Expectation Maximization Algorithm In Phylogenetic Tree Construction

Phylogenetics studies the evolutionary relationships between species. The basic idea of phylogenetics is to compare their characteristic of species, and through the analysis it concluded that the species having similar characteristic be near in genetics. The purposes of phylogenetic studies are (1) to reconstruct the correct genealogical ties between organisms and (2) to estimate the time of divergence (or distance, or branch) between organisms since they last shared a common ancestor.The nucleotide substitution models in phylogenetics usually assume that evolutions of sequences have neither missing nor censored, which is hard to be satisfied in fact. Facing to the fact above, this dissertation will use EM algorithm to estimate parameters, to construct a fine phylogenetic tree of the sequences which have the same length after deletions and insertions. Main points of this paper are as follows: (1) to explain emphatically and to prove the Jukes-Cantor Model, Kimura Model and the relationships of them; (2) to construct and to prove, using EM algorithm, the theorems of estimating best branches of DNA sequences having censored data for Jukes-Cantor Model under the conditions of rooted tree and unrooted tree respectively; (3) to construct and to prove, using EM algorithm, another three theorems of estimating best parameters of DNA sequences having censored data for Kimura Model under the conditions of rooted tree and unrooted tree.