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1  Introduction

Understanding ecological processes often require the numerical analysis of complex data [Legendre and Legendre, 1998]. Such data sets are typically organized in tables with rows corresponding to objects and columns to descriptors. For instance, in community ecology, variables describing the biological communities (species) or the physical environment are measured for sampling sites (objects) . In molecular ecology, objects correspond to individuals or populations while descriptors are molecular markers. As many variables are required to describe biological objects, these data sets are usually multidimensional and each object can be represented as a point of a ecological hyperspace where each axis corresponds to a descriptor. In this context, multivariate analysis provides an efficient way to identify ecological structures. The reasons of this choice are easy to understand [Gauch, 1982]:
Community ecology concerns assemblages of plants and animals living together and the environmental and historical factors with which they interact. [...] Community data are multivariate because each sample site is described by the abundances of a number of species, because numerous environmental factors affect communities, and so on. [...] The application of multivariate analysis to community ecology is natural, routine and fruitful.
According to Poidevin [1999], more than 85% of databases contain a geographical component associated to a specific location. This is probably true for ecological data and this quantity has probably increased with the development of GPS technology and geographic information systems (GIS). Hence, each object can also be represented as a point of a geographical space. Linking the ecological and geographical data allows the identification and the explanation of the spatial variability of ecological structures, a question of prime interest in ecology [Cormack and Ord, 1979,Smith, 2002]. Usually, space can be considered either as a factor responsible for ecological structures, or as a confounding variable leading to bias when analyzing a process of particular interest [Legendre, 1993]. Several approaches have been proposed to identify the spatial component of a multivariate ecological structure. For instance, in the pioneering work of Goodall [1954], principal component analysis (PCA) is firstly used to summarize ecological structures and PCA scores are then mapped in the geographical space to identify the spatial components.
In 2002, two journals published special issues on spatial statistics in ecology (Ecoscience volume 9, issue 2; Ecography volume 25, issue 5, 553-640). In these two issues, no paper concerned the spatial analysis of multivariate data. This absence seems surprising as multivariate methods are now standard tools to analyze ecological data. This absence is probably related to the relative small number of methods proposed in the litterature to deal explicitly with spatial multivariate data. In the last few years, several methods have been developped [Bellier et al., 2007,Dray et al., 2006,Dray et al., 2008,Wagner, 2004,Wagner, 2003,Couteron and Ollier, 2005] and it would be nice to have a synthesis paper on this question.

2  Objectives

There are two main objectives: a paper and a software (R package).
I would like to have a discussion/synthesis paper not a comparison paper in terms of results. We could try to answer the following questions:
  • For which ecological questions we need to analyze spatial multivariate data?
  • What are the conceptual differences between the methods?
  • What are the relevant methods to answer a particular ecological question?
  • And what are the need and perspectives in the field of spatial multivariate analysis?

3  Methods

4  Data

It would be nice to have one or two common data sets to illustrate the different methods. There is the famous oribatid data set in both ade4 and vegan. I have also added vegtf in ade4. 337 sites for 80 plant species used as an illustration in Dray et al. [2008].

5  Deliverables

  • Review/discussion paper (ecological journal)
  • R package with all methods.
  • Paper to present the package (Journal of Statistical Software ?)

6  And now...

This draft is only a basis to prepare the organization of the workshop. Use the list at http://listes.univ-lyon1.fr/wws/info/sedar08 to propose suggestions so that we can modify some parts of this text. As you can see, I need some references, precisions.

7  Presentations

The list of talks is available on the Practical Informations page.

References

[Banet and Lebart 1984]
Banet, T. and Lebart, L. (1984). Local and partial principal component analysis (PCA) and correspondence analysis (CA). In Computing., I. A. f. S., editor, COMPSTAT 84, pages 113-123. Physica-Verlag, Vienna.
[Bellier et al. 2007]
Bellier, E., Monestiez, P., Durbec, J., and Candau, J. (2007). Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches. Ecography, 30(3):385-399.
[Borcard and Legendre 2002]
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 et al. 2004]
Borcard, D., Legendre, P., Avois-Jacquet, C., and Tuomisto, H. (2004). Dissecting the spatial structure of ecological data at multiple scales. Ecology, 85(7):1826-1832.
[Borcard et al. 1992]
Borcard, D., Legendre, P., and Drapeau, P. (1992). Partialling out the spatial component of ecological variation. Ecology, 73:1045-1055.
[Cormack and Ord 1979]
Cormack, R. and Ord, J. (1979). Spatial and temporal analysis in ecology, volume 8 of Statistical Ecology. International Co-operative Publishing House, Fairland.
[Couteron and Ollier 2005]
Couteron, P. and Ollier, S. (2005). A generalized, variogram-based framework for multi-scale ordination. Ecology, 86:828-834.
[Dray et al. 2006]
Dray, S., Legendre, P., and Peres-Neto, P. (2006). Spatial modeling: a comprehensive framework for principal coordinate analysis of neighbor matrices (PCNM). Ecological Modelling, 196:483-493.
[Dray et al. 2008]
Dray, S., Saïd, S., and Débias, F. (2008). Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation. Journal of Vegetation Science, 19:45-56.
[Gauch 1982]
Gauch, H. (1982). Multivariate analysis in community ecology. Cambridge University Press, Cambridge.
[Gittins 1968]
Gittins, R. (1968). Trend-surface analysis of ecological data. Journal of Ecology, 56:845-869.
[Goodall 1954]
Goodall, D. (1954). Objective methods for the classification of vegetation III. An essay on the use of factor analysis. Australian Journal of Botany, 2:304-324.
[Griffith 1996]
Griffith, D. A. (1996). Spatial autocorrelation and eigenfunctions of the geographic weights matrix accompanying geo-referenced data. Canadian Geographer, 40(4):351-367.
[Legendre 1993]
Legendre, P. (1993). Spatial autocorrelation: trouble or new paradigm? Ecology, 74(6):1659-1673.
[Legendre and Legendre 1998]
Legendre, P. and Legendre, L. (1998). Numerical Ecology. Elsevier Science, Amsterdam, 2nd edition.
[Mantel 1967]
Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27(2):209-220.
[Norcliffe 1969]
Norcliffe, G. (1969). On the use and limitations of trend surface models. Canadian Geographer, 13(4):338-348.
[Poidevin 1999]
Poidevin, D. (1999). La carte moyen d'action : conception - réalisation. Ellipse, Paris.
[Smith 2002]
Smith, E. (2002). Ecological statistics. In El-Shaarawi, A. and Piergorsch, W., editors, Encyclopedia of Environmetrics, volume 2, pages 589-602. John Wiley and Sons, Chichester.
[Thioulouse et al. 1995]
Thioulouse, J., Chessel, D., and Champely, S. (1995). Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2:1-14.
[Wackernagel 2003]
Wackernagel, H. (2003). Multivariate geostatistics. Springer-Verlag, Berlin, 3rd edition.
[Wagner 2003]
Wagner, H. (2003). Spatial covariance in plant communities: integrating ordination, geostatistics, and variance testing. Ecology, 84(4):1045-1057.
[Wagner 2004]
Wagner, H. (2004). Direct multi-scale ordination with canonical correspondence analysis. Ecology, 85(2):342-351.
[Wartenberg 1985a]
Wartenberg, D. (1985a). Canonical trend surface analysis: a method for describing geographic pattern. Systematic Zoology, 34(3):259-279.
[Wartenberg 1985b]
Wartenberg, D. (1985b). Multivariate spatial correlation: a method for exploratory geographical analysis. Geographical Analysis, 17(4):263-283.


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