SIMPSON INDEX: FORMULA, INTERPRETATION AND EXAMPLE - BIOLOGY - 2025

The Simpson index is a formula used to measure the diversity of a community. It is commonly used to measure biodiversity, that is, the diversity of living things in a given place. However, this index is also useful to measure the diversity of elements such as schools, places, among others.

In ecology, the Simpson index (among other indices) is often used to quantify the biodiversity of a habitat. This takes into account the number of species present in the habitat, as well as the abundance of each species.

Associated concepts

Before discussing the Simpson Diversity Index in more detail, it is important to understand a few basic concepts as detailed below:

Biological Diversity

Biological diversity is the great variety of living things that exist in a particular area, it is a property that can be quantified in many different ways. There are two main factors that are taken into account when measuring diversity: wealth and fairness.

Richness is a measure of the number of different organisms present in a particular area; that is, the number of species present in a habitat.

However, diversity not only depends on species richness, but also on the abundance of each species. Fairness compares the similarity between the population sizes of each of the species present.

Wealth

The number of species taken in a habitat sample is a measure of richness. The more species are present in a sample, the richer the sample will be.

Species richness as a measure in itself does not take into account the number of individuals in each species.

This means that species with few individuals are given the same weight as those with many individuals. Therefore, a daisy has as much influence on the richness of a habitat as 1000 buttercups living in the same place would.

Fairness

Equitability is a measure of the relative abundance of the different species that make up the richness of an area; In other words, in a given habitat the number of individuals of each species will also have an effect on the biodiversity of the place.

A community dominated by one or two species is considered less diverse than a community in which the species present have a similar abundance.

Definition

As the richness and fairness of species increase, diversity increases. The Simpson Diversity Index is a measure of diversity that takes into account both wealth and fairness.

Ecologists, biologists who study species in their environment, are interested in the species diversity of the habitats they study. This is because diversity is usually proportional to the stability of the ecosystem: the greater the diversity, the greater the stability.

The most stable communities have large numbers of species that are fairly evenly distributed in large populations. Pollution often reduces diversity by favoring a few dominant species. Diversity is, therefore, an important factor in the successful management of species conservation.

Formula

Importantly, the term "Simpson diversity index" is actually used to refer to any of the three closely related indices.

The Simpson index (D) measures the probability that two randomly selected individuals from a sample belong to the same species (or the same category).

There are two versions of the formula to calculate D. Either one is valid, but you have to be consistent.

Where:

- n = the total number of organisms of a particular species.

- N = the total number of organisms of all species.

The value of D ranges from 0 to 1:

- If the value of D gives 0, it means infinite diversity.

- If the value of D gives 1, it means that there is no diversity.

Interpretation

The index is a representation of the probability that two individuals, within the same region and selected at random, are of the same species. The Simpson index ranges from 0 to 1, like this:

- The closer the D value is to 1, the lower the habitat diversity.

- The closer the D value is to 0, the greater the diversity of the habitat.

That is, the higher the value of D, the lower the diversity. This is not easy to interpret intuitively and could cause confusion, which is why the consensus was reached to subtract the value of D from 1, leaving it as follows: 1- D

In this case, the index value also ranges from 0 to 1, but now, the higher the value, the greater the diversity of the sample.

This makes more sense and is easier to understand. In this case, the index represents the probability that two randomly selected individuals from a sample belong to different species.

Another way to overcome the problem of the "counter-intuitive" nature of the Simpson index is to take the reciprocal of the index; that is, 1 / D.

Simpson's reciprocal index (1 / D)

The value of this index begins with 1 as the lowest possible figure. This case would represent a community that contains only one species. The higher the value, the greater the diversity.

The maximum value is the number of species in the sample. For example: if there are five species in a sample, then the maximum value of the reciprocal Simpson index is 5.

The term "Simpson diversity index" is often loosely applied. This means that the three indices described above (Simpson's index, Simpson's diversity index, and Simpson's reciprocal index), being so closely related, have been cited under the same term according to different authors.

Therefore, it is important to determine which index has been used in a particular study if diversity comparisons are to be made.

In any case, a community dominated by one or two species is considered less diverse than one in which several different species have similar abundances.

Example of the calculation of the Simpson diversity index

Wildflowers present in two different fields are sampled and the following results are obtained:

The first sample is more equitable than the second. This is because the total number of individuals in the field is fairly evenly distributed among the three species.

When observing the values ​​in the table, the inequality in the distribution of individuals in each field is evidenced. However, from the point of view of richness, both fields are equal because they have 3 species each; consequently, they have the same wealth.

In contrast, in the second sample, most of the individuals are buttercups, the dominant species. In this field there are few daisies and dandelions; therefore, field 2 is considered less diverse than field 1.

The above is what is observed with the naked eye. Then the calculation is carried out by applying the formula:

So:

D (field 1) = 334.450 / 1.000x (999)

D (field 1) = 334,450 / 999,000

D (field 1) = 0.3 -> Simpson index for field 1

D (field 2) = 868.562 / 1.000x (999)

D (field 2) = 868,562 / 999,000

D (field 2) = 0.9 -> Simpson index for field 2

Then:

1-D (field 1) = 1- 0.3

1-D (field 1) = 0.7 -> Simpson diversity index for field 1

1-D (field 2) = 1- 0.9

1-D (field 2) = 0.1 -> Simpson diversity index for field 2

Finally:

1 / D (field 1) = 1 / 0.3

1 / D (field 1) = 3.33 -> reciprocal Simpson index for field 1

1 / D (field 2) = 1 / 0.9

1 / D (field 2) = 1.11 -> reciprocal Simpson index for field 2

These 3 different values ​​represent the same biodiversity. Therefore, it is important to determine which of the indices has been used in order to make any comparative study of diversity.

A value for the Simpson index of 0.7 is not the same as a value of 0.7 for the Simpson diversity index. The Simpson index gives more weight to the most abundant species in a sample, and the addition of rare species to a sample causes only small changes in the value of D.

References

1. He, F., & Hu, XS (2005). Hubbell's fundamental biodiversity parameter and the Simpson diversity index. Ecology Letters, 8 (4), 386–390.
2. Hill, MO (1973). Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology, 54 (2), 427–432.
3. Ludwig, J. & Reynolds, J. (1988). Statistical Ecology: A Primer in Methods and Computing (1 ^st). John Wiley & Sons.
4. Magurran, A. (2013). Measuring Biological Diversity. John Wiley & Sons.
5. Morris, EK, Caruso, T., Buscot, F., Fischer, M., Hancock, C., Maier, TS,… Rillig, MC (2014). Choosing and using diversity indices: Insights for ecological applications from the German Biodiversity Exploratories. Ecology and Evolution, 4 (18), 3514–3524.
6. Simpson, EH (1949). Measurment of Diversity. Nature, 163 (1946), 688.
7. Van Der Heijden, MGA, Klironomos, JN, Ursic, M., Moutoglis, P., Streitwolf-Engel, R., Boller, T.,… Sanders, IR (1998). Mycorrhizal fungal diversity determines plant biodiversity, ecosystem variability and productivity. Nature, 396 (6706), 69-72.