Loading in 5 sec....

A statistic summarizing: Relative timing in treesPowerPoint Presentation

A statistic summarizing: Relative timing in trees

- By
**lieu** - Follow User

- 78 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' A statistic summarizing: Relative timing in trees' - lieu

**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

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

RRRRLL

RRLRRL

shuffles on a vertex

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:

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

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

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

Download Presentation

Connecting to Server..