Contents lists available atScienceDirect
Ecological
Modelling
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / e c o l m o d e l
Review
Advances
in
crop
insect
modelling
methods—Towards
a
whole
system
approach
Henri
E.Z.
Tonnang
a,m,∗,
Bisseleua
D.B.
Hervé
c,
Lisa
Biber-Freudenberger
d,
Daisy
Salifu
b,
Sevgan
Subramanian
b,
Valentine
B.
Ngowi
a,e,
Ritter
Y.A.
Guimapi
b,
Bruce
Anani
a,
Francois
M.M.
Kakmeni
b,f,
Hippolyte
Affognon
b,g,
Saliou
Niassy
b,
Tobias
Landmann
b,
Frank
T.
Ndjomatchoua
b,h,
Sansao
A.
Pedro
b,i,
Tino
Johansson
b,k,
Chrysantus
M.
Tanga
b,
Paulin
Nana
b,j,
Komi
M.
Fiaboe
b,
Samira
F.
Mohamed
b,
Nguya
K.
Maniania
b,
Lev
V.
Nedorezov
l,
Sunday
Ekesi
b,
Christian
Borgemeister
daInternationalMaizeandWheatImprovementCenter(CIMMYT)ICRAFHouse,UnitedNation,Avenue,Gigiri,P.O.Box1041VillageMarket,00621,Nairobi,
Kenya
bInternationalCentreofInsectPhysiologyandEcology(icipe),P.O.Box30772-00100,Nairobi,Kenya cWorldAgroforestryCentre(ICRAFT)P.O.Box30677,Nairobi,00100,Kenya
dCenterforDevelopmentResearch(ZEF),UniversityofBonn,Walter-Flex-Str.3,53113Bonn,Germany eTropicalPesticidesResearchInstitute,P.O.Box3024,Arusha,Tanzania
fComplexSystemsandTheoreticalBiologyGroup,LaboratoryofResearchonAdvancedMaterialsandNonlinearScience(LaRAMaNS),Departmentof
Physics,FacultyofScience,UniversityofBuea,P.O.Box63,Buea,Cameroon
gInternationalCropResearchInstitutefortheSemi-AridTropics(ICRISAT),BP320,Bamako,Mali hDepartementdePhysique,UniversitedeYaounde´ıI,Yaounde´ı,Cameroon
iDepartmentodeMatema´ıticaeInforma´ıtica,UniversidadeEduardoMondlane,Maputo,Mozambique
jSchoolofWood,WaterandNaturalResources,FacultyofAgricultureandAgriculturalSciences,UniversityofDschang,P.O.Box786,Ebolowa,Cameroon kDepartmentofGeosciencesandGeography,P.O.Box68,FI-00014UniversityofHelsinki,Finland
lInterdisciplinaryEnvironmentalCooperation(INENCO)ofRussianAcademyofSciences,Saint-Petersburg191187,nab.Kutuzova14,RussianFederation mUniversityofNairobi,CollegeofBiologicalandPhysicalSciences,InstituteforClimateChangeandAdaptation(ICCA),P.O.Box29053,Nairobi,Kenya
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:
Received10October2016
Receivedinrevisedform16March2017 Accepted17March2017
Keywords:
Insectmodellingapproaches Integratedpestmanagement Cropproduction Climatechange Impactassessment Yieldlosses Systemthinking
a
b
s
t
r
a
c
t
Awiderangeofinsectsaffectcropproductionandcauseconsiderableyieldlosses.Difficultiesresideonthe developmentandadaptationofadequatestrategiestopredictinsectpestsfortheirtimelymanagementto ensureenhancedagriculturalproduction.Severalconceptualmodellingframeworkshavebeenproposed, andthechoiceofanapproachdependslargelyontheobjectiveofthemodelandtheavailabilityof data.Thispaperpresentsasummaryofdecadesofadvancesininsectpopulationdynamics,phenology models,distributionandriskmapping.Existingchallengesonthemodellingofinsectsarelisted;followed byinnovationsinthefield.Newapproachesincludeartificialneuralnetworks,cellularautomata(CA) coupledwithfuzzylogic(FL),fractal,multi-fractal,percolation,synchronizationand individual/agent-basedapproaches.Aconceptforassessingclimatechangeimpactsandprovidingadaptationoptionsfor agriculturalpestmanagementindependentlyoftheUnitedNationsIntergovernmentalPanelonClimate Change(IPCC)emissionscenariosissuggested.Aframeworkforestimatinglossesandoptimizingyields withincropproductionsystemisproposedandasummaryonmodellingtheeconomicimpactofpests controlispresented.Theassessmentshowsthatthemajorityofknowninsectmodellingapproaches arenotholistic;theyonlyconcentrateonasinglecomponentofthesystem,i.e.thepest,ratherthan thewholecropproductionsystem.Wesuggestsystemthinkingasapossibleapproachforlinkingcrop, pest,andenvironmentalconditionstoprovideamorecomprehensiveassessmentofagriculturalcrop production.
©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
∗Correspondingauthorat:InternationalMaizeandWheatImprovementCenter (CIMMYT)ICRAFHouse,UnitedNation,Avenue,Gigiri,P.O.Box1041VillageMarket, 00621,Nairobi,Kenya.
E-mailaddress:[email protected](H.E.Z.Tonnang). http://dx.doi.org/10.1016/j.ecolmodel.2017.03.015
0304-3800/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4. 0/).
Contents
1. Introduction...89
2. Modellinginsectpestpopulationsgrowthanddynamics...90
2.1. Matrixmodels...90
2.2. Phenologymodels...90
2.3. Differentialequations...90
2.4. Competitionmodel...90
2.5. Fittingmodels...90
3. Modellinginsectstoidentifyareasofpestinvasionriskandmanagementpriority...91
3.1. Inductiveapproach...91
3.2. Deductiveapproach...92
3.3. Inductiveanddeductiveapproaches ... 92
3.4. Predictingtheefficacyofapestmanagementstrategy ... 92
4. Modellinginsectsfordecisionmakinginthecontextofchangingclimate ... 92
4.1. Overviewofclimatechangeinducedimpactsoninsects ... 92
4.2. Assessingclimatechangeinducedimpactsoninsectsviamodels...92
4.3. Challengesinmodellinginsectdistributions...93
4.4. Limitationsinassessingclimatechangeinducedimpactsoninsects...93
5. Innovationsonthemethodsandtoolsformodellinginsects...93
5.1. Artificialneuralnetworks...93
5.2. Cellularautomata(CA)coupledwithfuzzylogic(FL)...93
5.3. Fractalandmulti-fractal...96
5.4. Percolationandclusterdistribution...96
5.5. Synchronization...96
5.6. Agentbasedapproach...96
5.7. Roleofremotesensingincropinsectpestassessments ... 96
5.8. TheoreticalframeworkforassessingclimatechangeinducedimpactsoninsectswithnouseofIPCCscenarios...97
6. Modellingtheeconomicimpactofinsectpestscontrol ... 97
6.1. Economicsurplusapproaches...98
6.2. Computablegeneralequilibrium(CGE)models...99
6.3. Econometricapproaches...99
6.3.1. Averagetreatmenteffect(ATE)basedmethods...99
6.3.2. Instrumentalvariablebasedmethods(IV)...99
6.3.3. Differenceindifferencemethod(DD)...99
7. Towardstheinclusionofinsectpestimpactsinyieldlossesintocropmodel ... 99
8. Systemthinkingapproach–prospectforincludingpestimpactsintocropproduction...100
Acknowledgments...101
References...101
1. Introduction
Cropproductionschemescanbeconsideredascomplex
sys-tems with multiple interacting processes consisting of several
subsystems(particularlycropgrowthandinsectscropinteractions
inthiscontext)andcomponents,eachhavingtheirownunique
characteristics and behaviour while contributing to the overall
arrangementandfunctionofthecompletesystem(Wallachetal.,
2013;Fath,2014;Waltersetal.,2016).Incropproductionsystems,
manycomponentsinteractsimultaneouslyinahighlynonlinear
nature(Wallachetal., 2013;Walterset al.,2016).These
inter-actionsand nonlinearities need tobetaken intoaccount when
attemptsaremadetounderstandorpredictthesystembehaviour.
Understanding,managingandforecastingtheimpactsofpestsin
cropproduction,therefore,arechallenging(Garrettetal.,2013).
Although modelling efforts focusing on insect pests and their
interactions withplants, weather, nitrogen,water control,
sup-ply,demandandothersfactors(Gutierrezetal.,1988;Gutierrez
etal.,1991;Bawden,1991;VanIttersumetal.,2003)exists;still
studies that include the full range of interactions among
sys-temcomponentsarelimited(Wallachetal.,2013;Waltersetal.,
2016).Additionally,pestsimulation modelscommonly simulate
thedynamicsofsingleinsectasthehostandphysicalenvironment
affectit.Aholisticviewissupportedinwhichsystems
manage-mentispredicatedontheadmissionthatoverallsystembehaviour
willbeinfluencedbychangesinanysystemcomponent(Wallach
etal.,2013;Waltersetal.,2016).Whilemodelsareusefultoolsfor
synthesizinginformationandhypotheses,theirapplicationmust
beinthecontextofthesystemtobemanaged.Implicitinthelatter
isdeterminationoftheecologicalandsocio-economic
characteris-ticswithinwhichthemodel,itsoutputsorasimplifiedversionof
themodel,mustoperatetoassistindecision-makingforpest
man-agement.TherecentpublicationbyWaltersetal.(2016)applied
systemdynamicsmodellingtoexplorewaysofusingsustainable
practicesinagricultureproduction.Itissuggestedthatcomplete
modelsthatincludebiological,ecological,economicalandsocial
processesandtheirinteractionscanprovideconsiderableinsight
intothebehaviourofcropproductionandguideonthewaysof
managingthesystemwiththeaimofsustainablyincreasing
pro-ductivity(Waltersetal.,2016).
Thispaperhighlightssomeimportantresearchquestionsthat
stimulatedthedevelopmentofmethodsandtoolsforagricultural
pestmodelling.Asummaryofthemostcommonconcepts,tools,
methodstechniquesaregiven.Alistofsomechallengesis
spec-ifiedwithpossiblenewdirectionsthatconsidersystem-thinking
approachasaprospectforincludingpestimpactsincropmodels
isalsoprovided.
Theapproaches,methodsandtoolsforpestmodelling
devel-oped and usedduring the last decade focused onanswering a
numberofrelevantquestionsthatarosewhileconductingresearch
activities.Indeed,modelsareusefulinansweringrelevant
ques-tionssuchas:
a Howcanpestpopulationdynamicsbepredictedinthepresence
bHowdobioticandabioticfactorsaffecttheinteractionsbetween
pestsandtheirnaturalenemies?
cHowcanarea-wideimpactsofnaturalenemiesonpest
popula-tionsbemeasuredandpredicted?
dHowcanwebestdescribethespreadingpatternsofpestsand
assesstheriskofinvasiontootherareas?
eInsectpestsadapttoclimaticchangeandsurviveinnew
environ-mentalconditionsandcontrolpressures.Canwedevelopmodels
toaccountforandpredictthesechanges?
Thispaperpresentsanaccountofvariousmodellingapproaches
andstrategiesdevelopedandusedtoanswerthesequestion
(Sec-tions2–4)and furtherdiscuss thechallenges in modelling and
assessingclimatechangeinducedimpactsoninsects(Section5).
Thepaperalsodiscussesinnovationsonthemethodsand tools
formodelling−insects (Section6), −yieldlossdue toinsects in
cropmodel(Section8)and−theeconomicsofinsectpestcontrol
(Section7).Asawayforwardintheoverallcropproduction
mod-elling,asystemthinkingapproachisproposed(Section9)because
itcapturesmultiplesinteractionsandprovidessubstantial
under-standingintothecomportmentofcropproduction,and,therefore,
directonthewaysofmanagingthecrop(system)withtheaimof
increasingitsproductivity(Waltersetal.,2016).Throughoutthe
text,necessaryexamplesandillustrationsareprovidedforbetter
clarityandunderstanding.
2. Modellinginsectpestpopulationsgrowthanddynamics
Toanswerquestions1and2,matrixmodels,phenologymodels
anddifferentialequationshavebeenusedasdescribedbelow.
2.1. Matrixmodels
Overseveraldecades,fordescribingthechangesthatoccuron
thepopulationdensitiesofinsectsinaregion,matrixmodelshave
beenwidelyused (Leslie, 1945;Lefkovitch, 1965; Lewis,1977).
Whenusingthismethodforinsects,theagestructureofthe
pop-ulationwasdescribedinamatrixwithonesinglecolumnwiththe
numberoffemales(Lewis,1977).Overtimetheapproachevolved
toincludeotherfactorssuchastemperature(ChoiandRyoo,2003)
andagewidth.Thenotionofprobabilityforchangingstagegroup
ateachtimeintervalwasincludedandlatercontributedin
creat-ingintothemodeladistributionoftimesflowthroughstages(Choi
andRyoo,2003)
2.2. Phenologymodels
Severalauthorshaveshownthatthephysiologicalresponseof
mostpoikilothermicspeciesisadaptedtoaparticulartemperature
range,whichisoftenconsideredasanabioticfactorinfluencing
thespeciesabundanceandestablishmentinaregion(Briereetal.,
1999;Fand etal., 2014a,2014b).Using the optimum
tempera-tureconcept,lifetabledataof speciesare obtainedat constant
temperaturesinthelaboratory.Throughastep-by-stepapproach,
mathematicalfunctionsfordevelopmenttime,developmentrate,
mortality,senescence, survival and reproduction of the species
wereestablishedandcombinedtoyieldthespecies´ı phenology
model. To illustrate, their application phenology models were
developed for noctuid lepidopteranstem borers, Busseola fusca
(Fuller)and SesamiacalamistisHampson (Khadioli etal., 2014).
Thesemodelsassistedinestimatingthelowerandupper
tempera-turethresholdforsurvivaloftheinsects.Inaddition,phenology
modelscanbesimulatedeitherin a deterministicorstochastic
mannertoyieldthefollowinglifetableparametersofthespecies:
intrinsicrateofnaturalpopulationincrease(rm),netreproduction
rate(R0),finiterateofincrease(¯),meangenerationtime(G),and
thedoublingtime(t)(Khadiolietal.,2014).Theseparametersare
crucialinpopulationstudies.Forinstance,rmhelpstoestimatethe
rapidityofaspeciespopulationincreasewhenoccupyinganew
environment(Messenger,1964)andR0isoftenappliedtoestimate
theabilityofapopulationtocolonizeanewareawithR0<1.0
indi-catinganegativeordecliningpopulationgrowth(Pilkingtonand
Hoddle,2006;Fandetal.,2014a,2014b).
Successofinsectpestmanagementactionslargelydependson
theefficacyofthemanagement action,thelifestageofthepest
targetedandthetimingoftheintervention(WilbyandThomas,
2002;MillsandGetz,1996).Forexample,theefficientreleasesof
naturalenemiesorapplicationofanycontrolmeasuretoreduce
thepopulationdensityofaninsectpestneedtocoincidewithhigh
presenceofthemostsusceptible lifestageofthespeciesinthe
field(WilbyandThomas,2002;Sporlederetal.,2013).Similarly,
inpestcontrolprogrammes,targetingthelifestageofapestmost
efficienttodestroytheplantiscriticalforsuccess(Diuk-Wasser
etal.,2010).Inthisrespect,simulationofphenologymodelwitha
stagestructureapproachinaregionoverspecifiedperiods,could
providedetailsontheproportionofindividuallifestages ofthe
species(Sporlederetal.,2013).
2.3. Differentialequations
Severaldifferentialequationsincontinuousanddiscreteforms
areusedtoexplainempiricaldatasetsforsinglespeciespest
popu-lationfluctuationsovertime(Nedorezovetal.,2008;Tonnangetal.,
2009).Thestudyofpopulationdynamicsfocusesonmodel
parame-terestimation,comparisonwithempiricalresultsandevaluationof
systemsteadystates(NakanishiandCooper,1974;Gutierrezetal.,
1991;Tonnangetal.,2009).Thesemodelsarealsoemployedto
determinethelikelihoodofsuccessofclassicalbiologicalcontrol
programmes;thus,interactionbetweenpestspecies(host)andits
naturalenemy(parasitoid)(Barrattetal.,2010).Forinstance,how
theLotka-Volterraequation(Filhoetal.,2005)wasfittedto
popula-tiondensitydataofthediamondbackmoth(DBM),Plutellaxylostella
(L.)(Hellen),topredicttheperplantabundanceofthepeston
cab-bageovertime(Tonnangetal.,2009)(Fig.1).Thestudyrevealeda
satisfactoryfitofthemodeltofielddataandsuggestedthe
possi-bilityofusingtheLotka-Volterraequationtomimicthebehaviour
ofinsectpopulations(Tonnangetal.,2009).
2.4. Competitionmodel
Systemsofdifferentialequationsaredevelopedtoexplorethe
effects of resource (crop)and competition betweeninsect pest
species (Kaplanand Denno, 2007).Withtheapplication of
sta-bilitytheoryandqualitativeanalyses,numericalsimulationsare
performedaroundtheaxial,planarandinteriorequilibriumpoints
tounderstandtheinteractionsbetweenone,twoormorespecies
competingforasingleresource.Resultsshowthatifasinglespecies
interactswitharesource,thespeciescouldestablishandsustain
astablepopulationdensity.However,iftwoormorespeciesare
competingforthesameresource,thecombinationsofthree
param-eters(half-saturation,growthrate,andmortalityrate)determine
whichspeciesoutcompetestheother(Mwalusepoetal.,2014).In
otherwords,aspecieswithahighaffinityfortheresourcecanstill
loosethecompetitionifit hasalowgrowthandhighmortality
rate.Theseresultsdemonstratethatonecompetingspeciescould
displaceanotherone,independentlyoftheinitialsizeofits
popu-lation.Thismeansthatatequilibriumpointsandinahabitatwith
asinglelimitingresourcethebestcompetitoristhespeciesthat
hasthelowestequilibriumresourcevalue(Desharnaisetal.,2001;
Fig.1.Thirty-three(33)weeksfieldsamplingofpopulationdensityofaninsect(diamondbackmoth)perplantofcabbageandpredictionsofthesameusingLotka–Volterra model.
(adaptedfromTonnangetal.(2009)). 2.5. Fittingmodels
Infittingmodels,gradientmatchingmethodorthe
develop-mentofalossfunctionthatusesthedifferencebetweenpredictions
ofthemodelequationsandempiricaltime-seriesofthe
popula-tiondensityobtainedfromfieldsurveysisusuallyderived(Ellner
etal.,2002).Totestthemodelgoodnessoffitincapturingfield
data,thebehaviourofresidualsbetweenexperimentalvaluesand
theoretical trajectoriesare examined usingcriteria such asthe
Durbin–Watson (Nedorezov etal., 2008)and theresulting sign
seriessubjectedtoatestofrandomnessofdistribution(Swedand
Eisenhart,1943).Fromtheanalyses,resultsareoftenpresentedin
formofthemodelfitordidnotfittheinsectspecies
experimen-taltrajectoriesandsuggestionsaremadesuchastheinclusionof
abioticfactorstoimprovethemodelprediction.
3. Modellinginsectstoidentifyareasofpestinvasionrisk andmanagementpriority
Speciesdistributionmodels(SDMs)areusedtomeasureand
predictarea-wideimpactsofnaturalenemiesonpestpopulations,
todescribethespreadingpatternsofpestsandtoassesstherisk
ofinvasiontootherareas(Questions3–4),(ElithandLeathwick,
2009;Huntleyetal.,2004;GuisanandThuiller,2005).Thesemodels
helptopredictdistributionsacrosslandscapesandtogain
ecolog-icalandevolutionaryinsights.Thepredictionscanalsobeusedfor
theidentificationofareaswhereaninsectspeciesislikelytobe
found(Fiaboeetal.,2006).TheoutputsofSDMs,riskmaps,are
presentedascommunicationtoolstoinformspecifichypotheses
forcontrolledexperimentsorobservationalstudies(Venetteetal.,
2010)orutilizedinstrategicpestmanagementdecisionssuchas
restrictionsontheimportationofcertaincrops,implementation
ofquarantinemeasuresandthedesignofpestsurveys(Sporleder
etal.,2013).
SDMsarebroadlyundertakenthroughadoptionofan
induc-tiveordeductiveapproach(Venetteetal.,2010).Intheinductive
approach,thepresenceofanorganisminalocationisrelatedto
theprevailingbio-climaticvariableandthelikelihoodofthe
pres-enceoftheorganisminotherareasarepredicted.Thismodelling
techniquefollowsa‘top-down’approachrelyinguponthe
identi-ficationofrelationshipsbetweentherecordeddistributionofthe
targetorganismandenvironmentalvariablesandusedtopredict
distributionand/orabundanceinanunmappedareaofchanged
environmentalconditions(Stoklandetal.,2011).Algorithmsand
toolssuchastheMaximumEntropy(MaxEnt)andtheGenetic
Algo-rithmforRule-setPrediction(GARP)utilizetheinductiveapproach
(Venetteetal.,2010).Thedeductiveapproachstartsbymodelling
thespeciesresponsetoenvironmentalvariablesandappliesthe
modelforpredictingenvironmentalsuitabilityoftheorganism.It
isbasedona‘bottom-up’technique,wherebydirectmeasurements
oftherelationshipsbetweenaspectsoflife-history(development,
survival,productivity,etc.)andindividualenvironmentalvariables
areusedtoidentifytheenvironmentalspacewhereanorganism’s
persistenceshouldbefeasible(Khadiolietal.,2014;Kearneyand
Porter,2009).ToolssuchastheInsectLifeCycleModelling(ILCYM)
software(Sporlederetal.,2013)utilisethedeductiveapproach.
The CLIMEX-compare location function and the North Carolina
StateUniversity(NCSU)AnimalandPlantHealthInspection
Ser-vice(APHIS)PlantPestForecastingSystemNAPPFASTarebased
ona combinationof inductiveanddeductive approaches. In all
approaches, presence/absence dataare added toenvironmental
andbiologicalvariablestopredictthelikelihoodforalocationtobe
suitablefortheoccurrence/abundanceofanorganism(Sporleder
etal.,2013).
3.1. Inductiveapproach
GARP is an ecological niche modelling method based on a
geneticalgorithmusedtoestimatethepotentialspatial
distribu-tion of organisms with dispersal capabilities (Stockwell,1999).
Thisapproachwasinspiredbytheevolutionaryprocessof
natu-ralselectiontoobtainthemostinformativemodelfromaseries
ofpossiblesolutions(Stockwell,1999).Practically,GARPrelates
ecologicalcharacteristicsofknownoccurrencepointsofapestto
randomlysampledpointsfromtherestofthestudyregion,
seek-ingtodevelopaseriesofdecisionrulesthatbestsummarizefactors
associatedwiththepresence.GARPwasusefulinguidingthesite
selectionfornaturalenemyexplorationoftheinvasiveredspider
miteTetranychusevansiBakerandPritchard,animportantpestof
tomatoinEastandsouthernAfrica(Fiaboeetal.,2006).Together
withpestoccurrencesdatasetsfromKenyaandZimbabwe,aGARP
modelwasusedtopredictthenativeregionsofT.evansiinSouth
America.Theseregionshavesimilarenvironmentalconditionsto
areasinAfricawherethemitehasbecomeaproblem,andguided
researchersinthesearchfornaturalenemiesinthenativeregions
ofthepest(Fiaboeetal.,2006).
MaxEnttheoryisfoundedontheestimationoftheconsideration
thatindividualsoccurinproportiontotheirpopulationdensity.
Ifthetotal populationsizeisknown,themodelcanpredictthe
occurrencerateinagivencell,definedastheexpectednumber
ofindividualsin thatcell(Caoetal.,2013).However,whenthe
occurrenceratesaremeaningful,resultinginarelativeoccurrence rate(Caoetal.,2013;HastieandFithian,2013).Assumingthatan
individualwasobservedinaspecificlocation,therelative
occur-renceratebecomestherelativeprobabilitythattheindividualwas
derivedfromeachcellinthelandscape(HastieandFithian,2013).
Undertheseassumptions,MaxEntinputsalistoforganism
pres-encelocationsandasetofenvironmentalpredictors(precipitation,
temperature,etc.)acrossa landscapedividedintogridcells and
thenextractsasampleofbackgroundlocations,whichare
con-trastedagainstthepresencelocations.Therisk ofspreadofthe
invasivefruitflyBactrocerainvadensDrew,Tsuruta&Whiteacross
AfricawasinvestigatedwithMaxEnt(DeMeyeretal.,2010;
Biber-Freudenbergeretal.,2016).ItwasfoundthatWestAfrica,Central
Africa, Madagascar, and parts of East Africa, were predictedto
haveclimaticconditionshighlysuitableforthepestestablishment
andpersistence(DeMeyeretal.,2010;Biber-Freudenbergeretal.,
2016).
3.2. Deductiveapproach
Intherecentpast,phenologymodelshavebeenappliedto
esti-matethepotentialdistributionandtoconductriskassessmentsof
pestsinaspatiallyexplicitway(Sporlederetal.,2013).The
deduc-tivemodel approach estimates the stage-specificdevelopment,
survivalandreproductionratesofthepests,fromwhichriskindices
liketheestablishmentriskindex(EI), generationindex(GI)and
activityindex(AI)arederivedtoassessthepotentialdistribution
andabundanceofthespecies(Fandetal.,2014a,2014b).Climatic
factorsareusedtoestablishthelinkagebetweenindicesand
land-scape(Sporlederetal.,2013)fromwhichdistributionmapscan
bederived.TheILCYMsoftwareisatoolthatassistsindeveloping
phenologymodels,conductspopulationanalysisandriskmapping
usingthisprinciple(Sporlederetal.,2013).Severalphenology
mod-elsforkeypestsofstapleandcashcropsandtheirnaturalenemies
havebeendevelopedusingILCYMandappliedforspatial
predic-tionsofregionsofthepestsoccurrenceandabundance(Fandetal.,
2014a,2014b;Mwalusepoetal.,2015).
3.3. Inductiveanddeductiveapproaches
TheCLIMEXmodeltheoryisbasedontheestimatedresponse
ofpeststotemperatureandmoisture.Theapproachwas
devel-opedundertheassumptionthat,ifitisknownwhereanorganism
lives,theclimaticconditionsittoleratescanbeinferred(Sutherst
andMaywald,1985;Sutherst,2003)topredictotherregionswhere
thespeciescansurviveandreproduce. CLIMEXassumesthatan
organismatagivenlocationexperiencestwoseasonsduringayear,
onewithpopulationgrowthandtheotherwithpopulationdecline
(SutherstandMaywald,1985;Sutherst,2003).Overall,themodel
proposesthathabitatsuitabilityatalocationfor agiven
organ-ismisprovidedbyanEco-climaticIndex(EI),whichcombinesthe
annualpotentialforpopulationgrowth(GI),theannualstresses
that limit survival duringthe unfavourableseason (SI)and the
interactionsbetweenstresses(SX)(SutherstandMaywald,1985).
AstudybyTonnangetal.(2015)usingCLIMEXdemonstratedthat
thepotentialofinvasionofTutaabsoluta(Meyrick)(Lepidoptera:
Gelechiidae),adevastatingpestoftomato,isveryhighinpartsof
Asia,theMiddleEast,NewZealand,theUSandalargesectionof
Australia.
3.4. Predictingtheefficacyofapestmanagementstrategy
Amongthevariousinsectpestscontrolmanagementstrategies,
fungal-based biopesticidesare considered tobe quiteeffective,
speciesspecific andenvironmentally friendly(Auld,2002).
Tar-getpestsarekilledonly ifthefungus‘recognizes’theinsectas
asuitablehostandisabletogerminateandpenetrate the
cuti-cle,whichistheneventuallyresultingindeathanddevelopment
of mycosis onthehost (Ekesiet al., 2002;Dimbi et al., 2009).
With theenhanced efficacy achieved throughselection of
eco-logicallyadaptedfungiisolatesandefficientformulations,efforts
arebeingdevotedtooptimizetheeffectivenessofsuch
biopes-ticidesbyintegratingthemwithinanovelmodellingframework
toenhancetheirperformance inthefieldwithinthecontextof
integratedpestmanagement(IPM).Inthisregard,theeffectsof
temperature onthe virulence of theentomopathogenic fungus
MetarhiziumanisopliaetoadultsandsecondinstarsoftheWestern
FlowerThripsFrankliniellaoccidentalis(Pergande)wereassessed.
Non-linear mathematical expressions suchas Cubic and Lactin
(Loganetal.,2006;Maioranoetal.,2012)werefittedtodataofthe virulenceofM.anisopliaeisolateICIPE69onF.occidentalis(Kuboka,
2013).SpatialsimulationsofthefungusefficacyforEastAfricawere
undertakenusing(daily)temperaturesasoutlinedbyKroscheletal.
(2013).ALactinmodelprovidedabetterfitfortheefficacyofthe
fungusespeciallyatlowertemperaturesandthespatialmapping
ofthemodelindicatedthatthefunguscouldbeeffectiveinmost
midandlow-altituderegionsofeastAfrica.
4. Modellinginsectsfordecisionmakinginthecontextof changingclimate
This section provides answer to question 5 that stipulates,
“Insectpestsadapttoclimaticchangeandsurviveinnew
environ-mentalconditionsandcontrolpressures.Canwedevelopmodels
toaccountforandpredictthesechanges?”
4.1. Overviewofclimatechangeinducedimpactsoninsects
Rangeshiftsorchangesofmanyinsects mayoccurandnew
combinationsofpestscouldemergeasnaturalecosystemsrespond
toalteredtemperature andprecipitationprofiles (Garrett etal.,
2013).Theincreaseinfrequencyandmagnitudeofextremeevents
(heatwaves,heavyrainfall,stormsetc.)candisruptthesynchrony
betweenthegrowth,developmentandreproductionofbiological
controlagentsandtheirpesthosts/prey,leadingtointerferences
in both natural and implementedbiological (control) processes
(Auramboutetal.,2009;Guisanetal.,2013).Withinthiscontext,
assessmentandforecastingoffutureshiftsinthedistributionof
insectsatlocal,regionalandglobalscalesarenecessarytodeploy
pre-emptivemitigationstrategies(EhrlénandMorris,2015).Can
wedevelopmodelstoaccountfor,andpredictthesechanges
(ques-tion5)?
4.2. Assessingclimatechangeinducedimpactsoninsectsvia models
Themodellingapproachesandtoolspresentedabovehavebeen
usedtopredictthedistributionofinsectsunderpast,currentand
futureclimaticconditionsbyinferringtheenvironmental
require-mentsofthespeciesfromeitherlaboratoryexperiments(ILCYM)
orzoneswheretheyarecurrentlyknowntooccur(CLIMEX,
Max-EntandGARP).Basedontheserequirements,theinsectgeographic
distributionsarepredictedandtheresultscanbeusefulforland
managementanddecision-makingprocesses(Guisanetal.,2013).
Analysesareoftencarriedoutusingclimatedataunderacertain
climatechangescenarioobtainedfromglobalcirculationmodels
(GCM)(EhrlénandMorris,2015).Scenariosaregeneratedbased
onasetofassumptionsaboutdriversoffutureglobalemissions.
Thesemodellingexerciseshaverevealedthelikelyimpactsof
cli-matechangeforsomeinsectpestspecies(Fandetal.,2014a,2014b;
4.3. Challengesinmodellinginsectdistributions
Inpestpopulationanalyses,challengesalwaysexistwithregard
tothe rational of choosing one formof equation over another
orwhendecidingtoconstructanewmodelforfittingobserved
datasets(Nedorezovetal.,2008;Tonnangetal.,2009).
Paradoxi-cally,obtaininggoodfitdoesnotnecessarilyimplythattheselected
mathematical equationcan clearly explain the type of
dynam-icsandinteractionsbetweensystemcomponents(Tonnangetal.,
2009).Different equations may provide excellent and equal fit
toobserveddata,whiletheirmathematicalcharacteristicsyield
different behaviour under the same environmental conditions.
Anothergeneralproblemis thatthereisnoruleforfindingthe
globalminimumforthenumberofenvironmentalvariablesthat
yieldsthebestparametersofafittedmodel.Instead,avarietyof
techniqueshavebeendevelopedandtrialanderrorproceduresare
sometimesapplied.
Themodellingapproachesofinsectsusedtoidentifyareasof
priorityandestablishriskmappinghavecertainadvantagesand
disadvantages(Table1).Theydifferinthetypeofdatarequired,
complexityandnatureoftheestimatedfunctionsandtoacertain
extent,mostlikelydependonthespecificspecies,intheir
pre-dictiveperformance. Generally,theapproachwithdualfeatures
(inductiveanddeductive)seemstobemoreconvincingand
there-forepreferableovereitherinductiveordeductiveapproaches.One
advantageisthatithastheabilitytosimulatethroughlaboratory
manipulationstheeffectsofnewenvironmentalextremesonthe
targetspecies and toexamine theexistenceof suchthresholds
andrelationshipchanges,whereasinductiveapproachcontribute
toidentifyrelationshipswithinnaturallyobservedlimits(Venette
etal.,2010;Sporlederetal.,2013).Aconstraintofinductivemodels
isthattheytendtolinkequilibriumdistributionand/orabundance
withthemeanclimaticconditions.Inbothmodellingcategoriesa
considerablelimitationistheimpactofunexpectedchangesinthe
relationshipsbetweenprocesses/distributionandanygiven
envi-ronmentalvariableaboveorbelowthresholdsthatdwelloutside
currentlyobserved limits.Modelsusing theinductiveapproach
presentsomemeritsastheyarerapidlyimplementedand
exist-ingspatialdatasetsthatarecommonlyaccessiblecanbeutilised
(Venetteetal.,2010).
4.4. Limitationsinassessingclimatechangeinducedimpactson insects
Otherthanthedescribeddrawbacksofmodellingapproaches
used toassess climate changeinduced impact on insects have
somedrawbacks,theoveralloutcomeoftheassessmentalsosuffers
fromtheuncertaintiesinvolvedinfutureclimatemodelling,where
newbiotic and abioticinteractions mayaffect currently
estab-lishedrelationshipswithenvironmentalvariables(Hartleyetal.,
2006).Anothercrucialproblemistheambiguityforusingamodel
developedforcurrentdistribution,whichisthenextrapolatedin
spaceandtimetoanticipatethepest/pestsdistributionsunder
cli-matechange(Hartleyetal.,2006;EhrlénandMorris,2015).Future
climatescenariosandderiveddistributionmodelshavebeen
crit-icizedforbeingintrinsicallyunscientific,becausetheycannotbe
validated untilthe period oftheir projectionhasbeen reached
(Garrettetal.,2013;Fandetal.,2014a,2014b).Recentscientific
focusinaddressingthisissueisonthepromotionandadvocacyfor
anensemblemodellingapproach,whichconsistsofidentifyingthe
‘best’modelfromanensembleofscenariosofGCMs.Inthiscontext
thebestmodelisoftenjudgedtobetheonewhichoutputsmatch
observeddataascloselyaspossible(AraújoandNew, 2007).In
addition,noinformationisavailableonhowspeciesmayrespond
undernovelenvironments.Underthesecircumstances,itisargued
thatanewmodellingframeworkisneededtolimituncertainties
aboutfutureemissionsofgreenhousegasesandsulphateaerosols
aswellasuncertaintiesabouttheresponseoftheclimatesystemto
thesechangesatglobalandlocalscales(StottandKettleborough,
2002).
The first Intergovernmental Panel of Climate Change (IPCC)
guidelines(Carter,1996)outlineaprocesswithsevenstepsfor
assessingtheimpactsofpotentialclimatechangeandevaluating
appropriateimpactsthatincludethefollowing:definitionofthe
problem,selectionofthemethods,testingofthemethods,
selec-tionofthescenarios,assessmentofbiophysicalandsocio-economic
impactsofautonomousadjustments,andevaluationofadaptation
strategies(Watsonetal.,1998).However,thechoiceofascenario
andGCM,which directlycontributes tosuggestions ofadaption
optionsand decision-making,is fullwithahighlevelof
uncer-tainty.A‘wrong’selectionofascenarioorGCMcanleadtovery
differentrecommendations.Additionally,resultsareimpactedby
furtheruncertaintiessuchas:i)Howmuchtemperaturechangeis
likelytoresultfromagivenscenarioofhuman-causedincreasesin
greenhousegasconcentrations?ii)Whatwillbetheactualamounts
ofgreenhousegasesaddedtotheatmosphere inthefuture?iii)
Whatwillthatdotolocalandregionalclimates?
5. Innovationsonthemethodsandtoolsformodelling insects
As a means to overcome some of the challenges arising,
researchers aregradually opting for theuseand application of
morerobust,complexanddynamicalsystemsbasedonadvanced
mathematics, computerand physicstheories.These approaches
includeartificialneuralnetworks,cellularautomata(CA)coupled
withfuzzylogic(FL),fractal,multi-fractal,percolation,
synchro-nizationandindividual/agent-basedapproaches(Boneetal.,2006;
SmithandConrey,2007).
5.1. Artificialneuralnetworks
Mathematicalmodellingusingdifferentialequationshelpsto
gainunderstandingofthesystemdynamics,however,itisgenerally
lessaccuratewhenusedforpopulationdensityprediction(Chon
etal.,2000;ZhangandZhang,2008).Theartificialneuralnetwork
(ANN)approach issometimesselectedforpredictingthe
poten-tialpopulationdensities(Yangetal.,2009).ANNwasforexample
usedforpopulationdensitypredictionsofDBManditsexotic
ich-neumonidparasitoidDiadegmasemiclausumHellen(Tonnangetal.,
2010)andtoforecastepaddystemborerpopulationoccurrence
(Yangetal.,2009).Inthiscontext,ANNwasconsideredasapotent
toolforpredictingpopulationdensitieswithfewassumptionson
thefielddatasets.Theapproachallowedtheuseofdatacollected
atanyappropriatescaleofthesystem,bypassingtheassumptions
anduncertaintiesthatoccurredwhenfittingdifferentialequations
toestimateparameters(Yangetal.,2009).ANNhasfurtherbeen
suggestedasamethodtoevaluatetherelativeeffectivenessof
nat-uralenemiesandtoinvestigateaugmentativebiologicalcontrol
strategies(ZhangandZhang,2008;Tonnangetal.,2010).
5.2. Cellularautomata(CA)coupledwithfuzzylogic(FL)
Cellular automata(CA)models areimplemented in spatially
explicit,stage-structuredcellsgovernedbyrules,whicharecreated
basedonthebiologicalandecologicalofthepestdata(Kari,2005).
Thisinformationcanbederivedfromexistingfieldandlaboratory
dataonthephysiologicalresponsestoclimatevariablessuchas
rainfall,temperatureandhumidity.Fuzzylogic(FL)isusedto
rep-resentthedegreeofaccuracy,alsocalledtruth-values,thatisscaled
betweenaprobabilitythresholdof0and1(Andriantiatsaholiniaina
Table1
Advantagesanddisadvantagesofcommonlyusedtools,approachesandmethodsforpestanddiseasemodelling.
Approach Advantages Disadvantages
GARP(Inductive) Rulebased Easytoimplement
Inputcommonlyaccessibledatasets Accountsforrelevantvariables Providesstatisticalgoodnessoffit
Inferredrelationships
Linksonlytheequilibriumpoints Inputpresence-onlydatasets
Overestimates/underestimatesdistribution Nophenologyinformation
MaxEnt(Inductive) Generatesprobabilityvalues Providesstatisticalgoodnessoffit. Performswellindata-poorsituation Easytoextrapolate
Identifiesrelationships Inputpresence-onlydatasets Nophenologyinformation
ILCYM(Deductive) Accountsfordevelopmentalthresholds Allowsanalysisofhighresolutiondata Incorporatesnonlinearrelationships
Employssite/regionspecificparameters Nooccurrencedata
Onlyadaptedforinsectsanddiseasevectors Accountsonlyfortemperature
CLIMEX(Inductiveanddeductive) Dualfunctionality Validatesatcontinentallevel Establisheslinearrelationships
Difficulttoinputnewdatasets Difficulttofine-tuneandcalibrate Conductsanalysisatalowresolution
Fig.2.Diagramsummarizinganapproachformodellinginthefieldsituationthecropdamagesspreadcausebyphytophagouspestlarvae.Theapproachisbasedonthe combinedapplicationofcellularautomata(CA)andfuzzylogicsystems.Thegridcellsareabstractiverepresentationsoftheplantsinsideafield.NH=neighbourhood, ST=stemtunnelling,FIS=fuzzyinferencesystem,S=state,(i,j)=spatialcoordinates.
anappropriate membershipfunction that allows descriptionof theconvenientlevelofvaryingofintermediatestatesuchaslow, mediumandhighinfestationlevel.Insummary, insteadof sys-tematicmanipulationofnumericaldataandfittingmathematical equations,thisapproachisimplementedinformofcomputercodes inselectedprogramminglanguagesthatimproveflexibilityfor cap-turinglevelofpestdamageoncropinamodellingstructure(Bone etal.,2006;Guimapietal.,2016).Inafieldsituation,evaluationand
quantificationofpestcomplexityofspread,geometricalstructure
ofhowmobileorganismsinteractwiththeirenvironmentneedto
beincludedinthemodellingframework,forinstancetocapturethe
damagecausedbycerealstemborerstomaizeinAfrica(Fig.2).The
developmentstepsforthecentralcellofCAcanbedeterminedin
threesteps(Boneetal.,2006;Guimapietal.,2016):i)Estimatethe
minimumradiusoftheneighbourhood(NH)thenextractNHofCA
bytrainingdatausinganappropriatealgorithm.Forexample,the
datacouldrepresentenvironmentalfactorsorpresence/absenceof
stemtunnellingdamagescausedbytheinsectpestlarvaeandtheir
momentofoccurrence.Inthiscase,theCAcellstateswillbebinary
(infested/non-infested).ii)Withtheknowledgeofthestochastic
behaviouroftheovipositionandflightpatternoftheinsect,the
spatialandtemporal modelfortheovipositionprocessis
devel-oped.iii)Throughfuzzyinferencesystem,theinformationcanbe
linkedwiththevagueandimpreciseknowledgeofexperts(IPM
practitioners)aboutthedegreeofthecontagiontospreadgivena
degreeofabundanceofthepestorotherrelativedatasets.Tenyears
ofsimulations(2008–2017)ofCArulebasedmodelcalibratedwith
landvegetationcover,temperature,relativehumidityandyieldof
tomatoproductionwereusedtopredictyear-to-year,theriskofthe
invasionandspreadofT.absolutaacrossAfrica(Fig.3).By
infer-ringthepestnatural abilitytoflylongdistancerevealedthatT.
absolutacouldreachSouthAfricatenyearsafterbeingdetectedin
Spain(Guimapietal.,2016).TheSpatialandtemporalspreadof
maizestemborerBusseolafusca(Fuller)(Lepidoptera:Noctuidae)
damageinsmallholderfarmsisreportedin(Ndjomatchouaetal.,
2016).ByusingtheCAapproach,theauthorswereableto
deter-minetherulebywhichaplantgetsinfectedbyitsneighbors,it
wasobservedthatifanuninfectedplantis borderedbyatleast
fourinfected plants,itismostlikelytobecomedamagedinthe
Fig.3. ThespreadofT.absolutainAfricaobtainedthrougha10yearssimulationofcellularautomatarulesbasedmodelconsideringvegetation,humidity,temperatureand yieldoftomatoesproductionaskeysvariablesfortheinsectpestpropagation.Theareasinwhitearesusceptiblelocations.Zonesinbrownarezoneatlowriskofinvasion andspreadofthepest.Zonesingreenrepresentzonesathighriskofinvasionandspreadofthepest.(Forinterpretationofthereferencestocolourinthisfigurelegend,the readerisreferredtothewebversionofthisarticle.)
5.3. Fractalandmulti-fractal
The term fractal is used to describe the self-similarity that
appears in an object under varying degrees of magnification
(Addison,2002;Li,2000;Jonckheereetal.,2006).Withfractal
anal-ysis,theeffectof possessingsymmetry acrossscaleswitheach
smallpartoftheobjectiscapableofreplicatingthestructureof
thewhole(Addison,2002;Jonckheereetal.,2006).Although
frac-talmethodhasbeentocharacterizegeometricallytheoccupancy
ofinsectpestinvasioninacomplexlandscape(GamarraandHe,
2008)andtoanalysepossibleeffectsoffragmentedagro-ecological
landscapesinasuccessfulbiologicalcontrolwithnaturalenemies
ofinsect(Withetal.,2002);itssingleapplicationonlygives
exten-sivedescriptionoftheobject,leadinginpracticetotheapplication
ofmulti-fractaldimensions.Anobjectismulti-fractalifithasmore
thanonefractaldimension(Jonckheereetal.,2006).Multi-fractal
analysiscanprovidepropercharacterizationofthespatial
distri-butionofpestinfestations.Forinstance,itallowstheapplication
ofinformationdimension(Di),whichgivesthedegreeof
reparti-tionofelementsinsideasurfaceandthecorrelationdimension(Dc)
thatprovidesthedegreeoflocalizationofpestspreadbymeasuring
thelevelofclustering(Addison,2002;Li,2000;Jonckheereetal.,
2006).
5.4. Percolationandclusterdistribution
Thephenomenonthatevolvesintimeandspacefromrandomly
isolatedpatches in anareaand becoming connected toform a
giantclusterof thewholeareais calledpercolation(Grimmett,
1999). By applying percolation theory,the spread of pests can
bepredicted(Wiensetal.,1997).Theexistenceofapercolation
thresholdprobabilityofinvasionbetweenplantscanbeusedas
followed:Iftheprobabilityofcolonizinganeighbouringplantis
abovethisthresholdtheinsectpestmightspreadinvasively
creat-inglargepatches,butbelowthethresholdspreadingisfiniteand
restrictedtocomparativelysmallpatches(Baileyetal.,2000).The
predictionofinvasiveandnon-invasivespreaddependson
con-stantcolonizationefficiencywithtimeandpercolationtheorycan
elucidatehow insectpropagateandspread ina crop.With
dis-tributedlatticesrepresentingpatchesofpestdamage,percolation
theorycanpredictthethresholdfortransitionbetween
produc-inga small patchand themoment where theprogression of a
largepatchwilloccur.Priortotheapplicationofsuchamodelling
framework, advancemethods suchasKohonen neural network
(WattsandWorner,2009),K-means,GaussianmixedandMoran’s indicesfordistributionalclusteranalysisareappliedtoincreasethe
understandingofthepatternsthatexistinthedatasets(Recknagel,
2001).
In Ndjomatchoua et al. (2016)an illustration of how
multi-fractalmethodcoupledwithpercolationcanbeusedtoanalyse
thespatialandtemporalpropagationofinsectpestsinfestations
insmallholderfarms.Theauthorsdemonstratedthatwithagood
knowledgeandunderstandingofthebiologicalandecological
pro-cessesthatgoverntheinfestationofmaize farmsbytheAfrican
stemborerBusolafuscathereishighprobabilitytotractand
pre-dict the nextplant tobe damaged by the pest. Considering a
cluster(Fig.4)asasetofinfestedcells,whicharetotallyisolated
from one and others, the paper revealed that as the damages
oftheinsectspread,thetotalnumberofclustersincreaseswith
timeandstarttodecrease(percolationthreshold)whenthe
spa-tialexpansionofcompletelyisolatedclustersisnomorefeasible.
Afterthemanifestationofthepercolationthreshold,theinfested
clustersconnectandmerge,resultingonthereductionofoveral
numberofclusters.Themarginalscalewherethepercolationwas
observedwascogitatedasthespatialresolutionthresholdforthe
incidenceofthepercolationphenomenon(Ndjomatchouaetal.,
2016).
5.5. Synchronization
Synchronization is a process wherein many systems adjust
a given property of their motion due to a suitable coupling
configuration, or to an external forcing (Arenas et al., 2008).
The occurrence of synchronization in large-scale coupled pest
networks ofis a fundamental phenomenon observedin nature
(Arenas et al., 2008). In a tri-trophic system formed by a
plant, an insect herbivore and its natural enemy (Pearse and
Altermatt,2013),eachcomponenthasitsownbiologicalrhythm
and therefore can achieve rhythmic functional synchronization
under defined natural conditions (Zhang et al., 2010). It was
emphasised that correct application of synchronization
pro-cesses in networked systems by integrating explicitly spatial
andtrophic couplingsinto currentmeta-populationcommunity
approaches constitute a fundamental playground for
deepen-ing the understanding in pest dynamical behaviour (Thomas,
2001).
5.6. Agentbasedapproach
Theapplicationof individualandagent-based approachesto
studycomplexpestspreadingdynamicsifmultiplehosts(animal,
humanandpathogen)areinvolved isan openfield ofresearch
(Bonabeau,2002).Thismodellingapproachaccountsforthe
phys-icalcontactpatternsthat resultfrommovementsof individuals
(pestsandhosts)betweenlocations.Anagent-basedmodelis
con-structedbyconceptualizingthestructureofspatialandtemporal
dynamicsofthetransmissionofthepestwiththeoretical
analy-ses(asdescribedinFig.2)andbasedondataonthebiologyand
ecologyofthepestincludingthedynamics,landuse,andthe
inter-actions.Themodeloutcomeallowsforthetrackingandprediction
ofthespatio-temporaldynamicsofagiveninsectpestinaspecified
environment(Grimmetal.,2005).
5.7. Roleofremotesensingincropinsectpestassessments
Remotesensingcanprovidetimelyandspatiallyexplicitdata
onthetypesandacreagesofspecificcropsandgrowingperiods,
croppingsystem(e.g.intercroppingormonocropping),lengthof
fallowperiodandwithinfieldcropvitalityvariations(Forkuoand
Maathuis,2012).Thewithinfieldvariationcanbearesultofpests
thataffectcropleafpigmentsandwatercontentsaswellasleafarea
index(LAI)(Renetal.,2012).Ifscalingfunctionsaredeveloped,
remotelysenseddatasetscouldrenderspatiallyandtemporally
continuousobservationsofpesteffectsatregionalscales.Thisis
especiallytruefortime-seriesvariables,suchasLAIorLandSurface
Temperature(LST)thatareknowntobeassociatedwithpest
habi-tatfactors(Baretetal.,2007;Blumetal.,2015).Spatiallyexplicit
andarea-wideinformationismuchmoreeffectivethan‘point’data,
i.e.pestincidenceorclimatepointmeasures.Justasmany
estab-lishedcropmodelsessentiallyrelyonapproximationstoidentify
thepossiblelocationofcropsinaparticularstudyarea(Thornton
etal.,2009),thereisanincreasingtrendtointegrateclimateand
remotelysensedcropdatatoassessspecificclimatechangeimpacts
oncropyields(Sultanetal.,2014).Fieldlevelspectral
character-istics(or variablemeasures)of cropinfections might,however,
appearsimilartoothersourcesofcropstressandmostoftenvery
highresolutionand‘hyperspectral’datasets,whicharepresently
stillrelativeexpensive,areneededtoaccuratelymapwithin-field
pestinfestationratesandtobeabletoseparatecropsfromother
land cover types (Baret et al., 2007).Currently there is a need
Fig.4.VariationofthescaleofobservationofleafdamagespropagationofB.fuscainamaizefarmwithtime.Thefractiononthetopofeachsub-figurerepresentsthenumber ofplantsconsideredineachunitcellofthespatialgridduringtheobservation.Thescale1/kmeansthatk-plantsperunitcellweretakenintoconsideration.Theparticular case1/1meansthatoneplantisconsideredasonecell.Itisassumedthatifatleastoneplantamongthek×kplantsinsidethecellisinfectedthenthecellisconsideredas infected.Forafixedscalethecorrespondingtotalnumberofclusters(normalizedbetween0and1)isplottedasafunctionoftheweekofobservation(Ndjomatchouaetal., 2016).
data sets and innovative data processing routines for accurate
(explicit)cropmapping,includingpest infestationandinfection
rates.
5.8. Theoreticalframeworkforassessingclimatechangeinduced impactsoninsectswithnouseofIPCCscenarios
Thestudyontheeffectsoftheelevationonthepopulationsof
theolivefruitflyBactroceraoleae(Rossi)(Kounatidisetal.,2008) andthesimulationofthepest(Petacchietal.,2015)suggestedthat
differenceinthepresenceand abundanceofinsects inlocation
canbeinfluencedbyaltitudegradients.Motivatedbytheseresults
andownexperiencesweherebyproposeatheoreticalconceptual
framework for assessingclimate changeimpacts and providing
adaptionoptionsforcropinsectpestswithnoapplicationofIPCC
scenarios.Themodellingframeworkreliesontheassumptionthat,
althoughtheclimateischanging,allfuturelocalandregional
cli-matesalready exist today and nocomplete novelclimate with
currentlynon-existingcharacteristicswillbecreatedinthefuture.
If that is the case and considering the numerous uncertainties
thatalsoexistwiththeconcept,developmentandimplementation
ofimpactmodels,itissuggestedtoconductdetailedandregion
specificanalysesusinginformationofdifferentexistingand
well-knownregionalandlocalclimatesasinputtoimpactmodels,to
developappropriatepolicyoptionsandrecommendationsforthe
purposeofidentifyingadaptiveresponses.Theapproachwill
con-siderablyreducetheuncertaintiesfromIPCCscenarioscurrently
usedas input indifferent impacts assessment modelsand will
providethesocietywithmoreaccuratelocal/regionalspecific
adap-tiveresponsesthatcanbeusedwhennecessary.Similaranalyses
canbeconductedalong altitudinalgradients,wherea
consider-ablechangeinclimaticfactorsoccurfromlowtohighaltitudes.A
globaldatabaseencompassingtheresults,outputsandoutcomes
oftheassessmentsshouldbedeveloped,documentedandmade
availabletocommunitieswithsimilaragro-ecologicalconditions
andtheworldatlargeforfutureclimatechangeadaption
plan-ning. Anadditional meritfromthis conceptresides onthefact
thattheanalyseswillbeconductedatahighspatialand
tempo-ralresolution,whichenablescapturingtheinsectpestspotential
establishment, distribution and abundance in a more accurate
manner.
Inarecentstudyontheimpactsofclimatechangeoninsectpest
populationdynamics,twoaltitudegradientregionsweretargeted
(Mwalusepoetal.,2015):1)TaitaHills(Kenya)withelevation rang-ingfrom700to2000m.a.s.l.;latitude3◦25Sandlongitude38◦20E.
Themeanannualrainfalloftheregionis500mm(lowaltitude)
and>1500mm(uppermountainzone).Theannualaverage
tem-peraturevariesfrom16.5to23.5◦Cwhenshiftingfromlowtohigh
altitude.2)InTanzania,theselectedareacoversthesoutheastern
slopeofMountKilimanjarofrom700to1800m.a.s.l.,andislocated
betweenlatitude3◦4Sandlongitude37◦4.Meanannual
tempera-turevariesfrom18to23.6◦Candtheaverageannualrainfallranges
from1000to1300mm.Bothsitesshowedconsiderablevariation
in altitudegradients with graded climate characteristics
(rain-fallandtemperature)assurrogatesforchangesinclimate.Deep
understandingonthemechanismtheinsectsusedtoadaptinthe
transectsprovidesvaluableinformation,whichcanbeharnessed
intopestriskanalysesprocedurestoformulateenvironmentally
viableandlocalizedpestscontrolmeasuresfordifferentclimate
variablescontextfortodayandthefuture(Fig.5).
6. Modellingtheeconomicimpactofinsectpestscontrol
Impactevaluationofinsectpestcontroldeterminesthewelfare
changesfromagiveninterventiononindividualsandhouseholds
Fig.5.HighspatialandtemporalresolutionmapforthepotentialestablishmentofDiamond-backmoth(Plutellaxylostella),amajorinsectspestofcrucifercropsworldwide alongaltitudegradientofMountKilimanjaro.ThepredictionsweremadeusingtheIndexinterpolatormoduleoftheInsectLifeCycleModelling(ILCYM)Softwareasdescribed inMwalusepoetal.(2015).FromthetheoryofILCYM,anestablishmentindex>0.7meanstheinsectcansurvivepermanentlyinthearea.
(Sheltonetal.,2002).Theseevaluationscanbemadeex-anteor
ex-post.Theex-anteapproachevaluatestheimpactoffuture
inter-ventionsprovidinginformationonthelikelysocio-economicand
environmentalimpactsandhowtheflowofcostsandbenefitsis
distributedamongtheaffectedpopulation.Ex-postimpact
assess-mentsevaluatetheimpactof pastinterventions,measuringthe
benefitsandthecostsoftheinterventionsand providing
infor-mationonthepathwaysthroughwhich observedimpacts have
occurred. We describeherethecommonmethods used forthe
economicimpactmodellingofcropinsectpests.
6.1. Economicsurplusapproaches
Theeconomicsurplusapproachstemsfrompartialequilibrium
framework,whichisthemostcommonapproachforthe
evalua-tionoftechnologicalprogressinagriculture(Alstonetal.,1995).
The modelconsists of estimatingthe aggregatetotal monetary
benefitsforproducersandconsumers entailedbythe
introduc-tionofdevelopmentinterventionsinatargetedsocialenvironment
(Marediaetal.,2000).Theapproachhasbeenusedfortheimpactof
thebiologicalcontrolofthecassavamealybuginAfrica(Norgaard,
1988).In Benin,it hasbeenusedforthebiologicalcontrol
Fig.6.Flowdiagram,linkingcropmodeltopestdamagebyfuzzylogic(FL)system.Withitsrulesbasedapproach,multi-trophicinteractionsandfeedbacksareincluded intothecropmodelfordirectestimateoftheactualyield.
hyacinth(DeGrooteetal.,2003).Thewelfarebenefitsarecompared
tothemonetaryinvestmentsinordertoappreciatetheefficiency
ofinterventionsthroughthemeasureofthereturntoinvestment
(Soul-kifoulyetal.,2016).Economicbenefitsofinterventionsare
extendedtotheestimationandanalysisoftheNetPresentValue
(NVP),theInternalRateofReturn(IRR)andBenefit-CostRatio(B/C)
(Zeddiesetal.,2001).
6.2. Computablegeneralequilibrium(CGE)models
Unliketheeconomicsurplusmodelthatisapartialequilibrium
modelholdingononlyonemarket,CGEmodelscapturethefull
economy,showingthemanyrelationshipsbetweendifferentactors
andcommodities.CGEshavebeenbuilttosimulatetheeconomic
andsocialimpactsofawiderangeofscenariosincludingchangesin
thedomesticeconomicsuchastechnologicalchangeinagriculture
(DeJanvryetal.,2000).ElbehriandMacdonald(2004)appliedthe
CGEmodeltoestimatethepotentialimpactoftransgenicBt-cotton
inWestandCentralAfrica.
6.3. Econometricapproaches
Theeconometricestimateoftheimpactof insectpest
man-agementinterventionscapturesthemarginaleffectontheoutput
indicatoroftheinterventionperiod(Masters,1995).The
appro-priatecounterfactualismostusuallydefinedwithreferencetoa
control group,which hastobe identified in a waythat avoids
selectionbiasandthereforetheuseofeitherexperimentalor
quasi-experimentalapproaches(Muriithietal.,2016).
6.3.1. Averagetreatmenteffect(ATE)basedmethods
Assumingafarmerhasadoptedapestcontroltechnology,the
impactoftheprotectionstrategy is thedifferencebetweenthe
actual outcome Y1 and the outcome if it was not adopted Y0.
The estimation of this impact at the individual level (Y1−Y0)
becameincalculablebecauseoftheimpossibilityofobservingY0.
Assolution,thequantitytobeestimatedistheaveragetreatment
effect(ATE=E[Y1−Y0])(ImbensandWooldridge,2008).TheATE
methodsstem fromthesearchfor a solutiontotheabsenceof
thecounterfactualalsoreferredtoasmissingdataproblem.The
methodusedthePropensity-ScoreMatching(PSM)approachthat
canjustifiablyclaimtobethesolutiontothisproblem,andthusto
betheobservationalequivalentofarandomizedexperiment.Two
groupsareidentified:householdsthathavethetreatment(denoted
Di=1forhouseholdi)andthosethatdonot(Di=0).Treatedunits
arematchedtonon-treatedunitsonthebasisofthepropensity
score.Severalmethodsareusedinthecomputation oftheATE,
whichrepresenttherealimpactestimates.Nazli(2010)used
differ-entmatchingmethodsincludingradius,kernel,stratificationand
covariatematchingtoassesstheimpactoftheBt-cottonon
pesti-cideexpenditure,costofproduction,productivity,profit,income
and poverty inPakistan. Arecent studyby Sanglestsawaietal.
(2015)assessedtheimpactoftheparticipationinIPM Farmers’
FieldSchools(FFS)inthePhilippines.
6.3.2. Instrumentalvariablebasedmethods(IV)
The IV-basedmethods are usedin impactassessment when
thereisendogeneityintheplacementofthepestmanagement
pro-grams.Thismeansthatprogramsareplaceddeliberatelyinareas
withobservedornotobservedcharacteristicsthatarecorrelated
withoutcomesofinterestintheassessment(Khandkeretal.,2010).
TheIVapproachaimsatcleaningupthiscorrelationbetweenthe
participationintheprogramandtheunobservedcharacteristics.
TheIVaimstocleanupthiscorrelationbetweentheparticipation
intheprogramandtheunobservedcharacteristics.Thecommon
method usedis the two-stage leastsquare approach (2SLS).In
assessingtheimpactofanIPMprogramongroundnutproductivity
inGhana,Carlbergetal.(2012)usedthe2SLSmethodtoaccountfor
samplingselectionandendogeneityoftheprogram.Rejesusetal.
(2009)examinedtheimpactofdisseminatinginformationonIPM
intermsofinsecticideuseandefficiencyusingIVapproachthat
controlsforendogeneityandselectionbias.
6.3.3. Differenceindifferencemethod(DD)
This method is applied to non-experimental evaluations. It
comparestreatmentandcomparisongroupsintermsofoutcome
changesover timerelative totheoutcomesobservedfor a
pre-intervention baseline. The DD approach is a powerful way to
eliminatethebiascausedbytheunobservedtimeconstant
vari-ablesinestimatingimpacts.ItwasusedinFFSandBt-cottonin
ChinaandhasalsobeappliedtoassesstheeconomicimpactofIPM
technologiesforthecontrolofmangofruitfliesinKenya(Kibira,
2015).
7. Towardstheinclusionofinsectpestimpactsinyield lossesintocropmodel
Properestimationsofactualcropyieldwiththehelpofmodels
requiredetailedquantitativeandknowledgeofdifferentlevelsof
interactionsbetweenpestandcrop.Becauseofthecomplexityof
suchasystem,mostcropgrowthmodelsdonotincluderoutinesfor
Fig.7.Puttingthesystemperspectiveintopracticeinpestmanagementthroughintensifiedknowledgeofecosystemandtherapeuticsasbackups.Thesystemicdescription allowsidentifyinghowrelianceontherapeuticsolutionscanreinforcefurtherreliance‘sideeffect’.Bottomcirclehasadelay.Itrepresentsamorefundamentalresponseto thepestproblem,onewhoseeffectstakelongertobecomeevident.Leveragewillalwaysinvolvestrengtheningthebottomcircleand/orweakeningthetopcircle.
thepotentialimpactsofpestsoncropyieldlossor
environmen-taldamageoveraforecasthorizoncouldbeaccountedforusing
atwo-stepmodellingtactics.First,pestmodels/toolsare
indepen-dentlyrunandtheiroutputsareusedtodefinerulesthatcanbe
includedintocropmodels.Thesemeasurementscanbetranslated
toanindicatorofpotentialdamageduetopest.Second,withincrop
models,modulesusingarule-basedapproachcapableof
connect-ingallcompartmentsofthecropmodelsuchasFLsystemshould
bedeveloped.Withthis reasoningtheeffects ofclimatechange
onpestbehaviour,flighttimeandsynchronisationwiththecrop,
virusacquisitionandtransmissionrates,phenologychangesand
physiologicalresponsescaneasilybeincorporated.Asan
illustra-tion,adetailedflowdiagram,linkinge.g.themaizeplantmodel
tostemborers(pest)damageusingFLsystemisgiven(Fig.6).The
approachforincorporatingpestdamageintocropmodelshasthe
potentialforextendingthepracticalapplicationsofcropmodelsto
abroadrangeofproblemsthatwillnecessitateamultidisciplinary
approachandshouldinvolvegreatercooperationamongbiologists,
economists,ecologists,socialscientists,anddecisionmakers.Asa
wayforwardtoaddressthisproblemofincludingpestimpactsinto
8. Systemthinkingapproach–prospectforincludingpest impactsintocropproduction
Understandingcropgrowthand predictingactualcropyield,
requires the grasping of concepts suchas the food production
systems, the multi-trophic interactions, the crop-pest systems,
theecosystemfunctionsandprocesses,thesocio-economicand
socio-ecologicalchallengesaswellasrespectivefeedbacksloops,
biophysicalflows,timedelays,andnonlinearitywithinfunctional
fluctuating bounds. Most of insect pest modelling approaches
describedearlierarenotholisticbecausetheyconcentrateon
sin-glecomponentsofthesystemratherthanonthewhole.Indoing
so,theymiss thecrucial interactionsbetweenthecomponents.
Thus theyare failingtorecognize that theperformance of one
part may have consequences elsewhere that are damaging for
thewhole.Thisfaultisknownas‘sub-optimization’(Jonesetal.,
1998).However,managingcomplexandunpredictablevariables
in agricultural ecosystemsis similar to that for other systems,
including the human body and social systems. The key
weak-nesswithcurrentlyusedapproaches iscentraltoouroperating
philosophyinsciencetodividethingsintospecialized partsfor
studying,knownasreductionism(Jackson,2003).Inreality
com-ponentsofagriculturalecosystemsinteract,and,throughasetof
feedbackloops, maintain‘balance’withinfunctional fluctuating
bounds.Moreover,therapeuticinterventionsintothesesystems
might ameliorate symptoms for a time but counter-movement
onthelongtermwillneutralizetheireffectiveness.Toillustrate,
inproductionsystemssuchascocoaagroforestrysystems,
com-posedofseveralinteractingsub-systemsandcomponents(cocoa,
associatedcrops,non-cropplants,pests/diseases,beneficialinsects
andfarmers)apestmanagementstrategytargetingonepestcould
resultsintheremovalofnaturalenemieswhichregulateor
con-trolledanotherpestspecies(e.g.thesimplepresenceofaparasitoid
cancauseantstoremaininsidetheirnestanddisrupttheir
protec-tiveeffectonhemipteranmutualists).Thereforeconsideringcocoa
plantsasactivecomponentsofmultitrophiclevelinteractionsis
crucialtoa systems approachtopest management(Tscharntke
etal.,2011).Managementpracticesaddressingonecomponentor
sub-systemdirectlyorindirectlyaffectstheothercomponentsor
thebalanceofthelocalecosystem(Tscharntkeetal.,2012).Inthese
systems,planttraitsmayhaveimportantimpactsonboth
herbi-voresandtheirnaturalenemies(PerfectoandVandermeer2008;
Andersonetal.,2009).Suchmediatedindirectinteractionsbetween
herbivores mayhave a larger impactonbiodiversity
conserva-tionandcommunity structurethandirect competitionbetween
herbivores(Wielgossetal.,2012).Currentadvancesintritrophic
levelinteractionsamongplants,crops,non-crops,herbivoresand
beneficialinsects(parasitoidsandpredators)substantiatestrong
interconnectionsbetweenthesecomponentsandtheimportance
ofmultitrophicperspectivesaswellasrespectivefeedbackloops
(Fig.7).Long-termresolutionsforasystemapproachinpest
man-agementcanonlybeachievedbyrestructuringandmanagingthese
systemsinwaysthatmaximizethearrayoffundamental
‘built-in’ecosystempreventivestrengths,withtherapeutictactics(e.g.
theuseofpesticides)serving strictlyasbackups tothenatural
regulators(Fig.7).Systemthinkingapproachtopestmanagement
stressesholism,utilizingagroecologicalprinciplesbuttranslating
themintoa socio-economicand policyframework thatstresses
humanresourcedevelopment(Fig.7).
Theproposedsystemmodellingrecognizesthemultiplewaysin
whichpestproblemscanbeaddressedreachingfrommost
funda-mentalbasedonintensifiedknowledgeofagriculturalproduction
systems(Waltersetal.,2016)tomostsuperficial.Incorporationof
thisbasicprincipleintothemainstreamingofpestmanagement
scienceandstrategiesneedsalsotoconsiderthepossible
‘reinforc-ingprocesses’andnegative‘sideeffect’ofthetherapeuticsolutions
toinvokethefundamentalsolution(Fig.7).Alltheseapproaches
belongtothetraditional,scientificmethodforstudyingsystems
knownasreductionism(Jackson,2003).Reductionismperceives
thecomponentsasparamountandseekstoidentifyandunderstand
thecomponentsandthusderiveanunderstandingofthewhole
system.
In summary, current modelling conceptsof cropproduction
consistofbreakingdownasystemintocomponents,seeking
iso-latedunderstandingofindividualcomponentsandintervene.In
systemmodelling itis proposedtoputthe studyof thewhole
beforethatofthecomponents(Wallachetal.,2013;Fath,2014;
Waltersetal.,2016).Indoingso,theprincipleofthewholethat
emergesfromtheinteractionsbetweenthecomponents,which
affecteach otherthroughcomplexnetworksof relationships,is
respected.Indeed,weconcurthattherewillbeincreasingneedfor
modeltoimprovecontrolofpestsandothercomponentsofonfarm
management.However,untilthesecomponentsarecombinedinto
awholesystemapproach,itwillbedifficulttoachievetargetsof
sustainablemanagementincropproduction.
Acknowledgments
Thisworkispartofthefellowshipproject(VW-89362)ofHEZT
funded by theVolkswagen Foundation under theshame
Fund-ingInitiativeKnowledge for Tomorrow− CooperativeResearch
ProjectsinSub-SaharanonResources,theirDynamics,and
Sus-tainability−CapacityDevelopmentinComparativeandIntegrated
Approaches.TheauthorsthanktheFederalMinistryofCooperation
andDevelopment(BMZ),Germanythatprovidedthefinancial
sup-portthroughTutaIPMproject,andtheMinistryforForeignAffairs
ofFinlandthatprovidedfinancialsupportthroughCHIESA(Climate
ChangeImpactsonEcosystemServicesandFoodSecurityinEastern
Africa)project.
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