1. Species Richness, Simpson’s, and Shannon-Weaver…oh my…
Biodiversity Indices
Species Richness, Simpson’s, and Shannon-Weaver…oh my…

2. What is Biodiversity?
In its simplest form, biological diversity is the variety of different types of organisms present and interacting in an ecosystem. One could say that more species equals more diversity, although a closer look will soon require us to qualify that statement. There are, in fact many more factors beyond a simple count of species that determine whether biodiversity is higher or lower in any given ecosystem.

3. Species Richness D = s/√N s = the # of different species
Species richness (S) is a measure of the number of species found in a sample.
Since the larger the sample, the more species we would expect to find, the number of species is divided by the square root of the number of individuals in the sample. This particular measure of species richness is known as D, the Menhinick's index.
D = s/√N
s = the # of different species
N = total # of individuals

4. Simpson’s Index, Index of Biodiversity, and Reciprocal
The term 'Simpson's Diversity Index' can actually refer to any one of 3 closely related indices.
Simpson's Index (D) measures the probability that two individuals randomly selected from a sample will belong to the same species (or some category other than species). There are two versions of the formula for calculating D. Either is acceptable, but be consistent.
D = SUM n(n-1) / N (N-1)
The value of D ranges between 0 and 1
With this index, 0 represents infinite diversity and 1, no diversity. That is, the bigger the value of D, the lower the diversity. This is neither intuitive nor logical, so to get over this problem, D is often subtracted from 1 to give:

5. Continued… Simpson's Index of Diversity 1 – D
The value of this index also ranges between 0 and 1, but now, the greater the value, the greater the sample diversity. This makes more sense. In this case, the index represents the probability that two individuals randomly selected from a sample will belong to different species.
Another way of overcoming the problem of the counter-intuitive nature of Simpson's Index is to take the reciprocal of the Index:
Simpson's Reciprocal Index 1 / D
The value of this index starts with 1 as the lowest possible figure. This figure would represent a community containing only one species. The higher the value, the greater the diversity. The maximum value is the number of species (or other category being used) in the sample. For example if there are five species in the sample, then the maximum value is 5.

6. Simpson’s Interpretation
D is a measure of dominance, so as D increases, diversity (in the sense of evenness) decreases. Thus, Simpsonʼs index is usually reported as its complement 1-D (or sometimes 1/D or –lnD). Since D takes on values between zero and one and approaches one in the limit of a monoculture, (1-D) provides an intuitive proportional measure of diversity that is much less sensitive to species richness.

7. Shannon-Weaver
This diversity measure came from information theory and measures the order (or disorder) observed within a particular system. In ecological studies, this order is characterized by the number of individuals observed for each species in the sample plot (e.g., biofilm on a plexiglass disc). It has also been called the Shannon index and the Shannon-Weaver index. Similar to the Simpson index, the first step is to calculate Pi for each category (e.g., species). You then multiply this number by the log of the number. While you may use any base, the natural log is commonly used (ln). The index is computed from the negative sum of these numbers. In other words, the Shannon-Wiener index is defined as:
H = - SUM [Pi x lnPi], where Pi = ni/N

8. S-W Interpretation
Typical values are generally between 1.5 and 3.5 in most ecological studies, and the index is rarely greater than 4. The Shannon index increases as both the richness and the evenness of the community increase. The fact that the index incorporates both components of biodiversity can be seen as both a strength and a weakness. It is a strength because it provides a simple, synthetic summary, but it is a weakness because it makes it difficult to compare communities that differ greatly in richness.
Due to the confounding of richness and evenness in the Shannon index, many biodiversity researchers prefer to stick to two numbers for comparative studiescombining a direct estimate of species richness (the total number of species in the community, S) with some measure of dominance or evenness. The mostcommon dominance measure is Simpsonʼs index.