The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

中文翻译：

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揭示塑造收获蚁群觅食动态的力量：招募效率和环境变化

蚁群的集体觅食行为是行为生态学的焦点。本文通过引入非线性招募率并考虑环境变化，增强了收获蚁群觅食动态的经典模型。首先，我们分析确定性模型中稳态的存在性和稳定性。结果表明，平均募集时间的增加可以降低觅食阈值，从而导致前向和后向分叉。此外，平均招聘时间和招聘人员的干扰强度都会影响每个子组中的工人数量。随后，我们对随机环境中集体觅食的长期和瞬时动态进行分析，为群体维持觅食活动提供充分的条件。研究结果强调了环境随机性对觅食动态的场景依赖性影响。当蚁群确定性地停止觅食时，环境随机性可能会意外地延长觅食状态。相反，当群体确定性地坚持觅食时，环境随机性可能会破坏这种连续性。此外，环境随机性对觅食状态的影响随初始工蚁规模的不同而变化。非觅食状态和觅食状态之间吸引力盆地边界附近的体型对环境随机性表现出更大的敏感性，并且足够大的随机性可以影响更广泛的初始工蚁体型的觅食动态。这些发现强调了内在因素（例如，招募效率和干扰强度）和外在因素（例如，环境随机性）在塑造蚁群集体觅食动态方面的复杂相互作用。