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I am trying to quantify similarity between these two locations taking into account species frequency:

Chicago
  Blue Jay: 0.79
  American Crow: 0.25
  Blackpoll Warbler: 0.04

Houston
  American Crow: 0.6
  Great-tailed Grackle: 0.34
  Blue Jay: 0.3

What is the best statistical method to use? Is it Shannon-Wiener Index?

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I'm not sure about if this should be ans answer or a long comment, but I hope it can be helpful.

My first thought is that if you are going to compare only two points, you will have only one measure of distance, and a single measure is only meaningful if it can be compared with something else. Then, you need to use a measure that had been used for other locations.

Anyway, if you are going to measure distances between more than two locations (or samples, or times), you can get meaningful comparisons even using a distance nobody used before (e.g. you might be able to show that location A is close to location B and location C is very different from locations A and B).

I'm not a specialist in your field but I think Shannon-Wiener Index isn't useful for your goal. Shannon-Wiener Index is a measure of diversity, and by using it you will see if both locations have the same diversity or different diversities, but beware that two locations can have the same Shannon-Wiener Index if they have the same proportions of different species (e.g. location A with 100% blue jay and nothing else has exactly the same diversity than location B with 100% american crow and nothing else, in spite that proportions can't hardly be more different).

Your proportions are normalized histograms or profiles, that is, lists of proportions that sum 1. To compare such histograms, it may be useful to resort to correspondence analysis and use chi-squared distance.

Anyway, I'm not a specialist in correspondence analysis nor in ecology and I can't tell if use of chi-squared distance in your field is common.

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  • $\begingroup$ thank you for your thoughts. I am comparing thousands of points like this, so I am looking for a distance measurement. I started with Euclidean distance between the communities and this seems to work fairly well when I combine it in a correlation matrix. Your explanation of Shannon-Wiener index was helpful--not what I needed. $\endgroup$
    – zdebruine
    Commented Jul 22, 2016 at 11:19

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