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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:. β=1. β=0.98. - PowerPoint PPT Presentation
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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)
1D self-propelled particles
Position:
Velocity:
Tim
e
Space Time
Ave
rage
dire
ctio
n
,)()1()()1(
),()()1(
||
0
irjijii
iii
tuGtutu
tuvtxtx
1D self-propelled particles
Position:
Velocity:
Tim
e
Space Time
Ave
rage
dire
ctio
n
,)()1()()1(
),()()1(
||
0
irjijii
iii
tuGtutu
tuvtxtx
1D self-propelled particles
Position:
Velocity:
Tim
e
Space Time
Ave
rage
dire
ctio
n
,)()1()()1(
),()()1(
||
0
irjijii
iii
tuGtutu
tuvtxtx
1D self-propelled particles
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
High density experiment
time (mins)
Gro
up a
lignm
ent
20 40 60 80 100 120 140 160-1
-0.5
0
0.5
1
High 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
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
Collective Animal Behaviour
www.collective-behavior.com
Collective Animal Behaviour
www.collective-behavior.com
Collective Animal Behaviour
www.collective-behavior.com
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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