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

NATURA

L

TECHNOLOGICAL SOCIAL

food webs

airport networks

cell metabolism

neural networks

railway networks

ant nests

WWWInternet

electrical power grids

software maps

computing grids

E-mail patterns

innovation flows

telephone calls

co-authorship

nets

family networks

committees

sexual partnerships

DISEASE SPREAD

Food web of Little Rock Lake, Wisconsin, US

Internet structure

Network pictures from: Newman (2003) SIAM Review

HIV spread network

Some recent applications of network theory

urban road networks

Moslonka-Lefebvre et al. (2011) Phytopathology

Network analysis of barley seed flows in Ethiopia

Abay et al. (2011) Plant Genetic Resources – Characterization and Utilization

Researchquestions:

Is the networ

k

1) homogeneous?

2) symmetric?

3) a giantcomponent?

Network analysis of barley seed flows in Ethiopia

data from: Abay et al. (2011)

0

20

40

60

80

100

1 2 3 4 5 6number of links

num

ber

of n

odes incoming

links

outgoinglinks

…

0

1

2

3

4

5

6

0 2 4 6 8

number of outgoing links

num

ber

of in

com

ing

links

N nodes = 186, N links = 210node ID links in links out

218 1 0314 0 1

135 2 1120 1 1

Network structure

modified from: Keeling & Eames (2005) Interface

random

scale-free

local

small-world

one-way

two-ways

uncorrelated

and correlation between links in and out

step 1

step 2

step 3

step n

…

Simple model of spread and establishment in a network

pt probability of transmission

… 100

node 1

2 3 4 5 6 7 8

Moslonka-Lefebvre et al. (2011) Phytopathology

pp probability of persistence

SIS deterministic model, 100 Nodes, fixed structure, absence/presence continuum

P [i (x, t)] = { pp * P [i (x, t-1)] + pt * P [i (y, t-1)]}

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

probability of transmission

pro

bab

ility

of p

ersi

sten

ce

localrandomsmall-worldscale-free (two-way)scale-free (uncorrelated)scale-free (one way)

Lower invasion threshold for scale-free networks with positive correlation between

in- and out-degree

from: Moslonka-Lefebvre et al. (2011) Phytopathology

NO INVASION

INVASION

Network analysis of barley seed flows in Ethiopia

data from: Abay et al. (2011)

0

20

40

60

80

100

1 2 3 4 5 6number of outgoing links

num

ber

of n

odes

BuketMugulatMelfaAdinefasHabesAynalemBolentabridges

0

20

40

60

80

100

1 2 3 4 5 6number of incoming links

num

ber

of n

odes

BuketMugulatMelfaAdinefasHabesAynalemBolentabridges

0

2

4

6

8

10

1 2 3 4 5 6number of outgoing links

num

ber

of n

odes

BolentaAynalemHabesAdinefasMelfaMugulatBuket

0

2

4

6

8

10

12

1 2 3 4 5 6number of incoming links

num

ber

of n

odes

BolentaAynalemHabesAdinefasMelfaMugulatBuket

n = 11, y = -0.25x + 1.91

R2 = 0.29, p = 0.09

0

1

2

3

4

0 2 4 6 8

n = 14

0

1

2

3

4

5

6

0 2 4 6

n = 9

0

1

2

3

4

0 1 2 3 4

n = 16

0

1

2

3

4

0 1 2 3 4 5

n = 14, y = 0.32x + 1.33

R2 = 0.21, p = 0.10

0

1

2

3

4

0 1 2 3 4

n = 11, y = 0.32x + 1.48

R2 = 0.32, p = 0.07

0

1

2

3

4

0 1 2 3 4

n = 19

0

1

2

3

4

0 2 4 6data from: Abay et al. (2011)

Network analysis of barley seed flows in Ethiopia

number of outgoing links

nu

mb

er

of

incom

ing

lin

ks

n = 92, y = -0.37x + 0.80

R2 = 0.20, p < 0.01

0

1

2

3

0 1 2 3 4

Network simulation of barley seed flows in Ethiopia

R2 = 0.19

0

10

20

30

40

0 1 2 3 4 5 6Number of links from the starting node

Num

ber

of nod

es rea

ched

0

10

20

30

40

0 50 100 150 200Starting node

Num

ber

of nod

es rea

ched

0

1

2

3

4

5

6

7

8

9

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46

iteration

sum

p o

f in

vasi

on a

cros

s al

l nod

es

0

5

10

15

20

25

30

n n

odes

with p

inva

sion

>= 0

.01

Network analysis of barley seed flows in Ethiopia

modified from: Abay et al. (2011)

NETSEEDFRB-CESAB

NETSEED-CESAB

Seed exchange networks & agrobiodiversity

An interdisciplinary approach to study the role of seed exchange networks

in preserving crop biodiversity

Documenting/understanding/protecting agrobiodiversity

from: Oliveira et al. (2012) Tetraploid wheat landraces in the Mediterranean basin:

taxonomy, evolution and genetic diversity. PLoS One

0

25

50

75

100

0 25 50 75 1000

25

50

75

100

0 25 50 75 100

0

25

50

75

100

0 25 50 75 100

fin

al siz

e o

f in

vasio

n

(N o

f n

od

es w

ith

in

vasio

n s

tatu

s >

0.0

1)

0

25

50

75

100

0 25 50 75 100

(local) (sw)

(rand)(sf2)

0

25

50

75

100

0 25 50 75 1000

25

50

75

100

0 25 50 75 100

(sf0) (sf1)

starting node of the invasion

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8

-1.0

0.0

1.0

-1 0 1 2 3

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10 12

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6

su

m a

t eq

uilib

riu

m o

f in

vasio

n

sta

tus a

cro

ss a

ll n

od

es (

+0

.01

fo

r sf

netw

ork

s)

local

randsf2 (log-

log)

n of links from starting node

n of links from starting node

sw

sf0 (log-log)

sf1 (log-log)

Correlation of invasion final size with out-degree of starting node increases with network

connectivity

N replicates = 100; error bars are St. Dev.; different letters show sign. different means at p < 0.05

from: Pautasso et al. (2010) Ecological Complexity