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JE 201
Aug-Dec 2006
Problem Set: Unit 1
Due on Monday, 11-9-2006
1. The ABO blood group system in humans consists of three alleles – iA, iB and iO - and,
consequently, six possible genotypes at this locus - iAiA, iAiB, iAiO, iBiB, iBiO, and iOiO. The
dominance relations between these alleles are that iA and iB are codominant among
themselves, and both are dominant to iO. Thus, an individual with phenotype (blood
group) A can be genotypically iAiA or iAiO, one with phenotype B can be iBiB or iBiO,
whereas individuals with AB and O phenotypes are genotypically iAiB and iOiO,
respectively. In a sample of 1000 individuals from a population of humans screened for
ABO blood types, 400 were A, 240 AB, 270 B and 90 O. Estimate the frequencies of the
three alleles.
2. Can two bi-allelic loci that are in linkage disequilibrium, be in Hardy-Weinberg
equilibrium individually. Can two bi-allelic loci that are not in Hardy-Weinberg
equilibrium individually be in linkage equilibrium. Argue your case with example(s).
3. The frequency of white-eyed flies (X-linked recessive) in males of a Drosophila
population is 0.08. Assuming equilibrium, what are the expected frequencies of the three
genotypes among females? What is the expected proportion of white-eyed progeny
among the male progeny of red-eyed (wild type) females in this population, assuming
mating to be random with regard to eye colour. In general, will you expect to see more
white eyed males or females in the population.
4. Loci A and B are linked with 20% recombination between them. An initial population
is composed of AB/AB, AB/ab, and ab/ab individuals in a ratio of 1:2:1. The population
then breeds at random.
a. What are the frequencies of the four kinds of chromosomes in the next generation?
Keep in mind that the book-keeping of chromosomal (or haplotype) frequencies is done at
the gametic phase.
b. What is the frequency of the AB/aB genotype in the next generation?
c. Estimate the linkage disequilibrium constants Dij in the initial generation.
d. What are the chromosome and genotypic frequencies at equilibrium?
5. Two homozygous strains aabb and AABB are crossed. The A and B loci are on
separate chromosomes. Show that these loci are in linkage disequilibrium in the parental
generation, and in linkage equilibrium in the F2 generation. Why is there not a gradual
approach to linkage equilibrium in this population, as predicted by theory? Why does this
not, however, contradict the general theory?
6. Can loci that are unlinked be in linkage disequilibium? Argue your case.
7. Imagine a population of a diploid sexual species that shows an unusual phenomenon of
gene conversion in which, in every zygote, the paternally inherited allele gets converted
to be identical to the maternally inherited allele. In an ideal population of such a species
how will the allele frequencies and genotypic frequencies for a single biallelic autosomal
locus behave over generations.
8. Imagine a triploid species (3n = 3) in which males produce haploid gametes in a
manner such that each of the three homologous chromosomes has equal probability of
entering a gamete, and females produce diploid gametes in a manner such that each
possible pair of homologous chromosomes has equal probability of entering a gamete.
Imagine a bi-allelic locus in an ideal population of this species, with arbitrary genotypic
frequencies. Derive the relationships between allele frequencies and genotypic
frequencies in this system, and then derive the genotypic frequencies in the next
generation. Comment on your results.