2) As an anthropologist you discover a tiny, remote set of villages in Nepal whose inhabitants are practice polyandry (a marriage system in which a female has multiple husbands). Each breeding woman has three husbands, and mating outside of marriage is strictly prohibited. Given a total population size for all villages of 200 males and 50 females (assuming that all husbands are of reproductive age and that these populations meet all other Hardy-Weinberg assumptions), what is the effective population size of this polyandrous population?

3) Here is a fun non-human problem dealing with sociobiology. In a haplodiploid system, unfertilized eggs develop into males and fertilized eggs develop into females. This situation is found in most social insects. What is the coefficient of kinship between a mother and her daughters in a haplodiploid system? Between sisters? Between brothers and sisters? (Assume all daughters have the same father). The workers in an ant colony or bee hive are all female. Why should these females give up the chance to raise daughters for a chance to raise sisters? (Hint: the problem set-up is similar to an X-linked trait in humans).

4) You begin a genetic survey of four villages in Rwanda that are arranged around the base of a large volcano, each with an effective population size of 100 individuals. Until your arrival, these villages had been isolated. However, due to a need for economic and social ties to their neighbors, the villages begin to exchange mates. You observe that each village derives mates from adjacent villages, and that all of the villages practice an ambilocal system of post-marital residence (married couple can live with either the husband or wife's group), with 10% of individuals migrating out of each village. An occasional trader from the capitol city visits the village once every decade, so that the total long-distance migration rate for each village is 0.001.

From your survey data, you find that the frequency of a particular allele (at a diallelic locus) of the initial generation is:

Freq (T):  .40    .20   .10   .90

What does the migration matrix for these village look like? Using the migration matrix and the matrix of allele frequencies, what will the frequency of the T allele be in each village after three generations of ambilocal post-marital residence?

5) After three generations (60 years) of peaceful mate exchange among these villages, a European nation sets up a military base on the top of the volcano. The frequency of the T allele among the Europeans is 0.01, and because of the base's location, admixture is equally likely with any of the four villages. After 5 generations of admixture, the frequency of the T allele among the villages is 0.29 (Hint: the initial frequency of the A allele among villages can be estimated from the average allele frequency obtained in the solution to Question 4). Given these data, what is the estimated migration rate? What would your estimate of migration rate be if there had been 10 generations of admixture?

6) A protein polymorphism in a population of humans is know to be caused by a single locus with two alleles, S and F, resulting in three distinct phenotypes corresponding to the genotypes SS, SF, and FF. A population was screened with the following results: 2875 SS's, 4250 SF's, and 2875 FF's. Test the hypothesis that the population is in Hardy-Weinberg.

It was then noticed that 3750 of the people were nostril flarers, and 6250 were non-flarers. Among flarers, 234 were SS, 1406 were SF, and 2110 were FF. Among the non-flarers, 2641 were SS, 2844 were SF, and 765 were FF. Dividing the population by nostril-flaring ability, are the resulting subpopulations in Hardy-Weinberg equilibrium? Are the gene pools of the resulting subpopuations identical with respect to the S/F protein locus? What is going on here?

7) Now suspend disbelief regarding the genetic origin of nostril flaring.  Some of the flarers and non-flarers also differ at an isozyme locus, such that all individuals from one group have the genotype SN/SN (where S is a "slow" electrophoretic allele and N is the allele allowing individuals to flare both nostrils) and individuals from the other group are all Fn/Fn (F being the "fast" allele and n being the allele preventing flaring of nostrils). The two groups are combined in a 50:50 mixture. Assuming the loci are autosomal and linked with r = 0.25, calculate the genotype frequencies and the linkage disequilibrium for the offspring of the mixed population, and the offspring of the offspring, assuming random mating each generation.

Repeat the calculations assuming 100% positive Assortative mating for nostril flaring. Since the S/F electrophoretic locus causes no deviation per se from random mating, will it be in Hardy-Weinberg equilibrium in any of these generations?

8) Finally, repeat the above calculations assuming 100% negative Assortative mating for nostril flaring, whenever there is a phenotypic choice (that is, a person will always mate with someone with a different nostril-flaring ability, as long as such persons are still available in the population. However, if there is no choice they will mate with like-phenotypes). Assume that the N/n heterozygote flares only the left nostril. Once again, . since the S/F electrophoretic locus causes no deviation per se from random mating, will it be in Hardy-Weinberg equilibrium in any of these generations?