Using distance-based eigenvector maps (DBEM) in multivariate variation partitioning. Part 1: PCNM (principal coordinates of neighbor matrices), theory and applications.
Borcard, Daniel*,1, Legendre, Pierre1, 1 Université de Montréal, Montréal, Québec, Canada
ABSTRACT- Spatial heterogeneity of ecological structures plays a functional role in ecosystems, originating either from the physical forcing of environmental variables or from community processes. In 2002, we proposed PCNM analysis (Principal Coordinates of Neighbor Matrices) for detecting and quantifying spatial patterns over a wide range of scales. PCNM proceeds by eigenvalue decomposition of a truncated matrix of geographic distances among the sampling sites. This 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 the 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 method can be applied to any set of sites providing a good coverage of the sampling area. The behavior of the method has been explored using numerical simulations and an artificial pseudo-ecological data set of known properties. The simulations have shown a correct type I error and a great power of the PCNM analysis to reveal trends, bumps and periodic patterns, but also random autocorrelation in response variables. PCNM also successfully recovered the four deterministic components built into the pseudo-ecological data, despite the large amount of noise added. We also present applications of PCNM analysis to real ecological data representing combinations of: transect or surface, regular or irregular sampling schemes, univariate or multivariate data.
Key words: principal coordinates of neighbor matrices, distance-based eigenvector maps, multi-scale ordination, variation partitioning
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