Effects of Sample Size on Kernel Home Range Estimates

“We investigated the effect of (location) sample Sanchez and Rachlow Pygmy Rabbit Space Use 1305 size on fixed-kernel estimates of home range area to establish a minimum sample size before calculating home range estimates (Seaman et al. 1999).”

“locations for at least one season to estimate utilization distributions (UD; Seaman et al., 1999; Kernohan, Gitzen & Millspaugh, 2001).”

“By using each location only once, data sets for most of our animals became far smaller than recommended for this method (Seaman et al., 1999).”

“Home-range kernels at 95% (outer range) and 50% (core range) were calculated for all birds with at least 27 active positional fixes (n = 19, mean fixes = 44.6 15.6 sd, range = 27–72) following Seaman et al. (1999).”

“…(HRT; Rodgers et al. 2007) extension in ArcGIS 9.3 (ESRI) and Geospatial Modelling Environment (GME; Spatial Ecology LLC, http://www. spatialecology.com/gme/, Accessed 15 Jan 2013) to calculate 95% fixed-kernel home ranges (Worton 1989, Seaman et al. 1999) for each individual within each season.”

“Also, foxes for which fewer than 50 locations were available were excluded from home-range analysis (Kenward 1992; Seaman et al. 1999).”

“Although below the minimum of 30 observations recommended by Seaman et al. (1999), a minimum of 25 observations per individual allowed us to keep as many individuals as possible without potentially influencing the analysis with small sample sizes.”

“Only individuals with a minimum of 30 relocations (Seaman et al. 1999) and sufficient relocations within at least 1 season for home-range size to stabilize, based on area-observation curves (stabilization on average occurred at 29 relocations, range ¼ 16–50 relocations), were included in further…”

“Finally, collection of a few animal positions will likely underestimate home-range size (Harris et al. 1990, Seaman et al. 1999, Powell 2000, Girard et al. 2002), which is widely used to calculate habitat use at the landscape scale and to measure availability at the homerange scale (Garshelis 2000).”

“Percent Volume Contours (PVCs) used to visualize and compare the kernel densities (home ranges) of the tagged seals were derived from the KDE raster datasets (Sain et al., 1994; Seaman and Powell, 1996; Seaman et al., 1999; Gitzen and Millspaugh, 2003).”

“We used 90% kernel density estimation (KDE) with least-squares crossvalidation (Worton 1989; Seaman and Powell 1996; Seaman et al. 1999; Börger et al. 2006) to define the bear distribution.”

“1990; White and Garrott 1990) but remains one of the most commonly used (Seaman et al. 1999; Laver and Kelly 2008).”

“), adopting the same sampling scheme for all individuals, with a time distance between fixes of about 5 days, and ensuring the collection of an adequate sample of locations (Seaman et al. 1999).”

“1999), the fixed-kernel method with LSCV currently is recognised as the most accurate and least biased home-range estimator (Worton 1989, 1995; Seaman and Powell 1996; Seaman et al. 1999).”

“We estimated the 50% kernel home range sizes of all resident individuals based on PIT-tag data using the Animal Movement 2.0 extension for Arc View 3.3 (Hooge and Eichenlaub 2000), and least squares cross validation (LSCV) to choose the correct smoothing (Seaman and Powell 1996; Seaman et al. 1999).”

“parameter was selected by least square cross-validation [20].”

“Estimates of territory sizes by MCP strongly depend on sample size (Seaman et al. 1999; Powell 2000; Börger et al. 2006; Laver & Kelly 2008).”

“We also expected that at least 30 positions might be necessary to allow accurate calculation of the size of the home range based on computer simulations performed by Seaman et al. (1999).”

“We did this by iteratively truncating long data streams into shorter ones (2–9 months), calculating home range estimates, and then comparing the estimated home range sizes from the experimentally shortened data streams with estimates derived from the complete data sets using a metric of percent relative bias (Seaman e…”

“We only included woodpeckers in the home range analysis if we obtained P30 telemetry locations (Seaman et al., 1999) during the 12-month period from April 1 through March 31.”

“We developed wolf UDs from 2-h GPS collar data collected only from February to April 2004 because this was the time period for which we had sufficient wolf locations to produce monthly UDs ([50; Seaman et al. 1999) and a large enough elk sample size to measure exposure during winter.”

“We filtered lynx individuals, discarding animals with fewer than 50 telemetry locations to ensure a robust estimation of lynx home ranges (Seaman et al. 1999).”

“Although small numbers of observations tend to overestimate home range size (Seaman et al., 1999), Börger et al.”

“We used least squares cross-validation to select the kernel smoothing factor [40].”

“In addition to estimating overall home ranges for all five species, we also investigated the short-term temporal patterns of home-range utilization by individuals of four species (cattle, deer, pigs, possums) tracked by GPS, by focusing on animals for which we had four consecutive months of observations with at least…”

“All FK95 and FK50 estimates were based on >30 locations, the minimum number required when using kernel estimates with LSCV for bandwidth selection (Seaman et al. 1999).”

“For studies of wildlife, the application of KDEs has recently expanded from identifying boundaries of home ranges (e.g., Worton 1989; Seaman and Powell 1996; Seaman et al. 1999; Laver and Kelly 2008) to identifying hotspots of WVCs (e.g., Danks and Porter 2010).”

“We chose not to analyze habitat selection within individual home ranges (2nd order selection; Johnson 1980) because several animals lacked a suf cient number of telemetry locations to generate home-range estimates (Seaman et al. 1999).”

“…ravens’ home ranges as the two-dimensional extent of their three-dimensional utilization distributions (UDs) on the basis of point locations in ArcGIS 9.2 with the Home Range Tools (HRT) for ArcGIS 9.x (Rodgers et al. 2005) by implementing a 99% fixed-kernel estimator (Seaman et al. 1999).”

“We analyzed relocation data to determine sample size necessary for multi-annual home range estimation (Seaman et al. 1999).”

“We estimated annual home ranges using 50 locations (Seaman et al. 1999) and a mean of 83 locations (SE ¼ 3.76, range ¼ 50–141) per deer.”

“We estimated seasonal home ranges for hogs with 30 locations (Seaman et al. 1999) in either season (dry n = 10, wet n = 4).”

“…winter and summer home ranges using the fixed-kernel method (Worton 1989) in the Animal Movement extension (Hooge and Eichenlaub 2000) for ArcView 3.2, Geographic Information System (GIS) with a 95% probability contour and a least-squares cross-validation smoothing parameter (Seaman et al. 1999).”

“The 2D density matrices require a large number of samples to describe the distribution accurately [10, 11], hence in this study, we used 249 independent control samples for deriving the density matrices and we would envisage that with fewer samples, this methodology would not work as effectively.”

“In this way, the h value could be reliably estimated (Seaman et al., 1999).”

“To our knowledge there is no recommended minimum sample size for the plug-in bandwidth selector, although a minimum size of n[ 30 is recommended for the least-squares cross-validation bandwidth selector (Seaman et al. 1999).”

“This period was selected to ensure the sample size was large enough for kernel analysis (i.e. n > 30 locations; Seaman et al. 1999).”

“We chose the MCP because it is has been most widely used and therefore facilitates comparison between studies (Harris et al. 1990; Seaman et al. 1999).”

“We applied leastsquares cross-validation (LSCV; Seaman et al. 1999) to estimate the smoothing parameter.”

“The fixed-kernel method was used because it is sensitive to multiple areas of concentrated use (i.e., nonparametric) and pro - duces less area bias and better surface fit than adaptive-kernel estimates when sample sizes are small (Seaman and Powell 1996, Seaman et al. 1999).”

“Data exclusion principally adversely affects range estimates when it results in low sample sizes (Otis & White 1999, Seaman et al. 1999).”

“We excluded from the data 1) locations of individuals ,18 months old due to potential habitat-use biases (i.e., their locations would be subsets of their mothers); 2) individuals with ,50 locations (Seaman et al. 1999; panther ID nos.”

“[42] for estimating home ranges via kernel when a representative sample of ≥30 is available, all bats with a minimum of 30 fixes were included in the analyses.”

“Proportion of time spent diving The proportion of time spent diving (fdiving) was defined as the fraction of time spent below 4 m, that is, fdivingð%Þ ¼ 100 BIN0 4m where BIN0-4m is the first bin of the TAD histograms, that is, the proportion of time spent at the surface (above 4 m).”

“[29], I considered the 95% fixed-kernel estimates to best represent the home range of the groups for their respective periods of time (Fig.”

“For illustrative purposes, we produced 95% home range (use area) kernels from seasonal caribou location data using the fixed kernel and least squares cross validation methods of ANIMAL MOVEMENT (Seaman et al. 1999) (Fig.”

“Only bats with more than 30 telemetry locations were used in space and habitat analyses (Seaman et al. 1999).”

“We employed a minimum of 30 radiolocations for each estimate (Seaman et al. 1999).”

“We used individuals which had minimum 30 fixes (Seaman et al., 1999) within the twoonemonth sampling periods.”

“Moreover, several studies indicate that for simple simulated home ranges, fixed kernel estimates usually originate consistent home areas with as few as 10–20 locations (e.g. Seaman et al., 1999).”

“Seaman et al. (1999) suggested that 50 fixes were preferable for kernel home range estimation, but recent studies have suggested that <20 fixes can still produce accurate estimates (Saïd et al. 2005; Börger et al. 2006b).”

“tions for minimal sample sizes for estimating home range by Seaman et al. (1999) and Vokoun (2003).”

“We used least-squares cross validation to determine smoothing factors in the fixed-kernel estimation procedure because it is less biased and performs better than other methods, especially with sample sizes .50 (Seaman and Powell 1996; Seaman et al. 1999).”

“It is reported that a positive correlation can exist between estimated home range size and number of locations obtained per individual with telemetry equipment (Seaman et al., 1999; Girard et al., 2002).”

“As recommended by Seaman et al. (1999) and Hooge et al. (1999), the smoothing parameter was obtained using least squares cross validation (LSCV).”

“2 and dominant female: 80 points] exceeded the recommended minimum of 50 points for home-range estimations (Seaman et al., 1999).”

“We chose the fixed kernel method instead of the adaptive kernel method used in 1992 (Crooks and Van Vuren 1995) because it generally provides a better surface fit with lower bias (Seaman and Powell 1996; Seaman et al. 1999).”

“The least-squares cross validation (LSCV) method of selecting the smoothing parameter, recommended by Seaman et al. (1999), failed to minimize the mean integrated squared error (MISE) for most lizards; therefore, we used the reference bandwidth instead.”

“We therefore adopted a minimum of 30 resightings as suggested by Seaman et al. (1999).”