[R] reception of (Vegan) envfit analysis by manuscript reviewers

[Gavin Simpson]

On Wed, 2012-05-09 at 15:51 -0600, Matt Bakker wrote:
> I'm getting lots of grief from reviewers about figures generated with
> the envfit function in the Vegan package. Has anyone else struggled to
> effectively explain this analysis? If so, can you share any helpful
> tips?
> 
> The most recent comment I've gotten back: "What this shows is which
> NMDS axis separates the communities, not the relationship between the
> edaphic factor and the Bray-Curtis distance."

Without further context for that quote and your manuscript to see how
you are using the method it is difficult to say whether you are doing
something silly or the reviewer is bone-headed.

I've had similar comments from reviewers about my use of the ordisurf()
function. In each case it was the reviewers' failure to understand the
methods applied that was the cause of the confusion.

As you provide little or no context I'll explain what envfit() does etc.

The idea goes back a long way (!) and is in my 1995 edition of Jongman
et al Data Analysis in Community and Landscape Ecology (Cambridge
University Press) though most likely was in 1987 version too. See
Section 5.4 of the Ordination chapter by Ter Braak in that book.

The idea is to find the direction (in the k-dimensional ordination
space) that has maximal correlation with an external variable.
Essentially, we have:

E(z_j) = b_0 + b_1x_1 + b_2x_2

where E(z_j) is the expectation (or mean, or fitted values) of the jth
external (environmental) variable, x_1 and x_2 are the "axis" scores in
ordination dimensions 1 and 2, and b_y are unknown regression
coefficients. This generalises to more than 2 dimensions or axes.

The biplot arrow drawn goes from (0,0) to (b_1, b_2).

You can see that the aim is to model or predict the values of the jth
environmental variable (z_j) as a linear combination of the "axis" or
site scores of the samples in the ordination space. Exactly the same
idea underlies the ordisurf() function except that we use a GAM and for
the right hand side of the equation multivariate splines are used which
allow a non-linear surface instead of a plane.

When applied to nMDS, if the nMDS provides a reasonable approximation to
the original dissimilarities, then envfit() will estimate and show the
strengths of the correlation and direction of maximal correlation
between the nMDS configuration and the jth enviromental variable. This
technique can be used to indicate if one or more environmental variables
are associated with differences between sites/samples as represented in
the nMDS ordination.

The big caveat is the implication that the correlation or relationship
between z_j and the ordination space is linear. ordisurf() allows you to
relax this assumption as we fit a potentially non-linear surface to the
ordination space instead of the plane that envfit() effectively produces
(though we show only the direction of change with the arrow).

So without seeing your manuscript or more context (and I'm not promising
to read it or comment more if you provide it) I would suggest that, *if*
you have applied nMDS and used envfit() correctly the combined analysis
*does* reflect the *linear* "relationship between the edaphic factor and
the Bray-Curtis distance", assuming of course that the nMDS has low
stress (i.e fits the original dissimilarities well).

In future, you should consider posting similar questions
(ecological/environmental) to the R-SIG-Ecology list instead of the main
R-Help list. I know Jari (lead developer of vegan and author of
envfit() ) has stopped regularly reading the main R-Help list and you
will get far more eyes familiar with these techniques on the
R-SIG-Ecology list.

I have taken the liberty of cc'ing this to the R-Sig-Ecology list so
others can comment.

HTH

G

> Thanks for any suggestions!
> 
> 
> Matt
> 
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