Allele frequency and the Hardy-Weinberg principle are foundational concepts in population genetics. An allele is a gene variant, and allele frequency quantifies its commonness in a population’s gene pool. The Hardy-Weinberg principle models allele and genotype frequencies in a stable, non-evolving population.
Understanding Allele Frequencies
An allele is a version of a genetic sequence at a specific chromosome location. For example, a gene for eye color might have an allele for brown eyes and another for blue eyes. Each individual inherits two alleles for each gene, one from each parent. If these two alleles are identical, the individual is homozygous; if they differ, they are heterozygous. Allele frequency is calculated by counting a specific allele’s occurrences and dividing by the total number of alleles for that gene in the population. For instance, in a population of 100 individuals, there are 200 total alleles for a given gene. This differs from genotype frequency, which is the proportion of individuals with a specific combination of alleles (their genotype).
The Hardy-Weinberg Principle
The Hardy-Weinberg principle states that in a large, randomly mating population, allele and genotype frequencies remain constant from one generation to the next, assuming no evolutionary influences. This principle acts as a baseline, or null hypothesis, for comparing observed population changes. It describes a theoretical state of genetic equilibrium where a population is not evolving. For this equilibrium, five conditions must be met:
Absence of mutation: No new alleles are introduced or altered.
No gene flow: No migration of individuals or genes into or out of the population.
Random mating: Individuals mate without preference for specific genotypes.
Large population size: Prevents random fluctuations in allele frequencies (genetic drift).
No natural selection: All genotypes have an equal chance of survival and reproduction.
These ideal conditions are rarely met in natural populations, making the principle a useful tool for identifying when evolutionary forces are acting.
Calculating Allele Frequencies
The Hardy-Weinberg principle uses two fundamental equations for calculating allele and genotype frequencies.
The first equation, `p + q = 1`, relates the frequencies of two alleles for a given gene. Here, `p` is the dominant allele frequency, and `q` is the recessive allele frequency. Their frequencies must sum to 1.
The second equation, `p² + 2pq + q² = 1`, describes the frequencies of the three possible genotypes. `p²` represents the homozygous dominant genotype, `q²` the homozygous recessive genotype, and `2pq` the heterozygous genotype. These genotype frequencies also sum to 1.
For example, if a genetic condition expressed by the homozygous recessive genotype (aa) occurs in 16% of a population:
1. Determine `q²`: `q² = 0.16`.
2. Calculate `q`: `q = √0.16 = 0.4`.
3. Calculate `p` using `p + q = 1`: `p = 1 – 0.4 = 0.6`.
With `p` and `q` known, genotype frequencies are: `p² = (0.6)² = 0.36` (homozygous dominant) and `2pq = 2 0.6 0.4 = 0.48` (heterozygous).
Significance of Hardy-Weinberg Equilibrium
The Hardy-Weinberg principle is important in population genetics, providing a theoretical baseline for a non-evolving population. Researchers use it as a null hypothesis to test if evolutionary forces impact a population. If observed allele and genotype frequencies deviate from predictions, it indicates that factors like mutation, gene flow, non-random mating, genetic drift, or natural selection are changing the population’s genetic structure. The principle is also useful for estimating carrier frequencies for recessive genetic disorders. Even with only the frequency of affected individuals (homozygous recessive genotype) known, the equations allow calculation of the recessive allele frequency (`q`) and heterozygous carriers (`2pq`). This capability aids medical genetics in understanding disease prevalence and conservation biology in assessing genetic diversity.