Biologically-inspired rules for adaptive
network design
M.D. Fricker
C
N
P
Formation of fungal transport networks
µm
mm
cm
dm
m
km? – the Wood Wide Web
Foraging fungi explore a patchy resource environment, but must remain
connected to re-allocate resources through a responsive network
Self-organised network development –
a combinatorial optimisation problem
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Search efficiency
Transport efficiency
Resilience to attack
Adaptability
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Cost
Speed
Scaling
Control complexity
Macroscopic network development
Cord formation
Analysis of corded networks
Weighted network evolution
250 mm, 40 d
570 mm, 208 d
Semi-automated network extraction
Raw image
Phase-congruency tensor neuriteness
PCT-neuriteness cost-map
NE direction
Live-wire tracing algorithm
Comparison with defined model networks
Increasing efficiency
Increasing resilience
Increasing cost
Predicted transport efficiency
functional efficiency ( mm)
Root Efficiency - calculated as the sum of
the inverse of the shortest paths from the
inoculum to every other node
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
20000 30000 40000 50000
convex hull area (mm
)
2
Resilience of weighted networks
Predicted resilience
connected fraction
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
broken link fraction
1.0
In vivo dynamic resilience to interdiction
Grazing curtails further exploratory growth
ungrazed
I
R
I
R
I
R
grazed
I
I
(d
R
ij ( t  208)  d ij ( t 36) ) (d ij , max  d ij , min )
R
R
I
Link evolution
10 cm
-1.0 -0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8 1.0
1
0.9
36 d
0.8
57 d
0.7
78 d
0.6
99 d
0.5
155 d
0.4
208 d
proportion of connected mass
proportion of connected mass
…but yields a more resilient network
0.3
0.2
1
0.9
36 d
0.8
57 d
0.7
78 d
0.6
99 d
0.5
155 d
0.4
208 d
0.3
0.2
0.1
0.1
0
0
0
0.2
0.4
0.6
0.8
proportion of link area removed
ungrazed
1
0
0.2
0.4
0.6
0.8
proportion of link area removed
grazed
1
Functional significance of resilience?
Phanerochaete velutina in competition with Hypholoma fasciculare
when both are under grazing pressure from Collembola
Mapping nutrient flows
Photon-counting scintillation imaging
Resource allocation in heterogeneous
environments
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External C-resource induce a change in internal N-resource allocation,
promoting N accumulation and asymmetric growth
Estimate the total amount by sector, aligned to the inoculum-bait axis,
the centre of mass, its alignment and the angular concentration
Displacement of the centre of N mass
filter paper
35
35
30
30
CM displacement (µm)
CM displacement (µm)
control
25
20
15
10
5
0
-200
-50
100
normalised time (h)
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
250
25
20
15
10
5
0
-200
-50
100
250
normalised time (h)
N-resources are preferentially allocated to the Crich sector
The sensitivity decreases with developmental age
Linking network structure
and nutrient flows
Development of baited networks over 6 weeks
14C-AIB
transport in control and baited colonies
14C-AIB
transport only shows a partial correlation with
network measures…..
Final time point
Betweenness centrality
link evolution
link growth
PCSI image
Embryonic network transport conclusions……
6
5
Sector-based
SP-reallocation
model
[AIB]
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
final link weight
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Where 14C-AIB movement does occur it follows
expectations from basic network structure....
but overall control of routing is more
sophisticated….
The mechanistic basis of network formation –
parallel flow models….
The mechanistic basis of network
formation
Circuit analogue model
I
i
i
i
i
i
Parallel flow model predictions
Growth-induced flows
Feedback and network evolution
I
i
i
i
i
i
Changes in cord area depend on current flow
Oscillations
Pulsatile transport in Coniophora
Self-organisation of oscillatory phase domains
Bait
Cord
Mycelium
0
10
20
time (h)
30
40
Synchronised oscillations and transport during
colony fusion
C
-5
-2.5
0
2.5
5
lag (h)
E
-5
-2.5
0
2.5
5
lag (h)
Long distance transport following multiple
colony fusions
Gives a synchronized super organism
Adaptive network development in other
organisms
Maze solving in Physarum
Nakagaki, T., Yamada, H. and Toth, A. (2000) Nature, 407, 470
Winner of the Ig Nobel prize for cognitive science, 2008
Physarum and the Tokyo rail network
Toshiyuki Nakagaki, Seiji Takagi, Atsushi Tero, Hokkaido University
Growing a rail network
Multiple resource Physarum solver model
Tero et al., 2010, Science 327, 439 – 442
Evolution of the UK rail network
The largest network experiment on the planet
Resilience of the UK rail network
16
1845
1854
1875
1914
1922
1961
1969
1987
2008
Efficiency (x10-4)
14
12
10
8
6
4
2
0
0
500
1000
Links removed
1500
Slime mold to run the UK rail network
Physarum performs as well as real networks
root efficiency
resilience
1.20E+08
1
0.9
1.00E+08
0.8
Physarum
mst
rng
gab
del
rail network
Reachability
0.7
8.00E+07
6.00E+07
4.00E+07
0.6
0.5
0.4
0.3
0.2
0.1
2.00E+07
0
0
0.00E+00
Tokyo
UK
100
200
300
400
500
Number of links broken
600
Summary ideas
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Oscillatory behaviour is a recurrent theme
Biophysical coupling and conservation laws
transfer information
Microbes process in parallel
Fungi and slime moulds build networks with
comparable properties to real-world networks
However, the biological networks are selforganised, using local rules with no centralised
control
Thanks to……
Mycelial networks
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Dan Bebber
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Jessica Lee
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Dan Leach
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Lynne Boddy
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Juliet Hynes
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Jonathan Wood
Image analysis
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Boguslaw Obara
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Vincente Grau
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David Gavaghan
Network models
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David Smith
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Chiu-Fan Lee
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Neil Johnson (Miami)
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Nick Jones
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Luke Heaton
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Eduardo Lopez
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Philip Maini
Transport physiology
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Monika Tlalka
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Peter Darrah
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Sarah Watkinson
Network taxonomy
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Jukka-Pekka Onnela
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Daniel Fenn
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Stephen Reid
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Mason Porter
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Peter Mucha
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Nick Jones
Physarum networks
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Toshiyuki Nakagaki
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Seiji Takagi
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Atsushi Tero
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Ryo Kobayashi
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Kentaro Ito
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Tetsu Saigusa
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Kenji Yumiki
From function to structure?
time t
is agent
alive?
no
yes
Take up external resources
Remove maintenance cost
enough
resource to
grow?
no
enough
space to
grow?
yes
Recycle material using
resorption rules
no
yes
Grow a new agent using
growth rules
Remove growth cost
are there
unconnected
neighbours?
yes
Connect using anastomosis rules
no
is there any
resource
left?
yes
Distribute resources using allocation
rules
Remove transport cost
no
time t+1
Emergent canalisation in a resourcepushing agent simulation
OXFORD
Recycling and anastomosis agent models
Comparison with other networks –
Network taxonomy
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Based on community detection across scales
Gradually increase the repulsion (λ) between nodes and
watch how the network fragments
Define mesoscopic response functions based on the
effective energy (Heff), the effective entropy (Seff) and the
number of communities (neff)
ξ
λ
A taxonomy of fungal networks
Resinicium
Physarum
Phallus
Phanerochaete Stropharia
Agrocybe
Comparative network taxonomy
Synchonised phase and frequency shifts
STFFT phase
STFFT frequency