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Ch10 Problems and Topics

# Ch10 Problems and Topics - Problems and Discussion Topics...

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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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Ch10 Problems and Topics - Problems and Discussion Topics...

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