Collective motion of birds and locusts

Collective motion of birds and locusts

David J. T. Sumpter

Department of Mathematics

Uppsala University

Are there simple behavioural rules which explain all these very different outcomes?

How the two birds x and y change position:

2

2

2

)(exp)(/)(exp)(

2

)(exp)(/exp

b

a

b

a

r

yxyxrydyd

dt

dy

r

yxyxrxx

dt

dx

2

2

2

)(exp)(/)(exp)(

2

)(exp)(/exp

b

a

b

a

r

yxyxrydyd

dt

dy

r

yxyxrxx

dt

dx

β=1 β=0.98

Does distance between established routes explain these very different outcomes?

a

c

b

C 2

C 1

C 4

C 3

W 1

W 2

W 3

W 5 W 6

W 4

G 5

G 2

G 12

G 6

G 7

G 9

G 8 G 3

G 1

G 11G 10

G 4

Dominance Hierarchy

Proportion improvement in paired flight by singly more efficient bird

Proportion improvement in paired flight by

singly less efficient bird

dc

,)()1()()1(

),()()1(

||

0

irjijii

iii

tuGtutu

tuvtxtx

1D self-propelled particles

Position:

Velocity:

Czirok, Vicsek et al. (1999)


Position:

Velocity:

Tim

e

Space Time

Ave

rage

dire

ctio

n

,)()1()()1(

),()()1(

||

0

irjijii

iii

tuGtutu

tuvtxtx


Position:

Velocity:

Tim

e

Space Time

Ave

rage

dire

ctio

n

,)()1()()1(

),()()1(

||

0

irjijii

iii

tuGtutu

tuvtxtx


Position:

Velocity:

Tim

e

Space Time

Ave

rage

dire

ctio

n

,)()1()()1(

),()()1(

||

0

irjijii

iii

tuGtutu

tuvtxtx


Particle Density

Ave

rage

Dire

ctio

n

Model vs data

Model vs data

Collective vs individual motion

0 – 60 minutes 60 – 180 minutes

Treatment

Control

High density treatment

High density experiment

time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

0

1


time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

-0.5

0

0.5

1


time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

-0.5

0

0.5

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Control experimentsLow density experiment

time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

-0.5

0

0.5

1

Low density experiment

time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

0

1

Low density experiment

time (mins)

Gro

up a

lignm

ent

20 40 60 80 100 120 140 160-1

-0.5

0

0.5

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Alignment

Activity (moving locusts)

Activity vs Alignment

Some conclusions

• Activity is the key parameter in predicting alignment in locusts.

• Degree of conflict is the key parameter in predicting compromise in pigeons.

• In both cases there is a sharp transition from one type of behaviour as this parameter is changed.

Collective Animal Behaviour

www.collective-behavior.com









ReferencesBiro, D., Sumpter, D. J. T., Meade, J. & Guildford, T. (2006) From compromise to leadership

in pigeon homing, Current Biology, 2006 16: 2123-2128.

Buhl, J., Sumpter, D. J. T., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. & Simpson, S. J. (2006) From disorder to order in locust marching, Science, 312, 1402 - 1406. .

Yates, C., Erban, R., Escudero, C., Couzin, I. D. ,Buhl, J., Kevrekedis, I., Maini, P. K., Sumpter, D. J. T. (2009) Inherent noise can facilitate coherence in collective swarm motion, Proceedings of the National Academy of Sciences, almost accepted.

Hale, J. J. (2008) Automated tracking of locusts and humans, DPhil thesis, University of Oxford.

Sumpter, D. J. T., Krause, J. James, R., Couzin, I. D. and Ward A. J. W (2008) Consensus decision-making by fish, Current Biology, 18, 1773–1777.

Ward, A. J. W., Sumpter, D. J. T., Couzin, I. D., Hart, P. J. B. and Krause, J. (2008) Quorum decision-making facilitates information transfer in fish shoals Proceedings of the National Academy of Sciences, 105, 6948-6953.

Sumpter, D. J. T. (2006) The principles of collective animal behaviour, Philosophical Transactions of the Royal Society of London: Series B, 361, 5-22.

Webpage: http://www.math.uu.se/~david/web/

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Collective motion of birds and locusts