Biodiversity Index Calculator
Calculate biodiversity indices including Shannon-Wiener, Simpson's, Margalef's richness, and species evenness.
Biodiversity Index Calculator
Calculator
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Formula: Shannon H' = -SUM(pi * ln(pi)); Simpson D = SUM(ni(ni-1) / N(N-1)); Evenness E = H'/ln(S)
Worked example โ Shannon H' = 1.3925 | Evenness = 0.865 | Simpson 1-D = 0.72
Formula
Shannon H' = -SUM(pi * ln(pi)); Simpson D = SUM(ni(ni-1) / N(N-1)); Evenness E = H'/ln(S)
The Shannon-Wiener Index sums the product of each species' proportion (pi) and its natural logarithm across all species. Simpson's Index calculates the probability of selecting two individuals of the same species. Evenness divides the observed Shannon value by the theoretical maximum (ln of species count). Margalef's Index measures richness as (S-1)/ln(N) where S is species count and N is total individuals.
Worked Examples
Example 1: Forest Bird Community
Problem:Calculate diversity indices for a forest with: Robin (40), Sparrow (30), Woodpecker (15), Hawk (10), Owl (5).
Solution:Total N = 100, S = 5 p values: 0.40, 0.30, 0.15, 0.10, 0.05 Shannon H' = -(0.40*ln0.40 + 0.30*ln0.30 + 0.15*ln0.15 + 0.10*ln0.10 + 0.05*ln0.05) H' = -(โ0.3665 โ 0.3612 โ 0.2847 โ 0.2303 โ 0.1498) = 1.3925 Hmax = ln(5) = 1.6094 Evenness = 1.3925/1.6094 = 0.8652
Result:Shannon H' = 1.3925 | Evenness = 0.865 | Simpson 1-D = 0.72
Example 2: Degraded vs Healthy Stream
Problem:Healthy stream: species with 25, 22, 20, 18, 15 individuals. Calculate Shannon Index.
Solution:Total N = 100, S = 5 p values: 0.25, 0.22, 0.20, 0.18, 0.15 H' = -(0.25*ln0.25 + 0.22*ln0.22 + 0.20*ln0.20 + 0.18*ln0.18 + 0.15*ln0.15) H' = -(โ0.3466 โ 0.3330 โ 0.3219 โ 0.3084 โ 0.2847) = 1.5946 Hmax = ln(5) = 1.6094 Evenness = 1.5946/1.6094 = 0.9908
Result:Shannon H' = 1.5946 | Evenness = 0.991 (very even distribution)
Frequently Asked Questions
What is the Shannon-Wiener Diversity Index?
The Shannon-Wiener Diversity Index (H') is one of the most widely used measures of biodiversity in ecology. It accounts for both species richness (the number of different species) and evenness (how equally individuals are distributed among species). The formula is H' = -SUM(pi * ln(pi)), where pi is the proportion of individuals belonging to species i. Values typically range from 0 to about 4.5, with most ecological communities falling between 1.5 and 3.5. Higher values indicate greater diversity. A value of 0 would mean only one species is present. The index increases with more species and with more even distribution of individuals among species.
How does Simpson's Index differ from Shannon's Index?
Simpson's Diversity Index (1-D) measures the probability that two randomly selected individuals belong to different species. It ranges from 0 to 1, where higher values indicate greater diversity. Unlike Shannon's Index, Simpson's gives more weight to dominant species and is less sensitive to rare species. This makes Simpson's more appropriate when you are interested in the dominance structure of a community, while Shannon's is better when rare species are important to the analysis. Simpson's is also considered more robust with smaller sample sizes. The reciprocal form (1/D) gives the effective number of equally common species and is easier to interpret intuitively.
What does species evenness tell us?
Species evenness measures how equally individuals are distributed among species in a community. It is calculated as E = H'/Hmax, where Hmax = ln(S) and S is the total number of species. Evenness ranges from 0 to 1, where 1 indicates all species have exactly the same number of individuals and values approaching 0 indicate extreme dominance by one or a few species. A forest with 100 trees of 10 species where each species has exactly 10 trees would have perfect evenness (E=1). The same forest where one species has 91 trees and 9 species have 1 each would have very low evenness. Evenness is important because a community with 10 species but extreme dominance is functionally less diverse than one where species are more equally represented.
What is a good biodiversity index value?
There is no universal threshold for a "good" biodiversity index because values depend heavily on the ecosystem type and geographic location. Tropical rainforests might have Shannon values exceeding 4.0, while arctic tundra might naturally have values below 1.5. For temperate forests, Shannon values typically range from 2.0-3.5. Grasslands usually fall between 1.5-3.0. Marine coral reefs can exceed 4.0. Rather than comparing to absolute benchmarks, biodiversity indices are most meaningful when comparing similar habitats across different locations, tracking the same location over time, or assessing the impact of disturbance. A declining index over time in the same location is a clear warning signal regardless of the absolute value.
How many individuals should I sample for a reliable biodiversity index?
Sample size significantly affects the reliability of biodiversity indices. Generally, Shannon's Index requires at least 50-100 individuals for reasonable estimates, though 200+ is preferred. Simpson's Index is more robust at smaller sample sizes and can give reasonable results with as few as 30-50 individuals. Species accumulation curves (plotting cumulative species discovered versus sampling effort) help determine when you have sampled enough, as the curve should begin to plateau. Under-sampling systematically underestimates diversity because rare species are likely to be missed. For comparing sites, it is critical that sampling effort is standardized. Rarefaction techniques can be used to adjust for unequal sample sizes between comparison sites.
What does Margalef's richness index add that a raw species count does not?
Raw species richness S rises simply because you counted more individuals, so two sites sampled with different effort cannot be compared directly. Margalef's index, DMg = (S - 1) / ln(N), divides the extra species beyond the first by the natural log of total individuals, partially correcting for that effort bias. A sample of 5 species among 100 individuals gives (5 - 1) / ln(100) = 4 / 4.605 = 0.87. It is a richness measure only, so it ignores evenness entirely and is best paired with Shannon or Simpson.
What does the Berger-Parker index tell you about dominance?
The Berger-Parker index is the simplest dominance measure in the set: the abundance of the commonest species divided by the total number of individuals. If the top species contributes 45 of 100 individuals, d = 0.45. It ranges from 1/S when every species is equally abundant to 1.0 when a single species holds the entire sample, so rising values signal an increasingly skewed community. Because higher numbers mean less diversity, ecologists often report the reciprocal 1/d instead so the direction matches the other indices.
Why does Simpson's index use n(n-1)/N(N-1) rather than the sum of pi squared?
Both express the chance that two individuals picked from the sample are the same species, but they assume different sampling. The sum of pi squared assumes sampling with replacement, or equivalently an infinitely large population, and slightly overstates concentration in a finite sample. The n(n-1)/N(N-1) form assumes an individual is drawn and not returned, which matches how field counts are actually taken. The difference is negligible once N reaches a few hundred but is noticeable at small N, so the finite form is the safer default for quadrat or trap data.
Which logarithm base should I use for the Shannon index?
Any base works because the choice only rescales the result, but it must be stated and held constant. Natural logs give units called nats and produce the 1.5 to 3.5 range most ecological papers quote; log base 2 gives bits and log base 10 gives decits. Converting is a single multiplication, since H in bits equals H in nats divided by ln(2), roughly 1.4427 times larger. The maximum term Hmax = log(S) must use the same base, otherwise the evenness ratio H/Hmax is meaningless. Biodiversity Index Calculator uses natural logarithms throughout.
What is the difference between alpha, beta, and gamma diversity?
Whittaker separated diversity into three scales in 1960. Alpha diversity is what Biodiversity Index Calculator returns: the diversity within a single sample or habitat patch. Gamma diversity is the total diversity of the wider landscape or region containing those patches. Beta diversity is the turnover between them, expressed multiplicatively as gamma divided by alpha or additively as gamma minus alpha. Two reserves can each show identical Shannon values yet hold completely different species, which only shows up as high beta diversity, so conservation planning needs all three rather than an alpha index alone.
References
Background & Theory
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Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer ยท Editorial policy
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