Interpreting ecological patterns generated through simple stochastic processes

The analysis of spatial patterns is fundamental to understanding ecological processes across geographic scales. Through an analysis of two simple, one-dimensional stochastic models, we develop a framework for identifying the scale of processes producing pattern. We show that for some simple model systems spectral analysis identifies exactly the scale of pattern formation. In other, more complicated systems, autocorrelation analysis appears to yield greater insight into the scale of the dynamics producing pattern; in these, the relative importance of processes at different scales can be determined directly from the change in slope of the autocorrelation function. In general, it is not possible to state which technique will be most useful in the analysis of pattern. Spectral analysis and autocorrelation analysis represent duals that can be extended and applied to more complex systems, potentially yielding insight into the nature of a wide variety of spatially determined ecological processes.