Population genetics for plants · molecular and morphological data

Read the genetic history written in your populations

Microsatellites, AFLP bands, chloroplast sequences or morphological traits — the same guided workflow takes you from the raw genotype table to diversity indices, Hardy–Weinberg tests, AMOVA, genetic distances, Bayesian clustering and haplotype networks, and ends in editable, journal-ready figures. No programming, no installation.

Runs entirely in your browser Your data never leave your computer Codominant, dominant, haploid, sequence and morphological data Figures up to 900 dpi · PNG, TIFF, SVG Free for teaching and research

How it works

A guided route, in the order a population genetics paper is actually written. Each step explains the idea in plain language, checks whether your data can support it, and recommends what to do next.

STEP 1

Load & check

any format, then quality control

STEP 2

Describe diversity

how much variation, and where

STEP 3

Test equilibrium

HWE, inbreeding, linkage

STEP 4

Partition it

AMOVA and F-statistics

STEP 5

Find the groups

distance, ordination, clustering

STEP 6

Infer the history

gene flow, bottlenecks, expansion

STEP 7

Publish

editable figures and the report

Try it: watch drift, migration and selection at work

Six populations start with the same allele at p = 0.5. Every generation the model applies selection, migration, mutation and then draws 2N_e gene copies at random — the Wright–Fisher recursion, exactly as written in the textbooks. The right-hand panels are computed from the simulated frequencies: gene diversity within demes (H_S), in the whole metapopulation (H_T) and the F_ST that grows between them. Turn migration down and watch the populations drift apart.

Scenario

Allele frequency in each population · dashed line = metapopulation mean

Gene diversity and differentiation

N per deme100

Populations6

Migration m0.020

Selection s0.00

Mutation u0

Selfing rate0%

Generation

Mean p

0.500

H_S

0.500

F_ST

0.000

Fixed demes

0 / 6

N_e used

What's inside

Nine analysis blocks, built in order and released one at a time. Click a card to jump to it.

Every kind of data a plant study produces

The marker decides which statistics are even defined. PopGeneticsPro types your loci on import and then offers only the analyses that make sense for them — no silently wrong heterozygosities from an AFLP gel, no χ² test on haplotypes.

Methods covered

The classical toolkit of population genetics — diversity, equilibrium, differentiation and Bayesian clustering — plus the plant-specific analyses rarely found together: mating system, fine-scale spatial genetic structure and P_ST (or Q_ST) versus F_ST.

What it brings together

One guided path from the data sheet to the figure. The formulas come from the published methods, and every one is cited where it is used.

The theory, in plain language

Enough to run the analyses and defend them in a seminar. Every section names the papers the formulas come from; the full list is at the bottom of this page.

What population genetics actually asks start here

A species is rarely one big interbreeding unit. It is a set of populations that exchange genes at some rate, lose variation at some rate, and accumulate differences at some rate. Population genetics measures those three rates from a sample of individuals, and asks four questions in this order:

How much genetic variation is there, and is it the same in every population? (Block 3)
Is that variation organised the way random mating predicts, or is there inbreeding, selfing, clonality or a scoring problem? (Block 4)
How is the variation distributed — mostly within populations, or between them? (Blocks 5–7)
What history produced that pattern — gene flow, isolation, a bottleneck, an expansion? (Block 9)

The one number to remember In most outcrossing plants, 80–95% of the genetic variation sits within populations and only 5–20% between them. In selfers the proportions often reverse. Knowing which kind of species you have changes how you read every result that follows.

Hardy–Weinberg: the null model everything is measured against Block 4

Genotype frequencies under random mating

With two alleles at frequencies p and q, random mating in a large population with no selection, mutation or migration gives genotype frequencies p², 2pq and q² — and they stay there, generation after generation. That is the Hardy–Weinberg principle, and it is useful precisely because real populations depart from it.

expected heterozygosity He = 1 − Σ pᵢ² observed heterozygosity Ho = (number of heterozygotes) / N fixation index F = (He − Ho) / He

A positive F (fewer heterozygotes than expected) is the everyday result in plants, and it has several possible causes that the analysis must separate:

Selfing or biparental inbreeding — the biological explanation, consistent across all loci.
The Wahlund effect — you pooled two genetically distinct groups into one "population".
Null alleles — a primer site mutation hides one allele, so true heterozygotes are scored as homozygotes. Affects one locus, not all of them.

How to tell them apart Inbreeding raises F at every locus by a similar amount; a null allele raises it at one locus only. Block 4 reports F_IS per locus and per population side by side for exactly this reason.

The four forces: drift, migration, mutation, selection simulator

Independent populations drifting apart

Drift is the random sampling of gametes between generations. It is not a small correction: in a population of effective size N_e, heterozygosity decays as H_t = H₀(1 − 1/2N_e)^t, and alleles are eventually lost or fixed by chance alone. Small and fragmented populations lose variation fast.

Migration pushes the other way. In Wright's island model the equilibrium differentiation is F_ST ≈ 1/(1 + 4N_em), which is why one successful migrant per generation (N_em = 1) is enough to keep populations from diverging by drift.

Mutation creates new variation, slowly (10⁻⁵–10⁻³ per locus per generation for microsatellites, much lower for sequences). Selection changes frequencies systematically, but only at the loci it acts on — which is what makes neutral markers useful for reading demography.

Read N_em with care The conversion of F_ST into a number of migrants assumes an island model at equilibrium, with no selection and no mutation. Report it as an indicative value, never as a migration count.

F-statistics and AMOVA: where the variation sits Block 5

Pairwise differentiation between populations

Wright's three F-statistics describe the same sample at three levels: F_IS compares an individual with its own population (inbreeding), F_ST compares populations with the total (differentiation), and F_IT compares an individual with the total.

G_ST = (H_T − H_S) / H_T Nei (1973) θ (theta) Weir & Cockerham (1984), the estimator to report G'_ST = G_ST / G_ST(max) Hedrick (2005), corrected for high diversity D = (H_T − H_S)/(1 − H_S) · k/(k−1) Jost (2008), "true" differentiation

With highly polymorphic markers such as microsatellites, H_S can be so high that G_ST is mathematically capped far below 1 — two populations sharing no alleles at all may still give G_ST = 0.1. That is the reason to report G′_ST or Jost's D alongside it, not instead of it.

AMOVA (Excoffier et al. 1992) does the same job as an analysis of variance on a distance matrix, and it is the right tool when your design is hierarchical: individuals within populations, within regions. It gives a percentage of variation at each level and tests each one by permutation — and because it works from distances, it handles dominant markers and haplotypes as easily as microsatellites.

Dominant markers: what AFLP and ISSR can and cannot tell you binary data

A dominant band is present or absent. The heterozygote looks exactly like the dominant homozygote, so H_o cannot be observed and F_IS cannot be estimated from the data alone. Allele frequencies must be inferred from the frequency of the null phenotype:

q = √(freq of band-absent) assuming Hardy-Weinberg Lynch & Milligan (1994) small-sample correction Bayesian estimate with a prior on F when HWE cannot be assumed

Analyses that still work: Φ_PT and AMOVA, Nei's gene diversity, Jaccard/Dice distances, PCoA, Bayesian clustering, Mantel tests, spatial autocorrelation.
Analyses that do not: observed heterozygosity, HWE tests, F_IS, assignment based on genotype likelihoods, most bottleneck tests.

Two things to do before analysing bands Score the same gel twice and report the error rate, and drop bands present in fewer than ~5% or more than ~95% of individuals. Block 2 does both checks for you.

Plants are different: selfing, clones, pollen and seed plant-specific

Mating system: outcrossing, selfing and pollen flow

Most population genetics theory was written for animals that mate at random and move as adults. Plants do neither, and four consequences show up in every dataset:

Mixed mating. Outcrossing rates (t_m) range from near 0 to near 1, often within the same species. Selfing reduces N_e, inflates F_IS and speeds up differentiation between populations.
Clonality. Repeated multilocus genotypes must be detected before anything else — a clone counted as 40 individuals will distort every index. Block 2 flags them.
Two dispersal vehicles. Pollen carries nuclear genes, seed carries everything. Comparing nuclear with maternally inherited chloroplast markers separates the two, and their differentiation ratio estimates the pollen-to-seed flow ratio.
Fine-scale spatial structure. Limited seed dispersal makes neighbours relatives. That is what spatial autocorrelation and the S_p statistic quantify (Block 9) — and it is why a "population" sampled along a transect may not be one population at all.

Sampling design: how many individuals, how many loci before the lab

The honest answer is that it depends on the question, but the literature converges on useful minima:

Goal	Individuals per population	Loci
Diversity indices (He, Na)	20–30	8–10 SSR
Allelic richness, rare alleles	30–50	10–15 SSR
F_ST / AMOVA	20–25, ≥5 populations	10+ SSR or 100+ AFLP bands
Bayesian clustering	25–30	15+ SSR
Bottleneck tests	30+	15–20 SSR
Fine-scale spatial structure	100+ mapped individuals	8+ SSR

More loci beat more individuals For estimating differentiation, adding loci reduces the variance of F_ST faster than adding individuals. For finding rare alleles, the opposite is true.

Which analysis answers which question decision guide

Your question	The analysis	Block
Which population is most diverse?	He, uHe, allelic richness by rarefaction	3
Is this population inbred?	F_IS with bootstrap CI, HWE tests	4
Are my populations differentiated?	F_ST/θ, G′_ST, Jost's D, AMOVA	5
Does my hierarchical design matter?	Three-level AMOVA with permutations	5
How do populations relate to each other?	Nei's D, NJ/UPGMA tree, PCoA	6
Is differentiation just distance?	Mantel test, isolation by distance	6
How many genetic groups are there really?	Bayesian clustering, ΔK, DAPC	7
Where does this individual come from?	Assignment test, migrant detection	7
What is the history of my haplotypes?	Network, π, Tajima's D, mismatch	8
Did the population crash recently?	Heterozygosity excess, M-ratio, mode shift	9
Are neighbours relatives?	Spatial autocorrelation, kinship, S_p	9

How to cite

If PopGeneticsPro helped with an analysis in a thesis or a paper, please cite the software and the original method papers it implements — every result and the methods paragraph of Block 10 name them by author and year.

Barrera-Guzmán, L.Á. (2026). PopGeneticsPro: a browser-based platform for plant population genetics with codominant, dominant, sequence and morphological data (Version 1.0.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.22740171

This DOI always leads to the latest version; each version also has its own DOI in the archive.

References behind the calculations

Every statistic in this app comes from a published method, and each one is named again at the point where it is used.

Data & quality control

Load the file, agree on what it contains, and screen it before a single statistic is computed.

1 · Load your data

Everything stays on your computer: the file is read by the browser and never uploaded.

Drop your file here or click to choose one

.xlsx.csv.txt.str.gen .arp.fasta.vcf

Or try an example:

File loaded: none yet

Data template designer

Tell the app what your data will contain. It writes the sheet for you: IDs and populations already in place, one column per locus or trait, and a first row that declares the layout so nothing has to be guessed on import.

What did you score?

Sampling design

Each row of the sheet is

How the material was sampled

IDs

Geographic coordinates

Populations Plants in every population Region column (for a hierarchical AMOVA) Group column (e.g. racial complex)

Type the names and sizes below, or paste a column of names copied from a spreadsheet into the first cell.

Loci

Your template

Checks on this design

What you will be able to run

Preview of the sheet

When the sheet is filled in, save it and drop it into 1 · Load your data above.

Allele frequencies & diversity

How much genetic variation there is, and how it is spread among your populations.

1 · Settings

The defaults follow the most common conventions of the literature. Change them and the whole block recomputes.

A locus counts as polymorphic when

Rarefy allelic richness to (gene copies) Leave it empty to use the smallest sample available, the usual choice.

Bootstrap replicates over loci Gives the 95% intervals. Set 0 to skip it.

Random seed Report it in the methods and anyone can reproduce your intervals.

Hardy–Weinberg, inbreeding & linkage

Are the genotypes what random mating predicts — and if not, is it inbreeding, a null allele, or a mixture of populations?

1 · Settings

Permutations per exact HWE test Alleles are shuffled among individuals; 1 000 gives P-values to ±0.01.

Correction for multiple tests

Significance level α

Treat missing genotypes as null homozygotes Only if blanks come from failed amplification, not from plants that were never run.

Permutations for multilocus LD (r̄_d)

Permutations per locus pair Capped at 99 automatically when there are more than 400 pairs.

Random seed

2 · What the tests say

3 · Hardy–Weinberg tests, locus by population

The exact test conditions on the allele counts and asks how unusual the observed genotype table is (Guo & Thompson 1992, by Monte Carlo). The chi-square test is shown for comparison with older papers; it is unreliable whenever an expected count falls below five, which with microsatellites is almost always.

Show

4 · Inbreeding coefficient F_IS

f is Weir & Cockerham's (1984) estimator, multilocus as a ratio of summed variance components, with a bootstrap interval and a jackknife error over loci; the mean of Nei & Chesser's (1983) single-locus values is given for comparison. The selfing rate is the equilibrium value implied by f, s = 2F/(1+F) — a reference, not a measurement.

Locus by locus: the diagnostic

Inbreeding raises F_IS at every locus by a similar amount. A null allele raises it at one locus, in most populations. A locus is flagged when it shows a significant deficit in at least half the populations and its estimated null frequency exceeds 5%.

5 · Null alleles

Estimator

6 · Linkage disequilibrium

The index of association measures whether individuals that differ at one locus tend to differ at the others. r̄_d (Agapow & Burt 2001) is its version corrected for the number of loci, so it can be compared between studies. It works for codominant, dominant and haploid data alike, and is tested by shuffling each locus independently among individuals. In an outcrossing plant with unlinked markers it is close to zero; selfing, clonality and admixture push it up.

Locus pairs

Sample

Differentiation & AMOVA

How much of the variation separates your populations, which pairs differ, and whether the regional grouping is real.

1 · Settings

Permutations (global θ and AMOVA)

Permutations per population pair

Bootstrap replicates over loci Gives the 95% intervals of the multilocus estimates.

Random seed

Genetic distances, ordination & trees

How far apart the populations and individuals are, drawn as a map (PCoA), as a tree, and against geography.

1 · Settings

Distance between populations Nei's D for phylogeny-like questions with many loci; Cavalli-Sforza or Reynolds when populations diverged by drift alone (they recover the right tree more often, Takezaki & Nei 1996).

Distance between individuals Feeds the individual PCoA and the individual trees.

Bootstrap replicates over loci (tree support)

Lingoes correction for negative eigenvalues Makes the distance Euclidean before the PCoA, so the percentages of variation are exact.

Mantel permutations

Random seed

Bayesian clustering, DAPC & assignment

How many genetic groups the data themselves support, who belongs where, and which individuals are not from where they were collected.

1 · Bayesian clustering (admixture model)

The model of Pritchard, Stephens & Donnelly (2000): K clusters with their own allele frequencies, and for every individual the fraction of its genome drawn from each cluster (Q). It runs a Gibbs sampler in a background thread, so the page stays usable.

Model Allele frequencies are independent between clusters (the F-model is not implemented).

K from

K to

Replicates per K ΔK needs ≥ 2; publications usually run 10–20.

Burn-in iterations

Sampled iterations For a quick look use 1 000 + 2 000; for the paper, 50 000 + 100 000.

Random seed

4 · Discriminant analysis of principal components (DAPC)

Jombart, Devillard & Balloux (2010). A model-free alternative: a PCA summarises the genotypes, a discriminant analysis then finds the axes that best separate the groups — either your populations, or groups found in the data by k-means clustering with the number chosen by BIC. No Hardy–Weinberg or linkage assumptions, and fast.

Groups

Principal components retained Empty = the smaller of "90% of the variance" and N/3.

6 · Assignment tests and migrant detection

Each genotype is assigned to the population where it is most likely (Paetkau et al. 1995; Rannala & Mountain 1997), leaving the individual out of its own population. First-generation migrants are flagged by comparing L_home/L_max with the distribution obtained from genotypes simulated in the home population (Paetkau et al. 2004).

Allele frequencies

Simulated genotypes per population0 skips the migrant test.

Migrant threshold α

DNA sequences & haplotypes

What an alignment says about diversity, demographic history and the geography of lineages.

1 · Settings

Coalescent simulations (P-values of D, Fs, R₂ and raggedness)

Permutations (N_ST test and Φ_ST)

Mutation rate (per site per year, optional) Turns τ into years since expansion. Chloroplast non-coding DNA in angiosperms is often quoted at 1–3 × 10⁻⁹.

Generation time (years)

Random seed

2 · What the sequences say

3 · Sites

4 · Haplotypes

5 · Diversity and neutrality tests

Tajima's D compares two estimates of θ — one from the number of segregating sites, one from pairwise differences — that agree only under neutrality and constant size. Fu's Fs asks whether there are more haplotypes than expected given π; it is the most sensitive to population growth. Fu & Li's D* and F* weigh the singletons; R₂ (Ramos-Onsins & Rozas 2002) is the most powerful for small samples. All P-values come from coalescent simulations of a neutral population of constant size, not from tables; they assume at most one mutation per site.

Mismatch distribution

The distribution of pairwise differences is unimodal after a sudden expansion (Rogers & Harpending 1992) and ragged in a population of stable size; the raggedness r (Harpending 1994) measures it. τ = 2ut dates the expansion in mutational units.

Sample

6 · Structure among populations

Pons & Petit (1996): if N_ST, which weights haplotypes by their divergence, is significantly larger than G_ST, which treats every haplotype as equally different, then related haplotypes share populations — the lineages are geographically sorted.

7 · Haplotype network

Median-joining (Bandelt, Forster & Röhl 1999) with ε = 0: the minimum spanning network of the haplotypes, completed with the unsampled intermediates (median vectors) of the lowest connection cost. Node area is proportional to frequency, slices show the populations, and each tick on a link is one mutation.

8 · Divergence times — a dated tree

A molecular clock turns substitutions into time. Something external has to set the clock: fossils or published ages for nodes of a tree of species or genera, or a known substitution rate for haplotypes within one species, where fossils almost never apply. Two methods are offered: a fast least-squares dating (LSD; To et al. 2016) to explore, and a Bayesian relaxed-clock MCMC (Drummond et al. 2006) that gives a 95% credible interval for every node.

The tree to date

Tips of the tree

Topology

Root An outgroup is the reliable way to root a tree for dating.

Substitution model + Γ rate variation among sites

Outgroup tips

What sets the clock

How a fossil calibrates a node. A fossil that can be placed in a clade proves the clade existed by the time the rock formed, so it gives a minimum age — for the crown node when it has features of a living subgroup, for the stem node (the branch below the clade) when it only belongs to the lineage. Use the younger boundary of the stratigraphic unit as the minimum. A maximum is rarely known: it comes from the absence of the group in older, well-sampled rocks, and is expressed as a soft upper tail. A secondary calibration takes a node age from a published dated tree, with its uncertainty.

Geological ages: .

Date the tree

Fast · least-squares dating (LSD)

Seconds. Strict clock, weighted least squares with the calibrations as bounds; intervals from 100 resamplings of the branch lengths with rate variation among branches.

Rate variation (σ, CI only)

Resamplings

Bayesian · relaxed-clock MCMC

Clock

Tree prior

Chain length

Burn-in (%)

Root age at most (Ma, if not calibrated)

Seed

Sample from the prior only (no data) — to see the effective prior of each calibration

Demography & spatial structure

Has the population crashed, how large is it genetically, are neighbours relatives, how much does it self, and is trait divergence more than drift?

1 · Settings

Bottleneck: mutation models and simulations

IAM TPM SMM

accepted simulations per locus TPM single-step fraction TPM variance repeat motif (bp) for M-ratio

Piry et al. (1999) recommend the TPM with 95% single-step mutations and variance 12 for microsatellites. Needs ≥ 10 plants per population.

N_e (LD method): exclude alleles rarer than P_crit = 0.02 is the usual choice (Waples & Do 2010); rare alleles bias r² upward.

Spatial structure: distance classes and permutations

classes permutations pairs

Classes hold equal numbers of pairs, so each estimate has similar precision. Pairs within populations measure fine-scale structure; all pairs mix in the differentiation among populations.

P_ST: c / h² and the neutral F_ST to compare with

c h² F_ST

c is the fraction of the between-population phenotypic variance that is genetic; h² the heritability within. c/h² = 1 is the most optimistic assumption.

Random seed

2 · What the analyses say

3 · Recent bottlenecks

Cornuet & Luikart (1996): after a bottleneck, rare alleles disappear faster than heterozygosity declines, so for a while each locus shows more heterozygosity than its number of alleles predicts at mutation–drift equilibrium. That expectation is obtained here by coalescent simulation conditioned on the observed number of alleles (Piry, Luikart & Cornuet 1999). The distribution of He given the number of alleles is skewed, so the Wilcoxon test is applied to the position of each locus within its own equilibrium distribution (as a normal score), and with inbreeding the equilibrium is simulated for the n(2 − F) independent gene copies that n plants carry. Luikart's mode shift and the M-ratio of Garza & Williamson look at the same history from other angles.

Population Mutation model

Locus by locus

4 · Effective population size

The linkage-disequilibrium method (Hill 1981; Waples 2006; Waples & Do 2008): in a small population, drift creates associations between unlinked loci in proportion to 1/(3N_e). The r² expected from sampling alone is subtracted, and the remainder gives N_e of the parental generation. Jackknife over loci for the confidence limits.

5 · Fine-scale spatial genetic structure

6 · Mating system

At inbreeding equilibrium, a selfing rate s produces F = s/(2 − s), so s = 2F/(1 + F). The confidence limits come from a bootstrap over loci of Weir & Cockerham's f.

7 · P_ST versus F_ST

Q_ST is the F_ST of a quantitative trait; if it exceeds the neutral F_ST, populations have diverged more than drift allows — divergent selection. Without a common-garden or crossing design, its phenotypic proxy P_ST = cσ²_B/(cσ²_B + 2h²σ²_W) is what field measurements can give (Brommer 2011; Leinonen et al. 2013). The confidence limits are exact: they come from the F distribution of the one-way ANOVA (Searle, Casella & McCulloch 1992).

Figures & report

Everything you ran, as you left it: tables, interpretations, every figure as edited, the methods paragraph with its citations, and a ZIP for the paper.

1 · What goes into the report

Each figure is exported exactly as you edited it in its block (title, palette, fonts, size). Go back, change anything, and build the report again.

Report title

Author(s)

Notes for the header (optional)

Sections

Front and back matter

Executive summary (key numbers) Drafted results section (the interpretations of every block) Methods paragraph with the settings used and the methods cited (author, year) How to cite the software (BibTeX) Appendix: data as analysed

ZIP figures: raster format

ZIP figures: resolution

Read the genetic history written in your populations

How it works

Try it: watch drift, migration and selection at work

What's inside

Every kind of data a plant study produces

Methods covered

What it brings together

The theory, in plain language

How to cite

References behind the calculations

Data & quality control

1 · Load your data

Data sheet

Data template designer

What did you score?

Sampling design

Loci

Your template

Checks on this design

What you will be able to run

Preview of the sheet

Add sample information

2 · What this file contains

Preview

3 · What each column is

4 · Quality control

Checked against the layout declared in the file

Values to fix in the sheet

Locus by locus

Repeated and near-identical genotypes

Sampling and frequencies

5 · What you can run with these data

Allele frequencies & diversity

1 · Settings

2 · What the numbers say

3 · Diversity of every population

Standard errors over loci

4 · Locus by locus

5 · Allele frequencies

6 · Private alleles

Locally common alleles

Hardy–Weinberg, inbreeding & linkage

1 · Settings

2 · What the tests say

3 · Hardy–Weinberg tests, locus by population

4 · Inbreeding coefficient FIS

Locus by locus: the diagnostic

5 · Null alleles

6 · Linkage disequilibrium

Locus pairs

Differentiation & AMOVA

1 · Settings

2 · What the numbers say

3 · Analysis of molecular variance

4 · Global F-statistics, locus by locus

5 · Pairwise differentiation

Genetic distances, ordination & trees

1 · Settings

2 · What the distances say

3 · Distances between populations

Every coefficient, pair by pair

4 · Distances between individuals

5 · Principal coordinates

6 · Trees

Bootstrap support of every grouping

7 · Isolation by distance

Bayesian clustering, DAPC & assignment

1 · Bayesian clustering (admixture model)

2 · How many clusters?

3 · Membership of every individual

Mean membership by population

4 · Discriminant analysis of principal components (DAPC)

5 · DAPC results

6 · Assignment tests and migrant detection

7 · Assignment results

Every individual

DNA sequences & haplotypes

1 · Settings

2 · What the sequences say

3 · Sites

4 · Inbreeding coefficient F_IS

7 · P_ST versus F_ST