Tim and Jari,

Jari wrote:
"The problem with resampling is that you get randomized results, and the degree of randomization depends on the subsampling proportion. You can try with rrarefy() function in function that takes random rarefied samples. However, if your data 'x' has 12 000 butterflies, then rrarefy(x, 100) will be more random than if 'x' already had 100 individuals (and it is unchanged). The rrarefy() does resampling without replacement. If you try resampling with replacement, you will lose species in all cases as you take only about 63.2% of the individuals in your new samples.  The problems are how to comppare (different) random results, and how to handle the sampling proportions."


I did a resampling procedure similar to that. 
My intention was to obtain a ordination of sites and thus my solution to the problem cited by Jari was to combine ordinations of subsamples using a procrustes. 
This is the description in my joint article (J. Insect Conserv. 15:643-51):
"The procedure consisted of (1) random sampling of 103 species in each of the 26 localities,
(2) calculation of a Simpson dissimilarity matrix among the 27 localities, (3) ordination of the dissimilarity matrix using PCoA, and (4) repetition of steps 1-3 100 times. Similar ordination patterns can be differently expressed in a bivariate plot. We employed the procrustean analysis to compare the ordination of the full dataset and each of the 100 ordinations using subsamples. To summarize the comparisons, we obtained mean values of the procrustean scores of the subsamples on two axes, and plotted them in the same ordination diagram as the full samples."

The ordination figure included in the article includes the average-scores of the procrustes as well as the scores for the full samples (last sentence of the quoted text above). There was not a big difference (but notice we used the simpson index that is supposed to be quite insensitive to differences in species richness).

A final comment: Initially, I tried NMDS but got lots of problems to do the procrustes. PCoA worked fine. 

Sincerely, 
Adriano Sanches Melo
Departamento de Ecologia - ICB
Universidade Federal de Goiás - Brazil
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