wascores() for metaMDS?

Gabriel,

Hi sig-ecology!

Here comes a probably stupid question... I am looking for smart ways to
include information about underlying variables in MDS plots. In other
words, after having computed an ordination with isoMDS or metaMDS from a
community table, I would like to add something like species
coefficients/loadings as vectors to the plot of sites. As no species
coefficients exist in this case, the best I could come up with so far is
simply vectors calculated from correlation coefficients of the
individual species with the site scores (on two MDS axes).
The function metaMDS allows to compute "species scores" using the
function wascores().... I have now pondered for 2 days how these scores
are calculated and what their precise meaning would be. Would these
species scores be appropriate to show as vectors in the MDS?
Thanks for any answer...

I think these were documented... Please point out the unclear parts of the
documentation so that I can correct those.

The wascores are Weighted Averages Scores and they are calculated like
weighted averages, or similarly as species scores in correspondence
analysis. This means that (with some scaling) they show the centroid
("barycentre") of the species occurrence in the ordination graph. It is not
appropriate to present these as arrows which indicate a linear increase to
the direction of the arrow instead of the centre of abundance. Therefore the
species scores can (and as default in metaMDS, will) be presented as points.
If -- for any reason that is none of my business -- you want to get vectors
of species, you can fit species as vectors. This happens with metaMDS or
isoMDS like this:

library(vegan)
data(dune)
m <- metaMDS(dune)
# or m <- isoMDS(vegdist(dune))
vec <- envfit(m, dune)
plot(m, dis="site")
# or with isoMDS: ordiplot(m)
plot(vec)

I promised that I won't comment on this, but still I must say that I cannot
find a reason to do so.

Please note that you can also use ordisurf to fit nonlinear species
responses if you think that species are not points nor arrows. Vegan
tutorial (from the Web) gives an example.

Cheers, Jari Oksanen