Evaluating functions to describe point patterns

Three functions that analyze point patterns are the L (a transformation of Ripley's K function), pair correlation, and K2 functions. We tested these functions with Genton's spatial index, which measures the distance between observed and random theoretical lines for a function over all lag distances. We simulated points from random, moderately regular, extremely regular, and clustered distributions at different density levels and a fixed plot size and for regular distributions at varying plot sizes. The spatial index clearly was able to identify clustered patterns. However, there was overlap in spatial index values between random and moderately regular distributions at lower densities. The spatial index for the L function also became more negative as plot size increased, indicating edge effects, whereas the pair correlation and K2 function values fluctuated with plot size. Using confidence envelopes rather than a spatial index, we also identified distributions other than the known distribution at low densities. These results indicate that ecologists should be cautious about 1) assigning random or regular distribution, particularly for the L function and the K2 function, 2) comparing point patterns of different densities and plot sizes, and 3) interpreting the pair correlation and K2 functions.