Schonmann Roberto H, Boyd Robert
Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, USA.
School of Human Evolution and Social Change, Arizona State University, Tempe, AZ, USA Santa Fe Institute, Santa Fe, NM, USA
Philos Trans R Soc Lond B Biol Sci. 2016 Feb 5;371(1687):20150099. doi: 10.1098/rstb.2015.0099.
Humans cooperate in large groups of unrelated individuals, and many authors have argued that such cooperation is sustained by contingent reward and punishment. However, such sanctioning systems can also stabilize a wide range of behaviours, including mutually deleterious behaviours. Moreover, it is very likely that large-scale cooperation is derived in the human lineage. Thus, understanding the evolution of mutually beneficial cooperative behaviour requires knowledge of when strategies that support such behaviour can increase when rare. Here, we derive a simple formula that gives the relatedness necessary for contingent cooperation in n-person iterated games to increase when rare. This rule applies to a wide range of pay-off functions and assumes that the strategies supporting cooperation are based on the presence of a threshold fraction of cooperators. This rule suggests that modest levels of relatedness are sufficient for invasion by strategies that make cooperation contingent on previous cooperation by a small fraction of group members. In contrast, only high levels of relatedness allow the invasion by strategies that require near universal cooperation. In order to derive this formula, we introduce a novel methodology for studying evolution in group structured populations including local and global group-size regulation and fluctuations in group size.
人类在由互不相关的个体组成的大群体中进行合作，许多作者认为这种合作是由有条件的奖励和惩罚来维持的。然而，这种制裁系统也能稳定各种各样的行为，包括对双方都有害的行为。此外，大规模合作很可能起源于人类谱系。因此，理解互利合作行为的演变需要了解支持这种行为的策略在罕见时何时能够增加。在这里，我们推导出一个简单的公式，该公式给出了在n人重复博弈中，有条件合作在罕见时增加所需的亲缘关系。这条规则适用于广泛的收益函数，并假设支持合作的策略基于一定比例的合作者的存在。这条规则表明，适度的亲缘关系水平足以让那些使合作取决于一小部分群体成员先前合作的策略得以入侵。相比之下，只有高度的亲缘关系才能让那些要求近乎普遍合作的策略得以入侵。为了推导出这个公式，我们引入了一种新颖的方法来研究群体结构化种群中的进化，包括局部和全局群体大小调节以及群体大小的波动。
