Hardy–Weinberg Equilibrium

It is a common misconception that, over the course of generations in a population, the dominant alleles of a gene will eventually replace the recessive alleles of a gene. However, in the absence of evolutionary forces, the proportions of both dominant and recessive alleles in a population are maintained from one generation to the next. This feature of populations is explained by the Hardy–Weinberg rule.

To explore the Hardy–Weinberg rule, let's consider a large population in which the males and females mate randomly. Let's also assume that there is no migration, that mutation can be ignored, and that natural selection does not affect the alleles under consideration. Such random mating results in each gamete having an equal probability of obtaining either member (allele) of the gene pair.

In our population, a particular gene is represented by two alleles, A and a. If the frequency of alleles A and a among both eggs and sperm are represented by p and q, respectively, then the result that both the gametes will carry an A allele is determined by the multiplication rule: p x p = p2. This is the frequency of the AA homozygote in the next generation. There are two ways to generate a heterozygote, so the probability of the heterozygote Aa will be (p x q) + (q x p) = 2pq. The probability of the homozygote aa will be q x q = q2.

To better understand the Hardy–Weinberg rule, click/tap the Graph tab. The frequency of each of the three genotypes can be represented as the combination of single alleles from each gamete. One graph presents a two-dimensional illustration of this relationship with females (eggs) on the horizontal axis and males (sperm) on the vertical axis. Each axis is divided according to the frequency of the A and a alleles. The areas within the squares are proportional to the expected genotype frequencies. Because there are two ways of producing a heterozygote, the probability of this event occurring is the sum of the two Aa squares. The second graph shows the proportions of homozygotes AA, homozygotes aa and heterozygote Aa as a function of p, the frequency of the A allele.

p = 0.500AA = p2 = 0.250Aa = 2pq = 0.500
q = 0.500aa = q2 = 0.250 

Click/Tap an anchor box on either graph to select it. Move left/right or up/down to change the values of p and q. Click/Tap to deselect an anchor.

A population that is not changing genetically is said to be at genetic equilibrium. The conditions that result in an equilibrium population were discovered independently by two men—Hardy and Weinberg—in 1908. Simply stated, the conditions are that the population is very large, individuals mate randomly, there is no selection or mutation, and there is no migration in or out of the population.

If these conditions hold, then whatever the initial genotype frequencies of two alleles may be, after one generation of random mating, the genotype frequencies will be p2 : 2pq : q2. Further, these genotype frequencies and allele frequencies will remain constant from generation to generation, and the population is said to be in Hardy–Weinberg equilibrium. If some agent, such as non-random mating, were to alter the allele frequencies, the genotype frequencies would automatically settle into a predictable new ratio in the next generation.

The most important message of the Hardy–Weinberg equilibrium is that allele frequencies remain the same from generation to generation unless some agent acts to change them. Hence, simply because an allele may be dominant or recessive, does not mean that the frequency of this allele in the population will change unless a specific evolutionary force is acting on the genes.

You may already have recognized that populations in nature rarely meet the stringent conditions necessary to maintain them in Hardy–Weinberg equilibrium. Why, then, is the rule considered so important for the studies of population biology and evolution? The answer is that without it, we cannot tell whether evolutionary agents are operating. More importantly, the pattern of deviations from the equilibrium tells us which conditions are violated. Thus, we know on which agents of evolutionary change we should concentrate our attention.

Textbook Reference: Concept 15.3 Evolution Can Be Measured by Changes in Allele Frequencies