Martin Éloi, Lessard Sabin
Département de mathématiques et de statistique, Université de Montréal, Montréal, QC H3C 3J7, Canada.
Département de mathématiques et de statistique, Université de Montréal, Montréal, QC H3C 3J7, Canada.
J Theor Biol. 2024 Sep 7;592:111891. doi: 10.1016/j.jtbi.2024.111891. Epub 2024 Jun 28.
We investigate conditions for the evolution of cooperation in social dilemmas in finite populations with assortment of players by group founders and general payoff functions for cooperation and defection within groups. Using a diffusion approximation in the limit of a large population size that does not depend on the precise updating rule, we show that the first-order effect of selection on the fixation probability of cooperation when represented once can be expressed as the difference between time-averaged payoffs with respect to effective time that cooperators and defectors spend in direct competition in the different group states. Comparing this fixation probability to its value under neutrality and to the corresponding fixation probability for defection, we deduce conditions for the evolution of cooperation. We show that these conditions are generally less stringent as the level of assortment increases under a wide range of assumptions on the payoffs such as additive, synergetic or discounted benefits for cooperation, fixed cost for cooperation and threshold benefit functions. This is not necessarily the case, however, when payoffs in pairwise interactions are multiplicatively compounded within groups.
我们研究了在有限种群的社会困境中合作进化的条件，其中群体创建者对参与者进行分类，并给出了群体内合作与背叛的一般收益函数。在不依赖于精确更新规则的大种群规模极限下使用扩散近似，我们表明，当合作被表示一次时，选择对其固定概率的一阶效应可以表示为合作者和背叛者在不同群体状态下直接竞争所花费的有效时间的时间平均收益之差。将此固定概率与其在中性条件下的值以及背叛的相应固定概率进行比较，我们推导出了合作进化的条件。我们表明，在关于收益的广泛假设下，例如合作的加性、协同或贴现收益、合作的固定成本和阈值收益函数，随着分类水平的增加，这些条件通常不那么严格。然而，当群体内成对相互作用的收益以乘法方式复合时，情况不一定如此。
