# Network Structures of Multiple Sequences Induced by Mutation

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## Abstract

As fast multiple alignment (MA) algorithms become a reality, analyses and applications of their results become the central problem of genome research. In this chapter, we introduce the general methods of constructing the phylogenetic tree from multiple alignments, such as UPGMA, neighbor-joining, the maximum parsimony method, maximum-likelihood method and Bayesian methods. We then discuss the network structure theory of the multi-sequences induced by mutations. Using the distance matrix and the mutation information, we find the network structure of multi-sequences. Furthermore, we introduce the orthogonalization theorem for a mutation network. We may easily obtain the mutation relations for data structures among a multiple sequence from the network structure and the orthogonalization procedure of a mutation network. Finally, we give some examples of the network structure and explain the basic steps needed to analyze these multi-sequences.