Evolutionary stability in Lotka-Volterra systems
Evolutionary stability in Lotka-Volterra systems
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DOI：
10.1016/s0022-5193(03)00032-8
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发表时间：
2003-05-21
影响因子：
2
通讯作者：
Garay, J
中科院分区：
文献类型：
--
作者：
Cressman, R;Garay, J
种群生态学的Lotka-Volterra模型假设每个物种中的所有个体行为相同，并将其与进化博弈论的行为进化模型相结合。在所得到的单态情形下，分析了当被每个物种的突变表型扰动时，驻留Lotka-Volterra系统的稳定性条件。我们发展了进化生态稳定性的概念，称为单态进化稳定生态平衡，它包含了Maynard Smith对单个物种进化稳定策略的原始定义作为特例。启发式地，这一概念断言，居民生态系统必须是稳定的，以及“静止密度面”上的表型进化。这些条件也被证明是分析多态模型中稳定性问题的核心，该模型允许每个物种中有任意多个表型，特别是当物种数量较少时。数学技巧来自动力系统理论，包括线性化、中心流形和莫尔查诺夫定理。(C)2003爱思唯尔科学有限公司。保留所有权利。
The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem. (C) 2003 Elsevier Science Ltd. All rights reserved.