1. The document discusses the potential applications of network theory to plant epidemiology and pathology. 2. It provides examples of recent work modeling disease spread in networks and a case study on Phytophthora ramorum. 3. The author proposes further applications of network theory could include plant-vector interactions, conservation biology, and invasion ecology related to plant diseases.

1. Networks and
Epidemiology
Marco Pautasso,
Division of Biology,
Imperial College London,
Wye Campus, Kent, UK
Wye, 8 June 2007
number of passengers per day
from: Hufnagel et al. (2004) Forecast and control of epidemics in a globalized world. PNAS 101: 15124-15129

2. Relative concentration of Infections in case of a
infectious individuals in case smallpox outbreak starting
of an influenza pandemic from London (5*5 km cells)
t = 75
days in
both
cases
from: Riley (2007) Large-scale spatial-transmission models of infectious disease. Science 316: 1298-1301

3. Web of susceptible genera connected by Phytophthora ramorum (based on
genus co-existence in 2788 positive findings in England & Wales, 2003-2005)

4. Epidemiology is just one of the
many applications of network theory
Network pictures from:
Newman (2003) NATURAL
The structure and function
of complex networks. food webs
SIAM Review 45: 167-256
cell
metabolism
neural
networks Food web of Little Rock
ant nests Lake, Wisconsin, US
sexual
DISEASE partnerships
SPREAD
family
innovation networks
flows
Internet co-authorship HIV
structure railway nets spread
telephone calls
networks urban road network
electrical networks E-mail
committees
power grids airport Internet WWW patterns
computing networks
grids software maps
TECHNOLOGICAL SOCIAL

5. Epidemic spread of studies applying network theory
2005
2005
2005
2005 2005
2004
2005 2006
2004
2004
2001
2005
2002 2006
2004
2003 2005
2004
2005
2003 2005
2005
2005
2006
2005
2003
2005

6. Networks and Epidemiology
1. Introduction: interconnected world,
growing interest in network theory
and disease spread in networks
2. Examples of recent work modelling
disease (i) spread and (ii) control
in networks of various kinds
3. Case study: Phytophthora ramorum and
epidemiological simulations in networks of small size
4. Conclusion: further potential work applying
network theory in plant sciences

7. Different types of networks
local small-world
random scale-free
Modified from: Keeling & Eames (2005) Networks and epidemic models. Interface 2: 295-307

8. Epidemic development in different types of networks
scale-free
random
2-D lattice rewired
2-D lattice
1-D lattice rewired
1-D lattice
N of nodes of networks = 500;
p of infection = 0.1;
latent period = 2 time steps;
infectious period = 10 time steps
From: Shirley & Rushton (2005) The impacts of network topology on disease spread.
Ecological Complexity 2: 287-299

9. Super-connected individuals in scale-free networks
A reconstruction of the recent
UK foot-and-mouth disease
epidemic (20 Feb–15 Mar 2001).
Vertices marked with a label
are livestock markets,
unmarked vertices are farms.
Only confirmed infected
premises are included.
Arrows indicate route of
infection.
From: Shirley & Rushton (2005) Where diseases and networks collide:
lessons to be learnt from a study of the 2001 foot-and-mouth disease
epidemic. Epidemiology & Infection 133: 1023-1032

10. Degree distribution of nodes in a scale-free network
based on a reconstruction of
the UK foot-and mouth
disease network.
Fitted line:
y= 118.5x -1.6,
R2 = 0.87
From: Shirley & Rushton (2005) Where diseases and networks collide:
lessons to be learnt from a study of the 2001 foot-and-mouth disease
epidemic. Epidemiology & Infection 133: 1023-1032

11. Fraction of population infected (l) as a function of ρ0
uniform degree
distribution
scale-free network
with P(i) ≈ i-3
ρ0 is coincident with R0
for a uniform degree
distribution;
for a scale-free network,
theory says that
R0 = ρ0 + [1 + (CV)2],
where CV is the
coefficient of variation of
the degree distribution
From: May (2006) Network structure and the biology of populations.
Trends in Ecology & Evolution 21, 7: 394-399

12. Networks and Epidemiology
1. Introduction: interconnected world,
growing interest in network theory
and disease spread in networks
2. Examples of recent work modelling disease
(i) spread and (ii) control in networks of various kinds
3. Case study: Phytophthora ramorum
and epidemiological simulations
in networks of small size
4. Conclusion: further potential work applying
network theory in plant sciences

13. Sudden Oak Death in California
From Desprez-Loustau et al. (2007) The fungal dimension of biological
invasions. Trends in Ecology & Evolution, in press

14. Sudden Oak Death ground surveys,
Northern California, 2004
Map courtesy
of Ross Meentemeyer

15. Trace-forwards and positive detections across the USA, July 2004
Trace forward/back zipcode
Positive (Phytophthora ramorum) site
Hold released
Source: United States Department of Agriculture,
Animal and Plant Health Inspection Service, Plant Protection and Quarantine

18. England and Wales: records positive
to Phytophthora ramorum
n = 2788
Jan 2003-Dec 2005
Data source: Department for Environment, Food and Rural Affairs, UK

19. Own epidemiological investigations in four
basic types of directed networks of small size
local small-
world SIS-model
N nodes = 100
constant n of links
directed networks
probability of infection
for the node x at time
random scale- t+1 = Σ px,y iy where
free px,y is the probability
of connection between
node x and y, and iy is
the infection status of
the node y at time t

20. Examples of epidemic development in four kinds of
directed networks of small size (at threshold conditions)
sum probability of infection across all nodes
1.2 40 1.2 25
35
% nodes with probability of infection > 0.01
1.0 1.0
20
small-world network nr 4;
30
0.8 0.8
25
starting node = nr 14 15
0.6 20 0.6
10
15
0.4 0.4
local network nr 6; 10
5
starting node = nr 100
0.2 0.2
5
0.0 0 0.0 0
1 51 101 151 201 1 26 51 76
1.6 iteration 60
1.2 iteration 80
1.4
1.0
scale-free network nr 2; 70
starting node = nr 11
50
1.2 60
40 0.8
1.0 50
0.8 30 0.6 40
0.6
random network nr 8; 30
0.4
starting node = nr 80 20 0.4
20
10 0.2
0.2 10
0.0 0 0.0 0
1 26 51 76 1 26 51 76

21. Linear epidemic threshold on a graph of the
probability of persistence and of transmission
1.00
local
epidemic
develops small-world
probability of persistence
0.75 random
scale-free
0.50
0.25
no
epidemic
0.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
probability of transmission

22. Temporal development; England & Wales, 2003-2005; n = 2788
250
R ecords positive to P . ram orum
unclea r w hic h
200
n of records
esta tes/env ironm ent
150
nurseries/ga rden
centres
100
50
0
3
4
5
03
3
04
4
05
5
3
4
5
-0
-0
-0
l-0
l-0
l-0
-0
-0
-0
n-
n-
n-
pr
pr
pr
ct
ct
ct
Ju
Ju
Ju
Ja
Ja
Ja
O
O
O
A
A
A
Data source: Department for Environment, Food and Rural Affairs, UK

23. Spatially-explicit
modelling framework
Climate Long-distance trade
suitability
Local Trade
Heathland
Woodland

24. Networks and Epidemiology
1. Introduction: interconnected world,
growing interest in network theory
and disease spread in networks
2. Examples of recent work modelling disease
spread and control in networks of various kinds
3. Case study: Phytophthora ramorum and
epidemiological investigations in networks of small size
4. Conclusion: further potential work
applying network theory in plant sciences

25. Where are the applications to plant pathology?
LEGEND:
PLANT
no brackets = (plant
application existing (mycorrhiza) metabolomics –
(plant meta- cellular pathways)
(…) = application
existing, but not populations)
strictly involving
disease [nursery
networks]
[…] = would involve
plant pathology, but [quarantine] [plant-vector
application of network interactions
theory lacking [epiphytotics e.g. viruses]
management
& control]
(plant-
[recreation/ pollinator
amenities interactions)
(plant-
landscape] frugivore
(bats in
networks of interactions)
computer hollow trees)
viruses
Neisseria foot and fish diseases
(rumor gonorrhoeae mouth disease
propagation) Mycoplasma HIV Dengue avian flu bovine
pneumoniae Rotavirus SARS raccoon rabies
tuberculosis
HUMAN ANIMAL

26. Further potential work applying
network theory in plant sciences
• conservation biology (e.g. meta-populations,
reserve networks, botanical gardens)
• invasion ecology (for exotic organisms
particularly when spread by the nursery trade)
• gene-for-gene interactions?

27. Network of gene-for-gene relationships between
rice and diverse avrBs3/pthA avirulence genes in
Xanthomonas oryzae pv. oryzae
HR: High Resistance; R: Resistance; MR: Medium Resistance;
MS: Medium Susceptibility; S: Susceptibility
IRB IRB IRB Tet IR2
Avr IRBB1 IRBB2 IRBB3 IRBB4 IRBB7 IRBB8 IRBB10 IRBB11 B13 B14 B21 ep 4
gene Near isogenic lines of rice
clones a b c d e f g h i j k l m
PXO99 (p41) 1 MR R R HR HR R R MS MR HR HR MR HR
PX099 (p51) 2 HR HR HR HR HR R HR HR R R HR HR HR
PXO99 (p54) 3 S MR HR S MR MS R S MR MR R S MS
PXO99 (p56) 4 MS S S MS R HR R MS R S R S S
PXO99 (p58) 5 R HR R MR HR HR R HR R R R R R
PXO99 (p65) 6 S HR S S MR MS R S R S HR S S
PXO99 (p71) 7 MS MS S MS HR MR HR R MR MR HR HR HR
PXO99
(PUFR034) 8 MS S MS S MR MR MR S R MR HR S S
PX099 9 MS S MS S MR MR MR S R MR HR S S
JXOIII 10 MS MS HR MR HR R HR HR R S HR S MS
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

28. Network of gene-for-gene relationships between rice and diverse
avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae
(based on coexistence of High Resistance in the same isogenic lines of
rice for different gene clones; the number in the matrix is the number
of isogenic lines with HR in the two gene clones connected)
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

29. Network of gene-for-gene relationships between rice and diverse
avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae
(based on coexistence of High Resistance in the same isogenic lines of
rice for different gene clones; the strength of the lines reflects the
number of connections)
JXOIII PXO99
PXO99 (p41) PXO99 (pUFRO34)
PXO99 (p51) PXO99 (p71)
PXO99 (p65)
PXO99 (p54)
PXO99 (p58)
PXO99 (p56)
N of links:
1 2 3 4 5
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

30. Frequency distribution of the number of links for
isogenic lines of rice (based on coexistence of High
Resistance in the same pathogen gene clone for
different isogenic lines of rice)
7
number of gene clones
6
5
4
3
2
1
0
0-5 6-15 16-25
n u m b er of c on n ec tion s
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

31. Network of gene-for-gene relationships between rice and diverse
avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae (based
on coexistence of High Resistance in the same gene clone for different
isogenic lines of rice; the number in the matrix is the number of gene
clones with HR in the two isogenic lines of rice connected)
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

32. Network of gene-for-gene relationships between rice and diverse
avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae
(based on coexistence of High Resistance in the same gene clone for
different isogenic lines of rice; the strength of the lines reflects the
number of connections)
IRBB1 IR24
Tetep
IRBB2
IRBB21
IRBB3
IRBB14
IRBB4
IRBB13
IRBB7
IRBB8 IRBB11
IRBB10
N of links:
1 2 3 4
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

33. Frequency distribution of the number of links for Avr
gene clones (based on coexistence of High Resistance
in the same isogenic lines of rice for different
pathogen gene clones)
8
number of isogenic lines of rice
7
6
5
4
3
2
1
0
0 -5 6 -1 5 1 6 -2 5
n u m b er of c on n ec tion s
Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

34. Acknowledgements
Mike Jeger, Imperial College, Wye Campus
Mike Shaw & Tom Harwood, Univ. of Reading
Xiangming Xu, East Malling Research
Ottmar Holdenrieder, ETHZ, CH
Sandra Denman, Forest Research, Alice Holt
Judith Turner, Central Science Laboratory, York
Department for Environment, Food and Rural Affairs

35. References
Dehnen-Schmutz K, Holdenrieder O, Jeger MJ & Pautasso M (2010) Structural change in the international horticultural industry: some implications
for plant health. Scientia Horticulturae 125: 1-15
Harwood TD, Xu XM, Pautasso M, Jeger MJ & Shaw M (2009) Epidemiological risk assessment using linked network and grid based modelling:
Phytophthora ramorum and P. kernoviae in the UK. Ecological Modelling 220: 3353-3361
Jeger MJ & Pautasso M (2008) Comparative epidemiology of zoosporic plant pathogens. European Journal of Plant Pathology 122: 111-126
Jeger MJ, Pautasso M, Holdenrieder O & Shaw MW (2007) Modelling disease spread and control in networks: implications for plant sciences. New
Phytologist 174: 179-197
Lonsdale D, Pautasso M & Holdenrieder O (2008) Wood-decaying fungi in the forest: conservation needs and management options. European
Journal of Forest Research 127: 1-22
MacLeod A, Pautasso M, Jeger MJ & Haines-Young R (2010) Evolution of the international regulation of plant pests and challenges for future plant
health. Food Security 2: 49-70
Moslonka-Lefebvre M, Pautasso M & Jeger MJ (2009) Disease spread in small-size directed networks: epidemic threshold, correlation between
links to and from nodes, and clustering. J Theor Biol 260: 402-411
Moslonka-Lefebvre M, Finley A, Dorigatti I, Dehnen-Schmutz K, Harwood T, Jeger MJ, Xu XM, Holdenrieder O & Pautasso M (2011) Networks in
plant epidemiology: from genes to landscapes, countries and continents. Phytopathology 101: 392-403
Pautasso M (2009) Geographical genetics and the conservation of forest trees. Perspectives in Plant Ecology, Systematics & Evolution 11: 157-189
Pautasso M (2010) Worsening file-drawer problem in the abstracts of natural, medical and social science databases. Scientometrics 85: 193-202
Pautasso M & Jeger MJ (2008) Epidemic threshold and network structure: the interplay of probability of transmission and of persistence in directed
networks. Ecological Complexity 5: 1-8
Pautasso M et al (2010) Plant health and global change – some implications for landscape management. Biological Reviews 85: 729-755
Pautasso M, Moslonka-Lefebvre M & Jeger MJ (2010) The number of links to and from the starting node as a predictor of epidemic size in small-
size directed networks. Ecological Complexity 7: 424-432
Pautasso M, Xu XM, Jeger MJ, Harwood T, Moslonka-Lefebvre M & Pellis L (2010) Disease spread in small-size directed trade networks: the role of
hierarchical categories. Journal of Applied Ecology 47: 1300-1309
Xu XM, Harwood TD, Pautasso M & Jeger MJ (2009) Spatio-temporal analysis of an invasive plant pathogen (Phytophthora ramorum) in England
and Wales. Ecography 32: 504-516