[R-sig-eco] distances in NMDS ordination space

[Kate Boersma]

Hi all.

I have a methodological question regarding non-metric multidimensional 
scaling. This is not specific to R. Feel free to refer me to another 
venue/resource if there is one more appropriate to my question.

Correct me if I'm wrong: NMDS axes are non-metric, which is why NMDS 
frequently makes sense for community data, but it also means that 
distances in NMDS ordination space cannot be interpreted simplistically 
as they can in eigenvalue-based methods like PCA. This is why it is 
inadvisable (meaningless) to use NMDS axes as response variables in a 
linear modeling framework (e.g., with environmental variables as 
predictors).

My question is this: Does that mean that it is also inadvisable to use 
distances among points in ordination space as response variables?

My (potentially flawed) understanding: While the coordinates may not 
make sense in isolation, they should be meaningful relative to each 
other. In a 2D ordination, if communities A & B are closer together in 
ordination space than communities C & D, that means they have more 
similar species compositions. Therefore, I should be able to predict the 
distance between points in a linear modeling framework.

Alternately, I could use the actual distances among communities from my 
dissimilarity matrix with a method like db-RDA. But I used NMDS over RDA 
or CCA for a reason. It seems more straightforward to use the distances 
from my NMDS ordination instead of generating new coordinates from a 
PCoA to fit an RDA framework (as in db-RDA)... but this logic only works 
if NMDS distances are informative.

Are these comparable analyses? If not, why not?

I'd love your opinions.

Thank you,
Kate

-- 
Kate Boersma, PhD
Department of Biology
University of San Diego
5998 Alcala Park
San Diego CA 92110
kateboersma at gmail.com
http://www.oregonstate.edu/~boersmak/