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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク replicator equation ： ウィキペディア英語版 replicator equation In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness function to incorporate the distribution of the population types rather than setting the fitness of a particular type constant. This important property allows the replicator equation to capture the essence of selection. Unlike the quasispecies equation, the replicator equation does not incorporate mutation and so is not able to innovate new types or pure strategies. == Equational forms == The most general continuous form is given by the differential equation :$\backslash dot\; =\; x\_i\; (f\_i(x)\; -\; \backslash phi(x)),\; \backslash quad\; \backslash phi(x)\; =\; \backslash sum\_^$ where $x\_i$ is the proportion of type $i$ in the population, $x=(x\_1,\; \backslash ldots,\; x\_n)$ is the vector of the distribution of types in the population, $f\_i(x)$ is the fitness of type $i$ (which is dependent on the population), and $\backslash phi(x)$ is the average population fitness (given by the weighted average of the fitness of the $n$ types in the population). Since the elements of the population vector $x$ sum to unity by definition, the equation is defined on the n-dimensional simplex. The replicator equation assumes a uniform population distribution; that is, it does not incorporate population structure into the fitness. The fitness landscape does incorporate the population distribution of types, in contrast to other similar equations, such as the quasispecies equation. In application, populations are generally finite, making the discrete version more realistic. The analysis is more difficult and computationally intensive in the discrete formulation, so the continuous form is often used, although there are significant properties that are lost due to this smoothing. Note that the continuous form can be obtained from the discrete form by a limiting process. To simplify analysis, fitness is often assumed to depend linearly upon the population distribution, which allows the replicator equation to be written in the form: :$\backslash dot=x\_i\backslash left(\backslash left(Ax\backslash right)\_i-x^TAx\backslash right),$ where the payoff matrix $A$ holds all the fitness information for the population: the expected payoff can be written as $\backslash left(Ax\backslash right)\_i$ and the mean fitness of the population as a whole can be written as $x^TAx$. 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「replicator equation」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.