SpaceMaker 2

Generate spatial explanatory variables to be used in multiple regression or canonical ordination

Daniel Borcard and Pierre Legendre
Département de Sciences Biologiques
Université de Montréal
SpaceMaker 2 is a program generating spatial descriptors to be used as explanatory variables in multiple regression or canonical ordination. The two types of spatial descriptors produced are: The PCNM methods aims at identifying spatial patterns at any scale covered by a given sampling set. It consists in following steps:
  1. Build a matrix of Euclidean (geographic) distances among sampling points.
  2. Truncate this distance matrix (at a user-defind threshold) so as to retain only the distance values corresponding to the nearest neighbors.
  3. Replaced the deleted values by an arbitrarily large distance value. This large distance equals four times the truncated threshold defined at step 2. Now, the distance matrix accurately represents the distances among close sampling points, and considers all the other pairs of points as "far apart".
  4. Compute the principal coordinates of the matrix obtained at step 3 (without correction for negative eigenvalues).
  5. Retain the eigenvectors corresponding to positive eigenvalues. These are the spatial explanatory variables to use in multiple regression or canonical ordination of the dependent variables.

Program availability

Borcard, D., P. Legendre, C. Avois-Jacquet & H. Tuomisto. 2004. Dissecting the spatial structure of ecological data at multiple scales. Ecology 85(7): 1826-1832 [Statistical report]. Borcard, D., Legendre, P. & Drapeau, P., 1992. Partialling out the spatial component of ecological variation. Ecology 73: 1045-1055. Borcard, D. and P. Legendre. 2002. All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling 153: 51-68. Legendre, P., 1990. Quantitative methods and biogeographic analysis. In: D.J. Garbary and R.G. South (Editors), Evolutionary biogeography of the marine algae of the North Atlantic. NATO ASI Series, Vol. G 22. Springer-Verlag, Berlin, pp. 9-34. Legendre, P. & D. Borcard. 2006. Quelles sont les échelles spatiales importantes dans un écosystème ? Chapitre 19 (p. 425-442) in: J.-J. Droesbeke, M. Lejeune et G. Saporta (éds), Analyse statistique de données spatiales. Editions TECHNIP, Paris. [Manuscrit du chapitre en format PDF / Chapter manuscript in PDF format.] Legendre, P. & Legendre, L. 1998. Numerical Ecology, 2nd English edition. Elsevier Science BV, Amsterdam. xv + 853 pages.