You could calculate a Bray-Curtis similarity index matrix.  That will give you the percent similarity between each pair of sites.  That matrix can be used as a basis for a number of subsequent analyses.  You can then visualize the data with a non-metric multidimensional scaling plot  (n-MDS).  You can also run an analysis of similarity (ANOSIM) or a permutational ANOVA (PERMANOVA), both of which are mutivariate analogs of ANOVAs. 

A lot depends on what question you want to ask with this data and how it was collected.  Did you do multiple quadrats and identify all the species in each?  If that's the case (i.e., if you have multiple samples from each site) then you have a lot of options as far as comparing sites.  If you did a complete survey of each site and IDed all species, that could be a bit of a problem as sites with a smaller area are likely to have fewer species just by chance.  If that's the case you may need to account for area sampled.

Thanks William. I have used the Sorensen's similarity measure because I can use it to compare each site with one master "ghost" (or imaginary) site populated with the taxa that are the important ones in my study! If one uses other methods then each pair of comparisons do not necessarily compare the same set of taxa throughout, do they? I am afraid I am not a stats boffin, but I have struggled for some time to get my mind around them, with the result that this seems like the best method for my purposes. What I want to know is - has anyone else used the same method, and if so with good or bad results (and acceptance) and if not, why not! The question I am asking is quite simple, how much similarity is there between sites regarding a set of 50 important taxa hared by the sites. There are another 15 taxa of lesser importance which are sometimes shared as well and they are also put into the ghost site. The sites are widely scattered in about 6 Biomes and many different vegetation types, the fact that they are so similar tends to suggest a possible anthropogenic process. But I have to show statistically first that in fact they are similar!! I did a complete survey fo each site and Id'd all the species present - so that makes it difficult as you say! However the size of the site does not make much difference to the presence and absence data regarding the species which are most common - even the smallest site may have up to 15 important species present.  

The Sorensen's and B-C similarities are actually the same if used on presence-absence data.  B-C can be used on abundance/density data as well so it’s just a little more general.  Anyway, as long as you have a complete dataset, i.e. you have a 0 or 1 for every species at every site you are comparing the same set of taxa.  So no need of ghosts.  It is perfectly valid to cull the rare species if your question just concerns the common ones.  What you do, is get your similarity matrix and run an ANOSIM with Biome as the factor.  If the Biomes are as similar as you hypothesize you should get a low Global R value and a high p value.  p > 0.05 will allow you to say there is no statistical difference among the sites.  You can follow up with a SIMPER (similarity percentage) analysis again with Biome as a factor.  This will give you the average similarity within each of the Biomes, the average dissimilarity between each pair of Biomes and a list of the species that are most important in contributing to the similarity/dissimilarity.  What you should see (if the Biome are all similar) is the average similarity within each Biome is about the same as 1-dissimlarity between the Biomes.  That is, if the sites in Biome 1 are on average 60% similar and the average dissimilarity with Biome 2 is 40% then the sites in Biome 1 are as similar to the sites in Biome 2 as they are to each other.  These analyses should allow you to demonstrate clearly how similar the different Biomes are. 

I noticed you hail from South Africa and that was making me a bit homesick.  I grew up in Botswana (and somehow ended up in Alaska of all places) and we took plenty of holidays and trips down to South Africa as well.  I particularly miss Southern Africa this time of year when the days are so short and we don’t get much sun.

Hello William. You gave me a lot to think about and look up! And thanks for writing so that I can understand it! I would very much like to use the ANOSIM and SIMPER and can see how valuable this would be for my work. But I do not have the CAP package and it is horrendously expensive at the rate our Rand has sunk to. A friend tried to download it from his PC to my laptop a couple of years ago but at the time I simply did not understand it nor did it work properly, and then the laptop was stolen! I live a long way from Rhodes University in Grahamstown where I am registered, and get up there very seldom. Yesterday I tried downloading a trial and a demo version advertised as Free! They are both demo's which show you how to use it but you can't enter your own data, so no help there. I would very much like to ask you some more questions, but maybe we should email rather? My email is [email protected]

If I can set up my data so that someone else can run it for me maybe I can persuade someone at Rhodes - unfortunately they do not have an ecological stats person at the moment and can't seem to find one either, so have not been able to help me much. If I had research funding I could pay someone, but don't have any sadly.

I am sure you must get homesick for sun and wild places with wild animals and plants etc? I simply cannot imagine living in Alaska with the dark winters and freezing cold, although I am sure it is so beautiful too and lovely in summer? We are lucky here in the southern Cape (Hoekwil, a small village in the Outeniqua foothills above Wilderness), we have had wonderful rains and not too much heat this summer, unlike much of the rest of Southern Africa with drought and heatwaves.