# What is the Shannon index and what is it for?

1485
Sherman Hoover

The Shannon index, also known in the literature as Shannon-Weaver, it is used to quantify specific biodiversity. The symbol H 'is used to represent it, and its values ​​range between positive numbers, generally between 2, 3 and 4. In the literature, this index is one of the most popular for measuring biodiversity.

The index takes into account the number of species that exist in the sample and the relative number of individuals that exist for each of the species. That is, it contemplates the richness and abundance of species.

Since the formula involved in its calculation involves a logarithm, there is no maximum value for the index. However, the minimum value is zero, indicating the absence of diversity - the condition that exists in a monoculture, for example, where there is only one species..

Values ​​less than 2 are interpreted as ecosystems with relatively low species diversity, while values ​​greater than 3 are high. Desert regions are examples of not very diverse ecosystems.

Tropical forests and reefs, in contrast, are ecosystems with a fairly high biodiversity of species.

Article index

• 1 Historical perspective
• 2 Definition
• 3 Formula
• 5 Uniformity
• 6 Applicability
• 7 References

## Historical perspective

The Shannon index was proposed by Claude Elwood Shannon (1916 - 2001), with the aim of finding a measure that could quantify entropy. This researcher was a mathematician and electrical engineer, originally from the United States.

There is some confusion with the actual name of the index. The full name is Shannon-Weiner index. However, on many occasions the authors refer to it as the Shannon-Weaver index..

This error occurred, in part, because Claude Shannon worked in collaboration with the mathematician Warren Weaver on several occasions.

## Definition

Diversity is one of the most important parameters used to describe ecosystems.

The Shannon index is an index that seeks to measure the diversity of species, considering their uniformity. It is an application of information theory, and is based on the idea that greater diversity corresponds to greater uncertainty in randomly choosing a specific species.

In other words, the index formulates the uniformity of importance values ​​across all species in the sample..

It can take the following minimum and maximum values: zero indicates that there is only one species, while the logarithm of S (total number of species in the sample) means that all species are represented by the same number of individuals.

Suppose we have a hypothetical ecosystem with only two species. Let us also think that they are in the same frequency (they are equifrequent). Thus, the uncertainty is 50%, since the two alternatives are equally possible.

The identification that gives the certainty is the unit of information, called "bit". If we have, for example, four equifrequent species, the diversity will be two bits.

## Formula

Mathematically, we calculate the Shannon index by means of the following expression:

H ' = - Σ pi ln pi

In the index expression, the variable pi represents the proportional abundance of the species i, calculated as the dry weight of the species, divided, in turn, by the total dry weight in the sample.

In this way, the index quantifies the uncertainty in the prediction of the identity of the species of an individual that is taken at random from a sample..

Furthermore, the base of the logarithm used in the expression can be freely chosen by the researcher. Shannon himself discussed logarithms in base 2, 10 and and, where each corresponded to different units of measurements.

Thus, the units are binary digits or bits, decimal digits, and natural digits, for bases 2, 10 and and, respectively.

The Shannon index is one of the most used in ecological research, since its application entails certain advantages, compared to the other diversity indexes that are relatively popular..

First, the index is not significantly affected by the sample size. Various studies have sought to find the effect of the sample size and have concluded that, indeed, the sample size has a very slight effect on the measurements of the diversity of the species.

Second, the application of the index leads to the capture of a large amount of information, in just one mathematical expression. This is a very useful feature if you want to communicate a significant amount of information to a wide audience..

Furthermore, putting an index "in context" is crucial to its interpretation. The first part is to recognize the maximum and minimum values ​​that it returns. In the Shannon index it is easy to see that the maximum corresponds to the Log S, where S is wealth and the minimum is 0.

## Uniformity

The Shannon index is based on a very relevant concept in ecology: uniformity. This parameter refers to the degree to which the species are represented throughout the sample..

The extremes include a single dominant species and other species present in very low numbers (uniformity values ​​close to 0), to all species represented by equal numbers (uniformity values ​​close to 1).

Uniformity plays a fundamental role in the ecological analysis of diversity. For example, in more uniform communities, the Shannon index becomes more sensitive to wealth.

## Applicability

Diversity indices are widely used in monitoring, from the point of view of ecology and conservation of endangered species..

Species diversity indices have the particularity of summarizing a large and important amount of data that can be used to infer population characteristics..

This index has been used to study the different effects of disturbances and stress on the diversity of communities, both of animals and plants, since it provides complex information based on the number of species and uniformity..

Finally, the link between the diversity of ecosystems and their resilience has been the subject of wide debate. Some studies have been able to corroborate this approach.

## References

1. Gliessman, S. R. (2002). Agroecology: ecological processes in sustainable agriculture. CATIE.
2. Núñez, E. F. (2008). Silvopastoral systems established with Pinus radiata D. Don and Betula alba L. in Galicia. Santiago de Compostela University.
3. Jorgensen, S. E. (2008). Encyclopedia of ecology, edited by Sven Erik Jorgensen, Brian D. Fath.
4. Kelly, A. (2016). Developing Metrics for Equity, Diversity and Competition: New measures for schools and universities. Routledge.
5. Pal, R., & Choudhury, A. K. (2014). An introduction to phytoplanktons: diversity and ecology. Springer.
6. Pla, L. (2006). Biodiversity: Inference based on Shannon's index and wealth. Interscience31(8), 583-590.
7. Pyron, M. (2010) Characterizing Communities. Nature Education Knowledge 3 (10): 39

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