After graduating from college, Kimura began the theoretical work of genetics. At that time, Muhara was studying the nuclear-nuclear relationship. Through many backcross experiments, the chromosomes of one variety can be replaced by those of another variety. Muyuan asked the wood to study how many chromosomes can be left in the female parent after a certain number of backcrosses. Kimura's mathematical talent is once again displayed. He constructed a finite differential-integral equation and obtained the probability distribution relationship between the number of generations and the number of chromosomes. Later, this result was published in Cytology, which was Kimura's first paper.

After graduating from Kyoto University on 1947, Kimura read more than 60 pages of Wright's paper "The Evolution of Mendel Groups" published on 193 1, and learned that random drift in small groups can be handled by mathematical methods. But because mathematics is too theoretical, Kimura can't understand this paper, which aroused his desire to learn. Kimura listened in on some courses offered by the Department of Mathematics, often asked the mathematics professor for advice, and also found many mathematics monographs for self-study. It took him more than a year to understand the main part of Wright's paper. Kimura 1949 read two papers published by Wright 1945 and 1949 when he entered the National Institute of Genetics. Wright used a concise partial differential equation-"Fokker-Planck equation" to deal with random drift in finite groups.

After that, Kimura continued to study advanced mathematics and continued to follow Wright's footsteps. Wright once put forward the "island model" of group division. He believes that it is individual deletion mutations that play a role in evolution, rather than beneficial mutations in combination. In some small populations, the combination of beneficial genes is fixed by random sampling. The whole large population constitutes the gene pool of the population. For each small population, the effect of each generation migration is like random sampling from the whole gene pool. Kimura thinks that the influence of geographical distance should be considered, and migration only occurs between adjacent small groups. Kimura's model is "stepping stone model" The later work of his model was done by him and Weiss.

From 1954 to 1956, the cooperation between Kimura and Dr. Crowe was the happiest and most fruitful period in his academic career. He gave a complete solution of the random drift process of neutral alleles in a finite population, and obtained the final fixed probability formula of any dominant mutant alleles in a finite population. On this basis, he wrote his doctoral thesis "Diffusion Model in Population Genetics".

After returning to China, Dr. Kimura completed two monographs on population genetics, among which "Introduction to Population Genetics Theory" co-authored with Crocker is a reference book with high academic value. Since then, Kimura has published many valuable papers. But before 1967, his paper was particularly mathematical and difficult to read. At that time, most scholars thought that there were few neutral alleles, if any. Kimura believes that once the random treatment of gene frequency changes becomes important, his work will be valuable and of great significance to genetics.

Kimura met Mahler, the founder of American radiogenetics in 1955, and became interested in the achievements of molecular genetics. Kimura hopes to introduce the theory of population genetics into the study of molecular genetics. 1967, Akiko Ota, a female scholar with profound mathematical skills, joined Kimura's research group and finally realized Kimura's wish. Kimura showed Ota the book Evolutionary Genes and protein, and estimated the substitution rate of amino acids during evolution. Ota's works satisfy Kimura. When Kimura calculated the base substitution rate of mammalian genome from the amino acid substitution rate, he was surprised to find that base substitution occurred about every two years from the whole genome. According to the concept of natural selection cost, Haldane came to the conclusion that each mutation replacement takes about 300 generations on average, which is a hundred times different. Kimura has always worshipped Haldane, believing that the concept of natural selection cost can be used to estimate the number of individuals who adapt to evolution and are eliminated by natural selection. Later, Kimura called the price of natural selection replacement load. But once it is used to calculate the evolutionary consequences at the molecular level, the amount of individual elimination is unreasonable. Obviously, at the molecular level, most mutations caused by base substitution have not been eliminated by natural selection, and they are neutral to natural selection. The maintenance of neutral alleles is achieved through the balance between mutation input and random deletion. In this way, Kimura and Crowe's research on the number of alleles that can be maintained by a limited population in their early years found a factual basis in molecular evolution, and the stochastic process theory provided a mathematical means for molecular evolution research.

Neutral mutation-random drift hypothesis

The "neutral mutation-random drift hypothesis" of Kimura's molecular evolution theory, that is, the main content of the neutral theory, is that at the molecular level, most of the evolution and variation within a species are not caused by natural selection, but the genetic drift of mutant alleles that are neutral or close to neutral. From the neutral theory, we can draw the conclusion that the evolution rate remains constant in every position every year. The rich polymorphism of isozyme and other homologous proteins shows that these biomacromolecules have the same high-level structure, all of which can play their biological functions well, and none of them is superior to other molecules. That is, at the molecular level, favorable mutations are not considered. Pseudogenes are genes that have lost their functions and have not been eliminated by natural selection at all. Facts have proved that the base substitution of pseudogenes is indeed infinite, and its evolution speed is equal to the mutation speed of molecules.

Molecular evolution has five characteristics: (1) For each biomacromolecule, as long as the tertiary structure and function of the molecule are basically unchanged, the evolution rate of each evolution route represented by mutation substitution will remain approximately constant at every position every year. (2) The evolution rate of molecules or molecular fragments with less functions is higher than that of molecules or molecular fragments with more important functions. (3) In the process of molecular evolution, the mutation with less damage to the existing structure and function of the molecule has a higher substitution rate than the mutation with greater damage. (4) Gene replication usually occurs before genes with new functions appear. (5) Random fixation of neutral or slightly harmful mutations in obviously harmful selection and selection is more frequent than positive Darwinian selection of obviously beneficial mutations. Among the above five features, (1) and (5) are the most basic features. 1983, Kimura comprehensively summarized the neutral theory and wrote the monograph "Neutral Theory of Molecular Evolution".

The neutral theory, which dares to contend with Darwin's theory of natural selection, has caused an uproar in academic circles, and its influence is far beyond the scope of population genetics and even evolutionary biology. With the development of molecular genetics, the neutral theory is more and more correct and effective. It broke the situation that comprehensive evolution dominated the field of population genetics, and also made Kimura climb to a new height, from a population geneticist who emphasized mathematics to an evolutionary biologist with theoretical achievements.