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Hardy Weinberg Equation

Just wondering, why is the HWE the exact same thing as the expansion of (p+q)²? What is the relationship between a parabola and the HWE?

What does that mean?

Original post by alifleih

Just wondering, why is the HWE the exact same thing as the expansion of (p+q)²? What is the relationship between a parabola and the HWE?

The HWE is just an extended version of the condition that

p+q=1

p

and

q

represent frequencies (of the dominant and recessive allele respectively) and since these are only two options for a single allele, then their sum must be 1, since an allele can be either dominant or recessive. Compare this with probabilities of all possible outcomes having to sum to 1.

Since both sides of the equation are positive, we can square both sides and get

(p+q)^2=1^2 =1

and expanding the left hand side, we get

p^2 +2pq +q^2=1

- which is the HWE.

The HWE is an equation of degree 2 in

p

q

, so can be represented as a parabola in either

p

q

(edited 8 years ago)

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