Distance to the Border in Spatial Point Patterns

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The analysis of spatial point patterns is commonly focused on the distances to the nearest neighbor. The distance of organisms to the edge of the enclosure is also of interest in some biological studies performed in the laboratory. We define the B (border) function and derive its shape assuming complete spatial randomness (CSR) for square, rectangular, circular, and some three-dimensional arenas. The idea is then extended outside the laboratory setting to work with maps and points located in geographical regions. Commands in R ( R Core Team, 2012) to calculate and plot the empirical B̂ function are included. The B function, based on distances to the nearest edge, in addition to the G function, based on distances to the nearest neighbor, contributes to the understanding of the spatial distribution of the points.