The Sum Maximum Likelihood Estimator Of The Phylogenetic Tree

The phylogenetic analysis is an important topic in bioinformatics.With the increasing molecular data,people pay more attention on the information in the molecular data.In a general way,we reconstruct the phylogenetic tree with the nucleotide sequences or the protein sequences.The maximum like-lihood method,the maximum parsimony method and the distance matrix method,all of them are the popular methods.The maximum likelihood method and the maximum parsimony method predict the phylogenetic tree directly based on the sequences.The distance matrix method predicts the phylogenetic tree based on the distance between the sequences,and the two sequences which have the least changes are treated as the "neighbors".All the methods aim to estimate the topology of the tree and the branch length of the tree,and we hope that they have the same result,but it can not be true.Among the methods,the maximum likelihood method is often more accurate.However,the maximum likelihood method needs to calculate the likelihood of every possible topology with different arrangements of the sequences.At the same time,the number of the topology structures to be analysed will be large with an increasing number of the sites.Repeating the procedure,there are such a vast number of calculations to be performed.It proved to be a NP hard question.In most cases,people can not get the global optimal estimator.However,we could get a good estimator using the heuris-tic algorithm.B.B.zhou et al improve the speed and the range of the search-ing through the parallel implementation of maximum likelihood methods for phylogennetic analysis.This thesis explores the question how to estimate the branch length with the sum maximum likelihood method.And we use the particle swarm optimization to chose the good branch lengths.Based on the geometry of the space of phylogenetic trees by Billera,that is,we treat every possible tree as a quadrant.e suppose that the procedure of the nucleotide substitution of the site along the same branch is a Markov chain.Under the assumption,we calculate the sum of the likelihood function of all the sites,and estimate the branch length.The phylogenetic tree means a lot to do other research of bioinformatic-s.It provides the basis for investigating the origin of species and the molecu-lar evolution,and then helps to explore the gene function.The phylogenetic analysis has guiding significance for the control of the virus or the diagnosis of the disease.Therefore it is meaningful to explore the method of estimat-ing the phylogenetic tree.