Problems and Discussion Topics with Sample Answers
by Joseph Lachance and Paul Bourdeau
to accompany
Evolution,
Second Edition
Chapter 10: Genetic Drift: Evolution at Random
1. For a diploid species, assume one set of 100 demes, each with a constant size of 50
individuals, and another set of 100 demes, each with 100 individuals. (a) If in each
deme the frequencies of neutral alleles
A
1
and
A
2
are 0.4 and 0.6 respectively, what
fraction of demes in each set is likely to become fixed for allele
A
1
versus
A
2
? (b)
Assume that a neutral mutation arises in each deme. Calculate the probability that
it will become fixed in a population of each size. In what
number
of demes
(approximately) do you expect it to become fixed? (c) If a fixation occurs, how many
generations do you expect it to take?
Answer:
(a) In both sets of demes, 40% of the demes are expected to fix for allele
A
1
and 60% of
demes are expected to fix for allele
A
2
.
(b) The probability of fixation of a neutral mutation in a deme of 50 diploid individiuals
is 1%, and the probabilty of fixation in a deme of 100 individuals is 0.5%. Note that this
calculation takes into account that they are diploid individuals (i.e., there are 100 gene
copies in a deme of 50 individuals, each of which has an equal probability of fixation). In
both cases we have 100 different demes. I would expect the mutation to be fixed in 1 of
100 of the smaller (
N
= 50) demes, and fixed in 0 or 1 of the 100 demes in the larger
population size (
N
= 100) case.
(c) Fixation times by genetic drift are relatively slow. The average time to fixation is
equal to 4
N
. This means that fixation would take ~200 generations on average if deme
size is 50 individuals, and ~400 generations on average if deme size is 100 individuals.
Note that the variance in fixation times can also be quite large (actual fixation times can
vary quite a good deal from these expectations).
2. Assuming that the average rate of neutral mutation is 10
–9
per base pair per
gamete, how many generations would it take, on average, for 20 base pair
substitutions to be fixed in a gene with 2000 base pairs? Suppose that the number of
base pair differences in this gene between species A and B is 92, between A and C is
49, and between B and C is 91. Assuming that no repeated replacements have
occurred at any site in any lineage, draw the phylogenetic tree, estimate the number
of fixations that have occurred along each branch, and estimate the number of
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 Spring '10
 politz
 Genetics, Evolution, Population Genetics, Mutation

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