Biostatistics 666
Problem Set 3
Due February 8, 2006
Modeling Events in the Coalescent
1.
Consider the genealogy of a set of three sequences from a population of N = 2500
diploid individuals. Assume that the recombination rate per sequence per
generation is
r
= 10
-5
and the mutation rate is μ = 10
-5
per sequence per
generation.
When we move backwards in time by one generation, what is the probability of…
a)
… a coalescence event?
b)
… a mutation occurring?
c)
… a recombination event occuring?
d)
… one of these three events occuring?
In addition, calculate the following quantities …
e)
Number of generations do you expect to pass before a), b) or c) occurs?
f)
When one of these events occurs, what is the probability that it is a
recombination?
Finally, …
g)
Assume that the following events occur in order as we trace the ancestry of
the three sequences: mutation (event closest to the present), coalescence,
recombination, mutation, coalescence, coalescence (most distant event).

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