Zhang Yanling, Fu Feng, Wu Te, Xie Guangming, Wang Long
Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China.
Sci Rep. 2013;3:2021. doi: 10.1038/srep02021.
Amounts of empirical evidence, ranging from microbial cooperation to collective hunting, suggests public goods produced often nonlinearly depend on the total amount of contribution. The implication of such nonlinear public goods for the evolution of cooperation is not well understood. There is also little attention paid to the divisibility nature of individual contribution amount, divisible vs. non-divisible ones. The corresponding strategy space in the former is described by a continuous investment while in the latter by a continuous probability to contribute all or nothing. Here, we use adaptive dynamics in finite populations to quantify and compare the roles nonlinearity of public-goods production plays in cooperation between these two contribution mechanisms. Although under both contribution mechanisms the population can converge into a coexistence equilibrium with an intermediate cooperation level, the branching phenomenon only occurs in the divisible contribution mechanism. The results shed insight into understanding observed individual difference in cooperative behavior.
从微生物合作到集体狩猎，大量的经验证据表明，公共物品的产生通常非线性地依赖于贡献的总量。这种非线性公共物品对合作进化的影响尚未得到很好的理解。对于个体贡献量的可分性本质，即可分与不可分的贡献量，也很少有人关注。前者相应的策略空间由连续投资来描述，而后者则由贡献全部或不贡献的连续概率来描述。在这里，我们使用有限种群中的自适应动力学来量化和比较公共物品生产的非线性在这两种贡献机制之间的合作中所起的作用。尽管在两种贡献机制下，种群都可以收敛到具有中间合作水平的共存平衡状态，但分支现象只出现在可分贡献机制中。这些结果为理解观察到的合作行为中的个体差异提供了见解。
