RDA in Canoco; linear dependence between variables

I would be most grateful for help regarding the question that I was asked by the journal editor. I have reviewed several papers and this forum and did not found any good answer.

The investigation concerns the occurrence of bird communities in relation to some environmental variables. I performed the redundancy analysis (RDA) in Canoco. In twelve plots there were 49 species with abundance data, against four continuous environmental variables. The editor noted that RDA assumes linear dependence of the response and explanatory variables, and asked whether I have verified that my data are linearly dependent.

I'm not sure how to verify this dependence and if it's really necessary. Is that truth that each species should be treated a response variable? What about rare species? I did correlation matrix (in Statistica), most numerous species revealed a relationship close to linear, indeed, but not all of them. The log transformation does not help. Overall, I suppose that there may be a general error in the attempt, but I wonder where.

Thanks for help



Super Moderator
Just a quick comment,

Are your bird data counts? or actually abundance (per sq metre or something like that).

If they are counts, try a square root transformation or even arcsine and see how that goes.

As for the comments, yes RDA assumes linearity but dbRDA does not because it is a permutation based so you might want to look at that as an alternative.
Many thanks for the hint. I must check dbRDA, but it needs some effort.

My bird data include both, the counts (number of breeding pairs) and density (number of breeding pairs per 10 ha), but the former is used in computations of RDA. I checked the relationships between each of the response variables (species) and explanatory variables on either row data (not-transformed), log-transformed, and square root transformed. The log-transformed seem to work best but the difference is rather not very large, actually. Several most numerous species inevitably reveal relationships close to linear, the other act differently.

However, isn’t it true that the most numerous species are also most influential on RDA performance? Thus, maybe the linear dependence in these species is sufficient to conclude on RDA results?