Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, Zurich CH-8057, Switzerland.
Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, Zurich CH-8057, Switzerland.
J Theor Biol. 2019 Jan 7;460:56-63. doi: 10.1016/j.jtbi.2018.10.018. Epub 2018 Oct 6.
Cooperative interactions constitute the backbone of many biological and social systems. Since cooperation is prone to exploitation, these systems must incorporate mechanisms that prevent the spreading of defective behaviors. One such mechanism is modularity, i.e., the tendency of a social network to be organized in modules, where individuals within a module tend to interact strongly among themselves while avoiding interacting with individuals from other modules. This structure allows cooperation to prevail by having modules of cooperative individuals with a limited exposure to defectors. To address the rate and shape of the effect of modularity on the resilience of cooperation, here we study a variant of the Prisoner's Dilemma on modular networks. Our simulations reveal a sharp transition between a resilient and a vulnerable regime as modularity exceeds a critical threshold. By using a simplified mathematical model, we show that the observed threshold is equivalent to the epidemic threshold found in a certain class of SIR models. This allows us to derive an explicit condition under which a cooperative society is expected to be resilient to invasive defectors.
合作互动构成了许多生物和社会系统的骨干。由于合作容易受到剥削，这些系统必须包含防止缺陷行为传播的机制。其中一种机制是模块性，即社会网络倾向于组织成模块的趋势，其中模块内的个体往往在彼此之间强烈互动，同时避免与来自其他模块的个体互动。这种结构通过具有有限暴露于破坏者的合作个体的模块来允许合作占主导地位。为了解决模块性对合作弹性的影响的速度和形状，我们在这里研究了囚徒困境在模块化网络上的变体。我们的模拟显示，当模块性超过临界阈值时，合作弹性和脆弱性之间存在明显的转变。通过使用简化的数学模型，我们表明观察到的阈值与 SIR 模型的特定类中发现的传染病阈值等效。这使我们能够得出一个明确的条件，根据该条件，合作社会有望对入侵破坏者具有弹性。
