Hardy–Weinberg principle

The Hardy–Weinberg principle is a fundamental mathematical model in population genetics. It describes a state called equilibrium. In this state, the frequencies of alleles and genotypes remain constant from one generation to the next. An allele is a version of a gene. A genotype is the specific combination of alleles an organism carries. This principle is important because it provides a baseline for scientists. By knowing what a stable population looks like, researchers can detect when evolution is actually happening.

To understand the mechanism, imagine a very large population of organisms. Each organism is a diploid, meaning it carries two copies of every gene. Let us look at a single gene with two possible alleles, which we will call A and a. We use the letter p to represent the frequency of allele A, and q to represent the frequency of allele a. Because these are the only two options, p plus q must always equal 1. When these organisms mate randomly, they create a gene pool. The offspring inherit alleles from this pool to form new genotypes.

We can predict the resulting genotypes using a Punnett square or binomial expansion. The math shows that the frequency of the AA genotype is p squared. The frequency of the aa genotype is q squared. The frequency of the heterozygotes, or the Aa genotype, is 2pq. These three values must also add up to 1. Even if the starting genotype frequencies are uneven, the population will reach these specific proportions after just one generation of random mating. Once equilibrium is reached, the allele frequencies p and q will stay the same indefinitely, provided no outside forces act on them.

This mathematical discovery was made by G. H. Hardy and Wilhelm Weinberg. Hardy's work was actually intended to debunk a common misconception. At the time, some believed that a dominant allele would automatically increase in frequency over time. Hardy used mathematics to prove that dominance does not guarantee an increase in a population. This helped scientists realize that evolution requires specific driving forces. Today, these calculations are used to test for population stratification and non-random mating patterns.

For the Hardy–Weinberg equilibrium to hold perfectly, seven strict assumptions must be met. First, the organisms must be diploid. Second, they must reproduce sexually. Third, generations must not overlap. Fourth, mating must be completely random. Fifth, the population size must be infinitely large. Sixth, allele frequencies must be equal between males and females. Finally, there can be no migration, no mutations, and no natural selection. If any of these conditions change, the equilibrium is broken.

In the real world, these assumptions are almost always violated. When they are, we see deviations from the expected proportions. One cause is genetic drift, which is a random change in allele frequencies. This happens most often in small populations due to sampling effects. Another cause is natural selection, where certain traits help organisms survive better. Migration, or gene flow, also changes frequencies by bringing in new alleles from other groups. Even mutation can change things, though the rates are very low, often between 10 to the power of negative 4 and 10 to the power of negative 8.

Scientists use statistical tests to see if a population has deviated from the principle. A common method is the Pearson's chi-squared test. This test compares the observed genotype counts in a real sample to the expected counts calculated by the Hardy–Weinberg formula. If the difference is large enough, scientists conclude that evolution or other forces are at work. For example, researchers have used these tests on scarlet tiger moths to study their spotting patterns. In humans, these principles help explain how sex-linked traits, like red-green colorblindness, are distributed. In these cases, the frequencies in males and females follow specific mathematical patterns based on the X chromosome.