Allele Frequency

Definition and Basic Concepts

Allele

Allele: variant form of a gene at a specific locus. Diploid organisms carry two alleles per locus. Polymorphism: presence of multiple alleles at a locus in a population.

Allele Frequency

Allele frequency (or gene frequency): proportion of a specific allele among all alleles at a locus in the population’s gene pool. Expressed as decimal or percentage.

Gene Pool

Gene pool: total collection of alleles in a population. Frequency changes reflect evolutionary processes and population dynamics.

Calculation of Allele Frequency

Basic Formula

Allele frequency (p) = Number of copies of allele / Total number of alleles at locus.

Diploid Calculation

For diploid organisms: total alleles = 2 × number of individuals. Count homozygotes and heterozygotes for allele copies.

Example Calculation

Population: 100 individuals; Allele A: 40 AA, 50 Aa; Allele a: 10 aa.

Total allele copies: 2 × 100 = 200.

Allele A frequency (p) = (80 + 50) / 200 = 0.65.

Allele a frequency (q) = (0 + 50 + 20) / 200 = 0.35.

p = (2×Number_AA + Number_Aa) / (2×Total_individuals)q = 1 - p

Hardy-Weinberg Equilibrium

Definition

Hypothetical state where allele and genotype frequencies remain constant across generations in an ideal population.

Assumptions

Large population size, random mating, no mutation, no migration, no selection.

Equations

Allele frequencies: p + q = 1. Genotype frequencies: p² + 2pq + q² = 1.

Genotype frequencies:AA = p²Aa = 2pqaa = q²where p = frequency of A, q = frequency of a

Applications

Baseline for detecting evolutionary forces, estimating carrier rates, and population genetics modeling.

Evolutionary Forces Affecting Allele Frequency

Mutation

Source of new alleles. Alters allele frequency by introducing genetic variation.

Natural Selection

Differential survival and reproduction alter frequencies based on fitness.

Genetic Drift

Random fluctuations in allele frequencies due to sampling effects, especially in small populations.

Gene Flow

Migration introduces or removes alleles, homogenizing or differentiating populations.

Genetic Drift

Definition

Random changes in allele frequencies caused by chance events in finite populations.

Bottleneck Effect

Severe reduction in population size reduces genetic diversity, alters allele frequencies.

Founder Effect

New population established by few individuals carries subset of alleles, frequency deviation occurs.

Consequences

Loss or fixation of alleles, reduced heterozygosity, potential inbreeding depression.

Mutation and Allele Frequency

Mutation Rate

Frequency at which new mutations occur per locus per generation; typically low (10⁻⁸ to 10⁻⁵).

Types of Mutations

Point mutations, insertions, deletions, duplications; impact varies on allele function and frequency.

Mutation-Selection Balance

Equilibrium between introduction of deleterious alleles by mutation and their removal by selection.

q̂ = √(μ / s)where q̂ = equilibrium frequency of deleterious recessive allele,μ = mutation rate,s = selection coefficient

Gene Flow (Migration)

Definition

Movement of alleles between populations via migration of individuals or gametes.

Effect on Allele Frequency

Increases genetic similarity between populations; introduces new alleles or changes existing frequencies.

Migration Models

Island model, stepping-stone model; vary in assumptions about migration rates and population connectivity.

Equation for Allele Frequency Change

p' = (1 - m)p + m p_mwhere p' = allele frequency after migration,p = initial frequency,m = migration rate,p_m = allele frequency in migrants

Natural Selection and Allele Frequency

Directional Selection

Favors one allele, increases its frequency over generations.

Balancing Selection

Maintains multiple alleles at intermediate frequencies (e.g., heterozygote advantage).

Selection Coefficients

Measure fitness differences between genotypes; influence rate of allele frequency change.

Fitness and Allele Frequency Change

Δp = (p q / w̄) [p (w_AA - w_Aa) + q (w_Aa - w_aa)]where w̄ = mean fitness, p and q = allele frequencies

Population Structure and Subdivision

Definition

Existence of genetically differentiated subpopulations with limited gene flow.

Wright’s F-Statistics

F_ST measures genetic differentiation among subpopulations; ranges 0 (no differentiation) to 1 (fixed differences).

Effects on Allele Frequency

Subdivisions cause allele frequency divergence due to drift, selection, or reduced migration.

Implications

Important for conservation genetics, understanding speciation, and evolutionary history.

Applications of Allele Frequency Analysis

Population Genetics Studies

Track evolutionary processes: selection, drift, migration, mutation.

Conservation Biology

Assess genetic diversity, inbreeding, and viability of endangered populations.

Medical Genetics

Estimate disease allele prevalence, carrier rates, and design screening programs.

Forensic Science

Calculate match probabilities using allele frequency databases.

Anthropology and Evolutionary Biology

Reconstruct human migration patterns, adaptation, and speciation events.

Measurement Techniques and Molecular Tools

Genotyping Methods

PCR-based assays, SNP arrays, microsatellite analysis, sequencing.

Population Sampling

Representative sampling critical for accurate frequency estimates.

Data Analysis Software

Arlequin, STRUCTURE, Genepop, PLINK used for allele frequency and population structure analysis.

High-Throughput Sequencing

Enables genome-wide allele frequency estimation with high resolution.

Limitations and Challenges

Sampling Bias

Non-random or small samples distort frequency estimates.

Population Structure

Ignoring substructure leads to false assumptions of Hardy-Weinberg equilibrium.

Mutation Detection Sensitivity

Low-frequency alleles may be missed; sequencing errors can confuse data.

Assumption Violations

Real populations rarely meet all Hardy-Weinberg assumptions, complicating interpretation.

Temporal Changes

Allele frequencies can fluctuate over time; one-time measurements provide snapshots only.

References

• Hartl, D.L., Clark, A.G. Principles of Population Genetics, 4th ed., Sinauer Associates, 2007, pp. 1-600.
• Nei, M. Molecular Evolutionary Genetics, Columbia University Press, 1987, pp. 1-512.
• Charlesworth, B., Charlesworth, D. "Population genetics from 1966 to 2016," Genetics, vol. 204, 2016, pp. 3-17.
• Gillespie, J.H. Population Genetics: A Concise Guide, 2nd ed., Johns Hopkins University Press, 2004, pp. 1-216.
• Wright, S. "Evolution in Mendelian populations," Genetics, vol. 16, 1931, pp. 97-159.