Ferreira Fernando Fagundes, Campos Paulo R A
Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, 03828-000 São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):014101. doi: 10.1103/PhysRevE.88.014101. Epub 2013 Jul 1.
In the present work we investigate the emergence of cooperation in a multilevel selection model that assumes limiting resources. Following the work by R. J. Requejo and J. Camacho [Phys. Rev. Lett. 108, 038701 (2012)], the interaction among individuals is initially ruled by a prisoner's dilemma (PD) game. The payoff matrix may change, influenced by the resource availability, and hence may also evolve to a non-PD game. Furthermore, one assumes that the population is divided into groups, whose local dynamics is driven by the payoff matrix, whereas an intergroup competition results from the nonuniformity of the growth rate of groups. We study the probability that a single cooperator can invade and establish in a population initially dominated by defectors. Cooperation is strongly favored when group sizes are small. We observe the existence of a critical group size beyond which cooperation becomes counterselected. Although the critical size depends on the parameters of the model, it is seen that a saturation value for the critical group size is achieved. The results conform to the thought that the evolutionary history of life repeatedly involved transitions from smaller selective units to larger selective units.
在本研究中，我们在一个假设资源有限的多层次选择模型中探究合作的出现。遵循R. J. 雷克霍和J. 卡马乔的研究[《物理评论快报》108, 038701 (2012)]，个体之间的相互作用最初由囚徒困境（PD）博弈支配。收益矩阵可能会受到资源可用性的影响而发生变化，因此也可能演变为非PD博弈。此外，假设种群被划分为多个群体，其局部动态由收益矩阵驱动，而群体间的竞争则源于群体增长率的不均匀性。我们研究单个合作者能够入侵并在最初由背叛者主导的种群中立足的概率。当群体规模较小时，合作受到强烈青睐。我们观察到存在一个临界群体规模，超过这个规模合作就会被反向选择。尽管临界规模取决于模型参数，但可以看到临界群体规模会达到一个饱和值。这些结果符合这样一种观点，即生命的进化历史反复涉及从较小的选择单位向较大的选择单位的转变。
