Diversity Indices Calculator

About the Indices

Richness Measures

• Species Richness (S): The total number of species present.

• Margalef's Richness (DMg): Adjusts species count for sample size.
  Formula: DMg = (S-1)/ln(N), where S is the species richness and N is the total number of individuals.
  (Sample data only as it's designed to compensate for sampling effects.)

Diversity Measures

• Shannon-Wiener Index (H'): Also known as the Shannon Diversity Index or simply the Shannon Index. Accounts for both abundance and evenness.
  Higher values indicate greater diversity. Minimum value of 0 with no upper limit, although real-world ecological data usually falls between 1.5-3.5.
  Formula: H' = -Σ(pᵢ×ln(pᵢ)), where pᵢ is the proportion of individuals belonging to the i-th species.
  Shannon Diversity is often transformed to produce the effective number of species by taking its exponential, eᴴ' - this represents the number of equally common species that would produce the same diversity value.
  (Sample data only as it assumes the data represents a sample from a larger population; this calculator applies a bias correction factor of N/(N-1) to account for this, which is why other online calculators may give a slightly lower value for H'. To undo this correction and obtain the raw, unadjusted Shannon Index, simply multiply the calculator's output by ((N−1)/N).)

• Brillouin Index (HB): Similar to Shannon-Wiener but for complete enumeration, providing an exact calculation of diversity without relying on probability estimates from sample data.
  No fixed upper limit, with higher values indicating greater diversity.
  Formula: HB = (ln(N!)−Σln(nᵢ!))/N, where N is the total number of individuals and nᵢ is the number of individuals of the i-th species.
  (Complete census only as it's designed for when you've counted every individual and does not account for the sampling variability and potential biases that arise when not all individuals are observed.)

• Simpson's Index (D): Probability that two randomly selected individuals belong to the same species. Accounts for both abundance and evenness.
  Range: 0-1, where 0 = infinite diversity.
  Formula: D = Σ(pᵢ²), where pᵢ is the proportion of individuals belonging to the i-th species.
  Since a higher value indicating lower biodiversity can seem counterintuitive, Simpson's Index is instead sometimes expressed 1-D, which is known as the Gini-Simpson Index, or 1/D, the Inverse Simpson Index.
  (Complete census only as it assumes you know the true proportions of each species.)

Evenness Measures

• Pielou's Evenness (J'): Also known as Shannon's Evenness. Derived from H', measures how close species abundances are to being equal.
  Range: 0-1, where 1 = complete evenness.
  Formula: J' = H'/ln(S), where H' is the Shannon Index and S is the species richness.
  (Sample data only as it's based on Shannon-Wiener.)

• Simpson's Evenness (E1/D): Based on Simpson's Index, measures evenness independent of richness.
  Range: 0-1, where 1 = all species are equally abundant. E1/D can also be represented simply as E.
  Formula: E = (1/D)/S, where D is Simpson's Index and S is the species richness.
  (Complete census only as it's derived from Simpson's Index.)

Dominance Measure

• Berger-Parker Dominance (d): Simple measure of dominance, expressed as the proportional abundance of the most abundant species.
  Range: 1/S to 1, where higher values indicate greater dominance.
  Formula: d = n_max/N, where n_max is the number of individuals of the most abundant species and N is the total number of individuals.
  (Available for both as it's a simple proportion.)

Sample vs Census Data

The distinction between sample and complete census data is important:

• Use the Sample Data option when you've surveyed a portion of a larger population

• Use the Complete Census option when you've counted every individual in the population

Different indices are shown depending on your data type because some indices are mathematically designed for samples (incorporating sampling error), while others assume complete knowledge of the population.