I'm busy with the analysis of bird community change through time on a couple of sites and want to relate it to environmental covariates. I use the R-package
vegan for this task and do a canonical PCA (thus redundancy analysis).
In the discussion with my colleagues the idea arose if it is possible to use the bird count differences between consecutive years instead of the absolute counts per year. This approach would yield negative values for the species table in case the populations of given species decrease from one year to the next. According to Borcard et al. 2011 ("Numerical Ecology with R") PCA is not adapted to the analysis of raw species counts; after an adequate transformation (e.g. Chi-square or Hellinger transformation), however, PCA and RDA may be applied to abundance data.
I wonder which kind of data transformation would be necessary for "difference counts". When I add a constant to the values to get them non-negative, I can apply a Hellinger transformation, but the result of the transformation depends on the added constant (although the transformed values are not very different). Is there a way to treat "difference counts", should I apply another ordination method with less data restrictions, or should I dismiss the approach at all?