Describing spatial pattern in stream networks: A practical approach

The shape and configuration of branched networks influence ecological patterns and processes. Recent investigations of network influences in riverine ecology stress the need to quantify spatial structure not only in a two-dimensional plane, but also in networks. An initial step in understanding data from stream networks is discerning non-random patterns along the network. On the other hand, data collected in the network may be spatially autocorrelated and thus not suitable for traditional statistical analyses. Here we provide a method that uses commercially available software to construct an empirical variogram to describe spatial pattern in the relative abundance of coastal cutthroat trout in headwater stream networks. We describe the mathematical and practical considerations involved in calculating a variogram using a non-Euclidean distance metric to incorporate the network pathway structure in the analysis of spatial variability, and use a non-parametric technique to ascertain if the pattern in the empirical variogram is non-random.