https://scholars.lib.ntu.edu.tw/handle/123456789/626751
標題: | Gene-mating dynamic evolution theory: fundamental assumptions, exactly solvable models and analytic solutions | 作者: | Wang, Juven C JIUNN-WEI CHEN |
關鍵字: | Blood types and biological physics; Chaotic dynamics; Exactly solvable models; Hardy–Weinberg manifold; Population genetics and evolutionary biology; Time-dependent nonlinear differential equations | 公開日期: | 六月-2020 | 出版社: | SPRINGER | 卷: | 139 | 期: | 2 | 起(迄)頁: | 105 | 來源出版物: | Theory in biosciences = Theorie in den Biowissenschaften | 摘要: | Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. A model is studied to describe a large class of systems within population genetics. We focus on a single locus, any number of alleles in a two-gender dioecious population. Our governing equations are time-dependent continuous differential equations labeled by a set of parameters, where each parameter stands for a population percentage carrying certain common genotypes. The full parameter space consists of all allowed parameters of these genotype frequencies. Our equations are uniquely derived from four fundamental assumptions within any population: (1) a closed system; (2) average-and-random mating process (mean-field behavior); (3) Mendelian inheritance; and (4) exponential growth and exponential death. Even though our equations are nonlinear with time-evolutionary dynamics, we have obtained an exact analytic time-dependent solution and an exactly solvable model. Our findings are summarized from phenomenological and mathematical viewpoints. From the phenomenological viewpoint, any initial parameter of genotype frequencies of a closed system will eventually approach a stable fixed point. Under time evolution, we show (1) the monotonic behavior of genotype frequencies, (2) any genotype or allele that appears in the population will never become extinct, (3) the Hardy-Weinberg law and (4) the global stability without chaos in the parameter space. To demonstrate the experimental evidence for our theory, as an example, we show a mapping from the data of blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions. From the mathematical viewpoint, our highly symmetric governing equations result in continuous global stable equilibrium solutions: these solutions altogether consist of a continuous curved manifold as a subspace of the whole parameter space of genotype frequencies. This fixed-point manifold is a global stable attractor known as the Hardy-Weinberg manifold, attracting any initial point in any Euclidean fiber bounded within the genotype frequency space to the fixed point where this fiber is attached. The stable base manifold and its attached fibers form a fiber bundle, which fills in the whole genotype frequency space completely. We can define the genetic distance of two populations as their geodesic distance on the equilibrium manifold. In addition, the modification of our theory under the process of natural selection and mutation is addressed. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626751 | ISSN: | 1431-7613 | DOI: | 10.1007/s12064-020-00309-3 |
顯示於: | 物理學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。