Population Genetics Calculators

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Population genetics studies the distribution and change of allele frequencies in populations over time, under the influence of evolutionary forces: natural selection, genetic drift, mutation, gene flow, and non-random mating. Hardy-Weinberg equilibrium (HWE) provides the null model — a non-evolving population — against which deviations reveal evolution. Understanding population genetics is essential for conservation biology, human genetics, epidemiology (disease allele frequencies), and evolutionary biology. Key parameters include allele frequency (p, q), genotype frequency, effective population size (Ne), and measures of genetic differentiation (FST).

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Hardy-Weinberg Equilibrium

In a large, randomly mating population with no selection, mutation, migration, or drift: p + q = 1 (allele frequencies sum to 1). Genotype frequencies: p² (AA) + 2pq (Aa) + q² (aa) = 1. HWE reached in one generation of random mating (for autosomal loci). Deviations indicate evolution. Chi-square test detects deviations from HWE.

Evolutionary Forces

  • Natural selection: Changes allele frequencies directionally based on fitness differences; positive selection increases favored alleles; purifying selection removes deleterious alleles
  • Genetic drift: Random changes in allele frequency; proportional to 1/2Ne; dominant in small populations; causes fixation (allele reaches frequency 1) or loss (frequency 0)
  • Mutation: Creates new alleles; very slow (μ ≈ 10⁻⁸ per locus per generation); tends to increase diversity
  • Gene flow (migration): Movement of alleles between populations; homogenizes allele frequencies; counteracts drift and local adaptation

Effective Population Size (Ne)

Ne is the size of an idealized Wright-Fisher population that shows the same genetic drift as the actual population. Ne < N (census size) due to: unequal sex ratios; variance in reproductive success; population size fluctuations. Genetic drift rate = 1/(2Ne) per generation. Small Ne → rapid drift → inbreeding → reduced genetic diversity.

FST (Population Differentiation)

FST = (H_T − H_S) / H_T; measures genetic differentiation between populations. FST = 0: no differentiation (identical allele frequencies); FST = 1: complete differentiation. Human global FST ≈ 0.15 (modest population structure).

Glossary

Hardy-Weinberg Equilibrium (HWE)
p² + 2pq + q² = 1; the null model for a non-evolving population; deviations signal selection, drift, non-random mating, or population structure; chi-square test detects departures.
Genetic Drift
Random changes in allele frequency in finite populations; rate ∝ 1/(2Ne); causes fixation or loss of alleles; dominates evolution in small populations; reduces genetic diversity.
FST
(H_T − H_S)/H_T; measures genetic differentiation between populations; ranges 0 (identical) to 1 (completely fixed for different alleles); human global FST ≈ 0.15.

Frequently Asked Questions

HWE predicts genotype frequencies in a non-evolving population: p² + 2pq + q² = 1, where p = frequency of allele A, q = frequency of allele a, and p + q = 1. Predictions: if p = 0.7, q = 0.3 → expected genotype frequencies: AA = 0.49; Aa = 0.42; aa = 0.09. HWE requires: large population; random mating; no selection; no mutation; no gene flow. It is reached in a single generation of random mating and maintained indefinitely without evolutionary forces. Departure from HWE (detected by chi-square test) signals: non-random mating; selection; population structure; recent admixture; or genotyping error.

Genetic drift is the random change in allele frequencies due to sampling variation in finite populations. In each generation, allele frequencies change randomly around their current values, with variance = p(1−p)/(2Ne). Effects: alleles can become fixed (reach frequency 1) or lost (frequency 0) by chance alone, regardless of fitness; small populations drift faster; drift reduces genetic diversity. Drift dominates evolution when Ne is small (endangered species, founder effects, bottlenecks) or when selection coefficients are very small (|s| << 1/(2Ne)). In large populations (Ne > 10,000), selection dominates drift for alleles with |s| > 0.0001.

FST (fixation index) quantifies genetic differentiation between populations. FST = (H_T − H_S)/H_T, where H_T = expected heterozygosity in the total metapopulation and H_S = average expected heterozygosity within subpopulations. FST ranges 0–1: FST = 0 means subpopulations have identical allele frequencies (no differentiation); FST = 1 means subpopulations are fixed for different alleles (complete differentiation). Interpretation: FST 0–0.05 = minimal; 0.05–0.15 = moderate; 0.15–0.25 = large; > 0.25 = very large. Human FST ≈ 0.15 indicates most human genetic variation is within populations, not between them.

Natural selection changes allele frequencies when alleles differ in fitness (w = survival × reproduction rate). For selection coefficient s: a deleterious allele a with fitness w_aa = 1 − s will decline each generation; the rate depends on s and current q. For a dominant beneficial mutation (A allele, w_AA = w_Aa = 1+s; w_aa = 1): frequency of A increases rapidly once common; but increases very slowly when rare (because most A alleles are in Aa heterozygotes which are as fit as AA). For a recessive deleterious allele (q_aa = lethal): selection is inefficient when a is rare (hidden in Aa carriers); selection becomes efficient only when a is common enough that aa homozygotes are frequent. This is why purifying selection cannot completely eliminate rare recessive deleterious alleles.