Hardy-Weinberg Principle

The Hardy-Weinberg principle is a mathematical model that describes the relationship between allele frequencies and genotype frequencies in a population that is not evolving. It provides a baseline against which real populations can be compared to detect whether evolution is occurring.

---

Allele Frequency and Genotype Frequency

Key Definition: Allele frequency is the proportion of a particular allele among all the alleles for that gene in a population. Genotype frequency is the proportion of individuals in the population with a particular genotype.

For a gene with two alleles (A and a):

• Let p = frequency of the dominant allele (A)
• Let q = frequency of the recessive allele (a)

Since there are only two alleles: p + q = 1

---

The Hardy-Weinberg Equation

If a population is in Hardy-Weinberg equilibrium, the genotype frequencies can be predicted from the allele frequencies:

p² + 2pq + q² = 1

Where:

• p² = frequency of homozygous dominant genotype (AA)
• 2pq = frequency of heterozygous genotype (Aa)
• q² = frequency of homozygous recessive genotype (aa)

This equation is derived from the binomial expansion of (p + q)², which represents random mating between gametes carrying allele A (frequency p) and gametes carrying allele a (frequency q).

---

Conditions for Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle holds true only when the following five conditions are met:

1. No mutation — no new alleles are being created.
2. No natural selection — all genotypes have equal fitness and survival rates.
3. No migration (gene flow) — no individuals are entering or leaving the population.
4. Random mating — individuals mate without preference for particular genotypes.
5. Large population size — the population is large enough to prevent random fluctuations in allele frequency (genetic drift).

Key Point: In reality, no natural population perfectly meets all five conditions. The Hardy-Weinberg model is an idealised baseline. When a population departs from equilibrium, one or more of these conditions has been violated, and evolution is occurring.

---

Worked Example 1 — Cystic Fibrosis

Cystic fibrosis (CF) is an autosomal recessive condition caused by a mutation in the CFTR gene. In a particular UK population, approximately 1 in 2500 people is born with CF.

Step 1: Individuals with CF are homozygous recessive (aa). q² = 1/2500 = 0.0004

Step 2: Calculate q (frequency of the recessive allele). q = √0.0004 = 0.02

Step 3: Calculate p (frequency of the dominant allele). p = 1 − q = 1 − 0.02 = 0.98

Step 4: Calculate the carrier frequency (2pq). 2pq = 2 × 0.98 × 0.02 = 0.0392

Approximately 3.92% of the population (about 1 in 25 people) are carriers of the CF allele.

Step 5: Calculate the frequency of homozygous dominant individuals (p²). p² = 0.98² = 0.9604 (96.04%)

Summary:

Genotype	Frequency	Approximate ratio
AA (homozygous normal)	0.9604	~96.0%
Aa (carrier)	0.0392	~3.9%
aa (affected)	0.0004	~0.04%

---

Worked Example 2 — MN Blood Groups

The MN blood group system is controlled by a single gene with two codominant alleles (M and N). In a population of 1000 individuals:

• 360 are MM
• 480 are MN
• 160 are NN

Step 1: Calculate allele frequencies.

Frequency of M allele (p): p = (2 × number of MM + number of MN) / (2 × total) p = (2 × 360 + 480) / (2 × 1000) p = 1200 / 2000 = 0.6

Frequency of N allele (q): q = 1 − p = 1 − 0.6 = 0.4