Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants
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arXiv
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2025
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| author | Morimoto, Saori Katori, Makoto Nishimori, Hiraku |
| author_facet | Morimoto, Saori Katori, Makoto Nishimori, Hiraku |
| contents | Macroscopic changes of group behavior of eusocial insects are studied from the viewpoint of non-equilibrium phase transitions. Recent combined study of experiments and mathematical modeling by the group led by the third author suggests that a species of garden ant switches the individual foraging walk from pheromone-mediated to visual-cues-mediated depending on situation. If an initial pheromone-road between the nest and food sources is a detour, ants using visual cues can pioneer shorter paths. These shorter paths are reinforced by pheromone secreted by following ants, and then the detour ceases to exist. Once the old pheromone-road extincts, there will be almost no chance to reconstruct it. Hence the extinction of pheromone-road is expected to be regarded as a phase transition to an absorbing state. We propose a discrete-time model on a square lattice consisting of switching random walks interacting though time-dependent pheromone field. The numerical study shows that the critical phenomena of the present extinction transitions of pheromone-roads do not seem to belong to the directed percolation universality class associated with the usual absorbing-state transition. The new aspects are cased by the coexistence and competition with newly creating pheromone-roads. In a regime in the extinction phase, the annihilating road shows metastability and takes long time-period to be replaced by a new road. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_09475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants Morimoto, Saori Katori, Makoto Nishimori, Hiraku Statistical Mechanics Adaptation and Self-Organizing Systems Populations and Evolution Macroscopic changes of group behavior of eusocial insects are studied from the viewpoint of non-equilibrium phase transitions. Recent combined study of experiments and mathematical modeling by the group led by the third author suggests that a species of garden ant switches the individual foraging walk from pheromone-mediated to visual-cues-mediated depending on situation. If an initial pheromone-road between the nest and food sources is a detour, ants using visual cues can pioneer shorter paths. These shorter paths are reinforced by pheromone secreted by following ants, and then the detour ceases to exist. Once the old pheromone-road extincts, there will be almost no chance to reconstruct it. Hence the extinction of pheromone-road is expected to be regarded as a phase transition to an absorbing state. We propose a discrete-time model on a square lattice consisting of switching random walks interacting though time-dependent pheromone field. The numerical study shows that the critical phenomena of the present extinction transitions of pheromone-roads do not seem to belong to the directed percolation universality class associated with the usual absorbing-state transition. The new aspects are cased by the coexistence and competition with newly creating pheromone-roads. In a regime in the extinction phase, the annihilating road shows metastability and takes long time-period to be replaced by a new road. |
| title | Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems Populations and Evolution |
| url | https://arxiv.org/abs/2502.09475 |