Simpson index
Encyclopedia
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 belong to the same species. The simplicity of Simpson's Diversity Index has led it to be used frequently.
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
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
This quantity was introduced by Edward Hugh Simpson in 1949. The Herfindahl index
in competition economics is essentially the same.
If
is the number of individuals of species 
which are counted, and 
is the total number of all individuals counted, then
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.
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
, it is often used to quantify the biodiversity
Biodiversity
Biodiversity is the degree of variation of life forms within a given ecosystem, biome, or an entire planet. Biodiversity is a measure of the health of ecosystems. Biodiversity is in part a function of climate. In terrestrial habitats, tropical regions are typically rich whereas polar regions...
of a habitat. It takes into account the number of species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
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.
Overview
For plantPlant
Plants are living organisms belonging to the kingdom Plantae. Precise definitions of the kingdom vary, but as the term is used here, plants include familiar organisms such as trees, flowers, herbs, bushes, grasses, vines, ferns, mosses, and green algae. The group is also called green plants or...
species the percentage cover in a square is usually used; for animal
Animal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
species, for example in a river, the number of organisms
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...
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
is the fraction of all organisms which belong to the i-th species, then Simpson's diversity indexSimpson index
Simpson's 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...
is most commonly defined as the statistic
This quantity was introduced by Edward Hugh Simpson in 1949. The Herfindahl index
Herfindahl index
The Herfindahl index is a measure of the size of firms in relation to the industry and an indicator of the amount of competition among them. Named after economists Orris C. Herfindahl and Albert O. Hirschman, it is an economic concept widely applied in competition law, antitrust and also...
in competition economics is essentially the same.
If
is the number of individuals of species which are counted, and is the total number of all individuals counted, thenis an estimator for Simpson's index for sampling
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
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
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
in 1949.