Abstract
Spectral analysis allows the characterization of temporal (1D) or spatial (2D) patterns in terms of their scale (frequency) distribution. Cross-spectral analysis can also be used to conduct independent correlation analyses at different scales between two variables, even in the presence of a complex superposition of structures, such as structures that are shifted, have different scales or have different levels of anisotropy. These well-grounded approaches have rarely been applied to two-dimensional ecological datasets. In this contribution, we illustrate the potential of the method. We start by providing a basic methodological introduction, and we clarify some technical points concerning the computation of two-dimensional coherency and phase spectra and associated confidence intervals. First, we illustrate the method using a simple theoretical model. Next, we present a real world application: the case of patterned (gapped) vegetation in SW Niger. In this example, we investigate the functional relationships between topography and the spatial distribution of two shrub species, Combretum micranthum G. Don. and Guiera senegalensis J.F. Gmel. We show that both the global vegetation pattern and the distribution of C. micranthum are independent at all analyzable scales (i.e., from 10 to 50 m) from possible relief-induced determinisms. Additionally, the two dominant shrub species form distinct patches, thus suggesting separate niches