Effects of Sample Size on Kernel Home Range Estimates

“This amount of time provided at least 40 spatial locations which is generally regarded as a sufficient sample size for calculating home range size (e.g. Seaman et al. 1999).”

“Seaman et al. (1999)은 야생동물의 행동권 분석을 위해서는 최소 30개 이상의 위치자료를 이용해야 하며, 행동권의 오차를 최소화하기 위해서는 50개 이 상의 위치정보를 분석에 이용하는 것을 제안한 바 있다.”

“Correspondingly, numerous efforts have been directed at determining the minimum number of fixes (e.g., Seaman et al., 1999) and the methods used to accurately describe a home range (Burgman & Fox, 2003; Laver & Kelley, 2008).”

“Kernel home ranges were computed with the Animal Movement extension to ArcView 3.2 (Hooge and Eichenlaub 1997) using the 95% fixed kernel estimator and least squares cross validation (LSCV) to determine the optimal smoothing parameter value (Worton 1989, Seaman et al. 1999).”

“The bandwidth value was determined by performing the least-squares cross-validation procedure [39].”

“…season (as defined above), as well over each year to ensure sample size was sufficient to reach a home range size asymptote; the asymptote is the point on the curve at which additional locations result in a minimal increase in home range size (Harris et al., 1990; Hawes, 1977; Seaman et al., 1999).”

“Small sample sizes tend to overestimate kernel home range sizes (Seaman et al. 1999; Borger et al. 2006), so we discarded two pigs for which we had less than c. 40 locations (75 202 and 75 210; Fig.”

“Recognizing kernel home range estimations are subject to error, especially with small sample sizes as those presented here [71], our goal was not to estimate and report the ‘true’ size of home ranges, but to measure relative changes in home range size or location between risk groups and seasons.”

“Weused90%kernels to estimate the extent of activity shadows around each roost becauseoutliershavebeen suggested tohave agreater influence on density isopleths for >90% KDE home range analyses (Seaman et al. 1999, Borger et al. 2006).”

“Estimates derived based on the LSCV have been shown to have less bias compared with those for which the smoothing parameter was set at the ad hoc value href (e.g. Seaman and Powell 1996; Seaman et al. 1999).”

“Home ranges were calculated for individuals that had a minimum of 30 independent locations (Seaman et al. 1999), these included telemetry locations and direct observations.”

“We calculated home ranges only for bears that were monitored for ≥ 1 year and had ≥ 30 total locations (Seaman et al. 1999).”

“For kernel-based methods such as LoCoH, a minimum of 30 (or preferably >50) observations per individual has been suggested (Seaman et al. 1999), so one dolphin (H2) was excluded from this analysis.”

“We acknowledge that the kernel estimator is sensitive to small sample sizes of relocations (Seaman et al. 1999), but our sample was limited by the duration of the period between migration and transmitter battery failure, combined with the need to maintain temporal independence between observations.”

“Only groups with >30 fixes were used for the analysis (Seaman et al. 1999).”

“Only individuals with more than 50 radio-locations were included in the analyses (Seaman et al. 1999).”

“As suggested by Seaman and Powell (1996), Powell et al. (1997), Seaman et al. (1998, 1999) and Powell (2000), optimal bandwidths were determined using the LSCV technique.”

“Seaman et al. (1999) found that the least-square cross-validation value was approximately 50% of the reference value; therefore, we used this as our starting h value and increased or decreased h until we achieved a utilization distribution where the 95% fixed kernel was one complete isopleth.”

“…an unbiased estimate of space use, while 50% and 95% isopleths provide unbiased estimates of the core area and overall space use, respectively, with the latter excluding only locations from rarely used areas (Fletcher Jr. & Koford, 2003; Seaman et al., 1999; Seaman & Powell, 1996; Worton, 1989).”

“Yet MCP typically overestimates home range size because of sample bias; that is, home range increases with the number of locations plotted (Turner et al. 1969) and through the outsized impact of outliers (Seaman et al. 1999).”

“The number of geographic locations required for a robust estimate of home range has long been an important question in spatial ecology (Odum and Kuenzler 1955; Seaman et al. 1999; Börger et al. 2006).”

“Only those individuals with at least ~30 locations were considered for further analysis because a small number of locations often produces biased estimates (Seaman et al. 1999; Fieberg and Börger 2012).”

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

“We estimated seasonal home ranges and seasonal core areas for foxes with 30 observations in a given season (Seaman et al. 1999, Kernohan et al. 2001) and located >66% of the season.”

“Therefore, in order to meet the minimum sample size requirements of kernel density analysis and ensure a reasonable representation of space use without bias from interpolation [55], only bi-monthly samples with > 50 pseudolocations, and where the pseudolocation to raw location ratio was < 3 were included in analysis o…”

“We depicted a home-range boundary as the 95% isopleth of the kernel probability density function (Seaman et al. 1999).”

“…kernel) methods for discussing space use because they yield homerange estimates with less bias than other methods and are relatively robust to small sample sizes (i.e., number of locations used to generate kernel density estimates; Seaman and Powell 1996, Seaman et al. 1999, Powell 2000).”

“We calculated seasonal home ranges and core areas for animals with ≥30 locations in a season (Seaman et al. 1999).”

“The smoothing parameter for all FKHRUD calculations was selected using least squares cross validation (Silverman 1986, Seaman and Powell 1996, Seaman et al. 1999).”

“Small sample sizes prohibited use of the most accurate home range estimation methods currently available (e.g., kernel methods, Seaman et al. 1999).”

“A minimum sample size of 30 is recommended for the LSCV method (Seaman et al., 1999), whereas the HREF method can be applied based on at least a sample size of 10 (Webb et al., 2011).”

“…of the classification criteria can be found in the research methods KDE uses the kernel function, one of the nonparametric methods of density estimation, which uses the density distribution graph obtained based on the location coordinates of wildlife and represents it as a line-like curve [29, 30].”

“…to the area of the territory and can be affected by sample size (Boulanger and White 1990 ; Seaman et al. 1999; Downs and Horner 2008), we set h ref as the smoothing parameter to define the width of each isopleth (Calenge 2006), as recommended when having < 50 observations (Seaman et al. 1999).”

“To estimate home ranges, the minimum convex polygon (MCP) method [44,62,63] was used both in the urban and scrubland areas.”

“Home ranges and core areas were calculated using kernel estimates with ad hoc for smoothing method, and each estimate obtained a minimum of 50 fixes (Seaman et al., 1999).”

“For the fixed kernel method, smoothing parameters were estimated using least-squares cross-validation, providing the least-biased estimates for the 95% and 50% habitat range areas (Seaman et al., 1999).”

“We calculated 95% fixed-kernel density estimates (KDE) of home range size using a plug-in smoothing factor (Lesmeister et al. 2009) in the R package ‘adehabitatHR’ (Calenge 2021) for each skunk with ≥ 30 locations (Seaman et al. 1999).”

“We estimated monthly range areas as the 95% isopleth of the estimated ODs for every individual for each monthly period containing more than 30 locations following release (Seaman et al ., 1999).”

“Furthermore, this analysis performed well with multimodal data and can provide estimates based on specified contours (Börger et al. 2006; Seaman et al. 1999).”

“We chose the MCP method over kernel estimators because the kernel method requires a minimum of 30 locations to produce reliable results and tended to overestimate the home range sizes when we used small sample sizes (Seaman et al. 1999, Boyle et al. 2009).”

“Home-range size of individual birds and effect of sex on individual home-range We calculated individual home-range for 56 Redcapped Larks (31 males, 21 females, 4 not sexed) with more than 30 fixes (Seaman et al. 1999).”

“Hemson et al., (2015) suggest ignoring site fidelity in simulation studies leads to inappropriate conclusions advocating KDE LSCV ( e.g. Worton, 1995; Seaman & Powell, 1996; Seaman et al. , 1999).”

“Previous studies have shown that 20 unique locations and 95% surface areas can provide an unbiased estimate of territory size, while excluding outlying locations that are rarely used (Worton 1989, Seaman and Powell 1996, Seaman et al. 1999, Fletcher and Koford 2003).”

“imposed bias than other methods also corresponds with previous work (e.g., Börger et al., 2006; Seaman et al., 1999; Seaman and Powell, 1996).”

“For each situation studied (home range/sociability per individual and period), more than 50 locations were used and exceptionally (in tracking week to week) only between 30 and 50 locations were considered, which is the minimum number admissible (Seaman et al. 1999; Millspaugh et al. 2004).”

“One of the eight bats could not be used in this study, as a minimum of 30 GPS fixes were not obtained, resulting in an inaccurate prediction of home range size (Seaman et al. 1999).”

“However, this type of sampling is considered an appropriate trade-off in spatial ecology studies of shorter duration (see Seaman et al., 1999).”

“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).”