QUANTIFYING SPATIAL HETEROGENEITY IN STREAMS

Although theoretical and empirical studies show that spatial heterogen eity has important effects on the dynamics of populations and the stru cture of communities, there has been little rigorous quantification of terms like ''patchiness'' or ''spatial heterogeneity'' in studies of lotic systems. In order to compare the spatial heterogeneity of differ ent systems and understand the causes and consequences of that heterog eneity, we must first be able to quantitatively measure it. Spatial he terogeneity has many aspects that change with the scale of our observa tions, so we need a battery of descriptive measures that explicitly co nsider the scale-dependence of ecological pattern Response variables e xhibiting similar frequency distributions (i.e., similar overall varia bility) can have very different spatial distributions; consequently, d escriptions of spatial heterogeneity require spatial data, i.e., data related to geographic locations (maps). We review statistical techniqu es for quantitatively describing aspects of heterogeneity in spatial d ata, emphasizing the decomposition of heterogeneity into different sca les of variation (trends, overall variability and spatial dependence o r autocorrelation). Gradients in spatial data can be evaluated using t rend analyses (e.g., regressions), whereas the spatial structure of va riation around trends can be evaluated using geostatistical methods. T he central concept of geostatistics is spatial dependence, which is th e degree to which values of a response variable differ as a function o f the distance (lag) between sampling locations. Semivariograms plot v ariation among samples separated by a common lag Versus lag, and can b e objectively decomposed by piece-wise regression techniques to estima te the strength and scales of spatial dependence. A variety of other m ethods can be used to quantify spatial heterogeneity from categorical and numerical maps depending on the question of interest and the under lying structure of the spatial data (e.g., methods derived from fracta l geometry and information theory, nearest neighbor analysis, spectral analysis, Mantel's test). Spatial heterogeneity in stream organisms i s driven by local variation in environmental conditions, by interactio ns between individuals of the same or different species, and by the ef fects of organisms on their abiotic environment. By applying geostatis tical methods to spatial data collected from field experiments, stream ecologists can evaluate the effects of biotic and abiotic factors on the spatial arrangement of organisms in streams. We present examples o f data obtained from experiments examining how consumers affect, and r espond to, spatial heterogeneity in their resources. The results indic ate that consumer-resource feedbacks should be considered when modelin g the causes and consequences of spatial heterogeneity in streams.