  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.
