Exercise using the Hudson animator
Download and open the Hudson from www.coalescent.dk. It is
developed by Anders M. Mikkelsen, Jotun
Hein and Mikkel Schierup as a tool for the visualization of the following
continuous time processes.
·
The basic coalescent and the
Coalescent with recombination
·
Coalescent with exponential
growth
·
Coalescent with migration
Please consult the manual before doing the
exercises, it can be found under help at the start page. It briefly
describes how to control the applet.
The basic Coalescent without
recombination
Choose coalescent with recombination
(we will set recombination to zero)
1
The basic coalescent. Choose n=5
sequences and rho=0 (no recombination). Press recalc
and the animation starts. The speed can be controlled with speed. Details
regarding each node can be seen in the small window at the right when moving
the mouse over the node.
a
What is the time to the first
coalescence event? Write it down.
b
What is the time to the most
recent common ancestor? Write it down.
c
Repeat a and
b 5 times (by pressing recalc). How does the time to
first coalescence and time to most recent common ancestor vary?
2
Try with 10 and 20 sequences.
What are the times to the first coalescence and the most recent common ancestor
in these cases? Write it down for 5 different runs.
Coalescent with recombination
The recombination rate is determined by rho=2Nc.
In the animation, recombination events are marked as blue nodes (in contrast to
the green nodes of coalescent events).
Look at a couple of simulations in more
detail. Study where in the sequence, recombination events occur
a
Can you find examples that
different part of the sequence have different most recent common ancestors
(marked in green) at different time points?.
b
Can you find any examples of
“trapped” non-ancestral material (coloured white)
between blocks of ancestral material?
c
Try to press the trees window pane. Here it is possible to study each of the
different trees over the sequence. How many different trees are there and how
does this relate to the number of recombination events? Try to find examples of
each of the following recombination types
·
Recombination changing the
topology of the tree
·
Recombination changing the
branch length but not the topology of the tree
·
Recombination that does not
change the tree
What is the
total number of each of the tree types during the 5 replicate runs? How does that
match with theory.
Coalescent with exponential growth
Now choose coalescent with exponential
growth. This is controlled with the parameter exp,
which is equal to Nb. This parameter measure how many times the present
population is larger than the population 2N (N=size of present
day population) ago. In studies of human mitochondria (there is no
recombination in mitochondria) all estimates suggest that exp>100.
6
Try to simulate n=10
sequences and different runs with exp=1, 10,
100, 1000
a
How does the shape of the
genealogical tree depend on the value of exp?
b
How can that be?
c
How would this altered shape be
visible in a set of sequences evolving on the tree? Would there be fewer or
more “singletons”? How would Tajima’s D be affected?
Hint: If you push trees the same
tree will appear without any crossing branches
Coalescent with migration
Now choose coalescent with migration It is only possible to simulate two populations, but the
number of individuals and the migration rates between the populations can be
freely chosen. M1 is the migration rate from population 1 to population
2. The separation between populations is marked with a dotted line and
migration events are shown as blue nodes.
a
How many migration events occur
in total? Note it down.
b
How many of these happen from
there are 10 until there are two sequences left?
c
How many migration events occur
during the time interval when there are only two ancestors left?
d
Repeat the animation with the
same parameters three times – how large is the variance?
a
How many migration events can
you infer must have happened?
b
How does this correspond with
the true number?
c
Repeat this exercise a couple
of times
a
How is the shape of the tree
affected (e.g. if M1=M2=0.1)?
b
How would this change of tree
shape be expected to be visible in a set of real sequences (would there be more
or fewer singletons?).