Research On A Number Of Problems Of The Nucleotide Substitution Model

Since Darwin’s era, building phylogenetic tree (performancing out the evolutionaryrelationships between species in the form of tree) has become an important topic in thebiological study. Since the1980s, scholars mainly use modern bioinformatics tools toreconstruct the evolutionary tree. In the new method of constructing evolutionary tree, thefirst step is to select the appropriate nucleotide replacement model or amino acid substitutionmodel. Therefore, the choices of nucleotide substitution model directly affect thereasonableness of the constructed phylogenetic tree. Under this premise, some properties ofthe nucleotide substitution model were studied in this paper. The main contents includeseveral aspects as follow:1． The first chapter summarizes the commonly used phylogenetic tree building processof several nucleotide substitution models and the distance measures, briefly introduced theprogress of nucleotide substitution model and distance. Summed up the problems andlimitations of these models and distance measures.2． In the second chapter the changing processes of the frequencies of the four kinds ofnucleotide with the generations change under the Equal-input model and the Tamura modelwhich are more complicated nucleotide substitution models are discussed, so that the propertyof the entropy of a sequence could be got. The theoretical demonstrate is done through theLagrange Multiplier Method, and a series of computer simulations of the processes of thevariation of the nucleotide and the entropy of the DNA sequence is done in Mathematicaenvironment. If the mutation in the DNA sequence occur under the Equal-input model or theTamura model, the frequencies of the four kinds of nucleotide tends to equilibrium and theentropy of the sequence tends to the maximum. The nucleotide mutations maintain theirentropy and species evolve in the direction of biodiversity increasing.3． In the third chapter, we briefly introduced the transition/transversion dynamic model,and on this basis, two new nucleotide substitution models were presented. For the first model,we gave the function of the frequency changing of the four kinds of nucleotides. Thefrequencies of the nucleotide in this model is not monotonous tends to balance frequency, butthere is a shock phenomenon. Therefore, we hypothesized that the model reflects the realevolution of the law better, so that it can better fit the data. In addition, we give estimation ofthe three kinds of distance. They are p distance, distance and the selecting evolutionary distance. For the second model, we are inspired by the transition/transversion dynamic model.The model divided the transition frequency into two parts. With the spectral decompositionmethod, we gave the solution of the kinetic equation. But when we estimate the distance, wefound that the simultaneous equations were so complext that we could not directly obtain theanalytical solution.4． The fourth chapter put forward a new idea for solving the unrestricted model. Theunrestricted model unified the existed model. Since it was proposed, it was concerned bymany scholars, but due to too many free parameters, solving the problem is a difficult.Therefore progress to the study of the model is very small. We discussed the solution to themodel in seven cases and solved the model with a computer-aided method.5． The fifth chapter is a summary of the previous chapters. In this chapter, we brieflysummarize the problems still existed in studying the nucleotide substitution model andevolutionary distance and the direction of future research.