Abstract
Distance-based methods use point-to-point distances or random-location-to-point distances in a cloud of points to estimate characteristics of the point pattern. One such characteristics is the density of points. The difficulty with distance-based density estimators is that their distribution depends on the spatial pattern of points. In particular, the distribution of distances is untractable for usual clustered patterns, that are often observed in natural systems. Here, we propose a density estimator for clustered patterns, based on the random-location-to-pth-point distance X p . An approximate expression for the distribution function, F p , of X p was obtained by identifying the first two moments of the count of individuals in disks for a given point process with the first two moments of a negative binomial distribution. The approximate expression of F p was then used to derive a maximum-likelihood estimator of the intensity of the point process. The quality of the approximation of F p was assessed for homogeneous Poisson processes (for which the expression of F p is exact) and for Matérn processes. The intensity estimator based on Matérn processes was then used to estimate tree density in a tree savanna in Mali, and it compared favorably with six robust estimators found in the literature.
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Picard, N., Bar-Hen, A. Estimation of the density of a clustered point pattern using a distance method. Environ Ecol Stat 14, 341–353 (2007). https://doi.org/10.1007/s10651-007-0024-1
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DOI: https://doi.org/10.1007/s10651-007-0024-1