Nei's Genetic Diversity Calculators

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Nei's gene diversity (H) is the expected proportion of heterozygous individuals at a locus in a population under Hardy-Weinberg equilibrium: H = 1 − Σpᵢ², where pᵢ is the frequency of allele i. It is also called expected heterozygosity (He) and is the standard measure of genetic diversity within a population. Nei's H ranges from 0 (monomorphic locus — only one allele) to (n−1)/n maximum (where n = number of alleles with equal frequencies). Nei (1973) extended this concept to measure genetic distance between populations, providing fundamental tools for molecular population genetics.

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Nei's Gene Diversity Formula

H = 1 − Σpᵢ²

pᵢ = frequency of allele i at the locus. Σpᵢ² = homozygosity (probability that two randomly sampled alleles are identical). H = 1 − homozygosity = expected heterozygosity.

Example: locus with alleles A (frequency 0.6) and a (frequency 0.4): H = 1 − (0.6² + 0.4²) = 1 − (0.36 + 0.16) = 1 − 0.52 = 0.48.

H at Multiple Loci

Average gene diversity: H̄ = (1/L) × Σ Hₗ (mean over L loci). Used in conservation genetics to characterize overall genetic diversity of a population.

Nei's Genetic Distance

D = −ln(I), where I = Nei's genetic identity = Σ(Jxy) / √(Jx × Jy). Jxy = Σ pᵢₓ × pᵢᵧ (proportion of shared alleles); Jx = Σ pᵢₓ² (homozygosity of population X). D = 0: identical allele frequencies. D increases as populations diverge.

HT, HS, and GST

HT = total heterozygosity across metapopulation. HS = mean within-subpopulation heterozygosity. GST = (HT − HS) / HT = fraction of diversity due to differences between populations (analogous to FST). FST ≈ GST for biallelic loci.

Glossary

Nei's Gene Diversity (H)
H = 1 − Σpᵢ²; expected heterozygosity under HWE; ranges 0 to (n−1)/n; the standard measure of genetic diversity within a population; independent of sample size.
Nei's Genetic Distance (D)
D = −ln(I) where I = Jxy/√(JxJy); measures allele frequency divergence between populations; D = 0 = identical; increases with divergence time; D ≈ 2μt under infinite alleles model.
GST
(HT − HS)/HT; proportion of total genetic diversity between subpopulations; analogous to FST for multiallelic loci; GST = 0 = no differentiation; GST = 1 = complete differentiation.

Frequently Asked Questions

Nei's gene diversity (H or He) = expected heterozygosity = 1 − Σpᵢ², where pᵢ = frequency of allele i. It represents the probability that two randomly sampled alleles from the population are different. Example: three alleles with frequencies 0.5, 0.3, 0.2: H = 1 − (0.5² + 0.3² + 0.2²) = 1 − (0.25 + 0.09 + 0.04) = 1 − 0.38 = 0.62. H ranges from 0 (monomorphic locus) to (n−1)/n maximum when all n alleles are equally frequent. H is independent of sample size (unlike observed heterozygosity which requires a specified n). H is the standard metric reported for genetic diversity in population genetic studies.

Nei's standard genetic distance D = −ln(I). Nei's genetic identity I = Jxy / √(Jx × Jy). Jxy = Σpᵢₓpᵢᵧ (sum of products of allele frequencies in populations X and Y for each allele i). Jx = Σpᵢₓ² (homozygosity in X); Jy = Σpᵢᵧ². D = 0: populations have identical allele frequencies. D → ∞: populations are completely divergent (no shared alleles). Under the infinite alleles model: D ≈ 2μt (where μ = mutation rate per locus and t = divergence time in generations). D can be used to estimate divergence time when μ is known. Nei's D is calculated across multiple loci and averaged for a robust estimate.

He (expected heterozygosity, Nei's H) = proportion of heterozygotes expected under Hardy-Weinberg equilibrium = 1 − Σpᵢ². Calculated from allele frequencies; theoretical value; does not require genotype data if allele frequencies are known. Ho (observed heterozygosity) = actual proportion of heterozygous individuals in the sample = number of heterozygotes / total individuals counted. Inbreeding coefficient: F = 1 − Ho/He. F = 0: random mating (Ho = He). F > 0: deficit of heterozygotes (inbreeding). F < 0: excess heterozygotes (outbreeding, negative assortative mating). F is a sensitive indicator of non-random mating and population structure.

Nei's GST (coefficient of gene differentiation) = (HT − HS) / HT. HT = total expected heterozygosity across the entire metapopulation (treating all individuals as one gene pool). HS = mean expected heterozygosity within subpopulations. GST = proportion of total genetic diversity attributed to differences between subpopulations. GST = 0: no differentiation (all subpopulations have identical allele frequencies). GST = 1: complete differentiation (no shared alleles between populations). GST is analogous to Wright's FST for biallelic loci; for multiallelic markers (microsatellites): GST and FST give similar results but may differ because FST is defined differently. In practice, FST (from AMOVA or Wright's original formulation) is more commonly reported, but GST is used when multiple-allele loci or overall genetic diversity analysis is needed.