Institute of Marine Sciences, University of California, Santa Cruz, CA 95064.
Department of Computer Science, University of California, Davis, CA 95616.
Proc Natl Acad Sci U S A. 2022 Aug 16;119(33):e2120120119. doi: 10.1073/pnas.2120120119. Epub 2022 Aug 8.
Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.
考虑一个在栖息地斑块的空间网络上的合作博弈，其中如果玩家判断局部条件不利，他们可以在斑块之间重新定位。随着时间的推移，重新定位事件可能导致同质状态，即所有斑块都具有相同的合作者和背叛者的相对密度，或者可能导致自组织模式，其中一些斑块成为安全避难所，维持着较高的合作者密度。在这里，我们从数学上分析了这两种状态之间的转变。我们表明，一旦连接度达到某个阈值，安全避难所就会形成。这个阈值可以与斑块网络的结构，特别是与某些网络模式进行分析性的联系。令人惊讶的是，对背叛者宽容的回避策略可能对合作者最有利。我们的结果表明，在生态元社区模型中的合作博弈分析在数学上是可行的，并且有可能将宏观生态模式、行为进化和网络拓扑等主题联系起来。
