Traulsen Arne, Schuster Heinz Georg
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstrasse 40, 24098 Kiel, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046129. doi: 10.1103/PhysRevE.68.046129. Epub 2003 Oct 27.
Recently, Riolo et al. [Nature (London) 414, 441 (2001)] showed by computer simulations that cooperation can arise without reciprocity when agents donate only to partners who are sufficiently similar to themselves. One striking outcome of their simulations was the observation that the number of tolerant agents that support a wide range of players was not constant in time, but showed characteristic fluctuations. The cause and robustness of these tides of tolerance remained to be explored. Here we clarify the situation by solving a minimal version of the model of Riolo et al. It allows us to identify a net surplus of random changes from intolerant to tolerant agents as a necessary mechanism that produces these oscillations of tolerance, which segregate different agents in time. This provides a new mechanism for maintaining different agents, i.e., for creating biodiversity. In our model the transition to the oscillating state is caused by a saddle node bifurcation. The frequency of the oscillations increases linearly with the transition rate from tolerant to intolerant agents.
最近，里奥洛等人[《自然》（伦敦）414, 441 (2001)]通过计算机模拟表明，当主体仅向与自身足够相似的伙伴捐赠时，合作可以在没有互惠的情况下出现。他们模拟的一个显著结果是观察到，支持广泛参与者的宽容主体数量并非随时间恒定，而是呈现出特征性的波动。这些宽容潮的成因和稳健性仍有待探索。在此，我们通过求解里奥洛等人模型的一个最简版本来阐明这种情况。这使我们能够确定从不宽容主体到宽容主体的随机变化净盈余是产生这些宽容振荡的必要机制，这些振荡会在时间上分离不同的主体。这为维持不同主体，即创造生物多样性，提供了一种新机制。在我们的模型中，向振荡状态的转变是由鞍结分岔引起的。振荡频率随从宽容主体到不宽容主体的转变率线性增加。
