Document: JOH-3-91-4

Spatial pattern analysis in ecology based on the K-function: Testing the assumptions of stationarity and isotropy.

BATTLES, J.*, G.BIGING and D.NEWBURN

University of California, Berkeley, CA 94720 USA ¹

Abstract:
The K-function is widely used to document spatial patterns in mapped field data. As a descriptive tool, its primary advantage over quadrat based measures it that considers spatial information at multiple scales. In its typical implementation, K-function analysis assumes that the distribution of points is stationary and isotropic. However, there is yet no "common wisdom" to guide researchers when these assumption are violated. Therefore we used simulation modeling to examine the robustness of the K-function. Specifically, we focused on the quantifying the extent of the deviation in stationarity or isotropy needed to obscure the underlying point pattern. Our basic simulation consisted of 2000 points distributed in 100 by 100 m area. To avoid edge effects, we calculated the K-function for points only in the inner 40 by 40 m grid at distances from 0.3 to 30 m. To test stationarity, we created simulations with increasingly severe linear and unimodal trends in point density for random point processes. To test isotropy, we took clumped patterns and manipulated the orientation of the points in the patches. Throughout, 95 % confidence intervals were the minimum standards for significant results. Our simulations showed that the K-function was robust to linear trends in point density. Only when the gradient in point density approached 300% did we detect false signals indicating a clumped point distribution. In contrast, the K-function was sensitive to unimodal trends in point density. If the density of randomly distributed points varied from the edge to the center by 80% or more, the K-function implied either a uniform point distribution when point density increased toward the center or a clumped distribution when the density decreased toward the center. The K-function was also robust to anisotropy in a clumped point process. Even when there was strong linear orientation of points in a patch, the K-function still correctly identified the underlying clumped pattern. The costs of anisotropic arrangement were that the scale of the clumping was overestimated and the signal was weakened. Thus anisotropy reduces the accuracy and power of the K-function. We use the distribution of canopy gaps in a mangrove forest to demonstrate how the explicit consideration of stationarity and isotropy can improve the description of spatial patterning.

Keywords: point pattern detection, mapped data, canopy gaps, second-order analysis, K-function

This abstract is being presented at: 10:30 AM in session:
STATISTICAL ECOLOGY