“A mechanistic model of ant battles and its consequences for territory scaling”

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Frederick R. Adler, Sean Quinonez, Nicola Plowes, and Eldridge S. Adams (Aug 2018)

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Mathematical models show that even in ants, the rich get richer. Larger colonies get more than their share of space

Pavement ants (Tetramorium immigrans) ganging up on a member of another colony.
(Credit: Sean Quinonez)

Throughout much of the temperate world, battles between pavement ants are a common sight, popping up on a sidewalk on one day, slowly shifting position, and then disappearing. What are these ants fighting for? And who wins? Fred Adler, his former undergraduate researcher Sean Quinonez (now finishing medical school), and territorial ant experts Nicola Plowes and Eldridge Adams got together to develop a series of mathematical models to study these questions. They found that if the battle moves away from the colony with a larger number of battling ants, its location will settle down farther from the larger colony. More surprisingly, the mathematical models show that the larger colony always gets more than its fair share of the contested territory; that is, a colony that is twice as large will control more than 2/3 of the space. The strength of this effect depends on how ants join the battle—whether they recruit more ants when they are outnumbered or give up and accept defeat. If colonies grow faster when they have more territory, this creates a situation where the rich get richer, at least until they die and create space for small new colonies. This work provides a framework for the broad question of how resources get divided up among competitors, and how inequality itself can arise and increase.

The line of demarcation between two battling pavement ant colonies.
(Credit: Sean Quinonez)


Territory size in social insects depends on the rules by which border conflicts are resolved. We present three mechanistic mathematical models of conflict, inspired by the behavior of the pavement ant Tetramorium immigrans, to predict the advantage of larger colonies in pairwise contests and the resulting scaling of territory size with worker force. The models track the number of ants in the nest, traveling to and from the boundary, or engaged at the boundary. Ants at the boundary base their recruitment response on the relative numbers of ants from the two colonies. With two colonies, our central result is that the larger colony gains a territory disproportionately larger than the ratio of worker forces would indicate. This disproportionate territory control determines the scaling relation of territory size with worker force in a population. In two dimensions, if territory size were proportional to worker force, the slope of the scaling relation between log territory size and log worker force would be 1.0. With disproportionate territories, this slope is larger, and can be explicitly approximated in terms of model parameters, and is steepest when colonies are packed close to each other, when ants run quickly, or when colonies are small. A steeper slope exaggerates the advantage of larger colonies, creating a positive feedback that could amplify the inequality of the worker force distribution.