Detecting the Collapse of Cooperation in Evolving Networks

Matteo Cavaliere (1) , Guoli Yang (1) , Vincent Danos (2, 1) , Vasilis Dakos (3)

1 Edin. - University of Edinburgh
2 ANTIQUE - Analyse Statique par Interprétation Abstraite
3 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

The sustainability of biological, social, economic and ecological communities is often determined by the outcome of social conflicts between cooperative and selfish individuals (cheaters). Cheaters avoid the cost of contributing to the community and can occasionally spread in the population leading to the complete collapse of cooperation. Although such collapse often unfolds unexpectedly, it is unclear whether one can detect the risk of cheater's invasions and loss of cooperation in an evolving community. Here, we combine dynamical networks and evolutionary game theory to study the abrupt loss of cooperation with tools for studying critical transitions. We estimate the risk of cooperation collapse following the introduction of a single cheater under gradually changing conditions. We observe an increase in the average time it takes for cheaters to be eliminated from the community as the risk of collapse increases. We argue that such slow system response resembles slowing down in recovery rates prior to a critical transition. In addition, we show how changes in community structure reflect the risk of cooperation collapse. We find that these changes strongly depend on the mechanism that governs how cheaters evolve in the community. Our results highlight novel directions for detecting abrupt transitions in evolving networks. The sustainability of many biological, social, economic, and ecological communities is determined by the interplay between individual actions and collective dynamics 1. The successful performance of a community is often based on the cooperative attitude of individuals that pay a personal cost to distribute general benefits 2. Nonetheless, although cooperation favors in general the success of a community, it can also facilitate the appearance of cheaters who take advantage of cooperators, spread in the community, and may even cause its collapse 1. The failure of cooperation in the presence of cheaters has been observed in many systems at different scales. For instance, cooperating cells of Pseudomonas fluorescens build biofilms that help them to grow better, while mutant cells (cheaters)-that do not produce similar adhesive factors-take advantage of the existing structure in order to spread and to eventually cause the colony to collapse 3,4. Fruiting bodies formed under starvation by cooperative cells of Myxococcus xanthus can also be invaded by cheaters leading to the disruption of the fruiting body structure and forcing the cooperative survivors to reinvest in reconstruction 5. At a different scale and in a different context shifts in cooperation and cheating have been debated to be causes of economic crises 6 , as well as causes for the "tragedy" of common pool resources, (e.g., from fisheries to forests) 7,8. In all these systems a long-standing question has been to understand the mechanisms that allow cooperators to resist the reproductive advantage of selfish cheating individuals 2. Among the many theoretical and experimental studies on the maintenance of cooperation 2,9-11 , scenarios where strategies co-evolve with population structure 12 are of particular interest as they show how structural properties in the population can affect the evolution of cooperation 10-13. For instance, it has been shown that not only the number of cheaters in the community is important, but also how and to whom cheaters are connected 14 , as well as the mechanisms employed by the players to choose their interaction partners 15-17. The interplay between the way individuals are connected and the overall prosperity of a system 1,18 endogenously determines either the formation or the sudden collapse of cooperative communities 1. Despite our relative good understanding of the conditions that promote the failure of cooperation in a community, it is still difficult to predict whether the appearance of a cheater will cause the eventual loss of cooperation 7,8. This is because it is hard to identify the underlying conditions that increase the risk of collapse in practice. Thus, it is crucial to develop alternative ways for detecting the risk of collapse of cooperation in a structurally evolving community. Recent work has suggested that generic patterns in the dynamics of a system can be used to infer proximity to abrupt and unexpected changes termed critical transitions 19. These dynamical patterns are generic in the sense

Domaines: Informatique [cs]

Matteo Cavaliere, Guoli Yang, Vincent Danos, Vasilis Dakos. Detecting the Collapse of Cooperation in Evolving Networks. Scientific Reports, 2016, 6 (1), ⟨10.1038/srep30845⟩. ⟨hal-01976359⟩