Simpson index

The Simpson Index is an index of diversity in ecology .

It was developed in 1949 by Edward H. Simpson to describe diversity (cf. biodiversity ) and is one of the most frequently used diversity indices , along with the Shannon index and the evenness calculated from it .

The Simpson index expresses the probability that two individuals selected at random from all individuals in a recording do not belong to the same species. To do this, the probabilities of selecting a certain species and selecting this species again (the first individual is no longer available) are multiplied and then this product is added up for all species. ${\displaystyle i}$

So the Simpson index is calculated as follows: ${\displaystyle D}$

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

wherein the number of individuals of a species , representing the total number of individuals. D is equal to 0 if all individuals belong to the same species, i.e. there is no diversity at all. The greater the diversity, the closer D approaches 1. ${\displaystyle n_{i}}$ ${\displaystyle i}$ ${\displaystyle n}$

As a rule, no individuals are counted in vegetation surveys, but the area proportions ("cover") of the individual species are estimated. It is now a question of the probability of not finding the same species at two randomly chosen points within a recording area. With cover values ​​instead of individuals, the formula is simplified because the probabilities for the first and second point are the same:

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

where the proportion of the species in the sum of all individual coverages. ${\displaystyle p_{i}}$ ${\displaystyle i}$

literature

• Edward Hugh Simpson : Measurement of diversity , Nature , 1949, 163: 688, doi : 10.1038 / 163688a0