On Determining the Statistical Significance of Discontinuities with Ordered Ecological Data

Current ecological theory hypothesizes that boundaries between adjacent ecosystem units are important in determining ecosystem structure and function across heterogeneous landscapes, and that such boundaries are potentially important sites for early detection of global climate change effects. Hence, there is an increasing research effort to elucidate the structure and function of ecological boundaries. Yet traditional data analysis methods focus primarily on homogeneous units rather than on the boundaries between them; thus, new methods are being developed for detecting, characterizing and classifying boundaries, e.g., split moving—window boundary analysis (SMW). SMW is a simple yet sensitive method for locating discontinuities that may exist within multivariate, serial data (ordered in one dimension) at various scales relative to the length of the data series. However, SMW is subjective and relative, and therefore locates apparent discontinuities even within random, serial data. In this paper we present two nonparametric methods for determining the statistical significance of discontinuities detected by SMW. First, we describe a Monte Carlo method for determining the statistical significance of scale—dependent discontinuities (i.e., discontinuities that are significant relative to only one scale). Second, we propose a nonparametric, scale—independent method (it also is dependent upon scale size, but to a much lesser degree than the Monte Carlo method) that is more appropriate for locating statistically significant discontinuities that separate different, relatively homogeneous groups of varying size along a series. We examine the robustness of these two methods using computer—generated data having varying intensities of imposed discontinuities, and illustrate their application to locating boundaries between vegetation samples collected at systematic intervals across a desert landscape in southern New Mexico, USA.