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Biological Diversity

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Calculating Biodiversity Indices

This JavaScript outputs diversity indices (Species richness, Exponential Shannon, Inverse Simpson, Inverse Relative Dominance) of sites and their regional diversity indices (alpha, beta, and gamma), by using a community data matrix. The input data file should be a csv file (comma separated). The first row includes the area name, followed by the species names. The data on the first row are not used in the calculation. The community data matrix is on the second and following rows: the site names are on the first column followed by the number of individuals of each species at each site. The use of the results would like the responsibility of the user.

Open your data file (csv). You will see the results below.


Indices of Biodiversity

Biodiversity index measures complexity of ecological community compositions. Shannon's H' is very popular but other indices are also useful.

Diversity profile

Renyi's diversity profile can summarize several diversity indices, by changing a sensitivity parameter q. When S is the number of species, and pi is the proportion of abundance for species-i in the decreasing order of species rank abundance (p1 is the max of pi), the diversity is defined as: qD=(Σpiq)1/(1-q). Several popular indices can be represented within the series of q.

  • Species richness: 0D=S
  • Exponential Shannon: 1D=exp(-Σpilog(pi))
  • Inverse Simpson: 2D=1/Σpi2
  • Inverse relative dominance: ∞D=1/p1

Increasing the parameter q from 0 to ∞, the diversity qD decreases gradually. This curve is the diversity profile. The parameter q changes weights of species in calculating the diversity index. When q=0, all species from dominant to rare have the same weight. As increasing q, the weights of the dominant species increase and those of the rare species decrease. At q=∞, only the most dominant species contributes to the diversity calculation.

These indices have the same unit of the species richness, representing effective number of species.

The diversity index is based on the relative proportion of species pi, so the index value does not change when the abundance changes but the composition is the same.

Alpha, beta, and gamma diversity

Gamma diversity represents the diversity in the total region, and alpha diversity is the diversity of the sites (habitats) within the region. Beta-diversity is the spatial heterogeneity of the diversity defined as gamma / alpha. Where total number of sites is N and the proportion of i-th species at site-j is pij,

  • alpha diversity: qDalpha=(Σ(Σpijq)/N)1/(1-q), when q=1 1Dalpha=exp(-Σ(Σpilog(pi))/N)
  • beta diversity: qDbeta=qDgamma/qDalpha
  • gamma diversity: qDgamma=(Σ(Σj pij/N)q)1/(1-q), when q=1 1Dgamma=exp(-Σ(Σj pi/N)log(Σj pi/N)).

The average of the species richness over the sites shows the alpha diversity only when q=0, not in other cases. Averaging the proportion of species pij over the sites makes the gamma diversity. In this definition, beta diversity represents the number of unique community in the region.

References

  • Magurran AE, McGill BJ (2011) Biological Diversity: Frontiers in measurement and assessment. Oxford
  • Takada Y, Tezuka N (2016) Biodiversity indices in tidal-flat fisheries. Aquabiology 227: 633-640

This page is a part of activities of "A feasibility study on biodiversity assessment methods in fishing ground environment" supported by the Fisheries Research Agency, Japan.
Yoshitake TAKADA updated 2018/2/20

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