Phylogenetic Trees Tutorial 6

Measuring distance Bottom-up algorithm (Neighbor Joining) –Distance based algorithm –Relative distance based Phylogenetic Trees Tutorial 6

Problem: unrelated sequences approach a fraction of difference expected by chance  The distance measure converges. Jukes-Cantor Measuring Distance

Measuring Distance (cont) Euclidean Distance: Given a multiple sequence alignment, calculate the square root of the sum of the score at every position between two sequences the score increases proportionally to the extent of dissimilarity between residues

Star Structure Assumption: Divergence of sequences is assumed to occur at constant rate  Distance to root equals a d c b acbd fe

Star Structure Assumption: Divergence of sequences is assumed to occur at constant rate  Distance to root equals a d c b acbd fe Unweighted Pair Group Method using Arithmetic Averages UPGMA

7 abcd a0875 b8039 c7308 d5980 a d c b Basic Algorithm Initial star diagramDistance matrix UPGMA Constructs a rooted tree.

8 abcd a0875 b8039 c7308 d5980 a d c b Choose the nodes with the shortest distance and fuse them. UPGMA: Selection step

9 abcd a0875 b8039 c7308 d5980 -Even distance between c  e and b  e -e  a, e  d by average distance from c anb b UPGMA: Distance recalculation step a,d c e b f

10 a d c,b e a a,d c e b f d a c e b f D bf abcd a0875 b8039 c7308 d acbd f e 4

11 Neighbor Joining Algorithm Constructs unrooted tree.

Step by step summary: 1.Calculate all pairwise distances. 2.Pick two nodes (i and j) for which the distance is minimal. 3.Define a new node (x) and re-calculate the distances from the free nodes to the new node. 4.Calculate D ix and D jx - the distance of the chosen nodes I and J to the new node X, as well as the distance from X to all other nodes. 5.Continue until two nodes remain – connect with edge. Neighbor Joining’ (merging close sequences – not the actual algorithm)

Pick two nodes for which the distance is minimal (i,j)

Node 10 is a new node. 5,6

Re-calculate the distances from new node I,j : the fused nodes (5,6) X :a new added node (node 10) m :the remaining nodes in the star

Calculate D ix and D jx r : ~average distance to nodes L : number of leaves left in the tree (leaves nodes representing taxa, sequences,etc)

Calculate Dix and Djx r 5 =ΣD 5k /(L-2)= /(9-2)= r 6 =ΣD 6k /(L-2)= /(9-2)= ΣD 5k ΣD 6k

Calculate Dix and Djx D 10,5 =(D 5,6 +r 5 -r 6 )/2=( )/2) = D 10,6 =D 5,6 -D 10,5 = =

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Step 7

Problems

Step by step summary: 1.Calculate all pairwise distances. 2.Pick two nodes (i and j) for which the relative distance is minimal (lowest). 3.Define a new node (x) and re-calculate the distances from the free nodes to the new node. 4.Calculate D ix and D jx - the distance of the chosen nodes I and J to the new node X, as well as the distance from X to all other nodes. 5.Continue until two nodes remain – connect with edge. Neighbor Joining (Not assuming equal divergence)

Step 2. Pick two nodes (i and j) for which the relative distance is minimal (lowest).

Negative values As the average distance from the common ancestor to the rest of the nodes increases, M ij has a lower value. Select pair that produce lowest value Reevaluate M with every iteration J I X M

Re-calculate the distances from new node J I X M

33 EXAMPLE A B C D E B 5 C 4 7 D E F A B C D E B -13 C -11 D E F Original distance MatrixRelative Distance Matrix (Mij) The Mij Table is used only to choose the closest pairs and not for calculating the distances

Bacillus E.coli Pseudomonas Salmonella Aeromonas Lechevaliera Burkholderias Problems with phylogenetic trees

Software PHYLIP PAUP MEGA More