Evolving division of labor in a response threshold model

TL;DR

This paper models how division of labor emerges in populations through a response threshold framework, analyzing stimulus dynamics, bifurcations, and the effects of population structure on task specialization.

Contribution

It derives mean-field equations for stimulus dynamics, explores bifurcation phenomena, and demonstrates how structured populations lead to task specialization without penalizing switching.

Findings

Stimulus dynamics exhibit complex bifurcations with small noise.

Fixed thresholds can promote task specialization.

Structured populations naturally develop division of labor.

Abstract

The response threshold model explains the emergence of division of labor (i.e., task specialization) in an unstructured population by assuming that the individuals have different propensities to work on different tasks. The incentive to attend to a particular task increases when the task is left unattended and decreases when individuals work on it. Here 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. However, a complete explanation of the emergence of division of labor requires that we address the question of where the threshold variation comes from, starting from a homogeneous population. We then study a structured population scenario, where the population is divided into a large number of independent groups of equal size, and the fitness of a group is proportional to the weighted mean work performed on the tasks during a fixed period of time. Using a winner-take-all strategy to model group competition and assuming an initial homogeneous metapopulation, we find that a substantial fraction of workers specialize in each task, without the need to penalize task switching.