CCA vs NMDS and ordisurf

Dear Aur?lie,

About the dissimilarity measures and data you used:
Bray-curtis is usually the most appropriate, on raw 
abundance/biomass/cover data, or square root/log transformed. So why do 
you Hellinger transform before? This transformation is dedicated to be 
used with euclidean distance, and resulted ordinations (PCA or RDA) have 
a distinct meaning than PCoA or CAP/db-RDA (with bray-curtis) because 
joint abscence are included in first cases and excluded in the latter. 
See picture below from Anderson et al 2011 Navigating the multiple 
meanings of b diversity: a roadmap for the practicing ecologist

So, if you want do constrained ordinations (constrained by "drought 
disturbance gradient", I guess), I would suggest dbRDA (vegan::capscale) 
with bray curtis, or RDA on Hellinger transformed data, depending on 
what you want to emphasis.
For unconstrained ordinations, this will be respectively PCoA and PCA.

Pay attention in using NMDS. As you said,  it is rank-based, this is why 
fitting environmental vectors to NMDS biplot is not so appropriate, 
despite widely done. I don't see the problem about ordisurf and PCoA or 
CAP: Ordisurf enables you to fit environnemental variables that have 
non-linear relationships with PC of distance based ordinations.

If you use bray-curtis, I would suggest to use distance among group 
centroids instead of computing averages over groups followed by bray-curtis

About hypotheses testing (in capscale or adonis for instance), pay 
attention to the longitudinal nature of your data. Some questions about 
repeated measure and adonis are already in R-SIG-ECO archives, have a alook.

I guess you are interested in identifying the species which are the most 
responsible of community change over drought disturbance gradien?!
If yes, I think an appropriate way could be: a dbRDA (capscale) with 
bray curtis on square root transformed cover data (or not, depends if 
you have few predominant species that might mask the others) , and 
"drought disturbance gradient" as a continuous constraint. Then, you 
could overlay vectors of correlations between species cover and CAP1 axe 
(i.e. in vegan: scores(your.capscale, dis="sp", scaling=-2, const = 
sqrt(nrow(your.cover.data.matrix)-1),choices=1).

I hope my english is at least understandable, and that my answer helped you.

Cheers,
Pierre

Le 18/04/2013 13:31, Aur?lie Boissezon a ?crit :

CCA vs NMDS and ordisurf

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