pca or nmds (with which normalization and distance ) for abundance data ?

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"))

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 ?

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 R? 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
R? 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?

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 ?

c) Is there other method to apply? I?m going to try co-inertia with
ade4 package

Thanks in advance.

Cheers.

Claire Della Vedova




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