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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 Generalized Lotka–Volterra equation ： ウィキペディア英語版 Generalized Lotka–Volterra equation The generalized Lotka–Volterra equations are a set of equations which are more general than either the competitive or predator-prey examples of Lotka–Volterra types.〔 〕 They can be used to model direct competition and trophic relationships between an arbitrary number of species. Their dynamics can be analysed analytically to some extent. This makes them useful as a theoretical tool for modeling food webs. However, they lack features of other ecological models such as predator preference and nonlinear functional responses, and they cannot be used to model mutualism without allowing indefinite population growth. The Generalised Lotka-Volterra equations model the dynamics of the populations $x\_1,\; x\_2,\; \backslash dots$ of $n$ biological species. Together, these populations can be considered as a vector $\backslash mathbf$. They are a set of ordinary differential equations given by :$$ \frac = x_i f_i(\mathbf), where the vector $\backslash mathbf$ is given by :$$ \mathbf = \mathbf + A\mathbf, where $\backslash mathbf$ is a vector and A is a matrix known as the community matrix. ==Meaning of parameters== The generalised Lotka-Volterra equations can represent competition and predation, depending on the values of the parameters, as described below. They are less suitable for describing mutualism. The values of $\backslash mathbf$ are the intrinsic birth or death rates of the species. A positive value for $r\_i$ means that species i is able to reproduce in the absence of any other species (for instance, because it is a plant), whereas a negative value means that its population will decline unless the appropriate other species are present (e.g. a herbivore that cannot survive without plants to eat, or a predator that cannot persist without its prey). The values of the matrix A represent the relationships between the species. The value of $a\_$ represents the effect that species j has upon species i. The effect is proportional to the populations of both species, as well as to the value of $a\_$. Thus, if both $a\_$ and $a\_$ are negative then the two species are said to be in direct competition with one another, since they each have a direct negative effect on the other's population. If $a\_$ is positive but $a\_$ is negative then species i is considered to be a predator (or parasite) on species j, since i's population grows at j's expense. Positive values for both $a\_$ and $a\_$ would be considered mutualism. However, this is not often used in practice, because it can make it possible for both species' populations to grow indefinitely. Indirect negative and positive effects are also possible. For example, if two predators eat the same prey then they compete indirectly, even though they might not have a direct competition term in the community matrix. The diagonal terms $a\_$ are usually taken to be negative (i.e. species i's population has a negative effect on itself). This self-limitation prevents populations from growing indefinitely. 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「Generalized Lotka–Volterra 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.