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Persistence of mutualisms with bidirectional interactions in a two-species system

机译：两物种系统中具有双向交互作用的共生关系的持久性

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摘要

In Lotka-Volterra equations (LVEs) of mutualisms, population densities of mutualists will increase infinitely if the mutualisms between them are strong, which is called the divergence problem. In order to avoid the problem, a mutualism system of two species is analyzed in this work. The model is derived from reactions on lattice and has a form similar to that of LVEs. Population densities of species will not increase infinitely because of spatial limitation on the lattice. Stability analysis of the model demonstrates basic mechanisms by which the mutualisms lead to coexistence/extinction of the species. When in coexistence, intermediate mutualistic effect is shown to lead to the maximal density in certain parameter ranges, while a strong or weak mutualistic effect is not so good. Furthermore, the stability analysis exhibits that extremely strong/weak mutualisms will result in extinction of one/both species. (C) 2015 Elsevier B.V. All rights reserved.
机译：在共生主义的Lotka-Volterra方程（LVE）中，如果互惠主义者之间的相互关系很强，则互助主义者的人口密度将无限增加，这称为发散问题。为了避免这个问题，本文分析了两种物种的互惠体系。该模型源自晶格上的反应，其形式类似于LVE。由于晶格的空间限制，物种的种群密度不会无限增加。该模型的稳定性分析证明了相互影响导致物种共存/灭绝的基本机制。当共存时，在某些参数范围内，中间的互惠效应显示出最大密度，而强或弱的互惠效应却不是那么好。此外，稳定性分析表明，极强/弱的共生关系将导致一种/两种物种的灭绝。 （C）2015 Elsevier B.V.保留所有权利。

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