EEB 135/235: POPULATION GENETICS - HOMEWORK 7
Note: For full credit you must show your work. (1) (10 points) Describe the differences between the neutral theory of evolution and the nearly neutral
theory of evolution.
(2) (10 points) (a) Explain why under the neutral model, the rate of substitution is independent of the
population size. (b) If the rate of substitutions is 10 -5 per site per generation, what is the expected time
between substitutions?
(3) (20 points, From Nielsen & Slatkin) Suppose that a mutation rate is 2 x 10 -9 per site per year.
(a) What is the rate of substitution of deleterious mutations per million years if the selection
coefficient against them is 0.001 in a population with 10,000, 1,000, or 100 individuals?
(b) What fraction of the neutral rate (2 x 10 -9 per site per year) are the substitution rates that you
computed from (a)?
(4) (15 points) Because of redundancy in the genetic code, some changes to sequence do not lead to
changes in amino acids. Such changes are called "synonymous" changes, and others that do change the
amino acid are called "non-synonymous." If one aligns two genes between species, one can look to see
whether differences are synonymous or nonsynonymous. Let’s assume that synonymous changes are
completely neutral, while nonsynonymous changes are not.
(a) Suppose that at all synonymous sites, the observed pattern of differences leads to an estimated
rate of substitution of 2 x 10-8 per site per generation. What would you estimate the total mutation
rate per site to be?
(b) Suppose that at non-synonymous sites the estimate of the rate of substitution is 5 x 10-9 per site
per generation. Using your answer from (a), what is your estimate of the fraction of neutral
mutations at non-synonymous sites?
(c) Suppose instead that at non-synonymous sites the estimate of the rate of substitution is 5 x 10-8
per site per generation. What might explain the non-synonymous to synonymous rate ratio
observed?
(5) (15 points) When comparing the amino acid sequence of the α-hemoglobin molecule between dogs and
kangaroos, you find that 13.5% of the sites have different amino acids. Assume that the α-hemoglobin
molecule has been undergoing amino acid replacement at a rate of 10-9 amino acid replacements per amino
acid site per year. Estimate the divergence time between kangaroo and dog. Is this estimate the split time
between the populations or the coalescent time of the lineages? Please explain.
(6) (25 pts) Fay et al. (2002) surveyed polymorphism at 45 genes in D. melanogaster and in D. simulans.
The segregating sites are classified as either synonymous or nonsynonymous. The sequences of these genes
in the two Drosophila species were compared to assess the number of substitutions.
The results are summarized in the following McDonald-Kreitman table. Assume that the number of
synonymous sites of these 45 genes is LS = 8,000 and the number of nonsynonymous sites is LNS = 20,000. Synonymous
Nonsynonymous Polymorphisms
224
65 Substitutions
950
598 (a) Based on the ratio of the observed number of non-synonymous and synonymous substitutions
alone, and assuming synonymous substitutions are neutral, compute KA/KS.
(b) Using the estimate of KA/KS from (a), is there evidence this gene may have been under positive
selection (i.e. is KA/KS > 1 )?
(c) Using all of the data (both substitutions and polymorphism), does the gene appear to be
evolving neutrally? To assess this, compute the neutrality index (NI).
(d) Is the NI index consistent with positive selection? If so, estimate α, the fraction of
nonsynonymous substitutions that are due to adaptive substitutions.
(e) Is it possible for KA/KS as estimated in parts (a and b), to be less than 1 (arguing for selective
constraint on the gene), and have evidence for positive selection based on NI (parts c and d)?
Why or why not?
(7) (10 pts, graduate/Extra credit): Based on the paper by Justin Fay (Weighing the evidence for adaptation
at the molecular level; Trends in Genetics; http://www.genetics.wustl.edu/jflab/fay11_inpress.pdf), list and
briefly explain two possible reasons why some species show evidence for abundant positive selection using
the McDonald-Kreitman test and why other species show little such evidence.

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