翻訳と辞書 Words near each other ・ Evolutionary developmental biology ・ Evolutionary developmental psychology ・ Evolutionary developmental psychopathology ・ Evolutionary developmental robotics ・ Evolutionary dynamics ・ Evolutionary ecology ・ Evolutionary economics ・ Evolutionary educational psychology ・ Evolutionary epistemology ・ Evolutionary ethics ・ Evolutionary fauna ・ Evolutionary game theory ・ Evolutionary Games Infographic Project gallery ・ Evolutionary Governance Theory ・ Evolutionary grade ・ Evolutionary graph theory ・ Evolutionary guidance media ・ Evolutionary history of life ・ Evolutionary history of plants ・ Evolutionary Humanism ・ Evolutionary ideas of the Renaissance and Enlightenment ・ Evolutionary informatics ・ Evolutionary Informatics Lab ・ Evolutionary invasion analysis ・ Evolutionary landscape ・ Evolutionary leadership theory ・ Evolutionary linguistics ・ Evolutionary logic ・ Evolutionary Map of the Universe ・ Evolutionary medicine Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Evolutionary graph theory ： ウィキペディア英語版 Evolutionary graph theory Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. That the underlying topology can substantially affect the results of the evolutionary process is seen most clearly in a paper by Erez Lieberman, Christoph Hauert and Martin Nowak. In evolutionary graph theory, individuals occupy vertices of a weighted directed graph and the weight wi j of an edge from vertex ''i'' to vertex ''j'' denotes the probability of ''i'' replacing ''j''. The weight corresponds to the biological notion of fitness where fitter types propagate more readily. One property studied on graphs with two types of individuals is the ''fixation probability'', which is defined as the probability that a single, randomly placed mutant of type A will replace a population of type B. According to the ''isothermal theorem'', a graph has the same fixation probability as the corresponding Moran process if and only if it is isothermal, thus the sum of all weights that lead into a vertex is the same for all vertices. Thus, for example, a complete graph with equal weights describes a Moran process. The fixation probability is : $\backslash begin$ \rho_M = \frac } \end where ''r'' is the relative fitness of the invading type. Graphs can be classified into amplifiers of selection and suppressors of selection. If the fixation probability of a single advantageous mutation $\backslash rho\_G$ is higher than the fixation probability of the corresponding Moran process $\backslash rho\_M$ then the graph is an amplifier, otherwise a suppressor of selection. One example of the suppressor of selection is a linear process where only vertex ''i-1'' can replace vertex ''i'' (but not the other way around). In this case the fixation probability is $\backslash rho\_G\; =\; 1/N$ (where ''N'' is the number of vertices) since this is the probability that the mutation arises in the first vertex which will eventually replace all the other ones. Since for all ''r'' greater than 1, this graph is by definition a suppressor of selection. Evolutionary graph theory may also be studied in a dual formulation, as a coalescing random walk. Also evolutionary games can be studied on graphs where again an edge between ''i'' and ''j'' means that these two individuals will play a game against each other. Closely related stochastic processes include the voter model, which was introduced by Clifford and Sudbury (1973) and independently by Holley and Liggett (1975), and which has been studied extensively. ==Bibliography== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Evolutionary graph theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.