The Hardy-Weinberg principle is a foundational concept in population genetics, offering a mathematical model to understand how genetic variation persists within a population. It helps predict allele and genotype frequencies across generations in an idealized scenario. This principle provides a baseline to detect if evolutionary forces are at play, describing the conditions under which a population’s genetic composition remains stable and is not evolving.
Understanding the Foundation
Genetic equilibrium is a state where allele or genotype frequencies within a gene pool remain constant from one generation to the next. This theoretical condition occurs when evolutionary forces are balanced, preventing changes in the population’s genetic makeup. The Hardy-Weinberg equilibrium outlines the ideal conditions for stable allele and genotype frequencies.
For a population to be in Hardy-Weinberg equilibrium, five core assumptions must be met:
No mutation: No new alleles are introduced or existing ones altered. Mutations change allele frequencies.
Random mating: Individuals pair by chance without preference for specific genotypes. Non-random mating changes genotype frequencies.
No gene flow: No migration of individuals into or out of the population. Gene flow alters existing proportions.
Large population size: The population must be very large to minimize genetic drift. Genetic drift involves random fluctuations in allele frequencies, more pronounced in smaller populations.
No natural selection: All genotypes have equal chances of survival and reproduction. If certain genotypes have a survival advantage, their frequencies increase.
The Hardy-Weinberg Equations
The Hardy-Weinberg principle uses two primary equations to describe allele and genotype frequencies in a population.
Allele Frequencies
The first equation, p + q = 1, focuses on allele frequencies. ‘p’ represents the frequency of the dominant allele, and ‘q’ denotes the frequency of the recessive allele. The sum of all possible allele frequencies for a given gene must equal one.
Genotype Frequencies
The second equation, p² + 2pq + q² = 1, describes genotype frequencies. ‘p²’ represents the frequency of the homozygous dominant genotype (e.g., AA), ‘q²’ signifies the frequency of the homozygous recessive genotype (e.g., aa), and ‘2pq’ accounts for the frequency of the heterozygous genotype (e.g., Aa).
These two equations are directly linked through binomial expansion. If (p + q) = 1, then squaring both sides yields (p + q)² = 1², which expands to p² + 2pq + q² = 1. This relationship shows how individual allele frequencies combine to determine genotype frequencies. Like allele frequencies, genotype frequencies must sum to one, representing all individuals.
Applying the Equations: Step-by-Step Calculation
Calculating allele and genotype frequencies often begins by identifying the frequency of the recessive phenotype, as this directly corresponds to the homozygous recessive genotype.
Example 1: Calculating from Phenotype Frequency
Consider a population of plants where purple flowers (P) are dominant over white flowers (p). If 16% of the plants have white flowers, this represents the frequency of the homozygous recessive genotype (pp). So, q² = 0.16.
To find the frequency of the recessive allele (q), take the square root of q². Thus, q = √0.16 = 0.4.
Once ‘q’ is known, the frequency of the dominant allele (p) can be calculated using p + q = 1. So, p = 1 – q = 1 – 0.4 = 0.6.
With both ‘p’ and ‘q’ determined, the frequencies of the other genotypes can be found. The frequency of homozygous dominant plants (PP) is p², which is (0.6)² = 0.36. The frequency of heterozygous plants (Pp) is 2pq, calculated as 2 0.6 0.4 = 0.48.
Example 2: Calculating from Allele Frequencies
If allele frequencies are already known, say p = 0.7 and q = 0.3, calculating genotype frequencies is straightforward. The frequency of the homozygous dominant genotype (p²) would be (0.7)² = 0.49. The frequency of the homozygous recessive genotype (q²) would be (0.3)² = 0.09. The frequency of the heterozygous genotype (2pq) would be 2 0.7 0.3 = 0.42. These values confirm that 0.49 + 0.09 + 0.42 = 1, accounting for all genotypes.
Comparing observed allele and genotype frequencies in a real population to those predicted by the Hardy-Weinberg equations helps determine if the population is in equilibrium. If observed frequencies differ significantly from expected values, it indicates one or more Hardy-Weinberg assumptions are not being met. Such deviations suggest evolutionary forces, such as natural selection, genetic drift, gene flow, or mutation, are actively influencing the population’s genetic structure. This comparison provides valuable insights into evolutionary dynamics.