EEB 135/235: POPULATION GENETICS - HOMEWORK 5
Note: For full credit you must show your work. Use at least three significant digits.
Homework with multiple sheets must be stapled!
(1) (20 pts) In the arid southwest US, there are a number of populations that are found isolated on “sky-islands" - the moist summits of high
altitude mountains. These species cannot survive at lower altitudes where the climate is dryer and hotter. Their distributions may once have been
connected but as the climate warmed and dried as the last ice age ended (about 18,000 years ago), the populations moved upwards in altitude and
became isolated on the summits. A researcher studying a tree species isolated on the sky-islands measures HS = 0.15 and HT = 0.2 across the
populations. (a) Consider a pair of populations, each of size N = 5000 diploid individuals that split from a common ancestral population t
generations ago. Assume there was no subsequent gene-flow between the populations after they split from each other. What equation
describes the relationship between FST and the population split time? (b) Use the equation in (a) to estimate the split time of the two
populations, assuming that FST=0.25. (c) If there had been gene flow between the two populations after they had split, do you think that
your estimate of the split time computed in part (b) is older or younger than the true split time? Why? (d) Can the investigator use FST
alone to distinguish between the migration-drift equilibrium vs. complete isolation models described above? Explain. (2) (15 pts) (a) Imagine that two sub populations split from a common ancestral population 8,000 generations ago, with no subsequent
migration between them. Assume that all populations (population 1, population 2, and the ancestral population) each have a size of
N=2,000 diploid individuals. If you sample one chromosome from each of the two populations, what is the average time to the most recent
common ancestor of these two chromosomes? (b) Follow the same setup as in part (a). If you sample two chromosomes from the same
population, what is the average time to the most recent common ancestor of these two chromosomes? (c) What is the expected value of
FST under this model? (3) (20 points) If the fitnesses of AA, Aa, and aa are 1.0, 0.75, 0.6, and p0 = 0.45, calculate p1, p2, and p3. In other words, compute the
frequency of the A allele after 1, 2, and 3 generations of selection. (4) (20 points) A C to T mutation near the gene encoding the lactase enzyme (the gene is called LCT) allows persistence of the lactase enzyme
into adulthood. Individuals possessing this mutation are lactose tolerant because they can digest dairy products as adults. It is thought that the
lactase persistence allele is under positive selection throughout Europe as agriculture became widespread. It has been estimated that the lactase
allele confers a fitness advantage of 3% in the homozygous state. In other words, individuals with the TT genotype will have a 3% higher fitness
than individuals who carry the CC genotype. Assume the T allele has a frequency of 10% in the population. (a-c) Calculate the frequency of the
T allele in the population after 1 generation of selection assuming: (a) The T allele is codominant (b) The T allele is recessive (c) The T
allele is dominant (d) Provide the dominance coefficient (h) for the T allele under each of the 3 scenarios described above. (e) What is the
equilibrium frequency of the T allele, assuming selection is the only evolutionary force changing allele frequencies. (5) (10 points) A locus with two alleles, B and b, affects the viability of seeds of a plant population. Onefifth of the BB seeds germinate and
produce adult plants; 1/6 of the Bb seeds germinate and produce adult plants; and 1/10 of the bb seeds germinate and produce adult plants.
Fertility does not depend on the genotype at the B/b locus. If the frequency of B is ¼ in one generation, and the genotypes in that population
of seeds are in Hardy-Weinberg equilibrium, what will be the frequencies of the B and b alleles in the seeds of the next generation? (6) (15 points) Imagine that allele a is lethal in the homozygous state (i.e. s=1). Now, assume that this allele is at a frequency of 1.1% in the
population. After one generation of natural selection, the allele decreases in frequency to 1% in the population. Use these data to estimate h.
Hint: you should assume that q and qh are small compared to 1. This will allow you to ignore them, sometimes. Assume natural selection is the
only evolutionary force acting here. (7) (Extra credit/graduate: 10 pts) Suppose an island on the Gulf Coast of Florida, where the sand is light, is colonized by a population of
Peromyscus polionotus that is fixed for the dark colored allele at MC1R. Further assume that this population is of size 10,000. Imagine an
individual who is heterozygous for the light allele moves into the population. This individual then mates with one of the dark colored individuals.
How many generations will be required for the light colored allele to reach frequency 90% in the population? Assume selection is the only
force changing allele frequencies, and that s=0.2 and h=0.5. Credit to Slatkin and Nielsen as well as Hartl and Clark for several questions.

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