[R-sig-eco] pca or nmds (with which normalization and distance ) for abundance data ?

Thu Dec 13 21:03:47 CET 2012

On Thu 13 Dec 2012 09:24:41 AM CST, claire della vedova wrote:
>
> Dear all,
>
> I’m a biostatistician working for a French institute involved in
> environmental risk assessment, and I would need help to understand the
> results I obtained from several ordination analyses.
>
> I have a dataset of 25 sites. For these 25 sites I have abundance data 
> of 38
> species and also the measurement of 5 environmental variables.
>
> Here an extract of my abundance data for the 5 first sites:
>
> Anguinidae.ditylenchus Aphelenchidae Aphelenchoididae Aporcelaimidae
>
> 12 18 184 0
>
> 0 14 154 0
>
> 45 0 101 6
>
> 20 0 148 0
>
> 0 0 118 0
>
>
>
> Here the environmental data for the 5 first sites:
>
> ExtPond moist Corg pH DV50
>
> 0.946 9.086 4.269 5.24 171.33
>
> 0.682 27.139 23.813 3.82 75.45
>
> 2.480 14.322 7.191 4.48 230.90
>
> 3.069 18.380 11.404 3.58 211.19
>
> 2.615 16.693 7.128 4.12 224.45
>
>
>
> My aim was to study how the distribution of species is linked with
> environmental data.
>
> Firstly, I did a PCA (with vegan library), using a Hellinger 
> transformation,
> with commands like this :
>
> acp1<-rda(decostand(myDataSpec[,c(25:62)], "hellinger"))
>
>

Is the Hellinger transform done on relative proportions?

>
> The first axe represent 19.5% the second one 16.3%. A colleague of me said
> it is not so bad with abundance data, but it seems to me quite poor. 
> What do
> you think about ?
>
>

You could use something like the broken stick model or others to access 
how many axes are necessary, but two axes explaining <40% of the 
variation seems low.

>
> Then, I fitted environmental vectors with the envfit function (of vegan
> library), with commands like this :
>
> physCInd.fit3<-envfit(acp1,MyDataEnv[,c(13,18,20,21,23)], permut=4999,
> na.rm=T)
>
> It appeared that pH variable is significantly linked with the ordination,
> and the pval of ExtPond is 0.1.
>
> Next I did a RDA which is not significant.
>
> To finish I did two NMDS. For the first one I used the Hellinger
> normalization and the Bray-Curtis distance. The stress obtained value is
> 0.22, Non metric fit R² is 0.952 and Linear fit R2 =0.777. When I 
> fitted the
> environmental vectors , ExtPond was correlated with the ordination (pval
> =0.02) and p-val of pH = 0.23
>
> But then I read in “numerical ecology” page 449 that it’s better to
> standardize the data by dividing each value by maximum abundance for 
> species
> and then use Kulcynski distance. The stress value was 0.23 , Non 
> metric fit
> R² was 0.948 and Linear fit R2 =0.69. These values are a little less good
> than those of the first NMDS, but the stressplot seems to me more
> homogenous.
>
> Nevertheless, the results I obtained are very different... When I fitted
> the environmental data it appeared that ExtPond was not correlated 
> with this
> ordination (p-val=0.82) and p-val of pH=0.06. And obviously ExtPond is the
> most important variable for us ;-)
>
> With all these results, I’m quite confused, and I don’t know what to 
> think.
> So, if someone can help me, I would appreciate it very much. Be sure that
> all comments will be welcome.
>
> To summarize my questions are :
>
> a) Which ordination method would be better for my data : PCA knowing
> that the represented inertia is 35.62% or NMDS with a stress value about
> 0.22?
>
My opinion is PCA on hellinger transformed relative proportions "means" 
more than an NMDS

> b) If NMDS is more adapted which one is the better? with Hellinger
> normalization and Bray-Curtis distance, or with the normalization
> recommended by Legendre and Legendre and Kulcynski distance ?
>
I sounds like the normalization you are referring to is relative 
proportion which is si/sum(s); s is a vector of taxon at a site.

> c) Is there other method to apply? I’m going to try co-inertia with
> ade4 package
>
>
>
I am reading about co-inertia analysis now as it may be useful for some 
of the things that I am planning on doing.  This method looks promising.

You are going to have to decide on what type of ordination to use with 
COIA...

HTH,

Stephen

> Thanks in advance.
>
> Cheers.
>
> Claire Della Vedova
>
>
>
>
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>
>
>
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> -- 
> Stephen Sefick
> **************************************************
> Auburn University
> Biological Sciences
> 331 Funchess Hall
> Auburn, Alabama
> 36849
> **************************************************
> sas0025 at auburn.edu
> http://www.auburn.edu/~sas0025
> **************************************************
>
> Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods.  We are mammals, and have not exhausted the annoying little problems of being mammals.
>
>                                  -K. Mullis
>
> "A big computer, a complex algorithm and a long time does not equal science."
>
>                                -Robert Gentleman
>