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A Mathematical Framework Exhibiting the Emergence of Dynamic Expansion of Task Repertoire in \emph{Pheidole dentata}

The division of labor (DOL) and task allocation among groups of ants living in a colony is thought to be highly efficient, and key to the robust survival of a colony. A great deal of experimental and theoretical work has been done toward gaining a clear understanding of the evolution of, and underlying mechanisms of these phenomena. Much of this research has utilized mathematical modeling. Here we continue this tradition by developing a mathematical model for a particular aspect of task allocation, known as age-related repertoire expansion, that has been observed in the minor workers of the ant species \emph{Pheidole dentata}. In fact, we present a relatively broad mathematical modeling framework based on the dynamics of the frequency with which members of specific age groups carry out distinct tasks. We apply our modeling approach to a specific task allocation scenario, and compare our theoretical results with experimental data. It is observed that the model predicts perceived behavior, and provides a possible explanation for the aforementioned experimental results.