发表机构
National Research Council; BluEye Simulations; Universidad Carlos III de Madrid（国家研究委员会; BluEye Simulations; 马德里卡洛斯三世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过三个耦合逻辑方程复现阿克苏姆智能体模型，揭示合作虽可短暂提升种群峰值，但最终平衡不受影响，且缺乏反搭便车措施时合作崩溃并丧失环境收益。
AI 中文摘要
合作行为可以改善环境质量，而自私的背叛行为则会破坏共享资源。在最近一项关于阿克苏姆文明的基于智能体的研究中（Vasellini 等人，2025），一群智能体在重建的地形上移动并参与局部公共品博弈，当博弈被启用时，种群增长更快且峰值更高，但从长远来看，最终稳定在未启用博弈时的相同种群水平。在此，我们表明这种行为并不依赖于该模型的众多规则。我们建立了一个由三个耦合离散时间方程组成的理论生态模型，其中两个子种群按逻辑斯蒂方式增长，并共享一个承载能力，该承载能力在合作者数量足够多时上升，否则下降。在不拟合任何参数的情况下，这些方程重现了模拟的定性行为：初始激增、阻尼振荡和稳定；当合作机制激活时出现更高的峰值；以及最终不依赖于该机制的平衡。合作可以在一个过渡时期内自我维持，但在缺乏缓解搭便车行为的措施时，合作会崩溃，其产生的环境收益也随之消失。
英文摘要
Cooperative behavior can improve environmental quality, whereas selfish defection can degrade shared resources. In a recent agent-based study of the Aksum civilization (Vasellini et al., 2025), a population of agents moving over a reconstructed landscape and playing a local Public Goods Game grew faster and peaked higher when the game was enabled, but settled, in the long run, at the same population level as when it was not. Here we show that this behavior does not depend on the many rules of that model. We develop a theoretical ecological model of three coupled discrete-time equations, in which two sub-populations grow logistically and share a carrying capacity that rises when cooperators are sufficiently numerous and decays otherwise. Without fitting any parameter to the simulation, the equations reproduce its qualitative behavior: an initial boom, damped oscillations, and stabilization; a higher peak when the cooperative mechanism is active; and a final equilibrium that does not depend on it. Cooperation can be self-sustained for a transient period, but in the absence of measures that mitigate free-riding it collapses, and the environmental gains it produced are lost with it.
Comments14 pages, 3 figures, 2 tables. To be submitted soon
