Simulating trees

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# Simulating trees - PowerPoint PPT Presentation

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…

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?

Even simple models hard to analyze analytically!

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

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!

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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
• 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 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!

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Birth-death model

reconstructed tree

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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:

Dankeschön

Dennis Wong

Mike Steel

Erick Matsen

Klaas Hartmann