A systematic comparison of summary characteristics for quantifying point patterns in ecology

Many functional summary characteristics such as Ripley's K function have been used in ecology to describe the spatial structure of point patterns to aid understanding of the underlying processes. However, their use is poorly guided in ecology because little is understood how well single summary characteristics, or a combination of them, capture the spatial structure of real world patterns. Here, we systematically tested the performance of combinations of eight summary characteristics [i.e. pair correlation function g(r), K-function K(r), the proportion E(r) of points with no neighbor at distance r, the nearest neighbor distribution function D(r), the spherical contact distribution Hs(r), the kth nearest-neighbor distribution functions Dk(r), the mean distance nn(k) to the kth neighbor, and the intensity function (x)]. To this end we used point pattern data covering a wide range of spatial structures including simulated (stationary) as well as real, possibly non-stationary, patterns on tree species in a tropical forest in Panama. To measure the information contained in a given combination of summary characteristics we used simulated annealing to reconstruct the observed patterns based only on the limited information provided by this combination and assessed how well other characteristics of the observed pattern were recovered. We found that the number of summary characteristics required to capture the spatial structure of stationary patterns varied between one (for patterns with near random structures) and three (for patterns with complex cluster and superposition structures), but with a robust ranking g(r), Dk(r), and Hs(r) that was largely independent on pattern idiosyncrasies. Stationary summary characteristics [with ranking g(r), Dk(r), Hs(r), E(r)] captured small- to intermediate scale properties of non-stationary patterns, but for describing large-scale spatial structures the intensity function was required. Our finding revealed that the current practice in ecology of using only one or two summary characteristics bears danger that essential characteristics of more complex patterns would not be detected. The technique of pattern reconstruction presented here has wide applications in ecology.