Switching Particle Systems for Foraging Ants and Phase Transitions in Path Selections

8 November 2023, NPRM2023, ISM

Ayana EZOE (Department of Physics, Chuo University, Tokyo)

Joint work with M. Katori and H. Nishimori

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arXiv:cond-mat.stat-mech/2311.01946

Outline

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Introduction 1:�Switching of Cues by Foraging Ants

• Collective behavior and swarm intelligence of ants have been extensively studied.

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• Ants reach food by following pheromones dropped by other ants.

Edward O. Wilson and Bert Holldobler : `The Ants’, Belknap Press (1990), pp.265-279

https://mas.kke.co.jp/

Introduction 1:�Switching of Cues by Foraging Ants

• Nishimori’s group experiments

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• Ants also perform visual-cues-mediated-walks while foraging.

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• Ants switch between pheromone-mediated-walks and visual-cues-mediated-walks.

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• Whether optimal path is formed or not depends on the turning angle.

Ogihara, Yamanaka, Akino, Izumi, Awazu, Nishimori : in `Mathematical Approaches to Biological Systems’, Springer (2015), pp.119-137

Introduction 2: Switching Interacting Particle Systems and Dormancy Problems

• Two-layer model (switching interacting particle systems)

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Floreani, Giardina, den Hollander, Nandan, Redig : J. Stat. Phys. 186 (2022) 33 (pp.45)

fast particles

Introduction 2: Switching Interacting Particle Systems and Dormancy Problems

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simulation of two-layer model

Presented by Saori Morimoto

fast particles

Introduction 2: Switching Interacting Particle Systems and Dormancy Problems

• What is dormancy?

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Lennon, den Hollander, Wilke-Berenguer, Blath : Principles of seed banks and the emergence of complexity from dormancy, Nat Commun 12, 4807 (2021) (pp.16)

• Many organisms go dormant in suboptimal environments.

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• Dormant individuals enable same species to survive in sudden environmental changes.

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• Seed bank is a group of dormant individuals.

Stochastic Models for Foraging Path Selection by Ants

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situation-dependent switching

Stochastic Models for Foraging Path Selection by Ants

• pheromone-mediated-walks

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• Ants go forward or turn left or turn right.

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• The probability of choosing forward, left, or right turn depends on amount of pheromone placed at each site.

Stochastic Models for Foraging Path Selection by Ants

• visual-cues-mediated-walks

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• Proceed in a randomly chosen direction toward the nest (left or down).

nest

Stochastic Models for Foraging Path Selection by Ants

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Extreme　Cases

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Extreme　Cases

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Parameter Setting

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Almost Data-collapse with Respect to System Size

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(a)

(b)

Evaluations of Critical Values and Critical Exponents

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The phase transitions are continuous.

Evaluations of critical values and critical exponents

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Summary

• We proposed a discrete-time interacting random-walk model on a square lattice, in which two kinds of hopping rules are included.
• We reported the numerical simulation results which exhibit the global changes in selected homing paths from trailing paths of the “pheromone-road” to nearly-optimal-paths depending on the switching parameters.
• We discussed such global changes as phase transitions realized in path selections of ants.
• Critical phenomena associated with the continuous phase transitions were also studied.

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Please see our preprint;

arXiv:cond-mat.stat-mech/2311.01946

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Thank you very much for your attention!