EEB 135/235: POPULATION GENETICS - HOMEWORK 1 Note: For full credit you must show your work. (1) A lottery is held to award tickets to this weekend's basketball games. The probability of winning a ticket to Friday night's game is pF. For Saturday night's game, the probability is pS. Assuming the contest for each night's tickets are run independently, what is the probability that a single student wins: (a) both tickets (b) a Saturday night ticket but not a Friday night ticket (c) just one ticket (d) at least one ticket (e) Rewrite your answers for (a-d) for the case where pS = pF = p, and in each case, express your result in terms of p. (Problem from John Novembre) (2) Assuming Hardy-Weinberg proportions hold for a locus that has an allele A at frequency p and an allele a at frequency (1 - p) . Graph the frequency of AA homozygotes, Aa heterozygotes, and aa homozygotes as a function of the allele frequency p. At what allele frequency is the frequency of heterozygotes maximized? (Problem from John Gillespie) (3) The table below shows the number of individuals affected, per million individuals, for each of several autosomal recessive traits. Assuming Hardy Weinberg proportions in the population, what is the expected frequency of individuals who are heterozygous for each of the recessive alleles? (Problem from Hartl and Clark) Trait A B C D E Number of affected individuals per million individuals 2786 658 287 160 102 (4) A sample of poached elephant ivory is found. DNA is isolated from the sample and genotyped at a single locus, and the genotype is determined to be Aa . In elephants from Addo National Park in South Africa, the frequency of the A allele is 0.88 and for the a allele, the frequency is 0.12. In Tembe National Park, the frequency of the A allele is 0.55 and for the a allele it is 0.45. (a) Calculate the probability of the ivory sample's genotype if it was sampled from the Addo Park population; (b) Calculate the probability of the ivory sample's genotype if it was sampled from the Tembe National Park population. (c) Of these 2 populations, which population does the genotype data suggest the sample more likely to have come from? (d) [Extra/Graduate] In 100 words or less, what are some other factors you might consider before accusing one park or the other of not controlling poaching on their land? (Problem from John Novembre) (5) The beta chain of the hemoglobin protein contains a SNP that gives rise to sickle cell anemia when present in the homozygous state (HbS/HbS). A sample of individuals from Lagos, Nigeria were sampled and genotyped at this variant (Taiwo et al. 2011). The observed genotypes were found to be 366 HbA/HbA [this is the non-sickle-cell 2 genotype], 123 HbA/HbS, 12 HbS/HbS [this is the sickle-cell genotype]. (a) Calculate the -test statistic for Hardy-Weinberg proportions, the degrees of freedom, and its associated p-value. (b) Can we reject the null hypothesis that the population is in HWE at this locus? (c) [Extra credit/Graduate] It has been hypothesized that the HbS allele has been maintained in the population by balancing selection (we'll talk about what this means later in the course). Individuals who are HbA/HbS are more resistant to malaria and only have a slight sickle-cell effect. Given that the locus is under natural selection, are you surprised by the results of the HWE test? Give an explanation for this result. (6) Cystic fibrosis is a severe and often fatal disease. It is caused by a homozygous recessive mutation. The frequency of the disease in the population is approximately 0.0006. What is the frequency of the cystic fibrosis allele? What is the frequency of the heterozygous genotype in the population? (Problem from Halliburton). (7) A forensic scientist analyzes a bloodstain at a crime scene. She types 2 microsatellite (STR) markers and finds that the bloodstain has a genotype 15,15 at D3S1358 and genotype 11,12 at D13S317. (a) Assuming that D3S1358 is in HWE, what is the frequency of the 15,15 genotype in the population? (b) Assuming D13S317 is in HWE, what is the frequency of the 11,12 genotype in the population? Use the data contained in Table 2.3 of the Hamilton text. (c) List 3 assumptions that have gone into this calculation. (d) What is probability of selecting a random person from the population that would carry the 15,15 genotype at D3S1358 and the 11,12 genotype at D13S317? You may assume that the two markers are independent. (8) [Extra/Graduate] A small fraction of loci in the genome do not have perfect Mendelian segregation. They undergo meiotic drive, such that when a heterozygote produces gametes, they are not in the expected 50/50 ratio. Suppose a population at present has genotype frequencies of 0.64 AA, 0.32 Aa, and 0.04 aa. Suppose the locus under consideration has meiotic drive such that Aa heterozygotes produce 0.3 A gametes and 0.7 a gametes. (a) What will the change in allele frequency be from the present generation to the next? (b) Assuming random mating, what will the genotype frequencies be in the next generation? (c) What are the long-term consequences of meiotic drive on variation at this locus? (Problem from John Novembre)