A local nearest-neighbor convex-hull construction of home ranges and utilization distributions

We describe a new method for estimating the area of home ranges and constructing utilization distributions (UDs) from spatial data. We compare our method with bivariate kernel and alpha-hull methods, using both randomly distributed and highly aggregated data to test the accuracy of area estimates and UD isopleth construction. The data variously contain holes, corners, and corridors linking high use areas. Our method is based on taking the union of the minimum convex polygons (MCP) associated with the k-1 nearest neighbors of each point in the data and, as such, has one free parameter k. We propose a minimum spurious hole covering (MSHC) rule for selecting k and interpret its application in terms of type I and type II statistical errors. Our MSHC rule provides estimates within 12% of true area values for all 5 data sets, while kernel methods are worse in all cases: in one case overestimating area by a factor of 10 and in another case underestimating area by a factor of 50. Our method also constructs much better estimates for the density isopleths of the UDs than kernel methods. The alpha-hull method does not lead directly to the construction of isopleths and also does not always include all points in the constructed home range. Finally we demonstrate that kernel methods, unlike our method and the alpha-hull method, does not converges to the true area represented by the data as the number of data points increase.