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I have 2 batches of tree species and abundance data collected for a city. The difference between them is the sampling strategy - one was random unstratified, and the other was stratified and clustered. At a glance the species mixes and relative abundances are fairly similar but i want to test this statistically. I have considered Bray curtis but this test has the assumption that the samples come from identically sized areas, which these arent - the random sample covers a much smaller area of the city.

How can i compare these populations?

thanks

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Null model approaches are generally used in Ecology in these situations. I understand the question to mean: do the two sampling strategies draw from the same underlying species-abundance distribution?

Here is what I would do:

1) Randomly rarefy the dataset with more individuals until it contains the same number of individuals as the dataset with fewer individuals. Ultimately the entire analysis can be repeated several times, using different instances of the random rarefaction in this step.

2) Compute an appropriate dissimilarity metric between the two communities (Bray-Curtis is good, but other metrics can also be useful).

3) Compute two null distributions for the dissimilarity metric using the following procedures. A) Randomly swapping the totals corresponding to each species between datasets. Repeat many times, and calculate the dissimilarity metric each time. B) Pool all of the individuals in both datasets, and then randomly re-sample them into two separate communities. Repeat many times, and calculate the dissimilarity metric each time.

4) Compare the true dissimilarity value to the null distribution, to see whether it reflects samples that are more distinct than you could expect by random sampling from a single species abundance distribution.

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