Computerintensive Methoden - Coalescent Theory - Project C

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The following data were taken from the segregating sites in a sequence of nucleotides from the Y chromosome of 133 Asians. Fourteen segregating sites were found and 9 different alleles. At each site 0 represents the ancestral variant (as observed in the majority of a reasonably large sample of chimpanzees). The alleles observed and their frequencies are given below. 





 Alleles 

     1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   

  
  C   0   1   0   0   0   1   0   1   0   1   0   0   0   1   0  

  
  F   0   1   0   0   0   1   1   0   0   0   0   0   0   0   0  

  
  G   0   1   0   0   0   1   0   1   0   1   0   0   0   1   1  

  
  H   0   1   0   0   0   1   0   1   1   0   0   0   0   0   0  

  
  J   0   1   0   0   0   1   0   1   0   1   1   1   1   0   0  

  
  N   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0  

  
  P   0   1   1   1   1   0   0   0   0   0   0   0   0   0   0  

  
  Q   0   1   0   0   0   1   0   0   0   0   0   0   0   0   0  

  
  R   0   1   0   0   0   1   0   1   0   0   0   0   0   0   0

Task 1

Calculate the matrix given the Hamming distance between each allele. 

d=dist(alleles,method="manhattan")
d
 
#
  C F G H J N P Q

F 4              
G 1 5            
H 3 3 4          
J 4 6 5 5        
N 6 4 7 5 8      
P 7 5 8 6 9 5    
Q 3 1 4 2 5 3 4  
R 2 2 3 1 4 4 5 1

Task 2

Calculate the nucleotide diversity. 

theta.pi=sum(as.dist(as.matrix(d) * (freq %o% freq)))*(2/(sum(freq)*(sum(freq)-1)))
theta.pi
 
#
[1] 2.910686

Task 3

Carry out the Tajima test to verify the Wright-Fisher model. 

S=dim(alleles)[2]
n=sum(freq)

theta.l=S/sum(1/(1:(n-1)))

an=sum(1/1:(n-1))
bn=sum(1/((1:(n-1))^2))

e1 = (n+1)/(3*an * (n-1)) - 1/an^2
e2 = 1/(an^2+bn) * ( (2*(n^2+n+3))/(9*n*(n-1)) - (n+2)/(n*an) + bn/an^2 )

var.theta=e1*S + e2*S*(S-1)

D=(theta.pi - theta.l)/sqrt(var.theta) 
 
#


	Tajima Test

data:  
D = 0.1607, p-value = 0.8723
sample estimates:
 Theta L Theta Pi 
2.745342 2.910686 









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