Phylogenetic Tree Building Methods - Bioinformatics: A Swiss Perspective - page 350

be replaced by a leaf and hence decrease the complexity of the tree build-
ing. This subtree replacement can be repeated many times either until the
tree is small enough or until some other criteria based on the magnitude
of E S is met.

4.3.2. Subtree substitution

The only remaining part is to replace the subtree S with a new leaf in such
a way that all of the distance and variance information of S is preserved.
Let R * be the leaf that replaces S (which we will view as positioned at the
root of the subtree S ).

S X

A X

R

R *

Then,

d - T

2

Â

,

AX AR

d = s

XR * XR *

2

s

AS ΠAX

Where

= Ê

ˆ
˜

1

2

Â

.

s

Á

XR *

2

s

AS ΠAX

Once the tree with S replaced by R * is resolved (maybe recursively), R *
is replaced by S .

5. Outlook

In this chapter, we have given an overview of phylogenetic tree building
methods and have delved into the ones that optimize a score. In doing
so, we have focused solely on the construction of trees. A second goal
after the construction is to provide confidence statements about the con-
structed trees. From a statistical point of view, the trees are estimates and
as such have to be viewed as random variables. One difficulty is that a tree