Bioinformatics Algorithms: Techniques and Applications

38 GRAPH THEORETICAL APPROACHES
3.3 RECONSTRUCTING PHYLOGENIES
Consider a set of taxa, where each taxon is represented by a vector of attributes, the
so-called characters. We assume that every character can take one of a finite number
of states and the set of taxa evolved from a common ancestor through changes of
states of the corresponding characters. For example, the set of taxa can be described
by columns in multiple sequence alignment of protein sequences. In this case, each
column in the alignment is a character that can assume one of twenty possible states.
Parsimony methods seek a phylogenetic tree that explains the observed characters
with the minimum number of character changes along the branches of the tree.
In our working example for this section, the set of taxa includes eight species
shown in Fig. 3.4a; each species is described by two binary characters. As there
FIGURE 3.4 A set of eight species: Anopheles gambiae (Ag), Arabidopsis thaliana (At),
Caenorhabditis elegans (Ce), Drosophila melanogaster (Dm), Homo sapiens (Hm), Plasmodium
falciparum (Pf), Saccharomyces cerevisiae (Ag), and Saccharomyces pombe (Sp). (a)
The species are described by binary characters that correspond to the presence (value of 1) or
absence (value of 0) of introns. This is truncated data limited to just two introns (105 and 256)
out of about 7236 from the study of Rogozin et al. [59]. (b) A phylogenetic tree: the leaves
are the species in the set and are labeled with the input character states; the internal nodes are
ancestral species and are labeled with the inferred character states. This particular tree requires
three character changes , which are marked with solid bars on the corresponding edges.(c) The
character overlap graph. There are four vertices, one vertex per character state, 105 (state “1”
of the character “intron 105”), −105 (state “0” of the character “intron 105”), 256 (state “1” of
the character “intron 256”), and −256 (state “0” of the character “intron 256”). Two vertices
are connected by an edge if corresponding character states are observed together in some taxon.
The edge (105, −256), for example, is due to species Ag and Dm.