Qin Bo-Wei, Sheng Wenbo, Qian Xuzhe, Kurths Jürgen, Hastings Alan, Lai Ying Cheng, Lin Wei
Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China.
Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China.
PNAS Nexus. 2025 Jul 14;4(7):pgaf214. doi: 10.1093/pnasnexus/pgaf214. eCollection 2025 Jul.
It was once believed that large ecosystems with random interactions are unstable, limiting their complexity. Thus, large community size or numerous interactions are rare in nature. Later, a strict hierarchical complexity was revealed: competitive and mutualistic communities have the least complexity, followed by random ones, and then predator-prey communities. Recently, a hierarchy of recovery times for ecosystems with identical complexity was found, influenced by discrete time delays. A key question is whether this hierarchical complexity holds under noninstantaneous interactions. We surprisingly show that it does not. Specifically, the complexity of predator-prey communities is significantly affected by time delays, reordering the hierarchy at a critical threshold. These changes exhibit nonmonotonic behavior with continuous time delays, another realistic interaction type. We validated our findings in various realistic ecosystems. Our results indicate that incorporating factors like time delays and their appropriate forms can lead to correct and even deeper understanding about complexity of large ecosystems and other biophysical systems.
人们曾经认为，具有随机相互作用的大型生态系统是不稳定的，这限制了它们的复杂性。因此，大型群落规模或大量相互作用在自然界中很少见。后来，一种严格的层次复杂性被揭示出来：竞争和互利共生群落的复杂性最低，其次是随机群落，然后是捕食者 - 猎物群落。最近，发现了具有相同复杂性的生态系统的恢复时间层次结构，它受到离散时间延迟的影响。一个关键问题是，这种层次复杂性在非瞬时相互作用下是否成立。我们令人惊讶地发现它并不成立。具体而言，捕食者 - 猎物群落的复杂性受到时间延迟的显著影响，在一个临界阈值处重新排列层次结构。这些变化在连续时间延迟（另一种现实的相互作用类型）下表现出非单调行为。我们在各种现实生态系统中验证了我们的发现。我们的结果表明，纳入时间延迟等因素及其适当形式可以导致对大型生态系统和其他生物物理系统的复杂性有正确甚至更深入的理解。
