Department of Physics, <a href="https://ror.org/01easw929">Inha University</a>, Incheon 22212, Korea.
School of Computational Sciences, <a href="https://ror.org/041hz9568">Korea Institute for Advanced Study</a>, Seoul 02455, Korea.
Phys Rev Lett. 2024 Nov 8;133(19):198402. doi: 10.1103/PhysRevLett.133.198402.
Understanding the behaviors of ecological systems is challenging given their multifaceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully connected structures assumed in these previous studies are not realistic, as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the fully interacting systems, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.
考虑到生态系统的多方面复杂性，理解其行为具有挑战性。为此，动力平均场理论研究了具有随机相互作用的洛特卡-沃尔泰拉动力学等理论模型，以深入了解生物多样性和稳定性如何取决于相互作用强度的随机性等基本原理。然而，正如大量经验数据所揭示的那样，这些先前研究中假设的全连接结构并不现实。我们推导出了一个通用公式，用于在任意度分布（相互作用邻居的数量）下的丰度分布，这导致了物种的与度相关的丰度模式。值得注意的是，与完全相互作用的系统相比，随着社区在异质相互作用结构中变得合作，幸存物种的数量可以减少。因此，我们的研究表明，正确考虑种间相互作用结构的异质性对于理解大型生态系统中的多样性是必不可少的，并且我们的一般理论框架可以应用于更广泛的相互作用多体系统。
