Phylogenetic Trees' Construction Based On Stochastic Differential Equation And Structural EM Algorithm

In life sciences, people constantly explore evolutionary relationships among species, the phylogenetic tree is one of the best methods in all methods which describe this evolutionary relationships. With the completion of genomes sequencing of many species and the advance of microarray technology, we begin to possess a wealth of valuable biological data , and discover that some homomorphic genes can represent the species'feature. So at the same time people construct the phylogenetic trees based on the gene sequences of species. From 1980s ,many methods of phylogenetic trees'construction in molecule level have been raised. Most of methods are based on the reasonable definition of distances among gene sequences and certain hypothesis under the distance.In Chapter 3, the evolution is mainly affected not only by the the evolution law itself, but also by a variety of internal and external factors.This affect makes that evolution expresses some fluctuation characteristics. We approximatively consider that this kind of fluctuation is Brownian motion.Therefore,we use the means of stochastic differential equation(SDE) to build a SDE model between the evolution of sequences. After setting a limit to the drift and diffusion functions, we give the solution of this equation by Gibbs sampling.In Chapter 4, based on the hypothesis of neutral evolutionary theory and the evolutions between sequences being independent of each other, we consider the following question: if we only know a part of the distances among sequences for n DNA sequences, how do we construct the most valuable phylogenetic tree. We give the structural EM algorithm of the construction of phylogenetic trees after making use of the theory of structural EM algorithm and introduce the method to deal with Q function in this algorithm.