When ants go exploring in search of food they end up choosing collective routes that fit statistical distributions of probability, according to a team of mathematicians who analyzed the trails of a species of Argentine ant. 

It's unknown how flocks of birds, shoals of fish, lines of ants and other complex natural systems organize themselves so well when moving collectively so researchers from Spain and the U.S. analyzed the movements of Argentine ants (Linepithema humile, an invasive species in many parts of the world) while they forage or explore an empty space (a petri dish) and then they proposed a model explaining how they form their routes.

The authors started by observing the behavior of ants individually and subsequently as a collective group. They recorded all their movements and based on these experiments, detected that the random changes in the direction of the insects follow mathematical patterns.

Concentration of pheromone (more in red color) after 10000 time steps (6.67min.), 20000 time steps (13.33min.) and 40000 time steps (26.67min.). Credit: S. Garnier, M. Vela-Pérez et al.

“To be more specific, they are a mixture of Gaussian and Pareto distributions, two probability functions which are commonly used in statistics, and that in this case dictate how much the ant ‘turns’ at each step and the direction it will travel in,” María Vela Pérez, researcher at the European University in Madrid and co-author of the study, explained to SINC.

The scientists had already verified in previous studies that the 'persistence' of ants, or rather, their tendency not to change their direction while there are no obstacles or external effects, together with the ‘reinforcement’ occurring in areas which they have already visited (thanks to the pheromone trail that they leave) are two factors which determine their routes as they forage. Now mathematicians have been able to create the model describing the collective movement of the ants on a surface. The numerical simulations on the computer show the formation of ramified patterns very similar to those observed in the petri dishes during the real experiment with ants.

Aside from the mere biological interest, these advances could be applied in diverse technological fields. “For example, they could be used to design the coordination of a group of micro-robots or small robots to clean a contaminated area or other tasks,” Vela Pérez points out.


M. Vela-Pérez, M. A. Fontelos, S. Garnier. “From individual to collective dynamics in Argentine ants (Linepithema humile)”. Mathematical Biosciences 262: 56–64, 2015.

Marco A. Fontelos, Avner Friedman. “A PDE model for the dynamics of trail formation by ants”. Journal of Mathematical Analysis and Applications 425 (1): 1–19, 2015.