This paper considers consumer-resource systems, where the consumer moves on a fully-connected patch network and behaves like an agent. Using graph-theoretical method and dynamical systems theory, we show global equilibrium stability in the system. Analysis on the equilibrium demonstrates that when the dispersal rate is small, the effect of network topology is the result of the effect of each path in isolation. It is shown that varying network topology could lead to persistence and/or increase of the consumer. Moreover, agent-based selection on a network would make the network evolve to an evolutionary stable topology, where any small deviation to it will not lead to the increase of species. Our results have potential application in constructing ecological corridors and planning network topology under evolution.

中文翻译：

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消费者资源系统中网络拓扑结构对物种扩散和进化的影响


本文考虑了消费者资源系统，其中消费者在完全连接的修补网络上移动，其行为类似于代理。使用图论方法和动力系统理论，我们展示了系统中的全局平衡稳定性。对平衡的分析表明，当扩散速率较小时，网络拓扑的效果是每条路径孤立效果的结果。结果表明，不同的网络拓扑结构可能会导致持久性和/或使用者的增加。此外，网络上基于代理的选择将使网络进化为进化稳定的拓扑结构，其中任何微小的偏差都不会导致物种的增加。我们的结果在构建生态廊道和规划演化下的网络拓扑结构方面具有潜在的应用价值。