Hardy-Weinberg equilibrium describes what happens to allele and genotype frequencies in a population when no evolutionary forces are acting. It gives biologists a baseline for predicting how common different genotypes should be from one generation to the next. This matters because real populations can be compared to the Hardy-Weinberg expectation to detect evolution.
If the observed genotype frequencies differ from the prediction, something is changing the gene pool.
The model uses two allele frequencies, p and q, for a gene with two alleles. The allele frequencies add to 1, and the genotype frequencies are predicted by expanding (p + q)^2 into p² + 2pq + q² = 1. The five conditions are no mutation, random mating, no natural selection, very large population size, and no migration.
Scientists often use the frequency of a recessive phenotype to calculate q², then find q, p, and the expected genotype frequencies.
Understanding Biology: Hardy-Weinberg Equilibrium
Allele frequency is not the same as the number of people with a trait. A recessive allele can be fairly common while the recessive phenotype remains rare. This happens because many copies are carried by heterozygous individuals.
They have one recessive allele and one dominant allele, so they usually do not show the recessive trait. Carrier frequency is important in inherited disorders such as cystic fibrosis.
A population study may estimate how many people carry an allele even when the visible condition is uncommon. This distinction between alleles, genotypes, and phenotypes is one of the most important parts of the model.
The genotype prediction comes from the way gametes combine. Each parent contributes one allele to an offspring. If mating is random, the chance of receiving a particular allele from one parent is independent of the chance of receiving an allele from the other parent.
Multiplying those chances gives the frequencies of the two homozygous groups. There are two ways to make a heterozygote. One parent can pass on the first allele while the other passes on the second, or the order can be reversed.
That is why the heterozygote term includes a factor of two. The model describes probabilities across many births, not a guarantee for every family.
Each condition protects that prediction in a different way. Mutation creates new allele copies or changes existing ones. Migration brings alleles into a population or removes them.
Natural selection changes reproductive success when some genotypes survive or reproduce more effectively. Nonrandom mating changes which genotypes meet, often increasing homozygotes when relatives mate. Small populations are strongly affected by chance.
A few individuals may leave more offspring than expected, shifting allele frequencies through genetic drift. In a real population, more than one of these processes can act at the same time.
Biologists use departures from expected genotype frequencies as clues, but a difference does not identify one cause by itself. Too few heterozygotes may result from inbreeding, separated subpopulations, or selection. Too many heterozygotes can appear when a heterozygous genotype has an advantage.
Researchers must consider how the sample was collected. A sample from one neighborhood, one age group, or one habitat may not represent the full population.
Errors in identifying genotypes can create misleading results too. Statistical tests help decide whether an observed difference is likely due to random sampling or reflects a real biological pattern.
When solving problems, start by naming exactly what the data describe. A stated recessive phenotype gives the frequency of the recessive homozygous genotype. Take its square root to find the recessive allele frequency.
Then subtract that value from one to find the other allele frequency. Use those allele frequencies to calculate each expected genotype group. Finally, compare expected numbers with observed numbers only after multiplying frequencies by the population size.
Keep track of whether a number is a decimal, percentage, frequency, or count. Many mistakes come from treating these different forms as if they were interchangeable.
Key Facts
- Allele frequency equation: p + q = 1.
- Genotype frequency equation: p² + 2pq + q² = 1.
- p represents the frequency of one allele, often the dominant allele.
- q represents the frequency of the other allele, often the recessive allele.
- For a recessive phenotype, frequency of aa = q², so q = square root of q².
- Hardy-Weinberg equilibrium requires no mutation, random mating, no selection, a very large population, and no migration.
Vocabulary
- Allele frequency
- The proportion of all gene copies in a population that are a particular allele.
- Genotype frequency
- The proportion of individuals in a population that have a particular genotype.
- Gene pool
- The complete set of alleles present in a population.
- Hardy-Weinberg equilibrium
- A condition in which allele and genotype frequencies stay constant across generations because no evolutionary forces are acting.
- Recessive phenotype
- A trait that appears only when an individual has two recessive alleles for a gene.
Common Mistakes to Avoid
- Using q instead of q² for the recessive phenotype frequency is wrong because the recessive phenotype usually represents the homozygous recessive genotype aa.
- Forgetting that p + q = 1 is wrong because allele frequencies are proportions of the total allele pool and must add to 100 percent.
- Treating 2pq as the frequency of one allele is wrong because 2pq is the genotype frequency of heterozygotes, not an allele frequency.
- Assuming Hardy-Weinberg equilibrium proves no evolution forever is wrong because it is a model prediction that depends on specific conditions being met in that generation.
Practice Questions
- 1 In a population, 9 percent of individuals show a recessive phenotype. Assuming Hardy-Weinberg equilibrium, find q, p, and the expected frequencies of AA, Aa, and aa.
- 2 A population has allele frequencies p = 0.7 and q = 0.3. Calculate the expected genotype frequencies p², 2pq, and q², then state the expected percent of heterozygotes.
- 3 A population has many more heterozygotes than Hardy-Weinberg equilibrium predicts. Give one possible biological reason for this pattern and explain which Hardy-Weinberg condition may be violated.