Bray-Curtis similarity

The most commonly-used similarity coefficient for biological community analysis, because it obeys many of the ‘natural’ biological guidelines in a way that most other coefficients do not (see CiMC), is the Bray-Curtis similarity, defined between samples 1 and 2 as:

$$S _ {17} = 100 \left[ 1 - \frac{\sum_{i} | y_{i1} - y_{i2} | }{\sum_{i} y_{i1} + \sum_{i} y_{i2} } \right] \equiv 100 \frac{ \sum_i \min \left( y_{i1}, y_{i2} \right) }{ \left( \sum_{i} y_{i1} + \sum_{i} y_{i2} \right) / 2} .$$

The two forms may not look identical but they are! Here $y_{i1}$ is the count (or biomass, % cover, …) for the ith (of p) species from sample 1, and $\sum_i$(…) denotes summation over those species. Original references to coefficient definitions are not given here (nomenclature is always a source of debate!) – see L&L, whose numbering scheme is followed where possible, hence $S_{17}$ for Bray-Curtis.

Open the workspace C:\Examples v7\Ekofisk macrofauna\Ekofisk ws from earlier, and click on the Square root counts sheet (obtained earlier with Pre-treatment>Transform(overall)>Square root). Take Analyse>Resemblance>(Measure•Bray-Curtis similarity) & (Analyse between•Samples), which are the defaults for this data type. A lower triangular matrix is produced, Resem1, which you should rename B-C on sq rt. Edit>Properties (or right-clicking over the matrix to get Properties) shows it is of Resemblance type•Similarity from 39 samples. The History box carries through the knowledge of how it was created to a subsequent Cluster or MDS ordination plot. This box is not user-editable, though the Title and Description boxes can be altered; changes to the Title are carried forward to a subsequent plot but not backward to the data sheet Square root.

Now repeat Resemblance directly on the original Ekofisk macrofauna counts, without the Pre-Treatment transformation. PRIMER tries to help – a warning message appears that no transform has been applied; community matrices usually require some transformation before calculating Bray -Curtis (though you can happily ignore this warning if you are interested in the pattern of the few most dominant species only). Cancel the calculation and resave the Ekofisk ws workspace.