Question

(this is confusing!! help!)
A genetics researcher finds that a form of human albinism in a certain population is controlled by the recessive allele, a, for the absence of skin pigment and the completely dominant allele, A, for presence of skin pigment. If the recessive allele occurs in 30% of this population, what percent of the population has skin pigment but also carries the recessive allele?




21%


42%


51%


91%

Answer 1

Hey there,

I'll give this one a try - hopefully @blues can come by later and correct my work :D

You probably know that this will involve the Hardy-Weinberg equilibrium equations. Using these two equations: p^2+2pq+q^2=1 and p+q=1, where p and q represent the frequency of the dominant and recessive genes (respectively) in the population - you should be able to figure this out.

So we're given:
"If the recessive allele occurs in 30% of this population..."
and we want to find:
"percent of the population has skin pigment but also carries the recessive allele"

Okay: so a bit of background on the two equations above.
p+q = 1 refers to the frequency of *alleles* in the population. This is assuming that there are only two alleles - if this is true, then the frequency of one plus the frequency of other must equal one! Start with this one when you're told about the frequency of an allele in a population.

p^2+2pq+q^2 = 1 refers to the number of dominant (pp), recessive (qq), and heterozygotes (2pq). Start with this one when you're told about the number of people with a certain condition, or something similar to that.

So from the given, which equation can you go with?

Answer 2

this is a good explanation ! thanks! I think 51% ?

Answer 3

the first equation?

Answer 4

Hm - mind explaining how you got 51%?

And yes - I would go with the first equation as well. Since we're told the recessive frequency, we know q = 0.3 right? Simple algebra yields p to be 0.7

What we're told to find is a little bit tricky.
""percent of the population has skin pigment but also carries the recessive allele""
The presence of skin pigment is the result of a dominant gene. But - we also want the presence of a recessive allele. In other words, you're looking for the heterozygote frequency, represented by 2pq. Throw the above numbers in and you should be good :D

Answer 5

ohhh ! thats right! i miscalculated. so according to the equation you gave me i got 42%. will that be?

Answer 6

I think so :) blues, one of the awesome mods for the bio group, will probably be by later and hopefully will be able to verify that I didn't make a drastic mistake.

Answer 7

okay, thank you! that actually helped :)

Answer 8

Great question!

Answer 9

@kma230 and @andrea95,

These Castle-Hardy-Wienburg problems are fun and this one is especially so.

The crux of this very badly worded problem is the sentence, "The recessive allele occurs in 30% of the population." That is not quite synonymous with "The frequency of the recessive allele is 30%." The first interpretation refers to the proportion of individuals in the population who have the recessive allele - that is, the proportion who are homozygous recessive or heterozygous . The second interpretation refers to the frequency of the allele - that is, 30% of all alleles for this gene in a population are recessive.

You worked the second option and got one of the answers on the list.

Instead, I take the problem to mean exactly what it says: the proportion of individuals: the proportion of individuals who have at least one recessive allele is 30%.

That means that

0.3 = 2pq + q^2 from CHW.

Also, p = 1 - q by rearrangement of the other equation. This I substitute and solve for q:

0.3 = 2*(1-q)*q + q^2

q = 0.16334.

Substitute that into the equation for p and solve:

p = 1 - q
p = 1 - 0.16334
p = 0.8366

Now it asks you to compute how many individuals are heterozygous - that is, have the recessive allele but also one dominant allele:

proportion heterozygous = 2*p*q
= 2*0.16334 *0.8366
= 0.2733 or 27.3%.

Which is the correct interpretation of the given in the problem, but NOT one of the options on the list.

Answer 10

:o so wouldn't 21% be probably the answer , since yours was 27.3%?

Answer 11

No, if they had meant it to be roughly 27%, they would have put 27% as one of the options. They generally don't give you options which are accurate to the first digit and expect you to give or take 5% from whatever you calculate.

Particularly as the 42% came out on the money.

It is just a very, very sloppy question. :/

Answer 12

I agree. Thank you for the help though !

Answer 13

Not a prob. :D

Answer 14

:)

Answer 15

Thanks for the catch, @blues :D Great explanation.