Geostatistical Tools for Modeling and Interpreting Ecological Spatial Dependence

Geostatistics brings to ecology novel tools for the interpretation of spatial patterns of organisms, of the numerous environmental components with which they in- teract, and of the joint spatial dependence between organisms and their environment. The purpose of this paper is to use data from the ecological literature as well as from original research to provide a comprehensive and easily understood analysis ofgeostatistics' manner of modeling and methods. The traditional geostatistical tool, the variogram, a tool that is beginning to be used in ecology, is shown to provide an incomplete and misleading summary of spatial pattern when local means and variances change. Use of the non-ergodic covariance and correlogram provides a more effective description of lag-to-lag spatial dependence because the changing local means and variances are accounted for. Indicator transforma- tions capture the spatial patterns of nominal ecological variables like gene frequencies and the presence/absence of an organism and of subgroups of a population like large or small individuals. Robust variogram measures are shown to be useful in data sets that contain many data outliers. Appropriate removal of outliers reveals latent spatial dependence and patterns. Cross-variograms, cross-covariances, and cross-correlograms define the joint spa- tial dependence between co-occurring organisms. The results of all of these analyses bring new insights into the spatial relations of organisms in their environment.