Genetics 371B, Autumn 2000 -- Week 11 Practice problems

Genetics 371B Practice problems--Autumn 2000 week 11

Lectures 35-37

1.	(a)	In humans, the inability to tolerate caffeine is an autosomal recessive trait (t), while the ability to tolerate caffeine is dominant (T). In a certain remote country, 84% of the people can tolerate caffeine. What are the frequencies of T and t in that population? Assume that the alleles are at Hardy-Weinberg frequencies.
	(b)	In a strange turn of events, a fringe group (whose slogan is "Starbucks Everywhere™") overthrows the government and decrees that henceforth, caffeine-intolerants will not be allowed to have children. What will be the frequencies of T and t after one generation under this hyperactive regime?
	(c)	In the U.S., the frequency of allele T is 0.8. If T mutates to t at a rate of 2 x 10^-6 per generation, what will be the frequency of t after 10,000 generations? Assume that t does not mutate to T, and that the population is otherwise at Hardy-Weinberg conditions.
	(d)	How large would the U.S. population have to be, for mutation (T --> t) to prevent loss of allele t due to random genetic drift?

2.	A population is entirely homozygous for allele D. However, D can mutate to d at a rate of 0.00004 per generation, while d mutates to D at a rate of 0.00001 per generation. The population is otherwise at Hardy-Weinberg conditions.
	(a)	Given infinite time, which allele do you think will eventually predominate in the population? Why?
	(b)	What is the change in the frequency of D per generation? How about the change in the frequency of d? (Remember that for each part, you have to take into consideration both the forward mutation and the back mutation.)
	(c)	What will the two allele frequencies be when they reach an equilibrium (increase in frequency of d by forward mutation matched by decrease due to back mutation)?

3.	The frequency of a recessive allele in the population is 0.2. Assuming that the dominant and recessive alleles are at Hardy-Weinberg frequencies, predict the probabilities of each of the following matings:
	(a)	homozygous dominant x homozygous dominant
	(b)	heterozygous x homozygous recessive
	(c)	heterozygous x heterozygous

4.	From Final Exam, 1997 In a Caucasian population of 9000 individuals, the frequency of the allele for male pattern baldness is 0.3.
	(a)	What are the expected genotypes and their frequencies if the population is in Hardy-Weinberg equilibrium?
	(b)	The baldness allele is recessive in females but dominant in males. What are the expected phenotype frequencies in males and females?
	(c)	A group of 1000 new individuals joins the population. If p = 0.1 in the incoming group, what will be the frequency of heterozygotes in the population after one generation? (Assume random mating.)

From Final Exam, 1998

Charlene is a heterozygous carrier of cystic fibrosis, a recessive autosomal disease. What is the chance that her child will likewise be a heterozygous carrier, if we do not know the father's genotype? Assume that the father is chosen at random from the population (at least with regard to this locus), and that the allele frequency of cystic fibrosis in the population is p_c. Show your work.

[Hint: There are two ways of arriving at the correct answer -- an easy way and a more roundabout way.]

6.	Genetic testing reveals that in a small population, the number of individuals homozygous normal (AA) for PKU is 660, the number of heterozygotes (Aa) is 280, and the number of homozygous recessive (aa) individuals is 60.
	(a)	What are the frequencies of the wild type and the PKU allele in this population?
	(b)	Given these allele frequenceis, what are the expected number of individuals of each class (i.e., AA, Aa, and aa) in this population, assuming Hardy-Weinberg conditions?
	(c)	Using the chi-squared test, determine whether these data fit the Hardy-Weinberg model. Why is it appropriate to use df = 1 for this test?

7.	Assume that in a certain population, 99% of the individuals show the dominant phenotype (T) for a certain trait, while 1% show the recessive phenotype (t). The fitness of the various genotypes are as follows: `w_TT = 1.0` `w_Tt = 0.5` `w_tt = 1.0`
	(a)	If you were to assume that the Hardy-Weinberg model applied here, what would be the frequencies of genotypes TT, Tt, and tt in this population?
	(b)	Why would it not be suitable to apply the Hardy-Weinberg model here?
	(c)	What would the frequency of alleles T and t be in the next generation, assuming that the Hardy-Weinberg model applies EXCEPT for the difference stated in the question?

[Warning: This one requires actual algebra] [Horrors!]

You choose to examine the aesthetic appeal of the common Seattle slug. Aesthetic appeal in the slug is determined by a single autosomal locus "Slimy", at which there are three alleles. The alleles are Icky (Si), Yucky (Sy), and Gross (Sg). Icky is dominant over both yucky and gross. Yucky is dominant over gross.

After a long walk through the rain, you observe that the phenotypes of the slugs occur in the following proportions: 50% are icky, 30% are yucky, and 20% are gross. (Don't worry about statistical error in the measurement of these numbers.) Assuming that the alleles are at Hardy-Weinberg proportions, What are the allele frequencies p(Si), p(Sy), and p(Sg)? Which slugs would you rather step on, and why?

9.	Assume that the ability to ask for directions is determined by a single X-linked locus, at which there are two possible alleles. The alleles are the dominant D, which gives the ability to ask for directions, and the recessive d, which does not.
	(a)	We begin our observation of the population at generation 0. At generation 0, the frequency of the allele D in females = p_(0f) = 0.9, and the frequency of the allele D allele in males = p_(0m) = 0.1. Assuming random mating, what will be the frequency of allele D in males and females in the next generation? -- i.e., p_(1m) and p_(1f)? How about p_(2m) and p_(2f)? p_(3m) and p_(3f)? p_(4m) and p_(4f)? Plot gene frequency vs. generation number for p_(f) and p_(m). What trend do you see? [Hint: If the algebra gets difficult here, you've made a mistake.]
	(b)	Challenge question: If we were to continue the graph for an infinite number of generations, what would be the ultimate values of p_(f) and p_(m)? (This is more difficult than it might sound. To solve it, you'll need to write a small computer program, solve a differential equation, or have some very good intuition.)