evolutionary genetics: part 5 coalescent simulations · 2013-01-07 · population genetics: 4...
TRANSCRIPT
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Evolutionary Genetics: Part 5
Coalescent simulations
S. peruvianum
S. chilense
Winter Semester 2012-2013
Prof Aurélien TellierFG Populationsgenetik
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Color code
Color code:
Red = Important result or definition
Purple: exercise to do
Green: some bits of maths
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Population genetics: 4 evolutionary forces
random genomic processes
(mutation, duplication, recombination, gene conversion)
natural
selection
random demographic
process (drift)
random spatial
process (migration)
molecular diversity
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Simulating sequence data
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How to simulate?
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How to simulate?
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How to simulate?
Algorithm to generate sequence data
� Put k+n where n is the sample size
� Choose an exponential variable with parameter k(k-1+θ)/2
� With probability:
� (k-1)/(k-1+θ) the event is a coalescent event
� And with probability θ/(k-1+θ) the event is a mutation
� If a coalescent event occurs choose a pair of lineages to coalesce, k becomes then
k-1
� If a mutation event occurs, choose a lineage to mutate, k is unchanged
� Repeat all this until k=1
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Simulations 1
What is θ ?????
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Simulations 1
Do you see the same numbers? WHY?
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Simulations 1
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Simulations 1
pdf(file=‘‘constant_tree.pdf‘‘)
Dev.off()
4 –t 5 –T > treefile.tre
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Simulations 1: neutral and constant size
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Simulations 2: neutral and expansion
t1 = 0.5 = time at which the expansion starts in the past
x = 0.1 = the population in the past is 0.1*N0
Present population size = N0
Ancestral population size = x*N0
Time t1 of expansionIn 4N0 generations
Do you see a problem ??? What is N0 ???
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Simulations 2: neutral and expansion
-eN 0.5 0.1
0.5 = time at which the expansion starts in the past
0.1 = the population in the past is 0.1*N0
-eN 0.05 0.1 – T > expansion.tre
4
4
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Simulations 2: trees of expansion
pdf(file=‘‘expansion-tree.pdf‘‘)
Dev.off()
expansion.tre
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Simulations 3: crash or bottleneck?
For a crash:
./ms 10 4 –t 5 -eN 0.5 5
Present population size = N0
Ancestral population size = x*N0
Time t1 of expansionIn 4N0 generations
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Simulations 3: crash or bottleneck?
For a bottleneck:
./ms 10 4 –t 5 -eN 0.5 0.25 -eN 0.75 2
Present population size = N0
Ancestral population size = x2*N0
Time t1
Time t2
Bottleneck population size = x1*N0
t1 x1t2 x2
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Simulations 2: trees of expansion
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Exercise
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Summarize the ms output
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Exercise
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Exercise
Then save the output in a file:
> test1.out
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Exercise
Now using R
Load the file:
test <- read.table(“test1.out“,header=FALSE)
Then draw graphs:
pdf(file=‘‘summary_neutral_constant.pdf‘‘)
hist(test[,2],main=“Theta_Pi Tajima“)
hist(test[,4],main=“Theta_Watterson“)
hist(test[,6],main=“Tajima D“)
Dev.off()
Then do the same for an expansion, decline or bottleneck
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Exercise
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Final simulations
� Using msmsplay on your computer
� Command line is similar
� Can see directly the site Frequency-Spectrum
� Can you compare the site frequency spectrum with values of Tajima‘s D ?
� Lets simulate neutral model, expansion, decline
� What differences we see?
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Some data analysis
� Use datasets:
� Use DnaSP to calculate usual statistics:
� Diversity = θW , θπ
� Site frequency spectrum
� Tajima‘s D
� What do you conclude on these various data?
� Do you have an idea of the past demography of these populations?
� Why do you need several independent loci ?