Quantifying the spatial scales of animal clusters using density surfaces.

Animal clustering takes place at a variety of spatial scales. While methods to quantify clustering already exist, many of these methods are either scale independent, not parameter-free, or model proximity as a binary function, which makes them unsuitable for anisotropic systems and is not representative of the perception neighbourhood of animals. We describe a method to quantify the degree of clustering of point-location data at different spatial scales, which uses kernel density estimation to construct a density function from the underlying point-location data. We build upon this method to automatically detect cluster diameters using smoothing kernels that better represent the perception neighbourhood of animals. Finally, we test our methods on artificial datasets with varying clustering characteristics, as well as on a dataset of African bush elephants. Our method correctly assigns higher clustering values to spatial scales with high degrees of clustering and accurately outputs a set of spatial scales that correspond to cluster diameters. The accuracy of our method is insensitive to the chosen kernel function. Combined with the parameter-free nature of our method, this allows for easy detection of clustering scales in anisotropic and hierarchically clustered systems, such as animal groups.