Stochastic spatial model for the division of labor in social insects

TL;DR

This paper introduces a stochastic model to study how communication networks influence division of labor in social insects, revealing that optimal task allocation depends non-monotonically on network structure.

Contribution

It presents a novel stochastic particle system model for social insect behavior, analyzing how different network topologies affect task division efficiency.

Findings

Division of labor is poor without communication.

Complete graphs improve task balance.

Bipartite graphs with equal sets optimize division of labor.

Abstract

Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set of a graph representing a communication network. They are characterized by one of two possible tasks, which they update at a rate equal to the cost of the task they are performing by either defecting by switching to the other task or cooperating by anti-imitating a random neighbor in order to balance the amount of energy spent in each task. We prove that, at least when the probability of defection is small, the division of labor is poor when there is no communication, better when the communication network consists of a complete graph, but optimal on bipartite graphs with bipartite sets of equal size, even when both tasks have very different costs. This shows a non-monotonic relationship between the number of connections in the communication network and how well individuals organize themselves to accomplish both tasks equally.