**dylan's blog**, and kindly contributed to R-bloggers)

Principal Coordinates (of) Neighbor Matrices (PCNM) is an interesting algorithm, developed by P. Borcard and P. Legendre at the University of Montreal, for the multi-scale analysis of spatial structure. This algorithm is typically applied to a distance matrix, computed from the coordinates where some environmental data were collected. The resulting "PCNM vectors" are commonly used to describe variable degrees of *possible* spatial structure and its contribution to variability in other measured parameters (soil properties, species distribution, etc.)-- essentially a spectral decomposition spatial connectivity. This algorithm has been recently updated by and released as part of the PCNM package for R. Several other implementations of the algorithm exist, however this seems to be the most up-to-date.

**Related Presentations and Papers on PCNM**

- http://biol09.biol.umontreal.ca/ESA_SS/Borcard_&_PL_talk.pdf
- Borcard, D. and Legendre, P. 2002. All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling 153: 51-68.
- Borcard, D., P. Legendre, Avois-Jacquet, C. & Tuomisto, H. 2004. Dissecting the spatial structures of ecologial data at all scales. Ecology 85(7): 1826-1832.

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