Introduction

This website aims at summarizing the theory behind different methods to analyze count data:

It also describes reciprocal scaling (Thioulouse and Chessel 1992) (and its extensions with CCA and dc-CA). Reciprocal scaling is a method to compute and visualize the dispersion among count tables analyzed with multivariate methods.

Dataset

Throughout this document, we will use the data from Barbaro et al. (2012) on bird species distribution in New Zealand extracted from the CESTES database (Jeliazkov et al. 2020).

Throughout this document, we will analyze a matrix \(Y\) (\(r \times c\)) and two associated matrices \(E\) (\(r \times e\)) and \(T\) (\(t \times c\)). In our example:

  • \(Y\) (\(r =\) 26 \(\times\) \(c =\) 21) represents bird species counts in different sites
  • \(E\) (\(r =\) 26 \(\times\) \(l =\) 6) represents environmental variables in different sites
  • \(T\) (\(c =\) 21 \(\times\) \(k =\) 7) represents bird species traits

References

Barbaro, Luc, Eckehard G. Brockerhoff, Brice Giffard, and Inge van Halder. 2012. “Edge and Area Effects on Avian Assemblages and Insectivory in Fragmented Native Forests.” Landscape Ecology 27 (10): 1451–63. https://doi.org/10.1007/s10980-012-9800-x.
Jeliazkov, Alienor, Darko Mijatovic, Stéphane Chantepie, Nigel Andrew, Raphaël Arlettaz, Luc Barbaro, Nadia Barsoum, et al. 2020. “A Global Database for Metacommunity Ecology, Integrating Species, Traits, Environment and Space.” Scientific Data 7 (1): 6. https://doi.org/10.1038/s41597-019-0344-7.
Thioulouse, Jean, and Daniel Chessel. 1992. “A Method for Reciprocal Scaling of Species Tolerance and Sample Diversity: Ecological Archives.” Ecology 73 (2): 670–80. https://doi.org/10.2307/1940773.