 Dear R-listers,

I have been trying to do variation partitioning using using vegan and PCNM
packages and some questions have come out in the process. I am a beginner
on this type of analysis so I apologize if any of my questions are very
basic. I have tried to find the answers in the papers and on the R-list,
but without much success.

I will explain first what I am trying to do. I have species abundance as my
response variable and I want to see if community abundance/composition
changes in relation to physical distance (i.e. distance between sites) and
environmental variables. I have two spatial levels: a linear transect in
which samples are separated every 5m, and a regional scale in which samples
are separated on a range of 1km to 1000km, although it is only two samples
(i.e. sites) out of 21 that are at more than 1000km from the rest which are
closer together (range 1km to 140km). I have analysed each spatial scale
(i.e. transect and regional) separately by a partial mantel test and both
the physical distance and the environmental variables have come out as
significant predictors of the community when controlling for the other,
although the environment is much more significant than the physical
distance. However now I have been trying to do a redundancy analysis to be
able to account for the spatial correlation that might be present on the
environmental variables using PCNM to model the spatial structure.  I am
still analysing the transect and the regional data separately. I have
performed the analysis in the following way:

1. Trend-surface analysis on the coordinates (Lat & Long) using a third
degree polynomials and then perform an RDA with only the variables
selected, using anova.cca to test     the full model and each axis.
2. I detrend the data using a linear regression of the abundance
data~coordinates.
3. PCNM analysis with function PCNM on the Euclidean distance calculated
from the coordinates.
4. Run the PCNM analysis on the detrended data.
5. Variation partitioning, using first rda function to test and select for
the coordinates, environmental variables and PCNM variables on the
undetrended data (so three different       RDA analysis, using each time
forward.sel function to select for the significant variables in each case).
Then I do the variation partitioning using varpart function and test
  each fraction using anova.cca

My questions are the following:

Transect:
-  The global PCNM analysis comes out as not significant; does this mean
that there is no spatial structure on my response variable? It surprises me
because I have read that PCNM is good at detecting spatial structure at
fine scale, so how come the Mantel test come out significant but the PCNM
not significant?
-   If PCNM is not significant on the detrended data, is it valid to use
then PCNM on the undetrended data in the variation partitioning later? I am
confused because on the PCNM analysis on the undetrended data, PCNM comes
out significant. I don’t know what it means that it is non-significant on
the detrended data, but significant on the undetrended one.
-   Also in the variation partitioning analysis, the
rda(abundance~geographical coordinates) is significant, but when I do the
varpart (abundance~ coordinates +environment + PCNM), the coordinates are
not significant. Actually the only variables that are significant in
explaining some of the variation are the environmental ones, and in general
the residual (i.e. unexplained variation) is over 80%.

Regional scale:
-   When detrending the data, the rda (abundance~polynomials) the
proportion of constrained variance is 0.74, but when I forward select, no
variable is selected because Rsq Adj < 0. Does this mean that there is a
high percentage of the variation explained by some spatial structure in the
data? How should I proceed?
-   I have run the analysis at the regional scale with and without the two
samples that are over 1000km from the rest, but in general the results did
not change.

More general questions:
-  I have hellinger-transformed my abundance data to carry out the analysis
but I presume I could pretty much follow the same procedure using capscale
if I want to use a different non-euclidean index such as Bray-Curtis?
-  In case I don’t have the geographical coordinates, but only the physical
distance between sites how can I do a trend surface analysis?
-  I am confused as to how explanatory variables should be treated.
According the M.W. Palmer webpage (
http://ordination.okstate.edu/overview.htm#Environmental variables in CCA)
“explanatory variables can be of many types… and do not ned to meet
distributional assumptions". However I have seen that many people center
and standardize their variables because they are measured in different
units. What is the correct thing to do? Should explanatory variables be
transformed to meet normal distributions?

Any help/comments are highly appreciated.


Larisa Lee

*Seoul National University*
* *

*South Korea*

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