Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Say my mom has a gene (it's one of those regular gene, ignore X and Y chromosome)

The gene exist in p% of the population.

Things get complicated due to that p. If p is 100%, for example, then of course the probability that I have the gene to is 100%. If p is 1% then the probability that I got the gene will be 50%.

How to formalize this mathematically?

My gut feeling is it'll just be linear. if p is 1% then my chance will be 50.5% because that means my dad have a 1% chance to have that gamete.

Then i want to extend this to cousins.

share|improve this question
    
What is gammete? How does it work between generations? –  Patrick Li Nov 8 '12 at 4:32
    
a gene? Did I spell that correctly? –  Jim Thio Nov 8 '12 at 4:34
add comment

1 Answer 1

First by 'gamete', you mean allele correct? A gamete is when the sperm and egg have already fused together so there is no more probability. While an allele is a specific gene which can vary (as in your case). So I will assume that you are talking about an allele/gene.

In your case, the formula, that you are talking about is the Hardy-Weinberg formula.

Basically $$(p^2) + (2pq) + (q^2) = 1$$ where p and q are the percentage of two version of the alleles.

Say you have a gene with 2 possible alleles 'A' and 'a' which are present in p% and q% of the the population (so p would be 1% and q can be 99% in your case).

The percentage of the three possible genotypic frequencies in the offspring become:

$f(AA) = p^2$

$f(Aa) = 2pq$

$f(aa) = q^2$

To find the chance that you will get an allele A, you just need to add up $f(AA) + f(Aa)$ (because both of them have a gene/allele 'A' which is the gene that you want to know about)

If your case, if p = 100% = 1, this means $q=0$, then the probability that you will be an allele A would be 100% (because $f(AA) + f(Aa) = 1^2 + 2*1*0=1+0=1$).

In your second case, If p = 1%, this means q = 99% (because all the other eggs would have the other gene/allele). This means $f(AA) + f(Aa) = 0.01^2 + 2*0.01*0.99=0.0001+0.0198=0.0199$ or 1.99%.

share|improve this answer
    
And what about if my mom have that A allele? You haven't taken that into account. Say 50% of my Mom's allele is A. –  Jim Thio Nov 8 '12 at 4:46
    
Then p = 0.5 (and 0.5). So $f(AA)+F(Aa) = 0.5^2+2*0.5*0.5 = 0.75$ or 75%. It doesn't matter whether you are looking at the gene from mom or dad side since the frequency of the allele is known at a population level so its assumed that both the egg and sperm have the same chance of having that specific gene/allele. –  BYS2 Nov 8 '12 at 4:48
add comment

Your Answer

 
discard

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.