Practice Problem set #7

1.  Suppose a population of plants shows five different phenotypes - flowers with two, three, four, five, and six spots.  The plants are present in the following ratio 1:3:4:2:1.  What is the mean spot number in the population?  What is the variance and standard deviation?

2.  In 1770 a pair of College of Charleston students founded a new nation on an island in the Ashley River.  (One of these students was a female, unusual for 1770 but quite fortunate for the new nation.)  After generations of inbreeding, today the mean height of folks living on the island is 64 inches, with a standard deviation of 3 inches.  If the mean height of normal (downtown) CofC students is 66 inches with a standard deviation of 4 inches, what is the brad-sense heritability of CofC student height?

3.  In a population of 100 individuals, 16% are homozygous for the recessive allele a.  What is the expected gene frequency of a, if the population is in Hardy-Weinberg equilibrium?

4.  A new test has been developed that allows us to identify Aa heterozygous individuals.  In the same population of 100 individuals described above, there are 20 heterozygotes.  What is the probability that this population is, in fact, in Hardy-Weinberg equilibrium?

5.  In fruit fly populations, chromosomal inversions can be counted and scored as though they were codominant alleles.  In one fly population, a geneticist found two inversions, "Arrowhead" and "Tahoe," as well as the Standard form.  He counted the following genotypes: 25 AA, 11 AT, 23 TT, 3 AS, 9 TS, 29 SS.  What are the frequencies of the three inversions?

6.  Does this fly population appear to be in Hardy-Weinberg equilibrium?

7.  Two alleles, A1 and A2, are present in a population at Hardy-Weinberg equilibrium.  The frequency of the A1A2 heterozygotes is 0.30.  What are the frequencies of A1 and A2?

8.  Mutations occur from allele A1 to allele A2 at a frequency of 3 x 10-4, while reverse mutations occur at  7 x 10-5.  Predict equilibrium frequencies, if no other forces are acting.

9.  Assume now that allele A1 mutates to A2 at 3 x 10-4, but there is no back mutation.  How many generations will it take to reduce the frequency of A1 from 0.5 to 0.1?

10.  A population of 1,000 butterflies has allele frequencies A1 = 0.6 and A2 = 0.4 in Hardy-Weinberg equilibrium.  One day, a strong wind blows in 40 butterflies, all homozygous A2A2.  What are the new allele frequencies?

11.  Banded is dominant to unbanded in a certain type of land snail.  In one population the frequency of the unbanded allele was qb = 0.30.  If birds tend to eat 40% more unbanded than banded snails, what will be the frequency of the unbanded allele next generation?

12.  How many generations will it take a recessive lethal to decrease from a frequency of 0.3 to 0.2?  From 0.2 to 0.1?

13.  Gill coloration is controlled by two alleles, A1 and A2.  For every 100 offspring produced by a given number of A1A1 bluegills, 200 offspring are produced by the same number of A1A2 greengills and 50 offspring are produced by the same number of A2A2 yellowgills.  Predict ultimate gene frequencies.

(1) mean = 3.9,  s2 = 1.3,  s = 1.14.  (2) H2 = 43.7%   (3) qa = 0.40.   (4) X2 = 21.5,  p<<0.01.   (5) pA = 0.32, qT = 0.33, rS = 0.35   (6) No,  X2 approx. = 88   (7) 0.82 & 0.18   (8) p1 = 0.19, q2 = 0.81   (9) 5,364 generations.   (10) p1 = 0.58, q2 = 0.42.   (11) qb = 0.274   (12) 2 gens, 5 gens.   (13) p1 = 0.60, q2 = 0.40.

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