The Hardy-Weinberg principle is a foundational idea in population genetics that provides a mathematical model for how genetic variation should theoretically behave within a non-evolving population. It describes a hypothetical state known as genetic equilibrium, where the frequencies of alleles and genotypes remain constant from one generation to the next. The primary purpose of this principle is to establish a baseline or null hypothesis. By comparing the genetic makeup of an actual population to the stable predictions of the Hardy-Weinberg model, scientists can detect and measure the forces that are causing evolutionary change.
The Five Requirements for Equilibrium
To achieve and maintain genetic equilibrium, a population must satisfy five specific conditions that eliminate all mechanisms of evolutionary change.
- No mutation: No new alleles are introduced into the gene pool.
- No gene flow: Individuals cannot migrate into or out of the population, which would add or remove alleles.
- Large population size: This prevents random fluctuations in allele frequencies, known as genetic drift.
- No natural selection: All genotypes must have equal survival and reproductive success.
- Random mating: Individuals must not select mates based on a specific genotype or phenotype, as non-random mating alters genotype frequencies.
Defining Allele and Genotype Frequencies
Calculating Hardy-Weinberg equilibrium requires defining variables for the population’s genetic makeup. For a single gene with two possible alleles, \(p\) represents the frequency of the dominant allele, and \(q\) represents the frequency of the recessive allele. Since these are the only two variants, their frequencies must sum to one, resulting in the Allele Frequency Equation: \(p + q = 1\).
These allele frequencies relate to the frequencies of the resulting genotypes. The Genotype Frequency Equation is derived from the expansion of \((p+q)^2\): \(p^2 + 2pq + q^2 = 1\). Here, \(p^2\) represents the frequency of the homozygous dominant genotype, \(q^2\) represents the frequency of the homozygous recessive genotype, and \(2pq\) represents the frequency of the heterozygous genotype.
Solving for Population Frequencies: A Step-by-Step Guide
The most common starting point for calculating Hardy-Weinberg frequencies is the frequency of the recessive phenotype, since its corresponding genotype (\(q^2\)) is known with certainty. For example, consider a population of 1,000 animals where a recessive trait is observed in 160 individuals.
Step 1: Calculate the Recessive Genotype Frequency (\(q^2\))
The first step is to determine the frequency of the homozygous recessive genotype (\(q^2\)). If 160 out of 1,000 animals exhibit the recessive phenotype, the frequency is calculated by dividing the number of affected individuals by the total population size. In this example, \(160 / 1,000 = 0.16\). This means the frequency of the \(q^2\) genotype is \(0.16\).
Step 2: Calculate the Recessive Allele Frequency (\(q\))
Once the frequency of the recessive genotype (\(q^2\)) is known, solve for the frequency of the recessive allele (\(q\)) by taking the square root of the \(q^2\) value. Using the example, \(q\) is \(\sqrt{0.16} = 0.4\). This means \(40\%\) of all alleles for this gene in the population are the recessive variant.
Step 3: Calculate the Dominant Allele Frequency (\(p\))
With the value for \(q\) established, the frequency of the dominant allele (\(p\)) is calculated using the Allele Frequency Equation: \(p + q = 1\). Subtract \(q\) from one to solve for \(p\). In the example, \(p = 1 – 0.4\), resulting in a dominant allele frequency (\(p\)) of \(0.6\). This indicates that \(60\%\) of the alleles in the gene pool are the dominant variant.
Step 4: Calculate the Remaining Genotype Frequencies (\(p^2\) and \(2pq\))
The final step uses the calculated values for \(p\) and \(q\) to determine the frequencies of the remaining two genotypes: homozygous dominant (\(p^2\)) and heterozygous (\(2pq\)). The frequency of \(p^2\) is found by squaring \(p\): \(0.6 \times 0.6 = 0.36\). The frequency of \(2pq\) is found by multiplying \(2 \times p \times q\): \(2 \times 0.6 \times 0.4 = 0.48\). As a final check, the sum of all three calculated genotype frequencies should equal one: \(p^2 + 2pq + q^2 = 0.36 + 0.48 + 0.16 = 1.00\). The population is predicted to consist of \(36\%\) homozygous dominant, \(48\%\) heterozygous, and \(16\%\) homozygous recessive individuals, assuming equilibrium conditions are met.
Comparing Observed and Expected Frequencies
The calculations outlined above provide the expected genotype frequencies for a non-evolving population. The primary utility of the Hardy-Weinberg principle lies in comparing these expected frequencies against the observed frequencies counted directly from a real-world sample. Scientists count the actual number of individuals with each genotype in a population and convert those counts into observed frequencies.
If the observed frequencies align closely with the expected frequencies, the population is considered to be in equilibrium for that gene. Conversely, a statistically significant difference indicates that the population is not in Hardy-Weinberg equilibrium and is likely evolving. Such a deviation suggests that at least one of the five theoretical requirements is being violated. This comparison transforms the mathematical model into a diagnostic tool, helping researchers identify the specific evolutionary forces acting on a population.