Use this biodiversity measure when counts or incidences were collected with comparable sampling effort and the estimator matches the study design. It can summarize richness, dominance, evenness, or compositional difference.

Species A count

An integer count greater than or equal to 0, expressed in individuals.

Species B count

An integer count greater than or equal to 0, expressed in individuals.

Species C count

An integer count greater than or equal to 0, expressed in individuals.

The implementation follows this calculation rule: Compute the Brillouin diversity index HB = (ln(N!) - sum(ln(ni!))) / N from three species counts using loop-based log factorials for communities up to 10000 individuals.^[1]

Brillouin index

The calculated brillouin index.

Different diversity indices weight rare and common taxa differently. Detection probability, sample coverage, taxonomic resolution, zero counts, and unequal effort can dominate comparisons; proxy estimators are not interchangeable with their full published forms. Preserve the input values and units so the result can be audited and recalculated.

Report observed richness, abundance or incidence data, and sampling effort beside the index. Coverage-based rarefaction, accumulation curves, and more than one Hill-number order provide a fuller view of community structure.

• Simpson Index D

  Compute the Simpson diversity index D for three species counts in a sample.

• McIntosh Index

  Compute the McIntosh diversity index for a three species community from Euclidean distance in species space.

• Shannon Evenness

  Compute Shannon evenness E = H / ln(S) from the Shannon natural-log diversity index and species count, requiring at least two species.