Local convex hull
LoCoH (Local Convex Hull) is a method for estimating the size of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffalos) homerange, as well as for constructing a utilization distribution</ref>Getz, W. M. and C. C. Wilmers, 2004. A local nearest-neighbor convex-hull construction of home ranges and utilization distributions. Ecography 27: 489-505.View PDF</ref>,<ref>Getz, W.M, S. Fortmann-Roe, P. C. Cross, A. J. Lyonsa, S. J. Ryan, C.C. Wilmers, in review. LoCoH: nonparametric kernel methods for constructing home ranges and utilization distributions. View PDF<ref>. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its (homeranges) at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle. Utilization distributions are constructed from data providing the location of an individual or several individuals in space at different points in time by associating a local distribution function with each point and then summing and normalizing these local distribution functions to obtain a distribution function that pertains to the data as a whole<ref>Silverman BW. (1986) Density estimation for statistics and data analysis. London: Chapman and Hall. 176 p.Cite error: The opening <ref> tag is malformed or has a bad name (see the help page).,<ref>Worton BJ. (1987). A review of models of home range for animal movement. Ecological Modelling, 38: 277–298.Cite error: The opening <ref> tag is malformed or has a bad name (see the help page).,<ref>Worton BJ. (1989) Kernel methods for estimating the utilization distribution in home-range studies. Ecology 70: 164–168.Cite error: The opening <ref> tag is malformed or has a bad name (see the help page).,<ref>Seaman DE, Powell RA. (1996) An evaluation of the accuracy of kernel density estimators for home range analysis. Ecology 77: 2075–2085.Cite error: The opening <ref> tag is malformed or has a bad name (see the help page)..
- Locate the k-1 nearest neighbors for each point in the dataset.
- Construct a convex hull for each set of nearest neighbors and the original data point.
- Merge these hulls together from smallest to largest.
- Divide the merged hulls into isopleths where the 10% isopleth contains 10% of the original data points, the 100% isopleth contains all the points, etc.
The LoCoH method has a number of strong points:
- It generates a density distribution denoting.
- As more data is added, the homerange becomes more accurate.
- It is handles 'sharp' features such as lakes and fences well.
- The generated homerange has a finite region.
LoCoH has a number of implementations including a LoCoH Web Application.
LoCoH was formerly known as k-NNCH, for k-Nearest Neighbor Convex Hulls.