A Method for Determining Asymptotes of Home-Range Area Curves

Home-range Asymptotesfixed kernel estimator for our sample of bobwhitecoveys during the fall season. Our estimate usingfield data is similar to Seaman et al. (1999) who reportedthat bias and variance for the kernel estimatorapproached an asymptote at 50 locations usingcomputer simulation points. They recommendedusing a minimum ≥30 locations to obtain homerange estimates when using kernel estimators withLSCV, but preferably ≥50.Regarding the minimum convex polygon, wedocumented that in 2001 ≥50 locations were necessaryto obtain a representative home range estimatefor our sample of bobwhite coveys. However,in 2002 an area-curve asymptote was not reached toobtain a representative home range. Home range estimatesfrom the minimum convex polygon estimatorscontinued to increase with increasing locations(a property of this estimator), though this increasewas minimal in 2001. However, CV‘s remained relativelyconstant. This observation can occur becauseCV‘s are a ratio of mean:standard deviation. Therefore,similar CV‘s can result in spite of increasingmeans if their corresponding standard deviationsalso increase in similar proportion. Previous researchhas suggested a much larger number of locations(100-200) to estimate home range size using theminimum convex polygon (Bekoff and Mech 1984,Laundre and Keller 1981, Harris et al. 1990). Gautestadand Mysterud (1995) believed that asymptotesusing the minimal convex polygon method wouldonly occur when using more than several thousandlocations.Kernohan et al. (2001) evaluated 12 home rangeestimators, including the estimators used in thisstudy. Overall, Kernohan et al. (2001) favored thekernel home range estimator because it required areasonable sample size (≥50 location points), hadthe ability to compute home range boundaries thatincluded multiple centers of activity, was based oncomplete utilization distribution, was a nonparametricmethodology, and lacked sensitivity to outliers.However, kernel estimators have no real comparabilityto other home range estimators due to itsestimate being greatly affected by bandwidth choice.Minimum convex polygon also is a nonparametrichome range estimator, but unlike the kernel estimatorit is not impacted by bandwidth choice andcan be compared to other estimators. However, theminimum convex polygon estimator requires a largesample size (i.e., >100 locations total), does not useutilization distribution, does not account for outliers,and does not calculate multiple centers of activity(Kernohan et al. 2001, p. 140).Regardless of the estimator used, we recommendthat verification is needed showing that an areacurveasymptote had been reached prior to homerange estimation. However, identifying the asymptotesfor home-range area curves has been difficultbecause it generally has involved much subjectivity.Previous studies identified asymptotes through visualinspection (e.g., Bond et al. 2001) or when additionallocations produced