1. Lecture 14 CS5661 Neighbor Joining Generates unrooted tree, allowing for unequal branches Given: Distance matrix for sequences Steps: Repeat 1-3 till all branches generated 1.Take any two sequences i, j 2.Find branch lengths between i and j by treating remaining sequences as composite (c) 1.Calculate average i-C and j-C distances 2.Calculate branch lengths i and j 3.Treat ij as composite sequence now and generate new distance table. 4.Generate multiple trees by starting with different pairs 5.Compare resulting trees in terms of best fit to original distance matrix

2. Lecture 14 CS5662

3. 3 I and II are closest neighbors at distance 10. Question: Which of them is closer to the rest, and by how much? Average distance from I to III, IV = 40 Average distance from II to III, IV = 45 X + Z = 40 Y + Z = 45 => x = 2.5; y = 7.5 X + Y = 10 I II x y z

4. Lecture 14 CS5664 Established Now, consider (I,II) as composite sequence and find closest pairs I II 2.5 7.5

5. Lecture 14 CS5665 A + B = 20 2.5 + C + A = 30  7.5 + C + B = 50 I II 2.5 7.5 IV III C A B A = 2.5; B = 17.5; C = 25;

6. Lecture 14 CS5666 I II 2.5 7.5 IV III 25 17.5 2.5 Predicted Tree

7. Lecture 14 CS5667 Seq\SeqIIIIIIIV I 103045 (50) II 45 (40)45 (50) III 20 Predicted Distance matrix Error = (5 2 + 5 2 + 5 2 ) 1/2 = 8.66 Repeat entire process starting with a different pair Tree with lowest error is the best one