Statistics Calculators ▶ Shannon Diversity Index Calculator
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This Shannon diversity index calculator lets you estimate the diversity of species in an area of land. So without wasting time, scroll down to better know how this calculator assists you compare various lives in an ecosystem.
Let’s Move On!
The quantity that is used to represent the various life varieties on the Earth is termed biodiversity.
It includes each and every individual organism such as plants, bacteria, animals, and fungus. According to modern research, there exist around more than 8.7 million species on the planet. But only a figure of 1.2 million has been discovered yet. This free Shannon diversity index calculator is the best method used worldwide to estimate the diversity of these species. So let’s move on to the pivot of today’s discussion!
In the context of ecology:
“A particular parameter that determines the diversity of a species in an ecosystem is known as the Shannon diversity index”
Now you can easily estimate the diversity of a species in an ecosystem with the help of the following Shannon Index Equation given below:
$$ H = – \sum[\left(p_{i}\right) * \log\left(p_{i}\right)] $$
Where:
H = Shannon Diversity index
It corresponds to the abundance of an individual species with respect to the others.
$$ p_{i} = \frac{n}{N} $$
n = No of individuals in a given species
N = The total number of individuals in a community
Along with checking the diversity of a population in an ecosystem, you must go for determining the various factors that have a remarkable effect on the population of a species in the ecosystem. So let’s move towards them:
Average population size is actually the number of individuals living within one single unit of area.You can find the average population size within a locality by subjecting to the formula below:
$$ \text{Average Population Size} = \frac{\text{Total Individual Sum of Species}}{\text{No. of Species}} $$
Evenness corresponds to the closeness of various species in an ecosystem. Basically, it is an extent to which different species are distributed in an ecosystem. You can determine this quantity by subjecting to the following equation:
$$ – \sum \left(\frac{n_{i}}{N} * ln\left(\frac{n_{i}}{N}\right)\right) $$
The free Shannon diversity calculator also takes into consideration the use of the above mentioned formula to depict the final results in a fragment of seconds.
Richness corresponds to the total number of species residing in a particular habitat.
$$ Richness = \text{No. Of Individuals} $$
It is an alternative way to determine the species richness in an ecosystem. Go for determining the Margalef richness index by using the following equation:
$$ \frac{S-1}{lnN} $$
Where:
S = Number of Species
N = Total sum of the individuals
This particular parameter gives you organic information about the most abundant species in an ecosystem.
$$ \text{Inverted Berger Parker Dominance} = \frac{N}{n_{max}} $$
Where:
\(N_max\) = Maximum number of the individuals
This element determines the biodiversity of a species depending upon the relative species’ abundance along with the total individual families present.
$$ \text{Simpson’s Index} = \frac{\sum_{i} n_{i} \left(n_{i} – 1\right)}{N\left(N-1\right)} $$
The number of the most common species in a n ecosystem is calculated with the use of this index as follows:
$$ \text{Dominance Index} = \frac{1 – \sum_{i} n_{i} \left(n_{i} – 1\right)}{N\left(N-1\right)} $$
$$ \text{Alternative Reciprocal Simpson Index} = \frac{1}{Simpson’s Index} $$
You can measure this index by commencing to the formula as written below:
$$ \text{Menhinick Index} = \frac{S}{\sqrt{\sum_{i}n_{i}}} $$
$$ \text{Simpson’s Index Approximation} = \frac{\sum_{i}n_{i}^{2}}{N^{2}} $$
$$ \text{Reciprocal Simpson Index} = \frac{1}{\frac{\sum_{i}n_{i}^{2}}{N^{2}}} $$
$$ \text{Dominance Index Approximation} = 1-\frac{\sum_{i} n_{i}^{2}}{N^{2}} $$
$$ \text{Buzas And Gibson’s Index} = \frac{e- \sum_{i} \left(\frac{n_{i}}{N} * ln \left(\frac{n_{i}}{N}\right)\right)}{S} $$
It is another method used to determine biodiversity that compares the species cumulative proportion against the cumulative proportion of the individuals present in an ecosystem.
$$ \text{Gini Coefficient} = \frac{2 \sum_{i}in_{i}}{n \sum_{i}n_{i}} – \frac{N+1}{N} $$
Our best Shannon diversity index calculator also determines all these parameters but in seconds that save you a lot of time.
What about resolving an example that will make you learn the concept of diversity index clearly? Let’s move on together!
Example # 01:
How to calculate shannon-wiener index for the dispersion of the species in an ecosystem given as follows:
Specie Name |
Total Number Present |
Tiger |
31 |
Rabbits |
45 |
Lions |
4 |
Jaguars |
9 |
Snakes |
132 |
Parrots |
64 |
Hippo |
3 |
Alligators |
41 |
Solution:
Determining The Relative Abundance of Individual Species:
Here we will follow the formula given below to find this element:
$$ p_{i} = \frac{n}{N} $$
Tigers:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{31}{329} $$
$$ p_{i} = 0.094 $$
Rabbits:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{45}{329} $$
$$ p_{i} = 0.136 $$
Lions:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{4}{329} $$
$$ p_{i} = 0.012 $$
Jaguars:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{9}{329} $$
$$ p_{i} = 0.027 $$
Snakes:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{132}{329} $$
$$ p_{i} = 0.401 $$
Parrots:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{64}{329} $$
$$ p_{i} = 0.194 $$
Hippo:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{3}{329} $$
$$ p_{i} = 0.009 $$
Alligators:
$$ p_{i} = \frac{n}{N} $$
$$ p_{i} = \frac{41}{329} $$
$$ p_{i} = 0.124 $$
Determining The Natural Logarithm of The Relative Abundances:
Now we are moving ahead to determine the log of the abundances calculated aforementioned as follows:
Tigers:
$$ ln{p_{i}} = ln\left(0.094\right) $$
$$ ln{p_{i}} = -2.364 $$
Rabbits:
$$ ln{p_{i}} = ln\left(0.136\right) $$
$$ ln{p_{i}} = -1.995 $$
Lions:
$$ ln{p_{i}} = ln\left(0.012\right) $$
$$ ln{p_{i}} = -4.422 $$
Jaguars:
$$ ln{p_{i}} = ln\left(0.027\right) $$
$$ ln{p_{i}} = -3.611 $$
Snakes:
$$ ln{p_{i}} = ln\left(0.401\right) $$
$$ ln{p_{i}} = -0.913 $$
Parrots:
$$ ln{p_{i}} = ln\left(0.194\right) $$
$$ ln{p_{i}} = -1.639 $$
Hippo:
$$ ln{p_{i}} = ln\left(0.009\right) $$
$$ ln{p_{i}} = -4.710 $$
Alligators:
$$ ln{p_{i}} = ln\left(0.124\right) $$
$$ ln{p_{i}} = -2.087 $$
The free Shannon diversity index calculator also takes into consideration all of these calculations in order to find the biodiversity index of all the species present in an ecosystem.
Determining The Product of The Relative Abundance and The Natural Log of It With Each Other:
Tiger:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.094 * -2.364 $$
$$ = -0.222216 $$
Rabbits:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.136 * -1.995 $$
$$ = -0.27132 $$
Lions:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.012 * -4.422 $$
$$ = -0.053064 $$
Jaguars:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.027 * -3.611 $$
$$ = -0.097497 $$
Snakes:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.401 * -0.913 $$
$$ = -0.366113 $$
Parrots:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.194 * -1.639 $$
$$ = -0.317966 $$
Hippo:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.009 * -4.710 $$
$$ = -0.04239 $$
Alligators:
$$ \left(p_{i}\right) * \log\left(p_{i}\right) $$
$$ = 0.124 * -2.087 $$
$$ = -0.258788 $$
Determining the Shannon Diversity Index:
Using Shannon diversity index formula;
$$ H = – \sum[\left(p_{i}\right) * \log\left(p_{i}\right)] $$
$$ H = -[-0.222216-0.27132-0.053064-0.097497-0.366113-0.317966-0.04239-0.258788] $$
$$ H = -[-1.6299354] $$
$$ H = 1.6299354 $$
Apart from these lengthy calculations, you could better our free Shannon index calculator for fast results along with related parameters.
Get going to analyse a species’ diversity in an ecosystem with this free biodiversity calculator. Let’s find out how it works!
Input:
Output:
The free shannon wiener index calculator determines:
Whenever the influence of richness gets very high over the biodiversity, it creates a negative relation among both evenness of the species and their diversities. This will let the Shannon index become negative as well that could be verified by using our best Shannon diversity index calculator.
The diversity index lies in between 0 and 1. The more the value gets closer to the 1, it is considered more reliable.
As far as the ecological studies are concerned, the diversity depends upon only three factors that include:
All of the parameters can easily be determined by using this free Shannon diversity index calculator immediately and accurately.
The four major levels of the biodiversity include the following:
The highest biodiversity is recorded in Brazil. You can let this calculator instantly determine the diversity of any species in this country.
Let us define the given terms in brief detail:
Alpha Diversity:
It corresponds to the diversity of a species that may be present within any ecosystem.
Beta Diversity:
It represents the diversity of the species between two ecosystems.
Gamma Diversity:
The entire range of a diversity in different ecosystems corresponds to the gamma diversity.
In general, the Shannon index tells you about the abundance relativity of a species with respect to the others present.
The maximum biodiversity is seen in the tropical rain forests due to the balanced season out there. Infact, it is noted that these forests comprise about half of the total Earth’s biodiversity.
When it comes to the richest ecosystem on the planet, Amazonia Forests is the only name that stands out.
Shannon diversity index calculator lets the ecologists know more about the biodiversity of the organisms living on the Earth. This is very important because human beings can not live on earth in the absence of various species that create a healthy environment for living. So start using this free calculator to determine how rich your ecosystem is with species.
From the source of Wikipedia: Diversity index, Effective number of species or Hill numbers, Sensitivity of the diversity value to rare vs. abundant species, Richness, Shannon index, Simpson index, Berger–Parker index
From the source of Khan Academy: Community structure, Species richness, Species diversity, Foundation and keystone species
From the source of Lumen Learning: Quantitative Measures of Diversity, Shannon-Wiener Index, Rank Graphs, Similarity between Sites