HomeworkMarch27

Homework Due April 3

Question 1

Phylogenetic Trees
Consider the following triangular distance matrix:

B C D E

A 14 14 6 10

B 4 14 14

C 14 14

D 10

•

You should provide the sequence of (increasingly smaller) triangular matrices that
define the distances between the nodes and combinations of nodes.

•

Transform your unrooted tree into a rooted ultrametric tree by suitably adding
the root.

•

Represent your tree using parenthesis

You may use the steps suggested in the following URL where an example is also fully
worked out:

http://linneus20.ethz.ch:8080/5_4_9.html

Solution

Sequence of Triangular Matrices

B C D E

A 14 14 6 10

B 4* 14 14

C 14 14

D 10

The asterisk indicates the minimal distance
Combine nodes B and C

The resulting matrix becomes

D E BC
A 6* 10 14

D 10 14

E 14

The minimal distance is now 6 indicating that one has to combine nodes A and D
The next triangular matrix becomes:

AD BC
E 10* 14

AD 14

Finally one combines E with AD obtaining

BC
EAD 14

The unrooted tree becomes:

B 2                                                         | 3 A
                    |                                       2AD |
                    | BC                                |                  | 3 D
                    |7 EAD  |
                    |                                       | 5 E
                    |
C 2

By choosing a root in the segment (BC EAD) at a distance 5 from node BC and a
distance 2 from EAD one obtains an ultrametric tree because the distance from any node
A,B,C,D, E to that root is always 7.
The parenthesis representation of the rooted tree is ((B C) (E (A D))

Question 2

Character Based
Perfect Phylogeny
Consider the following character matrix with 5 objects A, B, C, D, E and 7 characters
C1, C2, …, C7

Determine if the above corresponds to perfect phylogeny and draw the corresponding
character tree

Solution