### 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 language | English (US) |
---|---|

Pages (from-to) | 45-73 |

Number of pages | 29 |

Journal | Mathematical Models and Methods in Applied Sciences |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2017 |

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### Keywords

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

### ASJC Scopus subject areas

- Modeling and Simulation
- Applied Mathematics

### Cite this

**Stochastic spatial model for the division of labor in social insects.** / Arcuri, Alesandro; Lanchier, Nicolas.

Research output: Contribution to journal › Article

*Mathematical Models and Methods in Applied Sciences*, vol. 27, no. 1, pp. 45-73. https://doi.org/10.1142/S0218202517400024

}

TY - JOUR

T1 - Stochastic spatial model for the division of labor in social insects

AU - Arcuri, Alesandro

AU - Lanchier, Nicolas

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - anti-voter model

KW - division of labor

KW - Interacting particle systems

KW - social insects

KW - task allocation

UR - http://www.scopus.com/inward/record.url?scp=85007524429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007524429&partnerID=8YFLogxK

U2 - 10.1142/S0218202517400024

DO - 10.1142/S0218202517400024

M3 - Article

VL - 27

SP - 45

EP - 73

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 1

ER -