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      LoCoH: Nonparameteric Kernel Methods for Constructing Home Ranges and Utilization Distributions

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          Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon (MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases. Here we extend the LoCoH in two ways: “fixed sphere-of-influence,” or r-LoCoH (kernels constructed from all points within a fixed radius r of each reference point), and an “adaptive sphere-of-influence,” or a-LoCoH (kernels constructed from all points within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal to a), and compare them to the original “fixed-number-of-points,” or k-LoCoH (all kernels constructed from k-1 nearest neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas (holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and irregular structures (e.g., rocky outcrops). We also demonstrate that a-LoCoH is generally superior to k- and r-LoCoH (with software for all three methods available at

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          Most cited references 49

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          Kernel Methods for Estimating the Utilization Distribution in Home-Range Studies

           B. Worton (1989)
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            Territoriality and Home Range Concepts as Applied to Mammals

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              A review of models of home range for animal movement

               B.J. Worton (1987)

                Author and article information

                Role: Academic Editor
                PLoS ONE
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                14 February 2007
                : 2
                : 2
                [1 ]Department of Environmental Science, Policy and Management, University of California, Berkeley, California, United States of America
                [2 ]Mammal Research Institute, Department of Zoology and Entomology, University of Pretoria, Pretoria, South Africa
                [3 ]Northern Rocky Mountain Science Center, U.S. Geological Survey, Montana State University, Bozeman, Montana, United States of America
                [4 ]Department of Ecology, Montana State University, Bozeman, Montana, United States of America
                [5 ]Environmental Studies Department, University of California, Santa Cruz, California, United States of America
                Imperial College, United Kingdom
                Author notes
                * To whom correspondence should be addressed. E-mail: getz@

                Conceived and designed the experiments: WG SF. Performed the experiments: SF AL. Analyzed the data: WG SF AL SR. Contributed reagents/materials/analysis tools: PC. Wrote the paper: WG PC SF SR CW.


                Current address: Department of Anthropological Sciences, Stanford University, Stanford, California, United States of America

                Getz et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                Page count
                Pages: 11
                Research Article
                Ecology/Spatial and Landscape Ecology



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