What Is Species Evenness? Pielou’s J, Formula and Worked Example

Species evenness describes how equally individuals are spread among the species in a sample, independent of how many species there are. A community of five species with 20 individuals each is perfectly even; a community of five species in which one species supplies 90 of 100 individuals is highly uneven. This guide defines evenness, gives the formulas for the three evenness indices implemented in scikit-bio (Pielou’s J′, Simpson’s E and Heip’s E), computes all three on one data set, and shows how to calculate and report them in Excel, R and Python.

What is species evenness? A definition

Species evenness (also called equitability) is the degree to which the individuals in a sample are distributed equally among its species. It is one of two components of diversity: richness counts how many species are present, evenness describes how the individuals are shared among them. Two samples can have the same richness and very different evenness, which is why a richness count alone, or a single diversity index that blends both ideas, can hide what is driving a difference.

The vegan package vignette “Diversity analysis in vegan” notes that the package has no dedicated evenness functions and that the most common measure is Pielou’s evenness, J = H′/log(S). That is the index most people mean by “species evenness,” but it is not the only one. For the diversity indices themselves, see the guides on the Shannon diversity index and the Simpson diversity index.

How to calculate evenness: the formulas

All three indices start from the proportion of each species. The symbols are shared:

• S: the number of species (taxa) in the sample, its richness.
• p_i: the proportion of all individuals that belong to species i (count of species i divided by the total count N).
• H′: the Shannon index, H′ = −Σ p_i ln(p_i), summed over the S species, with natural logarithms.
• D: Simpson’s dominance, D = Σ p_i², the sum of squared proportions.

Pielou’s evenness J′ (Shannon’s equitability)

J′ = H′ / ln(S). According to the scikit-bio documentation, S is the number of taxa, the index is also called Shannon’s equitability index (E_H), it is the ratio of the actual Shannon index to the maximum possible value when all taxa are equally abundant, and it ranges between 0 and 1. The usual reference is Pielou (1966), Journal of Theoretical Biology 13:131-144.

Simpson’s evenness E_D

E_D = 1 / (D × S), where D is Simpson’s dominance index and S the number of taxa (scikit-bio documentation; the references given there are Simpson 1949, Nature 163:688, and Pielou 1966). It compares the observed dominance with the minimum possible dominance. Because D is the sum of squared proportions, D is never below 1/S (equal proportions) and never above 1, so E_D runs from 1/S up to 1 (this follows from the formula).

Heip’s evenness

E_Heip = (e^H′ − 1) / (S − 1), with H′ computed with natural logarithms (scikit-bio documentation; reference Heip 1974, Journal of the Marine Biological Association of the UK 54:555-557). When all species are equally abundant, e^H′ = S and the index equals 1; it approaches 0 as one species takes almost all individuals.

Evenness as a ratio of Hill numbers

The vegan vignette defines the Hill numbers N0 = S, N1 = exp(H′), N2 = D2 (which works out to the inverse Simpson index, 1/D) and N∞ = 1/max(p_i); the framework comes from Hill (1973), “Diversity and evenness: a unifying notation and its consequences,” Ecology 54. Rewriting the formulas above with them shows that the three indices are the same idea at different orders: J′ = ln(N1)/ln(N0), E_D = N2/N0 and E_Heip = (N1 − 1)/(N0 − 1). Each asks how far the effective number of species falls below the actual number, which is why they rank communities in a similar but not identical way.

Worked example with real numbers

Take the quadrat survey used in the Shannon guide: five species with 40, 25, 20, 12 and 8 individuals. N = 40 + 25 + 20 + 12 + 8 = 105 and S = 5.

Species	Count	pi = count / 105	pi ln(pi)	pi²
A	40	0.3810	−0.3676	0.1451
B	25	0.2381	−0.3417	0.0567
C	20	0.1905	−0.3159	0.0363
D	12	0.1143	−0.2479	0.0131
E	8	0.0762	−0.1962	0.0058
Sum	105	1.0000	−1.4692	0.2570

1. Shannon index: H′ = −(−1.4692) = 1.4692.
2. Maximum possible H′ for S = 5: ln(5) = 1.6094.
3. Pielou’s J′ = 1.4692 / 1.6094 = 0.913.
4. Dominance: D = 2833 / 11025 = 0.2570 (the squared counts 1600 + 625 + 400 + 144 + 64 = 2833, divided by 105²).
5. Simpson’s E_D = 1 / (0.2570 × 5) = 1 / 1.2848 = 0.778.
6. e^H′ = e^1.4692 = 4.3459, so Heip’s evenness = (4.3459 − 1) / (5 − 1) = 3.3459 / 4 = 0.836.

The same data give 0.913, 0.778 and 0.836 depending on the index, so always name the index you used. The Hill-number view makes the gap visible: the effective number of species is N1 = 4.35 and N2 = 3.89 against N0 = 5, and the indices measure that shortfall in different ways.

Interpretation: what the value means

A value of 1 means every species has the same abundance; values near 0 mean one or a few species hold nearly all individuals. There is no standard verbal scale such as “above 0.8 is even,” so interpret a value by comparing it with other samples analysed the same way, or with the bounds below.

Sample (counts)	Pielou J′	Simpson ED	Heip
20, 20, 20, 20, 20 (perfectly even)	1.000	1.000	1.000
40, 25, 20, 12, 8 (worked example)	0.913	0.778	0.836
90, 5, 3, 1, 1 (one species dominates)	0.275	0.246	0.139

The table rows were computed with the formulas above. All three indices rank the three samples in the same order, but in the last row Heip’s index (0.139) falls furthest below J′ (0.275).

Assumptions and common mistakes

• Evenness depends on how S is counted. J′ = H′/ln(S) uses the number of species in your sample, so a rare species added or missed changes both the numerator and the denominator. Compare samples only when they were collected with comparable effort and the same definition of a species or taxon.
• Do not mix logarithm bases. J′ is a ratio, so using the same base for H′ and for log(S) gives the same result; Heip’s formula, however, requires natural logarithms, so compute H′ with the natural log there.
• Do not report evenness without richness. An evenness of 0.9 with two species and 0.9 with fifty describe very different communities.
• Zero counts. A species with a count of 0 has no defined p ln(p); leave it out of both the sum and S, so that S is the number of species actually present (vegan’s specnumber() counts the species present).
• One species. With S = 1, ln(S) = 0 and J′ is a division by zero. scikit-bio’s Heip function returns 1.0 for a single taxon.
• Name the index. “Evenness” alone is ambiguous; say Pielou’s J′, Simpson’s E_D or Heip’s evenness.

How to report evenness (APA example)

State the index, its formula or source, the logarithm base, S and N, and report it beside richness and the diversity index it comes from. A results sentence might read: “Species richness was S = 5 (N = 105), Shannon diversity H′ = 1.47 nats, and Pielou’s evenness J′ = 0.91 (J′ = H′/ln S).” Report the same number of decimal places for every value in a table, and follow your journal’s rules for statistical notation. For general reporting standards see the Journal Article Reporting Standards (JARS) entry, and for the descriptive-versus-inferential distinction see descriptive statistics vs inferential statistics.

To cite the software documentation, follow the APA 7th edition web-page pattern (Author or Group. (Year). Title. Site Name. URL), for example: scikit-bio. (n.d.). skbio.diversity.alpha.pielou_e. https://scikit.bio/docs/latest/generated/skbio.diversity.alpha.pielou_e.html. Cite Pielou (1966), Simpson (1949), Heip (1974) and Hill (1973) as journal articles using the details in the Sources section.

How to calculate evenness in Excel, R or Python

Excel

Put the counts in A2:A6. In B2:B6 enter =A2/SUM($A$2:$A$6) and fill down. Then:

H' (natural log):   =-SUMPRODUCT(B2:B6, LN(B2:B6))
Pielou J':          =H / LN(COUNT(A2:A6))
Dominance D:        =SUMSQ(B2:B6)
Simpson E:          =1 / (D * COUNT(A2:A6))
Heip:               =(EXP(H) - 1) / (COUNT(A2:A6) - 1)

Replace H and D with the cells holding those results. Delete rows with zero counts first, because LN(0) returns an error.

R (vegan)

The vegan vignette gives this pattern for Pielou’s evenness, with BCI being the example community table shipped with the package:

library(vegan)
H <- diversity(BCI)
J <- H / log(specnumber(BCI))

For a single vector of counts, x <- c(40, 25, 20, 12, 8); H <- diversity(x); H / log(specnumber(x)) returns 0.913.

Python

scikit-bio provides pielou_e, simpson_e and heip_e. A dependency-free version of the same arithmetic reproduces the worked example:

import math
counts = [40, 25, 20, 12, 8]
N, S = sum(counts), len(counts)
p = [c / N for c in counts]
H = -sum(x * math.log(x) for x in p)
D = sum(x * x for x in p)
print(round(H / math.log(S), 3))              # Pielou J'  -> 0.913
print(round(1 / (D * S), 3))                  # Simpson E  -> 0.778
print(round((math.exp(H) - 1) / (S - 1), 3))  # Heip       -> 0.836

# with scikit-bio installed:
# from skbio.diversity.alpha import pielou_e, simpson_e, heip_e
# pielou_e(counts), simpson_e(counts), heip_e(counts)

Frequently asked questions

What is species evenness in simple terms?

It is how equally the individuals in a sample are divided among its species. If every species has the same number of individuals, evenness is at its maximum of 1; if one species has almost all of them, evenness is close to 0.

How do you calculate species evenness?

The most common method is Pielou’s evenness: divide the Shannon index by the natural log of the number of species, J′ = H′/ln(S). For the data 40, 25, 20, 12, 8 this is 1.4692/1.6094 = 0.913.

What is the difference between richness and evenness?

Richness is the number of species (S); evenness describes how equal their abundances are. A sample can have high richness and low evenness, or the reverse.

What is a good evenness value?

There is no universal threshold. Values run from 0 to 1 for Pielou’s J′, and the useful comparison is between samples collected and analysed the same way.

Is Pielou’s evenness the same as Simpson’s evenness?

No. Pielou’s J′ divides the Shannon index by its maximum; Simpson’s E_D is 1/(D × S). On the same data they give different values (0.913 and 0.778 above), so name the index you report.

Sources

• vegan package vignette, “Diversity analysis in vegan,” CRAN: https://cran.r-project.org/web/packages/vegan/vignettes/diversity-vegan.pdf (checked 2026-10-29).
• scikit-bio documentation, pielou_e: https://scikit.bio/docs/latest/generated/skbio.diversity.alpha.pielou_e.html (checked 2026-10-29).
• scikit-bio documentation, simpson_e: https://scikit.bio/docs/latest/generated/skbio.diversity.alpha.simpson_e.html (checked 2026-10-29).
• scikit-bio documentation, heip_e: https://scikit.bio/docs/latest/generated/skbio.diversity.alpha.heip_e.html (checked 2026-10-29).
• Hill, M. O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology, 54.
• Pielou, E. C. (1966). The measurement of diversity in different types of biological collections. Journal of Theoretical Biology, 13, 131-144.
• Simpson, E. H. (1949). Measurement of diversity. Nature, 163, 688.
• Heip, C. (1974). A new index measuring evenness. Journal of the Marine Biological Association of the UK, 54, 555-557.