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Simpson's diversity index (also known as species diversity index) is one of a number of diversity indices, used to measure diversity. In ecology, it is often used to quantify the biodiversity of a habitat. It takes into account the number of species present, as well as the relative abundance of each species. The Simpson index represents the probability that two randomly selected individuals in the habitat will not belong to the same species. The simplicity of Simpson's Diversity Index has led it to be used frequently.

Overview

For plant species the percentage cover in a square is usually used; for animal species, for example in a river, the number of organisms of a species is used. The reason percentage cover is used is because it is usually very difficult to count all the individual plants.

If ${\displaystyle p_{i}}$ is the fraction of all organisms which belong to the i-th species, then Simpson's diversity index is most commonly defined as the statistic

${\displaystyle D=\sum _{i=1}^{S}p_{i}^{2}.}$

This quantity was introduced by Edward Hugh Simpson in 1949. The Herfindahl index in competition economics is essentially the same.

If ${\displaystyle n_{i}}$ is the number of individuals of species ${\displaystyle i}$ which are counted, and ${\displaystyle N}$ is the total number of all individuals counted, then

${\displaystyle {\hat {D}}={\frac {\sum _{i=1}^{S}n_{i}(n_{i}-1)}{N(N-1)}}}$

is an estimator for Simpson's index for sampling without replacement.

In this form, D ranges from 0 to 1, with 0 representing infinite diversity and 1 representing no diversity.

When using the Simpson Index for lower numbers, misleading results can be obtained, with obviously less diverse areas having a higher index than they should. One way around this when studying on land is to include bare earth as an extra species, which yields more realistic results. A low Simpson index value equates high diversity, whereas a high value correlates to a low diversity (thus the index is typically subtracted from 1, as in the above formula).

The Simpson index was first proposed by the British statistician Edward H. Simpson in a paper in Nature in 1949.

See also

• Biodiversity
• Species richness
• Shannon index

References

• Edward H. Simpson (1949) Measurement of diversity. Nature 163:688 see http://www.wku.edu/~smithch/biogeog/SIMP1949.htm

External links

• http://www.countrysideinfo.co.uk/simpsons.htm

• Measurement of biodiversity