Sharp thresholds limit the benefit of defector avoidance in cooperation on networks

Ashkaan K. Fahimipour, Fanqi Zeng, Martin Homer, Arne Traulsen, Simon A. Levin, Thilo Gross

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Article numbere2120120119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number33
StatePublished - Aug 16 2022

All Science Journal Classification (ASJC) codes

  • General


  • cooperation
  • dispersal
  • game
  • metacommunity
  • network


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