Hardy-Weinberg genetics

[arc5005]

Advertisement - Members don't see this ad

Do I need to know this equation for the MCAT? should I bother trying to remember it?




Example question from TBR:

Given that the ratio of 35Cl to 37Cl in a sample is three to one, what abundance ratio would be expected for 35Cl-35Cl to 35Cl-37Cl to 37Cl-37Cl after being put into a mass spectrometer?

A. 1 : 6 : 9
B. 9 : 6 : 1
C. 1 : 3 : 12
D. 12 : 3 : 1

B) 9 : 6 : 1
We will expect more 35Cl-35Cl species than the 37Cl-37Cl, so eliminate choices A & C. If you have studied Hardy-Weinberg genetics, then you may recall that the crossing-frequency ratio for two events is p2 + 2pq + q2 = 1, where p is the probability of the first event, and q is the probability of the second event. Using this equation yields the following ratio:
p2 + 2pq + q2
(3/4)2 : 2(3/4)(1/4) : (1/4)2
(9/16) : 2(3/16) : (1/16)
(9/16) : (6/16) : (1/16)
9 : 6 : 1
If you don't recall this equation or probability, consider all of the possible options for the dimer of chlorine atom. The first chlorine has a three-fourths chance of being 35-chlorine and a one-fourth chance of being 37-chlorine. The same odds are true for the second chlorine. This means that of sixteen possible outcomes (4x4), one time produce 37Cl with 37Cl, and nine times produces 35Cl with 35Cl.

 

[Zenabi90]

p2 + 2pq + q2 = 1?

Yes. I've seen it come out on the MCAT, and it doesn't take much memory space to remember it. And if you do memorize it, you'll save precious seconds.

P + Q = 1. Pretty basic right? Now square both sides.
P^2 + pq + pq + q^2 = 1^2
P^2 + 2pq + q^2 = 1

 

[NextStepTutor_1]

Hi @arc5005,

In addition to @Zenabi90 's point, one thing that might initially be surprising about this explanation is the reference to Hardy-Weinberg in what initially seems like a question about isotopes. Something that can be easy to overlook about Hardy-Weinberg is that the equations aren't specific to genetics, they're just applicable to any situation where you have two mutually exclusive outcomes of an event -- it could be having the allele p versus the allele q for a given gene, or it could be whether the Cl atom is 37Cl or 35Cl, or it could be any number of other things. For the MCAT, you definitely do need to be aware of Hardy-Weinberg equilibrium, and it is also helpful to have a sense of how the equation is rooted in probability.

Hope this is helpful!

 

[arc5005]

Thank you. 🙂

 

[NextStepTutor_1]

You're welcome, & best of luck!

 

[Zenabi90]

Hi @arc5005,

In addition to @Zenabi90 's point, one thing that might initially be surprising about this explanation is the reference to Hardy-Weinberg in what initially seems like a question about isotopes. Something that can be easy to overlook about Hardy-Weinberg is that the equations aren't specific to genetics, they're just applicable to any situation where you have two mutually exclusive outcomes of an event -- it could be having the allele p versus the allele q for a given gene, or it could be whether the Cl atom is 37Cl or 35Cl, or it could be any number of other things. For the MCAT, you definitely do need to be aware of Hardy-Weinberg equilibrium, and it is also helpful to have a sense of how the equation is rooted in probability.

Hope this is helpful!

Excellent point.

 

[aldol16]

I find that it's much easier to understand where equations come from than memorize them. Think of this equation as a mathematical representation of the chances of choosing various combinations of two things. In genetics, this is the mathematical representation of the Punnet square. So let me derive it for you.

Say you have two bags, each containing one red ball and one green ball. Let's call the chance of choosing a red ball p and the chance of choosing a green ball q. The first equation you know is this: p + q = 1. There are only green and red balls in a bag so the chance of choosing red or green from one bag is 1.

Now say you want to choose two balls, one from each bag. What are the chances of getting two red? Well, it's p^2. What are the chances of getting two green? q^2. What are the chances of getting one red and one green? Well, it's the chance of getting red and then green or green and then red. That's 2pq. That's all the possibilities. All probabilities sum to 1, so p^2 + 2pq + q^2 = 1. That's the equation.

Now let's apply this to genetic analysis and see how you can use this kind of math to simplify things and not have to draw Punnet squares. Say a male has genotype Aa and a female has genotype Aa. Furthermore, a is the recessive disease-causing allele. They mate. What is the probability that their offspring ends up affected by the disease? Well, imagine two gene "bags." One is from the father and the other is from the mother. In other words, both bags have one A and one a allele. By astute observation, you notice that this is the exact same scenario as above, but with alleles for balls. p = q = 1/2 in this case. Now what are the chances of having the aa genotype? Well, it's q^2 = 1/2*1/2 = 1/4.