Kumar Dinesh, Gupta Jatin, Raha Soumyendu
Department of Computational and Data Sciences, Indian Institute of Science, Bangalore 560012, India.
Proc Math Phys Eng Sci. 2019 Mar;475(2223):20180524. doi: 10.1098/rspa.2018.0524. Epub 2019 Mar 13.
The loss of dispersal connections between habitat patches may destabilize populations in a patched ecological network. This work studies the stability of populations when one or more communication links is removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modelled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between habitat patches. A reaction-diffusion system on the graph models the dynamics of the predator-prey system over the patched ecological network. The graph Laplacian's Fiedler value, which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that, when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses the criterion for both the local and global stability of populations in partitioned networks. A heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and is illustrated with examples.
栖息地斑块之间扩散连接的丧失可能会使斑块状生态网络中的种群不稳定。这项工作研究了当一条或多条通信链路被移除时种群的稳定性。一个例子是确定一条穿过包含斑块状集合种群网络的斑块状森林的高速公路的走向。这个问题被建模为寻找由集合种群网络诱导的图的稳定割集问题，其中节点代表栖息地斑块，加权边模拟栖息地斑块之间的扩散。图上的反应扩散系统模拟了斑块状生态网络上捕食者 - 猎物系统的动态。图拉普拉斯算子的菲德勒值表示图的连通性，它被证明会影响集合种群的稳定性。我们表明，当菲德勒值足够大时，有可能在不破坏网络动态稳定性的情况下移除边。我们给出了一个详尽的图划分过程，它适用于较小的网络，并使用了划分网络中种群局部和全局稳定性的标准。对于较大的网络，提出了一种启发式图二分算法，该算法保留了菲德勒值的预先指定下限，并通过示例进行了说明。
