A Model for Collective Dynamics in Ant Raids

TL;DR

This paper introduces a coupled PDE/ODE model to analyze ant raid dynamics, capturing collective lane formation and phase transitions, aligning with experimental observations of ant foraging behavior.

Contribution

The novel model integrates ant foraging and returning behaviors with pheromone dynamics, revealing self-organized lane formation and phase transition phenomena in ant raids.

Findings

Ants naturally form lanes moving in opposite directions.

The model exhibits a continuous phase transition with critical exponents.

Results match experimental observations of ant raiding behavior.

Abstract

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.