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. Tree statistics. Investigate the properties of reconstructed trees Colless [Colless, 1982] summarizes the information of the shape of the tree (i.e. balanced vs. unbalanced)

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a statistic summarizing relative timing in trees

A statistic summarizing:Relative timing in trees

Tanja Gernhard

joint work with

Erick Matsen, Daniel Ford

tree statistics
Tree statistics
  • 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)
relative timing
Relative Timing

Neutrality: Each ranking equally likely

how to summarize rank information
How to summarize rank information?

Each ranking equally likely

equivalent to

For each vertex: Each shuffle equally likely

RRRRLL

RRLRRL

shuffles on a vertex

runs summarize shuffle

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Runs summarize shuffle
  • 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:
combining all shuffles in tree

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Combining all shuffles in tree
  • Runs of a tree, R(T): Sum of runs of all shuffles in tree
  • Distribution for runs in tree T:
application to ant lineages
Application to Ant lineages
  • We investigated the tree of Ants [Moreau et al, 2007]
  • LTT plot show substantial increase during Late Cretacceous to Early Eocene
some comments
Some comments
  • 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

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