Simpson's Diversity Index

Simpson’s Diversity Index Definition

The Simpson's Diversity Index was created by Edward Hugh Simpson, an English scientist, in 1949. It is important to note that this is different than the Simpson's Similarity Index, which was founded by American scientist George Gaylord Simpson in 1960. In ecology, the Simpson's Diversity Index is used to measure the level of biodiversity in a given area. Specifically, it is concerned with the diversity of species present. In order to determine this, the Simpson’s Diversity Index looks at two factors - richness and evenness.

Richness in an Ecosystem

Species richness refers to the total number of species present in an ecosystem. The more species there are in an ecosystem, the higher the level of richness. Measuring richness alone does not allow for the relative abundance of species to be taken into account. In order to measure this, we need to look at species evenness.

Example of Richness in an Ecosystem

A good example of species richness is the most biodiverse ecosystem on Earth - the Amazon rainforest. The Amazon holds a very large amount of the world's living species, including a third of all tropical tree species. The Amazon is home to over three million different species of organism, including 1300 bird species, over 400 mammal species, almost 400 reptile species, more than 2500 species of tree, and it is predicted to have over 2.5 million species of insect, with many of them undiscovered. As with most of the world's most biodiverse locations, the Amazon is severely threatened by habitat destruction, which has increased significantly in recent years.

Evenness in an Ecosystem

Species evenness refers to the relative population size of each species present in an ecosystem. Measuring evenness is important because an ecosystem that is overwhelmingly dominated by a single or a small number of species has far less diversity than one that is more evenly partitioned between many different species.

Example of Evenness in an Ecosystem

The Brazilian Pantanal, for example, is a highly diverse ecosystem with numerous species and a high level of biodiversity. However, the ecosystem has an overwhelming abundance of two large vertebrate species - the yacare caiman (Caiman yacare), which are estimated to number nearly 10 million (Fig. 2), and the capybara (Hydrochoerus hydrochaeris).

In the case of the yacare caiman, this overwhelming dominance prevents other crocodilian species from gaining any significant foothold in the Pantanal ecosystem, with the only other nearby species being the Cuvier's dwarf caiman (Paleosuchus palpebrosus), which is relegated to the fringes of the Pantanal in relatively low numbers, due to the dominance of the yacare caiman in the area. This is in contrast to the Amazon, which holds five of the six extant species of caiman, sometimes four species within one area of habitat!

Simpson’s Diversity Index Formula

In order to determine an area’s diversity, we must use one of the equations associated with the Simpson’s Diversity Index. In the following equation, “N” indicates the total number of organisms, “n” indicates the population of each species, and “D” is the area’s diversity index (a higher number indicates a more diverse ecosystem).

\[D = \frac{\sum{n_i(n_i-1)}}{N(N-1)}\]

Simpson’s Diversity Index example

Using the above equation, we will determine the diversity index of each of these ecosystems and determine which area has the higher level of diversity. Follow along and try to determine the answers on your own.

Ecosystem A (Adelaide River)

Ecosystem B (Pantanal Wetlands)

Ecosystem A (Adelaide River)

\[D = \frac{24995000+1599960000+249500+561750+8997000}{49250(49250-1)} = \frac{1634763250}{2425316250} = 0.67\]

Ecosystem B (Pantanal Wetlands)

\[D = \frac{999999000000+62250+249500+15996000+99990000+249500 +999999000000}{2015250(2015250-1)} = \frac{2000114547250}{4061230547250} = 0.49\]

As you can see, the diversity index for the Adelaide River is 0.67, while it is 0.49 for the Pantanal Wetlands, thus the Pantanal Wetlands have a lower level of diversity than the Adelaide River.

The Shannon Diversity Index

The Shannon Diversity Index, also known as the Shannon-Wiener Index, is another way to measure an area's biodiversity. This index uses the formula for entropy created by Claude Shannon and uses it in the context of biodiversity. Like Simpson's Diversity Index, the Shannon Diversity Index considers both species richness and evenness. The index is denoted as "H" and uses the following equation, where Pi indicates the proportion of each species:

\[H = -\sum{[p_i \cdot \ln(p_i)]}\]

To determine "H", we must use the following steps:

1.) Determine the sum of all organisms in the sample.

2.) Determine the proportion each species occupies out of the total organism population (Pi).

3.) For each "Pi", multiply by ln(Pi).

4.) Determine the sum of all results, which is your "H".

Example

Ecosystem (Zambezi River)

Thus, our "H" (Shannon Diversity Index) is 1.21.

Which is better? Simpson's Diversity Index or Shannon Diversity Index?

Both indices have their uses and can be equally important, depending on the circumstances. The Simpson's Diversity Index tends to place a greater emphasis on evenness, whereas the Shannon Diversity Index is more concerned with species richness. In this way, the Simpson's Diversity Index places a greater value on species dominance than the Shannon Diversity Index.