Stochastic spatial model for the division of labor in social insects

Alesandro Arcuri, Nicolas Lanchier

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)45-73
Number of pages29
JournalMathematical Models and Methods in Applied Sciences
Volume27
Issue number1
DOIs
StatePublished - Jan 1 2017

Keywords

  • anti-voter model
  • division of labor
  • Interacting particle systems
  • social insects
  • task allocation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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