Download - Wiley Online Library

Review
Blackwell Publishing Ltd
Research review
Modelling disease spread and control in
networks: implications for plant sciences
Author for correspondence:
Marco Pautasso
Tel: +44 (0)20 759 42816
Fax: +44 (0)20 759 42669
Email: [email protected]
Mike J. Jeger1, Marco Pautasso1, Ottmar Holdenrieder2 and Mike W. Shaw3
Received: 13 December 2006
Accepted: 9 January 2007
Whiteknights, Reading RG6 6AS, UK
1
Division of Biology, Imperial College London, Wye Campus, Kent TN25 5AH, UK; 2Institute of
Integrative Biology, Department of Environmental Sciences, Eidgenössische Technische Hochschule,
8092 Zurich, Switzerland; 3The University of Reading, School of Biological Sciences, Lyle Tower,
Summary
Key words: complex networks, disease
management, epiphytotics, landscape
pathology, network structure, plant
pathogens, small-world, spatial dispersal.
Networks are ubiquitous in natural, technological and social systems. They are of
increasing relevance for improved understanding and control of infectious diseases
of plants, animals and humans, given the interconnectedness of today’s world.
Recent modelling work on disease development in complex networks shows: the
relative rapidity of pathogen spread in scale-free compared with random networks,
unless there is high local clustering; the theoretical absence of an epidemic threshold
in scale-free networks of infinite size, which implies that diseases with low infection
rates can spread in them, but the emergence of a threshold when realistic features
are added to networks (e.g. finite size, household structure or deactivation of links);
and the influence on epidemic dynamics of asymmetrical interactions. Models
suggest that control of pathogens spreading in scale-free networks should focus on
highly connected individuals rather than on mass random immunization. A growing
number of empirical applications of network theory in human medicine and animal
disease ecology confirm the potential of the approach, and suggest that network
thinking could also benefit plant epidemiology and forest pathology, particularly in
human-modified pathosystems linked by commercial transport of plant and disease
propagules. Potential consequences for the study and management of plant and
tree diseases are discussed.
New Phytologist (2007) 174: 279 –297
© The Authors (2007). Journal compilation © New Phytologist (2007)
doi: 10.1111/j.1469-8137.2007.02028.x
Introduction
Much scientific work is currently focusing on the properties
of networks (see Barabási & Albert, 1999; Newman, 2003;
papers cited therein). From a physical point of view, networks
may involve transport of energy, matter or information. From
a mathematical standpoint, networks are sets of elements and
www.newphytologist.org
of the relations between them. From both perspectives, networks
are models applicable to a wide variety of natural, technological
and social systems (e.g. Strogatz, 2001; Albert & Barabási,
2002; Table 1). Networks can be of interest to plant scientists
when they are formed by a physical structure, when they refer
to abstract relationships between connected entities (e.g. different
species), and when they underline processes or flows in a structure.
279
280 Review
Research review
Table 1 Examples of natural, technological and social networks that have been the object of recent analyses
Network
Type
Examples of references
Natural
Prebiotic mutually catalytic pathways
Microbial phylogenies (horizontal and vertical transfer of genes between microbes)
Cellular and metabolic dynamics (interactions of cellular components and biochemical molecules)
V
SF
SF
The topology of food webs (who eats whom in ecological communities)
V
Neural networks (the connections between neurons of e.g. the nematode
Caenorhabditis elegans)
Ant nests (a set of chambers interconnected by galleries)
Amphibian meta-populations in ponds
Bats roosting in hollow trees
Foraging walks of primates
Spatially remote thunderstorms
The Earth’s climate system (e.g. the correlations of monthly pressures on a 5 by 5 degrees grid)
Earthquake networks (links between strongly correlated earthquake events)
Syllable and word webs (the co-occurrence of syllables in words and of words in sentences)
SW
N
SF
SF
SF
SW
SW
SF
SF, SW
The decomposition of even numbers into two prime numbers (following the Goldbach conjecture)
SW
Shenhav et al. (2005)
Kunin et al. (2005)
Jeong et al. (2000);
Albert (2005)
Dunne et al. (2002);
Woodward et al. (2005)
Watts & Strogatz (1998);
Humphries et al. (2006)
Buhl et al. (2004)
Fortuna et al. (2006)
Rhodes et al. (2006)
Boyer et al. (2006)
Yair et al. (2006)
Tsonis & Roebber (2004)
Baiesi & Paczuski (2005)
Cancho & Solé (2001);
Soares et al. (2005)
Chandra & Dasgupta (2005)
Technological
Railways (stations and connecting trains)
Urban street networks (streets and intersections)
Electric power grids (power generators, substations, high-voltage transmission lines)
SW
SW
SF
Air transport (airports and connecting flights)
V
The Internet (transit backbone providers and their nodes)
V
Computing grids (a set of processors connected by some kind of communication network)
Software maps (the topology of complex software systems)
Electronic circuits in computers (logic gates connected by wires)
V
V
SW
Social
Family networks (who is related to whom)
Friendship groups (who knows whom)
SF
SW
Bookworm contacts (book buyers spreading recommendations)
Links between Wikipedia articles
SF
SF
The World Wide Web (links to web pages)
V
Virtual learning communities (cultural transmission as contagion)
Medieval heresies and inquisition
Committees (who is in a meeting with whom)
Telephone calls (sets of people with whom a telephone user communicates)
Email patterns (electronic messages between email addresses)
Co-authorship groups (who does research with whom)
?
SF?
?
SF
SF
SF
Citation webs of scientists (who cites whom)
Terrorist groups (webs of perpetrators of terror attacks)
Financial fluctuations (e.g. the cross-correlations of stock prices)
Innovation flows (e.g. the flow of technological improvements from firm to firm)
Human movements (tracked for instance following the dispersal of bank notes)
The UK horse racing network
The world trade web (trade relationships between different countries)
Sexual partnerships
SF
V
SF
SF
SF
SW
V
V
Sen et al. (2003)
Jiang & Claramunt (2004)
Amaral et al. (2000);
Chassin & Posse (2005)
Barrat et al. (2004a);
Guimerá et al. (2005)
Gorman & Malecki (2000);
Pastor-Satorras et al. (2001)
Costa et al. (2005)
Valverde & Sole (2005)
Cancho et al. (2001)
Coelho et al. (2005)
Milgram (1967);
Amaral et al. (2000)
Sornette et al. (2004)
Capocci et al. (2006);
Zlatic et al. (2006)
Adamic (1999);
Bornholdt & Ebel (2001)
Giani et al. (2005)
Ormerod & Roach (2004)
Porter et al. (2005)
Xia et al. (2005)
Ebel et al. (2002)
Newman (2001);
Barber et al. (2006)
Seglen (1992)
Qin et al. (2005)
Boginski et al. (2005)
Di Matteo et al. (2005)
Brockmann et al. (2006)
Christley & French (2003)
Serrano & Boguñá (2003)
Kretzschmar (2000)
Network types (SF, scale-free; SW, small-world; V, various types; N, none of the previous types) are assigned on the basis of the references
provided and do not rule out the possibility that other studies of networks of a similar nature may suggest a different structure. For other
references the reader is referred to reviews by, for example, Albert & Barabási (2002), Dorogovtsev & Mendes (2002) and Newman (2003).
New Phytologist (2007) 174: 279–297
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
Review
Table 2 Idealized network types discussed in the text (see Fig. 1 for a visual representation)
Type
Description
Properties
Examples of references
Local
Neighbourhood connectivity
(typically regular lattices)
Nodes connected with
probability P (Erdos–Renyi network)
Local network rewired with
shortcuts (Watts–Strogatz network)
Nodes preferentially connecting
to hubs (Barabási–Albert network)
High clustering,
high path length
Low clustering,
low path length
High clustering,
low path length
Proportion pk of vertices
connected to k other
vertices drops with increasing
k as k–α for some constant α
Harris (1974); Keeling & Eames (2005);
Shirley & Rushton (2005a)
Erdos & Renyi (1960); Bollobás (1985);
Roy & Pascual (2006)
Watts & Strogatz (1998); Barrat & Weigt (2000);
Moore & Newman (2000)
Barabási & Albert (1999); Balthrop et al. (2004);
Hwang et al. (2005); Newman (2005a)
Random
Small-world
Scale-free
Network theory (e.g. Bollobás, 1979; Chartrand, 1985;
Chen, 1997) has many practical biological applications in
plant sciences, for example biochemical networks (Aloy &
Russell, 2004; Arita, 2005; De Silva & Stumpf, 2005; Green
& Sadedin, 2005; Proulx et al., 2005; Sweetlove & Fernie,
2005; Uhrig, 2006), which form much of the focus of what
is now termed systems biology. But epidemiological studies
are also interesting dynamical problems in a system of connected entities (e.g. Matthews & Woolhouse, 2005; Zheng
et al., 2005). A number of papers have summarized recent
work modelling the spread of diseases in networks (to which
we refer for more details, elaboration and perspectives; e.g.
Wallinga et al., 1999; Watts, 1999; Koopman, 2004; Keeling
& Eames, 2005; Keeling, 2005b,c; Shirley & Rushton,
2005a; May, 2006; Parham & Ferguson, 2006). However, most
of this work has focused on human and animal diseases, thus
raising the question of whether a similar approach may also be
beneficial in plant and forest pathology.
The relevance of network theory to the epidemiology of
plant diseases is demonstrated by the growing literature on:
how landscape patterns affect the spread and establishment of
plant pathogens; large-scale site topographic, climatic and
edaphic characters predisposing to plant disease risk; and host
and pathogen genetic variation across their geographical
distribution. New genetic tools enable a much more precise
study of the dispersal of organisms on a geographic scale (e.g.
Banke & McDonald, 2005; Garrett et al., 2006; Stukenbrock
et al., 2006), and many questions in large-scale epidemiology
can be conveniently framed in terms of network theory. In
this review, we recapitulate important results of modelling
work on disease spread and control in networks, present
empirical studies applying network theory to a number of case
studies of human and animal pathologies, and discuss potential consequences for plant disease epidemiology (e.g. Gilligan, 2002; Jeger, 2004; Burdon et al., 2006) and for landscape
pathology, which is the study and management of tree diseases
on a larger scale than previously common and making use of
the tools of landscape ecology (e.g. Geils, 1992; Holdenrieder
et al., 2004; Lundquist & Hamelin, 2005; Pautasso et al.,
2005).
Modelling work
Epidemiological approaches based on networks study individuals and their contacts as a set of vertices (also known as
nodes, i.e. susceptible/infected entities) and connecting edges
(links and infection events) (e.g. May & Lloyd, 2001; PastorSatorras & Vespignani, 2001a; Newman, 2002). The contact
patterns between susceptible and/or infected individuals form
a network, which can be classified into various types (Table 2;
Fig. 1). In the approach most obviously related to network
theory, disease has been modelled on regular lattices, where
the probability of infection being passed to neighbouring cells
on a grid can be constant (zero-dimensional models, or massaction mixing; e.g. Anderson & May, 1991; Filipe & Maule,
2004) or random (epidemics in random graphs; e.g. Barbour
& Mollison, 1990), or can decrease as a certain function of the
distance from an infected cell (typically producing travelling
waves as in continuum models; e.g. Marchand et al., 1986;
Zadoks & Van den Bosch, 1994; Van den Bosch et al., 1999;
Russell et al., 2004). For plants, a further distinction can be
drawn between models that operate in a landscape of a more
or less fragmented natural environment and those studying
the behaviour of trade-based networks.
However, real populations rarely fall exactly into one of
these idealizations, being neither completely artificial nor
natural, and neither perfectly well-mixed, nor completely
random, nor located on regular lattices (e.g. Mollison, 1977;
Shaw, 1994; Kuperman & Abramson, 2001; Blyuss, 2005).
Networks where connectivity is neither local, nor regular nor
random but something in between these three extremes are
dubbed ‘small-world’ networks, because the shortest path
length between individuals increases only logarithmically
with increasing size of the network (Table 2; Fig. 1). It is on
these small-world networks, where global distances are low
and local interconnectedness (clustering) is high (Petermann
& De Los Rios, 2004; Roy & Pascual, 2006), that many
modellers have focused their recent epidemiological work.
Another type of network that has been the object of much
investigation is the scale-free network. In scale-free networks,
the probability that a given node has k connections follows an
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
281
282 Review
Research review
Fig. 1 Four basic kinds of network structure:
(a) local, (b) random, (c) small-world, and
(d) scale-free. Graphs are networks of 100
individuals with a constant number of links.
The circular layout does not reflect the spatial
arrangement of nodes.
inverse power-law distribution (Table 2; Fig. 1). This is called
the degree distribution of the network. Illustrations of such a
scale-free distribution in real-world networks can be found in
many recent papers (e.g. Shirley & Rushton, 2005b; Barber
et al., 2006; Montoya et al., 2006). Most scale-free networks
have small-world properties (e.g. Amaral et al., 2000), but
there are scale-free networks with low clustering, which are
thus not small-worlds, and there are small-world networks
that are not scale-free (see e.g. Jiang & Claramunt, 2004;
Humphries et al., 2006). A particular class of networks with
both scale-free and small-world properties is called Apollonian
networks (e.g. Andrade et al., 2005), but there are many kinds
of network with both scale-free and small-world properties
that are not Apollonian (e.g. Matsuyama et al., 2005; Palotai
et al., 2005). Each type of complex network described here
can be embedded in space (e.g. Rozenfeld et al., 2002;
Barthélemy, 2003; Morita, 2006). The distance between
two nodes will be reflected in the strength of the connection
between them, although it will not necessarily be the only
determinant. This is of particular interest to plant scientists,
as a plant lives in a single physical location.
Epidemiological models in networks can be roughly subdivided into those pertaining to disease spread and those
pertaining to disease control, although the interrelations are
obvious. Throughout, for ease of readability, mathematical
assumptions and notations of models are not reported from
the original papers, to which interested readers are referred.
Disease spread in networks
Recent work on disease spread in networks shows that the
probability of an epidemic occurring following an initial
New Phytologist (2007) 174: 279–297
infection is influenced by the contact structure in the first
phases of the epidemic (Gallos & Argyrakis, 2003; Brauer,
2005; Saramäki & Kaski, 2005). Depending on where it
originated, the first phase of an epidemic in a scale-free
network is often marked by super-spreading events, in which
a few infected entities with high numbers of connections are
responsible for the vast majority of infections (Barthélemy
et al., 2004; Brauer, 2005; Duan et al., 2005; James et al.,
2007). An immediate finding is thus that infectious diseases
can spread more easily in scale-free and small-world networks
than in regular lattices (e.g. Watts & Strogatz, 1998; Kuperman
& Abramson, 2001) and random networks (Kiss et al., 2006a;
Matthäus, 2006), although spread is less predictable because
of more stochasticity during the very early stages of the epidemic.
High degrees of local clustering can lead to a less than
exponential spread of diseases even at the very beginnings of
epidemics (Szendrøi & Csányi, 2004; Verdasca et al., 2005).
A second major result of models is that, in small-world
networks, the threshold for an epidemic to occur decreases as
a power-law with increasing number of shortcuts (longdistance infections) (Zekri & Clerc, 2001). As a result of the
heterogeneity in the number of links per node, epidemics in
scale-free networks of infinite size theoretically never die out,
no matter how low the basic reproduction rate is (PastorSatorras & Vespignani, 2001b; Moreno et al., 2002b; Boguñá
et al., 2003; Barthélemy et al., 2005). Therefore, in scale-free
networks, in order to correctly estimate R0, some measure of
the variance in the degree distribution of contacts is needed
(Woolhouse et al., 2005; Ferrari et al., 2006; Green et al., 2006;
May, 2006). The concept of a basic reproduction number R0
comes from studies of disease spread in homogenous landscapes
(e.g. Heesterbeek, 2002; Brauer, 2005; Green et al., 2006; for
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
plant epidemiology, e.g. Jeger, 1986; Jeger & van den Bosch,
1994). It is defined as the number of secondary infections
caused by a single infective individual introduced into a
wholly susceptible population, and depends normally on: the
number of potentially infectious contacts per individual; the
probability of infection per contact between infectious and
susceptible individuals; and the duration of infection (e.g.
Giesecke, 1994; Hethcote, 2000; Lloyd-Smith et al., 2005;
May, 2006). If R0 is less than 1 in a homogeneous population,
epidemics fail to establish.
In networks in which the probability of a node having a
certain number of contacts decreases exponentially as the number
of contacts increases, which are therefore not scale-free, a threshold R0 exists even in case of an infinite size (Pastor-Satorras
& Vespignani, 2001a). This is because the transmissibility
scales in non-scale-free networks with the average degree
(number of connections), whereas in scale-free networks it
scales with the variance of the degree distribution. For an epidemic threshold to be absent (in the infinite size limit, and
with the exponent of the power-law smaller than 3; see
Table 2), the connectivity of the network must thus be scalefree. A scale-free connectivity (i.e. a linear decrease in log-log
space of the number of links per node with increasing number
of nodes in a network) implies the existence of hubs, or highly
connected nodes. These hubs are largely responsible for the
observed differences between processes (not only epidemiological) modelled on scale-free networks and other kinds of
complex networks (e.g. Amaral et al., 2000). The key role of
hubs is corroborated by the finding that not only is the epidemic threshold lower in scale-free networks, but the time
needed for equilibrium levels of infection to be reached is
shorter (e.g. Shirley & Rushton, 2005a).
Work demonstrating the absence of an epidemic threshold
in scale-free networks of infinite size is not a mathematical
irrelevance, because, although scale-free networks of finite size
(with cut-offs at the lower and higher ends of the distribution
of connections) have thresholds, neglecting long-distance
connectivity still leads to an overestimation of the epidemic
threshold in finite populations (May & Lloyd, 2001; PastorSatorras & Vespignani, 2002a; Joo & Lebowitz, 2004; Hwang
et al., 2005; Ying et al., 2005). Whether or not epidemic
thresholds are really lower in real-world heterogeneous landscapes than in homogenous ones is an interesting question
and requires field work for it to be tested also empirically.
Whether or not scale-free networks are relevant for plant
meta-populations will be discussed in detail later in the review
(see ‘Potential implications for plant and forest pathology’).
Suffice it to say for now that, although plant networks are finite
(the world’s circumference has an order of magnitude of 107 m,
and individual leaves of diseased plants are around 10−2 m,
which would give potentially 10 orders of magnitude), if an
epidemic were to spread around the world during a period
substantially longer than its time of local development, then
it might not be too far-fetched to apply results from models
Review
of scale-free networks of infinite size to plant networks in
today’s globalized world. It would also be interesting to know
how relevant the distinction established by these thresholds
is for real epidemics. These might be theoretically unstable, but
last sufficiently long to make the threshold irrelevant in practice.
A third take-home message is that more complicated models
also have an epidemic threshold. Thresholds are predicted
in networks with high local clustering (Eguíluz & Klemm,
2002), in models taking into account differences in the rate of
infection for individuals with different connectivity (Olinky
& Stone, 2004), and, depending on the initial density of
infection, in models of disease spread in scale-free networks
created by the deactivation of links with probability inversely
proportional to their number of connections (Moreno &
Vázquez, 2003). Similarly, the combined effects of ageing
(older individuals in a network differing in their susceptibility)
and removal of links (dead individuals may no longer be connected to susceptible ones) on epidemic dynamics in scale-free
networks lead to a critical value of effective links in the network below which only local spread of disease takes place
(Chan et al., 2004; see also Amaral et al., 2000). The epidemic
threshold in community networks (where there are groups of
individuals with more connections between them than with
individuals outside the group), however, is still lower than in
a random network, other things being equal (Liu & Hu, 2005).
This issue is of relevance for plant diseases, because plants
in a field, forest or nursery may be at risk of infection from
pathogens present on plants in the same location, but also from
longer distance movements of disease propagules from other
fields, forests or nurseries (e.g. Parnell et al., 2006; Shaw et al.,
2006).
However, in scale-free networks with household structure
(which enables a distinction between infection among and
within households (Bian, 2004); for plant meta-populations,
the concept of household may be conveniently thought of in
terms of farms, pathosystems, or pathoregions (see Holdenrieder et al., 2004)), models predict that a disease can spread
through the network even if the recovery rate in single households is greater than the local infection rate (Liu et al., 2004).
However, as for homogenous networks, Grabowski & KosiNski
(2004) have found that in household networks disease spread
is slower when there is much local clustering. The same
authors have reported that, in these household network
models, diseases with a lower rate of spread have a greater
probability of surviving endemically. This finding is in agreement with the general theory of disease spread when there is
a high variance in contacts between individuals (Anderson &
May, 1991). Household structure also introduces into models
an asymmetry between individuals inside groups and individuals
connecting groups, with a higher probability of infection
from connecting individuals to those within a household than
vice versa (Meyers et al., 2003).
A fourth general finding is thus that asymmetries can have
an influence on disease spread in networks. It is known that
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
283
284 Review
Research review
models with symmetrical interactions are often unrealistic
approximations of real systems (e.g. Bauch & Galvani, 2003;
Bascompte et al., 2006; Chavez et al., 2006). Many real pathosystems present heterogeneities or asymmetries in the flow of
disease propagules carried by different links (e.g. Dall’Asta,
2005; Yan et al., 2005). A number of studies have started
investigating the spread of pathogens in directed networks of
various kinds (e.g. Newman et al., 2001; Schwartz et al., 2002;
Boguñá & Serrano, 2005; Meyers et al., 2006). For plants,
directed networks may be of relevance, for instance, in the
case of the trade among nurseries, garden centres and retail
centres, where the probability of movement from a certain
nursery to a given garden centre will tend to differ greatly
from the probability of movement in the reverse direction.
In many real-world examples, not only the number and
direction of connections of different nodes may be heterogeneous, but also their strength. Recent work has started to take
into account the variation in intensity of different links (e.g.
Yook et al., 2001; Barrat et al., 2004b; Jezewski, 2005), but
investigations of the implications of including weight in
models of disease spread and control in complex networks are
still in their infancy (e.g. Wu et al., 2005; Dall’Asta et al.,
2006). Intuitively, when higher connectivity strength per link
is assigned to highly connected individuals, the findings discussed for nonweighted scale-free networks will tend to be
present even more strongly. But it would be interesting to
know whether or not (and under which conditions) strong
links for the many nodes with few connections can cancel out
the effect of hubs if these have weak links. For plant diseases,
hubs with weak links may be a realistic model of control targeted
exclusively at plant movements from and to highly connected
traders, while strong links to many other nodes would be an
appropriate model if commercial growers with many customers
also tended to sell significantly more plants than small-scale
retailers with few connections.
Disease control in networks
A number of consequences for disease management can be
inferred from modelling work on disease spread in networks.
First, models show that random immunization of even a
high proportion of individuals is not an effective strategy to
control an epidemic operating in scale-free networks. This
result follows from the theoretical absence of an epidemic
threshold in scale-free networks with infinite variance in
connectivity: in this case, immunity is not conferred even by
high densities of randomly immunized individuals (e.g. PastorSatorras & Vespignani, 2002b; Zanette & Kuperman, 2002;
Takeuchi & Yamamoto, 2005). In networks with small-world
properties, as a result of the effect of shortcuts, the influence
of an untargeted immunization protocol is generally lower
than when only local infection is possible (KosiNski &
Adamowski, 2004). In a botanical context, protection may be
conferred by biological control or fungicides at the level of the
New Phytologist (2007) 174: 279–297
individual field, and by the intermixing of resistant varieties
and species at the landscape level.
Rather than random immunization, when disease spreads
on a scale-free network, an effective control strategy should
immunize highly connected nodes (e.g. Pastor-Satorras &
Vespignani, 2002b; Zanette & Kuperman, 2002; Liu et al.,
2003; Chang & Young, 2005; Hwang et al., 2005; LloydSmith et al., 2005). Models suggest that the more strategies
focus on immunization of highly connected individuals, the
more likely they are to bring under control an epidemic
spreading on a scale-free network, and the cheaper a successful
strategy will be (Dezsø & Barabási, 2002). These models
predict that in a finite population, even with small-world
properties, above some critical immunization level the disease
is confined locally (Zanette & Kuperman, 2002). Moreover,
just as local clustering slows down the spread of disease in
networks (see ‘Disease spread in networks’), a lower efficiency
in contact tracing is required to control disease in a clustered
network, other things being equal (Eames & Keeling, 2003).
For plant diseases, contact tracing often translates into removal
of infected plants and the containment of further pathogen
spread across a dispersal network through quarantine
measures. Even without human intervention, it is a common
observation – for example, in the saprotrophic invasion of
the soil-borne pathogen Rhizoctonia solani – that patches of
susceptible plants can remain uninfected because they are
surrounded by immune individuals (e.g. Jeger, 1989; Bailey
et al., 2000; Sander et al., 2002).
A number of parameters have been analysed to enable the
identification of highly connected individuals in small-world
and random networks: degree (number of contacts), betweenness (a measure of the probability of an individual being on
the path between other individuals), shortest-path betweenness (the same, but for the shortest path), and farness (the sum
of the number of steps between an individual and all other
individuals). Degree, the network parameter most easily
measured, was found to be at least as good as the other metrics
in identifying highly connected individuals and thus in
predicting risk of infection (Christley et al., 2005). This result
is to be expected from the common finding in real-world networks that the betweenness of a node is positively correlated
with the degree of the node (e.g. Lee et al., 2006).
From a practical point of view, however, there is often only
limited knowledge at the beginning of an epidemic outbreak
about the number of connections single individuals have
(Dybiec et al., 2004). For many airborne diseases, a substantial
fraction of contacts may be untraceable (Eames & Keeling,
2003). When contact tracing is possible in theory, if latent
periods are short there may not be time in practice to trace the
contacts of connected and infected individuals (Huerta &
Tsimring, 2002; Kiss et al., 2005). But in plant epidemiology,
where long latency periods are common, it may also be difficult to trace contacts. Researchers have thus tried to identify
control strategies that do not require pathologists to know the
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
complete structure of the network at risk. One of these is the
immunization of a small fraction of random acquaintances of
randomly selected individuals (acquaintance immunization).
As hubs have by definition a large number of links, the probability that a random neighbour of a random node is a hub is
very large. This is thus a simple way to identify and remove
highly connected individuals even without knowing who
they are in advance (Cohen et al., 2003; Holme, 2004; Madar
et al., 2004; May, 2006).
Alternatively, ring vaccination of individuals at less than a
certain radius from infected cases has been modelled (e.g.
Ahmed et al., 2002; Pourbohloul et al., 2005), which is both
more effective and more costly the larger the radius chosen
(Dybiec et al., 2004). This is essentially a local strategy and
has long been studied for regular lattices and carried out in
homogenous pathosystems. The same authors report that the
effect of including long-distance interactions in models
(thus moving from a regular network to a small-world one) is
that the radius of the local control strategy has to be greatly
increased, with proportionally poorer cost-effectiveness.
Similar implications for disease control are obtained from
models aiming to determine the best strategy for protecting
computer networks. In this case, of course, the finding that
random removal of links does not affect a scale-free network
is a good rather than a bad thing because it makes networks
more robust (e.g. Vázquez & Moreno, 2003). Similarly, in
computer networks highly connected individuals are not to be
removed to prevent disease spread, but protected to decrease
network vulnerability (e.g. Crucitti et al., 2003). This is because,
in networks with a heterogeneous distribution of connections,
when highly connected individuals are disconnected a global
cascade of failures is likely to follow (e.g. Moreno et al., 2002a;
Motter, 2004; Zhao et al., 2004). Further examples of this
kind include studies of the structural vulnerability of electric
power grids, which were found to be robust to most random
perturbations, but very sensitive to disturbances affecting key
power stations (e.g. Albert et al., 2004; Crucitti et al., 2004;
Chassin & Posse, 2005; Kinney et al., 2005). Similar conclusions about the general robustness of scale-free networks to
random disruptions of their components have been drawn
from studies of metabolic networks (e.g. Albert et al., 2000;
Dorogovtsev & Mendes, 2002), although for plant cells the
picture may be more complicated (Sweetlove & Fernie, 2005).
Case Studies
Not only has the impact of network structure on disease
development been modelled, but the tools of network theory
have been applied to a number of case studies. In this section,
we review some recent empirical applications, drawing
conclusions for epidemiology whenever possible.
An exemplary application of network theory to an epidemiologic case study is the investigation of how computer
network structure affects so-called epidemic algorithms. These
Review
are mechanisms that allow data dissemination (e.g. software
updates, peer-to-peer networks and database maintenance) to
computers connected in a network (e.g. Acosta-Elias et al.,
2004). Large-scale numerical simulations of epidemic algorithms suggest that in scale-free networks data transfer is more
efficient but less reliable than in homogenous topologies
(Moreno et al., 2004). This finding corroborates the higher
speed of disease spread in scale-free networks pointed out in
the section ‘Disease spread in network’. The lower reliability
emphasizes that disease development in scale-free networks is
stochastically affected by the number of connections of the
first individuals infected (e.g. Keeling, 1999; Verdasca et al.,
2005).
A similar suite of studies is related to the spread of memes
through social networks. By analogy with the susceptible/
infected/removed (SIR) model in epidemiology, individuals
of a population can be subdivided into those not having heard
an idea yet; those aware of the concept and communicating
it to others; and those having become uninterested and not
disseminating it any longer (e.g. Zanette, 2002). Also in this
case, models show that one strategy for a successful dissemination of memes is to target hubs (e.g. Duan et al., 2005).
Translated into terms of disease control, this finding suggests
again that disease spread can best be constrained in scale-free
networks by removing from the network individuals with the
highest number of connections. For plant diseases that are
spread through the nursery trade, the susceptible/infected/
susceptible (SIS) model may be more realistic, as infected
nurseries, unless under complete quarantine, may continue to
operate even if under surveillance or if plants within a certain
distance from the infected material are quarantined. The
implications of such models will be addressed in the last section
of the review. It is already clear, however, that there are many
examples of spatially structured host–pathogen systems where
the identification of highly connected nodes in the network
underlying the long-distance spread of disease might have
been an effective way to delay plant disease expansion (e.g.
chestnut blight, Dutch elm disease, black sigatoka of banana
and potato blight).
The spread of viruses via email messages in computer
networks is a further instance that has been analysed from a
network theory perspective. A remarkable finding of some
models is that the whole network of computers can be made
immune from infection by the targeted immunization of a
selected 10% of connected computers (Newman et al., 2002).
But further analyses have shown that the way in which a virus
replicates itself can affect the topology of the computer network,
thus making it difficult to control an epidemic (Balthrop et al.,
2004). In this case, epidemic control is also made difficult by
the increasing disparity between the speed of automated disease spread and that of manual eradication.
Apart from epidemic algorithms and the spread of ideas
and of computer viruses, work applying network theory to
empirical cases can be subdivided into that pertaining to
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
285
286 Review
Research review
human and animal diseases. Few applications have referred
to plant diseases.
Network theory applied to human diseases
A whole series of case studies involves human pathologies.
Here the motivation is the greater threat posed by human
pathogens in a more and more interconnected world (e.g.
Eubank et al., 2004; Hufnagel et al., 2004; Brockmann et al.,
2006; Colizza et al., 2006b; Tatem et al., 2006). Recent studies
have been motivated by the threat of pandemic influenza.
Detailed network models of this and of other globally relevant
infectious diseases need accurate estimation of model parameters (Ferguson et al., 2005; Longini et al., 2005; Arino
et al., 2006; Colizza et al., 2006a; Germann et al., 2006).
However, for the recent severe acute respiratory syndrome
(SARS) outbreak, modellers found that random networks did
not satisfactorily catch the observed dynamics of the epidemic,
and that only the addition of small-world properties allowed
realistic description of disease development. In particular,
small-world networks are able to account for the otherwise
puzzling disparities between the markedly different developments of outbreaks that started simultaneously in different
regions (e.g. Masuda et al., 2004; Small et al., 2004, 2006;
Bauch et al., 2005; Meyers et al., 2005). Incorporating the
heterogeneity in the contact structure into models also allows
an accurate matching of predictions with observed dynamics
at relatively small scales, as shown by an analysis of a dengue
outbreak on Easter Island (Favier et al., 2005).
A study of childhood infections dynamics in Canada
showed that it is possible to reconstruct the probable network
structure for a disease given the time-series data of the epidemics. The epidemic size distribution follows an inverse
power-law for rubella and mumps, implying heterogeneous
individual contacts and thus a scale-free network; whereas for
pertussis a homogenous transmission network is suggested by
the exponential distribution of epidemic sizes (Trottier &
Philippe, 2005). When the basic structure of a network is
known, as in the case of an outbreak of bacterial pneumonia
in a residential institution where a household structure was
clearly present in the different wards, models can help the
management of the disease by pointing out that nurses are the
super-spreaders who need to be immunized (Meyers et al.,
2003). A similar result, showing that preventive measures
need to be applied to individuals with many partners, was
found in analyses of an outbreak of gonorrhoea in Alberta,
Canada (De et al., 2004).
The last example is part of the research using network
theory to improve forecasts of the spread of sexually transmitted
diseases (STDs; e.g. Liljeros et al., 2001, 2003; Eames &
Keeling, 2002; Jolly et al., 2005). Modelling work on STDs
illustrates that for real populations of finite size, even though
organized in a scale-free network, there exists a non-null
epidemic threshold, so the spread of STDs can be stopped
New Phytologist (2007) 174: 279–297
(Gonçalves & Kuperman, 2003; Jones & Handcock, 2003).
Whether the dynamic nature (sexual partnerships may evolve
through time) of these networks will tend to facilitate (by
creating new connections) or hamper (by disrupting the
structure of the network) the spread of STDs deserves further
investigation, also in the context of venereal diseases of plants
(Antonovics, 2005). However, sexual partnership networks
tend to be scale-free, as the distribution of the number of
sexual partners cumulated over time typically follows an
inverse power-law. In this case, only targeted action (aimed at
individuals connecting subgroups of the population) can be
effective in preventing further spread of STDs (e.g. Liljeros,
2004; Schneeberger et al., 2004). An example is the use of
network data to predict the development of an AIDS outbreak in Houston, Texas, USA, where data on social network
structure were assessed as the most important requirement for
more effective management (Bell et al., 2002).
Network theory applied to animal diseases
A prime example of the application of network analysis to the
study of disease spread in animals is foot and mouth disease
(FMD). Much modelling work has been done following the
2001 outbreak in the UK (e.g. Woolhouse, 2003; Keeling,
2005a). But in this case too, it has been advocated that models
need to use aspects of network theory (e.g. Haydon et al.,
2003; Shirley & Rushton, 2005b; Woolhouse et al., 2005).
This is because of the long-distance dispersal exhibited by the
viral pathogen (via farm management, commercial exchanges,
and possibly airborne dispersal), and by the scale-free contact
structure of the farm network, including hubs such as markets
and animal shows (e.g. Keeling et al., 2003; Shirley &
Rushton, 2005b; Webb, 2005, 2006; Kiss et al., 2006b).
However, Woolhouse et al. (2005) argue that, even if the
network among livestock farms has a scale-free distribution of
contacts, the basic reproduction number is not increased by
this because the probability of one farm infecting another was
not significantly related to the probability of the first farm
becoming infected itself.
For the FMD outbreak of 2001 in the UK, a reconstruction
of epidemic trees (from putative sources of infection for
infected premises) revealed that, if the national ban on movement of cattle had been declared 2 d earlier, the size of the
epidemic would probably have been reduced by half (Haydon
et al., 2003). Even more effective would have been the removal
from the network of the three hubs from which nearly 80%
of subsequent infections are thought to have originated.
Unfortunately, livestock can spread the disease without showing clinical signs of it for up to 10 d (Shirley & Rushton,
2005b), so the rapid identification of the markets that caused
the long-range spread of the disease was not possible.
FMD is only one example of the many wildlife diseases
potentially spread by movements of animals (Woolhouse
et al., 2005). Network analyses related to wildlife diseases
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
include a study of bovine tuberculosis of African buffalo in
Kruger National Park, South Africa (Cross et al., 2004). This
showed that buffalo herds were less tightly clustered in years
of dry weather, and that this mixing of the overall population
could lead to faster spread of the disease. A somewhat different
example is an assessment of the role of long-distance dispersal
for the spread of raccoon rabies in Connecticut, USA (Smith
et al., 2005). In this case, establishment of disease foci from
small-world shortcuts was rare, and the disease can be managed with a local containment strategy. A different finding in
relation to Lyme disease is that in northern Spain there are
critical stepping-stone habitats with high tick densities, whose
removal can markedly alter the connectivity of the landscape
(Estrada-Peña, 2003).
Network theory applied to plant diseases
The applications of network theory discussed above prompt
the question of whether network theory can also improve our
understanding of the spread of plant and tree diseases. Of
course, plants are not as mobile as humans and animals
(although their pathogens are not static, and plants themselves
can cross long distances from one generation to the next
through seeds, pollen and, in some cases, vegetative material).
In fact, at a first glance plants do not seem to form social scalefree networks of highly mobile interactions such as, for instance,
fish are classically able to materialize, thus potentially facilitating
the spread of their epidemics (e.g. Croft et al., 2004, 2005).
This may explain why there has so far been relatively little
use of network theory in plant epidemiology. Models of
epidemics on networks, rather than in continuous space or
on lattices, might work better for animal or human than for
plant diseases (Bolker, 1999). But there exist threads of plant
epidemiological research that use meta-population theory,
and in many cases follow similar lines of reasoning to
modelling work on networks (e.g. Hanski, 1994; Park et al.,
2001, 2002; Gilligan, 2002; Franc, 2004; Otten et al., 2004,
2005; Vuorinen et al., 2004; Watts et al., 2005; Brooks, 2006).
Potential Implications for Plant and Forest
Pathology
Network theory may be relevant to plant diseases, but not
yet have been applied. If so, one explanation of the delayed
application may be that the theory is not yet sufficiently
mathematically developed to apply to epiphytotics, as plant–
pathogen networks in the real world are not only complex,
but transient and dynamic. Another explanation is that
plant epidemiologists need the development of appropriate
software tools to exploit the potential of network theory (see
Garrett et al., 2004). It may also be that data on the network
structure of plant communities are frequently harder to
obtain than the often meticulous records for human and
animal epidemics.
Review
But studies are beginning to show that plant communities
can be part of scale-free networks, at least when considered in
conjunction with other interacting species (on their own,
plants seem to depart from a true fractal spatial distribution;
e.g. Lennon et al., 2002; see also Erickson, 1945; Kunin,
1998). An intriguing related question is whether such an
absence of a fractal spatial distribution for plants would preclude the existence of a scale-free network (e.g. Berntson &
Stoll, 1997). For example, a network of plants and their pollinator species in Greenland was found to show small-world
properties (Lundgren & Olesen, 2005). High clustering and
small path length between plant species were also reported
from a study of the network of frugivorous birds and fleshyfruited plant species in Denmark (Lázaro et al., 2005). These
studies are only a few of many investigations of plant–pollinator
and plant–frugivore networks. However, these webs may not
generally show scale-free properties as, in an analysis of 53
such networks in natural communities, only roughly one-fifth
exhibited scale invariance in the connectivity distribution
(Jordano et al., 2003). The reasons for such a finding are
being debated, but the range of scales involved in each case
may be of relevance here (see also Khanin & Wit, 2006). Mycorrhizal networks, when seen from a mycocentric point of
view (i.e. considering individual trees as connecting fungal
morphotypes and not vice versa), can be scale-free (Southworth et al., 2005). There is much research potential in investigating whether this scale invariance is present more generally
in microbial, mycelial and host–parasitoid networks (e.g.
Davidson et al., 1996; Klein & Paschke, 2004; Cairney, 2005;
Károlyi, 2005; Killingback et al., 2006; see also Friesen et al.,
2006). Of course, scale-free networks may also be relevant in
plant sciences in relation to food webs (e.g. Dunne et al.,
2002) and from a metabolic point of view (e.g. Sweetlove &
Fernie, 2005; Uhrig, 2006), for instance in the context of the
pathways controlling stomata at different scales (Hetherington
& Woodward, 2003).
Provided that it is feasible to obtain network data from
plant and forest ecosystems, there are a number of reasons to
think that network theory may be a convenient tool when
dealing with the health of plant and forest pathosystems. In a
modern landscape, it may be relatively easy to recognize a scale
of description at which one should switch to a network. For
crop plants, the obvious unit are fields, farms and trading
units on a production chain; for trees, nodes may be forest
stands, plantations, urban parks and tree nurseries. The great
promise of network theory is that it can help in investigating
how disease development parameters vary within and across
individual meta-populations (Heesterbeek & Zadoks, 1987;
Parnell et al., 2006). Moreover, shipments of plants across
continents are a matter of routine nowadays, with often
unpredictable consequences for the introduction and spread
of exotic plants and their pathogens (e.g. Reichard & White,
2001; Stokstad, 2004; Dumroese & James, 2005; Perrings
et al., 2005; Dehnen-Schmutz et al., 2007).
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
287
288 Review
Research review
Fig. 2 Findings of Phytophthora ramorum on
plants at retail (crosses), nursery (diamonds),
estates/environment (squares) and other
(triangles) sites in England and Wales in
2003–2005. Data source: Department for
Environment, Food and Rural Affairs, UK.
There is thus a need to assess the properties of plant nursery
networks in a number of representative regions and for various
pathogens and endophytes (e.g. Stanosz et al., 2005; GiménezJaime et al., 2006; Menkis et al., 2006; Pinto et al., 2006;
Stepniewska-Jarosz et al., 2006). This need is immediate
wherever nurseries have been tested positive for the presence
of Phytophthora ramorum, the causal agent of sudden oak
death (e.g. Parke et al., 2004; Daughtrey & Benson, 2005;
Rizzo et al., 2005; Fig. 2). Figure 2 suggests that contact tracing
information about ongoing and eradicated outbreaks of
P. ramorum in the UK may enable the reconstruction of the
network underlying the spread of the pathogen, which in turn
might enable a more effective control strategy. Nurseries may
also be contributing to the spread of Phytophthora alni, as a
study from Bavaria suggests ( Jung & Blaschke, 2004), of the
western flower thrips Frankliniella occidentalis, which is the
vector of tospoviruses, both in North America and in Europe
(Kirk & Terry, 2003; Jones et al., 2005), and of Ralstonia
solanacearum, the bacterium causing potato brown rot, which
has been the object of individual-based modelling in the
Netherlands (Breukers et al., 2006). A network approach
seems sensible also in relation to botanical gardens, which
acted historically as hubs in the introduction of plants outside
their natural geographic range (e.g. Mamaev & Andreev,
1996; Ingram, 1999; He, 2002). It remains true that understanding the network, especially its topology, is useful in
New Phytologist (2007) 174: 279–297
devising effective disease management policies even if there is
probably no single immunization strategy that can be effective
for all types of scale-free networks (Volchenkov et al., 2002).
Network thinking may also be relevant for natural plant
communities because, although individuals cannot move,
seeds can, and provide a means of long-distance dispersal and
invasion for species with appropriate life history traits (e.g.
Grotkopp et al., 2002; Pysek et al., 2004; Richardson &
Rejmanek, 2004; Zedler & Kercher, 2004; Hamilton et al.,
2005). There is evidence that the level of long-distance dispersal in tree recolonization after glaciations can determine the
genetic pool of newly founded populations (Le Corre et al.,
1997; Petit et al., 2004; Bialozyt et al., 2006). It could be useful
to describe invasion processes with flows along the network
of locations where a plant species establishes itself; it is
possible that this would reveal differences between fast and
slow invaders. Network theory might be combined with
landscape genetics to improve our understanding of the consequences of rapid climate change, as now predicted, for plant
(and associated pathogen) distributions (e.g. Manel et al.,
2003; Bacles et al., 2004; Neilson et al., 2005; Simberloff
et al., 2005; Webber & Brasier, 2005).
Although contact tracing of disease is often impractical
both in plantations and in more pristine forests, recent studies
demonstrate that it is possible to track long-range spore dispersal of wood-decaying fungal organisms (e.g. Edman et al.,
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
2004). Will this enable the reconstruction of the colonization
history of these endangered species, so as to allow a rough
understanding of the type of network involved? It is known
that models predicting travelling waves of pathogen spread
at constant speed are unrealistic if spore dispersal of plant
pathogens is best fitted by a fat-tailed and not an exponential
distribution (e.g. Ferrandino, 1993; Shaw, 1995; see also
Scherm, 1996; Gibson, 1997; Jeger, 1999; Brown & Hovmøller,
2002; Bicout & Sache, 2003; Filipe & Maule, 2004; Shaw
et al., 2006). This issue is also relevant for investigations of the
effect of landscape structure on the spread of P. ramorum in
California (e.g. Meentemeyer et al., 2004; Rizzo et al., 2005).
In the landscape of forest and grassland patches where the
pathogen is currently spreading, dispersal gradients will be
affected by relatively efficient impaction and slow wind speeds
within forest patches but by inefficient deposition and faster
winds through open areas, with potentially different spore
dispersal functions in the two cases.
Insect vectors are another way for fungal pathogens of
plants to jump from patch to patch of potential hosts in a
landscape without other dispersal pathways (e.g. Geils, 1992).
Elm bark beetles (Coleoptera: Scolytidae), the vectors of Dutch
elm disease, attack clusters of debilitated trees, and in many
cases avoid local dispersal to neighbouring healthy trees by flying long distances to different forest patches. There is evidence
that the presence of elm trees (Ulmus spp.) in the landscape is
made more manifest to elm bark beetles by sesquiterpene
emissions induced on infected trees by the fungus responsible
for Dutch elm disease (McLeod et al., 2005). This implies that
the underlying network structure of the pathosystem is dynamic,
and can differ from that deduced from the distribution of trees
in the landscape. In the case of infections spread by vectors,
managers may profitably make use of models incorporating mobile
agents in the study of disease spread in complex networks
(e.g. Miramontes & Luque, 2002; González & Herrmann,
2004; Frasca et al., 2006; see also Rvachev & Longini, 1985).
Network modelling including mobile agents may, for instance,
help in understanding and predicting the progress of invasions such as that of the horse chestnut leaf miner, Cameraria
ohridella, which is facilitated by car movements and therefore
follows major roads (e.g. Gilbert et al., 2005). Other potential
applications of network theory in plant and forest pathology
include the spread of fire blight (Erwinia amylovora; e.g. Jock
et al., 2002) and of chestnut blight (Cryphonectria parasitica)
hypovirulence (e.g. Milgroom & Cortesi, 2004).
A network description of a tree pathosystem from a phytocentric point of view would specify nodes (host trees) and the
links between them by whatever transport mechanism is
responsible for spreading the disease, with or without any
explicit geography. If data were available at a sufficiently large
scale, it would be interesting to compare the networks of the
population structure of newly introduced, aggressive tree
pathogens (e.g. Phytophthora cinnamomi; e.g. Hardham, 2005)
with those of endemic, long established ones (e.g. Heteroba-
Review
sidion annosum s.l.; e.g. Asiegbu et al., 2005). Unfortunately,
to the best of our knowledge, only data from the local foraging
behaviour of pathogens are available (for e.g. Armillaria spp.;
Prospero et al., 2003a,b; Mihail & Bruhn, 2005), although
large-scale information is accumulating, for example for the
tree root endophyte and opportunistic pathogen Phialocephala
fortinii s.l. (e.g. Queloz et al., 2005; Grünig et al., 2006). Network models might help in predicting the outcome of the
dynamic interactions between pathogens of tree stumps and
saprotrophic fungi used as biological control agents (Holdenrieder & Greig, 1998; Boddy, 2000). Models suggest that by
manipulating the network structure it may be possible to
diminish the incidence of one of two competing species, to
the benefit of the other (Newman, 2005b). But other modelling work on the spread of two social norms in a network
suggests that the contact structure may not be the only factor
determining the outcome of the interactions between two
competing species (Nakamaru & Levin, 2004).
Heterogeneous forested landscapes are hard to represent as
regular grids and contain multiple layers of evolving interactions.
Elaborations of basic models of disease spread in networks
may allow us to use insights provided by network theory in
these ecosystems. Models making use of small-world networks in the simulation of the spread of forest fires are already
established (e.g. Moukarzel, 1999; Graham & Matthai, 2003;
Porterie et al., 2005) and have much more potential. It would
be most fascinating to use these models to integrate the
combined effects of sudden oak death and fire (Moritz &
Odion, 2005). The patchiness of the host distribution and of
environmental conditions may contribute to the heterogeneous spread of epidemics in forests (e.g. Sander et al., 2003;
Vannucchi & Boccaletti, 2004). Models trying to include in
their structure the variable susceptibility of hosts have certainly much scope for application in real forests (e.g. Sander
et al., 2002). Models investigating the effect of the contact
structure of networks on pathogen diversity (e.g. Buckee
et al., 2004; Nunes et al., 2006) also offer new insights and
possibly practical applications. Given the often long timescale of disease evolution in real forests, models can provide a
rapid forecast of the direction towards which a pathosystem
may evolve, given a certain network structure (e.g. Read &
Keeling, 2003; Ferrari et al., 2006; Kao, 2006). A network
perspective can also help in the selection of protected areas,
because of the importance for the success of conservation
efforts of understanding the connectivity within metapopulations (e.g. Brito & Grelle, 2004; Frank, 2004; Cerdeira
et al., 2005).
Conclusion
Network theory will be a useful addition to the set of concepts
and tools available to understand and manage disease in plant
populations. It may have its most obvious uses, as in our
examples, in human-modified pathosystems where discrete,
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
289
290 Review
Research review
separated units can be identified, and where commercial
transport may make distance a poor guide to the strength of
a link between two units. It is less likely to be useful where
the capacity of channels depends simply on proximity, and
homogeneity is a reasonable approximation to the plant spatial
distribution. But given the interconnectedness of today’s
world, it may matter less and less that the long-distance jumps
characteristic of wind-blown pathogens are hard to describe in
a network model. The key factor in an increasing number of
epiphytotics today is the transport by humans of disease
propagules. Anything involving human transport of plants or
their pathogens may be usefully modelled as a network, at
least at some stage. We argue that more use of network theory
in plant epidemiology would ensure that the critical features
of many real epidemics would be clarified and studied earlier
than if the normal task is regarded as modelling dispersal
on a grid or even growth in a homogeneous population.
Modelling work arising from issues in plant epidemiology
may also motivate the investigation of questions of basic
mathematical interest.
Acknowledgements
Many thanks to A. Ramsay, N. Russell and R. Smith for
comments on a previous version of this draft and to R. Baker,
S. Hardy, T. Harwood, A. Inman, N. Künzli, J. Parke, L. Paul,
V. Queloz, N. Salama, C. Sansford, T. Sieber, P. Todeschini,
J. Webber and X. Xu for insights and discussions. The comments of two anonymous reviewers were particularly helpful.
Work on this review was funded by the Department for
Environment, Food and Rural Affairs, UK and is partly based
on a talk on Epidemiology and Networks at the APS, CPS &
MSA joint meeting in Quebec City, July 2006.
References
Acosta-Elias J, Pineda U, Luna-Rivera JM, Stevens-Navarro E,
Campos-Canton I, Navarro-Moldes L. 2004. The effects of network
topology on epidemic algorithms. Lecture Notes in Computer Science 3046:
177–184.
Adamic LA. 1999. The small World Web. Lecture Notes in Computer Science
1696: 443–452.
Ahmed E, Hegazi AS, Elgazzar AS. 2002. An epidemic model on
small-world networks and ring vaccination. International Journal of
Modern Physics C 13: 189 –198.
Albert R. 2005. Scale-free networks in cell biology. Journal of Cell Science
118: 4947–4957.
Albert R, Albert I, Nakarado GL. 2004. Structural vulnerability of the North
American power grid. Physical Review E 69: 25 –103.
Albert R, Barabási A-L. 2002. Statistical mechanics of complex networks.
Review of Modern Physics 74: 47 – 97.
Albert R, Jeong H, Barabasi AL. 2000. Error and attack tolerance of
complex networks. Nature 406: 378 – 382.
Aloy P, Russell RB. 2004. Taking the mystery out of biological networks.
EMBO Reports 5: 349 – 350.
Amaral LAN, Scala A, Barthelemy M, Stanley HE. 2000. Classes of
small-world networks. Proceedings of the National Academy of Sciences, USA
97: 11149–11152.
New Phytologist (2007) 174: 279–297
Anderson RM, May RM. 1991. Infectious Diseases of Humans. Oxford, UK:
Oxford University Press.
Andrade JS, Herrmann HJ, Andrade RFS, da Silva LR. 2005. Apollonian
networks: simultaneously scale-free, small world, Euclidean, space filling,
and with matching graphs. Physical Review Letters 94, 018702: 1–4.
Antonovics J. 2005. Plant venereal diseases: insights from a messy metaphor.
New Phytologist 165: 71–80.
Arino J, Brauer F, van den Driessche P, Watmough J, Wu J. 2006. Simple
models for containment of a pandemic. Interface 3: 453–457.
Arita M. 2005. Scale-freeness and biological networks. Journal of
Biochemistry 138: 1–4.
Asiegbu FO, Adomas A, Stenlid J. 2005. Pathogen profile – conifer root and
butt rot caused by Heterobasidion annosum (Fr.) Bref. s.l. Molecular Plant
Pathology 6: 395–409.
Bacles CFE, Lowe AJ, Ennos RA. 2004. Genetic effects of chronic habitat
fragmentation on tree species: the case of Sorbus aucuparia in a deforested
Scottish landscape. Molecular Ecology 13: 573–584.
Baiesi M, Paczuski M. 2005. Complex networks of earthquakes and
aftershocks. Nonlinear Processes in Geophysics 12: 1–11.
Bailey DJ, Otten W, Gilligan CA. 2000. Saprotrophic invasion by the
soil-borne fungal plant pathogen Rhizoctonia solani and percolation
thresholds. New Phytologist 146: 535–544.
Balthrop J, Forrest S, Newman MEJ, Williamson MM. 2004.
Technological networks and the spread of computer viruses. Science 304:
527–529.
Banke S, McDonald BA. 2005. Migration patterns among global
populations of the pathogenic fungus Mycosphaerella graminicola.
Molecular Ecology 14: 1881–1896.
Barabási AL, Albert R. 1999. Emergence of scaling in random networks.
Science 286: 509–512.
Barber MJ, Krueger A, Krueger T, Roediger-Schluga T. 2006. Network of
European Union-funded collaborative research and development projects.
Physical Review E 73, 036132: 1–13.
Barbour A, Mollison D. 1990. Epidemics and random graphs. In: Gabriel
JP, Lefevre C, Picard P, eds. Stochastic processes in epidemic theory. New
York, NY, USA: Springer, 86–89.
Barrat A, Barthelemy M, Pastor-Satorras R, Vespignani A. 2004a. The
architecture of complex weighted networks. Proceedings of the National
Academy of Sciences, USA 101: 3747–3752.
Barrat A, Barthelemy M, Vespignani A. 2004b. Weighted evolving
networks: coupling topology and weight dynamics. Physical Review Letters
92: 228701.
Barrat A, Weigt M. 2000. On the properties of small-world network models.
European Physical Journal B 13: 547–560.
Barthélemy M. 2003. Crossover from scale-free to spatial networks.
Europhysics Letters 63: 915–921.
Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A. 2004. Velocity
and hierarchical spread of epidemic outbreaks in scale-free networks.
Physical Review Letters 92, 178701: 1–4.
Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A. 2005.
Dynamical patterns of epidemic outbreaks in complex heterogeneous
networks. Journal of Theoretical Biology 235: 275–288.
Bascompte J, Jordano P, Olesen JM. 2006. Asymmetric coevolutionary
networks facilitate biodiversity maintenance. Science 312: 431–433.
Bauch CT, Galvani AP. 2003. Using network models to approximate spatial
point-process models. Mathematical Biosciences 184: 101–114.
Bauch CT, Lloyd-Smith JO, Coffee MP, Galvani AP. 2005. Dynamically
modeling SARS and other newly emerging respiratory illnesses – past,
present, and future. Epidemiology 16: 791–801.
Bell DC, Montoya ID, Atkinson JS, Yang SJ. 2002. Social networks and
forecasting the spread of HIV infection. Journal of Acquired Immune
Deficiency Syndromes 31: 218–229.
Berntson GM, Stoll P. 1997. Correcting for finite spatial scales of
self-similarity when calculating the fractal dimensions of real-world
structures. Proceedings of the Royal Society of London B 264: 1531–1537.
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
Bialozyt R, Ziegenhagen B, Petit RJ. 2006. Contrasting effects of long
distance seed dispersal on genetic diversity during range expansion. Journal
of Evolutionary Biology 19: 12 –20.
Bian L. 2004. A conceptual framework for an individual-based spatially
explicit epidemiological model. Environment and Planning B 31: 381–
395.
Bicout DJ, Sache I. 2003. Dispersal of spores following a persistent random
walk. Physical Review E 67, 031913: 1–7.
Blyuss KB. 2005. On a model of spatial spread of epidemics with
long-distance travel. Physics Letters A 345: 129 –136.
Boddy L. 2000. Interspecific combative interactions between wood-decaying
basidiomycetes. FEMS Microbiology Ecology 31: 185 –194.
Boginski V, Butenko S, Pardalos PM. 2005. Statistical analysis of financial
networks. Computational Statistics and Data Analysis 48: 431– 443.
Boguñá M, Pastor-Satorras R, Vespignani A. 2003. Absence of epidemic
threshold in scale-free networks with degree correlations. Physical Review
Letters 90, 028701: 1– 4.
Boguñá M, Serrano MA. 2005. Generalized percolation in random directed
networks. Physical Review E 72, 016106: 1– 7.
Bolker BM. 1999. Analytic models for the patchy spread of plant disease.
Bulletin of Mathematical Biology 61: 849 – 874.
Bollobás B. 1979. Graph theory: an introductory course. New York, NY, USA:
Springer.
Bollobás B. 1985. Random graphs. London, UK: Academic Press.
Bornholdt S, Ebel H. 2001. World Wide Web scaling exponent from
Simon’s 1955 model. Physical Review E 64, 035104: 1–4.
Boyer D, Ramos-Fernández G, Miramontes O, Mateos JL, Cocho G,
Larralde H, Ramos H, Rojas F. 2006. Scale-free foraging by primates
emerges from their interaction with a complex environment. Proceedings of
the Royal Society of London B 273: 1743 –1750.
Brauer F. 2005. The Kermack-McKendrick epidemic model revisited.
Mathematical Biosciences 198: 119 –131.
Breukers A, Kettenis DL, Mourits M, van der Werf W, Lansink AO. 2006.
Individual-based models in the analysis of disease transmission in plant
production chains: an application to potato brown rot. Agricultural Systems
90: 112–131.
Brito D, Grelle CED. 2004. Effectiveness of a reserve network for the
conservation of the endemic marsupial Micoureus travassosi. Atlantic
Forest remnants in southeastern Brazil. Biodiversity and Conservation 13:
2519–2536.
Brockmann D, Hufnagel L, Geisel T. 2006. The scaling laws of human
travel. Nature 439: 462 – 465.
Brooks CP. 2006. Quantifying population substructure: extending the
graph-theoretic approach. Ecology 87: 864 – 872.
Brown JKM, Hovmøller MS. 2002. Aerial dispersal of pathogens on the
global and continental scales and its impact on plant disease. Science 297:
537–541.
Buckee CO, Koelle K, Mustard MJ, Gupta S. 2004. The effects of host
contact network structure on pathogen diversity and strain structure.
Proceedings of the National Academy of Sciences, USA 101: 10839–
10844.
Buhl J, Gautrais J, Sole RV, Kuntz P, Valverde S, Deneubourg JL,
Theraulaz G. 2004. Efficiency and robustness in ant networks of galleries.
European Physical Journal B 42: 123 –129.
Burdon JJ, Thrall PH, Ericson L. 2006. The current and future dynamics
of disease in plant communities. Annual Review of Phytopathology 44:
19–39.
Cairney JWG. 2005. Basidiomycete mycelia in forest soils: dimensions,
dynamics and roles in nutrient distribution. Mycological Research 109:
7–20.
Cancho RFI, Janssen C, Solé RV. 2001. Topology of technology graphs:
small world patterns in electronic circuits. Physical Review E 64, 046119:
1–4.
Cancho RFI, Solé RV. 2001. The small world of human language.
Proceedings of the Royal Society of London B 268: 2261– 2265.
Review
Capocci A, Servedio VDP, Colaiori F, Buriol LS, Donato D, Leonardi S,
Caldarelli G. 2006. Preferential attachment in the growth of social
networks: the internet encyclopedia Wikipedia. Physical Review E 74,
036116: 1–6.
Cerdeira JO, Gaston KJ, Pinto LS. 2005. Connectivity in priority area
selection for conservation. Environmental Modelling and Assessment 10:
183–192.
Chan KP, Zheng DF, Hui PM. 2004. Effects of aging and links removal on
epidemic dynamics in scale-free networks. International Journal of Modern
Physics B 18: 2534–2539.
Chandra AK, Dasgupta S. 2005. A small world network of prime numbers.
Physica A 357: 436–446.
Chang DB, Young CS. 2005. Infection dynamics on the Internet. Computer
and Security 24: 280–286.
Chartrand G. 1985. Introductory graph theory. New York, NY, USA: Dover
Publications.
Chassin DP, Posse C. 2005. Evaluating North American electric grid
reliability using the Barabasi-Albert network model. Physica A 355: 667 –
677.
Chavez M, Hwang DU, Amann A, Boccaletti S. 2006. Synchronizing
weighted complex networks. Chaos 16, 015106: 1–7.
Chen W-K. 1997. Graph theory and its engineering applications. Chicago, IL,
USA: World Scientific.
Christley RM, French NP. 2003. Small-world topology of UK racing: the
potential for rapid spread of infectious agents. Equine Veterinary Journal
35: 586–589.
Christley RM, Pinchbeck GL, Bowers RG, Clancy D, French NP,
Bennett R, Turner J. 2005. Infection in social networks: using network
analysis to identify high-risk individuals. American Journal of Epidemiology
162: 1024–1031.
Coelho R, Neda Z, Ramasco JJ, Santos MA. 2005. A family-network model
for wealth distribution in societies. Physica A 353: 515–528.
Cohen R, Havlin S, Ben-Avraham D. 2003. Efficient immunization
strategies for computer networks and populations. Physical Review Letters
91, 247901: 1–4.
Colizza V, Barrat A, Barthélemy M, Vespignani A. 2006a. The modeling
of global epidemics: Stochastic dynamics and predictability. Bulletin of
Mathematical Biology 68: 1893–1921.
Colizza V, Barrat A, Barthélemy M, Vespignani A. 2006b. The role of the
airline transportation network in the prediction and predictability of
global epidemics. Proceedings of the National Academy of Sciences, USA 103:
2015–2020.
Costa LD, Travieso G, Ruggiero CA. 2005. Complex grid computing.
European Physical Journal B 44: 119–128.
Croft DP, James R, Ward AJW, Botham MS, Mawdsley D, Krause J. 2005.
Assortative interactions and social networks in fish. Oecologia 143: 211–
219.
Croft DP, Krause J, James R. 2004. Social networks in the guppy (Poecilia
reticulata). Proceedings of the Royal Society of London B 271: S516 –S519.
Cross PC, Lloyd-Smith JO, Bowers JA, Hay CT, Hofmeyr M, Getz WM.
2004. Integrating association data and disease dynamics in a social
ungulate: bovine tuberculosis in African buffalo in the Kruger National
Park. Annales Zoologici Fennici 41: 879–892.
Crucitti P, Latora V, Marchiori M. 2004. A topological analysis of the
Italian electric power grid. Physica A 338: 92–97.
Crucitti P, Latora V, Marchiori M, Rapisarda A. 2003. Efficiency of
scale-free networks: error and attack tolerance. Physica A 320: 622 – 642.
Dall’Asta L. 2005. Inhomogeneous percolation models for spreading
phenomena in random graphs. Journal of Statistical Mechanics – Theory
and Experiment P08011: 1–38.
Dall’Asta L, Barrat A, Barthelemy M, Vespignani A. 2006. Vulnerability
of weighted networks. Journal of Statistical Mechanics – Theory and
Experiment P04006: 1–12.
Daughtrey ML, Benson DM. 2005. Principles of plant health management
for ornamental plants. Annual Review Phytopathology 43: 141–169.
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
291
292 Review
Research review
Davidson FA, Sleeman BD, Rayner ADM, Crawford JW, Ritz K. 1996.
Large-scale behavior of fungal mycelia. Mathematical and Computer
Modelling 24: 81–87.
De Silva E, Stumpf MPH. 2005. Complex networks and simple models in
biology. Interface 2: 419 – 430.
De P, Singh AE, Wong T, Yacoub W, Jolly AM. 2004. Sexual network
analysis of a gonorrhoea outbreak. Sexually Transmitted Infections 80: 280–
285.
Dehnen-Schmutz K, Touza J, Perrings C, Williamson M. 2007.
The horticultural trade and ornamental plant invasions in Britain.
Conservation Biology 21: 224–231.
Dezsø Z, Barabási AL. 2002. Halting viruses in scale-free networks. Physical
Review E 65, 055103: 1–4.
Di Matteo T, Aste T, Gallegati M. 2005. Innovation flow through social
networks: productivity distribution in France and Italy. European Physical
Journal B 47: 459–466.
Dorogovtsev SN, Mendes JFF. 2002. Evolution of networks. Advances in
Physics 51: 1079–1187.
Duan WQ, Chen Z, Liu ZR, Jin W. 2005. Efficient target strategies for
contagion in scale-free networks. Physical Review E 72, 026133: 1–5.
Dumroese RK, James RL. 2005. Root diseases in bareroot and container
nurseries of the Pacific Northwest: epidemiology, management, and effects
on outplanting performance. New Forests 30: 185 – 202.
Dunne JA, Williams RJ, Martinez ND. 2002. Food-web structure and
network theory: the role of connectance and size. Proceedings of the
National Academy of Sciences, USA 99: 12917 –12922.
Dybiec B, Kleczkowski A, Gilligan CA. 2004. Controlling disease spread on
networks with incomplete knowledge. Physical Review E 70, 066145: 1–5.
Eames KTD, Keeling MJ. 2002. Modeling dynamic and network
heterogeneities in the spread of sexually transmitted diseases. Proceedings of
the National Academy of Sciences, USA 99: 13330 –13335.
Eames KTD, Keeling MJ. 2003. Contact tracing and disease control.
Proceedings of the Royal Society of London B 270: 2565 – 2571.
Ebel H, Mielsch LI, Bornholdt S. 2002. Scale-free topology of e-mail
networks. Physical Review E 66, 035103: 1–4.
Edman M, Gustafsson M, Stenlid J, Ericson L. 2004. Abundance and
viability of fungal spores along a forestry gradient – responses to habitat
loss and isolation? Oikos 104: 35– 42.
Eguíluz VM, Klemm K. 2002. Epidemic threshold in structured scale-free
networks. Physical Review Letters 89, 108701: 1–4.
Erdos P, Renyi A. 1960. On the evolution of random graphs. Publication of
the Mathematical Institute of the Hungarian Academy of Sciences 5: 17–61.
Erickson RO. 1945. The Clematis fremontii var riehlii population in the
Ozarks. Annals of the Missouri Botanical Garden 30: 63 – 68.
Estrada-Peña A. 2003. The relationships between habitat topology, critical
scales of connectivity and tick abundance Ixodes ricinus in a heterogeneous
landscape in northern Spain. Ecography 26: 661– 671.
Eubank S, Guclu H, Kumar VSA, Marathe MV, Srinivasan A, Toroczkai Z,
Wang N. 2004. Modelling disease outbreaks in realistic urban social
networks. Nature 429: 180 –184.
Favier C, Schmit D, Muller-Graf CDM, Cazelles B, Degallier N,
Mondet B, Dubois MA. 2005. Influence of spatial heterogeneity on an
emerging infectious disease: the case of dengue epidemics. Proceedings of
the Royal Society of London B 272: 1171–1177.
Ferguson NM, Cummings DAT, Cauchemez S, Fraser C, Riley S,
Meeyai A, Iamsirithaworn S, Burke DS. 2005. Strategies for containing
an emerging influenza pandemic in Southeast Asia. Nature 437: 209–214.
Ferrandino FJ. 1993. Dispersive epidemic waves. 1. Focus expansion within
a linear planting. Phytopathology 83: 795 – 802.
Ferrari MJ, Bansal S, Meyers LA, Bjornstad ON. 2006. Network frailty and
the geometry of herd immunity. Proceedings of the Royal Society of London
B 273: 2743–27488.
Filipe JAN, Maule MM. 2004. Effects of dispersal mechanisms on
spatio-temporal development of epidemics. Journal of Theoretical Biology
226: 125–141.
New Phytologist (2007) 174: 279–297
Fortuna MA, Gómez-Rodríguez C, Bascompte J. 2006. Spatial network
structure and amphibian persistence in stochastic environments.
Proceedings of the Royal Society of London B 273: 1429–1434.
Franc A. 2004. Metapopulation dynamics as a contact process on a graph.
Ecological Complexity 1: 49–63.
Frank K. 2004. Ecologically differentiated rules of thumb for habitat
network design – lessons from a formula. Biodiversity and Conservation 13:
189–206.
Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S. 2006. Dynamical
network model of infective mobile agents. Physical Review E 74, 036110:
1–5.
Friesen TL, Stukenbrock EH, Liu Z, Meinhardt S, Ling H, Faris JD,
Rasmussen JB, Solomon PS, McDonald BA, Oliver RP. 2006.
Emergence of a new disease as a result of interspecific virulence gene transfer. Nature Genetics 38: 953–956.
Gallos LK, Argyrakis P. 2003. Distribution of infected mass in disease
spreading in scale-free networks. Physica A 330: 117–123.
Garrett KA, Hulbert SH, Leach JE, Travers SE. 2006. Ecological genomics
and epidemiology. European Journal of Plant Pathology 115: 35–51.
Garrett KA, Madden LV, Hughes G, Pfender WF. 2004. New applications
of statistical tools in plant pathology. Phytopathology 94: 999–1003.
Geils BW. 1992. Analyzing landscape patterns caused by forest pathogens: a
review of the literature. In: Frankle S, ed. Proceedings of the 40th Western
International Forest Disease Work Conference. Durango, CO, USA: USDA,
Forest Service, Pacific Southwest Region, 21–32.
Germann TC, Kadau K, Longini IM Jr, Macken CA. 2006. Mitigation
strategies for pandemic influenza in the United States. Proceedings of the
National Academy of Sciences, USA 103: 5935–5940.
Giani U, Romano A, Bruzzese D. 2005. An epidemiological model of
knowledge diffusion in virtual learning networks: an application to
learning statistics in medicine. Cybernetics and Systems 36: 445–456.
Gibson GJ. 1997. Investigating mechanisms of spatiotemporal epidemic
spread using stochastic models. Phytopathology 87: 139–146.
Giesecke J. 1994. Modern infectious disease epidemiology. London, UK:
Edward Arnold.
Gilbert M, Guichard S, Freise J, Gregoire JC, Heitland W, Straw N,
Tilbury C, Augustin S. 2005. Forecasting Cameraria ohridella invasion
dynamics in recently invaded countries: from validation to prediction.
Journal of Applied Ecology 42: 805–813.
Gilligan CA. 2002. An epidemiological framework for disease management.
Advances in Botanical Research 38: 1–64.
Giménez-Jaime A, Aroca A, Raposo R, García-Jiménez Armengol J. 2006.
Occurrence of fungal pathogens associated with grapevine nurseries and
the decline of young vines in Spain. Journal of Phytopathology 154: 598 –
602.
Gonçalves S, Kuperman M. 2003. The social behavior and the evolution of
sexually transmitted diseases. Physica A 328: 225–232.
González MC, Herrmann HJ. 2004. Scaling of the propagation of epidemic
in a system of mobile agents. Physica A 340: 741–748.
Gorman SP, Malecki EJ. 2000. The networks of the Internet: an analysis of
provider networks in the USA. Telecommunications Policy 24: 113–134.
Grabowski A, Kosinski RA. 2004. Epidemic spreading in a hierarchical
social network. Physical Review E 70, 031908: 1–7.
Graham I, Matthai CC. 2003. Investigation of the forest-fire model on a
small-world network. Physical Review E 68, 036109: 1–7.
Green DM, Kiss IZ, Kao RR. 2006. Parameterization of individual-based
models: comparisons with deterministic mean-field models. Journal of
Theoretical Biology 239: 289–297.
Green DG, Sadedin S. 2005. Interactions matter – complexity in landscapes
and ecosystems. Ecological Complexity 2: 117–130.
Grotkopp E, Rejmanek M, Rost TL. 2002. Toward a causal explanation of
plant invasiveness: seedling growth and life-history strategies of 29 pine
(Pinus) species. American Naturalist 159: 396–419.
Grünig CR, Duò A, Sieber TN. 2006. Population genetic analysis of
Phialocephala fortinii s.l. and Acephala applanata in two undisturbed
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
forests in Switzerland and evidence for new cryptic species. Fungal Genetics
and Biology 43: 410– 421.
Guimerá R, Mossa S, Turtschi A, Amaral LAN. 2005. The worldwide air
transportation network: anomalous centrality, community structure, and
cities’ global roles. Proceedings of the National Academy of Sciences, USA
102: 7794–7799.
Hamilton MA, Murray BR, Cadotte MW, Hose GC, Baker AC, Harris CJ,
Licari D. 2005. Life-history correlates of plant invasiveness at regional and
continental scales. Ecology Letters 8: 1066 –1074.
Hanski I. 1994. Spatial scale, patchiness and population dynamics on land.
Philosophical Transactions of the Royal Society of London B 343: 19–25.
Hardham AR. 2005. Pathogen profile – Phytophthora cinnamomi. Molecular
Plant Pathology 6: 589 – 604.
Harris TE. 1974. Contact interactions on a lattice. Annals of Probability 2:
969–988.
Haydon DT, Chase-Topping M, Shaw DJ, Matthews L, Friar JK,
Wilesmith J, Woolhouse MEJ. 2003. The construction and analysis of
epidemic trees with reference to the 2001 UK foot-and-mouth outbreak.
Proceedings of the Royal Society of London B 270: 121–127.
He SA. 2002. Fifty years of botanical gardens in China. Acta Botanica Sinica
44: 1123–1133.
Heesterbeek JAP. 2002. A brief history of R-0 and a recipe for its
calculation. Acta Biotheoretica 50: 189 – 204.
Heesterbeek JAP, Zadoks JC. 1987. Modelling pandemics of quarantine
pests and diseases: problems and perspectives. Crop Protection 6: 211–221.
Hethcote HV. 2000. The mathematics of infectious disease. Society for
Industrial and Applied Mathematics Review 42: 599 – 653.
Hetherington AM, Woodward FI. 2003. The role of stomata in sensing and
driving environmental change. Nature 424: 901– 908.
Holdenrieder O, Greig BJW. 1998. Biological methods of control. In:
Woodward S, Stenlid J, Karjalainen K, Huttermann A, eds. Heterobasidion
annosum. biology, ecology, impact and control. Wallingford, UK: CAB
International, 235–258.
Holdenrieder O, Pautasso M, Weisberg PJ, Lonsdale D. 2004. Tree diseases
and landscape processes: the challenge of landscape pathology. Trends in
Ecology and Evolution 19: 446 – 452.
Holme P. 2004. Efficient local strategies for vaccination and network attack.
Europhysics Letters 68: 908 – 914.
Huerta R, Tsimring LS. 2002. Contact tracing and epidemics control in
social networks. Physical Review E 66, 056115: 1– 4.
Hufnagel L, Brockmann D, Geisel T. 2004. Forecast and control of
epidemics in a globalized world. Proceedings of the National Academy of
Sciences, USA 101: 15124 –15129.
Humphries MD, Gurney K, Prescott TJ. 2006. The brainstem reticular
formation is a small-world, not scale-free, network. Proceedings of the Royal
Society of London B 273: 503 – 511.
Hwang DU, Boccaletti S, Moreno Y, Lopez-Ruiz R. 2005. Thresholds for
epidemic outbreaks in finite scale-free networks. Mathematical Biosciences
and Engineering 2: 317 – 327.
Ingram DS. 1999. Biodiversity, plant pathogens and conservation. Plant
Pathology 48: 433–442.
James A, Pitchford JW, Plank MJ. 2007. An event-based model of
superspreading in epidemics. Proceedings of the Royal Society of London B
274: 741–747.
Jeger MJ. 1986. Asymptotic behaviour and threshold criteria in model plant
disease epidemics. Plant Pathology 35: 355 – 361.
Jeger MJ. 1989. Spatial components of plant disease epidemics. Englewood
Cliffs, NJ, USA: Prentice Hall.
Jeger MJ. 1999. Improved understanding of dispersal in crop pest and disease
management: current status and future directions. Agricultural and Forest
Meteorology 97: 331– 349.
Jeger MJ. 2004. Analysis of disease progress as a basis for evaluating disease
management practices. Annual Review of Phytopathology 42: 61–82.
Jeger MJ, van den Bosch F. 1994. Threshold criteria for model-plant disease
epidemics. 2. Persistence and endemicity. Phytopathology 84: 28–30.
Review
Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási A-L. 2000.
The large-scale organization of metabolic networks. Nature 407: 651–
654.
Jezewski W. 2005. Scale-free properties of weighted networks with
connectivity-driven topology. Physica A 354: 672–680.
Jiang B, Claramunt C. 2004. Topological analysis of urban street networks.
Environment and Planning B 31: 151–162.
Jock S, Donat V, López MM, Bazzi C, Geider K. 2002. Following spread
of fire blight in Western, Central and Southern Europe by molecular
differentiation of Erwinia amylovora strains with PFGE analysis.
Environmental Microbiology 4: 106–114.
Jolly AM, Moffatt MEK, Fast MV, Brunham RC. 2005. Sexually
transmitted disease thresholds in Manitoba, Canada. Annals of
Epidemiology 151: 781–788.
Jones JH, Handcock MS. 2003. An assessment of preferential attachment as
a mechanism for human sexual network formation. Proceedings of the Royal
Society of London B 270: 1123–1128.
Jones GD, Perrings CA, MacLeod A. 2005. The spread of Frankliniella
occidentalis through the UK protected horticulture sector – scales and
processes. In: Alford DV, Backhaus GF, eds. Plant protection and plant
health in Europe. Introduction and Spread of Invasive Species Symposium.
Berlin, Germany: Humboldt University, 13–18.
Joo J, Lebowitz JL. 2004. Behavior of susceptible-infected-susceptible
epidemics on heterogeneous networks with saturation. Physical Review E
69, 066105: 1–6.
Jordano P, Bascompte J, Olesen JM. 2003. Invariant properties in
co-evolutionary networks of plant–animal interactions. Ecology Letters 6:
69–81.
Jung T, Blaschke M. 2004. Phytophthora root and collar rot of alders in
Bavaria: distribution, modes of spread and possible management
strategies. Plant Pathology 53: 197–208.
Kao RR. 2006. Evolution of pathogens towards low R0 in heterogeneous
populations. Journal of Theoretical Biology 242: 634–642.
Károlyi G. 2005. Fractal scaling of microbial colonies affects growth. Physical
Review E 71, 031915: 1–6.
Keeling MJ. 1999. The effects of local spatial structure on epidemiological
invasions. Proceedings of the Royal Society of London B 266: 859–867.
Keeling MJ. 2005a. Models of foot-and-mouth disease. Proceedings of the
Royal Society of London B 272: 1195–1202.
Keeling MJ. 2005b. The implications of network structure for epidemic
dynamics. Theoretical Population Biology 67: 1–8.
Keeling MJ. 2005c. Extensions to mass-action mixing. In: Cuddington K,
Beisner BE, eds. Ecological paradigms lost. Routes of theory change.
Amsterdam, the Netherlands: Elsevier, 107–142.
Keeling MJ, Eames KTD. 2005. Networks and epidemic models. Interface
2: 295–307.
Keeling MJ, Woolhouse MEJ, May RM, Davies G, Grenfell BT. 2003.
Modelling vaccination strategies against foot-and-mouth disease. Nature
421: 136–142.
Khanin R, Wit E. 2006. How scale-free are biological networks? Journal of
Computational Biology 13: 810–818.
Killingback T, Blok HJ, Doebeli M. 2006. Scale-free extinction dynamics
in spatially structured host-parasitoid systems. Journal of Theoretical
Biology 241: 745–750.
Kinney R, Crucitti P, Albert R, Latora V. 2005. Modeling cascading failures
in the North American power grid. European Physical Journal B 46: 101–
107.
Kirk WDJ, Terry LI. 2003. The spread of the western flower thrips
Frankliniella occidentalis (Pergande). Agricultural and Forest Entomology 5:
301–310.
Kiss IZ, Green DM, Kao RR. 2005. Disease contact tracing in random and
clustered networks. Proceedings of the Royal Society of London B 272: 1407 –
1414.
Kiss IZ, Green DM, Kao RR. 2006a. Infectious disease control using contact
tracing in random and scale-free networks. Interface 3: 55–62.
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
293
294 Review
Research review
Kiss IZ, Green DM, Kao RR. 2006b. The network of sheep movements
within Great Britain: network properties and their implications for
infectious disease spread. Interface 3: 669 – 677.
Klein DA, Paschke MW. 2004. Filamentous fungi: the indeterminate
lifestyle and microbial ecology. Microbial Ecology 47: 224 –235.
Koopman J. 2004. Modeling infection transmission. Annual Review of Public
Health 25: 303–326.
Kosinski RA, Adamowski L. 2004. Influence of the initial source of
epidemic and preventive vaccination on the spreading phenomena in a
two-dimensional lattice. International Journal of Modern Physics C 15:
755–765.
Kretzschmar M. 2000. Sexual network structure and sexually transmitted
disease prevention: a modeling perspective. Sexually Transmitted Diseases
27: 627–635.
Kunin WE. 1998. Extrapolating species abundance across spatial scales.
Science 281: 1513–1515.
Kunin V, Goldovsky L, Darzentas N, Ouzounis CA. 2005. The net of life:
reconstructing the microbial phylogenetic network. Genome Research 15:
954–959.
Kuperman M, Abramson G. 2001. Small world effect in an epidemiological
model. Physical Review Letters 86: 2909 – 2912.
Lázaro A, Mark S, Olesen JM. 2005. Bird-made fruit orchards in northern
Europe: nestedness and network properties. Oikos 110: 321– 329.
Le Corre V, Machon N, Petit RJ, Kremer A. 1997. Colonization with
long-distance seed dispersal and genetic structure of maternally
inherited genes in forest trees: a simulation study. Genetical Research 69:
117–125.
Lee SH, Kim PJ, Jeong H. 2006. Statistical properties of sampled networks.
Physical Review E 73: 16102.
Lennon JJ, Kunin WE, Hartley S. 2002. Fractal species distributions do not
produce power-law species-area relationships. Oikos 97: 378 – 386.
Liljeros F. 2004. Sexual networks in contemporary Western societies. Physica
A 338: 238–245.
Liljeros F, Edling CR, Amaral LAN. 2003. Sexual networks: implications for
the transmission of sexually transmitted infections. Microbes & Infection 5:
189–196.
Liljeros F, Edling CR, Amaral LAN, Stanley HE, Aberg Y. 2001. The web
of human sexual contacts. Nature 411: 907 – 908.
Liu Z, Hu B. 2005. Epidemic spreading in community networks. Europhysics
Letters 72: 315–321.
Liu ZH, Lai YC, Ye N. 2003. Propagation and immunization of infection
on general networks with both homogeneous and heterogeneous
components. Physical Review E 67, 031911: 1–5.
Liu JZ, Wu JS, Yang ZR. 2004. The spread of infectious disease on complex
networks with household structure. Physica A 341: 273 – 280.
Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. 2005. Superspreading
and the effect of individual variation on disease emergence. Nature 438:
355–359.
Longini IM, Nizam A, Xu SF, Ungchusak K, Hanshaoworakul W,
Cummings DAT, Halloran ME. 2005. Containing pandemic influenza at
the source. Science 309: 1083 –1087.
Lundgren R, Olesen JM. 2005. The dense and highly connected world of
Greenland’s plants and their pollinators. Arctic, Antarctic and Alpine
Research 37: 514–520.
Lundquist JE, Hamelin RC. 2005. Forest pathology – from genes to landscapes.
St Paul, MN, USA: American Phytopathological Society.
Madar N, Kalisky T, Cohen R, ben-Avraham D, Havlin S. 2004.
Immunization and epidemic dynamics in complex networks. European
Physical Journal B 38: 269 – 276.
Mamaev SA, Andreev LN. 1996. Importance of Russian botanical gardens
for preservation of floristic diversity. Russian Journal of Ecology 27: 432–
437.
Manel S, Schwartz MK, Luikart G, Taberlet P. 2003. Landscape genetics:
combining landscape ecology and population genetics. Trends in Ecology &
Evolution 18: 189–197.
New Phytologist (2007) 174: 279–297
Marchand PJ, Goulet FL, Harrington TC. 1986. Death by attrition – a
hypothesis for wave mortality of sub-alpine Abies balsamea. Canadian
Journal of Forest Research 16: 591–596.
Masuda N, Konno N, Aihara K. 2004. Transmission of severe acute
respiratory syndrome in dynamical small-world networks. Physical Review
E 69, 031917: 1–6.
Matsuyama S, Kunigami M, Terano T. 2005. Multi-agent modeling of peer
to peer communication with scale-free and small-world properties. Lecture
Notes in Computer Science 3684: 772–778.
Matthäus F. 2006. Diffusion versus network models as descriptions for the
spread of prion diseases in the brain. Journal of Theoretical Biology 240:
104–113.
Matthews L, Woolhouse M. 2005. New approaches to quantifying the
spread of infection. Nature Review of Microbiology 3: 529–536.
May RM. 2006. Network structure and the biology of populations. Trends
in Ecology and Evolution 21: 394–399.
May RM, Lloyd AL. 2001. Infection dynamics on scale-free networks.
Physical Review E 64: 66112.
McLeod G, Gries R, von Reuß SH, Rahe JE, McIntosh R, König WA,
Gries G. 2005. The pathogen causing Dutch elm disease makes host trees
attract insect vectors. Proceedings of the Royal Society of London B 272:
2499–2503.
Meentemeyer R, Rizzo D, Mark W, Lotz E. 2004. Mapping the risk of
establishment and spread of sudden oak death in California. Forest Ecology
and Management 200: 195–214.
Menkis A, Vasiliauskas R, Taylor AFS, Stenström E, Stenlid J, Finlay R.
2006. Fungi in decayed roots of conifer seedlings in forest nurseries,
afforested clear-cuts and abandoned farmland. Plant Pathology 55: 117 –
129.
Meyers LA, Newman MEJ, Martin M, Schrag S. 2003. Applying
network theory to epidemics: control measures for Mycoplasma
pneumoniae outbreaks. Emerging Infectious Diseases 9: 204–210.
Meyers LA, Newman MEJ, Pourbohloul B. 2006. Predicting epidemics
on directed contact networks. Journal of Theoretical Biology 240:
400–418.
Meyers LA, Pourbohloul B, Newman MEJ, Skowronski DM,
Brunham RC. 2005. Network theory and SARS: predicting outbreak
diversity. Journal of Theoretical Biology 232: 71–81.
Mihail JD, Bruhn JN. 2005. Foraging behaviour of Armillaria rhizomorph
systems. Mycological Research 109: 1195–1207.
Milgram S. 1967. The small world problem. Psychology Today 2: 60– 67.
Milgroom MG, Cortesi P. 2004. Biological control of chestnut blight with
hypovirulence: a critical analysis. Annual Review of Phytopathology 42:
311–338.
Miramontes O, Luque B. 2002. Dynamical small-world behavior in an
epidemical model of mobile individuals. Physica D 168: 379–385.
Mollison D. 1977. Spatial contact models for ecological and epidemic
spread. Journal of the Royal Statistical Society B 39: 283–326.
Montoya JM, Pimm SL, Solé RV. 2006. Ecological networks and their
fragility. Nature 442: 259–264.
Moore C, Newman MEJ. 2000. Epidemics and percolation in small-world
networks. Physical Review E 61: 5678–5682.
Moreno Y, Gómez JB, Pacheco AF. 2002a. Instability of scale-free
networks under node-breaking avalanches. Europhysics Letters 58:
630–636.
Moreno Y, Nekovee M, Vespignani A. 2004. Efficiency and reliability of
epidemic data dissemination in complex networks. Physical Review E 69,
055101: 1–4.
Moreno Y, Pastor-Satorras R, Vespignani A. 2002b. Epidemic outbreaks in
complex heterogeneous networks. European Physical Journal B 26: 521–
529.
Moreno Y, Vázquez A. 2003. Disease spreading in structured scale-free
networks. European Physical Journal B 31: 265–271.
Morita S. 2006. Crossovers in scale-free networks on geographical space.
Physical Review E 73, 035104: 1–4.
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
Moritz MA, Odion DC. 2005. Examining the strength and possible causes
of the relationship between fire history and Sudden Oak Death. Oecologia
144: 106–114.
Motter AE. 2004. Cascade control and defense in complex networks.
Physical Review Letters 93, 098701: 1–4.
Moukarzel CF. 1999. Spreading and shortest paths in systems with sparse
long-range connections. Physical Review E 60: R6263 –R6266.
Nakamaru M, Levin SA. 2004. Spread of two linked social norms on
complex interaction networks. Journal of Theoretical Biology 230: 57–64.
Neilson RP, Pitelka LF, Solomon AM, Nathan R, Midgley GF, Fragoso
JMV, Lischke H, Thompson K. 2005. Forecasting regional to global plant
migration in response to climate change. Bioscience 55: 749 – 759.
Newman MEJ. 2001. The structure of scientific collaboration networks.
Proceedings of the National Academy of Sciences, USA 98: 404 – 409.
Newman MEJ. 2002. Spread of epidemic disease on networks. Physical
Review E 66, 016128: 1–11.
Newman MEJ. 2003. The structure and function of complex networks.
Society for Industrial and Applied Mathematics Review 45: 167–256.
Newman MEJ. 2005a. Power laws, Pareto distributions and Zipf ’s law.
Contemporary Physics 46: 323 – 351.
Newman MEJ. 2005b. Threshold effects for two pathogens spreading on a
network. Physical Review Letters 95, 108701: 1–4.
Newman MEJ, Forrest S, Balthrop J. 2002. E-mail networks and the spread
of computer viruses. Physical Review E 66, 035101: 1–4.
Newman MEJ, Strogatz SH, Watts DJ. 2001. Random graphs with
arbitrary degree distributions and their applications. Physical Review E 64,
026118: 1–17.
Nunes A, Telo da Gama MM, Gomes MGM. 2006. Localized contacts
between hosts reduce pathogen diversity. Journal of Theoretical Biology
241: 477–487.
Olinky R, Stone L. 2004. Unexpected epidemic thresholds in heterogeneous
networks: the role of disease transmission. Physical Review E 70, 030902:
1–4.
Ormerod P, Roach AP. 2004. The Medieval inquisition: scale-free networks
and the suppression of heresy. Physica A 339: 645 – 652.
Otten W, Bailey DJ, Gilligan CA. 2004. Empirical evidence of spatial
thresholds to control invasion of fungal parasites and saprotrophs. New
Phytologist 163: 125 –132.
Otten W, Filipe JAN, Gilligan CA. 2005. Damping-off epidemics, contact
structure, and disease transmission in mixed-species populations. Ecology
86: 1948–1957.
Palotai Z, Farkas C, Lorincz A. 2005. Selection in scale-free small world.
Lecture Notes in Computer Science 3690: 579 – 582.
Parham PE, Ferguson NM. 2006. Space and contact networks: capturing
the dynamics of disease transmission. Interface 3: 483 – 493.
Park AW, Gubbins S, Gilligan CA. 2001. Invasion and persistence of plant
parasites in a spatially structured host population. Oikos 94: 162–174.
Park AW, Gubbins S, Gilligan CA. 2002. Extinction times for closed
epidemics: the effects of host spatial structure. Ecology Letters 5: 747–755.
Parke JL, Linderman RG, Osterbauer NK, Griesbach JA. 2004. Detection
of Phytophthora ramorum blight in Oregon nurseries and completion of
Koch’s postulates on Pieris, Rhododendron, Viburnum and Camelia. Plant
Disease 88: 87–87.
Parnell S, van den Bosch F, Gilligan CA. 2006. Large-scale fungicide spray
heterogeneity and the regional spread of resistant pathogen strains.
Phytopathology 96: 549 – 555.
Pastor-Satorras R, Vazquez A, Vespignani A. 2001. Dynamical and
correlation properties of the Internet. Physical Review Letters 87, 258701:
1–4.
Pastor-Satorras R, Vespignani A. 2001a. Epidemic dynamics and endemic
states in complex networks. Physical Review E 63, 066117: 1–8.
Pastor-Satorras R, Vespignani A. 2001b. Epidemic spreading in scale-free
networks. Physical Review Letters 86: 3200 – 3203.
Pastor-Satorras R, Vespignani A. 2002a. Epidemic dynamics in finite size
scale-free networks. Physical Review E 65, 035108: 1–4.
Review
Pastor-Satorras R, Vespignani A. 2002b. Immunization of complex
networks. Physical Review E 65, 036104: 1–8.
Pautasso M, Holdenrieder O, Stenlid J. 2005. Susceptibility to fungal
pathogens of forests differing in tree diversity. In: Scherer-Lorenzen M,
Koerner Ch, Schulze D, eds. Forest diversity and function: temperate and
boreal systems. Berlin, Germany: Springer, 263–289.
Perrings C, Dehnen-Schmutz K, Touza J, Williamson M. 2005. How to
manage biological invasions under globalization. Trends in Ecology and
Evolution 20: 212–215.
Petermann T, De Los Rios P. 2004. Role of clustering and gridlike ordering
in epidemic spreading. Physical Review E 69, 066116: 1–14.
Petit RJ, Bialozyt R, Garnier-Géré P, Hampe A. 2004. Ecology and genetics
of tree invasions: from recent introductions to Quaternary migrations.
Forest Ecology and Management 197: 117–137.
Pinto PM, Alonso JAP, Fernandez VP, Casero JJD. 2006. Fungi isolated
from diseased nursery seedlings in Spain. New Forests 31: 41–56.
Porter MA, Mucha PJ, Newman MEJ, Warmbrand CM. 2005. A network
analysis of committees in the US House of Representatives. Proceedings of
the National Academy of Sciences, USA 102: 7057–7062.
Porterie B, Zekri N, Clerc JP, Loraud JC. 2005. Un réseau de petit monde
local à sites pondérés pour les feux de forêts. Comptes Rendus de Physique
6: 151–157.
Pourbohloul B, Meyers LA, Skowronski DM, Krajden M, Patrick DM,
Brunham RC. 2005. Modeling control strategies of respiratory pathogens.
Emerging Infectious Diseases 11: 1249–1256.
Prospero S, Holdenrieder O, Rigling D. 2003a. Primary resource capture in
two sympatric Armillaria species in managed Norway spruce forests.
Mycological Research 107: 329–338.
Prospero S, Rigling D, Holdenrieder O. 2003b. Population structure of
Armillaria species in managed Norway spruce stands in the Alps. New
Phytologist 158: 365–373.
Proulx SR, Promislow DEL, Phillips PC. 2005. Network thinking in
ecology and evolution. Trends in Ecology and Evolution 20:
345–353.
Pysek P, Richardson DM, Williamson M. 2004. Predicting and explaining
plant invasions through analysis of source area floras: some critical
considerations. Diversity and Distributions 10: 179–187.
Qin JL, Xu JJ, Hu DI, Sageman M, Chen HC. 2005. Analyzing terrorist
networks: a case study of the Global Salafi Jihad network. Lecture Notes in
Computer Science 3495: 287–304.
Queloz V, Grünig CR, Sieber TN, Holdenrieder O. 2005. Monitoring the
spatial and temporal dynamics of a community of the tree-root endophyte
Phialocephala fortinii s.l. New Phytologist 168: 651–660.
Read JM, Keeling MJ. 2003. Disease evolution on networks: the role of
contact structure. Proceedings of the Royal Society of London B 270: 699 –
708.
Reichard SH, White P. 2001. Horticulture as a pathway of invasive plant
introductions in the US. Bioscience 51: 103–113.
Rhodes M, Wardell-Johnson GW, Rhodes MP, Raymond B. 2006.
Applying network analysis to the conservation of habitat trees in urban
environments: a case study from Brisbane, Australia. Conservation Biology
20: 861–870.
Richardson DM, Rejmanek M. 2004. Conifers as invasive aliens: a
global survey and predictive framework. Diversity and Distributions 10:
321–331.
Rizzo DM, Garbelotto M, Hansen EA. 2005. Phytophthora ramorum:
integrative research and management of an emerging pathogen in
California and Oregon forests. Annual Review of Phytopathology 43: 309 –
335.
Roy M, Pascual M. 2006. On representing network heterogeneities
in the incidence rate of simple epidemic models. Ecological Complexity 3:
80–90.
Rozenfeld AF, Cohen R, ben-Avraham D, Havlin S. 2002. Scale-free
networks on lattices. Physical Review Letters 89, 218701: 1–4.
Russell CA, Smith DL, Waller LA, Childs JE, Real LA. 2004. A priori
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
295
296 Review
Research review
prediction of disease invasion dynamics in a novel environment.
Proceedings of the Royal Society of London B 271: 21– 25.
Rvachev LA, Longini IM. 1985. A mathematical model for the global spread
of influenza. Mathematical Biosciences 75: 3 – 23.
Sander LM, Warren CP, Sokolov IM. 2003. Epidemics, disorder, and
percolation. Physica A 325: 1– 8.
Sander LM, Warren CP, Sokolov IM, Simon C, Koopman J. 2002.
Percolation on heterogeneous networks as a model for epidemics.
Mathematical Biosciences 180: 293 – 305.
Saramäki J, Kaski K. 2005. Modelling development of epidemics with
dynamic small-world networks. Journal of Theoretical Biology 234: 413–
421.
Scherm H. 1996. On the velocity of epidemic waves in model plant disease
epidemics. Ecological Modelling 87: 217 – 222.
Schneeberger A, Mercer CH, Gregson SAJ, Ferguson NM,
Nyamukapa CA, Anderson RM, Johnson AM, Garnett GP. 2004.
Scale-free networks and sexually transmitted diseases – a description of
observed patterns of sexual contacts in Britain and Zimbabwe. Sexually
Transmitted Diseases 31: 380 – 387.
Schwartz N, Cohen R, ben-Avraham D, Barabási AL, Havlin S. 2002.
Percolation in directed scale-free networks. Physical Review E 66, 015104:
1–4.
Seglen PO. 1992. The skewness of science. Journal of the American Society for
Information Science 43: 628 – 638.
Sen P, Dasgupta S, Chatterjee A, Sreeram PA, Mukherjee G, Manna SS.
2003. Small-world properties of the Indian railway network. Physical
Review E 67, 036106: 1–5.
Serrano MA, Boguñá M. 2003. Topology of the world trade web. Physical
Review E 68, 015101: 1–4.
Shaw MW. 1994. Modelling stochastic processes in plant pathology. Annual
Review of Phytopathology 32: 523 – 544.
Shaw MW. 1995. Simulation of population expansion and spatial pattern
when individual dispersal distributions do not decline exponentially with
distance. Proceedings of the Royal Society of London B 259: 243 – 248.
Shaw MW, Harwood TD, Wilkinson MJ, Elliott L. 2006. Assembling
spatially explicit landscape models of pollen and spore dispersal by wind
for risk assessment. Proceedings of the Royal Society of London B 273: 1705–
1713.
Shenhav B, Solomon A, Lancet D, Kafri R. 2005. Early systems biology and
prebiotic networks. Lecture Notes in Computer Science 3380: 14 –27.
Shirley MDF, Rushton SP. 2005a. The impacts of network topology on
disease spread. Ecological Complexity 2: 287 – 299.
Shirley MDF, Rushton SP. 2005b. Where diseases and networks collide:
lessons to be learnt from a study of the 2001 foot-and-mouth disease
epidemic. Epidemiology and Infection 133: 1023 –1032.
Simberloff D, Parker IM, Windle PN. 2005. Introduced species policy,
management, and future research needs. Frontiers in Ecology and
Environment 3: 12–20.
Small M, Shi PL, Tse CK. 2004. Plausible models for propagation of the
SARS virus. IEICE Transactions on Fundamentals of Electronics
Communications and Computer Sciences E87A: 2379 – 2386.
Small M, Tse CK, Walker DM. 2006. Super-spreaders and the rate of
transmission of the SARS virus. Physica D 215: 146 –158.
Smith DL, Waller LA, Russell CA, Childs JE, Real LA. 2005. Assessing the
role of long-distance translocation and spatial heterogeneity in the raccoon
rabies epidemic in Connecticut. Preventive Veterinary Medicine 71: 225–
240.
Soares MM, Corso G, Lucena LS. 2005. The network of syllables in
Portuguese. Physica A 355: 678 – 684.
Sornette D, Deschâtres F, Gilbert T, Ageon Y. 2004. Endogenous versus
exogenous shocks in complex networks: an empirical test using book sale
rankings. Physical Review Letters 93, 228701: 1–4.
Southworth D, He X-H, Swenson W, Bledsoe CS, Horwath WR. 2005.
Application of network theory to potential mycorrhizal networks.
Mycorrhiza 15: 589–595.
New Phytologist (2007) 174: 279–297
Stanosz GR, Smith DR, Albers JS. 2005. Surveys for asymptomatic
persistence of Sphaeropsis sapinea on or in stems of red pine seedlings
from seven Great Lakes region nurseries. Forest Pathology 35:
233–244.
Stepniewska-Jarosz S, Manka M, Asiegbu FO. 2006. Studies on
anastomosis groups of Rhizoctonia solani isolates causing disease in two
forest nurseries in Poland. Forest Pathology 36: 97–109.
Stokstad E. 2004. Nurseries may have shipped sudden oak death pathogen
nationwide. Science 303: 1959.
Strogatz SH. 2001. Exploring complex networks. Nature 410: 268– 276.
Stukenbrock EH, Banke S, McDonald BA. 2006. Global migration patterns
in the fungal wheat pathogen Phaeosphaeria nodorum. Molecular Ecology
15: 2895–2904.
Sweetlove LJ, Fernie AR. 2005. Regulation of metabolic networks:
understanding metabolic complexity in the systems biology era.
New Phytologist 168: 9–23.
Szendrøi B, Csányi G. 2004. Polynomial epidemics and clustering in contact
networks. Proceedings of the Royal Society of London B 271: S364–S366.
Takeuchi F, Yamamoto K. 2005. Effectiveness of vaccination strategies for
infectious diseases according to human contact networks. Lecture Notes in
Computer Science 3514: 956–962.
Tatem AJ, Hay SI, Rogers DJ. 2006. Global traffic and disease vector
dispersal. Proceedings of the National Academy of Sciences, USA 103: 6242 –
6247.
Trottier H, Philippe P. 2005. Scaling properties of childhood infectious
diseases epidemics before and after mass vaccination in Canada. Journal of
Theoretical Biology 235: 326–337.
Tsonis AA, Roebber PJ. 2004. The architecture of the climate network.
Physica A 333: 497–504.
Uhrig JF. 2006. Protein interaction networks in plants. Planta 224: 771–
781.
Valverde S, Sole RV. 2005. Network motifs in computational graphs: a case
study in software architecture. Physical Review E 72, 026107: 1–8.
Van den Bosch F, Metz JAJ, Zadoks JC. 1999. Pandemics of focal plant
disease, a model. Phytopathology 89: 495–505.
Vannucchi FS, Boccaletti S. 2004. Chaotic spreading of epidemics in
complex networks of excitable units. Mathematical Biosciences and
Engineering 1: 49–55.
Vázquez A, Moreno Y. 2003. Resilience to damage of graphs with degree
correlations. Physical Review E 67, 015101: 1–4.
Verdasca J, da Gama MMT, Nunes A, Bernardino NR, Pacheco JM,
Gomes MC. 2005. Recurrent epidemics in small world networks. Journal
of Theoretical Biology 233: 553–561.
Volchenkov D, Volchenkova L, Blanchard P. 2002. Epidemic spreading in
a variety of scale free networks. Physical Review E 66, 046137: 1–9.
Vuorinen V, Peltomaki M, Rost M, Alava MJ. 2004. Networks in
metapopulation dynamics. European Physical Journal B 38: 261–268.
Wallinga J, Edmunds WJ, Kretzschmar M. 1999. Perspective: human
contact patterns and the spread of airborne infectious diseases. Trends in
Microbiology 7: 372–377.
Watts DJ. 1999. Small worlds. The dynamics of networks between order and
randomness. Princeton, NJ, USA: Princeton University Press.
Watts DJ, Muhamad R, Medina DC, Dodds PS. 2005. Multiscale,
resurgent epidemics in a hierarchical metapopulation model. Proceedings of
the National Academy of Sciences, USA 102: 11157–11162.
Watts DJ, Strogatz SH. 1998. Collective dynamics of ‘small-world’
networks. Nature 393: 440–442.
Webb CR. 2005. Farm animal networks: unraveling the contact
structure of the British sheep population. Preventive Veterinary Medicine
68: 3–17.
Webb CR. 2006. Investigating the potential spread of infectious diseases of
sheep via agricultural shows in Great Britain. Epidemiology and Infection
134: 30–40.
Webber JF, Brasier CM. 2005. Invasive pathogens – from Dutch elm disease
to sudden oak death. In: Alford DV, Backhaus GF, eds. Plant protection
www.newphytologist.org © The Authors (2007). Journal compilation © New Phytologist (2007)
Research review
and plant health in Europe. Introduction and Spread of Invasive Species
Symposium. Berlin, Germany: Humboldt University, 35 – 42.
Woodward G, Ebenman B, Ernmerson M, Montoya JM, Olesen JM,
Valido A, Warren PH. 2005. Body size in ecological networks. Trends in
Ecology and Evolution 20: 402 – 409.
Woolhouse MEJ. 2003. Foot-and-mouth disease in the UK: what should we
do next time? Journal of Applied Microbiology 94: 126S–130S.
Woolhouse MEJ, Shaw DJ, Matthews L, Liu WC, Mellor DJ,
Thomas MR. 2005. Epidemiological implications of the contact
network structure for cattle farms and the 20–80 rule. Biology Letters 1:
350–352.
Wu ZX, Xi XJ, Wang YH. 2005. Properties of weighted structured scale-free
networks. European Physical Journal B 45: 385 – 390.
Xia YX, Tse CK, Tam WM, Lau FCM, Small M. 2005. Scale-free
user-network approach to telephone network traffic analysis. Physical
Review E 72, 026116: 1–7.
Yair Y, Aviv R, Ravid G, Yaniv R, Ziv B, Price C. 2006. Evidence for
synchronicity of lightning activity in networks of spatially remote
thunderstorms. Journal of Atmospheric and Solar Terrestrial Physics 68:
1401–1415.
Yan G, Zhou T, Wang J, Fu ZQ, Wang BH. 2005. Epidemic spread in
weighted scale-free networks. Chinese Physics Letters 22: 510 – 513.
Ying L, Yang L, Xiu-Ming S, Yong R, Jian J, Ben Q. 2005. Dynamic
Review
properties of epidemic spreading on finite size complex networks. Chinese
Physics 14: 2153–2157.
Yook SH, Jeong H, Barabasi AL, Tu Y. 2001. Weighted evolving networks.
Physical Review Letters 86: 5835–5838.
Zadoks JC, van den Bosch F. 1994. Expansion and spatial spread of disease.
Annual Review of Phytopathology 32: 503–522.
Zanette DH. 2002. Dynamics of rumor propagation on small-world
networks. Physical Review E 65, 041908: 1–9.
Zanette DH, Kuperman M. 2002. Effects of immunization in small-world
epidemics. Physica A 309: 445–452.
Zedler JB, Kercher S. 2004. Causes and consequences of invasive plants in
wetlands: opportunities, opportunists, and outcomes. Critical Review in
Plant Sciences 23: 431–452.
Zekri N, Clerc JP. 2001. Statistical and dynamical study of disease
propagation in a small world network. Physical Review E 64, 056115: 1–6.
Zhao L, Park K, Lai YC. 2004. Attack vulnerability of scale-free networks
due to cascading breakdown. Physical Review E 70, 035101: 1–4.
Zheng DF, Hui PM, Trimper S, Zheng B. 2005. Epidemics and
dimensionality in hierarchical networks. Physica A 352:
659–668.
Zlatic V, Bozicevic M, Stefancic H, Domazet M. 2006. Wikipedias:
collaborative web-based encyclopedias as complex networks. Physical
Review E 74, 016115: 1–9.
About New Phytologist
• New Phytologist is owned by a non-profit-making charitable trust dedicated to the promotion of plant science, facilitating projects
from symposia to open access for our Tansley reviews. Complete information is available at www.newphytologist.org.
• Regular papers, Letters, Research reviews, Rapid reports and both Modelling/Theory and Methods papers are encouraged.
We are committed to rapid processing, from online submission through to publication ‘as-ready’ via OnlineEarly – our average
submission to decision time is just 30 days. Online-only colour is free, and essential print colour costs will be met if necessary. We
also provide 25 offprints as well as a PDF for each article.
• For online summaries and ToC alerts, go to the website and click on ‘Journal online’. You can take out a personal subscription to
the journal for a fraction of the institutional price. Rates start at £131 in Europe/$244 in the USA & Canada for the online edition
(click on ‘Subscribe’ at the website).
• If you have any questions, do get in touch with Central Office ([email protected]; tel +44 1524 594691) or, for a local
contact in North America, the US Office ([email protected]; tel +1 865 576 5261).
© The Authors (2007). Journal compilation © New Phytologist (2007) www.newphytologist.org
New Phytologist (2007) 174: 279–297
297