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Hope this newbie question is the right question for this site:

Suppose I would like to compare the composition of ecological communities at two sites A, B. I know all three sites have dogs, cats, cows, and birds, so I sample their abundances at each site (I don't really have an "expected" abundance for each animal at each site).

If I count, say, five of each animal at each site, then the A and B are very "similar" (in fact, they're the "same").

But if I find 100 dogs, 5 cats, 2 cows, and 3 birds at site A. 5 dogs, 3 cats, 75 cows, and 2 birds at site B. Then I would say that the sites A and B are "dissimilar", even though they have the exact same species composition.

(I read up on the Sorensen's and Bray-Curtis indices, but looks like they only consider absence/presence of the dogs, cats, etc., and not their abundances.)

Is there a statistical test to determine this?

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    $\begingroup$ Bray-Curtis dissimilarity may do the job... A great ressource is the book 'Numerical Ecology' by Legendre & Legendre (1998). $\endgroup$ – EDi Apr 6 '11 at 22:31
  • $\begingroup$ All the answers so far have been very useful, and I really appreciate all the reference material you provided. I wish I could mark more than one answer! Thanks for everyone's help. $\endgroup$ – hpy Apr 7 '11 at 14:52
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I will concur with what has been mentioned that Bray-Curtis can handle abundance as well as presence/absence, also to add another good book to the mix: Analysis of Ecological Communities by McCune and Grace.

There are a lot of factors to consider as you compare ecological communities and I don't think there is a single test that will do the job. The appropriateness of the test will depend a lot on the type of question you are asking about the communities and the nature of your dataset. Common approaches include ordination techniques, which array sites within a multidimensional taxon-space. However if you truly only have 2 sites then this is not likely to work. Mantel tests correlate a the distance matrix based on composition (e.g., the pairwise Bray-Curtis distance across all sites) with a distance matrix based on other potential factors of influence. The simplest case can be just the euclidean distance between the sites in space. Cluster analysis groups sites with respect to their community composition.

In general I would take the approach of using a subset of the many statistical tools described in any of the above books to provide a statistical description of the differences between the communities in question. There is no single measure of the difference in community composition so the stats are used to synthesize multidimensional data into a more easily interpretable form.

EDIT: I also just thought of this paper which lays out many of the different options pretty clearly and thoroughly.

Anderson, M. J. et al. 2011. Navigating the multiple meanings of Beta diversity: a roadmap for the practicing ecologist. Ecology Letters 14:19-28

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If you want to test this hyothesis, you can use an Analysis of Similarity (based on Bray Curtis or other available ones), there is a procedure named ANOSIM wich is implemented in PRIMER software. You can do One way, nested or Two-way analysis. Another (better) option is to run a multiple permutational analysis of variances, a nice procedure is avalaible in the routine PERMANOVA (available at http://www.stat.auckland.ac.nz/~mja/Programs.htm) Once you have test for signficant differences among sites, you can follow up in order to know which species are responsable for the observed differences (IndVal routine, or SIMPER routine). hope it helps

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Since you mention Sorensen index, it seems you need a dissimilarity score rather than a dissimilarity test. (A score will give a numerical value indicating how different they are. A test will tell you whether the difference is significant with a given probability.)

You can represent species abundance at each location by a histogram. This histogram can be normalized if you just care about relative abundance (e.g. that cats are twice as abundant as dogs), or unnormalized if you care about absolute numbers as well.

There are many ways to measure dissimilarity of histograms. Some of the popular ones are:

  • Chi-squared statistic
  • L2 distance
  • Histogram intersection distance
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Bray-Curtis and other similar indices do incorporate differences in species abundance. In addition to Legendre and Legendre, I would also recommend Charles Krebs' book, Ecological Methology (1999).

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