A statistic summarizing relative timing in trees
This presentation is the property of its rightful owner.
Sponsored Links
1 / 10

A statistic summarizing: Relative timing in trees PowerPoint PPT Presentation


  • 50 Views
  • Uploaded on
  • Presentation posted in: General

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)

Download Presentation

A statistic summarizing: Relative timing in trees

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

1

1

1

1

¡

¡

¡

¡

¡

¢

¡

¢

¡

¢

¡

¢

m

n

m

n

+

k

k

k

k

1

1

¡

¡

f

g

k

P

X

2

1

+

=

=

m

n

+

¡

¢

m

n

;

m

1

1

¡

¡

¡

¢

¡

¢

m

n

2

k

k

1

1

¡

¡

f

g

k

P

X

2

=

=

m

n

+

¡

¢

m

n

;

m

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

k

k

i

¡

X

X

f

(

)

g

f

g

f

(

)

g

f

(

)

g

k

k

P

P

P

P

R

T

X

R

L

R

R

i

j

i

j

¡

¡

=

=

=

=

=

m

n

;

i

j

1

0

=

=

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


Dankesch n

Dankeschön


  • Login