Dissecting the spatial structure of ecological data at multiple scales

Spatial structures may not only result from ecological interactions, they may also play an essential functional role in organizing the interactions. Modeling spatial patterns at multiple spatial and temporal scales is thus a crucial step to understand the functioning of ecological communities. PCNM (principal coordinates of neighbor matrices) analysis achieves a spectral decomposition of the spatial relationships among the sampling sites, creating variables that correspond to all the spatial scales that can be perceived in a given data set. The analysis then finds the scales to which a data table of interest responds. The significant PCNM variables can be directly interpreted in terms of spatial scales, or included in a procedure of variation decomposition with respect to spatial and environmental components. This paper presents four applications of PCNM analysis to ecological data representing combinations of: transect or surface data, regular or irregular sampling schemes, univariate or multivariate data. The data sets include Amazonian ferns, tropical marine zooplankton, chlorophyll in a marine lagoon, and oribatid mites in a peat bog. In each case, new ecological knowledge was obtained through PCNM analysis.