Hardy-Weinberg Principle

The Hardy-Weinberg Principle (also Hardy Weinberg Equilibrium) states that the allele frequency (and genotype frequency) of a population remains constant over generations, unless a specific factor or combination of factors disrupts this equilibrium. Such factors might include non-random mating, mutation, natural selection, genetic bottlenecks leading to increased genetic drift, the immigration or emigration of individuals (gene flow) or meiotic drive. The Hardy-Weinberg Equilibrium does not actually exist in nature because one or more of these factors is always in play. The concept of an equilibrium exists instead as a baseline against which to measure genetic change between generations.

According to the Hardy-Weinberg principle, then, changes in allele frequency (and thus evolution) would be theoretically impossible if the following conditions were met:

1. There was no mutation
2. There were no selective pressures
3. The population size was infinite (this would bring the rate of genetic drift infinitely close to zero)
4. All members of the population were breeding
5. All breeding was random
6. All individuals produced the same amount of offspring
7. There was no migration of individuals into, or out of, the population (i.e. the rate of gene flow was zero)

Representing the equilibrium mathematically:

When considering a locus that has two alleles, A and a:

The frequency of A (the dominant allele) is denoted p
The frequency of a (the recessive allele) is denoted q
And p + q = 1, since every locus in the population must carry either allele.

If the population is in Hardy-Weinberg equilibrium, then the alleles are distributed evenly among heterozygotes and homozygotes:

Dominant homozygotes (genotype AA) are denoted p^2 because the probability of inheriting two dominant alleles is p*p
Recessive homozygotes (genotype aa) are denoted q^2 because the probability of inheriting two recessive alleles is q*q
Heterozygotes (genotype Aa) are denoted 2pq because the probability of inheriting both alleles is (p*q) + (q*p)
And p^2 + 2pq + q^2 = 1, since every individual in the population must be one of these genotypes

This equation can be used, for example, to predict the frequency of carriers of a disease in a population. Consider the autosomal recessive disease, phenylketonuria. If the frequency of the recessive (in this case, harmful) allele is 1% (q = 0.01), then the number of people who suffer (i.e. who are homozygous recessive) is q^2 = 0.0001 or 0.01% of the population.

The number of carriers - or heterozygotes - is 2pq = 2 x 0.99 x 0.01 = 0.198, or 1.98% of the population. That means that carriers of the disease exist in the population at a frequency of almost 200 times more than actual sufferers. This can help us to identify the likelihood of one carrier mating with another, and potentially producing an offspring who suffers from the condition.

One exception to the Hardy-Weinberg principle is a phenomenon called recurrent mutation.

When looking at the rate of mutation in a population, forward mutations (i.e. those that cause functional genes to become non-functional) are more common than reverse mutations (i.e. those that cause non-functional genes to restore functionality). This is simply because a forward mutation can involve any number of base changes, while a reverse mutation requires the specific reversal of the change that initially made the gene non-functional. Hence, forward mutations occur at far greater rate than reverse mutations, and will proliferate in a population when they pose no selective disadvantage. This is evident in the proliferation of the O allele (which does not code for a glycosyltrasnferase enzyme) in the ABO blood-grouping system, at the expense of the A and B alleles.

Thus if q to determines the frequency of the non-functional allele, and μ determines forward mutation rate while v determines reverse mutation rate, where μ is taken to be 10 times the value of v:

q(equilibrium) = μ / (μ + v)