Hardy Weinberg Problem - Need your help!

[texan2414]

I am trying to understand how to do this problem and I need your help in understanding how the right answer was achieved:

1. A population of lizards is in H-W equilibrium. The gene for green color is dominant (G) and the gene for brown color is recessive (g). If the population consists of 1000 individuals and 250 of them are brown, how many heterozygotes are there in a population?

a. 250

b. 500

c. 650

d. 750

e. 375





The correct answer is B. However, when I worked it out, the answer I got was E.
I got the recessive allele frequency by q = 250/1000 = 0.25 and then plugging into the "2pq" aspect of the equation → 2(0.25)(0.75) * 1000 = 375.

But the setup above was WRONG! If anyone can explain to me how the answer was B, I would very much appreciate it.

Thanks,

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[Cawolf]

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

G^2 + 2Gg + g^2 = 1

We know that there are 250/1000 individuals who are gg. Since it is in H-W equilibrium, there are 250/1000 who are GG.

So G^2 and g^2 are both = .25

.25 + 2Gg + .25 = 1

2Gg = 1 - .25 -.25 = .5

Hetero = 2Gg*1000 = .5*1000 = 500

 

[texan2414]

Hey Cawolf,

Thanks for your prompt reply.

I got a little confused why we were raising 0.25 to the power of 2. I thought that 0.25 would be the frequency of the recessive phenotype.
Also, why is the GG frequency also 0.25?

 

[kraskadva]

You're confusing genotype frequency (which is the same thing here as phenotype frequency) with allele frequency.
the equation for genotype frequency is:
p^2 + 2pq + q^2 = 1
The equation for allele frequency is:
p+q=1

So...

1. A population of lizards is in H-W equilibrium. The gene for green color is dominant (G) and the gene for brown color is recessive (g). If the population consists of 1000 individuals and 250 of them are brown, how many heterozygotes are there in a population?

Here they give you q^2=.25 (i.e. 250/1000)
which means q=.5 (sqrt of .25)
so if p+q=1, then p also =.5

2pq=2(.5)(.5)=.5
.5*1000=500

But if you've got a nice round number population like this in HWE, you should just remember your punnett squares and mendelian ratios (i.e. 1:2:1) and get 250:500:250 for GG:Gg:gg without any calculations.

 

[texan2414]

Thanks a lot! This makes the problem much easier!!

 

[kraskadva]

 

[kraskadva]

Though do beware of questions where the allele frequencies are not exactly 50/50.
Try a couple practice problems with different frequencies just to make sure you've got it down...like (p=.75, q=.25) or (p=.6, q=.4).

 

[Cawolf]

@texan2414

Sorry was out to dinner but they answered your question for me. GL!