The Hardy-Weinberg Equilibrium is a fundamental concept in population genetics, providing a theoretical framework for understanding how genetic variation behaves within a population. It describes a hypothetical state where allele and genotype frequencies remain constant across generations. This principle serves as a baseline, or null model, against which real-world populations can be compared to detect evolutionary change. By establishing this non-evolving ideal, scientists gain a tool to identify genetic shifts.
Foundational Principles
For a population to maintain Hardy-Weinberg equilibrium, specific conditions must be met. These include the absence of mutation, meaning no new alleles are introduced or altered. There must also be no gene flow, preventing individuals or gametes from migrating into or out of the population. Random mating is necessary, ensuring individuals pair by chance without preference for particular genotypes.
A very large population size is also required, as smaller populations are susceptible to genetic drift. Lastly, there must be no natural selection, meaning all genotypes have equal survival and reproductive rates.
Understanding the Equations
The Hardy-Weinberg principle relies on two equations that describe allele and genotype frequencies within a population. The first equation, p + q = 1, relates to allele frequencies. Here, ‘p’ represents the frequency of the dominant allele for a specific gene, while ‘q’ represents the frequency of the recessive allele. This equation signifies that the sum of all possible allele frequencies for a given gene must equal one.
The second equation, p² + 2pq + q² = 1, describes genotype frequencies. ‘p²’ denotes the frequency of the homozygous dominant genotype, ‘q²’ represents the frequency of the homozygous recessive genotype, and ‘2pq’ signifies the frequency of the heterozygous genotype. This equation illustrates that the combined frequencies of all possible genotypes for a gene must also sum to one.
Applying the Equilibrium: Step-by-Step Calculation
Calculating Hardy-Weinberg equilibrium often begins with the frequency of the homozygous recessive genotype. This is because individuals expressing a recessive trait will always have the homozygous recessive genotype, which directly corresponds to ‘q²’. For example, consider a population of 1,000 cats where 160 are white, and white fur is a recessive trait (bb).
The first step is to determine the frequency of the homozygous recessive genotype (q²) by dividing the number of recessive individuals by the total population. In this case, 160 white cats divided by 1,000 total cats yields a q² value of 0.16. From this, the frequency of the recessive allele (q) can be found by taking the square root of q². The square root of 0.16 is 0.4, so q = 0.4.
Once ‘q’ is known, the frequency of the dominant allele (p) can be calculated using the first Hardy-Weinberg equation, p + q = 1. By rearranging this, p = 1 – q. Substituting the value for q, p = 1 – 0.4, which means p = 0.6.
With both allele frequencies determined, the frequencies of the other genotypes can be found using the second equation, p² + 2pq + q² = 1. To find the frequency of the homozygous dominant genotype (p²), square the value of p: 0.6² = 0.36. This indicates that 36% of the cat population is homozygous dominant (BB).
For the heterozygous genotype (2pq), multiply 2 by p and by q: 2 0.6 0.4 = 0.48. Thus, 48% of the cats are heterozygous (Bb). The calculated genotype frequencies (0.36 for BB, 0.48 for Bb, and 0.16 for bb) should sum to 1.
Interpreting Deviations
When a population’s observed allele and genotype frequencies do not align with Hardy-Weinberg predictions, it indicates the population is not in equilibrium. This deviation signals that one or more of the five underlying assumptions are not being met. Consequently, the population is likely undergoing evolutionary change.
Deviations from equilibrium provide valuable insights into the specific evolutionary forces at play. If observed frequencies differ from expected values, it suggests that factors like mutation, gene flow, genetic drift, non-random mating, or natural selection are influencing the population’s genetic structure. Biologists can then analyze these deviations to infer which forces are acting upon the population. This comparative approach allows researchers to understand the dynamic processes shaping genetic diversity in real-world populations.