Phylogenetic Tree Calculation (PDF)

UPGMA Method Unweighted Pair Group Method with Arithmatic Mean It assumes constant rate of evolution It measure Pairwise distance to construct tree Produce mostly unrooted tree Most simple calculation as compare to other tree construction method It is ultrametric tree: Equal dist...

UPGMA Method Unweighted Pair Group Method with Arithmatic Mean It assumes constant rate of evolution It measure Pairwise distance to construct tree Produce mostly unrooted tree Most simple calculation as compare to other tree construction method It is ultrametric tree: Equal distance from root Construction Method: 1. Collect the sequences from different species 2. Do multiple sequence alignment of sequences 3. Make possible pairs with the help of matrix 4. Make cluster based on nearest values 5. Merge the cluster 6. Reconstruct the matrix-Construct tree accordingly  Assume we have 5 sequences Seq A A T C C T G A Seq B C T C C A A A Seq C A A G C T A C Seq D A T G C T G A Seq E A T G G T G T Step 1 A B C D E A 0 3 4 1 3 B 0 5 4 6 C 0 3 4 D 0 2 E 0 0.5 A D 0.5  Step 2 AD B C E 0.5 A AD 0 3.5 3.5 2.5 0.75 B 0 5 6 D C 0 4 0.5 E 0 E AD/B A—B=3 AD/E D—B=4 A—E=3 AD—B=(3+4)/2=7/2=3.5 D—E=2 AD—B=(3+2)/2=5/2=2.5 AD/C A—C=4 D—C=3 AD—B=(4+3)/2=7/2=3.5  Step 3 ADE B C ADE 0 4.75 3.75 0.5 A B 0 5 0.75 C 0 0.625 D 0.5 E ADE/B 1.25 AD—B=3.5 C 1.875 E—B=6 AD—B=(3.5+6)/2=9.5/2=4.75 ADE/C AD—C=3.5 E—C=4 AD—B=(3.5+4)/2=7.5/2=3.75  Step 3 ADEC B ADEC 0 4.875 0.5 A B 0 0.75 0.625 D 0.5 0.5625 E ADEC/B 1.25 ADE—B=4.75 C 1.875 C—B=5 B AD—B=(4.75+5)/2=9.75/2=4.875 2.4375  Neighbour Joining Method We will use hypothetical distance matrix of n=6 taxas A B C D E F A 0 B 5 0 C 4 7 0 D 7 10 7 0 E 6 9 6 5 0 F 8 11 8 9 8 0 Step 1 Calculate the net divergence for each taxa from all other taxa r(i) = total distance of taxa i from all other taxas = d(i,1)+ d(i, 2)+…….d(i,n) Example for calculating as: r(A) = 5+4+7+6+8 = 30 r(B) = 5+7+10+9+11 = 42 r(C) = 4+7+7+6+8 = 32 r(D) = 7+10+7+5+9 = 41 r(E) = 6+9+6+5+8 = 34  Step 1 Calculate the new distance matrix (M) using the formula for each pair of taxa M(i) = d(i,j) - (r(i) + r(j))/(n-2) Example for calculating M(A,B) M(A,B)= d(A,B)-((r(A)+r(B))/(n-2) = 5-(30+42)/6-2 = -13 A B C D E F A 0 B -13 0 C -11.5 -11.5 0 D -10 -10 0 E -10 -10 -10.5 -13 0 F -10.5 -10.5 -11 -11.5 -11.5 0 Now, We will start with a star tree Step 3: Using this new matrix, find the closest pair of taxa (i,j) consider the lowest distance and assign ‘U’ as the connecting node for the pair. Branch length is these calculated as: S(i,u) = d(i,j)/2 + (r(i)-r(j))/2(n-2) S(j,u) = d(i,j) - s(i,u) Through the matrix (M), the closest pair of taxa is : AB=-13 as well as DE=-13 For AB, The distance from U to A & U to B is as: S(A,U) = d(A,B)/2 + (r(A)-r(B))/2(n-2) = 5/2 + (30-42)/2(6-2) =1 S(B,U) = d(A,B) -S(A, U) = 5-1 = 4 1 A (i) U 4 B (j) Step 4: Calculate the new distance from U to all other taxas. The distance d (U, k) between U and taxa k is as: D(U,k) = [d(i,k) d(j,k)-d(i,j)]/2 Example: D(U, C) = [d(A,C)+d(B,C)-d(A,B)]/2= [4+7-5]/2 = 3 D(U, D) = [d(A,D)+d(B,D)-d(A,B)]/2= [7+10-5]/2 = 6 D(U, E) = [d(A,E)+d(B,E)-d(A,B)]/2= [6+9-5]/2 = 5 D(U, F) = [d(A,F)+d(B,F)-d(A,B)]/2= [8+11-5]/2 = 7 A B C D E F A 0 B 5 0 C 4 7 0 D 7 10 7 0 E 6 9 6 5 0 F 8 11 8 9 8 0 Other distances remain as it is. So the new distance matrix will be: U C D E C 3 D 6 7 E 5 6 5 F 7 8 9 8 The resulting tree will be Now N= n-1= 5 The entire step is repeated till we get N=4 And then again until we get N=0 Step 5: Evaluating the phylogenetic tree The longer the branch length the longer the divergence