U01.01.052 Hardy-Weinberg population genetics

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Learning Objectives

  • Master the Hardy-Weinberg equations for allele and genotype frequencies.
  • Identify the five essential assumptions for equilibrium.
  • Calculate carrier frequency (2pq) given disease prevalence (q^2).
  • Distinguish between autosomal and X-linked frequency calculations.

1. The Fundamental Equations

In a stable population with random mating, allele frequencies remain constant. We use two primary equations:

  • Allele Frequency: p + q = 1
    • p = frequency of dominant allele (A)
    • q = frequency of recessive allele (a)
  • Genotype Frequency: p^2 + 2pq + q^2 = 1
    • p^2 = frequency of homozygous dominant (AA)
    • q^2 = frequency of homozygous recessive (aa/disease prevalence)
    • $Latex2pq$ = frequency of heterozygotes (carrier frequency)

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2. Hardy-Weinberg Assumptions

For a population to stay in equilibrium (where $p$ and $q$ do not change), five “No” rules must apply:

Requirement Meaning
No Mutation The alleles themselves do not change.
No Selection Natural selection does not favor one genotype over another.
Random Mating No consanguinity or mate choice based on the trait.
No Migration No gene flow in or out of the population.
Large Population Prevents genetic drift from altering frequencies.

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3. Clinical Calculations (High-Yield)

Autosomal Recessive (e.g., Cystic Fibrosis)

For rare diseases, we assume $p \approx 1$. Therefore, the carrier frequency $2pq \approx 2q$.

  • If prevalence (q^2) = 1/3200
  • Then q = \sqrt{1/3200} \approx 0.017 (1.7%)
  • Carrier frequency (2pq) \approx 2 \times 0.017 = 0.034 (3.4%)

X-Linked Recessive

The frequency in males equals q (because they only have one X chromosome). The frequency in females equals q^2.

 

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