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doi: 10.1098/rstb.2007.2181, 741-7593632008Phil. Trans. R. Soc. B

Christopher A Gilligan perspectiveSustainable agriculture and plant diseases: an epidemiological

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Sustainable agriculture and plant diseases:an epidemiological perspective

Christopher A. Gilligan *

Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK

The potential for modern biology to identify new sources for genetical, chemical and biologicalcontrol of plant disease is remarkably high. Successful implementation of these methods withinglobally and locally changing agricultural environments demands new approaches to durable control.This, in turn, requires fusion of population genetics and epidemiology at a range of scales from theeld to the landscape and even to continental deployment of control measures. It also requires anunderstanding of economic and social constraints that inuence the deployment of control. HereI propose an epidemiological framework to model invasion, persistence and variability of epidemicsthat encompasses a wide range of scales and topologies through which disease spreads. Byconsidering how to map control methods onto epidemiological parameters and variables, some new

approaches towards optimizing the efciency of control at the landscape scale are introduced.Epidemiological strategies to minimize the risks of failure of chemical and genetical control arepresented and some consequences of heterogeneous selection pressures in time and space on thepersistence and evolutionary changes of the pathogen population are discussed. Finally, someapproaches towards embedding epidemiological models for the deployment of control in aneconomically plausible framework are presented.

Keywords: epidemiological model; crop mosaics; genetical, chemical and biological control;population genetics; economic models

1. INTRODUCTIONAgriculture is changing fast and with it the landscape

through which disease spreads. This imposes newdemands on our understanding of epidemiology if weare to control disease efciently, whether by genetical,chemical, biological or cultural means. The sorts of questions that need to be addressed ( table 1 ) are focusedon discovering the factors that inuence the invasionandpersistence of new pathogenic strains, how and why theyoutcompete resident pathogens and how to promotedurable methods of control. This requires an under-standing of what controls the variability of epidemicsbetweenonelocation andanother andfrom oneseasontoanother, and how this impinges upon local, national andsometimes international crop loss. Can we do all this?

Not yet but I shall argue here that we are beginning to beable to do so andillustratesomeprobable newdirections.To help motivate the discussion, I summarize someillustrative questions in table 1 from which I concludethat weneed to embed modernapproaches to sustainabledisease control within an epidemiological framework.

Why is agriculture changing so fast? What is theevidence? In large parts of the world, intensivelymanaged farms are becoming larger, interspersed withsmaller, organically and conventionally managed farmswith diverse livestock and cropping patterns. Globalwarming is changing the national and internationalranges of pests and disease ( Coakley et al . 1999 ).

Economic pressures and global trade are changing

national cropping patterns. It is anticipated that thedemand for cereals will increase by 20% by 2020 as

world population grows ( Rosegrant et al

. 2001 ). Thecorresponding increase in demand for animal productsis estimated to be 50%, in response to increasingafuence and urbanization, notably in southeast Asia( Evans 1998 ; Rosegrant et al . 2001 ). The recentaccession of 10 new states into the EU along withreform of the Common Agricultural Policy is likely tochange cropping patterns in Western Europe. Novelcrops for biofuel, plastics and intensive specializedproduction of pharmaceutical crops under glass areprobable. Meanwhile, our understanding of the geneti-cal and chemical bases of disease control is acceleratingfollowing investment in molecular biology ( Stuiver &

Custers 2001 ; Strange 2003 ). The costs, though, forrelease of new varieties and for the development andregistration of new chemicals have escalated. The questfor durable control itself rests on a paradox. Since mostplants are self-evidently resistant to most pathogens, itseems perfectly reasonable to assume that advancingknowledge of the molecular and cellular bases of host pathogen interaction will identify the means not only toengineer or to select durable resistance but also toproduce effective and environmentally neutral formsof chemical control. Yet failures still occur, whetherfrom the release of novel resistance genes ( Brown &Hovmller 2002 ) or from new pesticides and fungicides

(Chin e t a l . 2001 ). Agriculture continues to beconfronted with new and recurrent epidemics. Notableexamples include recent epidemics of cassava mosaicvirus in West Africa ( Legg 1999 ), citrus canker inFlorida (Gottwald et al . 2001 ; 2002 a ), rhizomania

Phil. Trans. R. Soc. B (2008) 363 , 741759doi:10.1098/rstb.2007.2181

Published online 7 September 2007

One contribution of 15 to a Theme Issue Sustainable agriculture II.

* [email protected]

741 This journal is q 2007 The Royal Society

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disease of sugar beet in the UK and Western Europe(Stacey et al . 2004 ), and the arrival and spread of Asiansoya bean rust, caused by Phakopsora pachyrhizi, inSouth America and subsequent entry into the UnitedStates ( Schneider etal . 2005 ). Similar problems arise innatural and semi-natural communities, where theeffects are especially noticeable on forest and amenitytrees: sudden oak death, caused by Phytophthoraramorum is spreading rapidly on coast live oak andtanoak in California ( Rizzo et al . 2002 ), for which theprobable strategy for control is sanitation and contain-ment. Meanwhile, Dutch elm disease may recur in theUK ( Swinton & Gilligan 1996 ) as may chestnutblight caused by Cryphonectria parasitica in the US( Milgroom & Cortesi 2004 ), for each of which there iscontinued interest in biological control by RNA viruses(Swinton & Gilligan 1999 ; Milgroom & Cortesi 2004 ).

Most forms of disease control are screened foreffectiveness at the small scale. Often this is done atscales as small as the single plant for initial screening,thoughmore usually it involves eld plots andultimatelyelds. Yet successful deployment, and the risk of failure,occurs at scales much larger than this, at the regional,national or even international scales. We can reconcilethese scales using an epidemiological framework thatallows us to predict how measurable changes in latentand infectious periods or transmission rate might affectthe regional spread of disease. This, in turn, requiresfusionof population genetics andepidemiology at scalesextending from the eld to the landscape and even tocontinental deployment of control measures. Progressin sustainable disease control measures also requires anunderstanding of economic and social constraints.These are all too frequently ignored in epidemiologicalmodels, while economic models are often biologicallynaive, failing particularly to allow for the dynamical

nature of most epidemics ( Gilligan 2003 ).An epidemiological framework for sustainable diseasecontrol requires a suite of models to analyse and predictthe effects of control on the spatial and temporaldynamics of disease, together with methods to

parametrize the disease. One important switch of emphasis is from within-eld to regional control of disease. Underlying this analysis is a shift in emphasisfrom private to public benet ( Geoffard & Philipson1997 ), whereby optimization of control strategies mayincreasinglybe exercisedfrom a regional perspective overa population of growers rather than seeking to optimizecontrol in each eld. Many of the components for anepidemiological framework have been individually stu-died but not always at the same scale and often with littleoverlap. These include models from both medical and

botanical epidemiology (to analyse andpredict theeffectsof control strategies on thespatial andtemporaldynamicsof disease), population genetics (for the evolution of virulence and pesticide resistance), landscape ecology(for the spatial structure of susceptible host populations)and environmental economics (to allow for cost con-straints and decision making under uncertainty).Progress in developing an epidemiological frameworkfor sustainable control of disease also depends upontheoretical advances in mathematics and statisticalphysics (particularly for transient behaviour, spatiallyextended dynamics, percolation and network theory) aswell as in probability and statistics (for stochastic

dynamics and parameter estimation of nonlinear modelsusing modern computer-intensive methods to explorelarge regions of parameter space). The relationshipsamong some of these areshown schematically in gure 1 .Here discussion is conned to strategic issues: math-ematical details are not given but may be found in citedpublications. Comprehensive treatments of modelstructure and analysis are also available in Gilligan(2002) for epidemics of fungal and fungal-like diseasesand by Madden et al . (2000) for virus diseases.

2. EPIDEMIOLOGICAL FRAMEWORK

(a ) Scale: within-plant, eld, farm, regional,national and continental scalesWhereas, convention suggests that the plant is thenatural unit to monitor epidemiological dynamics, thisis not necessarily so for many diseases or for the

Table 1. Some illustrative questions that may be answered from an epidemiological framework that involves a synthesis of epidemiology and population genetics embedded in a biologically plausible economic framework for management of disease.

How are invasion and persistence of agricultural parasites and the variability of epidemics affected by dynamical landscapeswhereby the mosaic and connectivity of the landscape change due to:

cropping patterns within and between seasons? spatial and temporal deployment of novel resistant varieties? spatial and temporal deployment of chemical control?

How are these processes affected by differences in: transmission, dispersal, recombination and intercrop survival typical of the principal classes of plant pathogens? How can epidemiological considerations of invasion, persistence and variability in heterogeneous temporal and spatial

environments be introduced to economic models for management of resistance and decision making under uncertainty? What are the consequences for the optimal deployment of novel chemical, genetical and engineered biocontrol agents so as to

minimize the risks of breakdown of control? Is there a critical density of susceptible crops below which a virulent race of the pathogen cannot invade? How is the risk of invasion affected by the geometry of the susceptible crops relative to the dispersal mechanisms of the

parasite? How do differential tness costs of invading and resident strains during the parasitic and saprotrophic or survival phases affect

the probabilities of persistence? Can we predict durability of resistance and how is this affected by the deployment of resistance? What is the time to extinction or time to invasion of a novel pathogen strain? What are the consequences for the evolution of dispersal rates and switching between asexual and sexual phases? What will happen to the threat of disease in organic (pesticide-free farms) when there is less control on surrounding farms?

742 C. A. Gilligan Sustainable agriculture and plant diseases

Phil. Trans. R. Soc. B (2008)



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development of optimal control strategies. The appro-priate scale of interest may occur both up and downfrom the level of the plant.

(i) Within-plant dynamics, topology and crop ideotypeFor a crop plant, such as wheat, that can produce 10 ormore leaves, 40 or more roots and several tillers, thesingle plant is frequently too crude a measure tounderstand the dynamics of infection. It is not unusualfor all plants to be scored as diseased within a eld( Werker & Gilligan 1990 ) yielding a spuriouslyasymptotic level of infection of 100%. This may havelittle impact on yield, when levels of infection withinplants are low, while masking highly nonlinear changesin infection within plants and in the availability of susceptible tissue for infection. Although much atten-

tion has been focused on the molecular and physio-logical interactions at the hostpathogen interface andtheir genetical control, relatively little attention hasbeen given to the importance for epidemics of thedynamics and topology of host growth within crops.

The amount and location of susceptible tissue changesas leaves and roots are produced, expand and die.Accordingly, the individual leaf, root, tiller or stem mayappropriately be considered the natural unit forinfection and disease. Each unit is then categorized asto whether or not it is susceptible ( S ), infected ( I ) orremoved ( R , an epidemiological euphemism thatencompasses dead, recovered or moribund tissue).This categorization leads to SIR models, common tohuman, animal and botanical epidemiology.

The availability of susceptible tissue modulates theinvasion and persistence of epidemics, yet is oftenoverlooked. For wheat infected by the take-all fungus,small levels of disease early on in an epidemic lead to anovercompensation of the plant in producing susceptibleroots to replace diseased roots ( Bailey & Gilligan2004 ). The extra roots enable the plant to compensatefor loss of tissue but the pathogen also benets from theprovision of new susceptible roots. The birth and deathof roots therefore changes the topology of the systemthrough which disease spreads. These function as

Molecular biologyof pathogenesis

Populationgenetics

Epidemiology

Economicmodelling

Transmission kernel R0

Infectiousness

Fitness costTrade-off

relationships

Percolation andnetwork theory

Landscapedynamics

Optimizingcontrol

Minimizingrisk of failure

P a r a m e t e r e s

t i m a t

i o n a n d

m o d e l

t e s t

i n g

Figure 1. Schematic relationships of selected components of an epidemiological framework encompassing population dynamic,population genetic, landscape dynamics and economic approaches.

Sustainable agriculture and plant diseases C. A. Gilligan 743




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epidemiological stepping-stones in bridging the gapbetween infected and otherwise susceptible roots,perhaps on adjacent plants, and so facilitate continuedinvasion by the pathogen. Only as the epidemicprogresses and the average burden of diseased rootsper plant increases, does the plant fail to compensateand the epidemic slow down ( Bailey & Gilligan 2004 ;Bailey et al . 2006 ). Further analysis of this epidemio-logical response for disease escape by the host suggeststhat there is differential expression among cultivars(Bailey et al . 2006 ) from which selection may beinitiated. Analogous properties hold for the dynamicsand geometry of leaf growth and dispersal of aerialpathogens. Thus, Lovell et al . (1997) and Arraino et al .(2006) have shown how cultivars of wheat differ withrespect to the orientation of leaves and propensity forsplash dispersal of Mycosphaerella graminicola withinand between leaves. We conclude from these and otherstudies that, in the renewed interest in re-constructingcrop ideotypes ( Denison e t al . 2003 ), includingreconstruction of genomes to bypass evolutionarybottlenecks, there is scope also for selection of traitsthat impinge on epidemiological dynamics.

(ii) Beyond the eld: treating elds as natural units for infectionThe switch of emphasis from within-eld to regionalspread of disease leads naturally to considering the eldas the natural unit for epidemiological analysis. Thiscan occur in two obvious ways. The rst is simply toclassify elds as susceptible, infected or removed, andto analyse the spread of disease through populations of elds using the same mathematical machinery as forepidemics within elds. The second is to allow fordynamics of disease within and between elds byconsidering elds as structured metapopulations(Gyllenberg et al . 1997 ; Park et al . 2001 , 2003 ; Gilligan2002 ). Epidemics now occur within elds but aresubject to dual sources of inoculum from within andbetween elds ( Park et al . 2001 ). In this case, there istherefore a transit time as a eld rst becomes infecteduntil it begins to export inoculum that causes infectionin other elds ( Swinton 1998 ; Gilligan 2002 ). In eachof these paradigms, the topological arrangement of susceptible crops within the landscape and thedispersal dynamics of the pathogen, or its vector,

together determine the dynamics of disease spread.How far the infection spreads within and between eldsis dened by the dispersal kernel. For many splash-borne pathogens, dispersal may be restricted toneighbouring elds, but for wind-dispersed pathogensdispersal may extend over several kilometres andexceptionally over hundreds of kilometres ( Limpert1999 ; Linde et al . 2002 ). For systems with large-scaledispersal, farms, counties or even larger regions mayform the natural scales of interest ( Stacey et al . 2004 ).

( b ) Simple modelsEpidemiological understanding of the sustainable

deployment of disease control requires simple yetrealistic models that capture not only the deterministic(average) behaviour but also stochastic dynamicswithin and between epidemics. The models can beused to compare alternative strategies for control by

mapping the effects of disease control onto the modelparameters ( gure 2 ). Finding the appropriate balancebetween simplication and detail remains a seriouschallenge for epidemiological analyses of sustainabledisease control. Another challenge is how to deal withtemporal and spatial heterogeneities. Temporal hetero-geneities occur due to uctuations in environmentalvariables within seasons that can appear to start andstop epidemics ( Truscott & Gilligan 2003 ). Fluctu-ations also impinge at the longer scale on the multi-seasonal dynamics of many botanical epidemics withperiods of survival interspersed between periods of parasitic activity on susceptible crops ( Gubbins &Gilligan 1997 a ,b). This exposes the pathogen to quitedifferent selection pressures within and betweenseasons and is particularly acute for pathogens inwhich re-establishment each season from residentinoculum has a marked effect on subsequent epidemics(Bailey et al . 2004 ). Spatial heterogeneities arise fromthe mosaic of susceptible and non-host crops encoun-tered by a pathogen as it spreads at the landscape orregional scales ( Gilligan 2002 ). Surprisingly littleattention has until recently been given to theseimportant processes in understanding the dynamicsof epidemics and the deployment of control.

Historically, there has been a tendency to focus onenvironmental variables, such as temperature andrainfall, often leading to multiple regression equationsfor disease progress ( Kranz 1990 ). This reected, inpart, the ease with which abiotic variables could bemeasured relative to biotic variables such as infectionand disease. Although these models may be useful asblack-box predictors of disease progress, they lack

mechanistic interpretation of the epidemiological pro-cesses. Increasingly, therefore, mathematical models forbotanical epidemics resemble those for animal andhuman diseases, centring upon the susceptible infectedremoved (SIR) framework, although the nedetails may differ. Some common variants used foranalysis of the dynamics and control of botanicalepidemicsare illustratedin gure2 . Thebalancebetweenprimary and secondary infection is particularly import-ant for many plant diseases ( Gilligan & Kleczkowski1997 ). Primary infection is drivenby ingress of inoculumfrom outside the system. For soil-borne pathogens,this often means infection from the reservoir of inoculum

in soil; for aerial pathogens, it usually means allowancefor inoculum coming from a different eld or even adifferent region. Models for botanical epidemics alsoincreasingly reect seasonal dynamics accentuated bysurvival during intercrop periods. The emphasis onseasonal dynamics, together with the balance betweenprimary and secondary infection, leads to SIX or SIR- X models for botanical epidemics in which X reects theamount of free living or simply surviving inoculum(gure 2 ). Detailed accounts of model structures for viraland fungal pathogens are given by Madden et al . (2000)and Gilligan (2002) , respectively.

Just like animal diseases, many plant pathogens

have a latent period between infection and sporulationand an incubation period between infection andsymptom expression. Often these are short comparedwith the infectious period and can be ignored(Anderson & May 1991 ). The incubation period is





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important only when it is longer than the latent period,allowing cryptic infection to occur ( gure 2 ). Thishappens with many virus diseases. The phenomenon of cryptic infection becomes important for almost allpathogens when the epidemiological unit of interest

switches to large units such as trees or to entire elds. Ineach case, signicant transmission of infection canoccur between trees or elds before symptoms aredetected. The delay is of immense practical importancewhen, as is usual, symptom expression triggers a

Stochastic SIX

Dispersal kernel

Control

Single pathogen strain Metapopulation

Two pathogen strains

SIRSEIR

SIDR SIX

s

sp

s

s

ss s s

s

s

s

r r

r

m

m m

m

m

p pp

Pr

Pr

ed d

Figure 2. Some common epidemiological models. The principal state variables are: S (susceptible), E (exposed, i.e. latentlyinfected), I (infected and infectious), D (detected, i.e. symptomatic and infectious), R (recovered or removed) hosts; X free-living inoculum. The following models are illustrated. SIR model with secondary infection, infectious period and net birth of susceptibles together with criterion for invasion ( R 0 ). SIDR model with secondary infection, cryptic u

K 11 and symptomatic

u K 12 infectious periods with xed host population size ( Dybiec et al . 2004 ). SIX model with primary bp and secondary b sinfection, net birth of susceptibles and decay of inoculum. Demographic stochastic version of SI model ( Gibson

et al . 1999 ).SEIR model with secondary infection, latent ( s K 1 ) and infectious ( mK 1 ) periods for xed host population size. Dispersal kernel

(with parameters, q) for probability that susceptible ( s) is infected by secondary infection from all infected hosts ( i ) within aneighbourhood N hood and by a constant source of primary infection ( 3) ( Keeling et al . 2004 ). Metapopulation with transmissionbetween subpopulations in a neighbourhood of interaction for a given strength of coupling ( 3) in addition to transmission withinsubpopulations: model also shows separate density-dependent birth and death processes for susceptibles and criterion forinvasion within a patch or subpopulation ( R p ) and entire metapopulation ( R 0 ) ( Park et al . 2001 ). Effect of control agent ontransmission rate and infectious period for a single pathogen strain and for two pathogen strains typied by a fungicide-sensitive(I s) and a fungicide-resistant ( I r) strain with tness costs r b , r m, in which the efciency is a function of fungicide concentration(C ). A criterion for invasion of the resistant strain is given that links the ratio of reproductive numbers and the efciency of control, for constant fungicide treatment ( Gubbins & Gilligan 1999 ; Hall et al . 2004 ). Note that all of the deterministic modelscan be readily adapted to stochastic treatments: further details are given in the cited literature and a general mathematicaltreatment in Gilligan (2002) .





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control response. This may be as diverse as theimplementation of removal policies for trees infectedwith notiable diseases such as citrus canker ( Gottwaldet al . 2001 ), or the implementation of a regionalstrategy for disease control, as in the recent attemptsto control rhizomania disease of sugar beet in UK (Stacey et al . 2004 ). In each case, signicant spread of disease occurred before control was implemented.Cryptic infection also means that control must betargeted at symptomless as well as infected sites if theepidemic is to be brought under control.

(i) The role of variabilityVariability is an integral part of epidemics. It is manifestat a range of spatial and temporal scales. The timing,intensity and expansion of epidemics differ from oneseason to another: there are good and bad diseaseyears for some pathogens, while other pathogensgenerate epidemics in most years. Even within thesame season, the rates of spread of disease within andbetween adjacent elds sown to identical host varietiesdiffer. Ideally therefore we would like to be able topredict not only the average trajectory of disease

progress but also the variability. This centres on theestimation of the probability distribution for theprobable occurrence of disease over time, and possiblyalso over space, in a population of susceptible sites.Individual sites can comprise entire farms, elds,

orchards or glasshouses. By mapping the effects of alternative control strategies onto the probabilitydistribution for disease progress, it is possible to predictnot only the effect of treatment on the average amountof disease but also the risk of severe failure and in whatproportion of elds or farms that failure might occur.The general approach is illustrated in gure 3 a alongwith an example ( gure 3 b) for a model experimentalsystem involving biological control of damping-off disease on radish by the hyperparasite Trichodermaviride (Gibson et al . 1999 ; Gilligan 2002 ).

There are two broad types of variability ( Nisbet &Gurney 1982 ). Demographic stochasticity relates todifferences among individuals. For epidemics, it simplyreects the probabilistic nature of transmission of infection between an infected and a susceptible hostunder identical environmental conditions. This leads toa series of stochastic events giving rise to differenttrajectories for different epidemics, even though thetransmission and other parameters remain the samethroughout the course of the epidemic. It is equivalentto saying that if epidemics were initiated in identicalelds under the same initial conditions and exposed to

identical environmental conditions, the resulting epi-demics occurring in each eld could still be markedlydifferent. How different depends upon the inherentdemographic stochasticity of the system. This is clearlydifcult to demonstrate in the eld, although extensive

n o . o

f i n f e c t

i o n s

( I )

0.1 0.2 0.3 0.40

1020304050

0 0.1 0.2 0.3 0.4 0 0.02 0.06 0.10 0 0.02 0.06 0.10

0.2 0.4 0.6 0.8 1.00

1020304050

0 0.2 0.4 0.6 0.8 1.0 0 0.1 0.2 0.3 0 0.1 0.2 0.3

T. viride

+T. viride

t = 1 t = 3 t = 5 t = 15

n o .

o f i n f e c t e

d p l a n

t s / s i

t e ( I )

frequency of sites with I infected plants

(b)

frequency of sites with I infections0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

Good controlwith risk of failure

(a )

Figure 3. Use of stochastic models to analyse the dynamics and control of epidemics. ( a ) Probability distributions for nal levelsof disease at different sites showing skewness towards the origin for a good control agent but with a risk of some failures.(b) Evolution over time of the probability distribution for epidemics of damping-off disease caused by R. solani in the presenceand absence of a biological control agent, T. viride . The pale bars represent data from a replicated experiment, the darker bars

are model predictions for a large number of trials after tting to the experimental data. Application of the control agent doesreduce disease but there is a signicant risk of failure at some sites. Further details are given in Gibson et al . (1999) .





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data collection for the evolution of epidemics such ascitrus canker in Florida ( Gottwald et al . 2002 b) andcitrus tristeza disease ( Gottwald et al . 1996 ), in which acomplete census of the infection status of trees inreplicate sites, comes close to this.

Analysis of demographic stochasticity allows us toidentify the underlying variability of an epidemic, theso-called dynamical landscape ( Gilligan 2002 ). Environ-mental stochasticity is superimposed upon this bychanging model parameters in time and space. Histori-cally, most attention has been given in botanicalepidemiology to environmental stochasticity due to theobvious sensitivity of plants and micro-organisms totemperature, relative humidity and other environmentaldriving variables. Here the focus has been more ontreatingparameters as smootheddeterministic functionsof environmental variables. Hence, the rate of trans-mission changes, for example with average temperaturethroughout the season ( Webb et al . 2000 ). While thisallows for seasonal forcing, it does not show howuctuations in environmental variables affect thevariabilityamong replicate epidemics in a way analogousto the data in gure 3 . Yet, owing to the inherentnonlinearity of epidemics, small differences in par-ameters, may become amplied or, conversely, largedifferences may be dampened. Some analytical work onthis form of dynamically generated variability has beendone for the R. solani- radish systems by Kleczkowskiet al . (1996) . Large numbers of experiments on thissystem have subsequently shown that variability amongepidemics, whether driven by demographic or environ-mentalvariability, is as mucha signature of theepidemicsas is the intrinsic rate of increase. There is continualdebate about how to quantify, distinguish, analyse andmodel the components of variability ( Nisbet & Gurney1982 ; Engen et al . 1998 ; Coulson et al . 2004 ). Futurework in devising sustainable methods of control willcontinue to address these issues. The problems for datacollection in theeld are accentuated by sampling errorssince complete census is seldom possible, though theprospects for remote sensing may improve this. Never-theless, it will be increasingly important to quantify thevariability within and between epidemics. This meansthat, wherever possible, we should exploit the availabilityof sampling and replicate data that so often in the pasthave been aggregated to produce averages that hide thenatural variability.

(ii) Spatial dynamics and mechanisms of spread Pathogens are dispersed through the landscape byabiotic agents and by invertebrate and other vectors.Dispersal also occurs by human intervention throughmovement of machinery and produce and by importa-tion of seed. These features are increasing in import-ance in modern agriculture as farms become larger,with single ownership of multiple farms, sharedmachinery and cultivation by contractors operatingover large regions. Disease spread occurs through anagricultural landscape that reects these changes in

commercial and agricultural pressures. This generatesan epidemiological system with two or more scales of dispersal, a local scale, driven largely by abiotic andvector biology, and a global scale, driven by commercialarrangements. Depending upon the type of pathogen,

the local scale operates at the within-eld and betweenadjacent elds scales and the global scale operates atlonger distances.

There are three ways in which to view this dualityof dispersal scales. Long-distance movement may beseen as sources of primary infection, with local spreadreecting secondary infection. Dispersal though theheterogeneous landscape can be viewed as a networkprocess, with nearest neighbour movement betweenadjacent elds and occasional, long-distance move-ments giving rise to small-world connections ( Strogatz2001 ). Finally, for some diseases where most dispersaloccurs within elds (or farms) and movement betweenelds (or farms) is less common, the system can beregarded as a metapopulation in which elds (orfarms) comprise more or less self-contained sub-populations. Strategies for the deployment of durableand sustainable control need to address these issues of how dispersal scales with the unit of interest and howto prevent invasion and persistence of pathogens inthe landscape.

The conventional question concerning dispersalkernels is, how far can a disease spread? By this isusually meant, what is the furthest distance over whichtransmission of inoculum can give rise to infection anddisease? This simple question, however, is confoundedby very low probabilities of very long-distance dis-persal. More enlightened questions are, how far isinfection likely to spread? and how might thedeployment of control strategies affect the dynamicsof spread and the likelihood of disease invasion? Thetail of the distribution for dispersal kernels is certainlyimportant. Much thought and experimental ingenuity

has been given to the distinction between exponentialand thick-tailed distributions (Shaw 1994 , 1995 , 1996 ;Sackett & Mundt 2005 a ). Exponential kernels result inexpanding waves about an initial focus, tending to aconstant velocity of expansion after an initial period of build-up. Thick-tailed distributions give rise to distinctdaughter foci and an entirely different spatial dynamicfor epidemic spread ( Shaw 1995 ; Sackett & Mundt2005 a ) with dispersive spread in which the velocity of spread increases with time. Owing to the complicationsof controlling experimental conditions, most experi-ments to identify dispersal gradients have beenconned to single foci spreading through single

homogeneous eld plots ( Sackett & Mundt 2005 b).Scaling-up to predict what happens at the larger scales( Frantzen & van den Bosch 2000 ) is still in its infancyfor spread through heterogeneous landscapes. It is amajor problem for emerging epidemics of new, rare ormutated forms of pathogens. Here we need to rely uponanalogous results for related pathogens or to extractestimates for dispersal and other parameters from theemerging epidemic.

The challenge of estimating parameters forepidemics with multiple sites of initial infection has,with some notable exceptions, received little attention.Gibson & Austin (1996) and Gibson (1997) have made

progress using likelihood-based and Markov chainMonte Carlo methods (MCMC) for citrus tristezadisease for which there was a complete census of infected and susceptible trees in citrus groves. Themethod involves taking successive snapshots of disease





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and estimating the parameters of a dispersal kernel byinferring the temporal sequence in which individualtrees became infected. Gibson & Austin (1996) andGibson (1997) used a simple model for dispersal inwhich they compared an exponential with a power-law(thick-tailed) kernel with and without allowance for theentry of external infections from outside the groves.They showed that there was more evidence for thepower-law model. By simulating the control of epidemics by removal of trees around infected trees,they showed that the critical removal distance of 14 m,previously advocated by Marcus et al . (1984) , couldlead to a serious risk of failure of eradication. Collectionof census data is expensive and the number of temporalsnapshots will often be limited. Exceptionally, progressis possible even when there is only one snapshot. Bymaking certain assumptions about the status of anepidemic, Keeling et al . (2004) successfully inferredboth spatial and temporal dynamics from singlesnapshots of disease, including the citrus tristeza

example. These analyses showed preferential evidencefor a power-law dispersal in common with the MCMCanalyses of Gibson (1997) and with a similar estimatefor the dispersal parameter. Importantly, however, thisproved possible using just the rst of two annualsnapshots. Clearly, more work needs to be devoted notonly to the methods of statistical analysis but also toefcient collection of data for parameter estimation of emerging epidemics. Prior knowledge helps, butexperience from animal epidemiology militates forcaution: it is striking how different were the dispersalmechanisms for the widespread 2001 foot and mouthepidemic in the UK from the previous major, but much

more localized, epidemic in 1967 ( Keeling et al . 2001 ).The difference partly reects changes in pathogenstrain but more signicantly changes in agriculturalpractice, with much more frequent movement of animals over long distances occurring in 2001.Comparable large changes are evident in crophusbandry, with major changes in sowing dates, shorterintercrop periods, as well as changes in fertilizer andpesticide applications and the genotypes and frequencyof crops being sown.

(iii) Long-distance continental spread Historically, much attention has been given to thecharacterization of wave speeds for focal expansionthrough susceptible elds around isolated sites of initialinfection (van den Bosch et al . 1988 a c, 1999 ). Thisstill has an important part to play, especially in thecontinental-scale spread of disease in which it isreasonable to assume that there is enough crop totrap incoming aerially dispersed spores, withoutrecourse to detailed analysis of the topological arrange-ment of susceptible crops on the ground.

Aylor (2003) constructed a stochastic dispersal modelto estimate the rate and extent of seasonal incursions of two aerially dispersed diseases, stem rust of wheat and

tobacco blue mould, from southern into northern areasof the US. The model treats the availability of thesusceptible crop as a continuum in space, but one thatchanges over time, sandwiched in a seasonal greenwave. The leading northerly edge is determined by crop

sowing date. The receding southerly edge is determinedby an advancing wave of crop maturity.

Both wheat stem rust and tobacco blue mouldappear to spread northward on average at about thesame rate as the seasonal advance of the green wave of available susceptible host tissue. Aylor (2003) con-cludes that the concordance of the disease wave with

the green wave underscores two important points.First, it suggests that disease spread over long distancesmay be limited more often by failure of the pathogen toestablish than by the ability to be dispersed over longdistances. The green wave also reduces the stochasticvariability and speed of disease spread by presenting abarrier to potential long-distance, low-probabilitydispersal events. Second, it helps to focus attentionon alternative pathways for disease spread and onpossible unappreciated niches for overseasoning, bothof which can have important implications for diseasecontrol strategies.

(c ) Mapping control strategies onto epidemiological variables and parametersNot surprisingly, the effects of different controlmethods may be mapped onto each of the epidemio-logical parameters ( gure 2 ). Thus, genetical, chemicalor biological methods may affect one or more of transmission rates, infectious periods, detection ratesas well as latent periods. Control can also affect thedispersal parameters by interfering with vectors or bypreventing long-distance movement. Removal of infecteds and susceptibles also allows control of epidemics by reducing the availability of infectious

tissue and susceptible tissue. At the larger (eld) scale,this is manifested by the application of protectant oreradicant chemicals, by changing cropping density orby introduction of resistant or partially resistantvarieties. In the extreme, the target of most geneticaland chemical control is to achieve immunity, so shiftingplants from the susceptible to an unavailable class.

Once a control strategy can be interpreted within amodel structure, it is possible to compare efciencies of control for different strategies and intensities ( table 1 ).In principle, this allows simple calculations about theability of pathogen strains to invade by computationand analysis of invasion criteria such as R 0 , a measureof the number of new infections per infected unit. Italso allows computation of invasion and persistencetimes of resident pathogen strains that are sensitive tothe control method, as well as fungicide-resistant orvirulent strains. Here the temporal and spatial deploy-ment of the control strategy in the landscape isimportant in determining whether virulent and aviru-lent strains coexist in the pathogen population, or if one is competitively excluded by the other. Theconsequences of this affect the durability of resistance( Vera Cruz et al . 2000 ; Parlevliet 2002 ). Moreimportantly, it also begs the question as to howgenetical control can be deployed in the populationso as to promote the durability of resistance. Similarquestions apply to the deployment of chemical controlagents and to the fates of fungicide-sensitive andfungicide-resistant pathogen strains.





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3. CROP MOSAICS, HETEROGENEITY ANDTOPOLOGY OF CROPS IN THE LANDSCAPEMuch thought has been given to the construction anddeployment of crop multilines and mixtures to slow thespread of disease within elds ( Mundt 2002 ). Followingearly work by Browning & Frey (1969) on multilines andWolfe (1985) on mixtures, interest in the strategieswaned, partly due to resistance from processors.Recently, however, interest has been revived in China(Zhu et al . 2000 ) and Western Europe ( Finckh et al .2000 ). Slowing the increase of disease within elds mayhave a knock-on effect in slowing the spread of diseasebetween elds and, hence, restricting invasion throughthe landscape.By thinking ofeldsas subpopulations in astructured metapopulation ( Gyllenberg et al . 1997 ), theeffect of mixtures in the landscape can conveniently bethought of as delaying the transit time between elds. Wedene the transit time as the time from when the rstindividual becomes infected in one eld and starts anepidemic in another eld. Most theoretical work ontransit times in metapopulations has focused on persist-ence. Thus, Swinton (1998) showed that above a certaincritical subpopulation size, the expected extinction timefor a metapopulation scales with the number and size of subpopulations. There is a phase transition (i.e. a switchin behaviour from short to long extinction times) aroundthe critical subpopulation size, N C . Below N C ,thetimetoextinctionis very short because theamountof susceptiblehosts is not sufcient to maintain the epidemic before itspreads to the next subpopulation. As the population of susceptibles increases above N C , there is a suddentransition to long extinction times. Increasing thenumbers of subpopulations in themetapopulation delays

extinction but does not affect the critical value of N

C atwhich the phase transition occurs ( Swinton 1998 ). Thishas been demonstrated for animal disease ( Swinton etal .1998 ) and proposed for botanical epidemics ( Gilligan2002 ), with additional theoretical work on invasion aswell as persistence (Park et al . 2001 , 2003 ). It is nowready to be tested in the eld.

How far and how fast a pathogen spreads through alandscape and, indeed, whether or not it persists andfor how long, depends upon the crop mosaic within thelandscape. Whether or not invasion occurs dependsupon the relative magnitude of the modal dispersaldistances and the scale of heterogeneity in the land-

scape ( gure 4 ). Considering disease spread in this wayis still at an early stage. A convenient starting point is toassume that disease spreads on a lattice and then tointroduce gaps and so to advance to spread through arealistic population of elds. For a given pathogen, eacheld of a susceptible crop is classied as susceptible(i.e. healthy), infected or, if appropriate, recovered.Non-host crops are unavailable to the pathogen and aretreated as gaps. The application of a protectantfungicide temporarily renders a susceptible eldunavailable for infection ( gure 4 ). Whether or not apathogen invades now depends upon the spatial andtemporal dynamics of the crop mosaic. A simple

analysis based upon ideas from percolation, derivedin statistical physics ( Stauffer & Aharony 1994 ),illustrates an important relationship between dispersalkernels and invasion. When spread occurs betweenadjacent elds, i.e. by nearest-neighbour spread, the

dispersal kernel then describes the probability distri-bution for transmission of infection between aninfected eld and its susceptible neighbour ( gure 4 ).It follows from percolation theory that there is a criticalprobability above which disease spreads and belowwhich it dies out. By increasing the distance betweensusceptible elds, it is possible to bring the percolationprobability for a given lattice below the threshold andso prevent invasion ( gure 4 ). These results arestochastic: it follows that there will be some spreadwhen the percolation probability is below the thresholdand occasionally invasion may occur but, on average,we would expect the strategy to work, albeit underthese idealized conditions. Suppose now that thedensity of susceptible crops per unit area of landexceeds the threshold and invasion is expected.Introducing gaps into the lattice by the application of localized chemical control could switch an invasive intoa non-invasive mosaic ( gure 4 ). The neness of thecontrol and the precision of the phase transition issufciently striking ( gure 4 d ) to lead us to questionwhether or not it is necessary to treat all elds in thelandscape in order to prevent invasion. The answersfrom these theoretical investigations would suggest not.The ideas have yet to be tested in the eld, however;something that presents signicant challenges in large-scale testing of new approaches towards sustainablecontrol. Meanwhile in order to gain more insight intothese approaches and, in particular, to understandvariability between replicate epidemics, we have testedsome of the ideas in a series of microcosm experimentsinvolving R. solani spreading between nutrient sites atdifferent densities with and without gaps ( Bailey et al .

2000 ; Otten et al

. 2004 ). The results support theinferences proposed above.As an epidemic spreads through a heterogeneous

landscape, the dynamical contact structure, whichmeasures the exposure of susceptible to infected sites,also changes. This too can slow down or speed up anepidemic and is a property of the topology of thesystem. So far, we have discussed susceptibles andgaps. What if there are differential susceptibilities forsusceptible crops in a mosaic? This could reectincomplete chemical control in treated elds or partialgenetical resistance. By extending the model experi-mental system to include spread through mixed

populations of radish and mustard in replicatedmicrocosms, we simulated experimentally the spreadthrough a heterogeneous landscape. Not surprisingly,the inclusion of a less susceptible host can slow the rateof spread of an epidemic compared with spread thougha homogeneous mosaic ( Otten et al . 2005 ). However,the rate of spread changes nonlinearly with the relativedensities. If this holds for the large-scale transmissionbetween elds, it follows that the introduction of acritical proportion of a less susceptible crop could slowthe spread of infection through the landscape. More-over, the differential rates reect not only differences insusceptibility but also differences in infectivity. This

means that for two types of host, four types of transmission rates occur, depending upon which hostis the donor (infected) or recipient (susceptible). Ottenet al . (2005) showed how to calculate transmission ratesfrom empirical data which, in turn, can be used to





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predict the effects of changes in the topology andcomposition of the mixture. By treating elds as unitsthis approach can, in principle, be extended to gaininsight into the effects of different levels and densities of partial control at the landscape scale.

(a ) Matching the scale of control with theepidemic scaleThe foregoing discussion suggests that control could beallocated to a proportion of elds in a landscape in

order to prevent invasion. For some emerging diseases,in which initial foci are identiable, local control maybe implemented. This may involve removal of theinfected site along with protection of surroundingsusceptible sites. This is a classical example of ringvaccination that has been widely debated in animal( Keeling et al . 2003 ) and human ( Ferguson et al . 2003 )epidemiology. Obviously, by getting ahead of theinfection, local vaccination can bring the epidemicunder control and prevent further spread. Problems

(b)(a )

(c)

(d )

(i) (ii)

(i)

1.0

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0 2 4 6 8 10 12 14 16 18 20distance ( r )

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i l i t y o f c o

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invasion

(ii)

Figure 4. Spread through a landscape with nearest neighbour transmission between infected and susceptible sites. ( a ) Aerialphotograph showing a typical example of a UK crop mosaic. ( b) Probability distribution for transmission of infection tosusceptible sites at different distances from the infected source showing the percolation threshold ( P c) for a triangular lattice. ( c)Effects of a small change in the distance between susceptible (open circle) sites (i) above and (ii) below the threshold distance onthe invasion of an epidemic measured by the spread of infected (lled circle) sites. ( d ) Effects of introducing gaps to simulatechemical control in the landscape upon a percolating system, showing the neness of the control about a phase transition; whitesquares indicate control, light grey indicate susceptible and dark infected. ( b,c) Derived from experimental microcosms ( Baileyet al . 2000 ; Otten et al . 2004 ). ( d ) Derived from a computer simulation by kind permission of Dr J. Ludlam.





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arise, however, when there is cryptic spread of infectionso that infectious elds export inoculum to adjacentelds before the disease is detected. This requiresjudgement of the size of the zone of cryptically infestedelds around a symptomatic eld. It is furthercomplicated when local spread is augmented by global,long-distance movements. Taking a stochastic suscep-tibleasymptomatically infecteddetectably infected removed (SIDR) model ( gure 2 ) on a two-dimensionallattice with long-distance movements, Dybiec et al .(2004 , 2005 ) examined a series of control strategies of different sizes centred around a symptomatic site(gure 5 a ,b). They showed that for small to moderatelysevere incidences of infection with a small number of non-local links, it is possible to bring the spread of disease under control. The efciency of a local controlstrategy is very sensitive to the choice of the radius.

Importantly, it was also possible to show that there is aminimum radius associated with such a controlneighbourhood leading to the lowest severity of theepidemic when costs of treatment and disease are takeninto account ( gure 5 c). Below the optimal radius, the

local strategy is unsuccessful; the disease spreadsthroughout the system, necessitating treatment of thewhole population. Clearly, at the other extreme, astrategy involving a neighbourhood that is too largecontrols the disease but is wasteful of resources.Relatively little is yet known about the topology of networks for the transmission of crop disease, althoughthis is an area of intensive theoretical investigation inanimal and human epidemiology ( Newman 2002 ;Keeling 2005 ). It is possible that transmission of somepathogens may be approximated by scale-freenetworks, in which there is marked variability innumbers of contacts, with the rich nodes equatingto nurseries and wholesalers that inadvertentlydisseminate infected plants. This makes the localdeployment of control more difcult, especially whenthere is cryptic infection. Dybiec et al . (2004 , 2005 )

showed that it was not possible to stop an epidemic onscale-free networks by preventive actions, unless a verylarge proportion of the population is treated ( gure 5 ).

A practical instance of the problem of controlling adisease in which there is cryptic infection may be seen

local disease control neighbourhood, z(b)

(d )(c)

shortcuts

(a ) local epidemic neighbourhood

100

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60

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05

1015 0

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Figure 5. Matching the scale of control with the epidemic scale when there is cryptic infection. ( a ) Local epidemic

neighbourhood. There are two scales of spread: local spread in which a region of cryptically infected sites surround asymptomatic site. Key: susceptible (white), cryptic (black), symptomatic (grey). ( b) Example of a neighbourhood of controlsurrounding a symptomatic site; shaded sites have been treated. ( c) Simulations show that there is a critical size for controlneighbourhoods ( z) that minimizes the cost of an epidemic ( X, calculated as a simple weighted linear sum of treatment andinfection costs) for spread on a two-dimensional lattice with nearest neighbour transmission and different probabilities, p(expressed as a percentage), for transmission between an infected and a susceptible site. ( d ) Equivalent results for a scale-freenetwork. Further details are given in Dybiec et al . (2004) .





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from experience with the control of rhizomania, asoil-borne disease of sugar beet in the UK ( Stacey et al .2004 ). The disease is transmitted by a plasmodiophor-omycete vector, with spread between elds occurringprincipally on agricultural machinery. Prior to theavailability of partially resistant varieties, control waseffected by a mandatory containment policy wherebysugar beet could not be grown in elds that had shownsymptoms of rhizomania. But by the time symptomsshow, an infested eld has already been exportinginoculum to other elds over several seasons ( Staceyet al . 2004 ). Accordingly the containment policy wasabandoned. Successful control of disease was shown todemand a farm scale, rather than a eld-scale, responsein which the scale of treatment more closely matchesthe scale of epidemic advance ( Gilligan et al. 2007 ).

( b ) Durability of control The risk of failure, particularly of genetical andchemical control but also of biological control, within

a few seasons is a major concern for sustainable controlof endemic diseases in agriculture, not least due to thedevelopment and registration costs that can approach 500 M. For new diseases or pathogen strains, theconcern is whether or not often untried methods cansuccessfully contain the emerging epidemic. Althoughmuch experimental work has focused on the molecularand biochemical aspects of the breakdown of hostresistance or of fungicide sensitivity in the pathogen,relatively little is known about the processes thatunderlie the durability of control at the populationscale. Some resistance genes are known to haveremained effective for a long time: resistance to cabbage

yellows caused by Fusarium oxysporum f . sp.conglutinans has lasted for more than 90 years ( VeraCruz et al . 2000 ); resistance to leaf rust, Pucciniatriticina , conferred by Lr34 has lasted for 30 years( Kolmer 1996 ). Others are remarkably ephemeral, forexample Yr17 for the control of yellow rust on wheat,was rapidly overcome in two to three seasons byvirulent isolates of Puccinia striiformis f. sp. tritici in theUK followed by Denmark, France and Germany(Bayles et al . 2000 ). The durability of various riceblast resistance genes is often less than 3 years( Kiyosawa 1982 ; Zeigler et al . 1994 ). Broad spectrumfungicides remained effective for long periods, but for

those with single-site action the durability is oftenshort. Following the introduction of strobilurins in1996 to control a range of cereal pathogens, highfrequencies of resistance in Blumeria graminis had beendetected within 4 years over large areas of Germany,France and the UK ( Chin et al . 2001 ). Clearly, thedurability of control depends upon the selectionpressure imposed upon the pathogen population andthe tness of virulent or fungicide-resistant strainsrelative to resident, avirulent and fungicide-sensitivestrains. McDonald & Linde (2002) recently reviewedthe durability of resistance for a large number of fungaland oomycete pathogens and proposed that the risk of

failure of genetical control depended not on the natureof the resistance genes but on the evolutionary potentialof the pathogen. They identied three factors, popu-lation size, rate of gene and genome ow (migration)and the reproduction or mating system (i.e. asexual or

sexual), from which to produce a risk factor for loss of resistance. Garca-Arenal & McDonald (2003) sub-sequently extended the analysis to viral diseases, notingthat resistance to viruses was generally more durablethan resistance to fungal and fungal-like pathogens.

Traditionally, analyses of virulence dynamics andfungicide dynamics tended to focus only on therelative frequencies of genotypes in the pathogenpopulation. More insight into the likelihood of invasion and persistence of novel strains is gained bycombining population genetics and epidemiologicaldynamics ( Gubbins & Gilligan 1999 ; van den Bosch &Gilligan 2003 ; Gudelj et al . 2004 ; Hall et al . 2004 ;Parnell et al . 2005 ). Combining the approaches takesaccount of the inuence of a dynamically changingsupply of susceptible tissue on the outcome of competition between pathogen strains ( Gubbins &Gilligan 1999 ). It allows for the inuences of spatialstructuring of the host population (Parnell et al . 2005 ,2006 ) and for local stochastic elimination of strains(Gubbins & Gilligan 1999 ) on the invasion andpersistence of novel strains. It also allows greaterinsight into the denition of durable control. Johnson(1979 , 1981 , 1984 ) originally proposed that durabilityof a resistance gene should be empirically assessed interms of area, time-span, degree of exposure to thetarget pathogen. Subsequent analyses have sought todene and quantify the mechanistic bases for durableresistance. A population genetics approach leadsnaturally to a convention for measurement of thedurability of resistance as the time-span from intro-duction of the resistant cultivar to the time when thefrequency of the virulence gene reaches a preset

threshold, above which the resistance is consideredto have broken down. This denition fails to takeaccount of the area receiving the treatment within thelandscape ( Johnson 1984 ; van den Bosch & Gilligan2003 ). Consider a resistant crop. The conventionalapproach to preserve the durability of newly releasedresistance genes is to introduce resistant cultivars atlow cropping ratios ( Pink & Puddephat 1999 ). Butanalysis of durability in this way fails to take account of the yield benet from sowing the resistant crop over agreater area. The conventional denition for durabilityalso assumes that breakdown is inevitable and that thevirulence matching the resistant genotype is already

present in the population, which, of course, may notbe the case. Durability is enhanced, if it is not alreadypresent, by the delay for the virulent genotype to enterthe system, through mutation or immigration, and toestablish a population. These considerations lead to twonew measures of durability ( van den Bosch & Gilligan2003 ). One is the expected time until invasion of thevirulent genotype, by mutation or immigration, andexpected establishment of a population. Theother is theadditional yield measured by the expected number of uninfected host growth days. Each was compared withthe conventional measure for a range of cropping ratiosfor a newly released resistant variety ( gure 6 ). The

results challenge the universality of the buffering effectof lowcropping ratios by showing that theexpected timeto invasion canbe delayedby high aswell as lowcroppingratios. Surprisingly, too, yield gain through cultivationof the resistant variety is only slightly inuenced by





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cropping ratio ( gure 6 c). There are cases in whichresistant cultivars have been widely grown withoutbreakdown of resistance: Steffenson (1992) , forexample, describes how the gene Rpg1 successfullyconferred resistance to Puccinia graminis f. sp. tritici onbarley for more than 40 years in the northern greatplains of the US and Canada. Arguably, however,intentional widescale routine testing of the advantagesof high cropping ratios for the release of resistant

cultivars may be premature. One possible alternativewould be to use a high cropping ratio in a restricted partof the crops area and none in the rest of the area in amanner similar to refugia for pest resistance ( Tabashniket al . 2005 ). I anticipate that this will be an area of

intense research, not only for the deployment of resistant varieties but also for the release and use of new forms of chemical control.

(c ) Invasion and persistence of virulent and fungicide-resistant strainsEpidemiological models for the invasion and persist-ence of chemical control are similar to those forgenetical control. Until quite recently, most modelsignored stochasticity and density dependence imposedby the dynamical changes in the availability of untreated tissue. Moreover, by invoking exponentialgrowth of the pathogen, invasion of fungicide-resistantforms is inevitable, and attention focuses not onwhether or not a resistant strain can invade but thetime to reach a critical level. This is unrealistic. Byallowing for competition for susceptible (untreated)sites, it is possible to show that there is a thresholdbelow which resistance cannot develop within the hostpopulation ( Gubbins & Gilligan 1999 ). The threshold

depends upon the relative tness of the resistant andsensitive strains and the effectiveness of control. Thelatter may inuence one or more of the following:reduction in the transmission of infection, the durationof infectiousness and the conversion of host toinfectious pathogen tissue ( Hall et al . 2007 ). Therelative tness of the resistant strain is given by the ratioR 0r /R 0s , where R 0s and R 0r are the basic reproductivenumbers for the sensitive and resistant strains,respectively. Even crude estimates for the efciency of control and the basic reproductive numbers canprovide a simple rule of thumb for whether or notinvasion may be expected.

Fungicides differ from many forms of geneticalcontrol in being subject to decay over time, requiringrepeated application. By including parameters for theamount of fungicide applied, longevity and applicationfrequency of the chemical, it is possible to predict theoutcome of invasion of the resistant strain, even whenthere is a time-varying selection pressure on thepathogen population ( Gubbins & Gilligan 1999 ; Hallet al . 2004 ). Notably, these models share a commongeneric structure with antiviral drug resistance andantibiotic resistance ( Hall et al . 2004 ).

The durability of genetical and chemical controldepends not only on the ability of a virulent or

fungicide-sensitive strain to invade an existingpathogen population but also whether the wild type iscompletely replaced or can coexist. Complete exclu-sion of the resident (controllable) pathogen strain bythe invading strain means that the gene or fungicidecannot be used again as a sole method of control.Empirical evidence shows both scenarios with coex-istence ( Chin et al . 2001 ; Bierman et al . 2002 ) andcompetitive exclusion ( Barofo et al . 2003 ). To developeffective resistance management strategies, it is impera-tive to understand the processes that inuence which of these outcomes is likely to occur. Initially, it wasthought that models could be of little assistance

because coexistence was predicted to occur onlyunder exceptional circumstances with restrictiveassumptions about the magnitudes of the parametervalues ( Gubbins & Gilligan 1999 ). The obvious way toaccount for a spectrum from competitive exclusion to

T i n v a s i o n

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Figure 6. Measures for durability of resistance. Effects of cropping ratio ( f ) of a newly released resistant variety anddifferent transmission rates ( b ) for infection on: ( a ) theexpected time until the virulent pathogen invades ( T invasion ),(b) the time until the virulent genotype comprises a criticalproportion (arbitrarily set to 90%) of the pathogen popu-lation ( T take-over ), ( c) the total number of additional

uninfected crop growth days due to the release anddeployment of the resistant variety ( T additional ). Further detailsare given in van den Bosch & Gilligan (2003) .





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coexistence is to allow for spatial heterogeneity in theselection pressures. This is conveniently done using ametapopulation framework. Thus, when Parnell et al .( 2005 , 2006 ) allowed for differential selectionpressures due to incomplete coverage of plants byfungicide either within or between crops, threescenarios were possible, ranging from failure to invade,through coexistence, to competitive exclusion of theresident strain. The outcome within elds dependsupon the balance between incomplete spray coverageand a cost to resistance, with healthy host densitymaximized when there is coexistence. Recent work bySalathe et al . (2005) suggests that coexistence ispossible within stochastic systems without invokingcosts of resistance.

At the regional scale, invasion of resistant strains isdetermined by a trade-off between the fraction of eldsthat aresprayed and the intrinsic reproductiveability R 0of the target pathogen ( Parnell et al . 2006 ). If thebetween-eld movement of the pathogen is high (highR

0), the resistant strain dominates all treated elds but

the sensitive strain dominates all untreated elds. Thisoccurs because, in the long term, resistant strains arecompetitively superior in treated elds and sensitivestrains are competitively superior in untreated elds. If R 0 is very high, mixing is complete and all treated eldsbecome infested with the resistant strain and alluntreated elds become infested with the sensitivestrain. If, however, R 0 is low, strains cannot movebetween elds to the extent that allows them tocapitalize on their within-eld competitive advantageand may therefore be excluded. The outcome is thendependent on the fraction ofelds sprayed ( Parnell etal .

2006 ). Once again the analogy with refugia is apparent.Further work on the invasion and persistence of virulent and fungicide-resistant pathogen strains willincreasingly focus on the integration of genetical andepidemiological mechanisms. Foremost among thesewill be empirical evidence or otherwise for tness costs( Vera Cruz et al . 2000 ; Brown 2003 ) as well as researchon the evolution of tness modiers and evolutionarytrade-offs among epidemiological parameters. Clearly,there is also a need to identify control strategies thatbalance the conicting aims of resistance management(to reduce the risk of failure) and yield enhancement byapplication of genetical, chemical and other control

methods to suppress disease. Some initial models thatintegrate crop yield have been explored by Hall et al .(2007) . Most strategies depend upon host diversica-tion within the landscape. We do not, however, knowhow introducing host diversity into the landscapeaffects evolutionary divergence towards specialist orgeneralist pathogens, or even if it might lead to a switchin pathogenicity from one host to another. This can beinvestigated by analysing the evolutionary trade-offsthat occur over successive generations of a pathogenexposed to two or more hosts. Preliminary results showthat evolutionary outcomes strongly depend on theshape of the trade-off curve between pathogen

transmission on sympatric hosts ( Gudelj et al . 2004 ).Using methods based upon adaptive dynamics, it hasbeen possible to determine criteria under whichevolutionary branching occurs from a monomorphicinto a dimorphic population, as well as the conditions

that lead to the evolution of specialist (single hostrange) or generalist (multiple host range) pathogenpopulations ( Gudelj et al . 2004 ). Since some pathogenspecies can undergo 2030 generations in a growingseason, the consequences of this form of evolution maybecome apparent within decades.

4. OPTIMIZATION OF DISEASE CONTROL USINGAN EPIDEMIOLOGICAL FRAMEWORKThecontrol ofdiseaseepidemics often requiresexpensiveresources. These include investment costs for breedingprogrammes, the development, testing and registrationof new chemicals or biological control agents. There arealso variable costs for the application of control methods.There may be economic, environmental or ecologicalrestrictions on the use of different methods associatedwith the accumulation of toxic chemicals in theenvironment, or the risk of failure through prematurebuild-up of virulence to resistance genes or insensitivityto pesticides in pathogen populations that could renderthe control and investment ineffective. This creates twoproblems for the implementation of control.The rst is astrategic issue about the long-term effectiveness and thecorresponding risks of failure associated with differentcontrol strategies. We discuss briey how the risks can beameliorated by bufferedimplementationof novel control.The second is how to optimize thedeployment of controlwhen resources are limited or there are other restrictionson use (such as the risk of failure through over-use).

(a ) Buffered implementation of genetic and chemical control

Following some spectacular failures, increasing atten-tion is being given to the buffered implementation of genetical and chemical control methods through timeand space. This is variously done by the cultivation of refugia of non-resistant or untreated crops, by alter-nating pesticides through time and space to imposedifferent selection pressures, and by diversifying thegenetic bases for control. Each demands an under-standing of the dynamical landscape in order to matchthe scale of control with the scale of the epidemic. Thisis most well advanced for a pest problem involving thedeployment of Bt -resistance for insect pests on maizeand cotton in the US and elsewhere, where there are

mandatory requirements for refugia ( Rausher 2001 ;Cerda & Wright 2004 ). By permitting multiplicationand persistence of the sensitive form of the pestpopulation on susceptible crops within refugia, thebuild-up of mutant pests that can feed and reproduceon the Bt -resistant crops is delayed. Arguably though,with this and other schemes most attention has focusedon relatively local scales, yet there may be broaderissues for larger scales. For example, should a newpesticide or resistant variety be released at a continentalscale? Would heterogeneity at a local scale be sufcientto prevent problems of invasion of pesticide-resistant orvirulent strains at a much larger scale? We do not yet

know. Recent examples for the apparent widescaleoccurrence and spread throughout Western Europe of fungicide resistance forms in the eyespot and mildewpathogens of wheat suggests that large-scale dynamicsmust be considered. These pathogens differ in dispersal





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mode, with eyespot predominantly spread by short-distance rainsplash whereas mildew can spread overlonger distances by wind. A combination of theanalyses of Aylor (2003) for continental spreadwith those of network ( Dybiec e t a l . 2004 ) andlandscape ( Keymer et al . 2000 ) models may help toanswer these questions.

( b ) Economic considerations in the optimizationof disease control All too often, optimization of epidemiological modelsoccurs without any formal consideration of economicor social constraints. Meanwhile, economists and socialscientists frequently address problems that inuencepolicy for the implementation and deployment of disease control strategies, but many of the under-pinning models are biologically naive, lacking, inparticular, insights into stochastic and spatial dynamicsof disease propagation. The two need to be integrated.Two promising approaches can be adapted from

economic theory. The rst concerns decisions aboutthe implementation or release of new methods forcontrol under uncertainty. The method is based onoptions approaches, originally derived for nancialmarkets ( Dixit & Pindyck 1994 ) and has been appliedby Morel et al . (2003) and Wesseler (2003) to therelease of Bt resistant maize. Essentially, the problemsuggests that a government or other organizationobtains the right to deploy a genetically resistant cropwithin a given time frame. Conventional analysis wouldlook at a simple costbenet analysis, so that a newvariety is released immediately if the net benets(calculated as the difference between variable benets

(e.g. increased yield and revenues) and variable costs(e.g. decreased pesticide costs)) are greater than for theconventional crop. Otherwise the variety is shelved. Butthis ignores uncertainty in year-to-year variation in pestdamage and yield due to epidemiological and environ-mental factors, as well as variability in price and othervariables such as input costs. Conventional cost benet analysis also ignores irreversible benets andirreversible costs that may accompany the release of anew variety. Foremost among the irreversible costs isthe risk of the pest overcoming resistance. Reduction inpesticide residues in groundwater or a decreased risk of pesticide resistance occurring in the pathogen popu-

lation are examples of irreversible benets. It followsthat there are now three decisions: to release immedi-ately; to release at some time in the future when there ismore information to assess whether the benets exceedthe costs; or not to release at all ( Morel et al . 2003 ;Wesseler 2003 ). The time (if at all) for release isobtained by optimization of a function that incorpor-ates benets and costs under uncertainty with adiscount rate on the investment ( Morel et al . 2003 ;Wesseler 2003 ). These exploratory analyses show thatthe critical value that must accrue for release of atransgenic crop is amplied in the presence of uncertainty. Some counter-intuitive results emerge for

analysis of Bt maize, whereby mandatory refuge areasand tax incentives that might be expected to delayrelease actually promote earlier release ( Wesseler2003 ). Conversely, in illustrating the applicationof real options analysis to the release of Bt maize,

Morel et al . (2003) argue that while a simple cost benet analysis would favour release, preliminaryallowance for uncertainty did not. The analyses arebased upon assumptions that breakdown of resistanceis inevitable, instantaneous and ubiquitous when itoccurs, and hence that mean eld models capture aspatially heterogeneous system adequately. The con-sequences of these assumptions for the release of transgenic crops and pest resistance are discussed froman epidemiological perspective by Gilligan (2003) . Itwill be increasingly important in devising strategies forsustainable disease control to enhance the cross-disciplinarity between economists and epidemiologists.

A further area of current interest in linking epide-miological with economic modelling arises whenresources for treatment are scarce or when there areother constraints over the amount of control (usuallychemical or cultural, but sometimes genetical orbiological) that can be applied. Finding the optimalcontrol strategy subject to constraint requires estimatesfor the cost of treatment and the cost of infection. It alsorequires knowledge of the effectiveness of control andthe way that this affects the dynamics of disease, which,in turn affects the way that control maps onto anepidemiological model. A simple example for chemicalcontrol is given in gure 2 for an eradicant. Applicationof the chemical renders infected plants no longerinfectious, if the scale of interest is the eld. A similarmodel applies at the regional scale in which theapplication of chemical stops an infected eld exportinginoculum. Finding an optimal strategy depends not onlyon the instantaneous cost of treatment and cost of infection but also on the way these change during the

course of an epidemic. Suppose that a treatment has along-lasting effect either from a single application or byrepeated applications. Treating too early may be costlyin unnecessary use of chemical. Leaving it till theepidemic is advanced may be too late to preventsignicant disease losses. It might also mean that thereare more elds to treat, making treatment moreexpensive. Finding an optimal solution is challengingfor systems with nonlinear dynamics, even withoutallowing for uncertainty andthe inherentstochasticityof the system. Progress can be made using methods fromcontrol theory ( Pinch 1993 ). This requires thedenition of an objective function that incorporates

thecosts of treatmentand infection. Thepotential lies inbeing ableto determinewhetheror not to spray and ifso,when and forhowlong. Surprisingly, however, for manysimple epidemiological models, the optimal solutioninvolves a so-called bang bang solution in which allinfecteds are treated and then treatment is stopped at aparticular level of infection or vice versa. Abruptchanges in turning on or off a control method aresurprising and do not t comfortably with currentagricultural practice. The introduction of nonlinearitiesinto the epidemiological model, however, can lead tointeriorsolutions in which there is variable treatment of some but not all infected sites, depending upon the

prevalence of infection. Following early theoretical work(Gupta & Rink 1973 ; Sethi 1974 , 1978 ; Greenhalgh1987 ) directed at medical applications, there has beenrenewed interest in these methods, particularly forantibiotic resistance and for susceptibleinfected





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susceptible (SIS)models ( Goldman& Lightwood 2002 ;Rowthorn & Brown 2003 ) and more recently to thecontrol of botanical epidemics ( Forster & Gilligan2007 ). Since they provide a rigorous yet parsimoniousmeans of analysing the effectiveness of strategies forcontrol under budget constraints, they are an importantfuture tool for the analysis of botanical systems.

5. CONCLUDING REMARKSAlthough much national and international attention iscurrently focused on animal and human disease,research on the epidemiology of plant pathogens andthe development of sustainable strategies for themanagement and control of plant disease has perhapsnever been so pressing. Supported by the potential of molecular biology to identify new sources for genetical,chemical and biological controls, the implementationwithin globally and locally changing agriculturalenvironments demands new approaches to durable

control. This, in turn, requires fusion of populationgenetics and epidemiology at a range of scales from theeld to the landscape and even to continentaldeployment of control measures. It also requires anunderstanding of economic and social constraints thatinuence the deployment of control. This will involve aswitch in focus from within-eld to regional control of epidemics. I have argued here that this will besupported by stochastic, spatio-temporal models thatalso describe the changing crop mosaic through whichdisease spreads.

The support of a professorial fellowship from the Bio-technology and Biological Sciences Research Council isgratefully acknowledged. I am also grateful to current andformer members of the Epidemiology and ModellingResearch Group at Cambridge, notably Dr Adam Klecz-kowski, Dr Wilfred Otten, Dr Simon Gubbins, Dr RichardHall, Dr Bartek Dybiec and Dr Doug Bailey and to numerouscollaborators, especially Dr Frank van den Bosch, DrStephen Parnell and Dr Ivana Gudelj at RothamstedResearch, and Dr Gavin Gibson at Heriot Watt Universityfor their permission to cite joint wo

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