Session: Research Posters

Paper Number: 172900

A Dynamic Model for Activity Rhythms in Ant Colonies 

The spontaneous synchronization of weakly coupled oscillators has long fascinated scientists, beginning with Peskin’s 1975 model of pacemaker cell excitation [1]. In the decades since, researchers have uncovered synchronous behavior across a wide range of biological systems – from the pulse-coupled flashing of fireflies [2] to seasonal predator-prey cycles [3] and the collective, short-term bursts of activity in ant colonies [4]. These systems exemplify emergent temporal patterns driven by local interactions, underscoring the importance of understanding how simple rules at the individual level can produce complex group-level dynamics.

 

Observations of ant behavior by Franks et al. in 1990 [5], then by Cole in 1991 [6], have demonstrated the emergence of activity bursts in ant colonies, in which ants collectively become active following a nearly constant clock, and are immobile otherwise. To explain experimentally observed activity bursts in ants, Goss and Deneubourg developed the celebrated autocatalytic model, in which ants transition between three compartments – active, inactive, and refractory – either spontaneously or via interactions with already active ants [7]. Each activation is followed by a refractory delay, during which ants are temporarily unresponsive. This model successfully captures the essential features of short-term activity bursts and has become a seminal reference for studies aiming to predict the temporal dynamics of ant activity in colonies of a given size.

 

While the emergence of activity rhythms and the importance of the autocatalytic mechanism have been well-established in the literature, less is known about how colony-scale parameters – such as interaction frequency – influence the form, frequency, and stability of collective activity bursts. To address this gap, we introduce two biologically inspired extensions to the original model: (1) a social deactivation mechanism, analogous to self-inhibition or crowding effects, and (2) a size-dependent average degree, where the expected interaction frequency scales sublinearly with the colony size [8]. These enhancements allow us to systematically investigate how scaling laws and feedback structure shape rhythmic dynamics in large ant colonies. Our dynamic model is in the form of a system of coupled nonlinear delay-differential equations for the proportion of individuals in the three compartments.

 

Through analytical and numerical methods, we find that the burst period is primarily determined by the refractory delay, while the burst amplitude scales hypometrically with colony size. Our model reveals that as the size of the colony increases, the critical delay – above which the system exhibits limit-cycle behavior – also increases monotonically, while the radian frequency decreases, approaching zero in large systems. This implies that larger colonies can support stable, low-frequency rhythmic behavior given the expected delay in individuals remains fixed. To validate our model, we analyze published activity time-series data from Temnothorax rudis ant colonies of varying size [9]. Consistent with our theoretical predictions, we find that the burst period remains approximately constant, indicating that the tempo of colony activity is invariant with respect to size, while the burst amplitude scales sublinearly, reflecting the saturating effect of social crowding. 

 

Together, these findings support the hypothesis that refractory delays and interaction topology jointly constrain the expression of collective rhythms in insect societies. More broadly, our results illustrate how size-dependent coupling and delayed feedback shape emergent rhythms in distributed systems, offering broader implications for understanding synchronization, rhythmicity, and control in both biological collectives and engineered swarm systems.

 

[1] C. S. Peskin, “Mathematical Aspects of Heart Physiology,” Courant Inst. Math, 1975, [Online]. Available: https://cir.nii.ac.jp/crid/1573105974954768640

[2] S. H. Strogatz and I. Stewart, “Coupled Oscillators and Biological Synchronization,” Scientific American, vol. 269, no. 6, pp. 102–109, 1993

[3] M. H. Cortez and J. S. Weitz, “Coevolution can reverse predator–prey cycles,” Proceedings of the National Academy of Sciences, vol. 111, no. 20, pp. 7486–7491, May 2014

[4] L. Hemerik, N. F. Britton, and N. R. Franks, “Synchronization of the behaviour within nests of the ant Leptothorax acervorum (Fabricius)—II. Modelling the phenomenon and predictions from the model,” Bulletin of Mathematical Biology, vol. 52, no. 5, pp. 613–628, Sep. 1990

[5] N. R. Franks, S. Bryant, R. Griffiths, and L. Hemerik, “Synchronization of the behaviour within nests of the ant Leptothorax acervorum (fabricius)—I. Discovering the phenomenon and its relation to the level of starvation,” Bulletin of Mathematical Biology, vol. 52, no. 5, pp. 597–612, Sep. 1990

[6] B. J. Cole, “Short-Term Activity Cycles in Ants: Generation of Periodicity by Worker Interaction,” The American Naturalist, vol. 137, no. 2, pp. 244–259, Feb. 1991,

[7] S. Goss and J. L. Deneubourg, “Autocatalysis as a source of synchronised rhythmical activity in social insects,” Insectes Sociaux, vol. 35, no. 3, pp. 310–315, Sep. 1988,

[8] M. Porfiri, N. Abaid, and S. Garnier, “Socially driven negative feedback regulates activity and energy use in ant colonies,” PLOS Computational Biology, vol. 20, no. 11, p. e1012623, Nov. 2024

[9] G. N. Doering, M. M. Prebus, S. Suresh, J. N. Greer, R. Bowden, and T. A. Linksvayer, “Emergent collective behavior evolves more rapidly than individual behavior among acorn ant species,” Proceedings of the National Academy of Sciences, vol. 121, no. 48, p. e2420078121, Nov. 2024

Presenting Author: Michael Napoli New York University

Presenting Author Biography: Michael Napoli is a Ph.D. student in the Department of Mechanical and Aerospace Engineering at New York University’s Tandon School of Engineering and a member of the Dynamical Systems Laboratory. He earned a Bachelor of Science in Mechanical and Aerospace Engineering from The Ohio State University in 2022, graduating with a minor in Computer and Information Science and Research Distinction. He went on to receive a Master of Science in Robotics and Autonomous Systems from Boston University in 2024. His research focuses on collective behavior in organic systems, with applications to the design of biologically informed mechanical and robotic technologies.

Authors:

Michael Napoli New York University
Maurizio Porfiri New York University