Biology Stack Exchange is a question and answer site for biology researchers, academics, and students. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have this equation: Corresponds to HW in equilibria with three alleles:


Expanding the square results:

$p^2+2pq+r^2+2pr+q^2+2qr = 1$

I need to separate homozygous and heterozygous, that means: $2pq+2pr+2qr=1-p^2-q^2-r^2$

How I can use a equivalence similar to $(p=1-q) or (q=1-p)$ in two alleles to resolve the last equation?

share|improve this question
in this case it will be r=1-p-q and similarly for others – WYSIWYG May 24 '13 at 6:48
Why do you need to separate homozygotes from heterozygotes? – jkadlubowska May 24 '13 at 8:52
I'm with jkadlubowska - what's the purpose of separating hetero and homozygotes? – MCM May 24 '13 at 12:40
To calculate the proportion of the alleles (p, q and r), if the homozygotes are three times than heterozygotes. – Cristian Velandia May 24 '13 at 21:56
So you omitted some data of this question? The thing is, you can substitute whatever you want, e.g. 1-p=q+r or p=1-q-r, but that leads you nowhere if you don't have any more data. Something like p^2+q^2+r^2=3pq+3pr+3rq is crucial to solving this problem. Anyway - these are two equasions, you still need a third to ba able to assign specific numbers to p, q and r. – jkadlubowska May 25 '13 at 5:08
up vote 2 down vote accepted

Everybody said it already, but there is none. The original HWE equation ($(p+q)^2=1$) works because you've got two variables and two equations ($p+q=1$) to work with (in reality, these are just one equation and one variable, since $q=1-p$ so $p+(1-p))^2=1$). Now you have three variables and still only the one equation ($p+q+r=1$) which is, mathematically, impossible.

You need go out and measure some frequencies. In particular, you need to measure two of them - I'd choose two of the homozygous types for convenience's sake.

This basically summarizes everything nicely for ya:

share|improve this answer
mathematically impossible -> mathematically insolvable. Its quite possible. – shigeta Feb 9 '14 at 6:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.