Choudhary Anshul, Sinha Sudeshna
Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli PO 140 306, Punjab, India.
PLoS One. 2015 Dec 28;10(12):e0145278. doi: 10.1371/journal.pone.0145278. eCollection 2015.
We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric connectivity matrix J, with fraction 1 - C of zero entries, where C reflects the over-all connectivity of the system. The non-zero elements of J are drawn from a Gaussian distribution with mean μ and standard deviation σ. The signs of the elements Jij reflect the nature of density-dependent interactions, such as predatory-prey, mutualism or competition, and their magnitudes reflect the strength of the interaction. In this study we try to uncover the broad features of the inter-species interactions that determine the global robustness of this network, as indicated by the average number of active nodes (i.e. non-extinct species) in the network, and the total population, reflecting the biomass yield. We find that the network transitions from a completely extinct system to one where all nodes are active, as the mean interaction strength goes from negative to positive, with the transition getting sharper for increasing C and decreasing σ. We also find that the total population, displays distinct non-monotonic scaling behaviour with respect to the product μC, implying that survival is dependent not merely on the number of links, but rather on the combination of the sparseness of the connectivity matrix and the net interaction strength. Interestingly, in an intermediate window of positive μC, the total population is maximal, indicating that too little or too much positive interactions is detrimental to survival. Rather, the total population levels are optimal when the network has intermediate net positive connection strengths. At the local level we observe marked qualitative changes in dynamical patterns, ranging from anti-phase clusters of period 2 cycles and chaotic bands, to fixed points, under the variation of mean μ of the interaction strengths. We also study the correlation between synchronization and survival, and find that synchronization does not necessarily lead to extinction. Lastly, we propose an effective low dimensional map to capture the behavior of the entire network, and this provides a broad understanding of the interplay of the local dynamical patterns and the global robustness trends in the network.
我们考虑一个多物种群落，将其建模为一个种群的复杂网络，其中链接由一个随机非对称连接矩阵(J)给出，(J)有(1 - C)比例的零元素，(C)反映了系统的整体连通性。(J)的非零元素取自均值为(\mu)、标准差为(\sigma)的高斯分布。元素(J_{ij})的符号反映了密度依赖相互作用的性质，如捕食 - 被捕食、互利共生或竞争，其大小反映了相互作用的强度。在本研究中，我们试图揭示决定该网络全局鲁棒性的种间相互作用的广泛特征，这由网络中活跃节点（即未灭绝物种）的平均数量以及反映生物量产量的总种群数量来表示。我们发现，随着平均相互作用强度从负变为正，网络从完全灭绝的系统转变为所有节点都活跃的系统，并且对于增大的(C)和减小的(\sigma)，这种转变会变得更加尖锐。我们还发现，总种群数量相对于乘积(\mu C)呈现出明显的非单调缩放行为，这意味着生存不仅取决于链接的数量，还取决于连接矩阵的稀疏性和净相互作用强度的组合。有趣的是，在(\mu C)为正的中间窗口内，总种群数量最大，这表明过少或过多的正相互作用对生存都是有害的。相反，当网络具有中等净正连接强度时，总种群数量水平是最优的。在局部层面，我们观察到在相互作用强度的均值(\mu)变化时，动态模式有显著的定性变化，范围从周期为(2)的反相簇和混沌带，到不动点。我们还研究了同步与生存之间的相关性，发现同步不一定导致灭绝。最后，我们提出了一个有效的低维映射来捕捉整个网络的行为，这为理解网络中局部动态模式和全局鲁棒性趋势之间的相互作用提供了广泛的认识。
