This document discusses network analysis methods for studying seed exchange networks in agrobiodiversity conservation. It provides examples of network analysis applications in natural, technological, and social networks. The key concepts of network structure, homogeneity, symmetry, and giant components are introduced. Simple models are described for analyzing spread and establishment within networks using concepts like persistence probability and transmission probability. Challenges are noted around applying these network-based approaches to studying seed circulation systems.

1. Seed circulation networks in
agrobiodiversity conservation:
concepts, methods and challenges
Marco Pautasso (CEFE,
CNRS, Montpellier, France)
marpauta at gmail.com
ICE2012, S28, 24 May 2012

3. Some recent applications of network theory
Network pictures from: NATURAL
Newman (2003)
SIAM Review food webs
cell
metabolism
neural Food web of Little Rock
networks Lake, Wisconsin, US
ant nests sexual
partnerships
DISEASE
SPREAD
family
innovation networks
Internet flows co-authorship HIV
structure railway urban road nets spread
electrical networks networks network
power grids telephone calls
WWW
computing airport Internet E-mail
committees
grids networks software maps patterns
TECHNOLOGICAL SOCIAL
Moslonka-Lefebvre et al. (2011) Phytopathology

4. Network analysis of barley seed flows in Ethiopia
Research
questions:
Is the network
1) homogeneous?
2) symmetric?
3) a giant
component?
Abay et al. (2011)
Plant Genetic Resources – Characterization and Utilization

5. Network analysis of barley seed flows in Ethiopia
N nodes = 186, N links = 210 data from: Abay et al. (2011)
node ID links in links out
218 1 0
314 0 1
135 2 1
120 1 1
…
100 6
number of incoming links
incoming
number of nodes
80 5
links
4
60 outgoing
links 3
40 2
20 1
0
0
0 2 4 6 8
1 2 3 4 5 6
number of links number of outgoing links

6. Network structure and correlation between links in and out
one-way
random
uncorrelated
local
scale-free
two-ways
small-world
modified from:
Keeling & Eames (2005) Interface

7. Simple model of spread and establishment in a network
SIS deterministic model, 100 Nodes, fixed structure, absence/presence continuum
P [i (x, t)] = Σ { pp * P [i (x, t-1)] + pt * P [i (y, t-1)]}
node 1 2 3 4 5 6 7 8 … 100
step 1
pp probability of pt probability of
persistence transmission
step 2
step 3
…
step n
Moslonka-Lefebvre et al. (2011) Phytopathology

8. Lower invasion threshold for scale-free networks with
positive correlation between in- and out-degree
1.00
local
probability of persistence
random
0.75 small-world
INVASION
scale-free (two-way)
scale-free (uncorrelated)
0.50 scale-free (one way)
0.25
0.00
0.00 0.25 0.50 0.75 1.00
NO INVASION probability of transmission
from: Moslonka-Lefebvre et al. (2011) Phytopathology

9. Network analysis of barley seed flows in Ethiopia
100
10 100
12
80
Buket 10
80
8 Bolenta
Mugulat Buket
Aynalem Bolenta
Mugulat
Melfa
number of nodes
number of nodes
number of nodes
Habes 8 Aynalem
Melfa
number of nodes
Adinefas
60
6 Adinefas
Habes
60 Habes
Adinefas
Melfa Adinefas
Habes
Aynalem
6 Melfa
Aynalem
Mugulat
Bolenta
40
4 Buket
bridges 40 Mugulat
Bolenta
Buket
bridges
4
20 20
2 2
0
0 00
1 2 3 4 5 6 1 2 3 4 5 6
1 number of outgoing5links6
2 3 4 1 number of incoming links6
2 3 4 5
number of incoming links
number of outgoing links
data from: Abay et al. (2011)

10. Network analysis of barley seed flows in Ethiopia
4 6 4 4
n = 11, y = -0.25x + 1.91 n = 14 n = 16
n = 11, y = 0.32x + 1.48
2
R = 0.29, p = 0.09 5 2
R = 0.32, p = 0.07
3 3 3
4
2 3 2 2
2
number of incoming links
1 1 1
1
0 0
0 0
0 1 2 3 4
0 2 4 6 8 0 2 4 6 0 1 2 3 4 5
3 4 4 4
n = 92, y = -0.37x + 0.80 n=9 n = 19 n = 14, y = 0.32x + 1.33
2 2
R = 0.20, p < 0.01 R = 0.21, p = 0.10
3 3 3
2
2 2 2
1
1 1 1
0
0 0 0
0 1 2 3 4 0 1 2 3 4
0 1 2 3 4 0 2 4 6
number of outgoing links data from: Abay et al. (2011)

11. Network simulation of barley seed flows in Ethiopia
40
Number of nodes reached
30
20
10
0
0 50 100 150 200
Starting node
40
9 30
2
Number of nodes reached R = 0.19
sum p of invasion across all nodes
8
n nodes with p invasion >= 0.01
25
30
7
6 20
5 20
15
4
3 10
10
2
5
1
0
0 0
0 1 2 3 4 5 6
Number of links from the starting node
1
4
7
31
10
13
16
19
22
25
28
34
37
40
43
46
iteration

12. Network analysis of barley seed flows in Ethiopia
modified from: Abay et al. (2011)

13. NETSEED-CESAB
Seed exchange networks & agrobiodiversity
An interdisciplinary approach to study
the role of seed exchange networks
in preserving crop biodiversity
NETSEED
FRB-CESAB

14. Documenting/understanding/protecting
agrobiodiversity
from: Oliveira et al. (2012) Tetraploid wheat landraces in the Mediterranean basin:
taxonomy, evolution and genetic diversity. PLoS One

15. 100 100
75
(local) 75
(sw)
(N of nodes with invasion status > 0.01) 50 50
25 25
0 0
0 25 50 75 100 0 25 50 75 100
final size of invasion
100 100
(rand)
75 75
(sf2)
50 50
25 25
0 0
0 25 50 75 100 0 25 50 75 100
100 100
75
(sf0) 75 (sf1)
50 50
25 25
0 0
0 25 50 75 100 0 25 50 75 100
starting node of the invasion

16. 2.0 3.0
1.5
local 2.5 sw
across all nodes (+0.01 for sf networks) 2.0
sum at equilibrium of invasion status
1.0 1.5
1.0
0.5
0.5
0.0 0.0
0 1 2 3 4 5 6 0 2 4 6 8
3.0 1.0
2.5 rand sf2 (log-log)
2.0
1.5 0.0
1.0
0.5
0.0 -1.0
-1 0 1 2 3
0 2 4 6 8 10 12
2.0
2.0
1.5 sf0 (log-log) 1.5
sf1 (log-log)
1.0 1.0
0.5 0.5
0.0 0.0
-0.5 -0.5
-1.0 -1.0
0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8 1.0
n of links from starting node n of links from starting node

17. Correlation of invasion final size with out-degree of
starting node increases with network connectivity
from: Pautasso
et al. (2010)
Ecological N replicates = 100; error bars are St. Dev.;
Complexity different letters show sign. different means at p < 0.05