[R-sig-eco] quantifying directed dependence of environmental factors

[Jay Kerns]

Hello,

I'm posting to this list because I believe it's the best place to
go.  My question is R related only inasmuch as all the work I've
done so far has been with R and I expect any answers I get from
here will lead me to more R work.

I'm consulting with an ecologist and an engineer on a project
related to a reservoir nearby.  They've collected data on diatoms
in the reservoir via core samples; they have sections of data over
the past 100yrs.  They are looking at the community structure
plus other environmental factors over the same time period.

We've done a ton of work already and there's no point trying to
hash all of that out here.  Short story: we did an NMDS, it fits
OK (stress 0.17), there are obvious clusters in the ordination
which correspond to a-priori clusters from ecological
considerations (and which match an independent cluster analysis),
we're really quite pleased overall.  We checked for relationships
with =envfit=, most environmental variables are *highly*
significant, yet there are a couple which aren't significant at
all.  Here comes my question:

The ecologist pointed out to me that our environmental variables
don't have equal status (ecologically speaking); some variables
lead to others.  For instance, there are so-called ultimate
factors (population, percentage farmland) which contribute to
intermediate factors (suspended solids, total phosphorous) which
in turn contribute to direct factors (AREA, pH,...) which then in
turn contribute to diatom structure.

We have measured data on all the above and several more.  The
model we are fitting with =envfit= is symmetric in those n
environmental variables, but the ecology of the situation isn't
symmetric, it's a directed top-down kind of relationship.  He
asked me, "How can we quantify that?  How can we demonstrate
that?  Can we quantify/demonstrate that?"  I don't know.

There are ecologists on this list: what am I looking for, here?
What methods do ecologists use to answer this (or related)
question(s)?  Feel free to direct me to papers, literature,
textbooks, whatever.  I'm trying to help answer this question
and (this not being my subject specialty) I'm at a bit of a loss.

If there are relevant R packages/vignettes/manuals you can point
me to, that'd be cool too.

Thanks for reading all the way down to here.

Jay

P.S. If it hadn't been for the archives of this list containing
lengthy and poignant answers to *several* questions I've had
already then I couldn't even have made it this far.  Thank you!



-- 
G. Jay Kerns, Ph.D.
Youngstown State University
http://people.ysu.edu/~gkerns/