The role of colony size on activity rhythms of ants

Thirty years of research into activity rhythms of ant colonies have contributed an improved understanding of this fascinating form of collective behavior. Yet, little is known about how the colony size influences the intensity and tempo of the rhythms. Here, we address this knowledge gap through a two-pronged approach, combining the re-evaluation of published experimental observations on California ant, Temnothorax rudis, with the formulation of a novel mathematical model. From the analysis of published data, we discover that the period of the activity bursts is nearly independent of the colony size, while the number of ants activated during the bursts scales hypometrically with the colony size. In search of the biological mechanisms underpinning this evidence, we put forward a compartmental model consisting of three classes: active, inactive, and refractory ants. The study of the resulting system of nonlinear delay-differential equations explains the emergence of activity rhythms as stable limit cycles. The period of these limit cycles is controlled by the refractory delay for the resting phase, independently of the colony size, but their amplitude allometrically varies with the colony size due to social deactivation. During activity rhythms, ants spontaneously deactivate when socially interacting with active individuals.