HWE Tutorial (October 2007) Mary Jo Zurbey PharmD Candidate 2008

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1 HWE Tutorial (October 2007) Mary Jo Zurbey PharmD Candidate 2008 Definition: The Hardy-Weinberg equation, which relates genotype and allele frequencies for a population, is as follows, where p = the frequency of the dominant allele and q = the frequency of the recessive allele: p 2 + 2pq + q 2 = 1 Allele and genotype frequencies for a population in Hardy-Weinberg Equilibrium (HWE) do not change from generation to generation. The Hardy-Weinberg equation can be used to predict if a population exists in HWE if the following conditions related to the gene of interest are met within the population (Holtzclaw): 1. Large breeding population 2. Random mating 3. No change in allelic frequency due to mutations 4. No immigration or emigration 5. No natural selection The chi-square (χ 2 ) test can be used to determine whether a population is in HWE. The following problem will help you practice this. Practice Problem: Given the observed results below, determine whether each racial group is in HWE. A/A A/G G/G Total African American Hispanic White Other Step 1: State the null and alternative hypothesis. H o : The population is in HWE, i.e. there is no difference in the observed (O) and expected (E) genotype frequencies for this population (O=E). H a : The population is not in HWE, i.e. (O E). Step 2: Calculate p for the African American population. There are 77 African American s with the A/A genotype, which represents 154 A alleles since each person has 2 alleles. There are 39 African American s with the A/G genotype, which represents 39 A alleles, since each of these 39 people has one A and one G allele. We have

2 genotype information for 125 African Americans, which represents 250 alleles. Therefore, the frequency of the dominant allele (p) in the African American population is (154+39)/250 = Step 3: Calculate q for the African American population. The sum of allelic frequencies for a population in HWE = 1, i.e. p + q = 1. Therefore, q = 1-p or q = = Or you can calculate q the same way you did above for p: There are 9 African Americans with the G/G genotype, which represents 18 G alleles. There are 39 African American s with the A/G genotype, which represents 39 G alleles. Therefore, the frequency of the recessive allele (q) in the African American population is (18+39)/250 = Step 4: Based on p and q you calculated above, determine the number of African Americans you expect to have each genotype if the population is in HWE. According to the Hardy-Weinberg equation, the expected frequency of individuals homozygous for the dominant allele A is p 2, the expected frequency of heterozygotes is 2pq and the expected frequency of individuals homozygous for the recessive allele is q 2. Multiply each value by the number of African Americans in our population (N=125) to determine the number of African Americans expected to have each genotype if the population is in HWE. p 2 *N = (0.772) 2 *125 = *p*q*N = 2*0.772*0.228*125 = q 2 *N = (0.228) 2 *125 = Step 5: Calculate χ 2. χ 2 = ((O-E) 2 )/E A/A p= A/G q= G/G Total 125 χ 2 = ((O-E) 2 )/E Step 6: Look up the critical value for χ 2 that you will use to determine if you will reject the null hypothesis. We used 3 parameters, i.e. p, q and N, to calculate the expected genotype frequencies. If we know 2 of these parameters, we can calculate the third. Therefore, we use 1 degree of freedom (DOF) when looking up χ 2 in the table. Choose α to be the customary For 1 DOF and α=0.05, χ 2 = Therefore, reject Ho if χ 2 (calculated above) Since <3.84, we do not reject Ho and conclude that the African American population is in HWE.

3 MORE PRACTICE: 1. Use the above data to complete the following table to determine if the Hispanic population is in HWE. Hispanics: A/A 110 p= A/G 115 q= G/G 30 Total 255 χ 2 = ((O-E) 2 )/E 2. Is the Hispanic population in HWE? How do you know? 3. Use the above data to complete the following table to determine if the White population is in HWE. Whites: A/A 174 p= A/G 285 q= G/G 133 Total 592 χ 2 = ((O-E) 2 )/E 4. Is the White population in HWE? How do you know? 5. Based on your calculated χ 2 you determine you should reject your null hypothesis, what is the most likely reason for the deviation from HWE? More HWE problems and tutorial: Note: the following website will calculate χ 2 for you:

4 REFERENCES Holtzclaw TK. "Population Genetics and Evolution." LabBench Pearson Education, Inc. Accessed online October 28, 2007 at <

5 ANSWERS 1. Hispanics: A/A p= A/G q= G/G Total 255 χ 2 = ((O-E) 2 )/E 0 2. The Hispanic population is in HWE because 0< Whites: A/A p= A/G q= G/G Total 592 χ 2 = ((O-E) 2 )/E The White population is in HWE because < The Hardy-Weinberg equation can be used to predict if a population exists in HWE if certain conditions related to the gene of interest are met within the population (see above). If the required conditions are satisfied, the observed deviation from HWE is likely do to laboratory error. Go back and check your work.