[R] procrustes results affected by order of sites in input file

Gavin Simpson gavin.simpson at ucl.ac.uk
Thu Dec 2 13:02:07 CET 2010

On Wed, 2010-12-01 at 14:19 -0600, Christine Dolph wrote:
> Dear All,
> I am using a Procrustes analysis to compare two NMDS ordinations for the
> same set of sites. One ordination is based on fish data, the other is based
> on invertebrate data. Ordinations were derived using metaMDS() from the
> {vegan} library as follows:
> fish.mds<-metaMDS(fish.data, distance="bray", k=3, trymax=100,
> wascores=TRUE, trace=TRUE, zero="add")
> invert.mds<-metaMDS(bugcal.a, distance="bray", k=3, trymax=100,
> wascores=TRUE, trace=TRUE, zero="add"),
> where fish.data and invert.data are site-by-abundance matrices for fish and
> invertebrates, respectively.
> I have then used protest() to test the significance between the two
> ordinations:

Simple things first:

You did have a set.seed() call before the protest() call didn't you? In
fact, I'd probably put set.seed() calls before the two metaMDS() calls
as well.

The ordering should have no impact at all, but the random starts in
metaMDS() and the random permutations in protest() will vary from run to
run unless you set the random seed to some known value.


> protest.results<-protest(fish.mds, invert.mds, scale=TRUE, symmetric=TRUE,
> permutations=999)
> The problem is, the results of the protest analysis seem to be affected by
> the original ordering of sites in the data input files. That is, if I
> re-sort one of the input files based on some criteria, I sometimes see a
> change in the strength and significance of the concordance results. In an
> attempt to figure out what is happening, I have re-ordered each dataset in a
> number of ways, and plotted the resulting ordinations. I have seen that
> while the ordering of sites in the input file does not change the spatial
> relationship between them (i.e., does not change the fundamental ordination
> solution), it can change how the sites are oriented with respect to the
> different NMDS axes. I was of the belief that a difference in orientation
> with respect to the NMDS axes should not affect the Procrustes comparison of
> two ordinations, as the protest function should be rotating and reflecting
> one matrix with respect to the other to find the closest match between them
> (i.e., it should be accounting for differences in how the two solutions are
> oriented in space). However, I appear to see different results depending on
> how sites are oriented with respect to each NMDS axis.
> When comparing two ordination solutions with Protest, is it necessary to
> ensure that the original data input files are ordered in the same way?
> Thanks in advance for any insight.
> Sincerely,

 Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
 ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
 Pearson Building,             [e] gavin.simpsonATNOSPAMucl.ac.uk
 Gower Street, London          [w] http://www.ucl.ac.uk/~ucfagls/
 UK. WC1E 6BT.                 [w] http://www.freshwaters.org.uk

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