Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication. (21st January 2021)

• Record Type: Journal Article
• Authors: Sun, T. Anthony; Hilker, Frank M.
• Is Part Of: Journal of theoretical biology. Volume 509(2021)
• Publication Date: 2021-01-21
• Subjects: Social-ecological system -- Coupled human-environment system -- Make-or-break dynamics -- Replicator dynamics -- Logit best-response dynamics -- Oscillations; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2020.110491
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: We consider two social-ecological models with the same ecological part. We represent the social part using either the replicator or a best-response dynamics. The two models' equilibria differ in number and in stability. The two models become more similar to each other when agents behave more rationally. The replicator dynamics tends to allow for make-or-break dynamics. Abstract: Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.