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Simulating trees…. … a tricky task !? Tanja Gernhard, Klaas Hartmann . 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?.

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simulating trees

Simulating trees…

… a tricky task !?

Tanja Gernhard, Klaas Hartmann

why simulations
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!

aspects of simulations
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)
standard method
Standard method

Simulate until n species are obtained.

Stop at following speciation or extinction event.

Example for n=5 species:

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

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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
special models
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
memoryless pure birth models

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Memoryless pure birth models

Time between sn and sn+1 does not depend on the current tree (e.g. Yule model, Coalescent).

Correct simple approach:

Simulate until

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Yule model / Coalescent

Simulating until the (n+1)-th speciation event yields the desired results!

birth death model

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reconstructed tree

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available program
Available Program

Tool TreeSample implemented in Pearl by Klaas Hartmann. Available as a stand-alone application or as a Pearl script.

Demonstration:

dankesch n
Dankeschön

Dennis Wong

Mike Steel

Erick Matsen

Klaas Hartmann