Acronym trick for Hardy-Weinberg equilibrium

Hardy–Weinberg can feel like it shows up out of nowhere on test day: a stem gives you a disease prevalence and suddenly you’re expected to reverse-engineer carrier frequency in 20 seconds. The trick is to memorize the “shape” of the equation and what each piece means, so you can move fast without re-deriving anything.

The Acronym Trick: H-W = “P² + 2PQ + Q²” (the “2 Peas & a Q” rule)

Say it out loud:

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“P-squared plus 2 P Q plus Q-squared… two peas and a Q.”

That phrase locks in the only equation you really need: $p^2 + 2pq + q^2 = 1$

And the other one: $p + q = 1$

The Visual/Mnemonic Device (shareable)

Think of a pea pod with two peas and one Q:

• Left pea = $p$
• Right pea = $p$
• The “middle mash” (two peas + a Q) = $2pq$ (heterozygotes)
• The lone Q = $q^2$ (homozygous recessive)

One-liner meaning:
$p^2$ = homozygous dominant, $2pq$ = heterozygous (carriers), $q^2$ = homozygous recessive.

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What $p$ and $q$ Actually Are (don’t mix this up)

• $p$ = frequency of the normal (dominant) allele (often $A$)
• $q$ = frequency of the mutant (recessive) allele (often $a$)

So:

• $p^2$ = $AA$
• $2pq$ = $Aa$
• $q^2$ = $aa$

Micro-table: genotype ↔ what Step wants you to say

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The High-Yield Move: “Prevalence = $q^2$” (for Autosomal Recessive)

Most Step questions quietly assume autosomal recessive unless stated otherwise. If it’s AR:

1. Prevalence (affected individuals) = $q^2$
2. Take square root: $q = \sqrt{q^2}$
3. Find $p$: $p = 1 - q$
4. Carrier frequency = $2pq$
   • If $q$ is small, $p \approx 1$, so $2pq \approx 2q$ (fast approximation)

Example you can do in your head

If an AR disease prevalence is 1 in 10,000:

• $q^2 = 1/10{,}000 = 10^{-4}$
• $q = 10^{-2} = 0.01$
• Carrier frequency $2pq \approx 2q \approx 0.02$ = 2% ≈ 1 in 50

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When Hardy–Weinberg Applies (and when it doesn’t)

Hardy–Weinberg assumes a “boring” population with:

• Random mating
• No selection
• No mutation
• No migration (gene flow)
• Large population size (minimizes genetic drift)

USMLE nuance

• Consanguinity increases homozygosity (more $q^2$) and reduces heterozygosity (less $2pq$) relative to H–W expectations—classic reason a real population deviates from H–W.

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Classic Step Pitfalls (avoid these)

• Mistaking $2pq$ for disease prevalence:
  For autosomal recessive disease, prevalence is $q^2$, not $2pq$.
• Forgetting the square root:
  If they give affected frequency, you still need $q = \sqrt{q^2}$.
• Overcomplicating $p$:
  For rare diseases, $p \approx 1$, so carrier $\approx 2q$ is usually enough.

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Quick Recall Box (screenshot-worthy)

• “2 peas & a Q” → $p^2 + 2pq + q^2 = 1$
• AR prevalence = $q^2$
• Carrier frequency = $2pq \approx 2q$ (when rare)
• Alleles sum = $p + q = 1$