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Hardy-Weinberg

In a large population where mating is random and there is no selection, migration or mutation that matters, the allele frequencies stay put. If we call the frequency of a by q and of A by p, then p plus q equals 1. The share that shows a recessive trait is q squared. The share of carriers, Aa, is 2pq. The formula is used to estimate how many carry a hidden allele when you only see the recessive individuals. It is a model. Real populations often break the assumptions a little.

p+q=1p + q = 1allele frequencies
2pq2pqshare of carriers Aa

Symbols

q2q^2share with genotype aa
ppfrequency of A
qqfrequency of a

Example

1% have genotype aa, so q2=0.01q^2 = 0.01, q=0.1q = 0.1 and p=1−0.1=0.9p = 1 - 0.1 = 0.9.

Carriers: 2⋅0.9⋅0.1⋅100=182 \cdot 0.9 \cdot 0.1 \cdot 100 = 18%.

18% carriers is much more than the 1% who show the trait. Most recessive alleles sit in carriers.
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Part of Biology 1: Heredity and genetics.