So I needed to quickly calculate the basic Simpson and Shannon Diversity Indices for a dataset, I found a useful online calculator which calculates multiple indices when you input your data. (https://www.alyoung.com/labs/biodiversity_calculator.html)
Annoyingly though, several different results are labelled 'Shannon Index', I can tell they're different from the equations but I'm not great at maths and can't use them to work out which Index is the basic one.
I'm fairly certain the first 'Simpson Index' is the basic Simpson index, but I'm not completely sure! If anyone could take a quick look and tell me which Indices are the basic Shannon and Simpson indices?
Dear Alex - you are right. Exist some peculiarities, may be interesting for non-professionals in biodiversity indices.
Like a base paper for my explanation I used (with my notes and translation into English from Russian original !):
"Geography and monitoring of biodiversity".
Moscow: publishing house of the Scientific and educational center, 2002. 432 p.
Authors: Lebedeva Natalia, Krivolutsky Dmitry, Puzachenko Yuri G., Diakonov Kirill Nikolayevich, Aleshchenko Gleb M., Smurov Andrey V., Maksimov V. N., Tikunov Vladimir S., Ogureeva Galina Nikolaevna Kotova Tatiana
The editorial Board of the book: Kasimov N., Romanova E. P., Tishkov, A. A.
Complete explanation is given in attached file, as needs some mathematical equations. Here just text, SO:
The Simpson there is OK. The Simpson index describes the probability of belonging to any two individuals randomly selected from an indefinitely large community, different types of formula:
D = åpi2, where pi is the proportion of individuals of the i-th species.
With increasing D the diversity is reduced. Therefore, the Simpson index, often used in the form (1– D). This value is called the "probability of interspecific meetings" and ranges from 0 to 1. He is very sensitive to the presence in the sample the most abundant species but only weakly dependent on species richness. High or low index value is determined by the type of distribution of the species abundance for cases when the number of types exceeds 10. Several papers is given like the best measure is the "index of polydominancy":
The Index of Shannon – Weaver as well OK but should know some peculiarities. MacArthur [1955] and Margalef [1957] was first used to assess the study species sustainability and diversity of the community by information theory. Information theory is based on the study of the probability of the chain of events. The result is expressed in units of uncertainty, or information. Shannon in 1949 derived a function that became known as the Shannon diversity index. Calculations of Shannon diversity index suggest that individuals enter the sample randomly from an "indefinitely large" (i.e., practically an infinite population) the General population, and the sample represented all types of the General population. Uncertainty is maximal when all events (N) will have the same probability of occurrence (pi = ni/N). It decreases as the frequency of certain events is increased compared with the other, until reaching the minimum value (zero) when there is one event and have the confidence in his offensive.
The Shannon index is calculated according to the formula:
H’= -å pi ln pi,
where the value pi is the proportion of individuals of the ith species.
In the sample, the true value of pi is unknown, but is estimated as ni/N.
The causes of errors in the estimation of diversity using this index are that it is impossible to include in the sample all kinds of real community.
When calculating the Shannon index is often used a binary logarithm, but also acceptable to use other bases of the logarithm (decimal, natural).
The Shannon index usually varies from 1.5 to 3.5, rarely exceeding 4,5.
If the values of the Shannon index to calculate for multiple samples, the resulting distribution of the variables obeys the normal law. This property enables the use of powerful parametric statistics, including analysis of variance. A comparative application of parametric and analysis of variance useful in the evaluation of diversity of different habitats, when there is repetition.
Andrey
There is only one Simpson Index on that page, so use that (not the approximation). For Shannon, use ln i.e. natural log (the second formula) :)
Odum recommend for Shannon natural logarithms but if need for bytes of information so log2.
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