20.3 Hardy-Weinberg Equilibrium
Key Takeaways
If p is the frequency of allele A and q is the frequency of allele a, then p + q = 1, and equilibrium genotype frequencies satisfy p squared + 2pq + q squared = 1.
Equilibrium assumes no mutation, no gene flow, no selection, random mating, and a very large population so that drift is negligible.
If the recessive phenotype aa is 1 percent under those assumptions, q squared is 0.01, q is 0.1, p is 0.9, and the carrier frequency 2pq is 0.18.
Inbreeding changes genotype frequencies by producing more homozygotes, without by itself changing allele frequencies.
Mutation, gene flow, selection, nonrandom mating, and genetic drift change populations; a bottleneck and a founder effect are drift, and a recessive phenotype frequency is q squared, not q.
20.3 Hardy-Weinberg Equilibrium
Hardy-Weinberg equilibrium is the null model. You calculate genotype frequencies from allele frequencies when evolution is not occurring. The arithmetic is short. The meaning is that the listed forces are not changing the population.
The null model and the two equations
Consider one gene with two alleles, A and a. Let p be the frequency of A and q the frequency of a. Every copy is one or the other, so p + q = 1. A frequency is a proportion of allele copies. Subtract a known frequency from 1 to get the other.
When a population is in Hardy-Weinberg equilibrium, random mating produces genotype frequencies given by . The term p squared is the frequency of AA. The term 2pq is the frequency of Aa, the carriers when a is recessive. The term q squared is the frequency of aa. An A gamete meets an A gamete with probability p times p, two a gametes meet with probability q times q, and the two mixed orders add to 2pq.
Allele frequencies stay the same from generation to generation, and genotype frequencies sit at those three values. That is what happens when evolution is not occurring. Equilibrium is not a population that selection is improving.
The assumptions that keep the null model true
Five assumptions define the model. Grant the whole list before you take a square root of a phenotype frequency.
- No mutation. Alleles are not being converted into other alleles.
- No migration, which means no gene flow. Individuals are not bringing alleles in from another population or carrying alleles out.
- No selection. Every genotype has the same reproductive success, so differential reproduction is not changing allele frequencies.
- Random mating. The chance that two genotypes form a pair does not depend on the genotype at this gene.
- A very large population, so genetic drift is negligible. Chance sampling of gametes does not noticeably move allele frequencies.
If an item tells you to assume Hardy-Weinberg equilibrium, it is granting this list. The arithmetic that follows is the null calculation. It is not a measurement of how strong selection is.
A recessive phenotype at 1 percent
Work the standard problem in this order, and use it only under the equilibrium assumptions. Suppose the recessive phenotype aa is 1 percent of the population. One percent as a proportion is 0.01. Under the model, the frequency of aa is q squared, so q squared is 0.01. The allele frequency q is the square root of 0.01, which is 0.1. Because p + q = 1, p is 0.9. The carrier frequency is 2pq, which is 2 times 0.9 times 0.1, which is 0.18, or 18 percent.
Under these assumptions, most copies of a recessive allele sit in carriers. Affected individuals are 1 percent of people and carry two copies. Carriers are 18 percent and carry one copy. One percent affected is q squared, not q. Skipping the square root is the usual trap.
Report 18 percent only because the equilibrium assumptions hold. If selection is removing aa individuals, or if mating is not random, you cannot treat the current aa frequency as q squared and 2pq as the carrier frequency in this same way. The 1 percent item is granting those assumptions unless it says otherwise.
What changes genotype frequencies, and what changes allele frequencies
Nonrandom mating, including inbreeding, changes genotype frequencies without by itself changing allele frequencies. Relatives share alleles, so offspring are more often AA or aa and less often Aa. The extra homozygotes still carry the same alleles. Inbreeding rearranges genotypes. It does not, by itself, prefer one allele.
Five processes change populations. Mutation introduces new alleles and is random with respect to usefulness. Gene flow moves alleles between populations by migration. Selection changes allele frequencies when genotypes differ in reproductive success. Nonrandom mating changes genotype frequencies. Genetic drift changes allele frequencies by sampling error and is stronger in small populations. A very large population keeps that sampling error negligible, which is why the null model requires one.
A bottleneck and a founder effect are drift, not selection. In a bottleneck the population crashes, and the survivors are a small sample, so allele frequencies can jump by chance. In a founder effect a few individuals start a new population, and their alleles are a small sample of the source. Colonists on a ship, or a few birds on a new island, are the usual founder picture. The sample need not be the individuals with the highest fitness.
| Process | What changes | Exam note |
|---|---|---|
| Mutation | Allele frequencies, by adding new alleles | Random with respect to usefulness |
| Gene flow | Allele frequencies, by migration | Also called migration |
| Selection | Allele frequencies, by unequal reproduction | Not a predetermined goal |
| Nonrandom mating | Genotype frequencies | Inbreeding produces more homozygotes |
| Genetic drift | Allele frequencies, by sampling error | Bottleneck and founder effect; stronger when small |
How to read a frequency stem
Translate the words into the null model before you take a square root.
- A recessive phenotype frequency, under equilibrium, is q squared. For 1 percent, q squared is 0.01, q is 0.1, p is 0.9, and 2pq is 0.18.
- Those steps use the equilibrium assumptions.
- Inbreeding adds homozygotes without by itself changing allele frequencies.
- A bottleneck or a founder event is drift, and drift is stronger in a small population.
Warning
Hardy-Weinberg equilibrium is what happens when evolution is not occurring. It is the null model, not a force that changes allele frequencies. A recessive disease frequency is q squared, not q. Reading 1 percent affected as q equal to 0.01 skips the square root and gives the wrong carrier frequency.
Assume Hardy-Weinberg equilibrium. The recessive phenotype aa is 1 percent of the population. Which values follow?
q is 0.01, and the carrier frequency 2pq is 0.01.
q is 1, and the carrier frequency 2pq is 0.5.
q squared is 0.01, q is 0.1, p is 0.9, and the carrier frequency 2pq is 0.18.
q is 0.9, p is 0.1, and the carrier frequency 2pq is 0.18.
Which statement correctly describes Hardy-Weinberg equilibrium and inbreeding?
Equilibrium is produced by strong directional selection, and inbreeding by itself changes allele frequencies.
Equilibrium means a recessive disease frequency equals q, and inbreeding increases the proportion of heterozygotes.
Equilibrium is the null pattern when evolution is not occurring, and inbreeding changes genotype frequencies without by itself changing allele frequencies.
Equilibrium requires continual mutation, and inbreeding is the same event as a population bottleneck.
Which list matches the processes that change populations, and which events are genetic drift?
Inbreeding changes allele frequencies by itself and leaves genotype frequencies unchanged.
Mutation, gene flow, selection, nonrandom mating of genotypes, and drift change populations; a bottleneck and a founder effect are drift.
Only selection changes a population, and drift is strongest when the population is extremely large.
Hardy-Weinberg equilibrium is a force that shifts allele frequencies whenever the recessive phenotype is rare.
Sections you finish are checked off in the contents.