Biologische bestrijding van Floridamot, Spodoptera exigua, met. Spodoptera exigua Nuclear Polyhedrosis Virus
Be vat:
- programma beschrijving SPONPV - listing SPONPV - de Moed, van der Werf & Smits, in prep.
Guido de Moed Vakgroep Theoretische Productie Ecologie Landbouwuniversiteit, Wageningen augustus 1990 Ihtern rapport no 19
Handleiding SPONPV programma door Guido de Meed
1 lnleiding. Het SPO(doptera exigua)NPV(irus) programma beschrijft de epizootiologie van het SeMNPV virus in een Floridamot populatie in een groeiend Chrysanten gewas. Dit verslag bespreekt de modelstructuur en de achterliggende aannames. Voor verdere informatie verwijs ik naar De Moed et al., (in prep.) In H2 zal kort de structuur van het model besproken worden. Deze wordt samen met de parameter schattinging, uitgebreid besproken in de Moed et al. (in prep.). In H3 wordt de opzet van het programma besproken, met de algemene methode van indeling bij de gebruikte integratiemethode (3.1 ),
de verschillende programma
onderdelen (3.2) en de verwijzingsstructuur van het hooftprogramma en de verschillende subroutines. In H4 zullen van de elementen uit 3.2 de programmerings- en wiskundige details besproken worden. Ten slotte wordt in Apendix 1 de variabele namen besproken. 2
Model structuur. Het programma beschrijft de epizootiologie van het SeMNPV
virus in een Floridamot populatie in een groeiend Chrysanten gewas. We hebben hier dus te maken met een tritroof systeem (Fig 1), waarbij we met een aantal, interacties te maken hebben: ia De infectie van de mot. ib vrijkomen van virus deeltjes na sterven geinfecteerde larve. ii De invloed van het gewas op de ruimtelijke en temporele verdeling van het virus. iii De verdeling van de larven in het gewas. Deze verdeling bepaald de ontmoetingskans van de larven met het virus en daarmee gedeeltelijk de infectiesnelheid.
Virus
Floridamot
ii
Gewas Figuur 1: lnteracties, beschreven in model, tussen verschillende trofische niveaus.
In het model wordt de Floridamot populatie ingedeeld in clusters. Elke cluster bestaat uit een eipakket en de uit dit eipakket voortkomende larven. De ruimtelijke verdeling van de larven van een cluster binnen het gewas zijn bepaald door de leeftijdsverdeling binnen het cluster. De ruimtelijke coordinaten van een cluster worden niet meegenomen, omdat wordt aangenomen dat bij de lage dichtheden waarin wij geinteresseerd zijn, de clusters niet overlappen. Hierdoor speelt de ruimtelijke verdeling van de clusters geen rol. De dynamiek van de clusters wordt nagebootst d.m.v. compound simulation (Ward et al., 1990; Fig 2). De clusters worden ingedeeld naar een tweetal criteria: i de tijd sinds ovipositie, d.w.z. de leeftijd van het cluster. ii Het aantal geinfecteerde eieren in het eipakket. De leeftijd van de cluster wordt ingedeeld in 10 opeenvolgende klassen, elk 1/10 van de maximale leeftijd. Deze maximale leeftijd is die leeftijd waarbij 99.9°/o van de larven, die niet zijn besmet of zijn dood gegaan door andere redenen, zijn verpopt en dus uit het cluster zijn verdwenen. D.m.v. ovipositie ontstaan nieuwe clusters, die in de eerste leeftijdsklasse terecht komen. Het aantal geinfecteerde eieren wordt ingedeeld in een 2-tal parallelle en een nul klasse. Deze parallelle klasses worden bepaald door transmissie methode van het virus naar het ei, door verticale of door z.g. male transmission. Daarnaast worden aile clusters zonder geinfecteerde eieren, dus ook die clusters van geinfecteerde vrouwtjes die door toeval niet geinfecteerd zijn, ingedeeld in een nul klasse.
I I I I I
------~-1 I I I
--------- ----- _. I
1
I
I
I
I
I
I I
I
__.. Number of infected eggs Figuur 2: Diagram dat de overgang tussen verschilende clusterklasses weergeeft.
Van elke klasse wordt het aantal daarin aanwezige clusters bijgehouden (PATCH) en wordt voor de gemiddelde cluster de ontwikkeling van de verschillende stadia bijgehouden. Het virus komt voor in twee vormen: i in de gastheer en ii een vrij-levende vorm. De ontwikkeling van geinfecteerde stadia van de mot wordt berekend en het aantal daarvan vervloeide larven per cluster. Deze vervloeide larven kunnen weer via horizontale transmissie infecties veroorzaken bij larven uit het zelfde cluster. Gespoten virusmateriaal heeft een bepaalde halfwaardetijd. In het midden van de bloembedden is het verticaal verdeeld volgens een uitvangcurve. Aan de randen is een homogene verticale verdeling verondersteld. Chrysant wordt geteeld in circulatie systeem, waarbij om de week bedden geoogst worden en nieuwe bedden geplant bij een lengte van 15cm. Doordat Floridamot een sterke voorkeur voor jonge planten heeft en er dus bijna continu jonge planten aanwezig zijn, is de lengte van de gastheerplant en de leeftijd van het cluster gekoppelt.
3 Programma structuur. 3.1 programma structuur en integratie mehode Het programma is ingedeeld in 4 sectie:
-Declaraties van variabelen -lnitialisatie van variabelen -Simulation loop -Terminal section
Bij het gebruik van de Euler integratie mehode moet de simulation loop een vaste volgorde hebben. Bij deze integratiemethode wordt de veranderingssnelheid over de komende tijdstap berekend aan de hand van de huidige aantallen. Om er voor te zorgen dat de snelheden berekend worden aan de hand van de juiste aantallen, moet de reken volgorde worden aangehouden, zoals beschreven in Van Kraalingen & Rappoldt (1989). -integratie -genereren van driving variables -snelheidsberekeningen -output van resultaten Binnen subroutines, die verschillende van deze onderdelen bevatten b.v. de BOXCAR subroutines, moeten deze elementen worden gescheiden en apart worden aangeroepen op de daartoe bestemde plaats. Dit is bebeurt door het gebruik van een TASK variabele, die aangeeft welk onderdeel van de subroutine moet worden uitgevoerd (TASK=1: integratie; TASK=2: snelheidsberekeningen). Het omrekenen van state variables komt neer op het alvast uitvoeren van een deel van een snelheidsberekening. De berekening wordt in een aantal deelberekeningen
uitgevoerd. Daarom zou deze berekening in het gedeelte met snelheidsberekeningen horen. Voor de duidelijkheid zou het echter beter zijn om dat het in het integratie gedeelte staat. Dit moet dan wei gebeuren na de integratieberekeningen van aile onafhankelijke hoeveelheden in de berekening. Het zelfde geldt voor het omrekenen van snelheden in het gedeelte met snelheidsberekeningen. Dit moet gebeuren op grond van de nieuw berekende snelheden. Bij het doorschuiven van hoeveelheden binnen een array, zoals b.v. in de boxcartrain-methode, worden geen snelheden gebruikt. Het is meer een herordening van de aantallen in de boxcar-train, geen overgang naar een nieuwe toestand. Daarom moet het doorschuiven gebeuren tussen berekening van de integraal en de berekening van de nieuwe snelheid. lk zou daarom de indeling van Van Kraalingen & Rappoldt (1989} iets willen uitbreiden: -integratie
state=f( rate)
-doorschuiven boxcars -berekening state hulpvariabelen
state=f( state)
-genereren van driving variables -berekening snelheden
rate=f( state)
-berekening rate hulpvariabelen
rate=f(rate)
-output van resultaten Deze indeling minimaliseerd welliswaar de integratiefout, maar maakt het programma niet leesbaarder. Daarom zijn in SPONPV de berekeningen voor de hulpvariabelen en het doorschuiven van de boxcars niet volledig gescheiden, maar wei steeds na de berekening van de onafhankelijke variabelen geplaatst.
3.2 programma onderdelen Bij de declaratie en initialisatie secties wordt zo veel mogelijk een vaste volgorde van de variabelen aangehouden, elk aangegeven met een eigen kopje. Dit om het programma meer leesbaar te houden. -States -Rates -Parameters Bij correct gebruik van de programmeervolgorde uit 3.1 mogen binnen deze onderdelen de statements in elke willekeurige volgorde gezet worden, afgezien van DO-loops etc. De statements zijn onderverdeeld in een aantal onderwerpen. Deze onderdelen zijn in de verschillende secties van het model (zie 3.1) zo vee I mogelijk in de zelfde volgorde gezet om de leesbaarheid te vergroten. De onderwerpen worden bij de declaratie en initialisatie van variabelen aangegeven met een 3 of 4 letter code
op de eerste 4 tekens van de commentaarregel. In de simulation loop krijgt elk onderwerp een eigen kopje: -General
-Dead larvae
-Patches
-Free-living
-Healthy
-Crop
-Vertical transmission
-Output
virus
-Horizontal transmission 3.3 Samenhang hoofdprogramma en subroutines Figuur 3 geeft aan naar welke subroutines in het hoofdprogramma wordt verwezen, en van welke subroutine naar welke subroutine.
POISSO RIRSPR RIRHOR
LIN EXT ENTDRE
BOXCAR
SHIFT
BOXC3D
SUM1 D
BOXINF
SHIFT3D
BOXPAR
SUM3D
Figuur 3: Structuur SPONPV-programma
4
Programma onderdelen
4.1 Patches Array PATCH bevat aantal clusters per klasse, met 0-NI als de infectie klasses en 1-NJ als de leeftijdsklasses. Het verloop van de clusters door de leeftijdsklassen wordt geregelt als in een boxcartrain zonder dispersie. Elke 1/10 van de totale ontwikkelingsduur van een cluster wordt CDSPAT>.1 en PUSH=1. De inhoud van de clustergebonden state variabelen wordt dan doorgeschoven. De aantallen uit het laatste bakje worden weggegooid. Omdat het eerste bakje continu wordt gevuld, is de verblijftijd in dit bakje half zo lang als de andere bakjes en moet de totale verblijftijd worden gecorrigeerd door vermenivuldiging met 10/(1 0-.5) en de
ontwikkelingssnelheid met de reciproke.
4.2 Healthy De ontwikkeling van zowel de gezonde als geinfecteerde mot stadia wordt nagebootst met de Boxcar-train methode. De boxcars voor de verschillende cluster klasses zijn geordend in een array, geordend als (infectieklasse, leeftijdsklasses, boxcarnummer). De berekeningen voor de boxcars gebeuren in de BOXCAR subroutine voor de pop en adulte stadia en de BOXC3D voor het ei en BOXINF voor de eerste vier larvale stadia en BOXPAR voor het L5 stadium. Dit zijn aile vier aangepaste versies van het BOXCAR subroutine van Goudriaan & van Roermund (1989; zie 5.3). Na verpopping verdwijnen de poppen uit het cluster en worden weer als een groep behandeld. De verpoppings-snelheden uit de verschillende stadia worden daarom gesommeerd tot TPUPM en TVPUPM. De eilegsnelheid wordt berekend aan de hand van de ontpoppingssnelheid van de poppen, gecorrigeerd voor de fractie vrouwtjes dat besmet raakt door sexuele horizontale transmissie, de sexratio en de fecunditeit.
4.3 BOXCAR I BOXC3D-subroutines De subroutines BOXCAR I BOXC3D gebruiken de boxcartrain-met-gecontroleerdedispersie methode van Goudriaan & Van Roermund (1989). De gez'onde individuen bevinden zich in array A en stromen door deze array volgens de standaard methode. In de subroutine BOXC3D bevindt deze array zich in een 3 dim. array op de plaats A(I,J,O:N) met N als het aantal boxcars. Om het aantal infectie- en leeftijdsklasses Nl en NJ variabel te houden, worden die uit het hoofdprogramma ingelezen. Met een relatieve snelheid RMR vindt sterfte plaats die niet wordt opgevangen. Bij TASK=1 worden nieuwe waardes voor A en CDS berekend en ATOT berekend in de subroutine SUM1 D en worden de boxcars eventueel doorgeschoven in de subroutine SHIFT. De door te schuiven fractie
F wordt berekend in subroutine FRACT. Bij TASK =2 worden
de snelheden DA (sterfte + infectie) en OUTFL (uitstroom) berekend. Om te voorkomen dat er meer uit het laatste bakje stroomt dan er in zit, is een extra beveiliging ingebouwd. Omdat in BOXC3D de train zich in een 3-Dim. array bevind, zijn hiervoor aparte SUM3D en SHIFT3D subroutines.
4.4 Horizontale transmissie I Dode larven M.b.v. de relatieve infectiesnelheid wordt in de BOXINF subroutine de
infectiesnelheid berekend. BOXINF is een aangepaste BOXCAR subroutine met de mogelijkheid van een extra uitstroomsnelheid. Met deze subroutine gaat wei het relatieve ontwikkelingstadium binnen een stadium verloren. Dit wordt ondervangen in de subroutine BOXPAR, waar de individuen in de boxcar wei direct besmet raken, maar pas uitstromen op het moment van overgang naar een volgend stadium. Dit is van belang voor het LS stadium i.v.m. verticale transmissie. De relatieve infectiesnelheid RIR wordt in twee delen berekend: een deel AIRS t.g.v. vrij levend virus en een deel RIRH door horizontale transmissie. RIRH wordt berekend in subroutine RIRHOR, zoals beschreven in De Moed et al. (in prep.: Eq.S). AIRS wordt berekend in subroutine RIRSPR. Geinfecteerde larven vervloeien na een incubatietijd INCUS met snelheid IDRL. De dode larven DLAR verdwijnen na het doorlopen van de laatste leeftijdsklasse van het cluster.
4.5 RIRSPR subroutine Deze subroutine berekend een bespuitingsprofiel in het gewas aan de hand van een uitvangconstante K en de LAI op het moment van spuiten (LAISPR) en de momentane LA I.
LAI
""'1111(
DLAI LAISPR
""'1111(
,,
-""'1111(
;
... 111(
profile
-----~
;
,, ,
;
,
, ,,
,
, ,,
,
,,
, ,,
;
;
, ;tf ;tf ;
;
,11
Leaf layers
.... .... ....
.... Corrected Leaflayers
Figuur 4: Berekening virus verdeling binnen gewas. Per bladlaag wordt eerst de hoogte van boven- en onderkantkant van de bladlaag berekend, gerekend in LAI eenheden vanaf de grond (Fig.4). DLAI is hoeveelheid bladoppervlak dat bijgegroeid is sinds de bespuiting. De berekende bladlaaghoogtes moeten nu gecorrigeerd worden door DLAI er bij op te tellen. Je krijgt nu de bladlaaghoogtes binnen het profiel op het moment van spuiten. Met de formule van Spitters et al. (1989} voor het lichtprofiel in een gewas, maar dan zonder reflectie, kan de influx en outflux in de bladlaag berekend worden.
Flux
= Flux0 x
e-diepte x K
(1)
met diepte in LAI eenheden en uitvangcoefficient K. Deze formula gebruikt echter de dieptein het gewas i.p.v. hoogte vanaf het grondoppervlak, zodat dit moet worden omgerekend. Als nu door de bespuitingscorrectie de boven of onderkant van een bladlaag boven het gewas uitkomt, wordt de hoogte van zo'n laag gereduceert tot de hoogte van het gewas. Liggen nu beide hoogtes boven de LAISPR, dan zou zich hier geen virus moeten bevinden. Als een bladlaag boven de bespuitingshorizon ligt (bovenste bladlaag fig 4), dan komen na correctie zowel de onder- als de bovenkant van een bladlaag boven het gewas uit en worden beiden gereduceerd tot de hoogte van het gewas. De influx door de bovenlaag is dan even groot als de outflux via de onderlaag (Vergelijking 1) en bevinden zich dus geen virusdeeltjes in deze bladlaag. Een deel FRAND heeft een homogene verticale verdeling. Aan de hand van deze twee profielen wordt de gemiddelde virusdichtheid per bladlaag berekend. Aan de hand van de gevoeligheid CP en de tijdsverdeling van de larven over de bladlagen wordt de gemiddelde infectiesnelheid berekend.
4.6 Verticale transmissie I BOXPAR-subroutine De L5 larven splitsen zich in drie groepen: i de gezonde larven, ii de fractie (1PERAD) van de geinfecteerde larven die zullen vervloeien en iii de fractie PERAD die verder ontwikkeld verder tot adult. Voor ii geldt dat het moment van infectie bepalend is voor het moment van vervloeien, onafhankelijk van het op dat moment bereikte ontwikkeling. Hierdoor hoeft de bereikte ontwikkeling niet behouden te blijven. Voor iii moet de relatieve ontwikkeling wei bewaard blijven omdat de infectie geen gevolgen heeft op de verdere ontwikkeling. Deze drie processen zijn in de subroutine BOXPAR samengebracht. BOX PAR is een aangepaste versie van de subroutine BOXINF. Naast de array A voor gezonde individuen kent deze de array B voor geinfecteerde individuen (fig. 5). Hiervoor gelden de zelfde doorschuif principes als A. De instroom gebeurt niet aileen in het eerste bakje, maar vanuit aile bakjes van A naar het bakje van B met het zelfde relatieve ontwikkelingsstadium. De berekeningen worden parallel uitgevoerd voor A en B met de zelfde ontwikkelingssnelheid DVR en spreiding CV. De overgangssnelheid van A naar B wordt berekend als een vaste fractie P van de relatieve infectiesnelheid RIR. De resterende fractie (1-P) vormt de momentane infectiesnelheid INFR.
INFR
INFL
---JI~
OUTA
+-----
A1
A4
81
OUTS 84 +-----.-
t
t
Figuur 5: Relatiediagram BOXPAR-subroutine. De geinfecteerde L5 larven die verder ontwikkelen (VL5) worden pop VPUP. Na verpoppen Ievert dat wat adulte mannetjes VMAL en het aantal vrouwtjes wordt omgerekend tot het aantal ongelegde eieren VOVA 1. De aantallen gezonde MAL en geinfecteerde mannetjes VMAL worden berekend om de fractie geinfecteerde mannetjes te weten. Deze fractie is gelijk aan de fractie gezonde vrouwtjes dat geinfecteerd raakt door sexuele horizontale transmissie. Het aantal geinfecteerde vrouwtjes wordt omgerekend naar het aantal geinfecteerde ongelegde eieren VOVA2. De snelheid waarmee eieren beschikbaar komen voor ovipositie (OVOUT, VOUT1 ,VOUT2) wordt verdeeld over de infectie klassen. Eieren van gezonde vrouwtjes komen allemaal in de gezonde klasse terecht. Van VOUT1 en VOUT2 blijft ook een deel onbesmet. Dit deel komt overeen met de kans op nul bij een Poissonverdeling met een steekproefgrootte van 35 bij een kans per ei van LAMB/35, waarbij LAMB het gemiddeld aantal geinfecteerde eieren per legsel is. Deze gezonde legsels komen ook in de gezonde klasse terecht. De rest van VOUT1 en VOUT2 komen in resp. klasse 1 en 2 terecht. Het gemiddeld aantal geinfecteerde eieren in deze klasses is nu echter groter dan LAMB, omdat de nul-klasse er van af is. Het gemiddelde wordt nu LAMB/(1.-Poisson(O)). Het aantal gezonde eieren binnen de geinfecteerde klassenwordt nu 35 min dit aantal. Verticale en male transmission treedt pas op gedurende de generatie die bespoten wordt. Omdat hiervoor een grote hoeveelheid parallelle berekeningen uitgevoerd moeten worden die veel rekentijd vergen, wordt deze berekeningen pas gedaan als verticale transmissie gaat optreden. Dit kan worden gedaan door het aantal infectieklassen op 1 te zetten (NIVAR=O). Zodra geinfecteerde vrouwtjes eieren gaan leggen (VOUT1 >0 of VOUT2>0) wordt NIVAR op 2 gezet.
4.7 Vrij
levend virus
Het aantal vrij-levende virus polyeders POLYHD heeft een fractie PERPUN dat stabiel is. Dit Ievert een stabiel populatie POLMIN op. De resterende fractie neemt af met een vaste relatieve snelheid 0.71HLF en een snelheid INACT. De bespuiting met virus wordt geregelt met de centrale variabele SPRAY. Als TIME>= DSPRAY (het bespuitingsmoment), dan wordt SPRAY=1 en DONE=1. Hierdoor neemt POLYHD toe met NSPRAY. De volgende tijdstap wordt SPRAY weer op 0 gezet omdat DONE=1. 4.8 Gewas Er wordt met slechts een kenmerk van het gewas rekening gehouden, n.l. de LAI. De LAI is is gekoppelt a an de leeftijd van een cluster. Bij beplanting wordt de LAI op 1.5 gezet. De LAI neemt toe met .1 dag-1 . AIs SPRAY= 1 bij een bespuiting wordt de LAISPR, die specifiek is voor elke leeftijdsklasse, vastgelegd. Deze wordt weer in de subroutine RIRSPR gebruikt. 4.9 Output De output wordt gegeven in een TTPLOT format in de file SYSLO.dat. In de initialisatie sectie wordt een kopje naar deze file geschreven. Output wordt gedurende de simulatie loop opgeslagen in een array met een waarneming per dag. Deze arrays worden als lijsten x-y waardes weggeschreven, inclusief een kopje per lijn.
Apendix 1: Variabelenamen De naam van de variabelen is opgebouwd uit een aantal delen, waaruit de betekenis kan worden afgeleid. Het eerste deel geeft veelal de functie weer en het tweede deel het stadium waarop het betrekking heeft. De toevoeging van een extra T geeft aan dat het een array is, die de relatie tussen temperatuur en de variabele zonder deze T bevat. eerste deel naam i = h.orizontale transmissie v = verticale
transmissie
tot = totaal aantal
(# )
cds = cyclic development stage. Relatieve ontwikkeling in boxcar-train nr = snelheden binnen tussen boxcars binnen boxcar-train dur
= tijdsduur, vertraging
dvr = developmental rate, ontwikkelingssnelheid
(#It ) ( t) ( 1 It)
(-)
sd = standard deviatie in vertraging
(t)
cv = coefficient of variation van vertraging
(
mit = moult, vervelling naar stadium
(#It)
emr/em = emergence, ontpopping
(#It)
rir = relative infection rate. relatieve infectie snelheid
( 1 It)
ir = infectiesnelheid
(#It)
rmr = relative mortality rate, relatieve sterfte snelheid
( 1 It)
idr = infection death rate, stertte snelheid t.g.v. infectie
(#It)
out = snelheid verdwijnen uit systeem
(#It)
f, per = fractie /percentage
( -)
-)
tweede deel naam pat/patch = cluster L1-LS = larvale stadia pup= pop ad= adult fern
=
vrouwtje
mal/ml = mannetje dlar= vervloeide larven Counters hebben altijd de zelfde betekenis:
I = infectie klasse cluster:
0 = no infection 1 = vertical transmission 2 = male transmission
J = leeftijdsklasse cluster
8 = box nummer in boxcar-train L = Bladlaag nummer
1= onder
4 =top S = larvaal stadium, infectious stadium R = larvaal stadium, stadium dat besmet wordt
T = dag nummer Een aantal variabelenamen zijn minder eenvoudig te interpreteren en worden daarom hieronder gegeven. CDSV0112
CDS geinfecteerde eieren in infectieklasse 1 en 2
( -)
CUMP(U)
Cumulatief aantal verpoppingen
(# )
CUMVP(U)
Cumulatief aantal verpoppingen van geinfecteerde LS larven (#)
DONE
Controle variabele bij bespuiting (zie 5. 7)
( -)
DSPRAY
Dag bespuiting
( t)
FECUN
Fecunditeit gezonde vrouwtjes
FINTIM
Eindtijdstip simulatie
(# ) (t)
HATCH
Snelheid uitkomen gezonde eieren
(#It)
HLF
Halfwaardetijd vrij-levende virusdeeltjes
(t)
ILAR13115145 : Aantal geinfecteerde larven in aangegeven range
(#}
ontwikkelingsstadia IN
Aantal infectieklassen
(- )
INACT
lnactivatiesnelheid vrij-levende virusdeeltjes
(#It)
INCUS
lncubatietijd geinfecteerde larven
(t)
INTIM
Startmoment simulatie
(t)
JN
Aantal leeftijdsklasses clusters
(-)
LAI
Leaf area index.
LAISPR
LAI op moment bespuiting
LAM1 12
Gemiddeld aantal geinfecteerde eieren in legsel vrouwtje
(m 21m2) (m 21m2) (# )
uit inf. klasse 1 of 2 LARL(A)R
Aantal gezonde larven L4+L5
(# )
MEAN112
gemiddeld aantal geinfecteerde eieren in legsel vrouwtje
(# )
uit inf. klasse 1 of 2 na coorectie voor afwezigheid nul-klasse (zie 4.6) NIVAR
Aantal infectieklassen dat wordt doorgerekend (zie 4.6)
NSPRAY
Bespuitingsdichtheid virus
( -) (#1m2)
OUTTIM
Variabele die uitvoer regelt
(t)
OVIN
Ovipositiesnelheid gezonde eieren na verdeling
(#It)
over infectieklasses OVOUT
Ovipositiesnelheid gezonde eieren voor verdeling
(#It)
over infectieklasses P0112
Poisson-kans op nul in infectieklasse 1 of 2
(
-)
PERAD
Fractie geinfecteerde LS larven dat zich ontwikkeld tot adult (-)
PER PUN
Fractie stabiele vrij-levende virusdeeltjes
(- )
POLMIN
Aantal stabiele vrij-levende virusdeeltjes
(# )
POLYHD
Aantal vrij-levende virusdeeltjes
(# )
PUSH
Controle-variabele die doorschuiven leeftijdsklasses
( - )
clusters regelt (m 21m 2.t)
RLAI
Toenamesnelheid LAI
SEXR
Sexratio motten
(
SMAL(A)R
Aantal L1-L3 larven
(# )
SPRAY
Controle variabele die bespuiting regelt (zie 5.7)
(-)
TEMP
Temperatuur
(OC)
TIME
Tijd
(t)
TMLTP
Totale verpoppingssnelheid gezonde LS larven
(#It)
TMLTVP
Totale verpoppingssnelheid geinfecteerde LS larven
(#It)
VERT
Controle variabele die start verticale transmissie regelt
-)
(zie 5.6)
(- )
VOUT112
Ovipositiesnelheid geinfecteerde eieren voor verdeling over infectieklasses ( # 1t )
VOVIN
Ovipositiesnelheid geinfecteerde eieren na verdeling over infectieklasses
(#It)
************************************************************************ PROGRAM SPONPV * * * Author : Guido de Moed * * Date : 29/8/90 * Purpose: Simulating the Beet army worm - S.exigua NPV system. * * * Age and infection differences between patches are simulated * * using compound simulations. Paternal and maternal transmission * are recognized. * * ************************************************************************ PROGRAM SPONPV ************************************************************************ DECLARATIONS * * ************************************************************************ IMPLICIT REAL (A-Z) *-----NI: I patch infection classes, NJ: I patch age classes. INTEGER NI,NJ PARAMETER (NI=2,NJ=l0) *---------------------------------------------------------------------* * States * *---------------------------------------------------------------------* PAT---Number of patches in each class REAL PATCH(O:NI,NJ) HEAL--Healthy: for the moths 10 development stages are distinguished: *-----eggs, Ll's, L2's, L3's, L4's, larvae in last (5th or 6th) stage, *-----pupae, males and eggs developing in the ovaries of the females. *-----Four 'boxcars' are distinguished within most stages. In the adult *-----stages only two boxcars are used to mimick the large coefficient *-----of variation of lifespan REAL EGG(O:NI,NJ,0:4),Ll(O:NI,NJ,0:4),L2(0:NI,NJ,0:4), $ L3(0:NI,NJ,0:4),L4(0:NI,NJ,0:4),L5(0:NI,NJ,0:4), $ PUP(0:4),MAL(0:2),0VA(0:4) VERT--Boxcars REAL VPUP(0:4),VL5(0:NI,NJ,0:4),VOVA1(0:4),VOVA2(0:4), $ VMAL(0:2),VEGG(O:NI,NJ,0:4) HOR---Boxcars REAL IL1(0:NI,NJ,0:4),IL2(0:NI,NJ,0:4),IL3(0:NI,NJ,0:4), $ IL4(0:NI,NJ,0:4),IL5(0:NI,NJ,0:4) *-----Total numbers within each stage HEAL--Healthy REAL TOTEGG(O:NI,NJ),TOTL1(0:NI,NJ),TOTL2(0:NI,NJ), $ TOTL3(0:NI,NJ),TOTL4(0:NI,NJ),TOTL5(0:NI,NJ), $ TOTPUP,TOTMAL,TOTOVA VERT--Vertical transmission REAL TOTVEG(O:NI,NJ),TOTVLS(O:NI,NJ),TOTVPU,TOTVML, $ TOTVOl,TOTV02 HOR---Horizontal transmission REAL TOTIL1(0:NI,NJ),TOTIL2(0:NI,NJ),TOTIL3(0:NI,NJ), $ TOTIL4(0:NI,NJ),TOTIL5(0:NI,NJ) DEAD--Number per batch. Last index is instar number REAL DLAR(O:NI,NJ,5) *-----Variables keeping track of development within each stage HEAL--Healthy REAL CDSEGG(O:NI,NJ),CDSLl(O:NI,NJ),CDSL2(0:NI,NJ), $ CDSL3(0:NI,NJ), CDSL4(0:NI,NJ), CDSLS(O:NI,NJ), $ CDSPUP,CDSMAL,CDSOVA VERT--Vertical transmission REAL CDSVEG(O:NI,NJ),CDSVPU,CDSV01,CDSV02 HOR---Horizontal transmission REAL CDSIL1(0:NI,NJ),CDSIL2(0:NI,NJ),CDSIL3(0:NI,NJ), $ CDSIL4(0:NI,NJ),CDSIL5(0:NI,NJ)
*---------------------------------------------------------------------* * Rates * *---------------------------------------------------------------------* HEAL--Transfer rates from one stage to the next REAL OVOUT,OVIN(O:NI,NJ),HATCH(O:NI,NJ),MLTL2(0:NI,NJ), $ MLTL3(0:NI,NJ),MLTL4(0:NI,NJ),MLTL5(0:NI,NJ), $ MLTPUP(O:NI,NJ),MLTAD,EMRFEM,EMRMAL,FECUN VERT--Transfer rates from one stage to the next REAL MLTVP(O:NI,NJ),EMRVAD,VFECUl,VFECU2,EMVFEM,EMRVML,VOUTl, $ VOUT2,VOVIN(O:NI,NJ),VHATCH(O:NI,NJ) HOR---Rate of infection REAL IRLl(O:NI,NJ),IRL2(0:NI,NJ),IRL3(0:NI,NJ), $ IRL4(0:NI,NJ),IRL5(0:NI,NJ) DEAD--death rates infected stages REAL IDRLl(O:NI,NJ),IDRL2(0:NI,NJ),IDRL3(0:NI,NJ), $ IDRL4(0:NI,NJ),IDRL5(0:NI,NJ) HEAL--Net-transfer rates between boxes in boxcartrain REAL NREGG(O:NI,NJ,0:4),NRL1(0:NI,NJ,0:4),NRL2(0:NI,NJ,0:4), $ NRL3(0:NI,NJ,0:4),NRL4(0:NI,NJ,0:4),NRL5(0:NI,NJ,0:4), $ NRPUP(0:4),NRMAL(0:2),NROVA(0:4) VERT--Net-transfer rates between boxes in boxcartrain REAL NRVL5(0:NI,NJ,0:4),NRVPUP(0:4),NRVML(0:2),NRVOV1(0:4), $ NRVOV2(0:4),NRVEGG(O:NI,NJ,0:4) HOR---Net-transfer rates between boxes in boxcartrain REAL NRIL1(0:NI,NJ,0:4),NRIL2(0:NI,NJ,0:4),NRIL3(0:NI,NJ,0:4), $ NRIL4(0:NI,NJ,0:4),NRIL5(0:NI,NJ,0:4) *---------------------------------------------------------------------* * Parameters * *---------------------------------------------------------------------* GEN---timer variables REAL INTIM,FINTIM,DELT,TIME *-----Counters INTEGER I,J,B,S,T PAT---Shifting parameter INTEGER PUSH HEAL--Duration of stages as a function of temperature REAL DVREGT(8),DVRL1T(8),DVRL2T(8),DVRL3T(8),DVRL4T(8), $ DVRL5T(8),DVRPUT(8),DVRMAT(8),DVROVT,DVRPTT(8) *-----standard deviation of stage duration REAL SDEGG(8),SDL1(8),SDL2(8),SDL3(8),SDL4(8),SDL5(8), $ SDPUP(8),SDMAL,SDOVA *-----proportion female pupae in broods healthy and infected females REAL SEXR *-----relative mortality rate. REAL RMRET(6),RMRLT(4),RMRPT(6) VERT--Parameter controling vertical transmission INTEGER NIVAR,VERT HOR---relative infection rates for different stages. REAL RIRLl(O:NI,NJ),RIRL2(0:NI,NJ),RIRL3(0:NI,NJ), $ RIRL4(0:NI,NJ),RIRL5(0:NI,NJ) *-----incubation period REAL INCUBT(6) VIRUS-Spray parameters INTEGER SPRAY,DONE
CROP--leaf area index REAL LAI(NJ),LAISPR(NJ) OUTP--Output. REAL ILAR15(0:150),LARLAR(0:150),SMALAR(0:150) REAL CUMPU(0:150),CUMVPU(0:150) *********************************************************************** * INITIALIZING VARIABLES * *********************************************************************** *---------------------------------------------------------------------* * States * *---------------------------------------------------------------------* PAT---Number of patches per class DATA ((PATCH(I,J), J=1,NJ),I=O,NI) I 30*1./ HEAL--At the start of simulation, 10 reproductive female moths *-----with a fecundity of 500 eggs are in the greenhouse. No other stages *-----are present. DATA (((EGG(I,J,B) ,B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((L1(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((L2(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((L3(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((L4(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((L5(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (PUP(B),B=0,4) /5*0./ DATA (MAL(B),B=0,2) /3*0./ DATA (OVA(B),B=0,4) /5*0./ VERT--Vertical transmission. DATA (((VL5(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (VPUP(B),B=0,4) /5*0./ DATA (VMAL(B),B=0,2) /3*0./ DATA (VOVA1(B),B=0,4) /5*0./ DATA (VOVA2(B),B=0,4) /5*0./ DATA (((VEGG(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ HOR---Horizontal transmission. DATA (((IL1(I,J,B), B=0,4), DATA (((IL2(I,J,B), B=0,4), DATA (((IL3(I,J,B), B=0,4), DATA (((IL4(I,J,B), B=0,4), DATA (((IL5(I,J,B), B=0,4),
J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI)
/150*0./ /150*0./ /150*0./ /150*0./ /150*0./
DEAD--Disintegrated larvae DATA (((DLAR(I,J,S), S=1,5),J=1,NJ),I=O,NI) /150*0./ OUTP--Cummulative number of pupae DATA CUMP/0./CUMVP/0./ *-----Cyclic developmental stage, used in BOXCAR subroutines. PAT---Patches. DATA CDSPAT/0./ HEAL--Healthy. DATA ((CDSEGG(I,J), J=1,NJ),I=O,NI)/30*0./ DATA ((CDSL1(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSL2(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSL3(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSL4(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSL5(I,J), J=1,NJ),I=O,NI) /30*0./ DATA CDSPUP/0./CDSMAL/0./CDSOVA/0./ VERT--Vertical transmission. DATA CDSVPU/O./CDSVML/O./CDSV01/0./CDSV02/0./ DATA ((CDSVEG(I,J), J=1,NJ),I=O,NI) /30*0./ HOR---Horizontal transmission. DATA ((CDSIL1(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSIL2(I,J), J=1,NJ),I=O,NI) /30*0./
DATA ((CDSIL3(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSIL4(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((CDSIL5(I,J), J=1,NJ),I=O,NI) /30*0./ *---------------------------------------------------------------------* * Rates * *---------------------------------------------------------------------* HEAL--Transfer rates to next stage DATA ((MLTPUP(I,J), J=1,NJ),I=O,NI) /30*0./ DATA TMLTP/0./MLTAD/0./EMRMAL/0./ DATA FECUN/0./0VOUT/0./ DATA ((OVIN(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((HATCH(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((MLTL2(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((MLTL3(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((MLTL4(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((MLTL5(I,J), J=1,NJ),I=O,NI) /30*0./ VERT--Transfer rates to next stage DATA ((MLTVP(I,J), J=1,NJ),I=O,NI) /30*0./ DATA TMLTVP/0./EMRVAD/0./EMRVML/0./ DATA VFECU1/0./VFECU2/0./VOUT1/0./VOUT2/0./ DATA ((VOVIN(I,J), J=1,NJ),I=O,NI) /30*0./ DATA ((VHATCH(I,J), J=1,NJ),I=O,NI) /30*0./ HOR---Transfer rates to DATA ((IRL1(I,J), DATA ((IRL2(I,J), DATA ((IRL3(I,J), DATA ((IRL4(I,J), DATA ((IRL5(I,J),
next stage J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI)
DEAD--Disintegrated larvae DATA ((IDRL1(I,J), J=1,NJ),I=O,NI) DATA ((IDRL2(I,J), J=1,NJ),I=O,NI) DATA ((IDRL3(I,J), J=1,NJ),I=O,NI) DATA ((IDRL4(I,J), J=1,NJ),I=O,NI) DATA ((IDRL5(I,J), J=1,NJ),I=O,NI)
/30*0./ /30*0./ /30*0./ /30*0./ /30*0./ /30*0./ /30*0./ /30*0./ /30*0./ /30*0./
HEAL--Net-transfer rates between boxes in boxcartrain DATA (((NREGG(I,J,B), B=0,4), J=1,NJ),I=O,NI)/150*0./ DATA (((NRL1(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRL2(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRL3(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRL4(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRL5(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (NRPUP(B),B=0,4) /5*0./ DATA (NRMAL(B),B=0,2) /3*0./ DATA (NROVA(B),B=0,4) /5*0./ VERT--Net-transfer rates between boxes in boxcartrain DATA (((NRVL5(I,J,B), B=0,4), J=1,NJ),I=O,NI)/150*0./ DATA (NRVPUP(B),B=0,4) /5*0./ DATA (NRVML(B),B=0,2) /3*0./ DATA (NRVOV1(B),B=0,4) /5*0./ DATA (NRVOV2(B),B=0,4) /5*0./ DATA (((NRVEGG(I,J,B), B=0,4), J=1,NJ),I=O,NI)/150*0./ HOR---Net-transfer rates between boxes in boxcartrain DATA (((NRIL1(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRIL2(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRIL3(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRIL4(I,J,B}, B=0,4), J=1,NJ),I=O,NI) /150*0./ DATA (((NRIL5(I,J,B), B=0,4), J=1,NJ),I=O,NI) /150*0./ *---------------------------------------------------------------------* * Parameters * *---------------------------------------------------------------------*
PAT---Total residence time in patch (=egg and larval stages plus *-----3*standard deviation). DATA DVRPTT/20.,.0290,25.,.0431,30.,.0556,33.,.0682/ HEAL--Tables of development rates as a function of temperature *-----(Fye and McAda, USDA Techn. Bull. 1454, 1972). DATA DVREGT/20.,.179,25.,.345,30.,.500,33.,.556/ DATA DVRL1T/ 20.,.278,25.,.313,30.,.385,33.,.5/ DATA DVRL2T/ 20.,.345,25.,.526,30.,.667,33.,.833/ DATA DVRL3T/ 20.,.357,25.,.588,30.,.833,33.,.833/ DATA DVRL4T/ 20.,.303,25.,.476,30.,.667,33.,.769/ DATA DVRLST/ 20.,.164,25.,.244,30.,.323,33.,.4/ DATA DVRPUT/20.,.096,25.,.130,30.,.196,33.,.196/ DATA DVRMAT/20.,.065,25.,.069,30.,.067,33.,.099/ DATA DVROVT/.2/ *-----Tables of standard deviations of development times. DATA SDEGG/20., . 7 ,25., .5,30., .5,33., .1/ DATA SDL1/ 20.' .5,25., .5,30., .5,33. ,0. I DATA SDL2/ 20., .5,25., .5,30., .5,33., .5/ DATA SDL3/ 20., . 7 ,25., .5,30., .4,33., .3/ DATA SDL4/ 20., .6,25., .6,30., .6,33., .5/ DATA SOLS/ 20., .9,25., .9,30., . 7 ,33., .6/ DATA SDPUP/20. ,1.2,25. ,1.2,30., .6,33., .6/ DATA SDMAL/5./ DATA SDOVA/2./ *-----Sexratio (proportion females) SEXR=.S *-----Relative mortality rate (1/day) of eggs (RMRET), *-----larvae (RMRLT) and pupae (RMRPT). DATA RMRET/16.,.026,20.,.019, 33.,.059/ DATA RMRLT/ 20.,.0087, 33.,.020/ DATA RMRPT/ 20.,.016,30.,.032,33.,.10 / VERT--Proportion infected LS larvae developing into adults DATA PERAD/0.5/ *-----LAMB is the mean number of infected L1 larvae per batch. DATA LAM1/5.25/ DATA LAM2/2.1/ VERT--parameter controling start vertical transmission *-----when VERT=1 at the oviposition of infected eggs, NIVAR *-----(= number of active infection classes minus 1) becomes 2 DATA NIVAR/0/VERT/0/ HOR---Relative infection DATA ((RIRLl(I,J), DATA ((RIRL2(I,J), DATA ((RIRL3(I,J), DATA ((RIRL4(I,J), DATA ((RIRLS(I,J),
rate J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI) J=1,NJ),I=O,NI)
/30*0./ /30*0./ /30*0./ /30*0./ /30*0./
*-----incubation time DATA INCUBT/20.,8.,25.,6.,30.,4./ VIRUS-virus application parameters DATA DONE/0/ DATA SPRAY/0/ CALL ENTDRE('NUMBER OF POLYHEDRA PER M2',1e8,NSPRAY) CALL ENTDRE('PERCENTAGE POLYHEDRA UNEXPOSED',O.,PERPUN) POLMIN=PERPUN*NSPRAY *-----number of polyhedra in the glasshouse DATA POLYHD/0./ DATA INACT/0./
CROP--Leaf DATA DATA DATA
area index (LAI(J),J=1,NJ) /1.6,9*0./ (LAISPR(J),J=1,NJ) /100.,9*0./ RLAI/.1/
OUTP--Results are written in files OPEN(20,FILE='SYSLD.TTP',STATUS='UNKNOWN') CALL ENTDRE('NPV SPRAY ON DAY',40.,DSPRAY) *-----heading ttplot-file WRITE(20,*)'*' WRITE(20,*)'*' WRITE(20,'(1X,A,I2)')'SYSLAR5' WRITE(20,*)'X 1 14 0 100 20 10 0 0' WRITE(20,*)'time (days)' WRITE(20,*)'Y 1 8 0 10 51 0 0' WRITE(20,*)'log(number of larvae)' WRITE(20,*)'10 9' GEN---timer parameters CALL ENTDRE('START TIME',O.,INTIM) CALL ENTDRE('FINISH TIME',120.,FINTIM) CALL ENTDRE('TIME STEP',.OS,DELT) OUTTIM=1. TIME=INTIM *-----Dimensies adjustable arrays IN=NI JN=NJ ************************************************************************ * Parameters sensitivity analyses * ************************************************************************ *-----Development Beet army worm CALL ENTDRE('FDVR',1.,FDVR) CALL ENTDRE(~FRMR',1.,FRMR) *-----Development Nuclear Polyhedrosis Virus CALL ENTDRE ( ' FHLF ' , 1 • , FHLF) *-----Infection proces CALL ENTDRE('FRIRS',1.,FRIRS) CALL ENTDRE('FRIRH',1.,FRIRH) CALL ENTDRE('LAMBDA FEMALE PARENT?',LAMl,LAMl) CALL ENTDRE('LAMBDA MALE PARENT?',LAM2,LAM2) CALL ENTDRE('PROP. FECUNDITY REDUCTION DUE TO INFECTION', $ FECRED,FECRED) CALL ENTDRE('FINCUB',1.,FINCUB) CALL ENTDRE('FPERAD?',1.,FPERAD) PERAD=PERAD*FPERAD ********************************************************************* SIMULATION LOOP * *
*
10
IF (TIME.LE.FINTIM) THEN
*
IF (((VOUT1.NE.O.).OR.(VOUT2.NE.O.)).AND.VERT.EQ.O) THEN NIVAR=NI VERT=1 WRITE(*,'(12X,A)')'Vertical transmission started' END IF ********************************************************************* * INTEGRATION * ********************************************************************* DO 30 I=O,NIVAR *-------------------------------------------------------------------*
* Patches * *-------------------------------------------------------------------* *-------number of patches per class PATCH(I,l)=PATCH(I,l)+(OVIN(I,l)+VOVIN(I,l))/35.*DELT *-------cyclic development stage patches CDSPAT=CDSPAT+DVRPAT*DELT-REAL(PUSH)/REAL(NJ) *--------------------------------------------------------------------* * Healthy * *--------------------------------------------------------------------* DO 20 J=l,NJ CALL BOXC3D(l,l,DELT,OVIN(I,J),EGG,4,DVREGG,CVEGG, $ RMREGG,I,J,IN,JN,TOTEGG(I,J),CDSEGG(I,J), $ NREGG,HATCH(I,J)) CALL BOXINF(2,l,DELT,HATCH(I,J),L1,4,DVRL1,CVL1, $ RMRLAR,I,J,IN,JN,RIRLl(I,J),TOTLl(I,J), $ CDSLl(I,J),NRLl,MLTL2(I,J),IRLl(I,J)) CALL BOXINF(3,l,DELT,MLTL2(I,J),L2,4,DVRL2,CVL2, $ RMRLAR,I,J,IN,JN,RIRL2(I,J),TOTL2(I,J), $ CDSL2(I,J),NRL2,MLTL3(I,J),IRL2(I,J)) CALL BOXINF(4,l,DELT,MLTL3(I,J),L3,4,DVRL3,CVL3, $ RMRLAR,I,J,IN,JN,RIRL3(I,J),TOTL3(I,J), $ CDSL3(I,J),NRL3,MLTL4(I,J),IRL3(I,J)) CALL BOXINF(S,l,DELT,MLTL4(I,J),L4,4,DVRL4,CVL4, $ RMRLAR,I,J,IN,JN,RIRL4(I,J),TOTL4(I,J), $ CDSL4(I,J),NRL4,MLTLS(I,J),IRL4(I,J)) *---------infected LS larvae partially (=PERAD) develop into *---------infected pupae and females. CALL BOXPAR(6,l,DELT,MLTL5(I,J),L5,VL5,4, $ DVRLS,CVLS,RMRLAR,I,J,IN,JN,RIRLS(I,J), $ TOTL5(I,J),TOTVL5(I,J),CDSL5(I,J),NRL5, $ NRVLS,MLTPUP(I,J),MLTVP(I,J),IRLS(I,J),PERAD) 20 CONTINUE 30 CONTINUE *-----pupae CALL BOXCAR(7,l,DELT,TMLTP,PUP,4,DVRPUP,CVPUP,RMRP, $ TOTPUP,CDSPUP,NRPUP,MLTAD) *-----adult males CALL BOXCAR(8,1,DELT,EMRMAL,MAL,2,DVRMAL,CVMAL,O., $ TOTMAL,CDSMAL,NRMAL,MALOUT) *-----eggs in females' oviduct, healthy parents CALL BOXCAR(9,l,DELT,FECUN,OVA,4,DVROVA,CVOVA,O., $ TOTOVA,CDSOVA,NROVA,OVOUT) *----------------------------------------------------------------------* * Vertical transmission * *----------------------------------------------------------------------* *-----infected pupae CALL BOXCAR(l0,l,DELT,TMLTVP,VPUP,4,DVRPUP,CVPUP,RMRPUP, $ TOTVPU,CDSVPU,NRVPUP,EMRVAD) *-----infected adult males CALL BOXCAR(ll,l,DELT,EMRVML,VMAL,2,DVRMAL,CVMAL,O., $ TOTVML,CDSVML,NRVML,VMLOUT) *-----eggs in females' oviduct, infected female CALL BOXCAR(l2,l,DELT,VFECUl,VOVA1,4,DVROVA,CVOVA,O., $ TOTVOl,CDSVOl,NRVOVl,VOUTl) *-----eggs in females' oviduct, only male infected CALL BOXCAR(l3,l,DELT,VFECU2,VOVA2,4,DVROVA,CVOVA,O., $ TOTV02,CDSV02,NRVOV2,VOUT2) DO 50 I=O,NIVAR *-------development infected oviposited eggs DO 40 J=l,NJ CALL BOXC3D(l4,l,DELT,VOVIN(I,J),VEGG,4,DVREGG,CVEGG, $ RMREGG,I,J,IN,JN,TOTVEG(I,J),CDSVEG(I,J),NRVEGG,
VHATCH(I,J)) $ *---------------------------------------------------------------------* * Horizontal transmission *---------------------------------------------------------------------* *---------development and desintegration of infected larvae CALL BOXC3D(15,1,DELT,IRL1(I,J)+VHATCH(I,J),IL1, $ 4,INCUB,.1,0. ,I,J,IN,JN,TOTIL1(I,J),CDSIL1(I,J), $ NRIL1,IDRL1(I,J)) CALL BOXC3D(16,1,DELT,IRL2(I,J),IL2,4,INCUB,.1,0.,I,J, $ IN,JN,TOTIL2(I,J),CDSIL2(I,J),NRIL2,IDRL2(I,J)) CALL BOXC3D(17,1,DELT,IRL3(I,J),IL3,4,INCUB,.1,0.,I,J, $ IN,JN,TOTIL3(I,J),CDSIL3(I,J),NRIL3,IDRL3(I,J)) CALL BOXC3D(18,1,DELT,IRL4(I,J),IL4,4,INCUB,.1,0.,I,J, $ IN,JN,TOTIL4(I,J),CDSIL4(I,J),NRIL4,IDRL4(I,J)) CALL BOXC3D(19,1,DELT,IRL5(I,J),IL5,4,INCUB,.1,0.,I,J, $ IN,JN,TOTIL5(I,J),CDSIL5(I,J),NRIL5,IDRL5(I,J)) 40 CONTINUE 50 CONTINUE
*
*----------------------------------------------------------------------* * Free-living virus *
*----------------------------------------------------------------------*
*-----number of polyhedra on the infested crop POLYHD=POLYHD+SPRAY*NSPRAY-INACT*DELT
*-----number of disintegrated larvae in class DO 70 I=O,NIVAR DO 60 J=1,NJ DLAR(I,J,1)=DLAR(I,J,1)+IDRL1(I,J)*DELT DLAR(I,J,2)=DLAR(I,J,2)+IDRL2(I,J)*DELT DLAR(I,J,3)=DLAR(I,J,3)+IDRL3(I,J)*DELT DLAR(I,J,4)=DLAR(I,J,4)+IDRL4(I,J)*DELT DLAR(I,J,5)=DLAR(I,J,5)+IDRL5(I,J)*DELT 60 CONTINUE 70 CONTINUE *-----------------~----------------------------------------------------*
* Crop * *----------------------------------------------------------------------* *-----leaf-area index DO 75 J=1,NJ LAI(J)=LAI(J)+RLAI*DELT 75 CONTINUE
*----------------------------------------------------------------------* * Patches: shifting age classes * *----------------------------------------------------------------------* *-----after 1/J of residence time in larval stage content age *-----classes is shifted to next age class. PUSH=O IF (CDSPAT.GE.(1./NJ)) THEN PUSH=1 END IF IF (PUSH.EQ.1) THEN DO 110 I=O,NIVAR DO 90 J=NJ-1,1,-1 PATCH(I,J+1)=PATCH(I,J) DO 80 B=0,4 EGG(I,J+1,B)=EGG(I,J,B) L1(I,J+1,B)=L1(I,J,B) L2(I,J+1,B)=L2(I,J,B) L3(I,J+1,B)=L3(I,J,B) L4(I,J+1,B)=L4(I,J,B) L5(I,J+1,B)=L5(I,J,B)
VL5(I,J+1,B)=VL5(I,J,B) VEGG(I,Jt1,B)=VEGG(I,J,B)
80
IL1(I,J+1,B)=IL1(I,J,B) IL2(I,Jtl,B)=IL2(I,J,B) IL3(I,J+l,B)=IL3(I,J,B) IL4(I,J+l,B)=IL4(I,J,B) IL5(I,J+l,B)=IL5(I,J,B) CONTINUE
85
DO 85 8=1,5 DLAR(I,J+1,8)=DLAR(I,J,8) CONTINUE CD8EGG(I,J+1)=CD8EGG(I,J) CD811(I,J+1)=CD8Ll(I,J) CD812(I,J+1)=CD8L2(I,J) CD8L3(I,J+1)=CD8L3(I,J) CD814(I,J+1)=CD814(I,J) CD8L5(I,J+1)=CD8L5(I,J) CD8VEG(I,J+1)=CD8VEG(I,J)
90
CD8IL1(I,J+1)=CD8IL1(I,J) CD8IL2(I,J+1)=CD8IL2(I,J) CD8IL3(I,J+1)=CD8IL3(I,J) CD8IL4(I,J+1)=CD8IL4(I,J) CD8IL5(I,J+1)=CD8IL5(I,J) CONTINUE PATCH(I,1)=1. DO 100 B=0,4 EGG(I,1,B)==O. L1(I,1,B)=O. L2(I,1,B)=O. L3(I,1,B)=O. L4(I,1,B)=O. L5(I,1,B)=O. VL5(I,1,B)==O. VEGG(I,1,B)=O.
100
IL1(I,1,B)==O. IL2(I,1,B)==O. IL3(I,1,B)==O. IL4(I,1,B)==O. IL5(I,1,B)=O. CONTINUE
105
DO 105 8=1,5 DLAR(I,1,8)=0. CONTINUE CD8EGG(I,1)=0. CD8L1(I,1)=0. CD8L2(I,1)=0. CD8L3(I,1)=0. CD8L4(I,1)=0. CD8L5(I,1)==0. CD8VEG(I,1)=0.
110
CD8IL1(I,1)=0. CD8IL2(I,1)=0. CD8IL3(I,1)=0. CD8IL4(I,1)=0. CD8IL5(I,1)=0. CONTINUE
115
DO 115 J=NJ-1,1,-1 LAI(J+1)=LAI(J) LAISPR(J+1)=LAISPR(J) CONTINUE
*-------new plants are planted at a size of 20cm and are non-infected *-------(LAISPR=O.) LAI(1)=1.6 LAISPR(1)=0.
END IF ************************************************************************
GENERATING DRIVING VARIABLES ************************************************************************* * *----------------------------------------------------------------------* * General * *----------------------------------------------------------------------* *-----temperature is fixed TEMP=25.
*----------------------------------------------------------------------* * Patches * *----------------------------------------------------------------------* *-----development rate patches, corrected for missing outflow boxcar DVRPAT=LINEXT(DVRPTT,B,TEMP)*(NJ-0.5)/NJ *----------------------------------------------------------------------* * Healthy * *----------------------------------------------------------------------* *-----development moth: Interpolation to find development *-----times and their CV DVREGG=LINEXT(DVREGT,8,TEMP)*FDVR DVRL1=LINEXT(DVRL1T,8,TEMP)*FDVR*.85 DVRL2=LINEXT(DVRL2T,8,TEMP)*FDVR*.85 DVRL3=LINEXT(DVRL3T,8,TEMP)*FDVR*.85 DVRL4=LINEXT(DVRL4T,8,TEMP)*FDVR*.85 DVRL5=LINEXT(DVRL5T,8,TEMP)*FDVR*.85 DVRPUP=LINEXT(DVRPUT,8,TEMP)*FDVR*.85 DVRMAL=LINEXT(DVRMAT,8,TEMP)*FDVR DVROVA=DVROVT*FDVR CVEGG=LINEXT(SDEGG,B,TEMP)*DVREGG CVL1=LINEXT(SDL1,8,TEMP)*DVRL1*1.15 CVL2=LINEXT(SDL2,8,TEMP)*DVRL2*1.15 CVL3=LINEXT(SDL3,8,TEMP)*DVRL3*1.15 CVL4=LINEXT(SDL4,8,TEMP)*DVRL4*1.15 CVL5=LINEXT(SDL5,8,TEMP)*DVRL5*1.15 CVPUP=LINEXT(SDPUP,8,TEMP)*DVRPUP*1.15 CVMAL=SDMAL*DVRMAL CVOVA=SDOVA*DVROVA *-----relative mortality is temperature dependent RMREGG=LINEXT(RMRET,6,TEMP)*FRMR RMRLAR=LINEXT(RMRLT,4,TEMP)*FRMR RMRPUP=LINEXT(RMRPT,6,TEMP)*FRMR
*---------------------------------------------------------------------* Crop * *---------------------------------------------------------------------* IF (SPRAY.EQ.1) THEN *
118
DO 118 J=1,NJ LAISPR(J)=LAI(J) CONTINUE END IF
*---------------------------------------------------------------------*
* Horizontal transmission * *---------------------------------------------------------------------* *-----'development rate' of infected larvae depends on temperature INCUB=(1/LINEXT(INCUBT,6,TEMP))*FINCUB DO 130 J=1,NJ *-------RIR values using-exponential model CALL RIRSPR(1,POLYHD,LAI(J),LAISPR(J),RIRL1S) CALL RIRSPR(2,POLYHD,LAI(J),LAISPR(J),RIRL2S) CALL RIRSPR(3,POLYHD,LAI(J),LAISPR(J),RIRL3S) CALL RIRSPR(4,POLYHD,LAI(J),LAISPR(J),RIRL4S) CALL RIRSPR(5,POLYHD,LAI(J),LAISPR(J),RIRL5S) DO 120 CALL CALL CALL CALL CALL
I=O,NIVAR RIRHOR(1,DLAR,I,J,IN,JN,PATCH(I,J),LAI(J),RIRL1H) RIRHOR(2,DLAR,I,J,IN,JN,PATCH(I,J),LAI(J),RIRL2H) RIRHOR(3,DLAR,I,J,IN,JN,PATCH(I,J),LAI(J),RIRL3H) RIRHOR(4,DLAR,I,J,IN,JN,PATCH(I,J),LAI(J),RIRL4H) RIRHOR(5,DLAR,I,J,IN,JN,PATCH(I,J),LAI(J),RIRL5H)
RIRL1(I,J)=RIRL1S*FRIRS+RIRL1H*FRIRH RIRL2(I,J)=RIRL2S*FRIRS+RIRL2H*FRIRH RIRL3(I,J)=RIRL3S*FRIRS+RIRL3H*FRIRH RIRL4(I,J)=RIRL4S*FRIRS+RIRL4H*FRIRH RIRL5(I,J)=RIRL5S*FRIRS+RIRL5H*FRIRH 120 130
CONTINUE CONTINUE
************************************************************************ RATE CALCULATIONS (TASK=2) * * ************************************************************************ *----------------------------------------------------------------------* * Healthy * *----------------------------------------------------------------------* *-----pupation rates are summarized TMLTP=O. TMLTVP=O. DO 150 I=O,NIVAR DO 140 J=1,NJ CALL BOXC3D(1,2,DELT,OVIN(I,J),EGG,4,DVREGG,CVEGG, $ RMREGG,I,J,IN,JN,TOTEGG(I,J),CDSEGG(I,J), $ NREGG,HATCH(I,J)) CALL BOXINF(2,2,DELT,HATCH(I,J),L1,4,DVRL1,CVL1, $ RMRLAR,I,J,IN,JN,RIRL1(I,J),TOTL1(I,J), $ CDSLl(I,J),NRL1,MLTL2(I,J),IRLl(I,J)} CALL BOXINF(3,2,DELT,MLTL2(I,J),L2,4,DVRL2,CVL2, RMRLAR,I,J,IN,JN,RIRL2(I,J),TOTL2(I,J), $ $ CDSL2(I,J),NRL2,MLTL3(I,J),IRL2(I,J)) CALL BOXINF(4,2,DELT,MLTL3(I,J),L3,4,DVRL3,CVL3, $ RMRLAR,I,J,IN,JN,RIRL3(I,J},TOTL3(I,J), $ CDSL3(I,J),NRL3,MLTL4(I,J),IRL3(I,J)) CALL BOXINF(5,2,DELT,MLTL4(I,J},L4,4,DVRL4,CVL4, $ RMRLAR,I,J,IN,JN,RIRL4(I,J),TOTL4(I,J), $ CDSL4(I,J),NRL4,MLTL5(I,J),IRL4(I,J)) CALL BOXPAR(6,2,DELT,MLTL5(I,J},L5,VL5,4,DVRL5, $ CVL5,RMRLAR,I,J,IN,JN,RIRL5(I,J),TOTL5(I,J), $ TOTVL5(I,J),CDSL5(I,J),NRL5,NRVL5,MLTPUP(I,J), $ MLTVP(I,J),IRL5(I,J),PERAD) TMLTP=TMLTP+MLTPUP(I,J) TMLTVP=TMLTVP+MLTVP(I,J) 140 150
CONTINUE CONTINUE
*-----pupae CALL BOXCAR(7,2,DELT,TMLTP,PUP,4,DVRPUP,CVPUP,RMRPUP, $ TOTPUP,CDSPUP,NRPUP,MLTAD) *-----adult males CALL BOXCAR(8,2,DELT,EMRMAL,MAL,2,DVRMAL,CVMAL,O., $ TOTMAL,CDSMAL,NRMAL,MALOUT) *-----emerging adults are recalculated to number of eggs in adult oviducts. EMRFEM=MLTAD*SEXR EMRMAL=MLTAD*(1.-SEXR) FECUN=500.*EMRFEM*(TOTMAL/(TOTMAL+TOTVML+1.)) *-----eggs in females' oviduct, healthy male CALL BOXCAR(9,2,DELT,FECUN,OVA,4,DVROVA,CVOVA,O., $ TOTOVA,CDSOVA,NROVA,OVOUT) *----------------------------------------------------------------------* * Vertical transmission * *----------------------------------------------------------------------* *-----development of infected pupae, females and eggs *-----in females' oviduct. Infected L5 developing into *-----pupae are delt with in previous section. EMVFEM=SEXR*EMRVAD EMRVML=(1.-SEXR)*EMRVAD VFECU1=500.*EMVFEM*(1.-FECRED) VFECU2=500.*EMRFEM*(TOTVML/(TOTMAL+TOTVML+1.))*(1.-FECRED) *-----infected adult pupae and males CALL BOXCAR(10,2,DELT,TMLTVP,VPUP,4,DVRPUP,CVPUP,RMRPUP, $ TOTVPU,CDSVPU,NRVPUP,EMRVAD) CALL BOXCAR(11,2,DELT,EMRVML,VMAL,2,DVRMAL,CVMAL,O., $ TOTVML,CDSVML,NRVML,VMLOUT) *-----eggs in females' oviduct, infected female CALL BOXCAR(12,2,DELT,VFECU1,VOVA1,4,DVROVA,CVOVA,O., TOTV01,CDSV01,NRVOV1,VOUT1) ,$ *-----eggs in females' oviduct, only male infected CALL BOXCAR(13,2,DELT,VFECU2,VOVA2,4,DVROVA,CVOVA,O., TOTV02,CDSV02,NRVOV2,VOUT2) $ *-----Number of uninfected OVOUT and infected eggs VOUT1 and VOUT2 *-----are distributed over infection classes. *-----The number of eggs are distributed over a fraction infected (I/35.) *-----and non-infected eggs ((35-I)/35). P01=EXP(-LAM1) P02=EXP(-LAM2) OVIN(0,1)=0VOUT+P02*VOUT1+P02*VOUT2 VOVIN(0,1)=0. MEAN1=LAM1/(MAX(.001,(1.-P01))) OVIN(1,1)=VOUT1*(1.-P01)*(35.-MEAN1)/35. VOVIN(1,1)=VOUT1*(1.-P01)*MEAN1/35. MEAN2=LAM2/(MAX(.001,(1.-P02))) OVIN(2,1)=VOUT2*(1.-P02)*(35.-MEAN2)/35. VOVIN(2,1)=VOUT2*(1.-P02)*MEAN2/35. DO 170 I=O,NIVAR *-------development infected oviposited eggs DO 160 J=1,NJ CALL BOXC3D(14,2,DELT,VOVIN(I,J),VEGG,4,DVREGG,CVEGG, $ RMREGG,I,J,IN,JN,TOTVEG(I,J),CDSVEG(I,J),NRVEGG, $ VHATCH(I,J)) *---------------------------------------------------------------------* * Horizontal transmission *
*---------------------------------------------------------------------* *---------development and desintegration of infected larvae CALL BOXC3D(15,2,DELT,IRL1(I,J)+VHATCH(I,J),IL1, $ 4,INCUB,.l,O.,I,J,IN,JN,TOTIL1(I,J), $ CDSILl(I,J),NRILl,IDRLl(I,J)) CALL BOXC3D(16,2,DELT,IRL2(I,J),IL2,4,INCUB,.l,O.,I,J, $ IN, JN, TOTIL2 (I, J) , CDS IL2 (I , J) , NRIL2, IDRL2 (I , J) ) CALL BOXC 3D ( 17 ., 2 , DELT, IRL3 (I , J) , IL3 , 4 , INCUB, .1, 0 . , I, J, $ IN,JN,TOTIL3(I,J),CDSIL3(I,J),NRIL3,IDRL3(I,J)) CALL BOXC3D(18,2,DELT,IRL4(I,J),IL4,4,INCUB,.1,0.,I,J, $ IN,JN,TOTIL4(I,J),CbSIL4(I,J),NRIL4,IDRL4(I,J)) CALL BOXC3D(19,2,DELT,IRL5(I,J),IL5,4,INCUB,.l,O.,I,J, $ IN,JN,TOTIL5(I,J),CDSIL5(I,J),NRIL5,IDRL5(I,J)) 160 CONTINUE 170 CONTINUE *----------------------------------------------------------------------* * Free-living virus * *----------------------------------------------------------------------* *-----spray IF(TIME.GE.DSPRAY.AND.DONE.NE.l)THEN SPRAY=! DONE=l ELSE SPRAY=O END IF *-----inactivation, corresponding to a halflife of 1 day HLF=l.*FHLF INACT=MAX(O.,(POLYHD-POLMIN)*(0.7/HLF)) ************************************************************************ OUTPUT DURING SIMULATION * * ************************************************************************ CUMP =CUMP + TMLTP *DELT CUMVP=CUMVP + TMLTVP*DELT
185 190 200
IF (OUTTIM.GE.1.) THEN OUTTIM=OUTTIM-1. SMALR=O. LARLR=O. ILAR13=0. ILAR45=0. DL=O. PAT=O. DO 200 I=O,NI DO 190 J=1,NJ SMALR =SMALR+TOTL1(I,J)+TOTL2(I,J)+TOTL3(I,J) LARLR =LARLR+TOTL4(I,J)+TOTL5(I,J) ILAR13=ILAR13+TOTIL1(I,J)+TOTIL2(I,J)+TOTIL3(I,J) ILAR45=ILAR45+TOTIL4(I,J)+TOTIL5(I,J)+TOTVL5(I,J) DO 185 S=1,5 DL =DL+DLAR(I,J,S) CONTINUE PAT =PAT+PATCH(I,J) CONTINUE CONTINUE T=NINT(TIME) SMALAR(T)=MIN(15.,LOG10(SMALR+1.)) LARLAR(T)=MIN(15.,LOG10(LARLR+1.)) ILAR15(T)=MIN(15.,LOG10(ILAR13+ILAR45+1.)) CUMPU(T) =CUMP CUMVPU(T)=CUMVP
*
counter on screen (for VAX) WRITE(*,'(1X,2A)')CHAR(27),'[2A' WRITE(*,'(1X,A,F8.2)')'TIME=',TIME
END IF *-----time updating TIME=TIME+DELT OUTTIM=OUTTIM+DELT *-----jumpback to time loop control GOTO 10 END IF
*
*
END OF SIMULATION LOOP ·* * ************************************************************************ *-----data are written to outputfile in ttplot format WRITE(20,*)'*' WRITE(20,*)'1 1 0' WRITE(20,*)'L1-L3' DO 1001 T=O,FINTIM-1.,1 WRITE(20,'(2X,I3,F6.2)')T,SMALAR(T) 1001 CONTINUE
1002
WRITE(20,*)'*' WRITE(20,*)'1 2 0' WRITE(20,*)'L4-L5' DO 1002 T=O,FINTIM-1.,1 WRITE(20,'(2X,I3,F6.2)')T,LARLAR(T) CONTINUE
1003
WRITE(20,*)'*' WRITE(20,*)'1 3 0' WRITE(20,*)'Infected larvae' DO 1003 T=DSPRAY,FINTIM-1.,1 WRITE(20,'(2X,I3,F6.2)')T,ILAR15(T) CONTINUE
1006
WRITE(20,*)'*' WRITE(20,*)'0 6 0' WRITE(20,*)'Cumm. I of pupae' DO 1006 T=O,FINTIM-1.,1 WRITE(20,'(2X,I3,F15.2)')T,CUMPU(T) CONTINUE
1007
WRITE(20,*)'*' WRITE(20,*)'0 7 0' WRITE(20,*)'Cumm. I of infected pupae' DO 1007 T=O,FINTIM-1.,1 WRITE(20,'(2X,I3,F15.2)')T,CUMVPU(T) CONTINUE STOP 'End of simulation' END
**----------------------------------------------------------------------* SUBROUTINE BOXCAR * * Author: Guido de Moed * * * Date: 13/11/89 * Purpose: mimicking delay, development and dispersion during develop- * * ment. This subroutine is a version of the (fractional ) * *BOXCAR subroutine by Goudriaan and van Roermund (1987). *
** FORMAL *
name
PARAMETERS: (I=input,O=output,C=control,IN=init,T=time) type meaning units class
* * * *
TASK COUNT DELT INFL A
I4 I4 R4 R4 R4
*
* ** N * DVR ** CV * * RMR * ATOT * CDS * * OUTFL * MORR
I4 R4 R4 R4 R4 R4 R4 R4
* *F R4 * * I4 *K * * Execution
-------
1: integrating 2: calculating rates counter identifying the boxcar call time step of integration (same unit as time) d rate of inflow into the first boxcar #/d array containing numbers in different development classes I last element of array A development rate = fraction of total development completed per unit time 1/d coefficient of variation (proportion) of development period d relative mortality rate 1/d total number in the boxcar train I cyclic development stage. keeps track of development and triggers shifting. rate of outflow from the last boxcar #/d array containing mortality rates of different development classes #/d FRACTION F of DELT at which a FRACTION F of the contents of boxcars 1 through N-1 is shifted to the next boxcar Loop counter
I I
T I
I/O I I I I
0
I/0 0
I/0
is stopped when DELT exceeds F/(N*DVR)
** *
*
* * * * * * * * * * *
* * * *
*
* * *
*
* * *
*
*----------------------------------------------------------------------* SUBROUTINE BOXCAR(COUNT,TASK,DELT,INFL,A,N,DVR,CV,RMR, ATOT,CDS,DA,OUTFL) IMPLICIT REAL (A-Z) INTEGER COUNT,N,K,TASK REAL A(O:N) , DA(O:N)
$
IF (TASK.EQ.1) THEN
*---------------------------------------------------------------------* * Calculation of the shift-fraction F * *---------------------------------------------------------------------* CALL FRACT(COUNT,DVR,CV,N,DELT,F)
*---------------------------------------------------------------------* * Calculation of the states (integrals) * *---------------------------------------------------------------------* *-------amount in each boxcar (A), after mortality flow, inflow and *-------outflow in respectively A(O) and A(N). A(O) = A(O) - DA(O)*DELT + INFL*DELT DO 20 K=1,N-1 A(K)=A(K) - DA(K)*DELT 20 CONTINUE A(N)=A(N) -DA(N)*DELT-OUTFL*DELT *-------development CDS=CDS+DELT*DVR *-------Shifting of boxcar (A), after shift. IF (CDS.GE.F/N) THEN CALL SHIFT(N,F,A) CDS=CDS-F/N END IF
*-------Total number in boxcar train (ATOT) CALL SUMlD(N,A,ATOT) END IF IF (TASK.EQ.2) THEN
*---------------------------------------------------------------------Calculation of the rates
.*
*-----------------~----------------------------------------------------
*-------mortality rate (DA) and total mortality flow (MORFL) DA(O) = RMR*A(O) DO 10 K=l,N DA(K) =RMR*A(K) 10 CONTINUE *-------the rate of outflow (OUTFL) is calculated CN =A(N)/(1./N-CDS) OUTFL =MIN (DVR * CN , (A(N)-DA(N)*DELT)/DELT) END IF RETURN END
************************************************************************ * SUBROUTINE BOXC3D * * * Author: Guido de Moed * * Date: Jan 8, 1989 * Purpose: Idem BOXCAR subroutine. This version of BOXCAR reads state * * variable A from a 3-dimensional array. *
*
* ADDITIONAL FORMAL PARAMETERS type meaning * name
*
* units class * * * R4 3-dim. array containing numbers in I/0 * I *A different patch infection class, patch * * age class and developmental stage * * Coordinates of boxcar-train in A I4 I * I,J * ************************************************************************ SUBROUTINE BOXC3D(COUNT,TASK,DELT,INFL,A,N,DVR,CV,RMR,I,J,NI,NJ, $ ATOT,CDS,DA,OUTFL) IMPLICIT REAL (A-Z) INTEGER COUNT,N,I,J,K,TASK REAL A(O:NI,NJ,O:N), DA(O:NI,NJ,O:N)
-------
IF (TASK.EQ.l) THEN
*---------------------------------------------------------------------* Calculation of the shift-fraction F *---------------------------------------------------------------------CALL FRACT(COUNT,DVR,CV,N,DELT,F) *---------------------------------------------------------------------Calculation of states (integrals) *---------------------------------------------------------------------*-------amount in each boxcar (A), after mortality flow, inflow and *
*-------outflow in respectively A(O) and A(N). A(I,J,O) = A(I,J,O) - DA(I,J,O)*DELT + INFL*DELT DO 20 K=l,N-1 A(I,J,K)=A(I,J,K) - DA(I,J,K)*DELT 20 CONTINUE A(I,J,N)=A(I,J,N) -DA(I,J,N)*DELT-OUTFL*DELT *-------development CDS=CDS+DELT*DVR *-------Shifting of boxcar (A), after shift. IF (CDS.GE.F/N) THEN CALL SHIFT3D(N,F,I,J,NI,NJ,A) CDS=CDS-F/N END IF
*-------Total number in boxcar train (ATOT) CALL SUM3D(N,A,I,J,NI,NJ,ATOT) END IF IF (TASK.EQ.2) THEN
*---------------------------------------------------------------------* Calculation of the rates *---------------------------------------------------------------------*-------mortality rate (DA) DA(I,J,O) = RMR*A(I,J,O) DO 10 K=1,N DA(I,J,K) =RMR*A(I,J,K) CONTINUE
10
*-------the rate of outflow (OUTFL) is calculated CN A(I,J,N)/(1./N-CDS) OUTFL =MIN (DVR * CN , (A(I,J,N)-DA(I,J,N)*DELT)/DELT) END IF RETURN END *----------------------------------------------------------------------* * SUBROUTINE BOXINF * * Author: Guido de Moed * * Date: Nov 13, 1989 * Purpose: This version of the BOXCAR subroutine is used to mimick * * development and mortality of healthy larvae and the rate of infection* *with NPV's. *
**
** ADDITIONAL
FORMAL PARAMETERS type meaning
* name
* * * *
RIR
R4
INFR
R4
*
Relative infection rate individuals in boxcar A. Infection rate, cummulative over all developmental classes
units
class *
1/T
I
#/T
0
* * ** *
*----------------------------------------------------------------------* SUBROUTINE BOXINF(COUNT,TASK,DELT,INFL,A,N,DVR,CV,RMR,I,J,NI,NJ, RIR,ATOT,CDS,DA,OUTFL,INFR)
$
IMPLICIT REAL (A-Z) INTEGER COUNT,N,I,J,K,TASK REAL A(O:NI,NJ,O:N),DA(O:NI,NJ,O:N) IF (TASK.EQ.1) THEN
*---------------------------------------------------------------------* * Calculation of the shift-fraction F * *---------------------------------------------------------------------* CALL FRACT(COUNT,DVR,CV,N,DELT,F) *---------------------------------------------------------------------* Calculation of states (integrals) *---------------------------------------------------------------------*-------amount in each boxcar (A), after mortality flow and inflow and *-------outflow in respectively A(O) and A(N). A(I,J,O) = A(I,J,O) - DA(I,J,O)*DELT + INFL*DELT DO 20 K=1,N-1 A(I,J,K)=A(I,J,K) - DA(I,J,K)*DELT 20 CONTINUE A(I,J,N)=A(I,J,N) -DA(I,J,N)*DELT-OUTFL*DELT *-------development CDS=CDS+DELT*DVR *-------Shifting of boxcar (A), after shift.
IF (CDS.GE.F/N) THEN CALL SHIFT3D(N,F,I,J,NI,NJ,A) CDS=CDS-F/N END IF *-------Total number in boxcar train (ATOT) CALL SUM3D(N,A,I,J,NI,NJ,ATOT) END IF IF (TASK.EQ.2) THEN
*---------------------------------------------------------------------Calculation of the rates *---------------------------------------------------------------------*-------mortality and infection rate (DA) *
DA(I,J,O) = RMR*A(I,J,O) + RIR*A(I,J,O) INFR = RIR*A(I,J,O) DO 10 K=1,N DA(I,J,K) = RMR*A(I,J,K) + RIR*A(I,J,K) INFR = INFR + RIR*A(I,J,K) CONTINUE
10
*-------the rate of outflow (OUTFL) is calculated CN =A(I,J,N)/(1./N-CDS) OUTFL =MIN (DVR * CN, (A(I,J,N)-DA(I,J,N)*DELT)/DELT) END IF RETURN END *----------------------------------------------------------------------* * SUBROUTINE BOXPAR * * * AUTHOR: Guido de Moed Nov 13, 1989 * * Date: * * Purpose: This version of the BOXCAR subroutine is used to mimick * development and mortality of healthy (A) and infected (B) L5 * * larvae, the later partially developing into infected adults. * * * A and B show the same developmental rate, dispersion and * mortality. Healthy individuals A are infected with a * * relative rate RIR. A fraction 1-P of the infected larvae are * * lethally infected with a rate INFR and die before reaching * * the pupal stage. A fraction P will enter stage B, without * changing its relative development * * * * * ADDITIONAL FORMAL PARAMETERS * units class * type meaning * name * * * A,B R4 Array containing the number of healthy (A) I/0 * I * and infected {B) individuals in different * * develpomental classes * 0 * BTOT R4 Total numbers in boxcar B I * 0 * OUTB R4 Rate of outflow from last boxcar 1/d * I * P R4 Fraction of total infection rate flowing * * to B *
*----------------------------------------------------------------------* SUBROUTINE BOXPAR{COUNT,TASK,DELT,INFL,A,B,N,DVR,CV,RMR,I,J, $
NI,NJ,RIR,ATOT,BTOT,CDS,DA,DB,OUTA,OUTB,INFR,P)
IMPLICIT REAL (A-Z) INTEGER COUNT,N,I,J,K,TASK REAL A(O:NI,NJ,O:N),B(O:NI,NJ,O:N) REAL DA(O:NI,NJ,O:N),DB(O:NI,NJ,O:N) IF (TASK.EQ.1) THEN
*---------------------------------------------------------------------* Calculation of the shift-fraction F *----------------------------------------------------------------------
CALL FRACT(COUNT,DVR,CV,N,DELT,F)
*---------------------------------------------------------------------* Calculation of states (integrals) *---------------------------------------------------------------------*-------amount in each boxcar (A), after mortality flow and inflow and *-------outflow in respectively A(O) and A(N). A(I,J,O) = A(I,J,O) - DA(I,J,O)*DELT + INFL*DELT B(I,J,O) = B(I,J,O) - DB(I,J,O)*DELT DO 20 K=1,N-1 A(I,J,K) = A(I,J,K) - DA(I,J,K)*DELT B(I,J,K) = B(I,J,K) - DB(I,J,K)*DELT 20 CONTINUE A(I,J,N) DA(I,J,N)*DELT OUTA*DELT A(I,J,N) DB(I,J,N)*DELT B(I,J,N) OUTB*DELT B(I,J,N) *-------development CDS=CDS+DELT*DVR *-------Shifting of boxcar (A), after shift. IF (CDS.GE.F/N) THEN CALL SHIFT3D(N,F,I,J,NI,NJ,A) CALL SHIFT3D(N,F,I,J,NI,NJ,B) CDS=CDS-F/N END IF *-------Total number in boxcar train (ATOT,BTOT) CALL SUM3D(N,A,I,J,NI,NJ,ATOT) CALL SUM3D(N,B,I,J,NI,NJ,BTOT) END IF IF (TASK.EQ.2) THEN *---------------------------------------------------------------------* * Calculation of the shift-fraction F *
*---------------------------------------------------------------------* *-------mortality rate (DA,DB) DA(I,J,O) = RMR*A(I,J,O) + RIR*A(I,J,O) DB(I,J,O) = RMR*B(I,J,O) - RIR*P*A(I,J,O) INFR = RIR*A(I,J,0)*(1-P)
10
DO 10 K=1,N DA(I,J,K) = RMR*A(I,J,K) + RIR*A(I,J,K) DB(I,J,K) = RMR*B(I,J,K) - RIR*A(I,J,K)* P INFR = INFR + RIR*A(I,J,K)*(1-P) CONTINUE
*-------the rate of outflow (OUTA,OUTB) is calculated CNA = A(I,J,N)/(1./N-CDS) OUTA =MIN (DVR*CNA , (A(I,J,N)-DA(I,J,N)*DELT)/DELT) CNB = B(I,J,N)/(1./N-CDS) OUTB =MIN (DVR*CNB , (B(I,J,N)-DB(I,J,N)*DELT)/DELT) END IF RETURN END *********************************************************************** SUBROUTINE FRACT(COUNT,DVR,CV,N,DELT,F) *********************************************************************** IMPLICIT REAL (A-Z) INTEGER N,COUNT F = 1.-N*CV*CV IF(DELT.GT.F/(N*DVR+1.0E-10)) THEN WRITE(*,'(A/A,I4)')' DELT or number of boxcars too large for', $ 'mimicking variation in BOXCAR',COUNT STOP
END IF RETURN END ************************************************************************ SUBROUTINE SHIFT(N,F,A) ************************************************************************ IMPLICIT REAL(A-Z) INTEGER K,N A(O:N) REAL
20
A(N) = A(N) + A(N-1)*F DO 20 K=N-1,2,-1 A(K)=A(K)*(1.-F) + A(K-1)*F CONTINUE A(1)=A(1)*(1-F) + A(O) A(O)=O. RETURN END
************************************************************************ SUBROUTINE SHIFT3D(N,F,I,J,NI,NJ,A) ************************************************************************ IMPLICIT REAL(A-Z) INTEGER K,I,J,N REAL A(O:NI,NJ,O:N)
20
A(I,J,N) A(I,J,N) + A(I,J,N-1)*F DO 20 K=N-1,2,-1 A(I,J,K)=A(I,J,K)*(1.-F) + A(I,J,K-1)*F CONTINUE A(I,J,1)=A(I,J,1)*(1-F) + A(I,J,O) A(I,J,O)=O. RETURN END
************************************************************************** SUBROUTINE SUM1D(N,A,ATOT) ************************************************************************** IMPLICIT REAL(A-Z) INTEGER K,N REAL A(O:N) *-----Total number in boxcar train (ATOT) ATOT=A(O) DO 10 K=1,N ATOT=ATOT + A(K) 10 CONTINUE RETURN END ************************************************************************** SUBROUTINE SUM3D(N,A,I,J,NI,NJ,ATOT) ************************************************************************** IMPLICIT REAL(A-Z) INTEGER I,J,K,N REAL A(O:NI,NJ,O:N) *-----Total number in boxcar train (ATOT) ATOT=A(I,J,O) DO 10 K=1,N ATOT=ATOT + A(I,J,K) 10 CONTINUE
RETURN END ******************************************************************* SUBROUTINE RIRSPR(R,POLYHD,LAI,LAISPR,RIRS) ******************************************************************* IMPLICIT REAL (A-Z) INTEGER L,R REAL T(4,5),CP(5) *-----verdeling stadia overbladlagen DATA TI0.,0.5 ,0.25,0.25, $ 0.,0.5 ,0.25,0.25, $ 0.,0.17,0.33,0.5, $ 0.,0.17,0.33,0.5, $ 0.,0.17,0.33,0.51 *-----uitvangconstante DATA KI0.41 *-----consumptie*Pinf DATA CPI3.36E-7, 5.53E-6, 2.58E-7, 2.76E-7, 1.52E-BI DATA NLLI4.1 *-----Fractie virus in randzone (met homogene verticale verdeling) DATA FRAND I . 51
VT=O. DO 10 L=1,4 *---------verschuiving uitvangcurve door groei gewas DLAI=MAX(O.,(LAI-LAISPR)) *---------flux bovenzijde laag L LIN=MIN(LAI,LAI*LINLL+DLAI) FIN=EXP(-(LAI-LIN)*K) *---------flux onderzijde laag L LOUT=MIN(LAI,LAI*(L-1)INLL+DLAI) FOUT=EXP(-(LAI-LOUT)*K) *---------virus in laag L via uitvangcurve VUITV=POLYHD*(FIN-FOUT)*(1.-FRAND) *---------virus in laag L via homogene verdeling randen VHOM=(POLYHD*(LIN-LOUT)IMAX(.125,LAISPR))*FRAND VT=VT+(VUITV+VHOM)*T(L,R) 10 CONTINUE *-----deeltjes per laag I opp. per laag is dichtheid POLDEN=VTI(LAIINLL) RIRS=MIN(1.5,CP(R)*POLDEN) RETURN END ********************************************************************* SUBROUTINE RIRHOR(R,DLAR,I,J,NI,NJ,PATCH,LAI,RIRH) ********************************************************************* IMPLICIT REAL (A-Z) INTEGER L,S,R,I,J REAL T(4,5),P(5),LPD(5),DLAR(O:NI,NJ,5) *-----fraction of time in leaf layer for each stage DATA TI0.,0.5 ,0.25,0.25, $ 0 . ' 0 . 5 ' 0 . 25 ' 0 • 25 ' $ 0.,0.17,0.33,0.5, $ 0.,0.17,0.33,0.5, $ 0.,0.17,0.33,0.51 *-----number of plants in range DATA P 15. , 10. , 12. , 15. , 22.1 *-----number of leaves visited per day DATA LPDI1.,1.,1.,3.,5.1 *-----number of leaf layers DATA NLLI4.1 *-----number of leaves per plant
LPP=LAI*4.5 RIRB=O. DO 20 L=1,4 RIRA=O. DO 10 S=1,5 *-------------fraction horizontal overlap range stage R by stage S O=MIN(1.,P(S)/P(R)) *-------------mean number of dead larvae per patch D=DLAR(I,J,S)/PATCH *-------------fraction leaves infected by S in leaf layer L F=1.-EXP(-T(L,S)*D/(P(S)*LPP/NLL)) RIRA=RIRA+LOG(1.-F*O) 10 CONTINUE RIRB=RIRB+T(L,R)*RIRA 20 CONTINUE RIRH=MIN(1.5,-LPD(R)*RIRB) RETURN END *------------------------------------------------------------------------* * REAL FUNCTION LINEXT * * Purpose: This is a linear interpolation function. * * Author: Wopke van der Werf. This function is largely equal to * * function LINT by Daniel van Kraalingen. It differs from LINT by * * allowing extrapolations * * (I=input,O=output,C=control,IN=init,T=time) FORMAL PARAMETERS: * * name type meaning units class * * * ** INTERP R4 function name, result of the interpolation 0 * I * TABLE R4 A one-dimensional array with paired * data: x,y,x,y, etc. * * I * ILTAB I4 The number of elements of the array * TABLE * * I * R4 The value at which interpolation should * X take place * * * ** FATAL ERROR CHECKS (execution terminated, message): * * TABLE(!) < TABLE(I-2) , for I odd * * ILTAB odd *
*
*
* A message is written on screen when extrapolation occurs
*
* No other SUBROUTINES and FUNCTIONS are called * No FILE's are used (error message with WRITE(*, .•. )...
*
* * * *
*------------------------------------------------------------------------* REAL FUNCTION LINEXT(TABLE,ILTAB,X) IMPLICIT REAL (A-Z) INTEGER I, IUP, ILTAB DIMENSION TABLE(ILTAB)
*
*
check on odd ILTAB IF (MOD(ILTAB,2).NE.O) THEN WRITE (*,' (A,I4/ ,A)') $ 'ERROR in function LINT: ILTAB=',ILTAB, $ 'ILTAB must be even I' STOP END IF DO 10 I=3,ILTAB-1,2 check on ascending order of X-values in function IF (TABLE(I).LE.TABLE(I-2)) THEN WRITE (*, '(A,I4/ ,A,I4,A/ ,A)') $ 'X-coordinates not in ascending order at element',!, $ 'LINT-function contains',ILTAB,' points', $ 'Run deleted!'
STOP END IF CONTINUE
10 *
extrapolation below given range IF (X.LT.TABLE(1)) THEN LINEXT=TABLE(2)+(TABLE(4)-TABLE(2))/(TABLE(3)-TABLE(1))* (X~TABLE(1))
$
c c *
c c * * 20
$
WRITE (*,'(A)') 'Extrapolation below defined region!!'
extrapolation above given range ELSE IF (X.GT.TABLE(ILTAB-1)) THEN LINEXT=TABLE(ILTAB-2)+(X-TABLE(ILTAB-3))*(TABLE(ILTAB)$ TABLE(ILTAB-2))*(TABLE(ILTAB-1)-TABLE(ILTAB-3)) WRITE (*,'(A)') $ 'Extrapolation above defined region!!' Interpolation ELSE determine place of interpolation IUP = 0 I=1 IF (IUP.EQ.O) THEN I=I+2 IF (TABLE(I).GE.X) THEN IUP = I END IF GOTO 20 END IF LINEXT TABLE(IUP-1)+(X-TABLE(IUP-2))*(TABLE(IUP+1)$ TABLE(IUP-1))/(TABLE(IUP)-TABLE(IUP-2)) END IF RETURN END
********************************************************************* SUBROUTINE ENTDRE (QUEST,XDEF,X) ********************************************************************* * Interactive entry of a REAL number with a default. Writes the * text QUEST on screen as a "question" returns entered number. * * *
QUEST - character string for instance 'waarde van P' (I) XDEF - default value assumed when is given (I) X - entered REAL number (0)
* Author: Kees Rappoldt * Date: August 1987, revised March 1988 ******************************************************************** IMPLICIT REAL (A-Z) INTEGER I,IDEC,IDIGIT,IL,INDEX,INT,IT,LEN,LQ,LQl CHARACTER QUEST*(*),FORM*8,HULP*30,INPUT*20,VRAAG*50 * number of significant digits PARAMETER (IDIGIT=4) *
get local copy of dafault value XDLOC = XDEF
*
write default value to string according to algorithm of LABEL IF (XDLOC.NE.O) THEN LABS = LOGlO (ABS(XDLOC)) number of decimal places necessary IDEC =MAX (O,INT(FLOAT(IDIGIT)-LABS)) IT= MAX (1,INT(l+LABS)) + 2 + IDEC IF (XDLOC.LT.O.O) IT=IT+l ELSE IT = 2
*
*
*
* 10
*
* 20 30
* 40
* 50 x 60
IDEC = 0 END IF write number WRITE (FORM,'(A,I2,A,I2,A)') '(F',IT,'.',IDEC,')' WRITE (HULP,FORM,IOSTAT=I) XDLOC ·correct for ".345" and "-.345" representation I= INDEX (HULP,' .') IF (I.GT.O) HULP(I:I) = '0' I= INDEX (HULP,'-.') IF (I.GT.O) HULP(I-1:I) = '-0' remove zero's IF (HULP(IT:IT).EQ.'O') THEN HULP(IT:IT) ' ' IT = IT - 1 GOTO 10 END IF remove decimal point if appropriate IF (HULP(IT:IT).EQ.'.') THEN HULP ( IT : IT ) = ' ' IT = IT - 1 END IF question length limited by available space DO 20 LQ=LEN(QUEST),2,-1 IF (QUEST(LQ:LQ).NE.' ') GOTO 30 CONTINUE LQ = 1 CONTINUE LQ1 = MIN (LQ,46-IT) ask the question and read the answer IS = 1 IF (HULP(l:l).EQ.' ') IS=2 CONTINUE VRAAG(1:LQ1) = QUEST(1:LQ1) concatenation with local string (IBM II) WRITE (*,'(ASO,A$)') VRAAG(1:LQ1)11' ['IIHULP(IS:IT)II']',': ' READ (*,'(A)',ERR=70,END=80) INPUT(2:20) length of input string ; default value when 0 INPUT ( 1 : 1 ) = ' ' DO 50 IL=LEN(INPUT),1,-1 IF (INPUT(IL:IL).NE.' ') GOTO 60 CONTINUE default X = XDLOC RETURN CONTINUE new value is decoded WRITE (FORM,'(A,I2,A)') '(F',IL,'.O)' READ (INPUT,FORM,ERR=70) X RETURN
70
JO
error during READ : give message and try again CONTINUE WRITE ( * ' ' ( I 'A' I 'A' I ) ' ) $ 'Enter a REAL value 11', $ ' (or Z to STOP execution)' GOTO 40 CONTINUE STOP 'End_Of_File detected by ENTDRE END
program STOP'
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
Biological control of beet armyworm, Spodoptera exigua, in greenhouse chrysanthemums with Spodoptera exigua nuclear polyhedrosis virus: feasibility studies with an epidemiological model
1 1 2 G.H. de Moed '*, W. van der Werf and P.H. Smits
1
Department of Theoretical Production Ecology, P.O. Box 430, 6700 AK Wageningen, The Netherlands. 2
Research Institute for Plant Protection (IPO), P.O. Box 9060, 6700 GW Wageningen, The Netherlands.
ABSTRACT A realistic and comprehensive simulation model was made to study the possibilities for optimizing the effect of Spodoptera exigua multiplyenveloped nuclear polyhedrosis virus (SeMNPV) in the control of beet armyworm, Spodoptera exigua, in greenhouse chrysanthemums. The model integrates most of the available ecological information on the insect, its virus pathogen, the crop and their interactions. The model correctly describes the short-term impact of SeMNPV on S. exigua populations in chrysanthemums. Evaluation of the correctness of the long-term predictions of the model was not possible because epidemiological data are lacking. The model was used to determine the scope for improving the control of S. exigua with SeMNPV by varying the persistence of the virus and the timing, dose and frequency of application. The model results indicate that in the chrysanthemum system, long term inoculative control is not a feasible option as chrysanthemum is cultured in a short cycle such that virus reservoirs are removed at harvest while lepidopteran eggs are laid on the young plants. For the same reason, the persistence of the virus is not crucially important in this system. Improvements in the effect of virus applications may be expected from multiple in stead of single applications and a careful timing of those applications, in order to hit the most vulnarable stages.
* Present adress: Department of Population and Evolutionary Biology. P.O.box
??? ,????, the Netherlands
1
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
INTRODUCTION Beet armyworm, Spodoptera exigua, is a serious pest in ornamental and vegetable crops in greenhouses in the Netherlands (Smits, 1987). In particular the later instar larvae cause feeding injury on the upper leaves and flowers of ornamental crops such as chrysanthemum and gerbera. This renders the flowers unmarketable. Chemical control has become difficult due to the development of resistance against the main groups of insecticides (Poe eta/., 1973, Cobb & Bass, 1975). Therefore, alternative methods of control were developed. Smits eta/. (1987b) showed that foliar application of S. exigua multiply-enveloped nuclear polyhedrosis virus (SeMNPV) provides up to 100°/o control of beet armyworm in chrysanthemum. The inundative use of SeMNPV as a biological insecticide was found to be economically feasible (Smits et a/., 1987b). Use of the virus for inoculative control of the insect however was not studied. The effect of SeMNPV sprays on S. exigua populations varies with dosage, timing, crop characteristics and the condition and behavior of the insects. Thus, only 55°/o control was recorded by McLeod et a/. (1978) in soybean, whereas Smits et a/. (1987b) in their studies in chrysanthemum obtained nearly 100°/o mortality. Gelernter et a/. (1986) observed that the levels of control obtained in head lettuce varied strongly between years. Young & Yearian (1986) regard the timing of NPV sprays as a major factor affecting effectiveness. The epizootiology of SeMN PV after sprays has not been studied despite the potential benefit of having to spray only once when the virus can maintain itself in the insect poulation while keeping the insect popuation at a tolerable level. Two reasons for this lack of epidemiological studies are the laboriousness of such work and the difficulty of choosing the right factors in a study among the many that are probably important. Simulation models that account for the main processes, provide a tool for carrying out 'substitute experiments', which providing insight in model (system) behavior on the basis of the existing knowledge. Such insight may guide experimental work and may also serve as a basis for the development of management strategies. In this paper, a simulation model of the epizootiology of SeMNPV in a S. exigua population in a greenhouse with chrysanthemums is presented. The performance of the model is compared with experimental results. Finally some application scenarios for SeMNPV, varying the timing and frequency of application and the persistence of the virus formulation, are evaluated with the model.
STRUCTURE OF THE MODEL Age-structure of the Spodoptera exigua population
2
de Moed, van der Werf & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
The model simulates the temporal dynamics of nine developmental stages of the insect: eggs, five larval stages (L 1-LS), pupae, male moths and female moths (in fact the eggs in the females' ovaries are represented, not the females themselves). The numbers within each stage are stratified according to the fraction of development in the stage accomplished, using the fractional boxcartrain method (Goudriaan & van Roermund, 1989). This method adequately handles temperature-dependent developmental period and temperaturedependent individual variation in developmental period. Mortality during development is calculated with a relative mortality rate varying with temperature and developmental stage. Infected individuals of each stage are represented using separate boxcars. The approach is outlined in the relational diagram of Fig. 1.
Spatial distribution and dispersal of Spodoptera exigua larvae Batches of 30-40 eggs are laid near the ground, on the oldest leaves of the hostplant (Smits et a/., 1986). Larvae migrate upwards, resulting in a vertical separation (with some overlap) of the larval stages in the canopy (Smits et al, 1987a). In the model four leaf layers are distinguished and the developmental stages are distributed over the different layers according to an experimentally derived distribution function (Table 1). Due to inter-plant dispersal, the number of (potentially) colonized plants increases with age (Table 1; Smits et al, 1987a).
Growth of the chrysanthemum canopy Chrysanthemums are commercially grown in long beds of 8 plants wide, with 14 em between the plants. About ten age-cohorts of chrysanthemums are present in a greenhouse at any time. Growers haNest flowers from the oldest age-group and plant a new cohort each week. Thus, young plants, which S. exigua females prefer for egg laying (Smits et al. 1986), are continuously present in the greenhouse. It is assumed that the hostplants are planted at a size of 20 em and grow subsequently at a constant rate of 10 em stem elongation per week or 0.1 m2 (leaf area).m-2 (ground area).day-1. In the model, the eggs are assumed to be laid on the youngest plants, such that the time since oviposition is linked to the size of the hostplant.
Distribution of SeMN PV in the canopy In practice, virus is sprayed by hand. Thereby the leaves in the outer two rows of the beds and in the top of the canopy are well covered with virus. The lowermost leaf layers of the middle four rows may be less well covered, depending upon the leaf area index of the canopy. In the model, sprayed
3
de Moed, van der Werf & Smits: modelling the epizootiology of SeMNPV
4
Thu, Sep 27, 1990 polyhedra have a homogeneous vertical distribution on the four outermost rows. For the innermost four rows, an exponential decay of virus concentration with depth, analogous with the penetration of light (Spitters et a/., 1990), is assumed. The intercepted fraction per unit leaf area index is 33°/o (de Heer et a/., 1984). The number of polyhedra intercepted in the Nth leaf layer of 2 -2 thickness L\.L. (m (leaf) m (ground)) in the canopy is thus:
VN = Vo
X
EXP ( - k
X
(N - 1) x L1L ) x ( 1 - EXP (- k x L1L ) )
(1)
is the sprayed dose (#.m-2) and k, the extinction coefficient, has a 0 value of 0.4 m2 (ground) m-2 (leaf). where V
The majority of polyhedra are assumed to be inactivated at a constant relative rate, analogous to radioactive decay. A small proportion of the polyhedra may be more stable, however, remaining active for longer periods, up to several years (Jacques, 1975; Podgwaite et a/., 1979; Olofsson, 1988). In the model, a fraction of stable virus particles remains infectious throughout the simulated period of 100 days. Infection-processes
Infection with SeMNPV causes premature death in the first four larval stages of S. exigua (Smits & Vlak, 1988). When a fifth larval instar is infected, however, the larva often survives. It then develops into an infected adult which transmits the virus to a proportion of its offspring. Other sublethal effects on e.g. sex-ratio, adult emergence, fecundity or egg mortality, as observed in other Spodoptera spec.-virus relationships (Abui-Nasr et a/., 1979; Young & Yearian, 1982; Perella & Harper, 1986; Young, 1990) were not found in SeMNPV-infected S. exigua (Smits & Vlak, 1988). Four routes of infection are distinguished in the model. Their position in the life cycle of S. exigua is indicated in Fig. 1:
( 1 ) lnundative control; caterpillars consume a sufficient amount of sprayed polyhedra; ( 2 ) Ordinary horizontal transmission; caterpillars eat from a leaf contaminated by a deceased caterpillar; ( 3 ) Vertical transmission; females, infected in LS stage, lay infected eggs; ( 4 ) Sexual horizontal transmission; males infect females during copulation resulting in the production of infected eggs. The transmission from male to egg will be called male transmission. ad 1) lnundative control. Caterpillars ingest polyhedra at a rate equal to the product of the feeding rate and the density of polyhedra on the leaf surface. The feeding rate increases with instar (Table 2). According to the description
5
de Moed, van der Werf & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990 of the infection process with a Poisson model (Hughes eta/., 1984), each ingested polyhedron has a chance (!2) of causing lethal infection (Table 2). The relative (
= per
capita) infection rate in the model is calculated from 12 and the
rate of virus intake according to:
i=pxCxV
(2)
with
l
= instar-specific relative infection rate due to sprayed virus; day-1
V = virus density; # m-2 (leaf)
.Q.
= instar-dependent leaf consumption rate; m2 (leaf) day-1
12 = instar-dependent probability of infection per ingested polyhedron; #-1 ad 2) Horizontal transmission. Dwyer (in press) showed for Orgyia
pseudotsugata that horizontal transmission is probably mainly a function of the encounter rate with dead larvae, not of susceptability to the virus. The relative infection rate due to horizontal transmission (RIRH) is therefore calculated as the encounter rate of contaminated leaves, i.e. leaves on which an infected larvae has died. The RIRH is determined by the frequency of visits of caterpillars to contaminated leaves. One visit is sufficient to cause a lethal infection, irrespective of the amount of leaf material consumed. Dead larvae are supposed to be randomly distributed over the leaves within their dispersive range, i.e. all the leaves that can be visited during an instar (as determined by the vertical and horizontal dispersal capabilities; Table 1). Assuming that the number of dead larvae per leaf has a Poisson-distribution with mean f..l., the proportion of leaves contaminated by virus-killed larvae of a certain instar equals: fL,j
= 1- EXP (- J.l)
(3 )
with
(4) with fL,j
= fraction of leaves contaminated within leaf layer L of the
dispersive range of in star j (-)
.ll.
J TL . 'J
1...
= number of virus-killed larvae of instar j (#/patch) =
fraction of time spent in leaf layer L by instar j
= number of leaves within leaf layer L of the dispersive range of
J
instar j (#/patch) The relative infection rate for an instar due to horizontal virus transmission
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV
6
Thu, Sep 27, 1990 equals the sum of the five relative transmission rates obtained by encounters with virus-killed first, second, third, fourth and fifth instar caterpillars. The encounter rate between stages is determined by both horizontal and vertical overlap of the dispersive ranges of each stage.
5
4
h-1 = - V·1 x £..J ~ £..J ~ TL,J· x In (1 -fiL ,J· x 0·1,J· )
(5 )
j=l L=l
with
1
h.= relative horizontal infection rate of a given instar i (day- ) I
Y...
I
= number of leaves visited per day by instar i
Q... = fraction of plants visited by in star i also visited by in star j (-) I ,J
Polyhedra emerging from dead infected larvae are more stable then sprayed polyhedra, probably due to the protection by the remnants of the dead larva (Podgwaite et a/., 1979; Young & Yearian, 1989; Olofsson, 1990}. A viruscontaminated leaf therefore remains infectious until all individuals in the patch have died or emerged as females. ad 3) Vertical transmission. Infected female fifth instar larvae may die or develop into infected adults. A proportion of the eggs laid by these infected females develops into infected L1's. Eggs infected by vertical transmission are supposed to be randomly (Poisson) distributed over the infected females' egg batches. ad 4) Male transmission. A proportion of the infected male fifth instar larvae develops into adults that transmit SeMNPV to the female during copulation. Most females copulate only with one male (Wakamura, 1979). Assuming that the infection does not influence the mating frequency, the fraction females infected by sexual horizontal transmission equals the fraction infected males at emergence of the females. Model
structure
Due to the laying of eggs in clusters and the limited dispersal of the caterpillars, beet armyworm populations consist of clusters. At low densities, overlap between clusters can be neglected, due to the large presumed radius of the flying female. Clusters differ with respect to the date of initiation (egglaying). In an infected population, the clusters also differ in the initial number of infected individuals (eggs). This initial number of infected eggs has a strong effect on the number of healthy and infected adult females that emerges from the cluster after the pre-adult period. As the relation between initial number of infected eggs and the production of offspring by a cluster is strongly curved (de Moed eta/., 1990}, a 'homogeneous' model, in which the calculations are
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV
7
Thu, Sep 27, 1990 based on the average number of infected eggs per cluster, yields results that differ from result obtained with a model that takes these differences between clusters into account. To minimize these averaging errors, we adopted the compound simulation approach. This appraoch was used and discussed before by Rabbinge et a/.(1984), Sabelis & Laane (1986) and by Ward et a/. (1989). In the compound simulation approach, the population is stratified according to criteria which vary over a strongly curved part of a crucial functional relationship in the model. Here, the crucial relationship is that between cluster reproduction and the
number~ of
initially infected eggs; the criteria are
initial number of infected eggs and time of cluster initiation. Thus, clusters are divided over classes, taking number of infected eggs and time since oviposition as stratification criteria (Fig. 2). Calculations for clusters of the same class are made with average values for all variables, assuming that due to the similarity of clusters in one class, curvilinear relationships can be approximated by straight lines, allowing the use of average values. Preliminary model runs were made to determine the minimum resolution (number of age x infection classes) needed. Satisfactory results were obtained by distinguishing between clusters without and clusters with infected eggs due to either maternal or paternal transmission, and by taking a resolution of ca. 1 week on the cluster-age scale, resulting in 10 classes along the cluster-age axis (Fig. 2). The developmental period of a cluster is the period from oviposition to pupation of 99.9°/o of the larvae. Thus in total, 3 x 10
= 30
classes are distinguished. Whole system population dynamics is the sum of the events in these 30 classes. During development of a cluster, larvae pupate and both healthy and infected adult females emerge. These females will initiate new clusters by oviposition (Fig. 2).
Validity range of the model The model is valid only at low densities as interactions between patches are neglected. These low density situations are most relevant from an economic point of view because damage tolerance in chrysanthemum is low due to the high value of the crop, ca. $75.000/ha.
Program The model (450 lines of code) is programmed in standard FORTRAN 77, using Euler integration with a time-step of 1h. The program is structured according to conventions of van Kraalingen & Rappoldt (1989) and makes use of the subroutine library of these authors. The program is available on request.
BIOLOGICAL PARAMETERS OF THE MODEL
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
Development of Spodoptera exigua The development rate (DVR) of the larval stages is a linear function of temperature (Fig. 3a,b). The slope of the relation is similar in all published studies. Only the temperature threshold varies, probably an effect of hostplant (Lambert & Kilen 1984). The model uses instar-specific DVR data of Fye & McAda (1972). As Fye & McAda (1972) grew the larvae on an artificial medium, on which the DVR is higher than on all hostplants studied, the temperature threshold in the model is corrected upwards: 12°C. No observations on chrysanthemum are available.
Mortality of Spodoptera exigua. Egg mortality is affected by temperature (Fig. 3c) but literature data are not consistent. Fig. 3c shows a trend for low mortality at intermediate temperatures of 15 to 25°C and increasing trends with deviations outside this range. For temperatures below 20°C the model uses the temperature relation of egg mortality, found by Poe et a/. (1973). At higher temperatures, egg mortality was set to 10°/o. Mortality during the larval stage strongly depends on the hostplant, varying between 12 and 53o/o (Hanna eta/., 1977; Lambert & Kilen, 1984). No relation with temperature is apparent in literature. Larval mortality on chrysanthemum seems to be low (P .H. Smits, unpublished data). In the model, it was set to 15°/o over the whole larval period. Mortality in the pupal stage varies between 0 and 15°/o at intermediate temperatures. It increases at temperatures above 30°C due to pupation failure (Fye & McAda, 1972). Mortality during the pupal stage is set to a constant rate 15°/o for temperatures below 30°C and to 40o/o at 33°C. At temperatures below 30°C, male longevity is 15 ± 5 days. Longevity is 10 ± 5 days at 33°C (Fye & McAda, 1972; Hogg & Gutierrez, 1980). The adult females are represented by the number of eggs in females' ovaries.
Fecundity of Spodoptera exigua. Fecundity is temperature dependent in most published studies, but a common trend in these studies is not present (Fig. 3d). Fecundity is therefore independent of temperature in the model. Fecundity is higher when larvae are grown on artificial medium than on hostplants (Fig. 3d). Fecundity was set to an intermediate level of 500 eggs for larvae grown on hostplants. Female longevity and age-dependent oviposition rate are combined to a time-distributed oviposition rate. The oviposition delay, defined as the time between emergence of the adult and laying of the average egg, decreases from 7.2 days at 15°C to 5 days at 25°C. It remains constant at higher temperatures (Fig. 3e). The distribution shows a coefficient of variation of 10°/o (Fye &
8
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV
9
Thu, Sep 27, 1990 McAda, 1972; Hogg & Gutierrez, 1980).
Infection-processes (1) lnundative control. The infection chance per ingested polyhedron (Q) depends on larval age (Table 2). This chance Q is estimated by fitting the exponential model of Hughes eta/. (1984; eqn 7) to experimental data of Smits & Vlak (1988).
(6) where Mt is the observed proportion mortality, Q is the infection chance per ingested polyhedron and Pt is the ingested dose. There is a fairly good agreement between the observed and the predicted values (Fig 4). (2) Horizontal transmission. Horizontal transmission depends on the number of encounters between healthy caterpillars and virus-killed larvae as determined by the spatial distribution and movement of the different stages (Eq. 3). L1's and L2's feed mainly in the lower leaf strata. L3 to L5 larvae mainly feed in the upper parts of the plant (Table 1). Due to inter plant movements, the number of plants potentially visited by the larvae increases during development (Table 1). (3) Vertical transmission. Vertical transmission has been shown for several Spodoptera spp., but little quantitative data are available. The late instars of lepidopterous larvae are the most susceptible stages to sub-lethal dosages (Young & Yearian, 1982; Perrella & Harper, 1986). Smits & Vlak (1988) found transmission rates of 10 to 28°/o after feeding SeMNPV to S. exigua LS's. Abui-Nasr et a/. (1979) found 20 to 30°/o vertical transmission after feeding NPV to both L3's and LS's of S. littoralis. Young (1990) found no vertical transmission after feeding sublethal dosages of NPV to S. ornithogalli L4's. In the model, only L5 instars are susceptible to sub-lethal dosages. Infected L5 instars develop into infected adults at a rate of 15°/o. (4) Male transmission. Transmission of NPV to S. littoralis females during copulation by males of infected as larvae, causes a reduction of the females fecundity and an increase of egg mortality (Vargas-Osuna & SantiagoAlvarez, 1988). After feeding of virus to the male, Elnager et a/. (1982) observed a transmission rate of up to 49°/o . The male transmission rate was generally lower than the rate of vertical transmission (Einager et a/. 1982). The transmission rate due to male transmission is therefore set to 7.5°/o, half the rate of vertical transmission.
Virus
inactivation
The inactivation of polyhedra is regarded as a Poisson process, resulting in an exponential decrease of the number of infectious polyhedra with time:
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV
10
Thu, Sep 27, 1990
( 7) where Pt is the number of polyhedra at time 1 and .d. is the relative inactivation rate. The parameter .d. is estimated by analysing experimental determinations of the decrease of virus infectivity with time using the exponential infection model (Eq. 6). Substituting Eq. 7 in Eq. 6, it follows that
Mt
= 1 - EXP (- p X Po x EXP (- d
x t ))
(8)
By some rearranging and substitution, it can be shown that .d. can be estimated from experimental data with:
i ~ ~~ ))
d = - l x In ( 1 - In ( t In ( 1 - Mo)
(9)
According to Jacques (1972) and Biache & Chaufaux (1980), who measured virus persistence within a greenhouse, virus-induced mortality reduces from 66o/o to 33°/o in 1 to 3 days. Thus, .d. is estimated to be 0.3 to 1.0 day-1 .
MODEL EVALUATION The results of simulations are compared to data of Smits et a/. (1987b, 1988) on the effect of sprayed dose, hostplant size and developmental stage of
S. exigua on the percentage larvae killed by the virus. No data are available to evaluate the performance of the model with respect to the epizootiology of the virus over successive generations. The experiments of Smits et a/. (1987b, 1988) were performed in small plots (1m2) in a greenhouse with 36 chrysanthemum plants. Some hours to 1 day after spraying, S. exigua was introduced as small larvae (72 L1s and 72 L2s, Fig. 5a,b), large larvae (72 L3s and 72 L4s, Fig. 5c,d) or eggs (1 0 batches, Fig. 5e). The percentage larvae killed by the virus was calculated by comparing the number of surviving caterpillars 14 days after spraying to the number surviving in a control plot without virus spraying. Temperature was approximately 25°C. In the model runs, individuals are introduced at the moment of spraying for the larvae and 1 day after spraying for the egg batches. The age of the introduced individuals is set to 50°/o of the total development in their stage. When introduced as larvae, the larvae show a homogeneous horizontal distribution. Comparison of experimental results and model predictions shows that the percentage killed larvae is slightly overestimated when the virus is applied during the initial larval stages (Fig. 5a,b). When S. exigua is introduced as L3
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990 and L4 larvae, model predictions are in good agreement with the observations (Fig. 5c,d). The same holds when virus is sprayed during the egg stage (Fig. 5e). Smits eta/. (1987b) showed that the percentage larvae killed decreases with hostplant size. Simulation results show these same trends (Fig. 5c,d). Thus the immediate effect of SeMNPV on S. exigua populations seems to be correctly described by the model.
FEASIBILITY STUDIES WITH THE MODEL Timing of virus applications Fig. 6a shows the effect of the application date on the percentage of larvae killed by SeMNPV sprayed at a rate of 1o8 polyhedra. m-2 (ground). A maximal reduction of 92°/o of the number of larvae is achieved when the virus is sprayed at the emergence of the first L3s, with the active period of the virus during the L3 stage. Spraying a week earlier or later than this stage reduces the percentage killed by ca. 50°/o. Young & Yearian (1986) and Huber (1986) recommend to synchronize the virus to the most susceptible larval stage, being the L2 stage in Beet armyworm (Table 2). However, not just susceptibility to the virus but also the behavior of the larvae and their position in the canopy determine which stage is most easily killed by a virus spray (Young & Yearian, 1986). Thus, L1s and L2s are susceptible to the virus, but are not easily hit by sufficient virus because they feed on the lower leaf strata. L4s and L5s feed on the upper leaves and are well hit by the virus, but they are much less susceptible. The L3 appears to be the most vulnerable stage, combining relatively high susceptibility with virus exposed behavior by feeding high in the canopy. The goal of applying the virus is not to maximize mortality, but to minimize economic damage as a result of feeding injury. Smits eta/. (1987a) noted that some 80°/o of the total leaf consumption occurred during the L5 stage. Thus, to minimize damage the larvae should be killed before the L5 stage. The effect of timing on feeding injury, calculated as the total leaf consumption during one generation, is shown in Fig. 6a. When sprayed during the large stages (Fig. 6a,b), the reduction of feeding injury is less successful compared to the reduction of larval numbers. However, the optimal application time for preventing feeding injury and maximizing mortality are hardly different. Thus the timing can be optimized to serve both goals, i.e. short-term prevention of feeding injury and the reduction of population size in order to prevent or delay future outbreaks.
Dose and multiple spraying Fig. ?a shows the population dynamics over three generations of S. exigua
11
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
as a function of virus dosage. A maximal reduction of the number of healthy larvae, 89°/o, is reached by spraying 1o8 polyhedra. m-2. A dose of 1o6 pol. m -2 causes a reduction of only 50°/o. Young & Yearian {1986) suggest that applying the virus several times might give better results. This possibility is evaluated in Fig. ?b. Splitting the single dosage of 1o8 pol. m-2 in three applications at 7 day intervals markedly enhances the killing effect of the virus. After this multiple application, the larval population size is reduced by 90°/o and feeding injury is reduced by 80o/o, compared to the single spray of 1o8 pol. m-2. A triple spray of 3*1 o6 pol. m-2 also improves upon a single spray of 10 7 pol. m-2, though the improvement is smaller here. The triple 3*1 o6 spray has an effect which is not very different from that of a single spray of 1o8 pol. m-2, while the quantity and costs of the virus involved are reduced by 90°/o. At the other hand, increasing the number of sprays increases labour costs. One of the mechanisms explaining the advantage of multiple spraying can be understood by means of a gross simplification of the system. The relative infection rate (RIR) shows a strong increase around the LC50 (Fig 4). A further increase in virus density has a minor influence on the Rl R. The overall infection rate will therefore be determined by the period during which virus density is above the LCso. If we compare a single spray of 3*1 o7 pol. m-2 to one with 1o8 pol. m-2, the active period will be ±1.5 days shorter in the former case. This loss will be compensated by the repeated application. So, multiple spraying will be advantageous if the gain due to the repeated application is larger then the loss due to the lower dose. This gain increases with the sprayed dose, as illustrated by fig. 78. When the total sprayed dose is reduced to 1o7 pol. m-2, the advantage of multiple spraying is strongly reduced. We have not attempted to optimize the timing of the triple sprays. An additional advantage of multiple spraying is the better distribution of the virus that is likely obtained. Leaves newly emerging after the first spray and newly planted hosts are hit by the following spray. In this way, the emergence of a virus-free refugium for the larvae on the top leaves is delayed.
Virus
persistence
Rapid inactivation of NPVs is a major limitation to their application in biocontrol (Young & Yearian, 1986). Considerable effort is put in research to improve virus persistence by formulation or genetic engineering. We therefore examined the effect of increasing virus persistence on shortterm control. The effect of increasing the halflife value of the virus is shown in Fig. 8a. The figure shows only minor effects of increasing the persistence of the virus, refuting the assumed importance of this factor. A further exploration of the importance of virus persistence is given in Fig. 8b. A small fraction of the virus population might be protected for inactivating
12
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990 influences like UV radiation. Introducing a stable virus population of two percent of the sprayed dose has hardly any effect on shortterm control and no effect on longterm control of beet armyworm (Fig. 8b). Due to the combination of larger instar larvae feeding on the upper leaves and a hostplant growing away from the virus deposit, the larger instar larvae are hardly affected by the sprayed virus. The main reason for this lack of longterm control is the high turnover rate of the crop. The stable virus reservoir is simply removed with every harvest. The newly planted hosts on which the egg batches are deposited, are therefore not contaminated and the virus can not survive to the next generation by means of the free-living stage. If, on the other hand, a virus like SeMNPV would be applied on a crop that does not rapidly produce leaves, e.g. a crop in the generative stage, the effect of a stable virus fraction would be much greater. This is illustrated by fixing the hostplant; i.e. no growth, no harvest and no planting (Fig. 8b). On such a fixed host, SeMNPV can, according to the model, yield a lasting and ongoing reduction of the pest population.
13
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
DISCUSSION In this paper, life cycle data of beet armyworm, S. exigua, and its viral pathogen, Spodoptera exigua multiply-enveloped nuclear polyhedrosis virus, were integrated in a simulation model to provide a tool for imaginary experiments on the population level. Such imaginary experiments do not replace real experiments, which are needed to verify the model results, but they may be used to hint directions for further research (Caswell, 1988). In order for a model to serve that purpose, it must be as realistic as possible, thus minimizing the danger of artifacts (Onstad, 1988). Evidence that artifacts are absent can be obtained by carrying out 'validation' experiments. The present model was only tested on its shortterm performance, which was found to be quite reasonable (Fig. 5). However, with regard to long term predictions, the only argument, and a good one, for trusting the model predictions is that the biological details have been included in a realistic and reasonably precise manner. Nevertheless, artifacts may occur due to incorrect parameter estimates or unidentified crucial structural elements. The model should therefore be regarded as a well underbuilt way of speculation about the possible, integrating most available knowledge on this system. Feasibility studies with the model give interesting results. Thus, while virus persistence is generally seen as an important determinant of success or failure of field application for control of insect pests (Yearian & Young, 1982), the model was only sensitive to persistence when the crop was static, i.e. with little leaf growth and no removal of persistent virus fractions. In field experiments in relatively stable crops, like cotton,effects of virus persistence have been demonstrated (Kinzer et a/., 1976), though no clear-cut relations between persistence and efficacy could be established (Yearian & Young, 1982). Other factors, like variable timing and crop characteristics, seem to obscure this relation in field trials. The model indicates that when leaf material of the crop has a high turnover rate, due to growth and senescence, harvesting, diseases or other factors, persistence may be not so important. The active period of the sprayed virus may not be limited by its persistence, but by the growth rate of the hostplant. Newly emerged leaves allow the pest to feed on virus-free foliage. Accurate timing is a major factor determining success of control (Young & Yearian, 1986; Huber, 1986). Virus has to be applied during the stage most susceptible and most exposed to the virus spray. The period during which virus can be successfully applied is determined by the active period of the virus. Increasing virus persistence might allow a less accurate timing of the application. In naturally occuring epizootics, most larvae are killed during the last two stages (Mason, 1981; Woods & Elkinton, 1987). After the primary infection of L1 instars by vertical transmission, the largest stages are the most susceptable to horizontal transmission because of their high activity, which
14
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990 increases the encounter rate with dead larvae (Dwyer, in press). A similar pattern was reported for an induced epizootic (McLeod eta/., 1982). Based on these observations, Dwyer (in press) states that virus applications should be done during the last stages. However, the optimal instar during which virus should be sprayed is determined by the factors limiting the infection. The spatial distribution is different for sprayed virus and secondary inoculum. Sprayed virus shows a much more homogeneous distribution. The infection rate after introduction of the virus will therefore be determined by susceptibility, feeding rate and distribution of the larvae and not by the encounter rate with virus clusters. Virus should therefore be applied during the early stages to get a high primary infection, as indicated by model results. The dynamics of virus-host interactions is dominated by the ability of the virus to survive periods of host absence (Evans, 1986). Due to the frequent harvest of chrysanthemum, the virus is unable to persist in cadavers or as free polyhedra, such that transmission between generations is limited to vertical and male transmission. The absence of cluster interactions at low densities obstructs the spread of virus among existing clusters. This results in decreasing virus prevalence during successive generations such that the S.
exigua population can increase (Figs 7 & 8). Thus, unless other mortality factors come at aid, SeMNPV cannot give long term control of S. exigua in chrysanthemum. Prospects for inoculative control are better in ornamental crops of which only the flowers are harvested and the foliage remains in the greenhouse, e.g. gerbera, bouvardia or roses. Our model can be used to evaluate prospects in different types of crop, taking differences in virus persistence (higher UV levels), crop height, caterpillar behavior and susceptibility etc. into account. Use of the model for such feasibility studies are worthwhile and will be further pursued. The other follow-up of the present work must be to test model predictions with polycyclic epidemiological experiments.
ACKNOWLEDGEMENT We are indebted to ir D.W.G. van Kraalingen and drs C. Rappoldt for providing us with their subroutine library.
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Spodoptera exigua Hbn. in Egypt, with record of five larval parasites.
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Thu, Sep 27, 1990 Z. Ang. Ent., 79, 362-368. AI-Zubaidi, F.S. & Capinera, J.L. (1983). Application of different nitrogen levels to the host plant and cannibalistic behavior of Beetarmy worm, Spodoptera
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Am. Soc. Microbiology, Washington DC. 184pp. Kinzer, R.E., Bariola, L.A., Ridgway, R.L. & Jones, S.L. (1976). Systemic insecticides anda Nuclear Polyhedrosis Virus for control of the Bollworm and Tobacco budworm on cotton. J. Econ. Entom., 69, 697-701. van Kraalingen, D.W.G. & Rappoldt, C. (1989). Subprograms in simulation models. Simulation report CABO-TT, 18, Centre for Agrobiological Research, Wageningen, The Netherlands. Lambert, L. & Kilen, T.C. (1984). Influence of three soybean plant genotypes and their F1 intercrosses on the development of five insect species. J. Econ. Entomol., 77, 622-625. Mason, R.R. (1981 ). Numerical analysis of the causes of population collapse in
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Mcleod, P.J., Young, S.Y. & Yearian, W.C. (1982). Application of a baculovirus of Pseudoplusia includens to soybean: efficacy and seasonal persistence. Environ. Entomol., 11, 412-416. de Moed, G.H., van der Wert, W. & Smits, P.H. (1990). Modelling the
epizootiology of Spodopera exigua nuclear polyhedrosis virus in a spatially distributed population of Spodoptera exigua in greenhouse chrysanthemums. SROP/WPRS Bull., Xlll/5, 135-141. Nasr, E.S.A., Nassif, P.M. & Emara, S.A. (1980). The threshold of development of the different stages of Spodoptera exigua Hb. Agric. Res. Rev., 58, 303-309. Olofsson, E. (1988). Environmental persistence of the nuclear polyhedrosis virus of the European pine sawfly in relation to epizootics in Swedish Scots pine forests. J. Invert. Pathol., 52, 119-129. Onstad, D.W. (1988). Population-dynamic theory: the role of analytical, simulation and supercomputer models. Ecol. model/., 43, 111-124. Perrelle, A.H. & Harper, J.D. (1986). An evaluation of the impact of sublethal dosages of nuclear polyhedrosis virus in larvae on pupae, adults and adult progeny of the fall armyworm, Spodoptera frugiperda. J. Invert. Pathol., 4 7, 42-47.
Podgwaite, J.D., Stone Shields, K., Zerillo, R.T. & Bruen, A.B. (1979). Environmental persistence of the nuclear polyhedrosis virus of the gypsy moth, Lymantria dispar. Environ. Entomol., 8, 528-536. Poe, S.L., Crane, G.L. & Cooper, D. (1973). Bionomics of Spodoptera exigua (Hub.), the beet armyworm, in relation to floral crops. J. Trop. Reg. Am. Soc. Hart. Sci., 178, 389-396.
Rabbinge, R., Kroon, A.G. & Driessen, H.P.J.M. (1984). Consequences of clustering in parasite-host relations of the cereal aphid Sitobion avenae: a simulation study. Neth. J. Agric. Sci., 32, 237-239. Sabelis, M.W. & Laane, W.E.M. (1986). Regional dynamics of spider-mite populations that become extinct locally because of food source depletion and predation by Phytoseiid mites. In Dynamics of physiologically structured populations, eds. J.A.J. Metz & 0. Diekman, Springer Verlag,
Berlin, pp. 345-375. Smits, P.H. (1986). Calculations on the polyhedra intake by beet armyworm larvae feeding on virus sprayed chrysanthemums. In Fundamental and applied aspects of invertebrate pathology, eds. A.A. Samson, J.M. Vlak &
D. Peters, Proc. 4th Int. Coli. Invert. Pathol., Veldhoven, The Netherlands, 616-619 Smits, P.H. (1987). Nuclear polyhedrosis virus as a biological agent of
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de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
Spodoptera exigua, Thesis Agricultural University, Wageningen, the Netherlands, 123 pp. Smits, P.H., van der Vrie, M. & Vlak, J.M. (1986). Oviposition of beet armyworm (Lepidoptera: noctuidae) on greenhouse crops. Environ. Entomol., 15, 1189-1191. Smits, P.H., van Velden, M.C., van der Vrie, M. & Vlak, J.M. (1987a). Feeding and dispersion of Spodoptera exigua larvae and its relevance for control with nuclear polyhedrosis virus. Entomol. exp. appl., 43, 67-72. Smits, P.H., van der Vrie, M. & Vlak, J.M. (1987b). Nuclear polyhedrosis virus for control of Spodoptera exigua larvae in glasshouse crops. Entomol. exp. appl., 43, 73-80. Smits, P.H. & Vlak, J.M. (1988). Biological activity of Spodoptera exigua Nuclear polyhedrosis Virus against S. exigua larvae. J. Invert. Pathol., 51, 107-114. Smits, P.H., Rietstra, I.P. & Vlak, J.M. (1988). Influence of application techniques on the control of beet armyworm larvae (Lepidoptera: noctuidae) with nuclear polyhedrosis virus. J. Econ. Entomol., 81, 470-475. Spitters, C.J.T., van Keulen, H. & van Kraalingen, D.W.G. (1989). A simple and universal crop growth simulator: SUCROS87. In Simulation and systems management in crop protection, eds. R. Rabbinge, S.A. Ward and H. H. van Laar, Pudoc, Wageningen, pp. 147-181. Vargas-Osuna, E. & Santiago-Alvarez, C. (1988). Differential response of male and female Spodoptera littoralis (Boiduvai)(Lep., Noctuidae) individuals to a nuclear polyhedrosis virus. J. Appl. Ent., 105, 374378. Ward, S.A., Wagenmakers, P.S. & Rabbinge, R. (1989). Dispersal and dispersion in space. In Simulation and systems management in crop protection, eds. R. Rabbinge, S.A. Ward and H.H. van Laar, Pudoc, Wageningen, pp. 99-116. Wakamura, S. (1989). Mating behaviour of the beet armyworm moth, Spodoptera exigua (Hubner)(Lepidoptera: Noctuidae). Japan. J. Appl. Entomol. Zoo/., 33, 31-33. Woods, S.A., & Alkinton, J.S. (1987). Bimodal patterns of mortality from nuclear polyhedrosis virus of gypsy moth (Lymantria dispar) populations. J. Invert. Patho/., 50, 151-157. Yearian, W.C. & Young, S.Y. (1982). Control of insect pests of agricultural importance by viral insecticides. In Microbial & viral pesticides. ed. E. Kurstak, Dekker, New York, pp 335-386. Young, S.Y., (1990). Effect of nuclear polyhedrosis virus infection in
Spodoptera ornithogalli larvae on post larval stages and dissemination by adults. J. Invert. Pathol., 55, 69-75. Young, S.Y. & Yearian, W.C. (1982). Nuclear polyhedrosis virus infection of Pseudoplusia includence [Lep.: Noctuidae] larvae: Effect on post larval stages and transmission. Entomophaga, 27, 61-66.
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de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990 Young, S.Y. & Yearian, W.C. (1986). Formulation and application of Baculoviruses. In The biology of baculoviruses. Vol. II. Practical
applications for insect control, eds. R.R. Granados & B.A. Federici, CRC press, Boca Raton, Florida, pp. 157-179. Young, S.Y. & Yearian, W.C. (1989). Persistence and movement of nuclear polyhedrosis virus on soybean plants after death of infected Anticarsia gemmatalis (Lepidoptera: Noctuidae). Environ. Entomol., 18, 811815.
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22
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
Table 1 Spatial distribution of Spodoptera exigua larvae.
I nstar
#plant1
Percentage of time spent in canopy layer2 1 (bottom)
2
3
4 (top)
----------------------------------------------------L1
5
0
50
25
25
L2
10
0
50
25
25
L3 L4
12
0
17
33
50
15
0
17
33
50
L5
22
0
17
33
50
1 The number of plants visited during a developmental stage is estimated on the basis of the cumulative number of plants which are damaged during development of one cluster. 2 Based on the distribution of feeding marks during each developmental stage. Data from Smits et a/., 1987a.
de Moed, van der Wert & Smits: modelling the epizootiology of SeMNPV Thu, Sep 27, 1990
2
1
Table 2 1 (leaf) day- ), infection chance per ingested SeMNPV
Leaf consumption rate (.Q., cm 1 2 polyhedron (Jl, #- ), product of .Q. and Jl, indicating the susceptibility to virus spray, and 1 number of leaves visited per day (V, #.day - ) for five larval in stars of Spodoptera exigua.
lnstar
Q
L1
0.024
.14
.030
1
L2
0.22
.26
.057
1
L3
1 .8
.014
.025
1
L4
7.3
.0038
.028
3
L5
14
.000056
.00078
5
1
. from Sm1ts (1986).
2 calculated with data from Smits & Vlak (1988)
23
inf. larvae
larvae
I
disintegr. :
horizontal
I I I
: spray
1 ...1 mal
1 ...
,I ,I inf
~-----•1
.
virus
~~-----
--------------~
spray vertical transmission
male transmission
Fig. 1. Simplified relation diagram of development of S. exigua and infection processes by SeMNPV, following the conventions of Forrester (1961)
(Rectangles: states; circles: auxiliary variables; solid lines: flows of matter; dashed lines: information flows).
halflife
pupae ------~-1
----- ;· I
I
I I
I
I
I
_... Number of infected eggs
Fig. 2. Diagram illustrating development of clusters (solid line) through different infection x age classes (delimited by dashed lines), as used in the model. Clusters are started by oviposition and terminated when all individuals have died or pupated. Arrays of age classes are stratified according to initial number of infected eggs (vertical transmission). In the model 3x1 0 classes are
used.
0.6~----------------------------------~
-i
0.1
~----------------------------------~
Developmental rate eggs
0.5
Developmental rate larvae & pupae
«< 0.4
s
!-a;
0.3
c E g. 0.2 Q)
!
B
A
0
0.1
100
2000
Egg mortality
Fecundity
x~
75
I
I
,'
g
$
>;t=
~1000 c
~0
50
25 CY
•
I
,'
\
::s (,)
lf) /'7
:e
I
I
I
I
0
Q)
u.
..:/···........ ······•
,,~
--7<:~ / ''·J
~-=----~
c
~',
[!)
~
0
0 8
5
15
D
''
25
""
Temperature ec)
Average age at oviposition '0 >«< :5!. c 0 ;e en
8. ·s:0
Model -c Afify et at. 1970 ... - .... Butler 1966 'fl-------9 8-RefaJ & Oegheele 1988 •--------.. Fye & McAda 1972 ______.. Hogg & Gutierrez 1980 e----o Nasr et aJ. 1980 'fl------9 Poe et aJ. 1973 + AJ-ZubaJdy & Caplnera 1983 x AJ-ZubaJdy & Caplnera 1984 e Griswold &Trumble 1985 a Guerra & Ouye 1968 1> Hanna et aJ. 1977 ~:t---
.....
6
/\.
-; Q)
Q
«<
ll
Q) C)
t!
E
~ 4
5
15
25
35
Temperature ec)
Fig. 3. Life history data of S. exigua at different temperatures, as reported in literature. Filled markers indicate the use of an artificial diet for growing the larval stage.
35
100~-------------------------------------
A c
75
0
,13
::::s
e Q)
c:n
50
~
- - ·. Number of lwvse - - -· Feeding Injury
Q)
f:! Q) a. 25
0 6 5 -
..
B
4 Q)
c:n
!
3 -
2 1 r-
0
30
I
40
50
Time (days)
Fig. 6. (A) Simulated effect of SeMNPV spray timing on mortality (drawn line) and damage reduction (hatched line). Application time is given as the number of days after introduction of the first females. Damage is total leaf consumption until the end of the LS stage (day 58). (B) Phenology of larval stages (25 to 75°/o interval).
100~-------------------------------------
A c
'' '
75
0
,u::s e
Q)
'
\
\ \
\
50
\
CD
~
- - ·. Number of lwvae - - -- Feeding Injury
Q)
e Q)
a.
\
25
0 6
5 :-
..
B
4 :Q)
CD
I
3 !-
2
1-
1 -
0
I
30
40
50
Time (days)
Fig. 6. (A) Simulated effect of SeMNPV spray timing on mortality (drawn line) and damage reduction (hatched line). Application time is given as the number of days after introduction of the first females. Damage is total leaf consumption until the end of the LS stage (day 58). (B) Phenology of larval stages (25 to 75°/o interval).
10 ~-------------------------------------------------------,
-~ -
- - - dose .. 10"'6 ----------· dose .. 10"'7 - - - dose "' 10"8 ------- dose = 10"9
Q)
~ 0
.... CD
5
.a
s :t s
C)
,g
A 10--------------------------------------------------------~
3 X 3*10"6 1 X 10"'7 3 X 3*10"7 1 X 10"8
5
1-
8 I
0
I
20
I
I
I
40
60
I
I
80
I
100
time (days)
Fig. 7. Simulated effect of SeMNPV spray dosage (A) and split application (B) on long term dynamics of S. exigua. Arrows indicate time of spray; day 40 for single applications and days 38, 45 and 52 for triple sprays. (temperature: 25°C; halflife time virus: 1 day, no stable polyhedra).
10~----------------------------------------------------~-HLF~~? days HLF• 1 day - - - - HLF• 2 days - - - HLF • 4 days
-~ I»
-. .!! 0
C1)
5
.c
e sC»= .2
A 10~--~------------~--~~~----------------~-------------
- - umO%, gr(~Vting hostplant ---- u•2%, gr~ing h~$tplant ~----· u•O%, fixect host):?lant ------ u•2%, fixed hos~plan~ G)
---
~
!· .! ··..,;.;
.
·o
C1) .
.a
5
e· :I
-f c
B 0
20
40
60
ao
100
time (days)
Fig. 8. Simulated effect of SeMNPV halflife (A) and proportion non-decaying stable polyhedra (B) on long term dynamics of S. exigua. (temperature: 25°C; spray: 1oB polyhedratm2 on day 40)
