Allele frequency represents the proportion of a specific allele within a population’s collective gene pool. This fundamental concept in population genetics helps scientists understand how genetic traits are distributed and change over generations, allowing them to observe evolutionary shifts.
Foundational Concepts
An allele is an alternative form of a gene. For example, a gene determining eye color might have alleles for blue, brown, or green eyes. The gene pool encompasses all genes and their alleles present in a population.
The Hardy-Weinberg Principle provides a mathematical model for describing allele and genotype frequencies in a non-evolving population. It serves as a baseline, allowing researchers to determine if real populations are experiencing evolutionary forces. This principle distinguishes between allele frequency, which is the proportion of specific alleles, and genotype frequency, which is the proportion of individuals with a particular combination of alleles.
The Hardy-Weinberg Equations
The Hardy-Weinberg principle uses two equations to describe a population’s genetic structure. The first equation, p + q = 1, relates to allele frequencies. Here, ‘p’ represents the dominant allele frequency, and ‘q’ represents the recessive allele frequency. For a given gene, their frequencies must sum to one.
The second equation, p^2 + 2pq + q^2 = 1, describes genotype frequencies within the population. In this formula, ‘p^2’ signifies the frequency of the homozygous dominant genotype, where an individual carries two copies of the dominant allele. ‘q^2’ denotes the frequency of the homozygous recessive genotype, meaning an individual possesses two copies of the recessive allele. The term ‘2pq’ represents the frequency of the heterozygous genotype, where an individual carries one dominant and one recessive allele. These genotype frequencies also sum to one, as the genotype frequency equation is an expansion of the allele frequency equation, derived by squaring (p + q) = 1.
Step-by-Step Calculation Examples
Calculating allele frequencies often begins with observable data, such as the frequency of a recessive trait. For instance, if 16% of a population exhibits a recessive genetic condition, this represents q^2. To find q, take the square root of 0.16, which yields 0.4.
Once q is known, p can be determined using p + q = 1. Subtracting 0.4 from 1 gives p = 0.6. With both p and q established, the frequencies of the other genotypes can be calculated: p^2 (homozygous dominant) is 0.6 0.6 = 0.36, and 2pq (heterozygous) is 2 0.6 0.4 = 0.48.
Alternatively, calculations can start from the frequency of a dominant phenotype if homozygous dominant and heterozygous genotypes are indistinguishable. If 91% of a population displays a dominant trait, 9% (100% – 91%) express the recessive phenotype. This 9% represents q^2, so q is the square root of 0.09, which is 0.3.
From q = 0.3, p is 0.7 (1 – 0.3). Then, p^2 is 0.7 0.7 = 0.49, and 2pq is 2 0.7 0.3 = 0.42. The sum of p^2, 2pq, and q^2 equals 1, confirming the calculations. This approach allows researchers to infer genetic proportions from observable population characteristics.
Conditions for Hardy-Weinberg Equilibrium
The Hardy-Weinberg Principle operates under five theoretical conditions for allele and genotype frequencies to remain constant across generations. First, there is no mutation, meaning no new alleles are introduced or existing ones altered. Second, no gene flow or migration occurs, preventing allele movement into or out of the population.
Third, mating is random, ensuring individuals do not select mates based on specific genotypes. Fourth, the population size is very large to avoid genetic drift, which is random fluctuations in allele frequencies that can occur in small populations. Finally, there is no natural selection, meaning all genotypes have equal survival and reproductive rates. These ideal conditions are rarely met in natural populations, making the Hardy-Weinberg Principle a valuable null model for detecting and measuring evolutionary change.