Hi,

I am trying to use pcnm in vegan to correct for spatial autocorrelation in
analyses of influences of environmental factors on multivariate community
composition, as well as univariate analyses of diversity and abundance.  I
have several questions.

1.  PCNM requires a threshold and I am aware that the value that keeps all
sites connected is most commonly used.  My data has a group of 4 sites
spaced <70 m apart that are over 3 km from another group of 30 sites spaced
less than 105 m apart, and one more site which is 700 m from that group.  It
seems more reasonable to me to use a threshold of 105 m than one of >3km,
especially since my study focuses on ground arthropods.  This would create 3
groupings of sites.  If I use the >3km threshold I get only 8 pcnm axes,
whereas if I use 105 m I get 23 pcnm axes.  What are the dangers of using
105 m for the threshold?

2.  I know that the standard procedure for pcnm involves removing or
ignoring axes with negative eigenvalues.  When I use the pcnm function in
vegan, I get more eigenvalues than I have axes.  If I assume that the first
values correspond to the first axes, then all the axes in my analyses have
positive eigenvalues, but then the "extra" values are all negative.  What
are these "extra" eigenvalues?

Example pcnm output where there were 23 pcnm axes:
$values
 [1] 340612.551794 275201.943899 254617.670597 249522.356402 241355.932111
 [6] 232599.706078 221011.191557 208556.972230 194474.144337 179033.878718
[11] 162579.353225 145582.679707 127575.743994 109566.616764  93787.878039
[16]  90927.033541  72913.847274  54674.111809  36327.172822  19435.731961
[21]   2953.768395   2473.083146   1232.488285     -3.043711 -12227.230353
[26] -26474.770134 -38750.362117 -50240.777206 -59844.032399 -67540.203768
[31] -73820.515090 -78557.683846 -81310.242921

3. The next step in pcnm involves selecting pcnm axes with significant
effects on responses.  I know that it has been suggested to use forward
selection routines in cca to select these axes.  I'm also aware of some of
the limitations of this technique and the suggestion that forward selection
should have additional criteria. Namely, that forward selection should only
be used if the full model with all terms is significant and should also
compare the adjusted R2 with each term added to that of the original full
model.  If I perform an analysis with all non-negative pcnm terms and the
model is not significant, does this mean there is no spatial autocorrelation
and no selection procedure is needed?  If it is significant, then I need
adjusted R2 values to perform the forward selection, but I don't see how to
get these using cca in vegan.

Additionally, for my multivariate analyses, I am using adonis to perform
statistical tests, not cca.  Therefore, should I also be using adonis to
look for significant pcnm axes?  I haven't seen this done, but do not see
potential drawbacks.  Are there any?

Thanks!

-- 
Kevin E. McCluney, PhD
Post-doctoral Researcher
Affiliate Scientist, Natural Resource Ecology Laboratory, Colorado State
University
Contractor, US Geological Survey, Fort Collins Science Center
Lab phone: 970-491-2414
Mail: Dept of Biology
1878 Campus Delivery
Colorado State University
Fort Collins, CO  80523-1878

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