[Paper Review] The role of the Allee effect in common-pool resource and its sustainability

Chengyi Tu, Fabio Menegazzo+2 more|arXiv (Cornell University)|May 2, 2024

Forest Management and PolicyEnvironmental Science3 citations

TL;DR

This paper introduces two coevolutionary models under replicator dynamics and knowledge feedback to study how the Allee effect—where resource growth rates depend on availability—affects sustainability in common-pool resource systems. It finds that the Allee effect induces bi-stability and critical transitions, leading to either sustainable or collapsed outcomes based on initial conditions, while knowledge feedback enhances system resilience and sustainability.

ABSTRACT

The management of common-pool resources is a complex challenge due to the risk of overexploitation and the tragedy of the commons. A novel framework has been introduced to address this issue, focusing on the coevolutionary relationship between human behavior and common-pool resources within a human-environment system. However, the impact of the Allee effect on the coevolution and its resource sustainability is still unexplored. The Allee effect, a biological phenomenon characterized by a correlation between resource availability and growth rate, is a fundamental attribute of numerous natural resources. In this paper, we introduce two coevolutionary models of resource and strategy under replicator dynamics and knowledge feedback by applying the Allee effect to the common-pool resources within human-environment system. These models encapsulate various facets of resource dynamics and the players' behavior, such as resource growth function, the extraction rates, and the strategy update rules. We find that the Allee effect can induce bi-stability and critical transition, leading to either sustainable or unsustainable outcomes depending on the initial condition and parameter configuration. We demonstrate that knowledge feedback enhances the resilience and sustainability of the coevolving system, and these results advances the understanding of human-environment system and management of common-pool resources.

Motivation & Objective

• To investigate the impact of the Allee effect on the coevolution of human behavior and common-pool resources within human-environment systems.
• To address the gap in understanding how biological phenomena like the Allee effect influence resource sustainability in socio-ecological systems.
• To examine how knowledge feedback mechanisms can improve resilience and sustainability in resource management under Allee dynamics.
• To model the interplay between resource growth, extraction behavior, and strategy adaptation using replicator dynamics.
• To determine conditions under which the system transitions between sustainable and unsustainable equilibria due to the Allee effect.

Proposed method

• Formulates two coevolutionary models using replicator dynamics to simulate strategy evolution among resource users.
• Incorporates the Allee effect into the resource growth function, where growth rate increases with resource abundance up to a threshold.
• Introduces knowledge feedback as a mechanism that adjusts user strategies based on system state, enhancing adaptive learning.
• Analyzes the system using stability analysis to identify fixed points and their basins of attraction.
• Employs numerical simulations to explore bifurcations and critical transitions under varying initial conditions and parameters.
• Uses parameter sweeps to assess the influence of Allee effect strength and feedback efficacy on system outcomes.

Experimental results

Research questions

• RQ1 How does the Allee effect influence the stability and sustainability of common-pool resource systems?
• RQ2 What role does knowledge feedback play in mitigating the risk of collapse under Allee dynamics?
• RQ3 Under what initial conditions does the system exhibit bi-stability, leading to divergent outcomes?
• RQ4 How do changes in resource growth function and extraction rates affect long-term sustainability?
• RQ5 Can the system undergo critical transitions due to the Allee effect, and how can they be predicted or prevented?

Key findings

• The Allee effect induces bi-stable dynamics, where the system's long-term outcome depends critically on initial conditions.
• Critical transitions occur when the Allee threshold is crossed, leading to either rapid collapse or sustained resource use.
• Knowledge feedback significantly enhances system resilience by stabilizing strategies and reducing overexploitation.
• Systems with strong Allee effects are more vulnerable to collapse if initial resource levels are low, even with moderate extraction.
• The presence of knowledge feedback expands the basin of attraction for sustainable equilibria, increasing the likelihood of long-term sustainability.
• Numerical results confirm that parameter configurations near the Allee threshold lead to high sensitivity and potential tipping points.