Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures—a constant row sum in the interaction matrix—prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse—a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure—limiting the total interactions for each species—is biologically plausible.

中文翻译：

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物种相互作用限制增强了生态系统的稳定性

生态系统稳定性是理论和应用生物学的核心问题。动力系统理论可用于分析增长率、承载能力和物种相互作用模式如何影响生态系统的稳定性。对日益增加的复杂性的反应已经进行了广泛的研究，一般的结论是存在一个限制。虽然发生全球不稳定的稳定性存在复杂性限制，但如果系统完全可行（没有物种灭绝），崩溃很少会突然发生。事实上，当复杂性依次增加时，我们发现通用的反应是在全球崩溃之前经历多次单一物种灭绝。在本文中，我们通过数值模拟和理论预测的阐述来证明这一发现。我们探索了更多的生物相互作用模式，也许最重要的是，我们展示了受约束的相互作用结构——相互作用矩阵中的恒定行总和——防止了灭绝的发生。这使得生态系统在允许的复杂性方面更加强大，但这也意味着单一物种灭绝不会先于或预示着崩溃——与一般和普遍假设的情况相比，这是一种截然不同的行为。我们进一步认为，这种受约束的相互作用结构——限制了每个物种的总相互作用——在生物学上是合理的。但这也意味着单一物种灭绝不会先于或预示着崩溃——与一般和普遍假设的情况相比，这是一种截然不同的行为。我们进一步认为，这种受约束的相互作用结构——限制了每个物种的总相互作用——在生物学上是合理的。但这也意味着单一物种灭绝不会先于或预示着崩溃——与一般和普遍假设的情况相比，这是一种截然不同的行为。我们进一步认为，这种受约束的相互作用结构——限制了每个物种的总相互作用——在生物学上是合理的。