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The Brillouin index, HB, is calculated using:
where N is the total number of individuals in the sample, ni is the number of individuals belonging to the ith species and s the species number.
The Brillouin index measures the diversity of a collection, as opposed to the Shannon index which measures a sample.
Pielou (1975) recommends this index in all situations where a collection is made, sampling was non-random or the full composition of the community is known.
The value obtained rarely exceeds 4.5 and both the Brillouin and Shannon Indices tend to give similar comparative measures.
This information measure should be used in favour of the Shannon index when the species differ in their capture rates.
To compare two indices see Testing for significant differences between indices.