[R-sig-eco] wascores() for metaMDS?

gabriel singer gabriel.singer at univie.ac.at
Thu Aug 20 11:17:37 CEST 2009

Dear Jari and Gavin,

thanks a lot, everything clear... with the connection to CCA I now get 
the meaning of the species scores, almost trivial after all...


Gavin Simpson wrote:
> On Wed, 2009-08-19 at 11:40 +0200, gabriel singer wrote:
>> 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.
> An individual taxon's "species score" is computed as the weighted
> average of the "site scores", weights being the abundance of that taxon
> in each site. It is the abundance weighted centroid of all the samples
> in which the species occurs. The motivation for this is that in CA,
> species scores are weighted averages of site scores that are themselves
> weighted averages of species scores and so on in the Two-way algorithm
> of Mark Hill - not that vegan computes the CA solution that way in cca()
> - so it is an analogous approach to computing species scores for nMDS.
>> Would these 
>> species scores be appropriate to show as vectors in the MDS?
> Not as vectors, as that implies directionality or increasing abundance
> and there is no reason to assume that the abundance of a given taxon
> will increase linearly or even monotonically in a given direction across
> the nMDS plot.
> Although I hesitate to call it that, the species score computed as the
> weighted average of the site scores, is an optima (of nMDS site scores)
> and thus abundance declines as one moves away from the point. So in this
> sense, you display the species scores in the same manner as on a CA or
> CCA plot, as a point, instead of the vector in PCA/RDA. However, the
> decline in CA is uniform in any direction (fitted not actual abundance),
> i.e. in 2-D the species score is the point at the top of a 2-D
> bell-shaped surface as this is the implied response model in CA. With
> nMDS there is no reason to assume this is the case.
> For one or two taxa, you could just project a surface of actual
> abundances using ordisurf() or you could just use the points as you
> would in a CA diagram, more or less. The problem with the surface
> approach is that you can only show a couple of species at most on a
> single ordination plot.
> ordisurf would likely be the best option for most extra data you wish to
> impose on to the nMDS plot, again for the reason that the relationship
> between nMDS axes and the variable of interest need not be a simple
> linear or monotonic surface.
> G
>> Thanks for any answer...
>> Gabriel Singer
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Dr. Gabriel Singer
Department of Freshwater Ecology - University of Vienna
and Wassercluster Lunz Biologische Station GmbH
gabriel.singer at univie.ac.at

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