R help - Dec 2010 - procrustes results affected by order of sites in input file

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:

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,



-- 
Christy Dolph
Ph.D. Candidate
Water Resources Science
University of Minnesota
200 Hodson Hall, 1980 Folwell Ave
St. Paul, MN 55108
dolph008@umn.edu
612-868-1565

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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.

G
> 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,
> 
> 
> 
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