[R-sig-eco] CCA vs NMDS and ordisurf

[Jari Oksanen]

Hello folks,

Only one point here:

On 18/04/2013, at 15:52 PM, Pierre THIRIET wrote:
> 
> 
> Pay attention in using NMDS. As you said,  it is rank-based, this is why fitting environmental vectors to NMDS biplot is not so appropriate, despite widely done. I don't see the problem about ordisurf and PCoA or CAP: Ordisurf enables you to fit environnemental variables that have non-linear relationships with PC of distance based ordinations.


This is not true. I have seen this sometimes in Internet, but this really is not true: The NMDS ordination space is strictly *metric*. In vegan it is even strictly *Euclidean*. So it is absolutely correct to fit vectors to NMDS ordination. (In MASS::isoMDS you can also have any Minkowski metric, but only Euclidean or Minkowski with exponent=2 is allowed in vegan even with isoMDS.)

What is non-metric is the monotonic regression from *metric* ordination to any dissimilarity measure. So NMDS finds metric solution from any dissimilarity measure.

I

-- 
Jari Oksanen, Dept Biology, Univ Oulu, 90014 Finland
jari.oksanen at oulu.fi, Ph. +358 400 408593, http://cc.oulu.fi/~jarioksa