[R-sig-eco] CCA vs NMDS and ordisurf

[Pierre THIRIET]

Dear Aurélie,

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, Aurélie Boissezon a écrit :
> Hi everybody,
>
> I have some questions about ordination analysis and interpretation of ordisurf() output. So huge thanks to people who will help me to clean up my confused brain.
> So I am working on cover data of aquatic plants (%). I made 7 quadrat sampling between 2009 and 2012 in a semi permanent shallow pond (n=1200 approximately without empty quadrat). Due to fluctuating water regime and small topographic variations, my sampling units are distributed along a gradient of inundation conditions from permanently wet to frequently dry. Clearly the vegetation responded to water level condition occurring the previous year. Community following several years of high levels was very different from the one occuring the year after a severe drought of the waterbody (a lot of charophytes, pionneer species). I quantified this "drought disturbance gradient" by calculating when (which season?), and for how many days each quadrat dried before each field sampling.
> My purpose is to explore the relationship between the composition of the community and those "drought indexes". And in particular to highlight the succession of species along the gradients.
> My first reflex was to implement a CCA but someone tell me to explore unconstrained approach and in particular NMDS.
> The CCA ordination shows a strong arch effect but is highly significant and perfectly ecologically interpretable and congruent with my field observations. To summarize submerged species are separated from helophytes species by duration of drought during growing season (submerged species need water from winter to summer). And submerged species succeeded each other along a gradient of duration of drought at the end of the growth season, in autumn.
> But to see if I had similar results when looking at the whole variation of the community data set and when using a more suitable distance measure, I run a NMDS on Hellinger-transformed data based on Bray-Curtis distances.
> With NMDS I didn't reach a "convergent solution" even after setting stricter criteria maxit and sratmax. Nevertheless the stress is acceptable (8 with k=3 ) and the species are ordinated similarly to the CCA. I implement the same analysis on a simplified version of my data set by averaging the cover of species by date, by depth clusters (10 centiles) and by area of the lake leading to 131 observations instead of 1200 quadrats initially (which is very large). Here the nmds reached quickly a convergent solution (after 20 or 50 runs) and gave always a similar ordination of species.
> So is it important not to reach a convergent solution with NMDS in my case?
>
> I tried to overlay environmental informations on NMDS ordination using envfit function and then ordisurf which allows the environmental parameter to vary non linearly in the ordination space (on the contrary to CCA). I am really satisfied with graphical outputs  which are ecologically meaningfull but I am afraid to misinterprete them.
> In ecological studies we are used to explain the distribution of species with environmental/ explanatory variables. Here is it the same? If I understand well, ordisurf implement a 2d surface gam of the explanatory/environmnetal variable with the scores of sites ordinated in the n dimensions of the nmds..... that means that the explanatory variable become the response variable.
> Thus can I interprete the position of species in the ordination space with GAM surface resulting from ordisurf???? Like species X is present in sites never dried during spring, but between 10 and 20 days during autumn...etc....
> I think yes since relevés were ordinated on the basis of the structure of the macrophytes community...but I am not so sure!
>
> Thanks a lot for your help!
> Best regards,
>
> Aurélie
>
> -----------------------------------------------------------------------
> Aurélie Rey-Boissezon
> Ph-D Student
> University of Geneva
> Section of Earth and Environmental Sciences - Institute F.-A. Forel
> Aquatic Ecology Group
> Uni Rondeau
> Site de Battelle - Bâtiment D
> 7, route de Drize - 1227 Carouge
> Geneva
> Switzerland
> Tel. 0041 (0) 22379 04 88
>
> Aurelie.Boissezon at unige.ch
> http://leba.unige.ch/team/aboissezon.html
>
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