Independence and interdependence in the nest-site choice by honeybee swarms: agent-based models, analytical approaches and pattern formation

TL;DR

This paper simplifies an agent-based model of honeybee nest-site selection, enabling analytical solutions and revealing pattern formation dynamics, thus reducing reliance on simulations.

Contribution

It introduces an analytically tractable simplified model and extends it spatially to study pattern formation in honeybee swarm decision-making.

Findings

Exact characterization of coordination outcomes

Emergence of transient spatial patterns

Analytical treatment reduces simulation dependence

Abstract

In a recent paper List, Elsholtz and Seeley [Phil. Trans. Roy. Soc. B. 364 (2009) 755] have devised an agent-based model of the the nest-choice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. We here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on our analytical approaches it is possible to characterize the co-ordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agent-based level. In the second part of the paper we present a spatial extension, and show that transient non-trivial patterns emerge, before consensus is reached. Approaches in terms of Langevin equations for continuous field variables are discussed.