Popgen practice problems Fall 2009 KEY

# Popgen practice problems Fall 2009 KEY - POPULATION...

This preview shows pages 1–3. Sign up to view the full content.

POPULATION GENETICS - PRACTICE PROBLEMS KEY FALL 2009 These problems are designed to help you understand the concepts covered in lecture and section. However, merely completing this set of practice problems is not sufficient preparation for the exam – be sure to review the lecture slides as well! You should start getting in the habit of showing your work and stating the assumptions you make in each problem. Problem 1: For the scenarios given below, circle the more important evolutionary force. N e = 4 , s = 0 . 04: drift selection N e = 4 , m = 0 . 6: drift migration m = 1 , s = 0 . 04: migration selection Problem 2: You study evolution by natural selection in guppies found in Trinidad. In one of your streams, there are two populations of guppies separated by a waterfall. In the population below the waterfall, adult guppies are often eaten by a cichlid fish. There are no natural predators above the waterfall. You want to know if predation on adults has caused the guppies to mature earlier. Pretend that age to maturity is controlled by a single gene with two alleles: A and a .You collect genotype data for your two populations ( above and below the waterfall) for two generations: Above the waterfall genotype: AA Aa aa generation 0: 4 3 3 generation 1: 6 3 1 Below the waterfall genotype: AA Aa aa generation 0: 8 11 11 generation 1: 16 8 6 (A) Is the population above the waterfall in generation 1 in HWE? (use a χ 2 test to check) First, calculate the expected genotype numbers: p = freq( A ) = 6 + 0 . 5(3) 10 = 0 . 75 q = freq( a ) = 1 - p = 0 . 25 expected # AA individuals = p 2 (total # individuals) = 0 . 75 2 (10) = 5 . 625 expected # Aa individuals = 2 pq (total # individuals) = 2(0 . 75)(0 . 25)(10) = 3 . 75 expected # aa individuals = q 2 (total # individuals) = 0 . 25 2 (10) = 0 . 625 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 FALL 2009 Then calculate the test statistic: χ 2 = X i (observed - expected) 2 expected = (6 - 5 . 625) 2 5 . 625 + (3 - 3 . 75) 2 3 . 75 + (1 - 0 . 625) 2 0 . 625 = 0 . 4 χ 2 < 3 . 841, the critical value for df = 1. Therefore, we CANNOT reject the null hypothesis that this population is in HWE at a significance level of p=0.05. (B) Can the observed change in allele frequencies in the population above the waterfall be explained by drift alone? Answer this question in two ways: by calculating binomial prob- abilities and by calculating the 95% confidence interval. We first need to calculate the allele frequencies in generation 0: p = freq( A ) = 4 + 0 . 5(3) 10 = 0 . 55 q = freq( a ) = 1 - p = 0 . 45 To answer this question by summing up the binomial probabilities of observing an allele frequency of equal to or more extreme than our data: we want to know the probability of observing 2(6) + 3 = 15 or more A alleles: n =# alleles sampled = 20 & p = allele frequency of parents = 0 . 55 Prob(at least 15 “ A ” in 20 alleles) = 20 X k =15 n k p k (1 - p ) n - k = 20 X k =15 20 k 0 . 55 k (0 . 45) 20 - k = 20 15 0 . 55 15 (0 . 45) 5 + 20 16 0 . 55 16 (0 . 45) 4 + ... + 20 20 0 . 55 20 (0 . 45) 0 = 0 . 0553 This probability is greater than 0.05, so we CANNOT reject our null hypothesis of drift.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern