A framework for modeling repertoire expansion in Pheidole dentata

Ants live in highly organized colonies where individuals perform specific tasks in a work dynamic that is both efficient and robust. Although a variety of experimental and theoretical models have been developed to explain their complex behaviors, a relatively new model, ‘repertoire expansion,’ basing task allocation with increasing repertoire size according to age has yet to be modelled. In this poster, I describe a novel mathematical approach for theoretically framing task allocation in ants with the theoretical underpinning of repertoire expansion. Specifically, I introduce the age-task frequency matrix where each entry represents the frequency with which members of a specific age group perform a specific task. Furthermore, I present a corresponding dynamical system to represent how the entries of the matrix may change in terms of colony size. Theoretically analyzing the dynamics provides a potential method for understanding and making predictions about colony work behavior.