Fixation Index Calculator

The Fixation Index Calculator calculates FST to quantify genetic differentiation between populations from allele frequency data and sample sizes.

About the Fixation Index Calculator

The calculator computes the fixation index, a population genetics metric that compares within-population heterozygosity to total heterozygosity. Heterozygosity is the probability that two randomly chosen alleles are different at a genetic locus. By contrasting these values, the tool quantifies how much genetic variation is partitioned among subpopulations rather than within them.

This tool supports common estimators used in research, including Nei’s gene diversity framework and the Weir and Cockerham estimator. You can input allele counts or genotype counts for each subpopulation. The calculator then standardizes the data into allele frequencies and applies the selected method.

A clear interpretation accompanies every result. Values near 0 suggest little genetic structure, while higher values indicate stronger differentiation. Negative values can occur due to sampling noise and are generally interpreted as zero differentiation.

Equations Used by the Fixation Index Calculator

The fixation index is often summarized as the proportion of total genetic variation explained by differences among subpopulations. For a single biallelic locus, a standard definition uses expected heterozygosity. Let p_i be the allele frequency of allele A in subpopulation i, and let p̄ be the mean frequency across subpopulations.

• Define total heterozygosity: H_T = 2 p̄ (1 − p̄).
• Define within-subpopulation heterozygosity: H_S = average over i of 2 p_i (1 − p_i) (weighted or unweighted).
• Basic fixation index: F_ST = (H_T − H_S) / H_T, for H_T > 0.
• Variance formulation: F_ST ≈ Var(p) / [ p̄ (1 − p̄) ], where Var(p) is the variance of p_i across subpopulations.
• Weir and Cockerham estimator (θ): a ratio of variance components that adjusts for sample size and provides near-unbiased estimates across multiple loci.

For multi-allelic markers, H_T and H_S generalize to 1 minus the sum of squared allele frequencies, using all alleles. The calculator implements both Nei’s heterozygosity-based approach and the Weir–Cockerham θ. When sample sizes differ across subpopulations, weighted averages are recommended.

How the Fixation Index Method Works

Fixation index methods partition genetic diversity into within- and among-population components. They rely on allele frequencies, which you can derive from genotype counts using ploidy rules. The key idea is to see how different subpopulations are in their allele frequencies compared with the pooled total.

• Compute allele frequencies in each subpopulation from genotype or allele counts.
• Compute mean allele frequency across subpopulations, with optional weighting by sample size.
• Calculate expected heterozygosity within each subpopulation and then average (H_S).
• Calculate total expected heterozygosity from the mean allele frequency (H_T).
• Form the ratio (H_T − H_S) / H_T to get F_ST; or use θ for an estimator with sample-size correction.
• Aggregate across loci by averaging numerators and denominators, or by using multilocus θ.

The method assumes a model where populations may exchange migrants and drift changes allele frequencies. Higher F_ST means greater divergence among subpopulations, often due to reduced gene flow, strong drift, or local selection.

What You Need to Use the Fixation Index Calculator

Gather basic genetic data for each subpopulation and each locus before you start. You may work with SNPs (biallelic markers) or markers with more alleles, such as microsatellites. The calculator will prompt you for the key quantities.

• Genotype counts per subpopulation (e.g., AA, Aa, aa for diploids) or allele counts per subpopulation.
• Sample sizes for each subpopulation (number of individuals or number of chromosomes).
• Ploidy level (e.g., haploid, diploid) for accurate allele counting.
• Marker type (biallelic vs. multiallelic) to apply the correct heterozygosity formula.
• Weighting choice (equal subpopulations vs. weight by sample size) for H_S and p̄.

Allele frequencies must be between 0 and 1. If H_T equals 0 because all subpopulations are fixed for the same allele, F_ST is undefined and effectively zero. With very small sample sizes, estimates can be noisy, and negative F_ST values can appear from sampling error.

Step-by-Step: Use the Fixation Index Calculator

Here’s a concise overview before we dive into the key points:

1. Select the estimator (Nei’s heterozygosity-based F_ST or Weir–Cockerham θ).
2. Choose your ploidy and marker type (biallelic or multiallelic).
3. Enter genotype counts or allele counts for each subpopulation at each locus.
4. Specify subpopulation sample sizes and weighting (equal or by sample size).
5. Review computed allele frequencies and heterozygosities for accuracy.
6. Run the calculation and view F_ST per locus and the multilocus summary.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

Two diploid subpopulations are sampled at a single SNP. Pop 1 has 20 AA, 10 Aa, 20 aa (N=50). Pop 2 has 40 AA, 10 Aa, 0 aa (N=50). In Pop 1, allele A count is 2×20 + 10 = 50; total alleles = 100, so p_1 = 0.5. In Pop 2, allele A count is 2×40 + 10 = 90; total alleles = 100, so p_2 = 0.9. The mean p̄ = (0.5 + 0.9)/2 = 0.7. H_T = 2×0.7×0.3 = 0.42. H_S = [2×0.5×0.5 + 2×0.9×0.1]/2 = (0.5 + 0.18)/2 = 0.34. F_ST = (0.42 − 0.34)/0.42 ≈ 0.19. What this means: Moderate differentiation, suggesting limited gene flow or recent drift between subpopulations.

Three diploid subpopulations at a microsatellite locus have allele A frequencies p_1 = 0.32, p_2 = 0.28, p_3 = 0.30, with similar sample sizes. Using multiallelic heterozygosity, H_S is the average of 1 − Σ_k p_{ik}^2 across subpopulations; assume multiallelic calculations yield H_S ≈ 0.74 and H_T ≈ 0.75 (based on pooled frequencies). Then F_ST ≈ (0.75 − 0.74)/0.75 ≈ 0.013. What this means: Very low differentiation, consistent with strong gene flow or recent common ancestry.

Assumptions, Caveats & Edge Cases

F_ST relies on population genetics models that simplify real populations. Results should be interpreted alongside sampling design, geography, and biological context. Be cautious with small sample sizes, rare alleles, and missing data.

• Hardy–Weinberg equilibrium within subpopulations is often assumed when deriving heterozygosity from allele frequencies.
• Selection, recent admixture, or hierarchical structure can bias F_ST or complicate interpretation.
• Monomorphic loci (H_T = 0) cannot inform F_ST and are excluded from multilocus summaries.
• Negative estimates arise from sampling error; they are typically set to zero for interpretation.
• Unequal sample sizes require weighting; unweighted averages can mislead if sample sizes differ strongly.

Always report the estimator used, the number of loci, and whether weights were applied. If possible, complement F_ST with confidence intervals or permutation tests to assess variability and significance.

Units & Conversions

F_ST is unitless, but inputs often come in different “units,” such as counts, proportions, or percentages. Converting these consistently prevents calculation errors. The table below shows common conversions needed before computing heterozygosity and F_ST.

Use the first three rows to prepare allele frequencies from raw genotype data. If subpopulation sample sizes vary, compute p̄ with the weighting formula shown. Consistent conversion ensures H_S and H_T are computed correctly.

Troubleshooting

Most calculation issues stem from inconsistent inputs or extreme allele frequencies. Check data formatting, ploidy settings, and sample sizes before recalculating. If a locus is monomorphic across all subpopulations, the calculator will skip it.

• If you see “division by zero,” H_T = 0; remove that locus.
• If results are negative, consider them as zero, and verify sample sizes.
• Large differences between weighted and unweighted results indicate unbalanced sampling.

For multi-allelic loci, ensure all allele categories are included and sum to one. When combining loci, prefer a multilocus estimator rather than averaging single-locus F_ST values unadjusted.

FAQ about Fixation Index Calculator

What is a typical range for F_ST, and how should I interpret it?

F_ST typically ranges from 0 to 1. Values near 0 indicate low differentiation; values above 0.15 are moderate; values above 0.25 are high. Negative values are treated as zero differentiation.

What is the difference between F_ST and θ (Weir–Cockerham)?

θ is an estimator of F_ST that adjusts for sample size and sampling variance. It is widely used for multilocus datasets and often preferred for unbiased inference.

Can I use multiallelic markers like microsatellites with this calculator?

Yes. The heterozygosity formulas generalize to multiple alleles by using 1 − Σ p_k^2 for each population. The calculator handles both SNPs and multiallelic markers.

How many loci do I need for a stable estimate?

More loci reduce variance. Dozens of SNPs may suffice for broad patterns, but hundreds or thousands provide more reliable, genome-wide estimates, especially with uneven sampling.

Fixation Index Terms & Definitions

Fixation Index (F_ST)

A unitless measure of genetic differentiation among subpopulations, defined as the standardized reduction in heterozygosity within subpopulations relative to the total population.

Total Heterozygosity (H_T)

The expected heterozygosity computed from the mean allele frequencies across all subpopulations, reflecting diversity in the pooled population.

Within-Subpopulation Heterozygosity (H_S)

The average expected heterozygosity computed within each subpopulation and then averaged across subpopulations.

Allele Frequency

The proportion of a specific allele among all allele copies at a locus in a population. For diploids, total alleles equal two times the number of individuals.

Genetic Drift

Random changes in allele frequency between generations, stronger in small populations, contributing to divergence among subpopulations.

Gene Flow

The movement of alleles between populations through migration or dispersal, which tends to reduce genetic differentiation.

Hardy–Weinberg Equilibrium

A null model stating genotype frequencies are determined by allele frequencies under random mating with no selection, migration, or drift.

Ploidy

The number of chromosome sets per cell, influencing how genotype counts translate into allele counts (e.g., haploid vs. diploid).

References

Here’s a concise overview before we dive into the key points:

• Weir, B. S., & Cockerham, C. C. (1984). Estimating F-statistics for the analysis of population structure. Evolution.
• Nei, M. (1973). Analysis of gene diversity in subdivided populations. The American Naturalist.
• Wright, S. (1951). The genetical structure of populations. Annals of Eugenics.
• Holsinger, K. E., & Weir, B. S. (2009). Genetics in geographically structured populations: defining, estimating and interpreting F_ST. Nature Reviews Genetics.
• Hedrick, P. W. (2005). A standardized genetic differentiation measure. Evolution.

These points provide quick orientation—use them alongside the full explanations in this page.