Patterns of Evolution Summary statistics based on segregating sites - - PowerPoint PPT Presentation

Patterns of Evolution

Summary statistics based on segregating sites

Site Frequency Spectrum

4 3 1 2 1 1

1 2 3

1 2 3 4 5

Patterns of Evolution

Summary statistics based on segregating sites

Site Frequency Spectrum

total number of segregating sites in an sample of size n number of mutants that appear in i copies in the sample

:

1 1



 



n i i

S S

1 2 3

1 2 3 4 5

:

i

S

i

S

: ) ( 1

1 1 2           

 

n i i n

S i n i 

average number of pairwise differences

i

: ) ( 1

1 1 2           

 

n i i n

S i n i 

Patterns of Evolution

Summary statistics based on segregating sites

Site Frequency Spectrum

total number of segregating sites in an sample of size n number of mutants that appear in i copies in the sample

:

1 1



 



n i i

S S

:

i

S

Each mutation of size i contributes to divergence in i (n – i) sequence pairs

1 2 3

1 2 3 4 5

i

S i

Coalescent Theory

Estimators

Unbiased estimators of the mutation parameter q = 4Nu:

 

   

 

1 1 1 1

1 ˆ

n i n i i n W

i S a S q

singleton estimator:

 

1 1

1 ˆ



  

n s

S S n n q

Watterson‘s estimator:  -based estimator:

i n i n

S i n i ) ( ˆ

1 1 1 2            

    q

singletons of the folded spectrum

i n i n H

S i



          



1 1 2 1 2

ˆ q

Fay and Wu‘s estimator: (equal weights) (intermediate frequencies) (high frequencies) (extreme frequencies)

Coalescent Theory

Test statistics

Test statistics for the deviation from neutrality:

 

W W T

D q q q q

 

ˆ ˆ Var ˆ ˆ   

Tajima‘s D: Fay and Wu‘s H: Fu and Li‘s D:

 

S W S W FL

D q q q q ˆ ˆ Var ˆ ˆ   

 

H H FW

H q q q q

 

ˆ ˆ Var ˆ ˆ   

0,2 0,4 0,6 0,8 1 1 2 3 4 5 6



T

D

Coalescent Theory

Test statistics

Test statistics for the deviation from neutrality:

 

W W T

D q q q q

 

ˆ ˆ Var ˆ ˆ   

Tajima‘s D: Fay and Wu‘s H: Fu and Li‘s D:

 

S W S W FL

D q q q q ˆ ˆ Var ˆ ˆ   

 

H H FW

H q q q q

 

ˆ ˆ Var ˆ ˆ   

0,2 0,4 0,6 0,8 1 1 2 3 4 5 6



T

D

Coalescent Theory

Test statistics

Test statistics for the deviation from neutrality:

 

W W T

D q q q q

 

ˆ ˆ Var ˆ ˆ   

Tajima‘s D: Fay and Wu‘s H: Fu and Li‘s D:

 

S W S W FL

D q q q q ˆ ˆ Var ˆ ˆ   

 

H H FW

H q q q q

 

ˆ ˆ Var ˆ ˆ   

0,2 0,4 0,6 0,8 1 1 2 3 4 5 6



FW

D

Coalescent Theory

Test statistics

Test statistics for the deviation from neutrality:

 

W W T

D q q q q

 

ˆ ˆ Var ˆ ˆ   

Tajima‘s D: Fay and Wu‘s H: Fu and Li‘s D:

 

S W S W FL

D q q q q ˆ ˆ Var ˆ ˆ   

 

H H FW

H q q q q

 

ˆ ˆ Var ˆ ˆ   

0,2 0,4 0,6 0,8 1 1 2 3 4 5 6



FW

H