# The physics of governance networks: critical transitions in contagion dynamics on multilayer adaptive networks with application to the sustainable use of renewable resources

## TL;DR

This paper models contagion and critical transitions in multilayer adaptive networks, applying it to sustainable resource governance, revealing how interaction timescales, adaptation rates, and taxation influence sustainability outcomes.

## Contribution

It introduces a multilayer adaptive network model for resource governance, analyzing how different governance structures and parameters affect sustainability and critical transitions.

## Key findings

- Sustainability favored by slow interaction timescales and high taxation rates.
- Trade-off observed between eco-dictatorship and polycentric governance in sustainability.
- Emergent critical transitions can be understood and approximated analytically.

## Abstract

Adaptive networks are a versatile approach to model phenomena such as contagion and spreading dynamics, critical transitions and structure formation that emerge from the dynamic coevolution of complex network structure and node states. Here, we study critical transitions in contagion dynamics on multilayer adaptive networks with dynamic node states and present an application to the governance of sustainable resource use. We focus on a three layer adaptive network model, where a polycentric governance network interacts with a social network of resource users which in turn interacts with an ecological network of renewable resources. We uncover that sustainability is favored for slow interaction timescales, large homophilic network adaptation rate (as long it is below the fragmentation threshold) and high taxation rates. Interestingly, we also observe a trade-off between an eco-dictatorship (reduced model with a single governance actor that always taxes unsustainable resource use) and the polycentric governance network of multiple actors. In the latter setup, sustainability is enhanced for low but hindered for high tax rates compared to the eco-dictatorship case. These results highlight mechanisms generating emergent critical transitions in contagion dynamics on multilayer adaptive network and show how these can be understood and approximated analytically, relevant for understanding complex adaptive systems from various disciplines ranging from physics and epidemiology to sociology and global sustainability science. The paper also provides insights into potential critical intervention points for policy in the form of taxes in the governance of sustainable renewable resource use that can inform more process-detailed social-ecological modeling.