Anonymous
Anonymous asked in Science & MathematicsBiology · 2 months ago

# Harvey Weinberg Equilibrium?

You are studying scale color in a fish population. You know the gene for color is diallelic and shows codominance. You know one allele encodes for red and the other for white scales. You sample 777 fishes. Of those sampled, 223 are all red, 348 are white and red, and 206 are all white.

Calculate the expected number of fish of each phenotype if this population were in Hardy-Weinberg Equilibrium.

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• 2 months ago

Fortunately your teacher phrased this question in such a way that you can answer it.

Let p = freq(red allele)

Let q = freq(white allele)

Count the alleles.

We have

223 + 223 + 348 = 794 red alleles

348 + 206 + 206 = 760 white alleles

Okay.  You can check to make sure that those two add up to 2*777 alleles total.

2*777 = 794+760?  Yes, yes, for a total of 1554 alleles.

Good so far.

p = freq(red allele) = 794/1554 = 0.511

q = freq(white allele) = 760/1554 = 0.489

Note:  rounding to three places. I think I am allowed three sig figs here, since we were given three digits for the census counts.

Check:  p+q = 1 ?  Yes, yes it does.

Good so far.

Now we want the expected proportions of population given that p and that q.

p + q = 1 (obvious)

(p+q)*(p+q) = 1  (Hey, you squared 1 on both sides!)

p^2 + 2pq + q^2 = 1 (did the math)

Okay, Hardy & Weinberg would say that

p^2 represents the portion of the population that is homozygous red

q^2 represents the portion of the population that is homozygous white

2pq represents the portion of the population that is the heterozygotes, phenotype "white and red"

Okay.  You multiply the portions by the population size to get the expected values.  Get it?  Got it?  Good.

...and you have to round to whole numbers because you can't have fractions of individuals.  LOL.

I expect:

777 * p^2 = 777 * (.511^2) = 203 red individuals (answer)

777 * q^2 = 777 * (.489^2) = 186 white individuals (answer)

777 * 2pq = 777 * 2 * .511 * .489 = 388 red&white individuals (answer)

Check:  203 + 186 + 388 = 777 ? Yes, yes it does.

We're done.

• Anonymous
2 months ago

That's a stupid question.  Tell your teacher that.  This better not be from a college course.  Hardy Weinberg cannot apply in this case because there is no recessive allele.