Seppänen Anne, Parvinen Kalle
Department of Mathematics and Statistics, University of Turku, FIN-20014 , Turku, Finland,
Bull Math Biol. 2014 Dec;76(12):3070-87. doi: 10.1007/s11538-014-9994-y. Epub 2014 Sep 12.
Cooperation is surprisingly common in life despite of its vulnerability to selfish cheating, i.e. defecting. Defectors do not contribute to common resources but take the advantage of cooperators' investments. Therefore, the emergence and maintenance of cooperation have been considered irrational phenomena. In this study, we focus on plastic, quantitative cooperation behaviour, especially on its evolution. We assume that individuals are capable to sense the population density in their neighbourhood and adjust their real-valued investments on public goods based on that information. The ecological setting is described with stochastic demographic events, e.g. birth and death, occurring at individual level. Individuals form small populations, which further constitute a structured metapopulation. For evolutionary investigations, we apply the adaptive dynamics framework. The cost of cooperative investment is incorporated into the model in two ways, by decreasing the birth rate or by increasing the death rate. In the first case, density-dependent cooperation evolves to be a decreasing function of population size as expected. In the latter case, however, the density-dependent cooperative investment can have a qualitatively different form as it may evolve to be highest in intermediate-sized populations. Indeed, we emphasize that some details in modelling may have a significant impact on the results obtained.
尽管合作容易受到自私作弊（即背叛）的影响，但在生活中合作却出奇地普遍。背叛者不向公共资源做出贡献，却利用合作者的投入。因此，合作的出现和维持被认为是不合理的现象。在本研究中，我们关注可塑性的、定量的合作行为，尤其关注其进化。我们假设个体能够感知其周围的种群密度，并基于该信息调整其对公共物品的实际投入。生态环境通过个体层面发生的随机人口事件（如出生和死亡）来描述。个体形成小种群，这些小种群进一步构成一个结构化的集合种群。为了进行进化研究，我们应用自适应动力学框架。合作投入的成本通过两种方式纳入模型，一是降低出生率，二是提高死亡率。在第一种情况下，密度依赖型合作如预期那样演变为种群规模的递减函数。然而，在后一种情况下，密度依赖型合作投入可能具有质的不同形式，因为它可能在中等可能在中等规模种群中进化到最高水平。实际上，我们强调建模中的一些细节可能对所获得的结果产生重大影响。
