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| '''Simpson's diversity index''' (also known as '''species diversity index''') is one of a number of ], used to measure diversity. In ], it is often used to quantify the ] of a habitat. It takes into account the number of ] 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 belong to the same species. The simplicity of Simpson's Diversity Index has led it to be used frequently. | |||
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| == Overview == | |||
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| For ] species the percentage cover in a square is usually used; for ] species, for example in a river, the number of ] of a species is used. The reason percentage cover is used is because it is usually very difficult to count all the individual plants.<!-- This is hardly unique to plants - what about barnacles, for example? --> | |||
| If <math>p_i</math> is the fraction of all organisms which belong to the i-th species, then ] is most commonly defined as the statistic | |||
| :<math> D = \sum_{i=1}^S p_i^2.</math> | |||
| This quantity was introduced by ] in 1949. The ] in competition economics is essentially the same. | |||
| If <math>n_i</math> is the number of individuals of species <math>i</math> which are counted, and <math>N</math> is the total number of all individuals counted, then | |||
| :<math> \hat{D} = \frac{\sum_{i=1}^S n_i (n_i -1)}{N (N-1)} </math> | |||
| is an estimator for Simpson's index for ] 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 ] in a paper in '']'' in 1949. | |||
| ==See also== | |||
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| == References == | |||
| * ] (1949) Measurement of diversity. '']'' '''163''':688 see http://www.wku.edu/~smithch/biogeog/SIMP1949.htm | |||
| == External links == | |||
| * http://www.countrysideinfo.co.uk/simpsons.htm | |||
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