Károlyi Adél, Scheuring István
Department of Zoology, University of Veterinary Medicine, Budapest, Rottenbiller utca 50, Hungary.
University of Potsdam, Institute of Biochemistry and Biology, 14469 Potsdam, Germany.
J Evol Biol. 2024 Apr 14;37(4):451-463. doi: 10.1093/jeb/voae029.
The threshold public goods game is one of the best-known models of non-linear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this article, we develop a dynamical model of a general N-player game in which there is no deme structure: Individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of individuals. We show that in the deterministic limit, the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e., coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, but below a critical density cooperators abruptly disappear from the population. Our numerical investigations show that weak density fluctuations enhance cooperation, while strong fluctuations suppress it.
阈值公共品博弈是最著名的非线性公共品困境模型之一。当假定种群遵循所谓的结构化群落模型时，合作者和背叛者通常会在这种博弈中共存。在本文中，我们开发了一个一般N人博弈的动力学模型，其中不存在群落结构：个体与随机选择的邻居相互作用，选择在随机选择的个体对之间进行。我们表明，在确定性极限下，该模型中的动力学导致与结构化群落模型中相同的复制者动力学，即，即使种群完全充分混合，在阈值公共品博弈中合作者和背叛者共存也是典型的。我们扩展该模型以研究密度依赖性和密度波动对动力学的影响。我们通过分析和数值模拟表明，降低种群密度会增加合作者的平衡频率，直到该策略固定下来，但低于临界密度时，合作者会突然从种群中消失。我们的数值研究表明，弱密度波动会增强合作，而强波动会抑制合作。
