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

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p tIndependence and interdependence in the nest-site choice by honeybee swarms: agent-based models, analytical approaches and pattern formation In a recent paper List, Elsholtz and Seeley [List et al. 2009] 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.

Model of the best-of-Nnest-site selection process in honeybees

“…There are similarities and differences between the meaning of the interdependence parameter and the signalling ratio r that is introduced in this paper. Similarly to [35,36], increasing the value of the ratio r corresponds to an increase in the signalling behaviour but, in contrast to previous studies, r is a weighting factor of both positive and the negative feedback. However, note that positive and negative feedback are not necessarily equal in our model, as these mechanisms are also modulated by the option's quality.…”

“…Previous work has investigated the role of signalling in collective decision making in a somewhat different framework. Galla [35] has analysed a model of house-hunting honeybees [36] where the cross-inhibition mechanism was not included. In this model, increasing signalling (referred to as interdependence) allows the swarm to select the best quality option more reliably.…”

Do small swarms have an advantage when house hunting? The effect of swarm size on nest-site selection by Apis mellifera

“…The standard problem examined in most modelling studies of the bees' decision-making process [15,22,28,29,[32][33][34][35][36][37][38] and in some controlled experimental studies (e.g. [6]) is to give swarms a choice between two to six nest sites (but see [39] for a modelling study with a choice between 120 distinct nest sites).…”

Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths

“…Two techniques can be used to derive these ODEs, either a mass action heuristic similar to the one a mathematician would use to derive the ODEs, or a more involved statistical physics approach described in section ‘Analysing noisy behaviour’ ( e.g . [15]). Both, however, have the same result.…”