Stone Lewi
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Victoria 3000, Australia.
Biomathematics Unit, Faculty of Life Sciences, Department of Zoology, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
Nat Commun. 2016 Sep 30;7:12857. doi: 10.1038/ncomms12857.
May's celebrated theoretical work of the 70's contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here May's random-matrix modelling approach is generalized to realistic large-scale webs of species interactions, be they structured by networks of competition, mutualism or both. Simple relationships are found to govern these otherwise intractable models, and control the parameter ranges for which biological systems are stable and feasible. Our analysis of model and real empirical networks is only achievable on introducing a simplifying Google-matrix reduction scheme, which in the process, yields a practical ecological eigenvalue stability index. These results provide an insight into how network topology, especially connectance, influences species stable coexistence. Constraints controlling feasibility (positive equilibrium populations) in these systems are found more restrictive than those controlling stability, helping explain the enigma of why many classes of feasible ecological models are nearly always stable.
梅在70年代著名的理论著作与既定范式相矛盾，它表明复杂性会导致生物系统的不稳定性。在这里，梅的随机矩阵建模方法被推广到现实的大规模物种相互作用网络，无论这些网络是由竞争网络、互利网络或两者共同构成。我们发现简单关系支配着这些原本难以处理的模型，并控制着生物系统稳定和可行的参数范围。只有引入一种简化的谷歌矩阵约简方案，我们才能对模型网络和实际经验网络进行分析，在此过程中产生了一个实用的生态特征值稳定性指数。这些结果为网络拓扑结构，尤其是连通性，如何影响物种稳定共存提供了见解。我们发现，控制这些系统可行性（正平衡种群）的约束条件比控制稳定性的约束条件更具限制性，这有助于解释为什么许多类可行的生态模型几乎总是稳定的这一谜团。
