Boi et al, 1999 - Coupled oscillators and activity waves in...

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Coupled oscillators and activity waves in ant colonies S. Boi 1 { , I. D. Couzin 2* , N. Del Buono 1 , N. R. Franks 2 and N. F. Britton 1 1 School of Mathematical Sciences and 2 Department of Biology and Biochemistry, Centre for Mathematical Biology, University of Bath, Claverton Down, Bath BA2 7AY, UK We investigated the phenomenon of activity cycles in ants, taking into account the spatial structure of colonies. In our study species, Leptothorax acervorum , there are two spatially segregated groups in the nest. We developed a model that considers the two groups as coupled oscillators which can produce synchro- nized activity. By investigating the e¡ects of noise on the model system we predicted how the return of foragers a¡ects activity cycles in ant colonies. We tested these predictions empirically by comparing the activity of colonies under two conditions: when foragers are and are not allowed to return to the nest. The activity of the whole colony and of each group within the colony was studied using image analysis. This allowed us to reveal the spatial pattern of activity wave propagation in ant colonies for the ¢rst time. Keywords: ants; activity cycles; coupled oscillators; mathematical model; image analysis; social insects 1. INTRODUCTION Social insects are the product of one of the major evolutionary transitions from solitary to collective organ- social insects, ants have the greatest ecological success in terms of the number of species, the variety of habitats colonized and biomass (Wilson 1971). The secret of this success is that colonies often act as a social unit, exhibiting an e/cient and £exible division of labour (Tofts & Franks 1992; Bourke & Franks 1995; Gordon 1996) and problem solving beyond the scope of the individual (Franks et al . 1991). Complex collective behaviour performed by ant colon- ies includes foraging (Beckers et al . 1990), building beha- viour (Franks et al . 1992) and £exible task allocation (Gordon 1995). Such collective behaviours might be regulated either by a centralized control mechanism (for example, in honeybees and Polistes wasps the queen has a dominant role during certain activities (Reeve control where the local interactions between the indivi- which occur within ant colonies of certain species, especially Leptothorax , are an example of distributed control (Franks & Bryant 1987; Franks et al . 1990 a ; Cole 1991; Cole & Hoeg 1996; tend to be active together and inactive together and there is no evidence that any particular individual acts as a pacemaker. Synchronicity arises because active ants can activate inactive ants through physical contact (Cole 1991). Synchronized bursts of activity, which in Leptothorax acervorum occur approximately every 20 min,
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This note was uploaded on 12/08/2011 for the course PHYSICS 340 taught by Professor Clarke during the Fall '08 term at University of Michigan.

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Boi et al, 1999 - Coupled oscillators and activity waves in...

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