Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur 741 246, West Bengal, India.
Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India.
Phys Rev E. 2017 Oct;96(4-1):042202. doi: 10.1103/PhysRevE.96.042202. Epub 2017 Oct 9.
Understanding the influence of the structure of a dispersal network on the species persistence and modeling a realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems was studied [M. D. Holland and A. Hastings, Nature (London) 456, 792 (2008)NATUAS0028-083610.1038/nature07395], where it was shown that a randomization of the structure of a dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power law. To explore the effects of power-law coupling, we take a realistic ecological model, namely, the Rosenzweig-MacArthur model in each patch (node) of the network of oscillators, and show that the coupled system is driven from synchrony to asynchrony with an increase in the power-law exponent. Moreover, to understand the relationship between species persistence and variations in power-law exponent, we compute a correlation coefficient to characterize cluster formation, a synchrony order parameter, and median predator amplitude. We further show that smaller metapopulations with fewer patches are more vulnerable to extinction as compared to larger metapopulations with a higher number of patches. We believe that the present work improves our understanding of the interconnection between the random network and the deterministic network in theoretical ecology.
理解扩散网络的结构如何影响物种的持久性，并对自然界中真实的物种扩散进行建模，这是空间生态学的两个核心问题。[M. D. 霍兰德和 A. 黑斯廷斯，《自然》（伦敦）456,792 (2008)NATUAS0028-083610.1038/nature07395]研究了有利于相互作用的生态系统持续存在的真实扩散结构，结果表明，通过聚类、延长暂态动力学和种群波动幅度，对猎物和捕食者的扩散网络结构进行元胞自动机模型中的随机化会增加物种的持久性。相比之下，在本文中，我们表明，如果物种的扩散遵循由距离依赖幂律控制的长程相互作用，那么在具有确定性网络拓扑的元胞自动机模型中也可以有利于异步和延长暂态动力学。为了探索幂律耦合的影响，我们采用了一个真实的生态模型，即在网络振荡器的每个斑块（节点）中的罗森茨威格-麦克阿瑟模型，并表明，随着幂律指数的增加，耦合系统从同步驱动到异步。此外，为了理解物种持久性与幂律指数变化之间的关系，我们计算了一个相关系数来表征聚类形成、同步阶参数和平均捕食者幅度。我们进一步表明，与具有更高斑块数量的较大元胞自动机相比，具有较少斑块的较小元胞自动机更容易灭绝。我们相信，这项工作提高了我们对理论生态学中随机网络和确定性网络之间相互联系的理解。
