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A statistic summarizing: Relative timing in trees

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A statistic summarizing:Relative timing in trees

Tanja Gernhard

joint work with

Erick Matsen, Daniel Ford

- Investigate the properties of reconstructed trees
- Colless [Colless, 1982] summarizes the information of the shape of the tree (i.e. balanced vs. unbalanced)
- Gamma [Pybus, Harvey 2000] summarizes the time between speciation events (graphical representation in LTT plots)

Neutrality: Each ranking equally likely

Each ranking equally likely

equivalent to

For each vertex: Each shuffle equally likely

RRRRLL

RRLRRL

shuffles on a vertex

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- Runs: Number of sequences in shuffle with same letter
- Consider (2,4)-shuffle RRLRRL: 4 runs
- Run distribuition of (m,n)-shuffle well-known from statistics:

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- Runs of a tree, R(T): Sum of runs of all shuffles in tree
- Distribution for runs in tree T:

- We investigated the tree of Ants [Moreau et al, 2007]
- LTT plot show substantial increase during Late Cretacceous to Early Eocene

- Testing the posterior of Bayesian methods for neutrality (phylogenies or populations)
- Population size might change arbitrary
- All programs available from my homepage in the Python package Cass

python Stats.dat YourTrees.tre