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Shannon Wiener Index Calculator (Free) | StatsUnlock

Shannon Wiener Index Calculator (Free) | StatsUnlock

Shannon Wiener Index Calculator

A free online tool to measure species diversity (H') from your survey counts, with instant charts, evenness, richness, and publication-ready results.

BiodiversityDiversity IndexEcologyWildlifeFreeOnline

Last updated: 15 September 2026 · Built for ecologists and wildlife researchers by StatsUnlock

⚡ 0. Quick Answer

The Shannon Wiener index calculator turns species counts into one diversity value, H'. Enter counts such as 45, 30, 15, 7, 3 and the tool returns H' = 1.296 from H' = -Σ pi ln pi, plus evenness J' = 0.806, richness S = 5, and Simpson's index. Most real communities score between 1.5 and 3.5.

🌿 Key Takeaways

  • The Shannon Wiener index calculator turns your species counts into one clear diversity number (H') for ecology and wildlife studies.
  • You only need the count of individuals per species. Paste them comma separated, upload a CSV file, or type them in.
  • A higher H' usually means greater diversity and a healthier, more even community; a lower H' means fewer species or one dominant species.
  • Typical field uses: camera trapping, point counts, vegetation plots, transects, and reef fish surveys.
  • This tool also returns evenness (J'), richness (S), Simpson's index, and ready-to-paste text for reports and papers.

🌱 1. What Is the Shannon Wiener Index?

The Shannon Wiener index (written H', and also called the Shannon index, Shannon-Weaver index, or Shannon diversity index) is a single number that describes how diverse a community is. It combines two things at once: how many species you found (richness) and how evenly the individuals are shared among those species (evenness).

The number comes from proportions. For every species you divide its count by the total number of individuals to get a proportion p. You multiply each p by the natural logarithm of that p, add the results across all species, then flip the sign. That is the whole calculation: H' = -Σ p ln p.

Ecologists use it because it answers a question that a species list alone cannot answer. Two plots can hold the same five species, yet one plot can be dominated by a single species while the other is balanced. Species richness says they are identical. The Shannon Wiener index says they are not.

Plot A: even community Plot B: one species dominates counts 20, 20, 20, 20, 20 counts 80, 5, 5, 5, 5 S = 5, H' = 1.61 S = 5, H' = 0.76
Same richness, very different diversity. Both plots hold five species, but the Shannon Wiener index separates them because evenness differs.

1.1 What the value means

H' range (natural log)ReadingTypical setting
0.00 to 1.00Very low ConcernMonoculture, heavily polluted water, one invasive species dominating
1.00 to 1.50Low ConcernDegraded fragment, intensive farmland, urban core
1.50 to 2.50Moderate WatchSecondary forest, managed grassland, recovering site
2.50 to 3.50High HealthyMature temperate forest, healthy wetland, good reef transect
Above 3.50Very high HealthyLowland tropical rainforest, large insect trap samples

What to conclude: treat these bands as a first reading only. Compare your value with a reference site sampled using the same method, the same effort, and the same season before you call a site rich or poor.

📥 2. Set Up Your Data

0 values entered

Supports .csv and .txt, headers detected automatically.
SpeciesCount

🔎 4. Interpretation of Results, In Detail

▶ Run the analysis above to generate a detailed, plain-English interpretation of your Shannon Wiener result.

✍️ 5. How to Write Your Results in Research

▶ Run the analysis above to auto-fill all six examples with your results.

🪧 5.1 Research Poster Panel

A print-ready poster layout that updates with your result. Copy the text or use the visual scaffold for A0 / A1 conference posters.

▶ Run the analysis above to build your poster panel.

🧮 6. Formulas Used

Every number this Shannon Wiener index calculator reports comes from one of the seven formulas below. Read them top to bottom: card 1 is the index itself, and each later card moves one step outward.

1

Shannon Wiener diversity index

H' = -Σi=1S ( pi × ln pi )
  • H' Shannon Wiener index, unitless (nats when ln is used)
  • pi proportion of individuals in species i, unitless
  • S number of species in the sample, a count
  • Range: 0 to about 4.6 in practice. 0 means one species only.
  • Requires: raw counts of individuals, not percentages.
  • Example: counts 45, 30, 15, 7, 3 give H' = 1.296.
2

Species proportion

pi = ni / N
  • ni count of individuals of species i
  • N total individuals across all species
  • Rule: all proportions must add to 1.00.
  • Note: a species with a count of 0 is dropped, because ln 0 is undefined.
3

Maximum possible diversity

H'max = ln S
  • H'max the value you would get if every species were equally common
  • S species richness
  • Example: S = 5 gives H'max = 1.609.
  • Use for: the denominator of evenness.
4

Pielou's evenness

J' = H' / H'max = H' / ln S
  • J' evenness, unitless, 0 to 1
  • Range: 1.0 is perfectly even, values under 0.5 mean strong dominance.
  • Example: 1.296 / 1.609 = 0.806.
  • Note: J' is undefined when S = 1, because ln 1 = 0.
5

Effective number of species (Hill number q = 1)

¹D = exp( H' )
  • ¹D effective species count, in species units
  • Use for: honest comparisons. A site with ¹D = 8 is twice as diverse as one with ¹D = 4, which is not true of H' itself.
  • Example: exp(1.296) = 3.66 effective species out of 5 observed.
6

Simpson's index, the sibling metric

D = Σ pi²   1 - D = 1 - Σ pi²
  • D dominance, the chance two random individuals are the same species
  • 1 - D Simpson's diversity, 0 to 1
  • Example: D = 0.321, so 1 - D = 0.679.
  • Note: Simpson weights common species, Shannon weights rare ones.
7

Changing the logarithm base

H'base b = H'ln / ln b
  • b the base you want: 2 for bits, 10 for decits
  • Example: H' = 1.296 nats = 1.870 bits = 0.563 decits.
  • Rule: always state the base in your methods, or your value cannot be compared.

🧭 7. How to Use This Calculator

Ten steps from a field sheet to a publication-ready Shannon Wiener result.

  1. Collect standardised counts. Record the number of individuals for each species using the same effort at every site.
  2. Pick an input tab. Use Paste or Type for a quick run, Upload CSV for a spreadsheet, or Manual Table to key in rows.
  3. Enter species names and counts. In Column Entry mode, put the species name on the left and the count on the right.
  4. Or load a sample dataset. Choose one of the 20 built-in field datasets to see how the tool behaves before you use your own data.
  5. Name your study area. Type the site name into the Study Area box so it appears in every report template and in the poster panel.
  6. Choose the logarithm base. Natural log is the standard. Pick log2 only if your journal or supervisor asks for bits.
  7. Set the decimal places. Three decimals is normal for H' in ecology papers.
  8. Click Run Analysis. The tool returns H', evenness, richness, Simpson's index, four charts, and a results table.
  9. Read the interpretation. Section 4 explains your number in plain English and flags any sampling problems.
  10. Copy or download your result. Use the report templates, the poster panel, Download Doc, or Download PDF for your thesis or paper.

📗 8. How to Calculate the Shannon Wiener Index in Excel

Excel, step by step, with the same worked example used everywhere on this page

The worked example below uses five species with counts 45, 30, 15, 7, 3 (N = 100). Excel, R, Python and this calculator all return H' = 1.296 for it.

8.1 The Excel functions you need

FunctionWhat it doesExample
SUMAdds your counts to get N=SUM(B2:B6)
LNNatural logarithm, the standard base for H'=LN(C2)
SUMPRODUCTMultiplies two ranges and adds the results in one step=-SUMPRODUCT(C2:C6,LN(C2:C6))
COUNTIFCounts species with a count above zero, giving S=COUNTIF(B2:B6,">0")
LOGLogarithm in any base, for bits or decits=LOG(C2,2)
IFERRORHides the #NUM! error a zero count produces=IFERROR(LN(C2),0)

What to conclude: if you only remember one line, remember SUMPRODUCT. It calculates the whole Shannon Wiener index in a single cell.

8.2 Step by step in the sheet

Step 1. Type your data and total the counts

=SUM(B2:B6)
shannon.xlsx - ExcelB7fx=SUM(B2:B6)ABCDESpeciesCountp = n/NLN(p)p*LN(p)2Bulbul453Babbler304Sunbird155Barbet76Drongo317Total N100

Species names go in column A, counts in column B. Cell B7 holds =SUM(B2:B6), which returns N = 100.

Step 2. Turn each count into a proportion

=B2/$B$7fill down to C6
shannon.xlsx - ExcelC2fx=B2/$B$7ABCDESpeciesCountp = n/NLN(p)p*LN(p)2Bulbul450.453Babbler300.304Sunbird150.155Barbet70.076Drongo30.031

C2 holds =B2/$B$7 and returns 0.45. The dollar signs lock the total so the formula fills down correctly to C6. Column C now adds to 1.00.

Step 3. Take the natural log of each proportion

=LN(C2)fill down to D6
shannon.xlsx - ExcelD2fx=LN(C2)ABCDESpeciesCountp = n/NLN(p)p*LN(p)2Bulbul450.45-0.79853Babbler300.30-1.20404Sunbird150.15-1.89715Barbet70.07-2.65936Drongo30.03-3.50661

D2 holds =LN(C2) and returns -0.7985. Every value in column D is negative, which is normal because every proportion is below 1.

Step 4. Add it all up and flip the sign

=E2*-1=-SUMPRODUCT(C2:C6,LN(C2:C6))=COUNTIF(B2:B6,">0")=E8/LN(5)
shannon.xlsx - ExcelE8fx=-SUMPRODUCT(C2:C6,LN(C2:C6))ABCDESpeciesCountp = n/NLN(p)p*LN(p)2Bulbul450.45-0.7985-0.35933Babbler300.30-1.2040-0.36124Sunbird150.15-1.8971-0.28465Barbet70.07-2.6593-0.18616Drongo30.03-3.5066-0.10521

Column E holds =C2*D2 for each row. The one-cell version in E8 is =-SUMPRODUCT(C2:C6,LN(C2:C6)) and returns H' = 1.296. Evenness follows as =E8/LN(5) = 0.806.

Tip: if you already have percentages instead of counts, divide them by 100 first. The Shannon Wiener formula needs proportions that add to 1.00, not to 100.
Warning: Excel's LOG function defaults to base 10, not base e. =LOG(C2) gives decits, not the nats every ecology paper reports. Use LN, or write =LOG(C2,EXP(1)) if you prefer LOG.

8.3 The awkward cases

CaseWhat breaksFix
A species with a count of 0LN(0) returns #NUM!Delete the row, or wrap it: =IFERROR(C2*LN(C2),0)
Blank cells inside the rangeSUMPRODUCT treats them as 0 and returns #NUM!Sort the data and remove empty rows before you calculate
Text mixed into the count columnSUM ignores it silently, so N is wrongCheck N by eye, or use =COUNT(B2:B6) against your species total
Counts recorded as percentagesThe total is 100, so every proportion is 100 times too smallDivide by 100, or go back to the raw counts
Duplicate species rowsThe same species is treated as two species, inflating H'Use a PivotTable to sum counts by species name first

What to conclude: nearly every wrong Shannon Wiener value in Excel traces back to one of these five. Check them before you check the formula.

8.4 Why answers differ between Excel, R and Python

They should not differ, and with this worked example they do not. All three return 1.296. When people do see a difference, the cause is almost always one of three things. First, the logarithm base: Excel's LOG is base 10, R's vegan uses natural log by default, and Python's scipy.stats.entropy uses natural log unless you pass a base. Second, zero counts: R's vegan drops them, Excel throws #NUM!. Third, rounding: if you round proportions to two decimals before summing, you can lose 0.01 on H'. Keep full precision until the final display step.

8.5 Charting the result in Excel

  1. Rank abundance curve. Sort counts largest to smallest, select column B, then Insert, Line chart. Set the vertical axis to a log scale to see the rare species clearly.
  2. Relative abundance pie. Select columns A and C, then Insert, Pie chart. This is the picture of evenness that a reviewer understands instantly.
  3. Site comparison bars. Put one H' value per site in a column and use a clustered bar chart. Add error bars if you have replicates.
  4. Label the axes with units. Write "H' (nats)" on the value axis so no one has to guess your log base.

8.6 Excel error messages and what they mean

MessageCauseFix
#NUM!LN of zero or a negative numberRemove zero counts or wrap in IFERROR
#DIV/0!The total N cell is empty or zeroCheck the SUM range covers every data row
#VALUE!Text inside a numeric rangeClear notes such as "none seen" from the count column
#REF!A row used by the formula was deletedUndo, then rebuild the range
Result is 0Only one species has a count above zeroThat is correct: H' is genuinely 0 for a single species
Result is negativeThe minus sign was left off the sumH' cannot be negative. Add the leading minus.

What to conclude: a negative H' or a value above 4.6 is a data problem, not an ecological finding.

📘 9. How to Calculate the Shannon Wiener Index in R

R, one complete script you can run top to bottom

9.1 The complete script

Copy this into RStudio and press Run. It needs no packages. Change only the counts line. It prints H' = 1.296 and saves one 300 dpi figure.

# ------------------------------------------------------------------
# Shannon Wiener Diversity Index in R
# StatsUnlock.com - free ecology and wildlife analysis tools
# ------------------------------------------------------------------
set.seed(42)

# 1. YOUR DATA -- change only this line
counts <- c(45, 30, 15, 7, 3)
species <- c("Bulbul", "Babbler", "Sunbird", "Barbet", "Drongo")

# Reading from a file instead? Uncomment the two lines below.
# dat <- read.csv("my_survey.csv")          # columns: species, count
# counts <- dat$count; species <- dat$species

# 2. CLEAN THE DATA
counts[is.na(counts)] <- 0        # missing values become zero
keep <- counts > 0                # drop zero counts, ln(0) is undefined
counts <- counts[keep]
species <- species[keep]

# 3. CALCULATE
N <- sum(counts)                  # total individuals
S <- length(counts)               # species richness
p <- counts / N                   # proportions
H <- -sum(p * log(p))             # Shannon Wiener index, natural log
J <- H / log(S)                   # Pielou's evenness
D <- sum(p^2)                     # Simpson's dominance
eff <- exp(H)                     # effective number of species

# Same answer using the vegan package:
# install.packages("vegan")
# library(vegan); vegan::diversity(counts, index = "shannon")

# 4. PRINT A PLAIN-ENGLISH VERDICT
verdict <- if (H >= 2.5) "high diversity" else if (H >= 1.5) "moderate diversity" else "low diversity"
cat("Shannon Wiener index H' :", round(H, 3), "\n")
cat("Evenness J'             :", round(J, 3), "\n")
cat("Species richness S      :", S, "\n")
cat("Total individuals N     :", N, "\n")
cat("Simpson 1 - D           :", round(1 - D, 3), "\n")
cat("Effective species       :", round(eff, 2), "\n")
cat("Verdict                 :", verdict, "\n")

# 5. SAVE ONE 300 dpi FIGURE
png("shannon_rank_abundance.png", width = 1800, height = 1200, res = 300)
ord <- order(counts, decreasing = TRUE)
barplot(counts[ord],
        names.arg = species[ord],
        col = "#3aab6d", border = NA, las = 2,
        ylab = "Number of individuals",
        main = paste0("Rank abundance, H' = ", round(H, 3)))
dev.off()
cat("Figure saved as shannon_rank_abundance.png\n")

9.2 What each line does

LineWhat it does
set.seed(42)Fixes anything random so your figure is reproducible.
counts <- c(45, 30, ...)Your species counts. This is the only line most users change.
counts[is.na(counts)] <- 0Turns missing values into zero so the script does not stop.
keep <- counts > 0Marks species actually present. Zero counts must go, because ln(0) is undefined.
p <- counts / NConverts counts to proportions that add to 1.00.
H <- -sum(p * log(p))The Shannon Wiener index itself. R's log() is the natural log.
J <- H / log(S)Pielou's evenness, 0 to 1.
eff <- exp(H)Effective number of species, the Hill number of order 1.
vegan::diversity(...)The package one-liner. It returns the same 1.296.
png(..., res = 300)Opens a 300 dpi device, the resolution most journals ask for.
dev.off()Closes the device and writes the file. Forget this and the PNG stays empty.

9.3 What the figure shows

The script saves a rank abundance bar chart: species sorted from most to least common, with H' printed in the title. A steep drop from the first bar means one species dominates and evenness is low. A gentle slope means a balanced community and a higher H'. This single figure explains your number better than the number alone.

9.4 Problems and fixes

ProblemCauseFix
Result is NaNA zero or negative count reached log()Keep the counts > 0 filter in the script
Error: could not find function "diversity"vegan is not loadedRun install.packages("vegan") then library(vegan)
Value is 1.870 not 1.296log2 was used instead of natural logUse log(p), not log2(p)
Empty PNG filedev.off() was never calledRun dev.off() once, then re-run the plotting block
Species labels overlapLong binomial names on the x axisKeep las = 2, or shorten to genus initials
Value changes every runData is being resampled somewhereKeep set.seed(42) at the top

9.5 One-liners worth keeping

CodeReturns
vegan::diversity(x, "shannon")H' straight from a count vector or a site-by-species matrix
vegan::diversity(x, "simpson")Simpson's 1 - D for the same data
exp(vegan::diversity(x, "shannon"))Effective number of species
vegan::specnumber(x)Species richness S
vegan::rarefy(x, sample = 100)Richness standardised to 100 individuals
iNEXT::iNEXT(x, q = 1)Rarefaction and extrapolation curves for Hill number q = 1

🐍 10. How to Calculate the Shannon Wiener Index in Python

Python, one complete script you can run top to bottom

Packages: numpy does the arithmetic, matplotlib draws and saves the figure, and scipy (optional) offers a one-line check. Install them once with pip install numpy matplotlib scipy. pandas is only needed if you read a CSV file.

10.1 The complete script

Save this as shannon.py and run it. Change only the counts line. It prints H' = 1.296 and saves one 300 dpi figure.

# ------------------------------------------------------------------
# Shannon Wiener Diversity Index in Python
# StatsUnlock.com - free ecology and wildlife analysis tools
# ------------------------------------------------------------------
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

np.random.seed(42)

# 1. YOUR DATA -- change only this line
counts = np.array([45, 30, 15, 7, 3], dtype=float)
species = ["Bulbul", "Babbler", "Sunbird", "Barbet", "Drongo"]

# Reading from a file instead? Uncomment the three lines below.
# import pandas as pd
# dat = pd.read_csv("my_survey.csv")          # columns: species, count
# counts, species = dat["count"].to_numpy(float), dat["species"].tolist()

# 2. CLEAN THE DATA
counts = np.nan_to_num(counts, nan=0.0)       # missing values become zero
keep = counts > 0                             # drop zero counts, ln(0) undefined
species = [s for s, k in zip(species, keep) if k]
counts = counts[keep]

# 3. CALCULATE
N = counts.sum()                              # total individuals
S = counts.size                               # species richness
p = counts / N                                # proportions
H = float(-np.sum(p * np.log(p)))             # Shannon Wiener index, natural log
J = H / np.log(S)                             # Pielou's evenness
D = float(np.sum(p ** 2))                     # Simpson's dominance
eff = float(np.exp(H))                        # effective number of species

# Same answer using SciPy:
# from scipy.stats import entropy
# H = entropy(counts)          # natural log by default

# 4. PRINT A PLAIN-ENGLISH VERDICT
verdict = "high diversity" if H >= 2.5 else "moderate diversity" if H >= 1.5 else "low diversity"
print(f"Shannon Wiener index H' : {H:.3f}")
print(f"Evenness J'             : {J:.3f}")
print(f"Species richness S      : {S}")
print(f"Total individuals N     : {N:.0f}")
print(f"Simpson 1 - D           : {1 - D:.3f}")
print(f"Effective species       : {eff:.2f}")
print(f"Verdict                 : {verdict}")

# 5. SAVE ONE 300 dpi FIGURE
order = np.argsort(counts)[::-1]
fig, ax = plt.subplots(figsize=(6, 4))
ax.bar([species[i] for i in order], counts[order], color="#3aab6d")
ax.set_ylabel("Number of individuals")
ax.set_title(f"Rank abundance, H' = {H:.3f}")
plt.xticks(rotation=45, ha="right")
plt.tight_layout()
plt.savefig("shannon_rank_abundance.png", dpi=300)
print("Figure saved as shannon_rank_abundance.png")

10.2 What each line does

LineWhat it does
matplotlib.use("Agg")Draws without a screen, so the script runs on a server or in a notebook.
np.random.seed(42)Fixes anything random so the figure is reproducible.
counts = np.array([...])Your species counts. The only line most users change.
np.nan_to_num(counts)Turns missing values into zero so the script does not stop.
keep = counts > 0Drops zero counts, because np.log(0) is negative infinity.
p = counts / NConverts counts to proportions that add to 1.00.
H = -np.sum(p * np.log(p))The Shannon Wiener index. np.log is the natural log.
J = H / np.log(S)Pielou's evenness, 0 to 1.
entropy(counts)The SciPy one-liner. It normalises counts for you and returns the same 1.296.
plt.savefig(..., dpi=300)Writes the 300 dpi figure most journals ask for.

10.3 What the figure shows

The saved PNG is a rank abundance bar chart with H' in the title, identical in meaning to the R figure. Use it directly in a thesis chapter or a supplementary file. If you want the pie chart of relative abundance instead, swap ax.bar for ax.pie(p, labels=species).

10.4 Problems and fixes

ProblemCauseFix
RuntimeWarning: divide by zeroA zero count reached np.logKeep the counts > 0 filter
Result is nanMissing values in the arrayKeep the np.nan_to_num line
ModuleNotFoundError: numpyThe package is not installed in this environmentRun pip install numpy matplotlib
Value is 1.870 not 1.296np.log2 was used instead of np.logUse np.log, or pass base=2 to scipy entropy on purpose
Figure window never opensThe Agg backend has no screen outputThat is expected. Open the saved PNG file.
Integer division gives zerosCounts stored as int in old Python codeKeep dtype=float in the array line

10.5 One-liners worth keeping

CodeReturns
scipy.stats.entropy(counts)H' in nats, straight from raw counts
scipy.stats.entropy(counts, base=2)H' in bits
np.exp(scipy.stats.entropy(counts))Effective number of species
1 - np.sum((counts/counts.sum())**2)Simpson's 1 - D
(counts > 0).sum()Species richness S
skbio.diversity.alpha.shannon(counts)H' from scikit-bio, base 2 by default

📋 11. Reference Tables

Six lookup tables for reading, converting, and sanity-checking a Shannon Wiener index value.

Table 11.1 Published H' values by habitat type

HabitatTaxonTypical H' (ln)Typical S
Lowland tropical rainforestBirds3.2 to 4.240 to 120
Dry deciduous forestBirds2.4 to 3.225 to 50
Temperate woodlandBirds2.0 to 2.815 to 35
Grassland, managedPlants1.5 to 2.410 to 30
Wetland, freshwaterWaterbirds1.8 to 2.812 to 40
Coral reef transectFish2.5 to 3.530 to 80
Camera trap gridLarge mammals1.2 to 2.26 to 20
Urban parkBirds1.2 to 2.28 to 20
Intensive croplandArthropods0.8 to 1.85 to 20
Polluted streamMacroinvertebrates0.3 to 1.23 to 10

What to conclude: a value of 2.0 is strong for a camera trap grid and weak for a rainforest bird survey. Always read your number against your own system.

Table 11.2 H' by logarithm base

H' natural log (nats)log2 (bits)log10 (decits)Effective species
0.5000.7210.2171.65
1.0001.4430.4342.72
1.2961.8700.5633.66
1.5002.1640.6514.48
2.0002.8850.8697.39
2.5003.6071.08612.18
3.0004.3281.30320.09
3.5005.0501.52033.12
4.0005.7711.73754.60

What to conclude: to convert, divide the natural log value by ln 2 (0.6931) for bits or by ln 10 (2.3026) for decits. Never compare bases without converting first.

Table 11.3 Maximum possible H' for a given richness

Species richness SH'max = ln SH' if J' = 0.8H' if J' = 0.5
20.6930.5540.347
51.6091.2880.805
102.3031.8421.151
202.9962.3971.498
503.9123.1301.956
1004.6053.6842.303

What to conclude: if your H' is close to ln S, your community is nearly perfectly even. If your reported H' is larger than ln S, you have a calculation error.

Table 11.4 Reading Pielou's evenness

J' rangeReadingWhat it usually means
0.90 to 1.00Very even HealthyNo species dominates. Common in stable, undisturbed systems.
0.75 to 0.90Even HealthyA normal, balanced community.
0.60 to 0.75Moderate WatchTwo or three species carry most individuals.
0.40 to 0.60Uneven WatchClear dominance. Check for disturbance or a feeding aggregation.
Below 0.40Very uneven ConcernOne species takes over. Often invasion, pollution, or heavy management.

What to conclude: report J' beside H' always. Two sites with the same H' can have very different evenness once richness differs.

Table 11.5 Minimum sampling effort by survey type

Survey typeMinimum effort for a usable H'Preferred effort
Bird point counts10 points, 30 individuals30 points across 3 visits
Line transects2 km walked10 km, repeated in 2 seasons
Camera trapping300 trap nights1,000 to 2,000 trap nights
Vegetation quadrats10 quadrats of 1 m²30 quadrats, stratified by habitat
Pitfall traps20 trap days100 trap days across 5 stations
Reef fish belt transects4 transects of 50 m12 transects across 3 depths
Light trap insects3 trap nights12 trap nights across the season

What to conclude: below the minimum column, H' mostly measures your effort, not the community. Plot a species accumulation curve before you trust the value.

Table 11.6 Which diversity index to report

IndexWeightsRangeBest used when
Shannon Wiener H'Rare species0 to ~4.6You want one balanced number for richness and evenness
Simpson's 1 - DCommon species0 to 1Dominance is the story, or samples are small
Species richness SAll equally1 upwardPresence lists only, no reliable counts
Pielou's J'Evenness only0 to 1Comparing communities with different richness
Berger-ParkerThe single commonest species0 to 1Quick screening for one dominant species
Hill numbersTunable by q1 upwardYou need a true, comparable diversity ratio
Margalef'sRichness, effort corrected0 upwardSample sizes differ between sites

What to conclude: most reviewers expect H' plus one companion index. Shannon with Simpson, or Shannon with Pielou, is the safest pair.

📊 12. Example Results

Scenario 1: High-diversity tropical forest

A bird survey records 28 species and 412 individuals with fairly even counts. H' works out to about 3.28. This high value points to an intact, species-rich community typical of undisturbed lowland forest.

Scenario 2: Disturbed, degraded site

A logged fragment holds just 6 species and 200 individuals, but one species makes up 150 of them. H' drops to about 0.98. The low value reflects strong dominance and reduced ecological integrity.

Scenario 3: Same richness, different evenness

Two plots each have 5 species. Plot A counts are 20,20,20,20,20 (H' = 1.61); Plot B counts are 80,5,5,5,5 (H' = 0.76). Same richness, very different diversity, this is exactly what the Shannon Wiener index reveals.

Scenario 4: Before vs after restoration

A grassland plot rises from H' = 1.9 before management to H' = 2.6 three years after invasive removal. The gain shows recovering evenness as native species return.

Scenario 5: Camera-trap mammal survey

Across 1,400 trap nights, 8 mammal species are detected with counts 40,35,30,25,20,15,10,5. H' = 1.96, a moderate value for a mid-sized mammal community in a wildlife corridor.

Scenario 6: Edge case / caution

Only 3 individuals across 3 species gives H' = 1.10, but the sample is far too small to trust. Always collect at least 30 individuals before reporting a Shannon Wiener value.

Scenario 7: Richness and evenness pull in different directions

Site X holds 5 perfectly even species (20 each) and scores H' = 1.61 with J' = 1.00. Site Y holds 12 uneven species (60,30,20,15,10,8,6,5,4,3,2,1) and scores H' = 1.94 with J' = 0.78. Site Y wins on H' only because it has more species, not because it is better balanced. Report S and J' beside H' or this is invisible.

Scenario 8: The worked example used in Sections 8, 9 and 10

Five species with counts 45, 30, 15, 7, 3 give N = 100, S = 5, H' = 1.296, J' = 0.806, Simpson 1 - D = 0.679, and 3.66 effective species. Excel, R, Python and this calculator all return the same value, so use this dataset to check your own setup.

🥾 13. How to Collect Raw Data in the Field

The Shannon Wiener index is only as good as the counts you feed it. Follow these ready-to-use steps in the field to collect clean, comparable species abundance data. Print this list and take it with you.

start end 🐾 🐾 Line Transect Walk the line, record perpendicular distance
Fig 1. Line transect. Walk a fixed straight line at steady pace and count every individual seen or heard, noting its distance from the line.
observer radius r Point Count Stand still, count within a fixed radius
Fig 2. Point count. Stand at a fixed station for a set time (e.g. 10 min) and count all individuals within a fixed radius; repeat at several stations.
Quadrat Count all plants inside a fixed frame 1 m × 1 m frame
Fig 3. Quadrat. For plants or sessile species, place a fixed frame (e.g. 1 m × 1 m) and count every individual of each species inside it.
camera Camera Trap Motion-triggered photos over trap nights
Fig 4. Camera trap. For shy mammals, fix motion-triggered cameras, run them for equal trap nights per site, and count independent detections per species.
FIELD DATASHEET · Site: Pine Ridge SpeciesCountDetect Robin|||| |||seen Blue Tit|||| |heard Wren||||heard Chaffinch|||seen Nuthatch||seen Date 14/07 Observer RP 0630–0700 Clear
Fig 5. Field datasheet. One row per species: tally each individual, note how it was detected, and record date, observer, time, and weather. Sum per species, then paste the totals into the calculator.
Per-station tallies Robin S1:3 S2:2 S3:2Blue Tit S1:2 S2:2 S3:2 Wren S1:1 S2:2 S3:1Chaffinch S1:1 S2:1 S3:1 Nuthatch S1:1 S2:0 S3:1 add across stations → Paste into tool 7, 6, 4, 3, 2 H' = 1.52 ✓ From datasheet to result Sum species totals, then enter
Fig 6. Sum, then enter. Add each species across all stations to get one total per species, then paste the comma-separated totals into the calculator to get H'.
  1. Define your question first. Decide what you are comparing (site vs site, season vs season, before vs after) before you collect a single count. This sets your sampling design.
  2. Pick one taxonomic group and stick to it. Count only birds, only trees, or only mammals. Mixing groups makes the index meaningless.
  3. Choose a standard sampling method and use it everywhere: point counts, line transects, quadrats, camera traps, pitfall traps, or mist nets. Do not switch methods between sites.
  4. Fix your sampling effort. Keep the same transect length, plot size, count duration, or number of trap nights at every site so results are comparable.
  5. Set a minimum sample. Aim for at least 30 individuals and several species per sample; small samples give unstable, misleading H' values.
  6. Use replicates. Place at least 3 stations, plots, or transects per site so you can estimate variation and run statistics later.
  7. Mark station locations with GPS. Record coordinates (to a few metres) so the exact spot can be resurveyed in future years.
  8. Record every individual, not just species presence. The index needs abundance counts. Tally each animal or plant, not just a species checklist.
  9. Count during a consistent time window. Survey birds in the first hours after dawn; keep the same window and avoid rain, high wind, or extreme heat.
  10. Avoid double-counting. Move in one direction, note flying birds separately, and use a set detection radius so the same individual is not tallied twice.
  11. Log detection method. Note whether each record was seen, heard, trapped, or photographed; this matters for later corrections.
  12. Identify to species where possible. If you cannot, use a consistent morphospecies label (e.g. "Warbler sp. 1") and keep it identical across all sheets.
  13. Use a prepared datasheet. Columns: Date, Site, Station, Observer, Species, Count, Detection type, Notes. One row per species per station.
  14. Record effort metadata on every sheet: start and end time, weather, observer name, and equipment used. You will need these to standardise later.
  15. Photograph or voucher tricky species. A quick phone photo settles identification disputes back at the desk.
  16. Enter counts as whole numbers. The tool needs raw individual counts, not percentages or densities. Keep any conversions for a separate column.
  17. Back up your data the same day. Photograph paper sheets or type counts into a spreadsheet each evening so nothing is lost.
  18. Keep a field notebook for anything unusual: disturbance, human activity, unexpected species, or equipment problems.
  19. Sum counts per species before entry. Add up all stations for a site, then paste the per-species totals into this calculator (for example 52, 48, 55, 61, 47).
  20. Never invent or round zeros away. A species truly absent from the sample is simply not listed; do not pad the data.

🎯 14. When to Use This Tool

14.1 Quick decision checklist

  • ✅ You have counts of individuals per species, not just a species list.
  • ✅ Every site was surveyed with the same method and the same effort.
  • ✅ You want one number that reflects both richness and evenness.
  • ✅ Your sample holds at least 30 individuals and 3 species.
  • ❌ You only know which species were present, with no counts. Use species richness instead.
  • ❌ Your data is percent cover for plants. Use Simpson's index or an ordination method.
  • ❌ Effort differs a lot between sites and cannot be standardised. Rarefy first.

14.2 Four real situations

SituationWhat you doWhat H' tells you
Comparing a protected reserve with a nearby farmSame point count protocol at both, same seasonWhether protection is holding a more diverse bird community
Monitoring a restored grassland over five yearsRepeat quadrats each June, same observersWhether native species are returning and evenness is rising
Reporting a camera trap survey to a forest department1,400 trap nights, independent detections per speciesA defensible single figure for mammal community diversity
A student thesis chapter on stream healthKick samples at 6 sites upstream and downstream of a dischargeWhether diversity collapses below the discharge point

14.3 Sampling design guidance

  1. Fix effort first. Decide trap nights, transect length, or quadrat count before you start, and keep it identical at every site.
  2. Replicate within sites. Three or more stations per site let you report a mean H' with a standard error instead of a bare number.
  3. Randomise or stratify placement. Placing stations where you expect wildlife inflates counts and biases evenness.
  4. Hold the season constant. Diversity swings with breeding, migration, and monsoon. Compare like with like.
  5. Record zero-count visits. A survey with nothing detected is data, not a blank line.

14.4 Which metric next

  • Want to know if one species dominates? Go to Simpson's index or Berger-Parker.
  • Want a fair ratio, for example "twice as diverse"? Convert to Hill numbers with exp(H').
  • Sample sizes differ? Use Margalef's index or rarefaction.
  • Comparing species turnover between sites? Use beta diversity, not H'.
  • Only presence data? Use species richness with a species accumulation curve.

🛠️ 15. Troubleshooting and Common Errors

Ten problems users hit with the Shannon Wiener index, and how to fix each one.

My H' is 0

Cause: only one species has a count above zero. Fix: nothing to fix. H' is genuinely 0 when a single species holds every individual. Check that other species were not lost during data entry.

My H' is negative

Cause: the leading minus sign was left off the sum, or a negative count was entered. Fix: H' cannot be negative. Re-check the formula sign and remove any negative values from the count column.

My H' is above 4.6

Cause: either you have more than 100 very even species, which is rare, or counts and proportions were mixed in the same column. Fix: confirm that your proportions add to 1.00 and that no row is a total row.

The tool says invalid input

Cause: text, symbols, or empty cells inside the count list. Fix: keep only numbers separated by commas, spaces, tabs, or new lines. Remove notes such as "none seen" and replace them with 0.

My two sites have the same H' but look very different

Cause: richness and evenness can trade off. Ten uneven species can score the same as five even ones. Fix: report S, J' and H' together, never H' alone.

H' keeps rising as I add more survey days

Cause: you have not yet reached an asymptote, so you are measuring effort. Fix: plot a species accumulation curve. Keep sampling until it flattens, or rarefy all sites to the smallest sample size.

My value does not match my supervisor's

Cause: different log bases, usually ln against log2. Fix: 1.296 nats equals 1.870 bits. Divide the natural log value by 0.6931 to convert, and state the base in your methods.

Uploading my CSV gives strange numbers

Cause: the wrong column was picked, or a header row was read as data. Fix: use the column picker, then check the 8-row preview before running the analysis.

Rare species seem to have no effect

Cause: that is expected behaviour. A species with 1 of 1,000 individuals contributes about 0.007 to H'. Fix: if rare species are the point of your study, report richness or Hill numbers with q = 0 as well.

Charts do not appear after I click Run

Cause: the Chart.js library was blocked by a network filter or an offline device. Fix: reload the page on a normal connection. The numbers and the results table still work without charts.

⚠️ 16. Assumptions and Limitations

The Shannon Wiener index is easy to calculate and easy to misuse. These are the conditions it assumes, and the things it cannot tell you.

16.1 What the index assumes

  • Individuals were sampled at random from the community.
  • All species had a fair chance of being detected. Shy or nocturnal species break this.
  • Every individual was identified to the same taxonomic level.
  • The sample is large enough that adding more individuals would not change H' much.
  • Counts are of individuals, not biomass, cover, or percentages.
  • Each record is independent. Ten photographs of one animal in one minute is one detection, not ten.

16.2 What it cannot tell you

  • Which species are present. Two sites with no species in common can score the same H'.
  • Whether the species are native, rare, threatened, or invasive. H' treats all species as equal.
  • Whether a difference between sites is statistically significant. That needs replicates and a test.
  • Ecosystem function. A high H' does not guarantee a healthy or stable system.
  • Population size or trend. Use density, occupancy, or abundance estimates for that.

16.3 The four limitations reviewers raise most

LimitationWhy it mattersWhat to do
Sample size dependenceH' rises with effort until it plateausRarefy, or report the accumulation curve
Not on a ratio scaleH' = 3 is not twice as diverse as H' = 1.5Convert to effective species with exp(H')
Detection biasCryptic species are systematically missedUse occupancy models, or state the bias openly
Insensitive to species identityLosing an endemic and gaining a weed can leave H' unchangedReport a species list and conservation status alongside

What to conclude: report H' as one line of evidence, with richness, evenness, effort, and a species list beside it. On its own it is a summary, not a conclusion.

🔍 17. Conclusion

▶ Run the analysis above to generate a personalised conclusion for your dataset.

❓ 18. Frequently Asked Questions

What is the Shannon Wiener index and when should I use it?

The Shannon Wiener index (H') measures species diversity by combining how many species are present with how evenly individuals are spread among them. Use it when you have species counts from a standardised survey and want a single number to compare diversity across sites, seasons, or treatments.

How is the Shannon Wiener index calculated step by step?

For each species, divide its count by the total to get a proportion p. Multiply p by the natural log of p. Add these values across all species, then flip the sign. With counts 45, 30, 15, 7, 3 the sum is -1.296, so H' = 1.296.

What is the Excel formula for the Shannon Wiener index?

Use =-SUMPRODUCT(C2:C6,LN(C2:C6)), where column C holds the proportions. Build the proportions first with =B2/$B$7, where B7 is the total count. Evenness follows as =H/LN(S). Avoid Excel's LOG function, because it defaults to base 10, not natural log.

How do I calculate the Shannon Wiener index in R?

Base R needs one line: H <- -sum(p * log(p)), where p is counts divided by their total. The package version is vegan::diversity(counts, index = "shannon"), which returns the same value. Use exp(H) for the effective number of species.

Which Python package calculates the Shannon Wiener index?

SciPy is the quickest: scipy.stats.entropy(counts) returns H' in nats straight from raw counts. NumPy does it manually with -np.sum(p * np.log(p)). scikit-bio also offers skbio.diversity.alpha.shannon(), but that one defaults to base 2.

What data do I need to calculate the Shannon Wiener index?

You need the count of individuals for each species in your sample. Paste them comma separated, upload a CSV file, or type them into the grid. Aim for at least 30 individuals and three or more species so the value is reliable.

What does a high vs low Shannon Wiener value mean ecologically?

Most communities fall between 1.5 and 3.5. A higher H' means more species and more even abundances, often a sign of a healthy, undisturbed habitat. A low H' means few species or one dominant species, which can signal disturbance, pollution, or invasion.

What is a good Shannon Wiener value for my habitat type?

There is no universal cutoff. Tropical forests often reach 3 to 4, temperate systems 2 to 3, and simple or harsh habitats below 1.5. A good value is one that matches or beats a reference site sampled with the same protocol, effort, and season.

How does the Shannon Wiener index differ from Simpson's index?

Shannon gives more weight to rare species, so it is sensitive to species richness. Simpson's index gives more weight to common, dominant species. Report both when you can, because they answer slightly different questions about the same community.

What is the difference between the Shannon index and species richness?

Species richness only counts how many species are present. The Shannon index also captures how evenly individuals are spread among them. Two plots with five species each can score 1.61 and 0.76 depending on evenness.

What units does the Shannon Wiener index use?

The index is dimensionless, but its size depends on the log base: natural log gives nats, log2 gives bits, log10 gives decits. H' = 1.296 nats equals 1.870 bits. Always state the base you used in your methods.

Does sample size affect the Shannon Wiener index?

Yes. Values usually rise with effort until they plateau, because larger samples detect more rare species. Standardise effort across sites, or use rarefaction, before comparing. Plot a species accumulation curve to check whether your sampling is adequate.

Can I compare Shannon Wiener values between sites or time periods?

Yes, but only when effort, protocol, taxonomic group, and season are comparable. If effort differs, rarefy to the smallest sample first. Converting to effective species with exp(H') makes the comparison easier to describe honestly.

How much sampling effort do I need for a reliable result?

Aim for at least 30 individuals and three or more replicate stations per site. Camera trap studies usually need 1,000 or more trap nights. Bird point counts need roughly 30 points across three visits before H' settles down.

How do I report the Shannon Wiener index in a journal or report?

Report the symbol and value in italics with richness and sample size, for example: H' = 3.28 (S = 28 species, N = 412 individuals, natural log). Add Pielou's evenness and state the software used in your methods.

What are the assumptions and limitations of the Shannon Wiener index?

It assumes a random, representative sample with standardised effort and correct species identification. It cannot tell you which species are present, whether they are native or threatened, or whether a difference between sites is statistically significant.

Is a higher Shannon Wiener value always better for conservation?

Usually, but not always. Some pristine habitats, such as salt marshes and alpine screes, are naturally low in diversity yet high in conservation value. Invasive species can also raise H' while damaging the native community.

My index value seems too high or too low, what went wrong?

Common causes are one species with a very high count, undetected species, data entry errors, mixing counts with percentages, or unequal effort between sites. A negative H', or one above 4.6, is almost always a calculation error, not a finding.

What are the most common mistakes when using the Shannon Wiener index?

Mixing counts with percentages, unequal survey effort, ignoring undetected species, using the wrong log base, duplicating a species across two rows, and treating H' as an absolute measure of habitat quality rather than one line of evidence.

Is this Shannon Wiener calculator free and accurate?

Yes. It is completely free, runs entirely in your browser, stores no data, and uses the standard published Shannon-Weaver formula. Results are cross-checked against R's vegan package and Python's SciPy, and match to three decimal places.

📝 19. Cite This Tool

Use one of these three formats when you mention this Shannon Wiener index calculator in a thesis, report, or paper.

APA 7th edition

StatsUnlock. (2026). Shannon Wiener index calculator: Free online species diversity tool [Computer software]. https://statsunlock.com/shannon-wiener-index-calculator/

BibTeX

@misc{statsunlock_shannon_2026,
  title        = {Shannon Wiener Index Calculator: Free Online Species Diversity Tool},
  author       = {{StatsUnlock}},
  year         = {2026},
  howpublished = {\url{https://statsunlock.com/shannon-wiener-index-calculator/}},
  note         = {Accessed: 2026-09-15}
}

Methods paragraph

Species diversity was summarised using the Shannon Wiener index (H'), calculated as H' = -Σ p ln p, where p is the proportion of individuals belonging to each species (Shannon & Weaver, 1949; Magurran, 2004). Pielou's evenness (J' = H' / ln S) and Simpson's index (1 - D) were calculated alongside it. All indices were computed with the StatsUnlock Shannon Wiener index calculator (https://statsunlock.com/shannon-wiener-index-calculator/) using natural logarithms, and verified in R with vegan::diversity().

🔗 20. Related Tools

Free ecology and wildlife calculators that pair well with the Shannon Wiener index.

Simpson's Diversity Index Calculator

The companion index. It weights common species, where Shannon weights rare ones. Report both.

Evenness Index Calculator (Pielou's J')

Separates evenness from richness when two sites share the same H'.

Hill Numbers Calculator

Converts H' into effective species so you can say one site is twice as diverse.

Relative Abundance Calculator

Turns raw counts into the proportions the Shannon formula needs.

Fisher's Alpha Diversity Calculator

A richness measure that is less sensitive to sample size than H'.

Camera Trap Analysis Calculator

Turns photo detections and trap nights into the standardised counts you feed into H'.

📖 21. Glossary of Terms

Abundance The number of individuals of a species recorded in a sample.
Alpha diversity Diversity within a single site or sample. The Shannon Wiener index is an alpha diversity measure.
Berger-Parker index The proportion of the sample made up by the single commonest species.
Beta diversity The change in species composition between sites.
Detection probability The chance a species present at a site is actually recorded during a survey.
Dominance The degree to which one or a few species hold most individuals. High dominance lowers H'.
Effective number of species exp(H'), the number of equally common species that would give the same diversity.
Evenness (J') How equally individuals are shared among species, from 0 to 1.
Hill number A family of diversity measures controlled by an order q. At q = 1 it equals exp(H').
Independent detection One record of a species separated from the next by a set time, usually 30 minutes for camera traps.
Nats The units of H' when natural logarithms are used. Bits are the units when log2 is used.
Natural logarithm (ln) The logarithm to base e (2.718). The standard base for the Shannon Wiener index.
Pielou's evenness H' divided by ln S. The standard evenness measure reported beside H'.
Proportion (p) A species count divided by the total count. All proportions in a sample add to 1.00.
Quadrat A fixed-size sampling frame, usually square, placed on the ground to count plants or slow-moving animals.
Rarefaction Standardising samples to the same number of individuals so diversity can be compared fairly.
Rank abundance curve A plot of species counts sorted from commonest to rarest. A steep curve means low evenness.
Sampling effort The amount of survey work done: trap nights, transect kilometres, point counts, or quadrats.
Shannon Wiener index (H') A diversity index combining species richness and evenness, calculated as -Σ p ln p.
Simpson's index The chance that two individuals drawn at random are the same species, usually reported as 1 - D.
Species accumulation curve A plot of species found against effort. When it flattens, sampling is adequate.
Species richness (S) The number of different species in a sample, with no weighting by abundance.
Trap night One camera trap active for 24 hours. The standard unit of camera trap effort.
Transect A fixed line along which observations are recorded at a steady speed and effort.
📚 22. References (20 Peer-Reviewed Sources)

The following references support the ecological methods used in this Shannon Wiener diversity index calculator, covering biodiversity measurement, species diversity, and best practices in ecological sampling and wildlife analysis.

  1. Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. University of Illinois Press.
  2. Simpson, E. H. (1949). Measurement of diversity. Nature, 163, 688. doi.org/10.1038/163688a0
  3. Magurran, A. E. (2004). Measuring biological diversity. Blackwell Publishing.
  4. Krebs, C. J. (1999). Ecological methodology (2nd ed.). Benjamin Cummings.
  5. Hill, M. O. (1973). Diversity and evenness: A unifying notation and its consequences. Ecology, 54(2), 427–432. doi.org/10.2307/1934352
  6. Jost, L. (2006). Entropy and diversity. Oikos, 113(2), 363–375. doi.org/10.1111/j.2006.0030-1299.14714.x
  7. Pielou, E. C. (1966). The measurement of diversity in different types of biological collections. Journal of Theoretical Biology, 13, 131–144. doi.org/10.1016/0022-5193(66)90013-0
  8. Chao, A., & Jost, L. (2012). Coverage-based rarefaction and extrapolation. Ecology, 93(12), 2533–2547. doi.org/10.1890/11-1952.1
  9. Oksanen, J., et al. (2022). vegan: Community ecology package. R package v2.6-4. CRAN.R-project.org/package=vegan
  10. Bibby, C. J., Burgess, N. D., Hill, D. A., & Mustoe, S. H. (2000). Bird census techniques (2nd ed.). Academic Press.
  11. Gotelli, N. J., & Colwell, R. K. (2001). Quantifying biodiversity: Procedures and pitfalls. Ecology Letters, 4(4), 379–391. doi.org/10.1046/j.1461-0248.2001.00230.x
  12. Colwell, R. K. (2013). EstimateS: Statistical estimation of species richness (v9). purl.oclc.org/estimates
  13. Whittaker, R. H. (1972). Evolution and measurement of species diversity. Taxon, 21(2/3), 213–251. doi.org/10.2307/1218190
  14. R Core Team. (2024). R: A language and environment for statistical computing. R-project.org
  15. Ahumada, J. A., et al. (2011). Community structure and diversity of tropical forest mammals. Phil. Trans. R. Soc. B, 366(1578), 2703–2711. doi.org/10.1098/rstb.2011.0115
  16. Chao, A., et al. (2014). Rarefaction and extrapolation with Hill numbers. Ecological Monographs, 84(1), 45–67. doi.org/10.1890/13-0133.1
  17. Niedballa, J., et al. (2016). camtrapR: An R package for camera trap data. Methods Ecol. Evol., 7(12), 1457–1462. doi.org/10.1111/2041-210X.12600
  18. Hsieh, T. C., Ma, K. H., & Chao, A. (2016). iNEXT: rarefaction and extrapolation of Hill numbers. Methods Ecol. Evol., 7(12), 1451–1456. doi.org/10.1111/2041-210X.12613
  19. Roswell, M., Dushoff, J., & Winfree, R. (2021). A conceptual guide to measuring species diversity. Oikos, 130(3), 321–338. doi.org/10.1111/oik.07202
  20. Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88(10), 2427–2439. doi.org/10.1890/06-1736.1

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