Bee Determined: A Mathematical Analysis of Trapline Formation

Ferdinand Gruenenwald

University of Victoria

"Bee Determined: A Mathematical Analysis of Trapline Formation"

Many foraging animals, including bees, develop near-optimal movement patterns based on memory. While models have simulated how bees establish deterministic traplines, formal mathematical proofs of their behavior remain scarce. We address this gap by adapting and simplifying the Dubois et al. (2024) model to enable mathematical analysis. We prove that simulated bees will always eventually converge to a single deterministic route. Additionally, we propose conjectures about the distribution of routes to which simulated bees may converge. Future work could explore inference methods for learned behavior based on this model. These findings have implications beyond biology, providing insights into reinforced random walks and reinforcement learning.

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