1. Clustering methods Tree building methods for distance-based trees
For a set of sequences, all possible pairwise distances are calculated using your method of choice (JC69, K2P, GTR, etc.)
Now, how do you build a tree?
This provides measures of dissimilarity that can then be clustered according to a several major tree building algorithms
U(W)PGMA - Unweighted (Weighted) Pair Group Method with Arithmetic Means
Minimum Evolution
Neighbor Joining

2. Clustering methods
U(W)PGMA - Unweighted (Weighted) Pair Group Method with Arithmetic Means
A single best rooted tree is built using the calculated distances to group pairs of OTUs
A molecular clock is assumed, thus terminal nodes are equidistant from the root
Summary –
Obtain distance matrix
Group two most closely related taxa
Find mean of distances
Group these two as a single new OTU
Continue until you run out of sequences

3. Clustering methods U(W)PGMA Summary – Obtain distance matrix
Group two most closely related taxa
Find mean of distances
Group these two as a single new OTU
Continue until you run out of sequences 2 1 3 4 5 5 3 4 1 2

4. Clustering methods U(W)PGMA Details – Start with your distance matrix
Group the taxa with the shortest distance
The depth of the divergence between A and B is their distance divided by 2
Recalculate the distances between AB and other taxa A B C D E 2 4 6 F 8 A B 1

5. Clustering methods U(W)PGMA Details –
Recalculate the distances between AB and other taxa
d(AB)C = (dAC + dBC)/2 = 4
d(AB)D = (dAD + dBD)/2 = 6, etc.
Repeat with next closest cluster, D & E
We could just as easily group C with AB AB C D E 4 6 F 8 A B 1 D E 2

6. Clustering methods U(W)PGMA Details –
Recalculate the distances between DE and other taxa
Join the next closest group AB & C AB C DE 4 6 F 8 A B 1 C 2 1 D E 2

7. Clustering methods U(W)PGMA Details –
Recalculate the distances between ABC and other taxa
How long should the branch joining ABC to DE be?
The distance between D (or E) and A, B or C should be a total of 6.
Join DE to ABC
ABC DE 6 F 8 A B 1 C 2 1 1 D E 2

8. Clustering methods U(W)PGMA Details –
This leaves only F to add to the tree
The total distance between F and any other taxon should be 8
ABCDE F 8 A B 1 C 2 1 1 F 1 4 D E 2

9. Clustering methods U(W)PGMA
Weakness – constant molecular clock assumption
Note that 3 and 5 are actually less divergent from one another than 4 and 5
This can’t be depicted in the tree using this method
Non-homogeneous rates can introduce serious problems with tree reconstruction when some taxa evolve much faster than others 2 1 3 4 5 5 3 4 1 2

10. Clustering methods U(W)PGMA is rarely used anymore
Other, newer methods avoid the weaknesses – ultrametricity due to the constant molecular clock assumption
Newer methods do not require ultrametricity (still require additivity)
Require that the distance between any pair of OTUs equal the sum of the lengths of their branch lengths, not the average
Allows for variable molecular clock among taxa A B C D E 5 4 7 10 6 9 F 8 11 1 A 1 4 1 B 2 1 C 3 D 1 2 E 4 F

11. Clustering methods Minimum Evolution Method
The tree that minimizes the lengths of the tree (the sum of the lengths of all branches) is the best tree
Reasonably good at finding the best tree
Major drawback – Must examine all possible trees, computationally onerous when dealing with large numbers of taxa

12. Clustering methods Neighbor Joining Method (Saitou and Nei, 1987)
A heuristic method for determining the best distance-based tree
Heuristic methods explore a subset of all possible trees in the hope that the best tree lies within that subset
Heuristic methods often fall into the ‘hill-climbing’ category
Start with a tree and alter it in some way
If the alteration makes it worse (using some optimality criterion), abandon it and try again.
If the alteration makes it better, keep it and continue
Heuristic methods include:
Stepwise addition
Branch swapping
More on these later
NJ is a star decomposition heuristic

13. Clustering methods
The major drawback to heuristics is that of finding local optima in the tree space

14. Clustering methods NJ
Combines computational speed with unique results (you always get a single best tree)
The NJ algorithm
Compute the net divergence, r, for every end node
rA = = 30
rB = = 42
rC = 32, rD = 38, rE = 34, rF = 44
Create a ‘rate-corrected distance matrix
Mi = dij – (ri + rj)/(N-2)
N = number of end nodes
MAB = 5 – ( )/4 = -13
MAC = 4 – ( )/4 = -11.5 A B C D E 5 4 7 10 6 9 F 8 11 A B C D E
-13
-11.5
-10
-10.5 F
-11

15. Clustering methods NJ The NJ algorithm Draw your star phylogeny A F BA B C D E
-13
-11.5
-10
-10.5 F
-11 A F B E C D

16. Clustering methods NJ The NJ algorithm
Define a new node, U, that groups minimally diverged taxa
Either AB or DE
U = AB
Determine branch lengths from U to A and B
SAU = dAB/2 + (rA – rB)/2(N – 2)
SAU = 5/2 + (30 – 32)/2(6 – 2) = 1
Because the distances are additive,
SBU = dAB – SAU = 4 A B C D E
-13
-11.5
-10
-10.5 F
-11 F A E B C D F E C D A B 1 4 U A B C D E 5 4 7 10 6 9 F 8 11
rA = 30
rB = 42
rC = 32, rD = 38, rE = 34, rF = 44

17. Clustering methods NJ The NJ algorithm
Redefine distances based on the new node
dCU = (dAC + dBC – dAB)/2
dCU = (4 + 7 – 5)/2 = 3, etc.
Repeat previous steps A B C D E 5 4 7 10 6 9 F 8 11 U C D E 3 6 7 5 F 8 9 F E C D A B 1 4 U

18. Clustering methods NJ The NJ algorithm
Calculate net divergences for every end node (U now counts as an end node so, N = N - 1)
rU = 21, rC = 24, rD = 27, rE = 24, rF = 32
Compute rate-corrected distances
Create new node, V, from either UC or DE
Calculate branch lengths from node V to C and U
SUV = dCU/2 + (rU – rC)/2(N – 2)
SUV = 3/2 + (21 – 24)/2(5 – 2) = 1
SCV = 2
Compute new distance matrix from V to all terminal nodes U C D E
-12
-10
-11 F
-10.7 U C D E 3 6 7 5 F 8 9 F E C D A B 1 4 U 1 2 B F E D V A 4 U V D E 5 4 F 6 9 8 C

19. Clustering methods NJ The NJ algorithm And so on… U F E C D A 1 V W 23 B 4 5 U F E C D A 1 V W 2 3 B 4 1 2 B F E D V A 4 U U F E C D A 1 V W 2 3 B 4 U F E C D A 1 V B 4 1 2 C

20. Clustering methods NJ The NJ algorithm
Note that this is an unrooted tree
Where do we put the root?
Using external information we can determine where the root belongs U F E C D A 1 V W 2 3 B 4 A B 4 1 C 2 D E 3 F 1 1 1 1 2

21. Clustering methods
UPGMA vs NJ

22. Clustering methods Alternatives to classical NJ Software
BIONJ (Gascuel, 1997)
Generalized neighbor joining (Pearson et al., 1999)
Weighted neighbor joining (Bruno et al., 2000)
Multi-neighbor-joining (Silva et al., 2005)
Relaxed neighbor joining (Evans et al., 2006)
Software
PHYLIP
MEGA
PAUP
DAMBE
TREECON

23. Clustering methods Pros Cons Easy to understand Easy to implement Fast
Produce a single, best tree
Use an explicit substitution model
Topology AND branch lengths are calculated (NJ)
Cons
Reduce most of the data to single value (reduce the amount of information)
Different data sequences can yield the same distance matrix