Modelling co-evolution of resource feedback and social network dynamics in human-environmental systems

TL;DR

This paper develops a co-evolutionary framework for human-environment systems in which knowledge feedback and signed social networks influence the sustainability of common-pool resources. It combines logistic resource dynamics with binary agent strategies on networks, analyzed via Monte Carlo simulations and macroscopic rate equations across three variants: NS, QBS, and EBS. The work reveals that knowledge feedback alone can sustain CPRs, but social interactions can either help or hinder sustainability depending on network degree and topology, with a critical mean degree marking a depletion-to-repletion transition and an absorbing-active phase shift in social dynamics. It also introduces a polarization metric and demonstrates robustness across network types, highlighting hubs’ role in promoting defection and underscoring the importance of network structure in resource governance.

Abstract

Games with environmental feedback have become a crucial area of study across various scientific domains, modelling the dynamic interplay between human decisions and environmental changes, and highlighting the consequences of our choices on natural resources and biodiversity. In this work, we propose a co-evolutionary model for human-environment systems that incorporates the effects of knowledge feedback and social interaction on the sustainability of common pool resources. The model represents consumers as agents who adjust their resource extraction based on the resource's state. These agents are connected through social networks, where links symbolize either affinity or aversion among them. The interplay between social dynamics and resource dynamics is explored, with the system's evolution analyzed across various network topologies and initial conditions. We find that knowledge feedback can independently sustain common pool resources. However, the impact of social interactions on sustainability is dual-faceted: it can either support or impede sustainability, influenced by the network's connectivity and heterogeneity. A notable finding is the identification of a critical network mean degree, beyond which a depletion/repletion transition parallels an absorbing/active state transition in social dynamics, i.e., individual agents and their connections are/are not prone to being frozen in their social states. Furthermore, the study examines the evolution of the social network, revealing the emergence of two polarized groups where agents within each community have the same affinity. Comparative analyses using Monte-Carlo simulations and rate equations are employed, along with analytical arguments, to reinforce the study's findings. The model successfully captures how information spread and social dynamics may impact the sustanebility of common pool resource.

Figures (14)

• Figure 1: Knowledge Feedback: consumers’ adaptation to environmental fluctuations. (A) Cooperators (white) are more likely to change their behavior in resource-rich environments, while defectors (blue) do so in resource-poor environments. (B) The consumers with different strategies are shown interacting in binary states: positive (cooperators) and negative (defectors). The "social interactions" can have two types of "social link" states: positive (solid) or negative (dashed). The combination of two nodes and connecting link is termed pair-connection, and the sign of each pair-connection is determined by multiplying the sign of constitute components. Three negative pair-connection on the left tend to become positive pair-connection on the right to increase the consumers’ satisfaction.
• Figure 2: Three models that capture different complex human-environmental dynamics. The white (blue) circles represent cooperator (defector) and solid (dash) links represent positive (negative) connections. (A) A unified update rule is derived from the node dynamics of knowledge feedback without interaction (NS). (B) A unified update rule is derived from the interplay between the knowledge feedback and the quenched binary-state interactions, which we call (QBS). (C) A unified update rule results from the interplay between the node dynamics of knowledge feedback and the evolving binary-state social links, which we call (EBS). The pair-connections $a$, $c$ and $e$ denote negative social interactions, while the pairs $b$, $d$ and $f$ indicate positive social interactions. We illustrate here the social dynamical rules that transform nanegative interactions into positive interactions through node or link updates. $R^{\prime}$ is the normalized resource level. In this work, we have implemented a sequential update scheme.
• Figure 3: Stationary states of the normalized level of resources ${<R^{\prime}>}^{\text{st}}$ and the density of cooperators $<x>^{\text{st}}$ as functions of network mean degree $\mu$. (A) and (C) The QBS dynamics shows a transition from a depleted state to a repleted state as $\mu$ increases. (B) and (D) The EBS dynamics shows a similar transition. We compare two dynamics with networks of different sizes $N=40, 400, 4000$, at $(\hat{e}_C=0.9,\hat{e}_D=1.9)$. We show in all figures the results from the Monte-Carlo simulation and numerical integration of differential rate equations, labeled by MC and RE. The initial value of the density of cooperators, the fraction of positive links, and the normalization level of the resource are $x_0=0.25$ and $l_0=0.5$, and $R^{\prime}_0=\frac{2}{3}$, respectively (see Appendix. \ref{['Appendix_ic']}). The ${<R^{\prime}>}^{\text{st}}$ (in panel (A) and (B)) is insensitive to different initial values, as evident in Fig. \ref{['results_R_initi_R']}.
• Figure 4: (A)&(B) Jammed states of the quenched binary state dynamics (QBS) and (C)&(D) examples of absorbing configurations of the evolving binary state dynamics (EBS) on a finite system with extraction coefficients ($\hat{e}_C=0.9,\hat{e}_D=1.9$). The network has $N=40$ nodes and mean degree $\mu=4$ and $\mu=8$. The initial values are $x_0=0.25$, $l_0=0.5$ (see Appendix. \ref{['Appendix_ic']}), and $R^{\prime}_0=\frac{2}{3}$. For both case of QBS and EBS, the fraction of defectors (blue circles) decreases as the network connectivity increases.
• Figure 5: The temporal evolution of normalized resource level, $R^{\prime}$, cooperator density, $x$, and pair-connection densities $\rho_i$, for evolving dynamical binary interaction (EBS). The top panels show the results of the Monte-Carlo simulation of a single run on an Erdős-Rényi network with $N=4000$. The bottom panels show the results of the corresponding rate equations. Panels (A) and (D) represent the parameters leading to an absorbing phase, while panels (C) and (F) represent the parameters leading to an active phase. Panels (B) and (E) represent the parameters leading to the critical region where the value of ${R^{\prime}}^{st}$ in panel (B) of Fig. \ref{['results_R']} reaches the maximum value. The initial values for all dynamics are $x_0=0.25$, $l_0=0.5$ (see Appendix. \ref{['Appendix_ic']}), and $R^{\prime}_0=\frac{2}{3}$.