在进化动力学中,理解合作行为如何在自私行为具有优势的情况下持续存在,仍是核心挑战之一。经典的公共品困境模型预测背叛者将占据主导,但自然系统与社会系统却常能维持合作。我们研究了一类定义在复杂网络上的生态-进化公共品博弈,其中合作者与背叛者的扩散速率不同。当孤立系统处于以背叛者为主导的共存状态时,若背叛者的扩散速率快于合作者,则会引发对称性破缺相变,从而形成局域化的合作者簇。在异质性网络中,连接度更高的节点显著更倾向于呈现合作主导状态。基于节点度的平均场约化支持该结论:网络连接度调控一种正比于节点度的有效耦合强度,由此产生分岔,将背叛者主导态与合作态分离开来。我们还通过多稳态分析解释了为何并非所有枢纽节点均呈现合作行为。这些结果揭示了非对称迁移能力与异质性连接性如何协同促进结构化种群中的合作演化。
Understanding how cooperation persists despite the advantage of selfish behavior remains a central challenge in evolutionary dynamics. Classical models of public goods dilemmas predict dominance of defectors, yet natural and social systems often sustain cooperation. We study an eco-evolutionary public goods game on complex networks where cooperators and defectors diffuse at different rates. When the isolated system is in a defector-dominated coexistence regime, faster dispersal of defectors than cooperators leads to a symmetry-breaking transition that produces localized clusters of cooperators. In heterogeneous networks, nodes with higher connectivity become significantly more likely to exhibit cooperative dominance. A degree-based mean-field reduction supports this result by showing that network connectivity controls an effective coupling strength proportional to node degree, thereby producing a bifurcation that separates defector-dominated and cooperative states. We also address why not all hubs become cooperative by means of a multistability analysis. These results reveal how asymmetric mobility and heterogeneous connectivity jointly promote cooperation in structured populations.