Scribd
Upload
54 views13 pages

Unit2 4

The three-point condition states that for any three taxa, the distance between the two most distantly related taxa must be equal to or greater than the sum of the other two distances. UPGMA assumes equal evolutionary rates among lineages, but if this assumption is violated, it can result in an incorrect tree topology. For example, if lineage B evolves at a faster rate than lineage A after their divergence, the three-point condition would be violated for taxa A, B, and D. Neighbor-joining is an alternative clustering method that is less sensitive to violations of the three-point condition.

Uploaded by

sadhanaa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
54 views13 pages

Unit2 4

The three-point condition states that for any three taxa, the distance between the two most distantly related taxa must be equal to or greater than the sum of the other two distances. UPGMA assumes equal evolutionary rates among lineages, but if this assumption is violated, it can result in an incorrect tree topology. For example, if lineage B evolves at a faster rate than lineage A after their divergence, the three-point condition would be violated for taxa A, B, and D. Neighbor-joining is an alternative clustering method that is less sensitive to violations of the three-point condition.

Uploaded by

sadhanaa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 13

UPGMA Contd.....

Final Step:
Pitfalls in UPGMA

The UPGMA clustering method is very sensitive to unequal


evolutionary rates. This means that when of the OTUs has
incorporated more mutations over time, then the other OTU one may
end up with a tree that has wrong topology

Clustering works only if the data are ultrametric

Ultrametric distances are defined by the satisfaction of the


three- point condition.

What is the three-point condition?

For any three taxa: dist AC <= max (distAB, distBC) or in words: the two
greatest distances are equal, or UPGMA assumes that the evolutionary
rate is the same for all branches. If the assumption of rate constancy
among lineages does not hold UPGMA may give an erroneous topology.
Suppose you have the following tree:

Since the divergence of A and B, B has accumulated mutations at a much


higher rate than A. The Three-point criterion is violated!

e.g. distBD <= max (distBA,distAD) or, 10 <= max (5,7) = False
The reconstruction of the evolutionary history uses the following distance matrix:
Correct Topology
Neighbour Joining Method

r(A) = 5+4+7+6+8=30
r(B) = 42
r(C) = 32
r(D) = 38
r(E) = 34
r(F) = 44
Step 2: Now we calculate a new distance matrix using for each pair of OTUs
the formula:

M(AB)=d(AB) -[(r(A) + r(B)]/(N-2) = -13

r(A) = 5+4+7+6+8=30
r(B) = 42
r(C) = 32
r(D) = 38
r(E) = 34
r(F) = 44
Now we start with a star tree:
Step 3: Now we choose as neighbors those two OTUs for which Mij is the
smallest. These are A and B and D and E. Let's take A and B as neighbors and
we form a new node called U. Now we calculate the branch length from the
internal node U to the external OTUs A and B.

S(AU) =d(AB) / 2 + [r(A)-r(B)] / 2(N-2) = 1


S(BU) =d(AB)-S(AU) = 4

Step 4: Now we define new distances


from U to each other terminal node:
d(CU) = d(AC) + d(BC) - d(AB) / 2 = 3
d(DU) = d(AD) + d(BD) - d(AB) / 2 = 6
d(EU) = d(AE) + d(BE) - d(AB) / 2 = 5
d(FU) = d(AF) + d(BF) - d(AB) / 2 = 7
The entire procedure is repeated starting at step 1

You might also like