SPATIAL COVARIANCE IN PLANT COMMUNITIES: INTEGRATING ORDINATION, GEOSTATISTICS, AND VARIANCE TESTING

Abstract

Spatial structure in plant communities occurs in the forms of (1) single- species aggregation and dispersion patterns, (2) distance-dependent interactions between species, and (3) the response to the spatial structure of environmental conditions. Different methods deal with these components of spatial variation: geostatistical analysis reveals autocorrelation in a spatial sample; the variance of species richness has been used as an indicator for interspecific interactions due to niche limitation; and ordination techniques describe multispecies responses to environmental factors. Based on the mathematical prop- erties of presence-absence data, it is shown how variogram modeling, the testing of in- terspecific associations, and multiscale ordination can be integrated using the same set of distance-dependent variance-covariance matrices (variogram matrix). The variogram matrix partitions the variance of community data into spatial components at the levels of the individual species, species composition, and species richness. It can be used to factor out the effects of single-species aggregation patterns, interspecific interactions, or environ- mental heterogeneity. The mathematical integration of traditionally unrelated methods in- creases the interpretability of variograms of plant communities, provides a spatial extension and an empirical null model for the variance test of species richness, and extends multiscale ordination to nonsystematic spatial samples. Beyond the individual applications, the var- iogram matrix provides a framework for a mathematical unification of geostatistics, mul- tivariate data analysis, and the analysis of variance that may enable ecologists from a broad range of fields to incorporate spatial effects into their research and to integrate analyses across different levels of biological organization.