Animal transportation networks

Animal transportation
networks
Andrea Perna, with Tanya Latty
Workshop on collective motion and
interaction networks
Helsinki, May 2014
Parawixia bistriata (image downloaded from the internet)
Interaction networks are spatial networks
The Gambit of the group
Interaction networks are spatial networks
The Gambit of the group
The spatial association of individuals is the
first pre-requisite before stronger social
bonds are formed
Bode Wood Franks Behav Ecol Sociobiol 2011 65:117
Interaction networks are spatial networks
The Gambit of the group
The spatial association of individuals is the
first pre-requisite before stronger social
bonds are formed
Bode Wood Franks Behav Ecol Sociobiol 2011 65:117
Jeanson (2012) Animal Behaviour
Mersch et al. (2013) Nature
Interaction networks are spatial networks
The Gambit of the group
The spatial association of individuals is the
first pre-requisite before stronger social
bonds are formed
Bode Wood Franks Behav Ecol Sociobiol 2011 65:117
Animal transportation networks
Animals form different kinds of
transportation networks
Human vs. animal transportation networks
Self- organized
Planned
Human vs. animal transportation networks
Self- organized
Planned
Passive morphogenesis vs. active formation
Passive morphogenesis
!  Walking through compacted
ground reduces energy
expenditure
!  Trails form spontaneously as a
result of each individual trying to
find a minimum cost path
through the ground
Helbing et al. 1997. PRE 56, 2527-2539.
Passive morphogenesis and pattern
formation in the physical domain
Visualization of
Argentine ant trails
Electric discharge pattern
in a luminglass disk
Termite galleries in a 2-D
layer of soil
Mississippi river delta
Doyle, P and Snell, L.
(1984)
Random walks and
electrical networks
Passive morphogenesis vs. active formation
Active formation
!  Can be similar to passive
morphogenesis, but animals
perform actions or release
substances with the specific
purpose of building a trail
Cost of infrastructure and cost of
transportation
Efficient
transportation
Cheap
infrastructure
Intermediate
networks
Predictions of optimization theory
Optimal rooted transportation
networks are trees
Durand (2007) PRL 98, 088701
Predictions of optimization theory
Central place foragers
food
food
nest
food
food
food
food
Predictions of optimization theory
Formica aquilonia foraging trails are “trees”
Formica aquilonia
Star graph
Minimum Steiner tree
Buhl et al. (2009) BES 63(3):451-460
How tree-like networks can be produced
Initiation and continuation of termite galleries
Robson et al. 1995, Naturwissenschaften, 82, 526-528
Bardunias and Su 2009,
Predictions of optimization theory
Loops should evolve also in
rooted transportation networks if
the load varies in time, or in the
presence of disconnections
Katifori and Magnasco 2010 PRL
How loops can be produced
Easier to make loops when
building than when digging
Cost of infrastructure and cost of
transportation
The cost of infrastructure is
paid immediately, but its
benefit is often delayed :
only highly social animals will
invest directly in
infrastructure.
The cost of infrastructure is
high in the case of digging,
but many animals have
evolved strategies to
minimize it.
Kimchi, T., Reshef, M. and Terkel, J. (2005). Evidence for
the use of reflected self-generated seismic waves for
spatial orientation in a blind subterranean mammal. J.
Exp. Biol. 208, 647-659
Growth and pruning
It is difficult to quantify the impact of a
new connection before making it:
Optimization is difficult to achieve from
growth only mechanisms
Growth and pruning
Pruning is widespread in many
biological networks
Growth and pruning
Path selection toward a food source
Choice occurs randomly
(Deneubourg et al., 1990)
Growth and pruning
1
1
Some corridors are closed during
nest life!!!
4
3
2
1
<k> = 2
Perna et al. 2008, Physica A
History versus optimality
90°
90° 180°
Ant trails
Ant galleries
~90°
Flanagan et al. (2013) PLoS ONE
=180°
Buhl et al. (2005) Naturwissenschaften
History versus optimality
Euclidean Steiner tree problem:
€
Given N points in the plane, connect
them by lines of minimum total length
in such a way that any two points may
be interconnected by line segments
either directly or via other points and
line segments.
120°
120° 120°
Latty et al. (2011) J. R. Soc. Interface
sin(α ) sin(β ) sin(γ )
=
=
A
B
C
Orientation and navigation
Orientation and navigation
Location based navigation vs. direction based navigation
Orientation and navigation
Location based navigation vs. direction based navigation
Rosvall M. et al. (2005) PRL
Orientation and navigation
Location based navigation vs. direction based navigation
Olfactory cues are present
Olfactory cues are absent
Limax pseudoflavus
Follow olfactory cues
Follow the trail
Cook (1980, 1992)
Summary
1.  Distinction between active and passive networks
"  The distinction is not strong, but it may be
relevant when considering the cost of
infrastructure
2.  Only highly social animals should invest in
infrastructure
• 
Often this requires acquiring specific
behavioural modules and morphological
adaptations
3.  Optimality theory can help make predictions about
what the real networks should look like
"  However, robustness-efficiency trade-offs often
make it difficult to make predictions for a given
network
120°
120°
Summary
4.  Loops are an important network feature, that allows
us to think both about morphogenesis and function
"  From the point of view of morphogenesis, they
may be associated with trail formation and
building behaviour (initially open space)
"  From the point of view of function, they are
often associated with robustness
5.  History of growth is visible in the final network when
the substrate is « hard » and the network cannot
evolve towards an « optimal » configuration
6.  Networks have two opposite effects on navigation
"  They reduce the dimensionality of space,
making it easier to detect position
"  They constrain the movement, making it more
difficult to follow a specific direction (e.g. from
internal compass)
~90°
=180°
Animal transportation
networks
Andrea Perna, with Tanya Latty
We invented
the web!
And the social
network
Workshop on collective motion and
interaction networks
Helsinki, May 2014
Parawixia bistriata (image downloaded from the internet)