Question

In a certain population of mice, a single gene controls fur color. There are two possible alleles: B, which leads to black fur; and W, which leads to white fur. Individuals with the genotype BB will have black fur; individuals with the genotype WW will have white fur; and individuals with the genotype BW will have gray fur. Scientists recorded the fur color of 1000 mice from the population. They found that 200 mice have black fur, 400 have gray fur, and 400 have white fur. Ten years later, the measurements are repeated. Again, they recorded the fur color of 1000 mice. They found that 400 have black fur, 400 have gray fur, and 200 have white fur. Part A: Show the Hardy-Weinberg calculations for the beginning and ending populations. Include the values for the equation as well as the p and q values. Show your work. Part B: Use the Hardy-Weinberg calculation to explain if this population is evolving or not. Then propose a hypothesis about the environment of these mice that would lead to these observations.

          In a certain population of mice, a single gene controls fur color. There are two possible alleles: B, which leads to black fur; and W, which leads to white fur. Individuals with the genotype BB will have black fur; individuals with the genotype WW will have white fur; and individuals with the genotype BW will have gray fur. Scientists recorded the fur color of 1000 mice from the population. They found that 200 mice have black fur, 400 have gray fur, and 400 have white fur. Ten years later, the measurements are repeated. Again, they recorded the fur color of 1000 mice. They found that 400 have black fur, 400 have gray fur, and 200 have white fur.

Part A: Show the Hardy-Weinberg calculations for the beginning and ending populations. Include the values for the equation as well as the p and q values. Show your work.

Part B: Use the Hardy-Weinberg calculation to explain if this population is evolving or not. Then propose a hypothesis about the environment of these mice that would lead to these observations.

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Added by Christopher H.

Biology for AP Courses

Julianne Zedalis, John Eggebrecht

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Solved by Expert Kaela Piechowicz

08/06/2023

Step 1

- We know that there are two alleles: B and W. - Let p be the frequency of the B allele and q be the frequency of the W allele. - The total number of alleles in the population is 2000 (since each mouse has two alleles). - From the given information, we can set up Show more…

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In a certain population of mice, a single gene controls fur color. There are two possible alleles: B, which leads to black fur; and W, which leads to white fur. Individuals with the genotype BB will have black fur; individuals with the genotype WW will have white fur; and individuals with the genotype BW will have gray fur. Scientists recorded the fur color of 1000 mice from the population. They found that 200 mice have black fur, 400 have gray fur, and 400 have white fur. Ten years later, the measurements are repeated. Again, they recorded the fur color of 1000 mice. They found that 400 have black fur, 400 have gray fur, and 200 have white fur. Part A: Show the Hardy-Weinberg calculations for the beginning and ending populations. Include the values for the equation as well as the p and q values. Show your work. Part B: Use the Hardy-Weinberg calculation to explain if this population is evolving or not. Then propose a hypothesis about the environment of these mice that would lead to these observations.

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Transcript

00:01 So this is the hardy -weinberg problem and we have capital b equals black fur and then we have capital w equals white.

00:12 And this color, this problem has three colors where the combination between black and white is gray.

00:19 So we got capital b, capital b.

00:21 This is generation 1.

00:22 There's 200 individuals.

00:25 Then we have gray, capital bw is 400.

00:31 And then white, ww is 400.

00:35 So we're going to start out just by finding the frequency of q squared.

00:40 That is our ww.

00:43 And to do that we just take 400, the number we have, by the population total which is 1000.

00:50 And that gives us a frequency of 0 .4.

01:00 Then we're going to find our frequency of 2pq which is our gray individuals, bw.

01:09 And to do that we just take the number we have, divided by the population which is 1000.

01:15 And that gives us another 0 .4.

01:17 And then our frequency of q squared, that is our bb.

01:27 Oops, sorry, that's p squared.

01:29 Frequency of p squared.

01:32 That's capital b.

01:36 That is 200 divided by the total of 1000, equal 0 .4.

01:43 So we want to know the frequency of the w allele, which is considered q.

01:56 And to do that we know that there are 2 times 400 individuals.

02:03 So 400 individuals each carrying 1 allele, or 2 alleles, sorry.

02:09 So 400 individuals each carrying 2 alleles, 2 times 400.

02:13 Plus the 400 individuals that are bw.

02:16 They carry 1 of those w alleles.

02:18 All divided by the number of alleles in the population, which is 2000.

02:25 So our frequency of the w white allele in this population is 0 .6.

02:32 And that means the frequency of p, which is the capital b, has to be 1 minus 0 .6, which is 0 .4.

02:42 So hardy -weinberg pretty much relies on everything adding up to 1, frequency -wise.

02:48 Okay, so this is the next year they go.

02:51 They find, or years later, they find that there are 400 black, there are 400 gray, and there are 200 white...

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