of bilbies released on the…”

“Turtles with <50 filtered relocation points were ex - cluded from estimation of utilization distributions (UDs) following the recommendation by Seaman et al. (1999).”

“The top two models had an effect for the number of radio-locations, which is known to influence home range size [64].”

“The estimation of home range using the KDE method is strongly affected by the number of locations used and, therefore, a minimum of 30 locations was used to calculate each home range (Seaman et al. 1999; Martin et al. 2007).”

“, anglers interviewed) increased, contrary to what has been suggested (Seaman et al. 1999), indicating that our sample sizes were larger than those typical of studies using kernel density estimation.”

“…in grasslands of the Chihuahuan Desert, such as the conversion of grasslands into farmland (Macı́as-Duarte et al. 2009), shrub encroachment (Van Auken 2000), and reduction in grass cover by overgrazing (Macı́as-Duarte et al. 2004) may be responsible for these population declines, but its…”

“This schedule provided the minimum of 30 fixes/period/individual that is required to perform least-square cross-validation (LSCV) kernel estimates (Seaman et al., 1999).”

“Other studies assessing the accuracy of kernel density estimation have looked at mixture functions of Gaussians [16–18] and experimentation with several other forms of functions did not change the results.”

“Simulations suggest that $ 50 locations are required for accuracy (Seaman et al., 1999), and location data for some animals may require considerably more (e.g. 200–500 locations; Hemson et al., 2005).”

“Seaman et al. (1999) recommend a minimum of 30 locations for an accurate representation of a home range, but we were limited by the short tenure of males in the chorus.”

“We only retained deer that had at least 50 points within a home range (Seaman et al. 1999).”

“The precision of home range size estimates is sensitive to the sample size [54].”

“Although we had sufficient points to calculate home range estimates for several individual bats [86], the layout of the study area prevented us from tracking the bats if they left the valley and therefore, any home range estimations would be heavily biased towards our study area.”

“We did not utilize Least Squares Cross Validation (LSCV) because of its sensitivity to sample size and recommendation of ‡50 observations per individual (Seaman et al., 1999).”

“Only months containing a minimum of five complete days were used in subsequent analyses, which appeared to be the minimum number of days which was representative of the areas visited by each group for that month (Seaman et al. 1999).”

“Home range asymptotes were reached for each flock after 50 locations, which is a typical number of sampling locations to reach an asymptote [2, 70].”

“We located each sparrow 1–2 times daily for 5– 6 d per week to obtain ≥ 30 locations over the lifetime of the transmitter, which is recommended as the minimum sample size for kernel-based home range analyses (Seaman et al. 1999).”

“We obtained 30 mapped points per bird across 30 days to reliably estimate their territory extent (Barg, Jones, & Robertson, 2004; Seaman et al., 1999).”

“Kernel density estimators, another technique used for home range calculation in previous studies (e.g., McGrath and Austin, 2009), would have produced bias in estimates because of low sample size (Seaman et al., 1999) and nonconsecutive detections.”

“Fixed KDEs remain less biased and more accurate than many newer methods (Börger et al. 2006; Lichti and Swihart 2011), and account for differential area use within an individual home range, but they require a large number of locations to accurately estimate areas of core use (Seaman et al. 1999).”

“HRs (95% fixed kernel; Worton, 1989) were calculated with a least-square cross-validation method (LSCV), as fixed kernel estimates were least biased in the outer contours (Seaman et al., 1999).”

“Home range typically reached an asymptote with of approximately 70 locations for the annual period, both for males and females, so this was the minimum number of locations used to estimate the home range size of each genet (Seaman et al. 1999 ).”

“The reference bandwidth href resulted in oversmoothing; given the large spatial extent and multimodal distribution of relocations, href was not appropriate for our study (Worton, 1995; Seaman et al., 1999).”

“The smoothing parameter value was estimated by using the reference bandwidth method since the least-squares cross-validation method did not converge for most of the pigs (31, 32).”

“The 95% and 50% home ranges were defined as the main and core home range, respectively, in accordance with Seaman et al. (1999), Hemson et al. (2005), and Laver and Kelly (2008).”

“Sample sizes were inadequate to run KDE for each year individually (Table 2; Seaman et al., 1999).”

“KDE computes the spatial utilization distribution based on a random sample of group locations (Seaman et al., 1999; Worton, 1989).”

“…for the subset of radiocollared individuals for which we had > 30 locations, and long-term home ranges for those with > 50 locations during the course of the study, using locations separated by ≥ 4 h to reduce problems related to spatial autocorrelation (Otis and White 1999; Seaman et al. 1999).”

“The home range size (95% KRE) of juvenile black-faced spoonbill was 45.2 km2 and the core size (50% KRE) was 8.4 km2.”

“We estimated home range size as the area (ha) within the 95% probability contour of a fixed kernel density estimate (Millspaugh and Marzluff 2001) for all Steller’s Jays with 30 locations (Seaman et al. 1999).”

“The UD approach quantified spatial overlap and shifts in spatial distribution over time in a probabilistic manner, but was prone to sample-size dependent variation in the estimation of smoothing parameters that can lead to over- or under-estimation of UD size (Seaman et al. 1999).”

“(9) Only locations that were obvious outliers were removed.(10) These corresponded to the does’ characteristic excursive behaviors that occur very briefly during the breeding season, when it is theorized that does travel considerable distances to augment their chances of finding suitable bucks with which to mate.”

“We used the fixed kernel method because it has lower bias, and better surface fit for a given bandwidth than the adaptive kernel method (Seaman and Powell, 1996; Seaman et al., 1999).”

“Further, all home range measurements had a reasonable number of location fixes to generate home range estimates [53].”

“Te least-squarescross-validation method failed to converge in animals with large sample sizes; therefore, kernels were estimated using the reference bandwidth method [39, 40].”

“We furthermore included 100% minimum convex polygons (MCP; Mohr 1947) to facilitate comparison with previous studies reporting this commonly used estimator (Seaman et al. 1999).”

“The least-squares cross validation (LSCV) method of selecting the smoothing parameter for the KDEs, recommended by Seaman et al. (1999) failed to minimise the Mean Integrated Squared Error for most lizards; therefore, we used the reference bandwidth instead.”

“Previous studies have found that small sample sizes can bias home range estimates [57], so analyses were restricted to birds with� 30 locations and� 20 locations not associated with a nest site.”

“…unused terrestrial habitats located between aquatic activity areas (Jennrich and Turner 1969; Anderson 1982; Worton 1989, 1995; Naef-Daenzer 1993; Piepgras 1998; Seaman et al. 1999; Piepgras and Lang 2000), we used them for comparing our results to those of other Blanding’s turtle studies.”