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Construction behaviour in social insects: who coordinates the individual’s work?

C Jost, S Weitz, A Khuong, S Blanco, R Fournier, C Sbai, J Gautrais, G Theraulaz

University Paul Sabatier, Toulouse, France

Rennes October 2011!

A single individual has only limited (local) knowledge …

… but its actions contribute to the functioning of the whole colony

From individual to collective behavior: the key role of self-organisation

6 mm

200 mm

Cornitermes cumulans

Cornitermes cumulans

Above ground

Below ground

Self-organisation also has to work in a structured

environment

Wind

6 mm

Humidity Temperature

Templates as a structuring element in construction processes

Apicotermes lamani

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Templates as a structuring element in construction processes

Pheromonal template created by a physogastric queen in the termite Macrotermes subhyalinus

Chemical template

!  The queen releases a pheromone that diffuses and creates a pheromonal template in the form of a decreasing gradient around her body

!  A concentration threshold controls the workers’ building activities:

Cmax Cmin Cmax Cmin

Bruinsma, O.H., PhD Thesis, (1979)

Construction of the royal chamber in termites

pillars!


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Construction of the royal chamber in termites Construction of the royal chamber in termites

Construction of the royal chamber in termites Adjusting the size of the royal chamber

Cmax Cmin Cmax Cmin Cmax Cmin Cmax Cmin

!  With this mechanism, the termite workers are able to build at any moment an adjusted chamber that fits the size of the queen!


!  The queen releases a pheromone that diffuses and creates a pheromonal template in the form of a decreasing gradient around her body

!  A concentration threshold controls the workers’ building activities

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Patterns resulting from the interplay between template and self-organization processes Nest building in the ant Temnothorax albipennis

Franks, N.R. & Deneubourg, J.L., Anim. Behav., (1997) Franks, N.R. & Deneubourg, J.L., Anim. Behav., (1997)

passages!

queen!

40 mm !  The mean number of workers

in a colony is 500

!  The mean size of the workers is 2 ~ 3 mm

Patterns resulting from the interplay between template and self-organization processes Nest building in the ant Temnothorax albipennis

r

!  The circular wall is constructed at a given distance from the brood, which serves as a chemical and physical template!

Franks, N.R. & Deneubourg, J.L., Anim. Behav., (1997)

Patterns resulting from the interplay between template and self-organization processes Construction rules in the ant Temnothorax albipennis

r

!  An additional self-organized mechanism is combined to the template: grains attract grains so that deposition behavior is also influenced by the local density of grains



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Picking-up probability Dropping probability

Size of the pile

Size of the pile

Distance from the center of the brood



passages!

Patterns resulting from the interplay between template and self-organization processes Simulation of the wall construction

Interaction with templates?

Corpses aggregation in ants

Talk structure

•  Corpse clustering in 1D: the basic mecanisms

•  Corpse clustering in 2D: a simple extrapolation from 1D?

•  Ant displacement: the role of borders

•  Corpse clustering in 2D with border following

•  Ongoing research: construction behaviour in ants

•  Conclusion and perspectives

Construction behaviour in social insects: who coordinates the individual’s work?

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Aggregation dynamics

I. Clustering in 1Din ants

- 5

0

5

1 0

1 5

2 0

-15 5 25

45

65

85

105

125

145

165

185

205

225

245

265

285

305

325

345

Angle

- 5

0

5

1 0

1 5

2 0

-15 5 25

45

65

85

105

125

145

165

185

205

225

245

265

285

305

325

345

Angle

Num

ber o

f obs

erva

tions

N = 15 N = 15

Ø : 25 cm (100 Corpses) Ø : 25 cm (200 Corpses)

Angle Angle

Num

ber o

f obs

erva

tions

Spatial distribution of clusters after 24 hours


"! "!

Size of the pile

Picking-up and dropping behaviors !  Unladen ants pick up corpses

with a probability that decreases with cluster size

!  Corpse-carrying ants drop corpses with a probability that increases with cluster size

Positive feed-back

(Theraulaz, G. et al., PNAS, 2002)


Size of a corpse cluster Size of the pile

!  The growth of clusters leads to a depletion of corpses in the arena that inhibits the further growth of other clusters

!  Unladen ants pick up corpses with a probability that decreases with cluster size

!  Corpse-carrying ants drop corpses with a probability that increases with cluster size

Negative feed-back


I. Clustering in 1Din ants Picking-up and dropping behaviors

Size of a corpse cluster

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Range of perception of an ant


!  The individual probabilities to pick-up and drop a corpse on a given cluster depend on the density of corpses which is perceived locally by the ant

!  Experimental measurements lead to characteristic radius of perception # ! 5mm

Spatio-temporal dynamics

0

5

1 0

0 5 1 0 1 5 2 0

Temps (h)

ø:25 cm 100 cadavres

modèle

ø:25 cm 100 cadavres

Model (IBM and PDE)

Experimental data (N = 15)

Mean number of clusters

Temps (h)



Spatio-temporal dynamics

0

5

1 0

1 5

0 5 1 0 1 5 2 0

Temps (h)

25/200

moyenne 25-200

25/200

Model (IBM and PDE)

Experimental data (N = 15)

Mean number of clusters

Temps (h)



!  The density of corpses is a bifurcation parameter that controls the collective behavior of the system : there exists a critical density of corpses below which no aggregation occurs

Critical density!

20 corpses - a

200 corpses - c

Mea

n nu

mbe

r of c

lust

ers

Corpse density is a bifurcation parameter I. Clustering in 1Din ants

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Aggregation in 1D and 2D

II. Clustering in 2D - a simple extrapolation of 1D clustering?

curvature ?

II. Clustering in 2D Experimental observation (duration 24h)

(Jost et al., J. Roy. Soc. Interface, 2007)

direction of the air flow (1-5 cm/s)

curvature ?

II. Clustering in 2D – Effect of air flow Experimental observation with air currents (duration 24h)


Cold wall

Hot wall

without air currents

with air currents

curvature ? Experimental observations (duration 24h)

II. Clustering in 2D – Effect of air flow


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Modeling displacement : do ants “diffuse” ?

II. Clustering in 2D: ant displacement in ants

(Casellas et al., J. Theor. Biol, 2008)

0 s

1 s

2 s 3 s

4 s

5 s

d1

d5

d4

d3

d2

<dt2>

Air current speed

prob

abili

ty

Isolated corpses Pile size 5 Pile size 10

!  Pick up probability increases with air current speed


curvature ? Modulation of picking-up by pile size and air speed

II. Clustering in 2D – Agregation behaviour

Air current speed

prob

abili

ty

Isolated corpses Pile size 5 Pile size 10

!  Dropping probability decreases with air current speed !  Ants clear corpses from areas of high wind speed and aggregate them in areas of low air current speed

Pile size 50


curvature ? Modulation of dropping by pile size and air speed

II. Clustering in 2D – Agregation behaviour curvature ? Calibration of air speed effect


local corpse density

Pick up

Low wind High wind

Drop

Pic

king

-up

k p /

drop

ping

coe

ffici

ent

1 cm / s

3 cm / s

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Modulation of wind speed around a corpse pile (diameter: 2cm, height: 4mm) !  Ants aggregate corpses on piles

that locally modify air flow

!  Individual probabilities to pick-up and drop corpses around the piles are modulated by the air flow speed

!  The consequence of these interactions is the appearance of a new spatial structure – elongated piles


curvature ? Interaction between aggregation process and air current

II. Clustering in 2D – Agregation behaviour curvature ? 3-dimensional air flows around complex obstacles

II. Clustering in 2D – Simulation of air flow

Discretized space: the distributions move from one node to the next one

curvature ? The lattice Boltzmann method


Air currents around the corpse piles after 24h, reference air speed 1cm/s (lattice Boltzmann simulation)

curvature ? curvature ? curvature ? curvature ? Simulation of 3-dimensionnal air flows in a complex geometry


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curvature ? Individual based model of ant behaviour


Dropping coefficient: kd = kd,0 + ! Np Picking-up coefficient: kp = " (Np)#

kd,0 = 0.496 m-1 ! = 5.4 m-1 " = 6.6 m-1 # = 0.14 (Weitz, S., Master thesis, 2008)

!

Pp = 1" e "kpdlL#

!

Pd = 1" e "kddlL#

curvature ? Calibration of air speed effect


local corpse density

Pick up

Low wind High wind

kp = " Np# · (1 + ϵp vair )

kd = (kd,0 + ! Np ) · (1 + ϵd vair )

Drop

Number of corpses in perception disc N

Pic

king

-up

k p /

drop

ping

coe

ffici

ent k

d

ϵp = +20 s·m-1 ϵd = -20 s·m-1

curvature ?

II. Clustering in 2D – spatio-temporal patterns Simulation without air currents (duration 24h)

(Weitz, S., Master thesis, 2008)

curvature ?

Experimental

Simulated



curvature ? without air currents

II. Clustering in 2D – spatio-temporal patterns

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curvature ?


direction of the air flow

curvature ? curvature ? Simulation with an air current of 1cm/s (duration 9.6h)




curvature ? curvature ? curvature ? Simulation with an air current of 3cm/s (duration 9.6h)


Simulated 1cm/s Simulated 3cm/s

air speed

Something is missing !

Experimental


curvature ? curvature ? with air currents



Do ants really diffuse?

curvature ? curvature ?

III. Ant displacement: the role of borders

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curvature ? curvature ?


empty arena 3 x 6 cm

7 x 4 cm 10 x 2 cm

•  measure the border following time •  study this time as a function of border curvature

curvature ? How to quantify thigmotactism ??


a

b

bc c

t " (s

) 0

2

4

6

8

10

12

curvature (cm-1) 0 0.2 0.4 0.6 0.8 1

( = 1 / radius ), ± se

(Casellas et al., J. Theor. Biol, 2008)

curvature ? Thigmotactism and border curvature ?

III. Ant displacement: the role of borders curvature ? Do corpse piles act as borders ?


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curvature ? Thigmotactic model for emerging piles


! Diffusion in free space

! Thigmotactism near borders

①  Principle ②  Effect of curvature



③  Border perception: “border direction” and “thigmotactic intensity” I

corpse ant

!

I =Ub

kI + Ub kI ! 0

||Ub ||



④  Choice of direction: modulate phase function

Phase function (g=0.53)

p = (1-kb) phomo + kb $"b

kb = kphase I Dirac in border direction

Standard forward-oriented phase function

Thigmotactic intensity



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⑤  Border following distance: modulate mean free path %

% = %free – (%min- %free) I

free path near border

free path far from border



! Mean border following distance

! Pile entering probability


Thigmotactic model for emerging piles

⑥  Calibration

Np,sat = 15 ! = 20 m#1 " = 9.5 m#1 $ = 0.3

Np = N / (N + Np,sat) kp = " Np

# · (1 + ϵp vair ) kd = (kd,0 + ! Np ) · (1 + ϵd vair )

ϵp = +25 s·m-1 ϵd = -25 s·m-1

curvature ? Calibration of the agregation behaviour

IV. Clustering with thigmotactism


curvature ? Simulation without air currents (duration 24h)


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Experimental

Simulated (Jost et al., J. Roy. Soc. Interface, 2007)

curvature ? without air currents


(Weitz et al., in preparation)

curvature ? Pattern dynamics



curvature ? curvature ? curvature ? Simulation with an air current of 1cm/s (duration 24h)





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IV. Clustering with thigmotactism curvature ?

Experimental

Simulated 1cm/s Simulated 5cm/s Simulated 3cm/s (Jost et al., J. Roy. Soc. Interface, 2007)

curvature ? curvature ? curvature ? with air currents


(Weitz et al., in preparation)

curvature ? curvature ? curvature ? curvature ? Pile dynamics with air currents

IV. Clustering with thigmotactism curvature ? curvature ? Termites, the masters of construction ….

Back to construction

Cubitermes, Guynée

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curvature ? curvature ? Termites, the masters of construction …. are they ?


Lasius, Roumania



Lasius, Roumania



Lasius niger, Toulouse

V. Construction in ants – simple extrapolation of 2D clustering?

Lasius niger

10 cm

~ 5.10 3 to 10 4 Ants

Behavioural mechanisms of construction in Lasius niger (ongoing work)

10 c

m

5 mm

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Quantification of the construction dynamics

V. Construction in ants

Setup for experimental construction

water

plaster

Add 500 ants Sand & clay

3D surface Scanner

V. Construction in ants Quantification of the construction dynamics

3D representation of the construction dynamics

Spatial pattern analysis

V. Construction in ants Quantification of the construction dynamics and spatial patterns

Time (h)

Aver

age

dist

ance

bet

wee

n ne

ighb

orin

g pi

llars

(mm

)

Dynamics of the average distance between pillars

!  The spatial pattern built by ants has a characteristic wavelength

V. Construction in ants Quantification of the construction dynamics

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V. Construction in ants Quantification of individual behaviour

Exp Julie

4-day construction experiments

V. Construction in ants Quantification of individual behaviour – encounters before deposition

Position (rad)% Time (h)

Cum

ulat

ed n

umbe

r of

dro

ppin

gs

!  The deposition of soil pellets in a place stimulates ants to accumulate more building material through a positive feed-back

Droppings Picking-up

V. Construction in ants Quantification of individual behaviour (ongoing research)

Position (rad)% Time (h)

Cum

ulat

ed n

umbe

r of

dro

ppin

gs

!  The deposition of soil pellets in a place stimulates ants to accumulate more building material through a positive feed-back

Droppings Picking-up


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Test pillar

Control pillar

5 cm

5

cm

10 cm

T C !  Ants add a pheromone to the building material

!  This chemical signal attracts ants over a short distance and stimulates the deposition of pellets on recently deposited pellets

Test pillar

Control pillar

Water


0.0

0.1

0.2

0.3

0.4

0.5

2 4 6 8 10 12 0 14

Dropping Picking up

Number of deposited pellets

!  Ants add a pheromone to the building material

!  This chemical signal attracts ants over a short distance and stimulates the deposition of pellets on recently deposited pellets

Pro

babi

lity


10 mm

4 mm

!  When a pillar reaches a critical height ants start to build lateral extensions

Probability of dropping a building block on the side of a pillar

Height (mm)

V. Construction in ants Quantification of individual behaviour (ongoing research) 3D agent-based model of ant nest construction

!  Ants are modeled by asynchronous automata with a stimulus-response behavior

!  Virtual ants move randomly in a 3-D discrete cubic lattice and their movement is physically constrained

!  Virtual ants have a local perception of their environment (the first 26 neighboring cells close the cell occupied by the ants)

Local neighborhood perceived by the ant

Position of the ant Building material


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3D agent-based model of ant nest construction


Partie modèle construction enlevée (travail en cours et non publié)

V. Discussion and perspectives

!  Coupling self-organisation with environmental templates is a powerful mechanism to achieve new forms

!  Environmental gradients can modulate positive feedback, and in turn are modulated by the emerging structures

!  Emerging structures influence animal displacement and thus determines where construction activity takes place

!  These interactions can let simple rules produce complex new patterns

simulated air current 5cm/s !  Elongated piles are a first stage towards wall building - a mechanism at work in the construction of Macrotermes ventilation systems?

!  Adapt the model to the construction of termite nests

V. Discussion and perspectives

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!  Elongated piles are a first stage towards wall building - a mechanism at work in the construction of Macrotermes ventilation systems?

!  Adapt the model to the construction of termite nests

!  More field work to obtain growth dynamics of ant/termite mound internal structures

!  Interaction with temperature templates? The simulation tools are available: the lattice Boltzmann algorithm can simulate both fluid flows and the temperature field in complex geometries

V. Discussion and perspectives Acknowledgements

Centre de Recherche sur la Cognition Animale CNRS UMR 5169, Toulouse, France

Guy Theraulaz Vincent Fourcassié Jacques Gautrais Christian Jost Anaïs Khuong Andrea Perna (Centre for Interdisciplinary Mathematics, Uppsala, Sweden)

Complex Systems Lab Universitat Pompeu Fabra, Barcelona, Spain

Ricard Solé Sergi Valverde

Pascale Kuntz Fabien Picarougne

Laboratoire Matière et Systèmes Complexes CNRS UMR 7057 Université Paris Diderot, Paris, France Stéphane Douady

Laboratoire d’Informatique de Nantes Atlantique CNRS UMR 6241 Ecole Polytechnique de l’Université de Nantes, France

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