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

TL;DR

This paper analyzes how network structure influences cooperation and defector avoidance in spatial habitat models, revealing sharp thresholds for safe haven formation and the surprising benefits of forgiving strategies.

Contribution

It provides a mathematical analysis of cooperation dynamics on networks, linking network motifs to the emergence of safe havens and highlighting the role of forgiveness in defector avoidance.

Findings

Safe havens form once a network connectivity threshold is crossed.

The threshold is analytically linked to network motifs.

Forgiving defector avoidance strategies can be most beneficial.

Abstract

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.