[R-sig-eco] Change in rotated NMDS scores as a response variable

[Gavin Simpson]

On Fri, 2011-02-18 at 10:41 -0800, Erik Frenzel wrote:
> Hello all,
> I'm interested in adapting a technique from a recent paper
> 
> Harrison, S., E. I. Damschen and J. B. Grace 2010. Ecological
> contingency in the effects of climate change on forest herbs.
> Proceedings of the National Academy of Sciences (USA), 107:
> 19362-19367.
> 
> In which a plot's change in NMDS scores over time was used as a
> response variable:
> 
> "To measure the overall resemblance of any given herb community to
> communities found in warm (steep, southerly) versus cool (moderate,
> northerly) topographic microclimates, we used an ordination approach
> (also see 28). We ordinated the
> herb data using NMS ordination in PC-ORD version 4.14 (39), excluding
> species found in <5% of samples. We rotated axis 1 of the ordination
> to maximize its correlation with Whittaker’s topographic moisture
> gradient, so that a low axis 1 score indicated a community in a mesic
> environment such as a moderate north-facing slope, and a high axis 1
> score indicated a community in a warm environment such as a steep
> south-facing slope. Under a warming climate, we expect the community
> at any given site to show a higher axis 1 score in 2007–2009 than in
> 1949–1951, indicating that herb composition has shifted over time in
> the same direction that composition changes over space from mesic
> (cooler and moister) to xeric (warmer and drier) topographic
> microclimates. For each site we calculated the difference between its
> 1949–1951 and 2007–2009 axis 1 ordination scores. In this case, a high
> value means a community that has shifted to become more dominated by
> xeric-adapted species."
> 
> Jari Oksanen has a post on the the r-forge page
> (https://r-forge.r-project.org/forum/message.php?msg_id=1311&group_id=68)
> warning against using rotated NMDS scores in a Structural Equation
> Model. Are there problems with using a "change in scores" as a
> response variable in this kind of hypothesis testing?

I'm genuinely underwhelmed by this approach. i) there isn't such a thing
as nMDS axes so does it make sense to take some 1-d coordinate system
out of a 2-d coordinate system and relate it to an external variable? It
would be like trying to identify patterns in all the cities of the world
on the basis of what line of longitude they happened to lie on. Where
this sort of thing does make sense is in methods that do identify
orthogonal components from a data matrix such that axis 1 explains a
component of the variation in the data, and axis 2 another, different
(orthogonal) component of the variation.

If this were me, I would have taken the 2-d nMDS configuration and
fitted a response surface for Whittaker's topographic moisture into the
ordination (using ordisurf) and then take the fitted values of the
response surface for each site as the species-related topographic
moisture "information", which could be plotted as a function of time.

HTH

G

> This was done in PC Ord.  Has anyone used "metaMDSrotate" in vegan to
> do this kind of analysis in R? Does anyone have any examples or code
> they'd be willing to share or point me to?
> 
> Thanks,
> Erik
> 
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