25.1 INTRODUCTION

The minimum evolution (ME) method is a distance‐based method, and simple enough to avoid the least‐squares approach to determine the optimal tree with minimum branch length. The ME method described here is different from the maximum parsimony (MP) method in its approach. ME identifies the number of sites differing among the input sequences to produce the distance matrix, and ME yields an unrooted tree from the given set of sequences.

25.2 OBJECTIVE

To construct a phylogenetic tree using the ME method from a given set of nucleotide sequences.

25.3 PROCEDURE

Start with four (an arbitrarily chosen number) nucleotide sequences:

1. First, the sequences (S1–S4) are to be aligned:

   	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	18	19	20
   S1	C	G	T	A	G	G	A	T	A	G	A	C	A	T	A	G	G	C
   S2	C	G	A	A	G	G	G	T	A	G	A	C	G	T	A	G	G	C
   S3	C	A	A	A	G	G	A	G	A	G	C	T	A	T	G	G	G	C
   S4	C	C	A	A	G	G	A	C	A	G	G	T	A	T	T	G	G	C

2. Next, determine the distance matrix by summing the number of different residues (designated by S) between each pair of sequences:

   	S1	S2	S3	S4
   S1	0
   S2	3	0
   S3	6	7	0
   S4	6	7	4	0

3. The phylogenetic tree is constructed from the distances between sequence‐pairs, indicating the difference between each pair of sequences:
   1. Just like UPGMA, the principle of ultrametric tree construction (assuming a molecular clock) is followed here. First, one needs to find out the sequence pairs (or taxa) with minimum distance (here, d(S1 – S2) = 3). Hence, S1 and S2 form a single cluster.
   2. The ultrametric three‐point condition is checked for the taxa: dxy <= max(dxz, dyz) when x, y and z are three taxa taken into consideration (Desper and Gascuel, 2005).
   3. Now, for four‐point condition, note that the sum of d(S1 – S2) + d(S3 – S4) <= d(S2 – S3) or d(S2 – S4). This implies that the two largest sums are equal (i.e., 7): d(S1 – S2) + d(S3 – S4) <= max{d(S1 – S3) + d(S2 – S4), d(S1 – S4) + d(S2 – S3)}
   4. The tree‐metric is thus constructed, and this enables one to place S1 and S2 as a cluster and S3 and S4 as another cluster.

25.3.1 Difference between minimum evolution and maximum parsimony methods (Figure 25.1)

25.4 INTERPRETATION OF THE ME TREE

Here, the ME tree is inferred, and the corresponding differences with the MP tree are shown.

ME is a distance‐based method that selects the unrooted tree based on optimality criteria, whereas MP is a discrete method that determines the branch length from the fit of the individual residue of sequence‐pairs to a tree.

The ME tree only specifies the number of differences (as distance) in a branch for each pair of sequence. However, the position‐specific differences are not indicated. MP identifies each site of difference between any pair of sequences and shows this in the respective branches.

25.5 QUESTIONS

1. 1. Construct a phylogenetic tree using the following homologous partial sequences by the ME method:

   > Bbu

   MASFRVKETVCPRTSQQPLEQCDFKENG

   > BtaTV4

   MTSFTVKETVCPRTSPQPPEQCDFKENG

   > BtaTV2

   MTSFTVKETVCPRTSPQPPEQCDFKENG

   > BtaTV1

   MVSFRVKETDCPRTSQQPLEQCDFKENG

   > BtaTV3

   MVSFRVKETDCPRTSQQPLEQCDFKENG

2. 2. Construct a phylogenetic tree using this set of peptide sequences (ME method):

   > Bbu

   NELQSVRRFRPRRPRLPRPRPRPLPL

   > BtaTV4

   NELQSVR‐FRP‐PIRRPPIRP‐‐‐PF

   > BtaTV2

   NELQSVRRIRPRPPRLPRPRPRPLPF

   > BtaTV1

   NELQSVRRIRPRPPRLPRPRPRPLPF

   > BtaTV3

   NELQSVR‐FRP‐PIRRPPIRP‐‐‐PF

3. 3. Now compare these two phylogenetic trees and explain what are the possible reasons for their differences, even though the source sequences are the same but from different portions of the peptide sequences.
4. 4. Enumerate the differences between ME and MP trees. Also, explain the conditions when these two algorithms are best suited.
5. 5. Discuss the assumptions and the practicality of the assumptions of the ME algorithm.