Biodiversity Indices Overview
Ecologists often describe biodiversity using two complementary ideas:
species richness (how many species are present) and evenness
(how evenly individuals are distributed among species). This calculator takes species counts and computes
the most widely used diversity indices—Shannon and Simpson—along with optional Pielou evenness.
Inputs and core definitions
Suppose you record counts for each species in a community:
ni = number of individuals of species i.
Total abundance and richness
\[
\begin{aligned}
N &= \sum_{i=1}^{S} n_i \\
S &= \text{number of species with } n_i > 0
\end{aligned}
\]
Relative abundance
\[
\begin{aligned}
p_i &= \frac{n_i}{N}
\end{aligned}
\]
Here, N is the total number of individuals in the sample, S is the number of species with nonzero counts,
and pi is the proportion contributed by species i. These proportions satisfy
\(\sum_i p_i = 1\).
Shannon diversity index (H′)
The Shannon index increases with both richness and evenness. It is based on the uncertainty of predicting
the species identity of a randomly chosen individual.
Shannon index
\[
\begin{aligned}
H' &= -\sum_{i=1}^{S} p_i \ln(p_i)
\end{aligned}
\]
This calculator allows choosing the logarithm base. If a base b is used, replace \(\ln\) with \(\log_b\).
Changing the log base rescales H′ but does not change comparisons within the same base.
Shannon with an arbitrary base
\[
\begin{aligned}
H'_b &= -\sum_{i=1}^{S} p_i \log_b(p_i)
\end{aligned}
\]
Practical notes: any species with \(p_i=0\) is excluded from the sum. (In the limit, \(p\ln(p)\to 0\) as \(p\to 0^+\).)
Simpson index family
Simpson’s index emphasizes dominance: it is strongly influenced by the most abundant species. The core quantity is
the sum of squared proportions.
Simpson dominance (D)
\[
\begin{aligned}
D &= \sum_{i=1}^{S} p_i^2
\end{aligned}
\]
Because different textbooks define “Simpson index” differently, this calculator lets you choose the reporting form:
Common reporting forms
\[
\begin{aligned}
\text{Dominance:} \quad & D \\
\text{Diversity:} \quad & 1-D \\
\text{Reciprocal:} \quad & \frac{1}{D}
\end{aligned}
\]
Interpretation:
D is the probability that two individuals drawn at random (with replacement) belong to the same species.
Larger D implies stronger dominance (lower diversity). The value 1−D increases with diversity,
and 1/D can be read as an “effective number of dominant species” (larger means more diverse).
Evenness (Pielou J)
Richness alone cannot tell whether one species dominates. Evenness measures how close the community is to perfectly
equal abundances. Pielou’s evenness rescales Shannon by its maximum possible value for a given richness.
Pielou evenness
\[
\begin{aligned}
J &= \frac{H'}{\ln(S)}
\end{aligned}
\]
If you selected a log base b for H′, the calculator uses the same base for the denominator:
\(J = \dfrac{H'_b}{\log_b(S)}\). This keeps J on a 0–1 scale (when \(S>1\)).
If \(S = 1\), evenness is not defined because \(\ln(1)=0\).
Rank–abundance table and curve
A rank–abundance view sorts species from most abundant to least abundant using \(p_i\). The table reports each
species’ rank, count, and relative abundance, and the curve plots rank on the x-axis against \(p_i\) on the y-axis.
Steeper curves indicate stronger dominance (lower evenness), while flatter curves indicate a more even community.
Community composition (stacked relative abundance)
The composition chart shows the proportions \(p_i\) as a stacked bar, helping you see which species contribute most to
the community. If there are many rare species, grouping them into an “Other” category can make the plot easier to read
without changing computed indices.
Multiple sites (optional)
When you provide multiple communities (sites), the calculator computes the same set of quantities for each site:
\(N\), \(S\), \(H'\), Simpson (your selected form), and \(J\) if enabled. A comparison table helps rank sites by
diversity and interpret how richness and dominance differ across samples.
Important data considerations
- Counts must be nonnegative; only species with \(n_i>0\) contribute to indices.
-
Indices depend on the sampling effort. Comparing sites is most meaningful when samples are collected using
consistent methods and similar effort.
-
Shannon and Simpson respond differently to dominance: Shannon is more sensitive to rare species than Simpson’s D,
while Simpson’s D is dominated by common species.
