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CHAPTER 21
Construction of Phylogenetic Tree: Unweighted‐Pair Group Method with Arithmetic Mean (UPGMA)

CS Mukhopadhyay and RK Choudhary

School of Animal Biotechnology, GADVASU, Ludhiana

21.1 INTRODUCTION

UPGMA is a clustering algorithm that works by joining the branches of a tree on the basis of maximum similarity criteria among pairs of sequences, and by calculating the means of joined pairs. UPGMA is “ultrametric”, so all the terminal nodes are equally distanced from the root. Hence, at the end, when a root is added, the rooted tree is produced.

Unweighted: It indicates equal contribution of all the pair‐wise distances. There is no weighting of any specific taxa‐pairs to indicate a different evolutionary rate compared with another pair(s). This is the opposite of the Weighted‐Pair Group Method with Arithmetic mean (WPGMA).
Pair‐groups: Any two taxa or any two clusters (clade) or one taxon and a cluster are always combined in pairs (that is, interpreted as dichotomies).
Arithmetic mean: Pair‐wise distance of each group is the mean distance to all members of that group.

21.2 ASSUMPTIONS

Constant rate of evolution (i.e., mutation‐rate) amongst all the sequences.
Distance data are ultrametric: This enables clustering by satisfying the “three point condition” to generate the tree.

TERMINOLOGIES AND POINTS

Neighbors: the external nodes with the smallest number of mismatches.
Ultrametric: in distance methods, an ultrametric tree is characterized by a “Three point condition”, where three points (a, b, c) satisfy the condition for the distance (d): d(a,b) ≤; max{d(a,c), d(b,c)}. Unless the data are ultrametric (i.e., the OTUs of any branch have different lengths), this condition will not be satisfied. The ultrametric tree assumes a molecular clock of consistent evolutionary rate.
Rate of evolution: UPGMA is very sensitive to the rate of evolution. If the assumption of equal evolutionary rate is not met, it will generate a rooted tree with the wrong topology.
When there is weak similarity between sequences, the distance methods (UPGMA, neighbor joining, minimum evolution, Fitch Margoliash) are the best options.
Note that the UPGMA will produce a rooted tree at the final step if a root is added; else the tree itself will be unrooted.

21.3 OBJECTIVE

To construct a phylogenetic tree (dendrogram), using the UPGMA method, from a set of molecular sequences.

21.4 PROCEDURE

Calculate the raw pair‐wise distance data from a set of sequences and construct a distance matrix:

TABLE 21.1

A B C D

B 3

C 7 7

D 10 10 10

E 10 10 10 8

Note: while constructing the tree from the distance values, one needs to select the closest pair (with minimum distance among all possible pairs) from the distance matrix, and then merge these two objects to yield one.
Identify the least‐distant pair: Here, the minimum distance is d(AB) = 3 (i.e., between the taxa “A” and “B”).
Place these two taxa in a single group as a cluster and consider the duo as a single external node.
The distance is d(AB) = AB = 3. Hence, the depth of divergence (for each branch) of this sub‐tree will be 3/2 = 1.5 units.

FIGURE 21.1
Now consider “AB” as a single taxon and repeat the same steps, as above. Find the shortest distance and make the respective taxa a single cluster.

TABLE 21.2

AB C D

C 7

D 10 10

E 10 10 8
Add the new taxa (C) with “AB” cluster, since “AB” and “C” have the least distance (i.e., 7), to produce the sub‐tree of ABC, in which the AB sub‐tree (drawn just in the last step) is attached to the point M. The length of AK + AN = OC.

FIGURE 21.2

For the sake of understanding, the internal nodes of the branches have been marked (as K, L, N, etc.). These are not required for tree construction in general.
Now, repeat the last two steps, – that is, calculate the mean distance between (AB)C cluster and Sequence “D” and then draw the phylogenetic tree:

TABLE 21.3

ABC D

D 10

E 10 8
Now, the least distance is DE = 8. We will repeat the same steps as before: The branch length will be 8/2 = 4 units.

FIGURE 21.3
Now, calculate the distance between these two clusters ABC and DE:

DIFFERENTIATING BETWEEN ULTRAMETRIC AND NON‐ULTRAMETRIC DATA

The example given above is of an ultrametric data‐set that follows the principle of “three point condition”, i.e., d(AC)<=max{d(AB, BC)}
Now let us take this example of non‐ultrametric data where the three point condition is not fulfilled, hence d(AC)>max{d(AB, BC)} The actual tree should look like this, and the non‐ultrametric dataset for this tree is as follows:

FIGURE 21.B1

Please note that d(AC) > max{d(AB), (BC)}, i.e., 8 > max{4,6}, so the dataset is non‐ultrametric.
Now, if this distance matrix is solved as earlier, we will ultimately get the following tree: In text iterations, as earlier, we get:

FIGURE 21.B2
Now we can compare how the actual tree topology has been totally changed due to the non‐ultrametric nature of the data.
The ultrametric dataset will give the same result in UPGMA and WPGMA; however, it is not necessary for non‐ultrametric data.
Branch length represents the evolutionary distance, not the time lapse of evolution. Thus, two sister taxa, though having the same evolutionary time, may have different distances or branch lengths (view NJ method). In distance‐based methods, the distances between the nodes are additive – that is, to get the distance between two taxa, add up the distances of all the branches (main and internal branches) connecting these two taxa.
The vertical width (perpendicular to the branches) does not carry any meaning in terms of evolutionary distance, time‐scale or mutation rate.
The terms “cladogram” and “phylogram” differ in that the latter represents true evolutionary history through the evolutionary time scale, while the former does not represent evolutionary time.
In the above diagram, the scale bar of 1 unit measures evolutionary distance by 1 residue.
The scale bar often represents values of 0.01, 0.02, etc., which indicates 1% or 2% divergence (or 99% or 98% homology, respectively) among the taxa. The percentage homology is calculated through multiple sequence alignment.
Base or amino acid substitution takes place after divergence of two homologous sequences. Such substitutions occur at different rates in different species; hence, this happens irrespective of the direction of time. The number of substitution of residue (nucleotide or amino acid) is the indicator of evolutionary distance.

21.5 INTERPRETATION OF UPGMA TREE

The distance from the root to the OUT of each cluster = 10/2 = 5 units.

Hence, the distance of TP = 5 – OC = 5 – 3.5 = 1.5 units.

The distance of US = 5 – 4 = 1.0 unit.

The UPGMA tree obtained in our example depicts evolutionary distances between the taxa. We need to add up the distances connecting these two taxa to calculate the distance between any two taxa (“A” and “D”): 1.5 + 2 + 1.5 + 1 + 4 = 10. This is exactly the value given in the distance table. Assuming equal evolutionary rates, these values indicate the evolutionary distances between the taxa.

Phylogenetic tree with two sub-trees. — **FIGURE 21.4**

Phylogenetic tree three sub-trees (left) and a table containing data (right). — **FIGURE 21.5**

21.6 QUESTIONS

1. Draw a phylogenetic tree manually using the following distance matrices:
1. TABLE 21.4
  A B C D E
  B 8
  C 18 18
  D 18 18 10
  E 18 18 10 4
  F 20 20 20 20 20
2. TABLE 21.5
  A B C D E
  A 0
  B 4 0
  C 8 8 0
  D 8 8 6 0
  E 8 8 6 2 0
2. What are the merits and demerits of the UPGMA method of phylogenetic tree construction?
3. Explain in detail why ultrametric data are needed for UPGMA tree construction.
4. Under what circumstances do we prefer the UPGMA tree? How do you interpret the results of the UPGMA tree?
5. Suppose we have morphological data from which similarity and distance matrices can be constructed. Can we use such a distance matrix for the construction of a UPGMA tree? Justify your answer.

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	ABC	D
D	10
E	10	8

Table of Contents for CHAPTER 21: Construction of Phylogenetic Tree: Unweighted‐Pair Group Method with Arithmetic Mean (UPGMA)

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