Requejo R J, Camacho J
Departament de Física, Universitat Autònoma de Barcelona, Campus UAB, E-08193 Bellaterra, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066112. doi: 10.1103/PhysRevE.85.066112. Epub 2012 Jun 11.
In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original structure of the interactions and allow for the survival of unconditional cooperators in well-mixed populations. Here, we present analytical simplified versions of two types of agent-based models recently published: one in which the limiting resource constrains the ability of reproduction of individuals but not their survival, and a second one where the limiting resource is necessary for both reproduction and survival. One finds that the analytical models display, with a few differences, the same qualitative behavior of the more complex agent-based models. In addition, the analytical models allow us to expand the study and identify the dimensionless parameters governing the final fate of the system, such as coexistence of cooperators and defectors, or dominance of defectors or of cooperators. We provide a detailed analysis of the occurring phase transitions as these parameters are varied.
在合作演化的研究中，通常假定资源限制仅仅是为了提供一个有限的种群规模。然而，最近基于主体的模型指出，资源限制可能会改变相互作用的原始结构，并使无条件合作者在完全混合的种群中得以生存。在此，我们给出最近发表的两种基于主体模型的解析简化版本：一种是有限资源限制个体的繁殖能力但不影响其生存，另一种是有限资源对于繁殖和生存都是必需的。人们发现，解析模型虽存在一些差异，但展现出了与更复杂的基于主体模型相同的定性行为。此外，解析模型使我们能够拓展研究范围，并确定控制系统最终命运的无量纲参数，例如合作者与背叛者的共存，或者背叛者或合作者的主导地位。随着这些参数的变化，我们对发生的相变进行了详细分析。
