Quantifying spatial heterogeneity in streams

Although theoretical and empirical studies show that spatial heterogeneity has important effects on the dynamics of populations and the structure 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 different systems and understand the causes and consequences of that heterogeneity, we must first be able to quantitatively measure it. Spatial heterogeneity has many aspects that change with the scale of our observations, so we need a battery of descriptive measures that explicitly consider the scale-dependence of ecological pattern. Response variables exhibiting similar frequency distributions (i.e., similar overall variability) can have very different spatial distributions; consequently, descriptions of spatial heterogeneity require spatial data, i.e., data related to geographic locations (maps). We review statistical techniques for quantitatively describing aspects of heterogeneity in spatial data, emphasizing the decomposition of heterogeneity into different scales of variation (trends, overall variability, and spatial dependence or autocorrelation). Gradients in spatial data can be evaluated using trend analyses (e.g., regressions), whereas the spatial structure of variation around trends can be evaluated using geostatistical methods. The central concept of geostatistics is spatial dependence, which is the degree to which values of a response variable differ as a function of the distance (lag) between sampling locations. Semivariograms plot variation among samples separated by a common lag versus lag, and can be objectively decomposed by piece-wise regression techniques to estimate the strength and scales of spatial dependence. A variety of other methods can be used to quantify spatial heterogeneity from categorical and numerical maps depending on the question of interest and the underlying structure of the spatial data (e.g., methods derived from fractal geometry and information theory, nearest neighbor analysis, spectral analysis, Mantel's test). Spatial heterogeneity in stream organisms is driven by local variation in environmental conditions, by interactions between individuals of the same or different species, and by the effects of organisms on their abiotic environment. By applying geostatistical 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 of data obtained from experiments examining how consumers affect, and respond to, spatial heterogeneity in their resources. The results indicate that consumer-resource feedbacks should be considered when modeling the causes and consequences of spatial heterogeneity in streams.