A statistic summarizing: Relative timing in trees
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Transcript of 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
• 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
Neutrality: Each ranking equally likely
How to summarize rank information?
Each ranking equally likely equivalent to
For each vertex: Each shuffle equally likely
shuffles on a vertex
RRRRLL RRLRRL
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:
P 5i=0 xi
PfXm;n = 2k+1g=
¡m¡ 1
k
¢¡n¡ 1k¡ 1
¢+
¡m¡ 1k¡ 1
¢¡n¡ 1
k
¢
¡m+n
m
¢
PfXm;n = 2kg=2¡m¡ 1k¡ 1
¢¡n¡ 1k¡ 1
¢
¡m+n
m
¢
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:
PfR(T) = kg=kX
i=1
PfXm;n = igk¡ iX
j =0
PfR(L) = jgPfR(R) = k¡ i ¡ jg
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
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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 Casspython Stats.dat YourTrees.tre
Dankeschön