How to apply RLQ ordination to communities with different species?

Question

I am analyzing the relationship between bird traits and environmental variation using the RLQ ordination corrected for spatial autocorrelation and phylogeny, i.e., the method in Pavoine et al. 2011

The dataset includes 120 species from communities in different and faraway sites in France. I want to understand how habitat fragmentation affects bird traits.

The site x species abundance matrix would include many missing values. In fact, many species only live in some areas of France (i.e., according to the RedList species range maps), so their abundance in any site outside their range map should not be analyzed (in my opinion) because the species might be missing for reasons independent of the site's measurable environmental characteristics. However, all the NAs in the site x species abundance matrix are converted to 0 before performing the statistical analyses because the site x species abundance matrix needs to be complete.

Do you have any advice on this issue? Can RLQ ordination be used to compare communities composed of species that belong to different eco-regions?

Alternative approaches that I have considered are:

• do one RLQ per biogeographic region with similar bird communities rather than for the whole country
• convert the NAs in the site x species abundance matrix into the mean species abundance so that the values fall on the centroid
• only analyze ubiquitous species
• use a different method, e.g., GLM with Lasso regularization as in Brown et al. 2014 (but then can we correct for phylogeny and spatial autocorrelation with Lasso regularization?)

Would any of these alternatives be more appropriate/complementary?

Please let me know if I did not explain myself sufficiently or forgot essential information.

Many thanks in advance for any help!

Answer 1

Not sure what you mean by "The site x species abundance matrix would include many missing values". These should be zero, not NA, if a given species is not present in a given site. To downweight the many zeros, you can use appropriate transformations, like some of the Box-Cox series before computing the Correspondence Analysis (CA) on the species abundance matrix. Answering your question at the end: yes, the RLQ was actually made to compare communities composed of different species. Since you're using the extended version of the RLQ, you're already taken into account phylogenetic autocorrelation, which could account for any biogeographical regionalization. Because the output of this analysis is gargantuan, I don't recommend conducting separate analysis for each region. Do not substitute for any mean abundance. Use appropriate transformations instead, see also vegan::decostand . The model-based approaches you're referring to only apply fourth-corner analysis, not RLQ which is an ordination technique.