Simulating trees

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Simulating trees
             

• a tricky task !?
• Tanja Gernhard, Klaas Hartmann

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Why simulations?

• How do typical trees look like under a specific
  model of speciation?
• expected Colless value?
• expected gamma value, LTT plot?
• p-values for statistical testing?

Even simple models hard to analyze analytically!
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Aspects of simulations

• Tree distribution ill-defined (expected age of
  the tree is infinite)
• Condition on age of tree (simulations
  straightforward)
• Condition on number of species in the tree
  (assuming a uniform prior for the age of the
  tree)

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Standard method

• Simulate until n species are obtained.
• Stop at following speciation or extinction event.

Example for n5 species

• Later periods with n species disregarded!
• Pendant edges are too long!
• Each simulation makes same contribution!

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General evolutionary model

• Simulate a tree, t, until n species or
  extinction is reached
• Find the expected number of trees to sample from
  t
• For each sample required
• Randomly choose an interval, i, according to the
  weights
• Choose the pendant edge length uniformly at
  random from (0, )
• Repeat from step 1 until the required number of
  samples has been obtained

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Special models

• Yule model Pure birth process. Individuals
  evolve independently. Speciation occurs at a
  constant rate.
• Constant rate birth-death model Add constant
  death rate to the Yule model.
• Coalescent Time between successive coalescent
  events is exponentially distributed

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Memoryless pure birth models
Time between sn and sn1 does not depend on the
current tree (e.g. Yule model, Coalescent).
Correct simple approach Simulate until
Determine
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Determining .
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Yule model / Coalescent
Simulating until the (n1)-th speciation event
yields the desired results!
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Birth-death model
reconstructed tree
point process
tor
s3
s1
s2
s4
1
2
3
4
5
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Available Program
Tool TreeSample implemented in Pearl by Klaas
Hartmann. Available as a stand-alone application
or as a Pearl script.
Demonstration
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Dankeschön
Dennis Wong
Mike Steel
Erick Matsen
Klaas Hartmann