Foraging dynamics in social insect colonies: Mechanisms of backward bifurcations and impacts of stochasticity

Abstract

This investigation presents a two-dimensional collective foraging model alongside its stochastic counterpart, simplifying the previous more complex three-dimensional framework utilized to examine foraging behaviors within social insect colonies. We first conduct a thorough examination of the global dynamics of the deterministic model. The results show that the two-dimensional model exhibits equilibrium dynamics, with the possibility of coexistence between non-foraging and foraging equilibrium states. This finding highlights the parallelism between the two-dimensional model and the traditional three-dimensional framework. Following this, an extensive exploration into the long-term collective foraging dynamics within a stochastic environment is conducted, elucidating the interplay between stochasticity and the transitions across distinct stable foraging states. Additionally, the investigation assesses the risk of foraging cessation across varying initial worker populations, subsequently delineating foraging termination warning thresholds. The findings illuminate the multifaceted influence of environmental stochasticity on the collective foraging dynamics observed in harvester ant colonies. Grasping these dynamics furnishes valuable understanding of ecological resilience and the adaptive strategies deployed by collective entities in navigating environmental fluctuations.