Evolution of division of labor in a response threshold model*

This work explores the evolving division of labor in a response threshold model. As we know,

division of labor is central to driving cooperative structures in societies, bacterial communities, and insect colonies.

Starting from the simplest case of an unstructured population with fixed response thresholds, we can derive threshold prescriptions to ensure division of labor. We derive mean-field equations for

the stimulus dynamics and show that they exhibit complex attractors through period-doubling bifurcation cascades when the noise disrupting the thresholds is small. In addition, we show how

the fixed threshold can be set to ensure specialization in both the transient and equilibrium regimes

of the stimulus dynamics. Using the framework of structured populations, we then address the fundamental question of determining the underlying conditions that lead to the division of labor from a homogeneous population. In the formulation, a group fitness function, W(T), acts as a guiding force that shapes the distribution of tasks among individuals while maximizing the collective work output of the group. The perfect division of labor, guided by specific threshold prescriptions, constitutes a global optimum of W(T). Our results demonstrate the emergence of an imperfect division of labor, which contrasts sharply with a previous study that found no such specialization. The degeneracy of the global fitness optimum is responsible for such an outcome, in which a fraction of agents act as generalists.