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, A^{1} and A^{2}, are present in a
population at Hardy-Weinberg equilibrium. The frequency of the A^{1}A^{2}
heterozygotes is 0.30. What are the frequencies of A^{1} and
A^{2}?

8. Mutations occur from allele A^{1} to allele A^{2}
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 A^{1} mutates to A^{2 }at
3 x 10^{-4}, but there is no back mutation. How many generations
will it take to reduce the frequency of A^{1} from 0.5 to 0.1?

10. A population of 1,000 butterflies has allele frequencies A^{1}
= 0.6 and A^{2} = 0.4 in Hardy-Weinberg equilibrium. One day,
a strong wind blows in 40 butterflies, all homozygous A^{2}A^{2}.
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 q_{b} =
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, A^{1} and
A^{2}. For every 100 offspring produced by a given number of
A^{1}A^{1} bluegills, 200 offspring are produced by the same
number of A^{1}A^{2} greengills and 50 offspring are produced
by the same number of A^{2}A^{2} yellowgills. Predict
ultimate gene frequencies.

Answers:

(1) mean = 3.9, s^{2} = 1.3, s = 1.14. (2) H^{2}
= 43.7% (3) q_{a} = 0.40. (4) X^{2}
= 21.5, p<<0.01. (5) p_{A} = 0.32, q_{T}
= 0.33, r_{S} = 0.35 (6) No, X^{2} approx.
= 88 (7) 0.82 & 0.18 (8) p_{1} = 0.19,
q_{2} = 0.81 (9) 5,364 generations. (10)
p_{1} = 0.58, q_{2} = 0.42. (11) q_{b}
= 0.274 (12) 2 gens, 5 gens. (13) p_{1 }=
0.60, q_{2} = 0.40.

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