Phylogenetic Tree Reconstruction: Geometric Approaches - Mathematical Concepts and Methods in Modern Biology - page 307

FIGURE 10.1
(A, (B,C));

is shown
explicitly; instead, vertical lines are used to indicate that a branching event occurs.
Shrinking these vertical edges to points would produce the nodes that would be com-
monly shown in a mathematical graphical representation of a tree. This is a common
difference between rooted trees as often represented in biology, and trees in mathe-
matical graph theory. Also, if a tree is unrooted, it is common to represent it in Newick
format by arbitrarily picking a root. In this case, still, drawing programs may neglect
to display interior vertices; they are to be inferred at a branching point. (This will be
seen in Exercise 10.1 below.)
Exercise 10.1.

Note that neither the root nor the parent node of the cherry { B , C }

1. Obtain the graph in Example 10.1 yourself, as follows:

a. Go to the link “TreeDyn” in the list “Tree Viewers” under the heading “Online
Phylogeny Programs” at the bottom of the homepage of Phylogeny.fr at
http://www.phylogeny.fr/ , or similarly from the pop-up menu for
“TreeDyn” that appears under “Tree Viewers” when mousing over the head-
ing “Online Programs” in the bar across the top of the Phylogeny.fr homepage.
b. In the available textbox at the top of the “TreeDyn” page, type (A,(B,C));
click the “Submit” button, and await the output.
c. Once a picture of a tree is displayed, scroll down the page to “Tree Style,”
and change from the default option “Phylogram” to the option “Cladogram.”
The program will automatically redraw the graph.

2. Compare the result of part (1) with the original drawing (produced by “Phy-
logram”), and with the figure in Example 10.1 provided above. How do they
differ?
3. Replace (A,(B,C)); by (A,(C,B)); in parts (1)-(2) with the “Cladogram”
setting as above. Describe how the output differs from Example 10.1 . Note that
you can restart “TreeDyn,” or more easily, after completing any drawing, you
can click on the “Data and Settings” tab at the top of the page to return to the
data you originally input into the textbox, and edit it.
4. Draw a rooted tree on three leaves A .

5. Draw an unrooted tree by inputing (A,(B,C)); but selecting “Radial (by
Drawtree)” under the “Tree Style” option. What, if anything, changes when the
letters A

, B , C with cherry { A , B }

, B , and C are permuted in the Newick input?