Hardy-Weinberg equilibrium — conditions and significance

The Hardy-Weinberg Principle (1908, independently by G.H. Hardy and W. Weinberg) states:

In a large, randomly mating population, allele frequencies and genotype frequencies remain constant from generation to generation, provided certain conditions are met.

Mathematically, for a gene with two alleles $p$ (dominant, frequency $= p$) and $q$ (recessive, frequency $= q$):

Where: $p^2$ = frequency of homozygous dominant (AA), $2pq$ = heterozygous (Aa), $q^2$ = homozygous recessive (aa).

The population is said to be in Hardy-Weinberg equilibrium when these frequencies do not change over generations.

Equilibrium is maintained ONLY when ALL five conditions are satisfied:

1. Large population size: No genetic drift (random fluctuations in allele frequency). Small populations are susceptible to chance events changing allele frequencies.

2. Random mating (panmixia): Every individual has an equal probability of mating with any other. No sexual selection, no mating preferences.

3. No mutation: No new alleles created; existing alleles not converted to other alleles.

4. No gene flow (no migration): No individuals entering or leaving the population, which would change allele frequencies.

5. No natural selection: All genotypes must have equal survival and reproductive success. No selective advantage for any allele.

When ANY of these conditions is violated, allele frequencies change → evolution is occurring.

Hardy-Weinberg equilibrium is a null hypothesis for evolution. It describes what a population would look like if it were NOT evolving. The significance:

1. Detecting evolution: If a real population deviates from Hardy-Weinberg frequencies, we know at least one condition is violated → evolution is occurring. This is the primary tool for detecting natural selection, genetic drift, etc.

2. Estimating allele frequencies: If we know the frequency of a recessive phenotype ($q^2$), we can calculate $q$, $p$, and the carrier frequency ($2pq$). For example, if 1 in 10,000 people has albinism ($q^2 = 0.0001$), then $q = 0.01$, $p = 0.99$, and carrier frequency $= 2 \times 0.99 \times 0.01 = 0.0198 \approx 1$ in 50 people.

3. Identifying mechanisms of evolution: Each violation corresponds to an evolutionary force:

• Violation of random mating → sexual selection
• Violation of no mutation → mutation pressure
• Violation of no migration → gene flow
• Violation of no selection → natural selection
• Violation of large population → genetic drift

Sickle cell anaemia occurs in 1 in 400 people in a population ($q^2 = 1/400 = 0.0025$).

$q = \sqrt{0.0025} = 0.05$

$p = 1 - 0.05 = 0.95$

Carrier frequency $= 2pq = 2 \times 0.95 \times 0.05 = 0.095 \approx$ 1 in 10 people are carriers.

This is much higher than the 1 in 400 affected — carriers vastly outnumber those who show the condition.