Cerea aphidpopuations : 010ogy ,sim uatio nan dpredictio n
rter ixon nae v_y Simulation Monographs Simulation Monographs is a series on computer simulation in agriculture and its supporting sience Cerealaphi dpopulations : aiology,simulatio nan dpredictio n
N.Carter, AFGDixo n&R.Rabbing e
Wageningen Centre for Agricultural Publishing and Documentation 1982 CIP eegevens
Carter, N. - Cereal aphid populations: biology, simulation and prediction / N. Carter, A.F.G. Dixon and R. Rabbinge- Wageningen:Pudoc , oktober 1982. 97 p.; 22 cm - (Simulation monographs) Met lit. opg. ISBN 90-220-0804-5 (W) SISO 573.3 UDC 574.9 Trefw.: populatiebiologie.
ISBN 90-220-0804-5
© Centre for Agricultural Publishing and Documentation (Pudoc), Wageningen, 1982.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise without the prior written permission of the publisher Pudoc, P.O. Box 4, 6700 AA Wageningen, Netherlands.
Printed in the Netherlands. Contents
1 Introduction 1 1.1 Reasonsfo r studyingcerea laphid s 1 1.2 Aimso fth estud y 2
2 Biologyo f thecerea laphi dsyste m 5 2.1 Aphids 5 2.2 Naturalenemie s 10 2.2.1 Aphid-specific predators 11 2.2.2 Polyphagous predators 13 2.2.3 Parasitoids 14 +* *s**^ Fungal pathogens 14 2.3 The crop 14
3 Themode l 16 3.1 Introduction 16 3.2 Theaphi d 19 3.2.1 Immigration 19 3.2.2 Development and survival 21 3.2.3 Reproduction and morph determination 24 3.2.4 Physiological processes 27 3.2.5 Adaptation of themode l for othercerea laphi d species 28 3.3 Naturalenemie s 29 3.3.1 Introduction 29 3.3.2 Parasitoids anddisease s 30 3.3.3 Coccinellids 31 3.4 Crop 33
4 Results 35 4.1 Comparison of modeloutpu t withobserve d results 35 4.1.1 Validation 35 ty» I •+* Modelprediction s 36 4.2 Sensitivityanalysi s 45 4.2.1 Introduction 45
"• £*•A * Finesensitivit yanalysi s 49 4.2.3 Coarsesensitivit yanalysi s 57
5 Generaldiscussio n 58 5.1 Simulation results 58 5.1.1 Validation 58 5.1.2 Sensitivityanalysi s 59 5.2 Simpledecisio nmodel s 60 5.2.1 Introduction 60 5.2.2 Attemptsa tcerea laphi dpopulatio npredictio ni n198 0 61 5.2.3 Resultsan ddiscussio n 65 5.3 Futureprospect s 65
References 68
Appendix A Program listing of the population model of theEnglis h grainaphi d(Sitobion avenae) 73
AppendixB Definition so f variablesuse di nmode l 87 1 Introduction
1.1 Reasons for studying cereal aphids
The large area of land devoted to cereal crops, with nearly40 % of allarabl e land underwheat , and theapparen t increase inth eincidenc eo f cereal pestsan d diseases over the last twenty years justify a study of cereal pests. In terms of hectaragewhea t ison e of themos t important cropsi nth eworl d andan ylos so f yieldcause d bypest s has serious consequences, both locallyan dworld-wide . In Great Britain cereal aphids were not considered as important pests until 1968, whenthe yreache dver yhig hlevel so nwhea t (Fletcher& Bardner , 1969).Georg e (1974, 1975) and Kolbe (1969, 1970) have shown that cereal aphids can cause considerable losses of yield in some years. Their abundance, however, varies from year to year(Carte r et al., 1980;Rabbing e et al., 1979) and from placet o place(Georg e& Gair , 1979).Fo ra neffectiv e advisoryservic eknowledg eo f loss of yield relativet o aphiddensit yan dth egrowt ho f aphidpopulation s oncereal s areneeded . Thelatte ri sdeal twit hi nthi sstudy ;th e former isdiscusse db y Rab bingee tal . (1981).T opredic tcerea laphi doutbreak si ti snecessar yt ounderstan d what causes the spatial and temporal differences in abundance.
Over the last decade considerable changes have occured in the cultivation of wheati nWester nEurope . Highsowin gdensities ,spli tnitroge ndressin gan dto p dressing at flowering have resulted in crops that remain suitable for cereal aphidsu pt o theen do f cropgrowth . To prevent losses of yield thereha sbee na marked increase in the amount of biocide (herbicides, fungicides and insecti cides) applied to wheat crops. There has also been a tendency to use insurance spraying, i.e. theregula rapplicatio n of biocides atparticula rcro pdevelopmenta l stageswithou t verifying thepresenc e of pestso rdisease . Thiscause sa noverus e of pesticides, which increases costs and reduces profit per hectare (Rijsdijk et al., 1981) and can result in the development of resistance to pesticides as has been recorded for orchard pests (Helle& Vand e Vrie, 1974), and may increase the incidence of secondary pests and diseases(Baronyovits, 1973; Potts, 1977). The improvement in growing conditions has resulted in wheat crops of 9000 - 10000 kg ha"1. This has also had consequences for the development of pests anddiseases , asthes ewhea tcrop ssuffe r relativelymor efro m pestsan ddisease s thanpoore r crops (Rabbinge and Rijsdijk, 1982). Inth e absence of more effec tivemean so f controlling thepest s anddisease s of wheat, pesticideswil lb euse d even more frequently inth e future. Zadoks et al. (inpress )hav e used asystem s approach to predict theincidenc e of wheat pathogens inth eNetherland s (called EPIPRE = EPIdemic PREvention). Those farmers who usethi ssyste mobtai n
1 yields similar to farmers who do not, but with fewer sprays, and hencelowe r costs.
Throughout Western Europecerea laphid sar eseriou spests ,an d inth eearl y seventiesstudie so nthei repidemiolog ywer estarte di nsevera lcountries . Several simulation modelso f cerealaphi d populations havebee ndeveloped , for exam pletha t of Rabbingee t al. (1979), which wasdevelope d for usei n conjunction withEPIPR E inth eNetherlands .Th emode lpresente d inthi sboo k was devel oped for Norfolk, England.
After Lincolnshire, Norfolk is themos t important cereal growing countyi n England and Wales (Anonymous, 1980).Althoug h more barley isgrow n than wheat,ther ewer estil love r 8500 0h aunde r wheati nNorfol k in 1979. This was a major factor inth edecisio n to worko ncerea laphid sa t Norwich.Fro m197 6 to 1980,wit h the notable exception of 1979, whenMetopolophium dirhodum was the most common aphid, the English grain aphid, Sitobionavenae, has beenth emos t numerous cerealaphi d specieso nwhea t inWester n Europe,an d as a consequence most research has been done on thisspecies .
4 1.2 Aimso f thestud y
Warning schemes are based on three components: monitoring, forecasting and communication. Monitoring involves sampling the pest either outside the crop(a toverwinterin gsite so rwhil ethe yar edispersing )o ro nth ecrop .Monito ring can becarrie d out byth e farmer or extension worker or, especially inth e developmental phase,b yth eresearc h scientist.T ob esuccessfu l themonitorin g mustb eeas yt ocarr yout , reliable,quic kan dchea p(Rabbinge , 1981). Thetim e spent monitoring, thedetai lan d thefrequenc y depend on thevalu eo f thecro p andth etim efro m sowingt oharvest .Approximatel y 1 hfield -1yr" 1(fiel d ^ 20 ha)o f monitoring cerealaphid s isacceptable .A rapi d flow of information be tweenfarmers , agriculturaladviser san dresearcher si svital .I fther ei sa lon gde lay between monitoring and issuing advice the schemewil lno t beattractiv e to farmers (Welch& Croft, 1979).
Our aimsi nthi smonograp h aret oexplai nth epopulatio n development of S. avenae on cerealsan d to indicate howcerea l aphid outbreaks might bepredic ted.T oachiev ethi scomprehensiv emodel sar edevelope dwhic hma yb ereduce d to simpledecisio n rulesan d incorporated intoa decision-makin g processinvol vingth ewhol esystem . Way& Cammel(1974 )hav eremarke d on theproblem s of early forecasting of outbreaks of S. avenae, due mainly to the widespread distribution ofit soverwinterin ghost san dth elac ko freliabl elong-ter mweathe r predictions (Lamb,1973) .
Several attempts have been made to predict outbreaks; these have been re- viewed by Dixon (1977) and Carter &Dewa r (1981). Dean (1973b) found no relationship between the numbers of cereal aphids caught in suction traps in May and June and the peak densities achieved on nearby crops. However suc tiontra pcatches , doindicat eth estar t of immigration intocrop si nspring .Thi s is correlated with the weather conditions prevailing inth e earlypar to f theyea r (Sparrow, 1974;Walters , 1982).A s thenumbe ro f suction trapsincreases ,espe cially in Germany, France and the Netherlands, an overall picture of cereal aphid migration will develop thatwil l result inmor eaccurat e predictions of the timing of theimmigratio n andi nth e future morereliabl eestimate s of thenum bers flying. However more information on the migratory behaviour of ceral aphids is needed to predict the time of arrival and number of aphids that will colonize specific fields.
At present, cerealaphi d population forecasting inEurop euse sa critica lpoin t model, i.e. thenumbe r of aphids at flowering. Fiveo rmor eaphid spe rea ran d increasing attha t stagei sthough t to indicatetha t theaphid swil l becomeabun dant enough to justify spraying (George, 1974, 1975). The evidence for this scheme is rather tentative, with no consensus on the critical infestation level at flowering, e.g. inBelgiu m andFranc ei ti s 15-20aphid spe rtiller , inth eNether landsi ti s70 %o f tillersinfeste d (5aphid spe rtiller )(Rabbing e& Mantel , 1981). Most field andlaborator yobservation s indicatetha t flowering incereal si sa cri tical period for S. avenae,bu t therei s no consistent relationship betweenaphi d numbers at flowering and the peak aphid population (see Chapter 5).
An alternative, though partly complementary, approach is to use sensitivity analysis in combination with asimulatio n model to study aspects of thesyste m that arepoorl y understood. Data on thebiolog y of S. avenaean d itsimportan t natural enemieshav ebee ncombine d injus t suchmodel s(Carter , 1978;Rabbing e et al., 1979).Th e predictions of these models arevalidate d by comparisonwit h trends incerea l aphid numbers collected overa number of years from different localities.Th eimportanc eo f eachmodelle dcomponen t of theaphid' sbiolog yi s evaluated by varying the value assigned to that component.
Such a sensitivity analysis may eventually result in cumbersome simulation models being replaced bysimpl e decision rules.Thi s hierarchical approach, i.e. comprehensive explanatory models —summar y models with many descriptive elements — decisionrule s(Loomis , etal. , 1979),wil llea dt o forecasts asreliabl e as the EPIPRE system (Subsection 5.2.2.).
Furtherfield an dlaborator ystudie sar eneede do nmorp hdetermination ,nat ural enemies and the interaction of biotic and abiotic factors on the loss of yield. In Chapter 2 the biology of the cereal aphid ecosystem is described in some detail, but for a fuller account seeVickerma n& Wratte n(1979 )an dCarte r etal . (1980). A simulation model for thedevelopmen t of S. avenaepopulation s onwinte rwheat , withreferenc et oth eothe raphi dspecie swher erelevant , is pre sentedi nChapte r3 .Th eprediction so f themodel , theirvalidatio nan dsensitivi tyt o changes inparamete r valuesar econsidere d in Chapter4 . InChapte r5 th e findings of thesimulatio n studyar ediscussed , someo f thesimpl edecisio nrule s that have beendevelope d for S. avenaear eintroduced , examples of theirappli cationar egive nan darea sfo r futureresearc har eindicated .A listingo f thesimu lation model is given in Appendix A. 2 Biology of the cereal aphid system
2.1 Aphids
Three species of cereal aphid commonly infest cereal crops in Western Europe: the English grain aphid (Sitobion avenae), the rose grain aphid (Metopolophium dirhodum) and the bird cherry-oat aphid (Rhopalosiphum padi). The numbers of alate adults of these three species caught from the beginning of May to the end of July by white (1942-1946) and yellow (1951-1969) sticky traps (Heath- cote, 1970) and a suction trap at Rothamsted (1968-1971) were used by Dean (1974a) to determine annual trends. He found that these results did not always correspond to crop infestation levelsa s reported byth eBritis h Ministry of Agri culture, Fisheries and Food. However, the suction and sticky trap catches give many years of quantitative information on the timing and abundance of cereal aphids.
nos of aphids 1000h
42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 year Figure 1. Numbero f alates ofM .dirhodum caugh teac hyea rfro m 1942-1980a t Rotham sted. From 1942-1971 thenumber spresente dar estick ytra pcatches ;fro m 1972 onwards theequivalen t catchespredicte d fromsuctio ntra pcatche susin gth erelationshi pbetwee n suction and sticky trapcatche s for the period 1965-1971, when both types of trapwer e used. Horizontal line represents an arbitrary level for assessing outbreaks. Asbot h stickyan d suction traps wereuse d at BroomsBar n and Rothamsted (Fig. 36) from 1965-1971 and the degree of association between the catches taken byth etw otype so f trapi sgoo d (BroomsBarn : M. dirhodumr = 0.7,S . avenae r - 0.9; Rothamsted: M. dirhodum r = 0.8, S. avenae r = 0.9), iti s possiblet ostandardiz eth ecatche san dobtai na nindicatio no fchange si nabun danceo fM. dirhoduman d S.avenae fro m yeart oyea rfro m 1942t o 1980(Fig ures1 and2) .Ther ei sa wea kcorrelatio nbetwee nth eyea rt oyea rabundanc eo f M.dirhodum andS. avenae ( r = 0.42,n = 35,p < 0.02),wit hyear swhe nonl y one species iscommon . Of the three species, S. avenae isconsidere d to beth e mostcommo npes to fwheat . M. dirhodum, however,i smor eabundan ttha nS. avenaei ntra pcatches . Theirrelativ eabundanc epossibl yreflect sth eproportio n of thecerea l hectaragetha t isunde r barley(Figur e3) ,th epreferre d cerealhos t ofM .dirhodum (Dean , 1973a). Since194 2th eare aplante dwit hcereal san dth e proportions madeu po f barley, oatsan dwhea thav echange d (Figure4) .Thes e changes are likely to affect the abundance of thetw o specieso f aphid; thede crease in the area sown to barley adversely affecting M. dirhodum. Figure2 show stha t S. avenaewa smor eabundan t inth elat e 1960s thanpre viously, eventakin g theincreas ei ncerea lhectarag eint oaccount .Th enumber s ofM . dirhodum haveals oincrease d since 1968.Althoug h iti sunlikel ytha t the trapcatche saccuratel yreflecte d aphidnumber so nth ecrop ,the yca nb euse dt o indicateth e frequency of outbreaks.Th earbitrar y levelsi nFigure s 1 and2 and
of aphids
424 44 64 85 05 25 45 65 86 06 26 46 66 87 07 27 47 67 88 0 year Figure 2. Numbero falat eS. avenae caughteac hyea rfro m 1942-1980 atRothamsted . Detailso ftrap sar edescribe di nlegen dt oFigur e 1. proportion of S.avena e incatc h 0.6 — © ^ 0.5-
0.4- (E)^
03-- © ® <®>^
Q2- ©
0.1-- © «
• » • i \ 0.2 0.3 0.4 0.5 0.6 0.7 proportion of wheat Figure 3. Relationshipbetwee nth eproportio no f S. avenaean d M. dirhodum inth esuc tion trapcatche sa t BroomsBar nan d Rothamsted andth eproportio n of wheatt obarle y eachyea ri nth ecount yi nwhic hth etrap sar esituated .Th e5 2plac eyear sar egroupe din to7 classe saccordin gt o theproportio n of wheat;4 , for example, isth enumbe ro fobser vations. area (1000 ha) 100r \ 90 r-v \/ Barley 80 v 60 WheQt 60 \/\ J y\\A /\/ 50 X X X-x.X V 40 / 30 X o-°-°r 20 *o. .o 10 "°^
424 44 64 85 05 25 45 65 86 06 26 46 66 87 07 27 47 67 88 0 year Figure 4. Changes in cereal hectarage under barley, oats and wheat in Hertfordshire from 1942-1978. a correction for thehectarag eunde rcereals , indicatetha t therehav ebee nmor e outbreaks of M. dirhodum and S. avenaei n the last twenty years than in the previous twenty years. Thus both species of aphid appear to bemor eabundan t andmor efrequentl y achievehig hlevel so f abundancetha npreviousl y - atleas t in the trapcatches . This may bepartl y duet o the increase in the proportion of the land under cereals (currently46 % in Suffolk). The main reasons, however, arechange si nagricultura l practices,whic hhav eresulte di nmor eaphid ssettlin g and an increase in their developmental and reproductive rates on cereals. This view is supported by an increase in cereal aphid outbreaks in those parts of Europewher ether eha sbee n adecreas ei nth ehectarag eunde rcereals , e.g., the Netherlands.
Af. dirhodum wasth emos tabundan t cerealaphi di nWester nEurop ei n197 9 (Figure 1)an d is in some other parts of the world the commonest species every year, e.g. in South America (Zuniga & Suzuki, 1976). It overwinters either viviparously oncereal san dgrasse s(Dean , 1978)o ra segg so nroses , itsprimar y host (Hille Ris Lambers, 1947). Egg-hatch occurs in March and April and the first generation is totally apterous. The proportion of alateadult s inth esecon d generation is variable but the third generation adults areal l alate. Migration to Gramineae occurs in late spring and early summer. In autumn, gynoparae and males appear in response to short day-length and low temperatures (Elkhider, 1979). These morphs return to the primary host where the gynoparae produce oviparae, which lay eggs after mating with the males. M. dirhodum feeds on the leaves of cereals and grasses, moving on to new leaves as they appear (Dedryver, 1978), in contrast to S. avenae, which feeds predominantly on theears .M. dirhoduminfestation s of spring barleyan dwin ter wheat can cause significant losses of yield (George, 1974; Wratten, 1975). Becausei nmos t yearsi n Britainthi saphi d israr eo nwheat , itwa signore dunti l theoutbrea k of 1979.I nth eNetherland sthi sspecie si smor eabundan t onwhea t than in Britain, but was not thought to cause significant yield losses as it does not feed on the ears (Vereijken, 1979). In 1979, whenAf . dirhodum wasabun dant and 5. avenaevirtuall y absent, yield losses were as high as in otheryears , so adetaile d analysis of thepreviou s yearsresult swa sundertake n (Rabbinge & Mantel, 1981). This revealed that bothAf . dirhodum and S. avenaema y cause considerable yield losses and in seven out of 21fields i n different yearsAf . dir hodum did most damage. Thus both aphid species contribute to yield loss. In 1979i n Great Britain therewa sa sever elos s of yield, thenumber s of M. dirho dum reaching 50-300 per tiller. Therefore both cereal aphid species have to be included inwarnin g andmonitorin g systems, asi nth eEPIPR Ewarnin gsyste m in 1980.
R. padi isth emos t important vectoro f barley yellow dwarf virus(BYDV) . It is one of the commonest aphids caught in suction traps in Western Europe (Dean, 1974a)an di spotentiall ya ver yseriou scerea lpes t(Dean , 1973a;Leathe r
8 & Dixon, 1981).However , itonl yachieve shig hnumber so ncereal si nScandina via (Markkula, 1978). Itca n eitheroverwinte r asa neg g on birdcherr y (Prunus padus), its primary host, orviviparousl y on cereals andgrasse s (George, 1974). Theeg gmortalit y is70% ,occurrin g at arat eo f 1.8% perwee k duringa winte r of 20 weeks, rising to 3% in spring (Leather, 1980). Similar high eggmortalit y has been recorded for other aphids (Dunn & Wright, 1955; Way & Banks, 1964). The eggs hatch in March andApril , andemigran t aphids areinduce db y crowding and poor nutrition (Dixon, 1971;Dixo n &Glen , 1971). Few of these alatae colonize cereals in theU.K . Its nonpest status in Western Europe ispuz zling asi t thrives on cereals in the laboratory. However, it has a greater prefer ence for grasses (Leather& Dixon, 1981). Inautum nR. padi likeM. dirhodum produces gynoparae and males in response to short day-length and low tempe rature (Dixon &Glen , 1971; Dixon & Dewar, 1974). These morphs return to birdcherry , whereth egynopara e produce oviparae, which matewit h themale s and then lay eggs.
S. avenae ismonoeciou s on Gramineae, onwhic h itma y overwinter asvivip - arae or as eggs (Figure 5), but no information is available on their relative im
Autumn \
Figure 5. Lifecycl eo fth eEnglis hgrai naphid ,S. avenae. a:fundatrix . b:apterou s fun- datrigeniae. c:emigrant ,d :apterou sexule .e :alat eexule . f: gynoparae.g :male ,h : ovi parae. i:egg . portance(Dean , 1974a). Iti sver ydifficul t tofind eithe raphid so regg so ngrasse s or cereals in Norfolk during the winter. As aconsequence , it has not beenpos sible to monitor spring populations to predict possible levels of infestation of cereals. However, this might be possible in those parts of Europe where over wintering aphids have been found on grasses, e.g., in Belgium and the Nether lands. Inmos t years, from theen d of Mayunti l theen do f June, alateso f S.avenae colonize winter wheat, in preference to most other cereals (Carter, 1978).Alat e aphids arecaugh t insuctio n traps, usuallybefor e theyar efoun d incerea l fields (George, 1974). At the start of immigration, wheat has not usually headed and thealate ssettl eo nth eleaves .A sth eear semerg ethe yar ecolonize d byth ealate s and their nymphs. Most of these nymphs develop into apterous adults whose reproductive ratei shighe r than that of alateadult s (Wratten, 1977). Therepro ductive rate of S. avenae is higher on the young ears (up to the start of the milky-ripestage )o f cerealstha no nth eleave so rth eolde rear s(Vereijken , 1979; Watt, 1979a). Reproductive rate also decreases with increase in aphid density (Vereijken, 1979). As the aphid density rises and the crop ripens an increasing proportion of the nymphs born to these apterae develop into alate adults (Ankersmit, personal communication; Watt &Dixon , 1981). InJul yan dearl yAugust , whenmos t of thesealate sar eproduced , thewinge d aphids leave the crop, which results in a rapid decline in field populations and largecatche s of cereal aphidsi nth esuctio n traps.Thi semigratio n isinduce db y acombinatio n of highaphi ddensit yan dpoo rhos t quality. Thelarg enumbe ro f naturalenemie si nth ecrop sa tthi stim edestro yan yremainin gaphid s(McLean , 1980). Theautum nmigration , asindicate d byth esuctio ntra pcatches , isver ysmall . Under short day conditions S. avenaeproduce s gynoparae first, followed bya short break in reproduction, after which mostly males are produced. This se quenceo f morphproductio n ensurestha tmale san dovipara ematur ea tapprox imately thesam etim e (Watt, 1979b).Ankersmi t (personal communication) and Watt (1979b)hav e evidence that some races of S. avenaed o not producesexua l forms. The life cycles of these species of cereal aphid are complicated, each having eight morphs, including the egg stage. However, they have agrea t deal incom mon; figure 6 presents a generalized life cycle that omits the daunting com plexity of the detailed life cycles (Figure 5).
2.2 Natural enemies
Cereal aphids have a large number of natural enemies: aphid-specific pre dators, polyphagous predators, parasitoidsan d fungal pathogens. Vickerman& Wratten (1979) remark that although there have been several estimates of the numbers of natural enemies, little has been done to quantify their effects on cereal aphid population growth. As with the aphids, little attention has been
10 ' *•* —'W>m IJ ' ,"V' ''jN
Figure 6. Generalized cerealaphi d lifecycle . given to natural enemies in habitats away from cereals, especially inwinte ran d spring. Vickerman & Wratten (1979) suggest that natural enemies might exerta major interseason effect on aphid abundance but their contribution to aphid population regulation does not seem promising at present. Further combined field andlaborator ystudie sar eneede dt oelucidat eth epotentia l of theseorgan isms. •
2.2.1 Aphid-specific predators
Much of the work carried out on the natural enemies of cereal aphids has centred on thisgroup . They belong mainly to three families: Coccinellidae(Co - leoptera), Syrphidae (Diptera) and Chrysopidae (Neuroptera). The larvae and adultso f thefirst family , butonl yth elarva eo f thelatte rtwo , eataphids .Ther e havebee nn odetaile d studies of theirpopulatio n dynamics. Thesepredator sar e also subject to mortality caused by otherpredators , parasitoids andpathogens ; these in turn have been studied even less. Coccinellids arrive in cereal fields in spring, about the same time as the aphids, but in cool summers they may take several weeks to become reproduc- tively mature. The threshold density of aphids, below which coccinellids will emigrate, is not known. Fecundity, however, is directly related to aphid con sumption(Dixon , 1959).Althoug h theysometime s laythei regg si nconspicuou s places it is difficult to get a reliableestimat e of egg density. McLean (1980)ha s studied the consumption rates of the different instars of Coccinella 7-punctata and C. 11-punctatai n the laboratory when supplied with excess aphids. The fourth larval (the last) instar is the most voracious, with that of C. 7-punetata
11 consuming up to 40 third instar S. avenae nymphs per day at 20 °C. Total con sumption per larva is potentially in excess of 300 aphids. As this study was car ried out at only two temperatures (15 and 20 °C), consumption rates at other temperatures are required to evaluate the regulatory potential of coccinellids under field conditions. Coccinellids are usually very common only in years of cereal aphid outbreaks, which indicates that they benefit from high aphid popu lations rather than regulate them. The data presented by Heathcote (1978) re veals a highly significant relationship between the logarithms of the total num ber of Coccinella, 7-, 10- and 11-punctata adults and cereal aphids caught on sticky traps at Brooms Barn from 1961 to 1975 (Figure 7: r = 0.74, n = 15, p< 0.01). The slope of the relationship (b = 0.93) is not significantly different from 1.0, which supports the view that aphid abundance could determine the num bers of coccinellids and not the reverse (Heathcote, 1978). However, much more information on the predatory behaviour of coccinellids is needed before their effect on cereal aphid abundance can be accurately judged. The percentage of time spent searching, the speed of search and the develop mental rate of the coccinellids are temperature dependent, which means coccinel lids are likely to be more effective in warm sunny years than in cool cloudy ones (McLean, 1980). However, as aphid development and reproduction are also temperature dependent, this view might not be correct, and indeed Vickerman
lg (coccinellid nos+1) x 1.6h x
1.4
1.2
1.0
0.8
0.6
0.4
02
nUJ.*-* ' i i—i—i—i—i—i—i—i—i—i—i—i—«- 2.0 2.2 2.4 2.6 28 3.0 3.2 3.4 lg aphid nos Figure 7. Relationship between thenumber s of coccinellids and cereal aphids caught on sticky traps at Brooms Barn, 1961-1975 (after Heathcote, 1978).
12 & Wratten (1979) suggest thatnatura lenemie s aremor eimportan t inyear swit h cool summers. A simulation model of the interaction between coccinellids and aphids is one way of testing which of these two ideas is correct. But this must wait until more information on the natural enemies is available. Only the larvae of syrphids eat aphids. The adults feed on nectar (energy source) andpolle n (protein source).Episyrphus balteatus is themos t important species incerea l fields inWester nEurope , although otherspecie sar ecommonl y found, e.g. Melanostoma mellinum, Sphaerophoriascripta and Metasyrphus luniger. Adult female syrphidswil loviposi t onplant scontaminate d withhoney - dew(Schneider , 1969), butther ei slittl einformatio n oneithe rthei r fecundityo r thedevelopmen t and consumption rates of their larvae incerea l fields. Inaddi tion syrphid eggs and larvae are difficult to find and it is usual for morepupa e to be found than would be expected from the numbers of larvae recorded. Chrysopa carnea is found incerea l fields, but only at low densities. Onlyth e larvae are aphidophagous, but they are very mobile and consume aphids very rapidly. Even less is known of their biology than for syrphids, but as they are rare they are unlikely to have a significant effect on cereal aphid populations.
2.2.2 Polyphagous predators
This group of predators includes Carabidae and Staphylinidae (Coleoptera), Dermaptera, Araneae and Acari. There is an inverse relationship between arthropod diversity (positively correlated withth epercentag e of predatoryindi viduals) and the density of apterous aphids inJun e (Potts & Vickerman, 1974). Although many of these predatory species consume aphids it isno t knownho w manyeac hconsum e (Sunderland, 1975).Exclusio n of mostgroun dpredator shas ) often resulted in higher aphid densities, but usually only when aphid densities were low. In 1979, however, at Rothamsted, the presence of ground predators reduced the aphid peak population of M. dirhodum from more than 200 to 50 pertiller . Rathersurprisingl y though, therewa sn odifferenc e betweenth etreat ments at North Farm in West Sussex (Sunderland et al., 1980). Except in the early part of the season, ground predators had no effect on aphid population build-up in Norfolk in 1977. This was because the large number of immigrant cereal aphids swamped any effect the predators had (McLean, 1980). There is little relevant information on the searching behaviour or consump tion rates of these predators and, as McLean (1980) remarks, few field studies takethe mint oaccount . Polyphagous predatorsar eals oeasil yoverlooke d in field surveys as many of them are more active at night (Vickerman &Sunderland , 1975). As a large number of species are involved, the evaluation of their effect on aphid populationsi sdifficul t andthi swil l remainth ecas eunti l moredetaile d fieldan d laboratory studies are carried out on these species.
13 2.2.3 Parasitoids
Theprimar yparasitoid so f cerealaphid sbelon gt otw ofamilie s ofHymenop - tera: the Aphelinidae and the Aphidiidae. The latter is the more important in Europe (Carter et al., 1980), but, as with the other natural enemies of cereal aphids,littl ei sknow no fthei rbiology ,an dthei rtaxonom yi sconfuse d (Powell, personalcommunication) .Th especie scompositio no f parasitoidschange s from yeart oyea ran d from placet oplac e(McLean , 1980), butAphidius ervi, A.pici- pes, A. uzbekistanicus andA. rhopalosiphi are the most common, although Praon volucre may also bequit enumerous .Ther ei sver y littlequantitativ ein formation on them as parasitoids of cereal aphids. A. rhopalosiphiis short-lived , witha maximu madul tlife-spa n oftwent yday s at 20°C .I t isver y fecund, realizesa fecundit y of moretha n 200eggs ,an dpre fers to oviposit in young aphids, i.e., those inth e first threeinstar s (Shirotae t al., to bepublished) . Untilsimila r studieshav ebee ncarrie d out onsevera lspe cieso f parasitoids, at a number of temperatures, it willb edifficul t to evaluate theireffec t oncerea laphi d populations.Onc emor ei sknow nabou t thebiolog y of thesespecie so f parasitoids, it mayb epossibl et oexplai n thechange si nspe cies composition that have been observed from year to year. One major factor limiting the increase in the numbers of parasitoids is the action of hyperparasitoids, which can rapidly increase in numbers and destroy many parasitoids at the end of the season. However, the degree of hyperpara- sitism varies from year to year (McLean, 1980)an d so it is difficult to predict theeffec t of hyperparasitoids earlyi nth eseason .Jone s(1972 )suggest stha tth e aphid-parasitoid-hyperparasitoid interaction is very important in determining whether an aphid outbreak will occur. Dendrocerus carpenteri isprobabl y the most common hyperparasitoid but a number of other species can also benu merous.
2.2.4 Fungalpathogens
Thesebelon gt oth egenu sEntomophthora. Quitefrequentl y thefirst sign s of diseaseoccu rlat ei nth eseaso n(Dea n& Wilding , 1971,1973) , although Latteur (1976)suggeste d that occasionallyEntomophthora havea significant effect on aphid population build-up.Funga l diseaseseem st ob emos t important inyear s withhig hrainfal l duringth esummer .Th eintroductio n ofEntomophthora int o cereal crops, early in the season has not met with much success (Dean et al., 1980), but their use in biological control deserves more attention. The useo f otherbiologica lcontro lagent scoul dprov ecostl ybu tth erestin gspore so fEnto mophthora and other fungi are relatively easy to propagate, store and apply.
2.3 The crop
Therear e several models of cropgrowth , but few of crop development. The
14 latter are descriptive formulae including, in some cases, field data. Maas and Arkin (1980) developed a general model of wheat development, whereas Selig- man& va n Keulen (1981) considered the effect of water shortage and nitrogen balance on the rate of development of winter wheat. The latter is suitable for usewit ha naphi d model butther ei sinsufficien t information onth eavailabilit y of nitrogen and water in the field. Therefore, asimpl e algorithm is used inthi s study. Iti sassume d thatcro pgrowt h isno t alimitin g factor for thebuild-u p of aphid populations. The crop developmental stage, however, is known to affect aphidbiology , especiallywin ginduction , fecundity, survivalan dadul tlongevit y (Ankersmit, to be published; Vereijken, 1979; Watt, 1979; Watt & Dixon, 1981).Thu scro pdevelopmenta l stage,describe d byth edecima lcod eo f Zadoks et al.» (1974), is a measure of the quality of this food source for cereal aphids.
15 3 The model
3.1 Introduction
Simulation models ordynami cmodel s (Jeffers, 1978)hav eonl yrecentl ybee n used in ecological studies, as they are dependent on computers to solve large numbers of equations quickly. Models areuse di n systems analysist o studyth e interactions between state variables, which quantify all properties that describe the state of the system. The underlying assumption is that the state of an eco system at any particular time can be expressed quantitatively and that changes in the system can be described in mathematical terms (de Wit &Goudriaan , 1978). These changes in the system, arecontrolle d by rate variables, which are assumed to remain constant over small timeintervals . Therefore thetim einter val usedi sdependen t onth erate so f changeo f thesystem , but for practicalrea sons it must not be too small. The duration of the time step is dictated by the rateo f changecalculate d from thetim ecoefficien t (deWi t& Goudriaan, 1978). This is difficult to determine for large systems, such as S. avenaepopulations , and in such cases trial and error is used to determine themos t appropriate time interval, which in this case was found to be 1hour . Besides state and rate variables, there are auxiliary, output and driving vari ables. Driving, or forcing, variables arethos etha t areno t affected by processes within thesyste m butcharacteriz e theinfluenc e from outside. Thesema yb e for instance the temperature or the temperature sum. Auxiliary variables arethos e which are used to simplify processes to increase understanding. Output vari ablesar ethos equantitie s which themode l produces for theuse ran dca nb ean y of the aforementioned variables.
Simulation models mayeithe rb edeterministi c (dependent onproportions ) or stochastic(dependen to nprobabilities ) ora mixtur eo f bothwher esom eprocesse s aretreate d stochastically. Inmos t cases iti s only themea n value that iso f inte restan dno t therang eo f possible values. Whenon ewant st o knowth erang eo f possible values a stochastic simulation is needed. Also, when some of therela tionships between the variables with a stochastic character and state variables are curvilinear deterministic models give erroneous results (Fransz, 1974;Rab - binge, 1976). In such cases stochastic models are needed. However stochastic models use a lot of computer time as each simulation has to be repeated many times (up to 1000) to produce the range of responses. To overcome this other methods have been developed, which are basically deterministic, but make use of classes of individuals (Rabbinge &Sabelis , 1980).
16 We use a deterministic model as the relations between rates and the forcing functions incorporated in the model are linear. When a more detailed predator- prey relationship is available the model will have to be modified. Barlow & Dixon (1980) in their simulation model of lime aphid populations also used a deterministic approach, with discrete time steps, as in our present model; a constraint imposed by the use of the computer language FORTRAN IV. At the University of East Anglia (UEA) it is difficult to run large models written in simulation languages, such as CSMP, which also treat processes in a discrete way but may make use of more complicated numerical integration procedures. The other S. avenae population model (Rabbinge et al., 1979) has the same structure but is written in CSMP. It incorporates a range of experimentally de termined developmental times (dispersion in time) (Goudriaan, 1973) and can be run on all computers with a FORTRAN compiler. As dispersion in time had little effect on predictions it is omitted from the present model (Carter &Rab binge, 1980).
The model describes the population growth of S. avenae on winter wheat in summer. No attempt has been made to simulate population growth on grasses or to model the relationship between years. The model starts with the coloni zation of the crop by alates in May and June, together with allowances for any aphids which have overwintered on the crop. accumulated number ofnymph s 30i-
2000 4000 6000 adult age (H°) Figure 8. Cumulative daily total production of nymphs by S. avenae reared onwhea t seedlings in aglasshous e at 20.0 ±5.0 °C.
17 There are two ways of initializing the aphid population. - The number of colonizing alates can be estimated from the catches of the nearest suction trap. - The initial numbers of aphids can be derived from field counts as long as subsequent immigration ismeasured . Theforme r is usedb yCarte re tal .(1980 ) andth elatte rb yRabbing ee tal . (1979).
The numbers of aphids in each instar are stored in elements in one-dimen sional arrays, in addition to an associated one-dimensional array containing theirage si n hour degrees(H°) .A t each iteration, thenumber s ineac helemen t aremove du pon ei nth earra yafte r correctingfo r developmentalmortality .Th e corresponding elements in the one-dimensional aphid-age arrays are also up dated. The survival rates of the nymphsan d adults aretemperatur e dependent and are also affected by the crop developmental stage: as the crop ripens the survival rates decline. Reproduction is also crop-an d temperature-dependent, but it does not depend on adult agea si t isassume d that they do not livelon g enough for this to become important (Figure 8; Wratten, 1977). Asth ecro pripen san d theaphi d densityincrease sth eproportio n of nymphs that develops into alates increases. It isassume d that these alates emigratebe fore depositing nymphs.Th eeffect s of coccinellids,parasitoid s and diseasear e modelled, albeit in a simpleway .
Themodel , a listing of which isgive n inAppendi x A, consists of a serieso f steps: 1. Model initialization. The arrays used in the program are declared and their elements are zeroed. 2. Datainput .Thes ear evariabl ean dparamete rvalue stha t havet ob edeclare d at the start of each simulation: - theday so nwhic hth esimulatio nwil lstar tan dfinish, followe d byth esen sitivityanalysi sfactors , whichi na standar d simulation arese tt ozer oo rone ; - daily maximum and minimum temperatures; - latitude of thesite ,initia lcro pdevelopmenta l stage,th eaccumulate d day degreesabov e6 ° C(Anonymous , 1943) necessaryt oreac hthi scro pdevelop mentalstag ean dth enumbe ro f tillerspe rsquar emetr ea t flowering or after; - the days on which aphid immigration starts andfinishes an d theconcen tration factor (normally 40), followed by the daily suction trap catches (for initialization withfield count s small changes have to bemade) . - threeparameter sar euse dt oomi t orinclud esection so f theprogra mcon cerned with thenatura l enemies:th estar t andfinish day sfo r thepresenc eo f coccinellids followed by the number present daily for each instar; the start andfinish day so fth emortalit ydu et oparasitis man ddiseas efollowe d byth e hourly mortalities attributable to these natural enemies; - thetime so f sunrisefo r eachda yar ecalculate dan dstore di na one-dimen sional array.
18 3. Hourly temperatures. A sine curve fitted through the minimum (at sunrise) and maximum (at 1400 h) temperatures. The number of H° for a particular hour is the temperature plus 3.6. 4. Immigration. Thenumbe r of immigrant aphidslandin g pertille reac hda yi s calculated usingth enumbe r of S. avenae caught inth eneares t suction trap,or , when the second method of initialization is used, from the number of alates counted in the crop. 5. Development and survival. Thisinvolve s hourlychange si nth enumber san d ages of aphids in each age class, dependent on the temperature andcro pdevel opmental stage. The number of aphids entering theadul t instar (both apterous and alate) is reduced due to the mortality caused by parasitism and disease. Alate adults emigrate immediately after they become adult. 6. Reproduction and morph determination. The numbers of new nymphspro duced each hour are dependent on temperature, crop developmental stagean d adult morph. The alate and apterous adults are treated separately but their nymphs are combined. The proportion that develop into alate adults is deter mined by a multiple regression equation that incorporates aphid density and crop developmental stage. 7. Predators. Mortality due to the activity of aphid-specific predators isdeter mined using a subroutine (listed at the end of the main program). 8. Output. Thisconsist s of thenumber san dmorp ho f aphids ineac hinsta rto gether with crop developmental stage, and the effects of predators, parasitoids and disease. It is given for 1200 h each day for comparison with field results. 9. Cropdevelopmen t model. Atth een do f eachda yth edevelopmenta l stageo f thecro pi supdate d dependent on theaccumulate d daydegree s (D°) above6 °C up to and including that day. 10. Input variables. At theen do f asimulation , numberso f aphidsimmigrating , predatornumbers , mortalitydu et o parasitism and diseases anddail yminimu m and maximum temperatures are also printed.
3.2 The aphid
3.2.1 Immigration
The submodel
Forinitializatio n theprocedur eusin g suction trapcatche s isgiven ;th emetho d using actual field counts is described by Rabbinge et al. (1979). The timing and the daily number of alates colonizing a cereal crop are esti mated from the number of aphids caught during the immigration period in a suction trap, 12.2 m above the ground. The number of alates colonizing one million tillers (ALATIM) each day (the number of tillers per square metre is needed here) iscalculate d by multiplying thedail y suction trapcatc h byth ede position factor (TAYPAL) and the concentration factor. ALTIM is the cor-
19 responding number of alates per tiller. It is assumed that these alates have recently moulted and that after colonizing the crop they do not emigrate but stay until they die.
The data
Aphids fly at heights of up to more than 1000 m. Their mean densitydimin ishes with height according to the equation (Taylor &Palmer , 1972) F(z) = C(z + Ze)'a where F(z)i sth edensit ya t height z, Ca constan t related to population size, a a densitygradien t andZt a measur eo f thedepartur efro m linearityo nlogarithmi c co-ordinates. Thusth enumbe r of aphids flying overa give n areao f groundca n beobtaine d byintegration . Inthos especie so f aphidi nwhic hth edensity-heigh t profile hasbee nmeasure dth emea ndail ydensit ygradien t(a ) ranges from - 0.5 to -1.5. In the absence of density-height profiles aphid numbers can be esti mated from the equation lgD = a + bl g Z in which b has the value -1 and D is aphid density and Z height. The rate at which the aphids aredeposite d on thegroun d depends on their flight time. De position rates (in aphids ha-1) for several mean flight times (0.5 to 24 h) and densitygradient s (0t o -2.0) havebee ncalculate d (Taylor & Palmer, 1972)an d arepresente d inTabl e 1.
To calculate the deposition rate it is assumed that the flight time is 2 h, the average flight time for aphids in southern England (Taylor & Palmer, 1972), and the density-height profile is -1.0, which gives 237 alates ha"1 (96 acre-1) for every aphid caught in a suction trap. As the number of tillers per square
Table 1. Numbero f aphidslandin g (ha-1) equivalent toon eaphi dcaugh t ina 12.2 m suction trap.
Density Meanfligh t time(h ) gradient(b ) 0.5 1.0 2.0 4.0 8.0 12.0 24.0
0 1031 5 2579 1289 645 430 215 -0.5 1660 mo 415 207 104 69 35 -1.0 948 474 237 119 59 40 20 -1.5 2016 1008 504 252 126 84 42 -2.0 1031 5 5157 2579 1289 645 430 215
AfterTaylo r &Palme r (1972).
20 (aerial popn)
crop ^^ immi gration
-H> \ s'l NN sett ling x / D Figure 9. Relational diagram for cerealaphi dimmigration . metrei s known for eachfield th enumbe ro f alatespe rmillio ntiller sca nb ecal culated - thisi sth edepositio n factor. This, however, underestimates thenum bero f alateslandin go ncereal sb ya facto ro f about 1/40. Thepredicte dnumbe r of alates is thus multiplied by 40 (the concentration factor), which has been constant for different wheatvarietie s from 1976t o 1980.Figur e9 i sth erelation al diagram for immigration. 3.2.2 Development andsurvival The submodel Development in insects is primarily determined by temperature, so that the stageo f development canb ecalculate db yusin ga temperatur esummatio ntech nique, usually accumulated day or hour degrees (above a threshold tempera ture). Not all individuals of a species develop at the same rate. With 5. avenae thevarianc e of the mean rate issmal l (Dean, 1974b;Rabbing e et al., 1979)an d ina sensitivit y analysisi twa sshow nt ohav elittl eeffec t onpredicte d population trends (Carter &Rabbinge , 1980). Therefore only mean values were used. De Wit& Goudriaa n(1978 )describ ethi sa sa BOXCA R routinewit hn odispersion . With this approach, aphids of the same physiological age remain together and aremove d from one BOXCAR, orarra yelement , to thenex t at eachiteration . 21 Table 2. Duration (H°) of the nymphal instars and pre-reproductive delay (PRD) at varioustemperatures . Temperature (°C) JPh-1 Instar PRD I II III IV 10.0 13.6 1339.60 1117.92 1249.84 1335.52 435.20 12.5 16.1 1379.77 1209.11 1130.22 1205.89 325.22 15.0 18.6 1164.36 1169.94 1076.94 1231.32 306.90 17.5 21.1 1137.29 1088.76 1114.08 1375.72 381.91 20.0 23.6 1224.84 1073.80 1005.36 1274.40 AAM A(\ 22.5 26.1 1200.60 1145.79 1143.18 1297.17 579.42 25.0 28.6 1198.34 1172.60 1106.82 1384.24 985.18 Mean 1234.97 1139.70 1118.06 1300.61 481.75 Standarderro r 34.18 18.43 27.89 25.97 76.96 Accumulated duration 1234.97 2374.67 3492.73 4793.34 5275.09 After Dean(1974b ) In the S. avenae model, development times, in H°, are constant for each nymphal instar (Table 2), but the longevity of the adult depends on thecro pde velopmental stage, and becomes very short towards the end of the season. Survival is calculated hourly from the number of H° for that particular hour (Figure 10). For computing convenience updating of the population arrays starts with the oldest age class of the adult instar and works backwards to the 5P 1—-SP r-*S- ! t ! t (temperature) Figure 10. Relational diagram for development and survival of cerealaphids . 22 youngest ageclas s of thefirst instar . Mortality is taken into account duringth e updating procedure: NUMBERS (I) = NUMBERS (I - 1) X PROPORTION SURVIVING AGE (J) = AGE (I - 1) + H°. Theag ei schecke d against thelimi t for that particularinstar . If theag ei sgreate r than this limit the aphids in that age class are moved into thefirst ag e class of thenex tinstar ,thei rag ei sse tt ozer oan dth eorigina larra yelement sar ezeroed . If theseaphid sar eadult sthe nthe yar eremoved . Thisproces s resultsi nth e first class of the first instar nymphs becoming vacant, ready for the production of new nymphs. All fourth instar alatiform nymphs emigrate on moulting to the adult stagethu sth eonl y adult alatesrecorde d inth esimulatio n arethos ewhic h migrated into the crop. The data Therelationshi p between developmental ratean dtemperatur ewa scalculate d for cereal aphidsreare do nlea f discso f barley(cv . Proctor) (Dean, 1974b).Th e relationship islinea rove rth etemperatur erang e 10-22.5 °C(Figur e 11). Outside this range the relationship is not linear and allowance is made for this in the model (Subsection 3.2.4): development rate (in thousands per hour) 20 25 temperature (°C) Figure 11. Relationship betweendevelopmenta l rateo f cerealaphid san dtemperatur e (after Dean, 1974b). 23 DEVELOPMENT RATE = TEMPERATURE x 0.000196 + 0.000706 for which r = 0.98,p < 0.001, 4 d.f. This equation givesa developmenta l threshold temperature of -3.6 °C.Thi s was used to calculate the mean development times, in H°, of the first few in- stars. It was assumed, based on studies of Brevicoryne brassicae (Hughes, 1963), that the fourth instar alatiform aphids take 1.5 times longer to develop than apterous fourth instar aphids, less detailed results for S. avenaeindicat e that this assumption is correct. The length of time that adult aphids survive in thefield wa sbase d on theassumptio n that theywil l not survivea slon ga sthos e reared in thelaborator y (Dean, 1974b). Inth emode l adult longevity is affected by crop developmental stage, although this has not yet been confirmed experi mentally. Adult longevity can also be calculated from the cumulative propor tiono f aphidsdying . Inmos tcase slongevit y isnormall ydistribute dan da prob abilityplo t linearizes therelationship . Themaximu m longevity used byRabbin - ge (1976) and Rabbinge et. al. (1979) was theaverag e plus threetime s thestan dard deviation. Nymphal survival ratesar eth emea n of theresult s obtained by Dean(1974b ) for a range of temperatures, but reduced after crop developmental stage 73 from 93.8% to 45% (birth to adult moult) for apterous aphids and 93% to 37.4% for alatiform aphids to conform with the observations of Watt (1979a). Adult survival rates used are 90% (adult moult to maximum age) before stage 73 and 60% after this, again estimated from Watt's (1979a) observations. 3.2.3 Reproduction and morph determination The submodel It is assumed that alate adults are reproductively mature on arrival in the crop, while apterous adults have to pass through a pre-reproductive delay be fore reproducing. Figure 12 is the relational diagram for reproduction and morph determination. Thus two variables areuse d to describe apterousadults : TOTAD - the total number of apterous adults, and TOTADR - the total number of reproductively mature apterous adults. TOTAD > TOTADR. Reproductive ratei sdependen t onth emorp ho f adult aphids, whether apterous or alate (Wratten, 1977), temperature and the crop developmental stage. Apte rousaphid shav emaximu mreproductiv erat ea t 20° Cwhe nfeedin g oncrop sa t developmental stages5 9t o73 .A t present noeffec t of intra-specific competition on reproduction is included in the model. The effect of adult age on reproduc tioni sno t takenint oaccoun ta si ti sassume dtha tadult sonl ysurviv efo ra shor t period. The nymphs produced by apterous and alate adults are summed before the 24 proportion that will develop into alates (ALATE) is calculated. Watt &Dixo n (1981) have shown experimentally that theoffsprin g of alateadult sca ndevelo p into alates. The proportion is calculated using a multiple regression equation that incorporates cropdevelopmenta l stagean daphi d density. As aphid density increasesan dth ecro pripens ,th eproportio n of nymphstha tdevelo pint oalate s increases. The data Wratten (1977) has shown that there is a marked difference between the reproductiverat eo f apterousan dalat eadults .Th ereproductiv erat eo fapterae , calculated from Dean (1974b), for aphids on barley seedlings (cv. Proctor) is 0.0062 nymphs H0"1 adult"1; for alates it is 0.0048 nymphs H0"1 adult"1. Watt (1979a) has shown that the reproductive rate of S. avenae is 1.6 times higher on theear s of oats than on theleaves . The ratesgive n above werethere fore assumed to apply before crop developmental stage 59 and between stages 73 and 83, i.e. milky-ripe stage. Between stages 59an d 73thes e ratesar emulti plied by 1.6, which gives 0.0100 nymphs H0-1 adult"1 for apterae and 0.0079 nymphs H0-1 adult"1 for alates. After crop developmental stage 80 and below 10 °C and above 30 °C the reproductive rate is set to zero. Between 20 and 30 °C the reproductive rate is reduced linearly to zero. Inth emodel , themorp ho f theaphi d isdecide d atbirt h(Dewar , 1977)an di s dependent on two variables: aphid density and crop developmental stage. The Table 3. Theproportio no foffsprin g born tosi xgroup s ofapterou s mothersdurin g the first twoday san dth ethir d to seventh dayso f reproduction that developed intoalata e whenreare di ngroup so nth esecon dlea f andear so f wheat(cv . Opal)a tvariou s devel opmentalstages . Group Proportion alateoffsprin g Alateoffsprin g born onday s3 to7 borno n days 1 and2 andreare do n developmental proportion developmental stage1 2 stage 1 0.51 12 0.70 2 0.45 59 0.30 3 0.50 65 0.36 4 0.54 71 0.71 5 0.50 75 0.87 6 0.44 >80 0.94 Ankersmit & Dijkman(t ob e published). 25 dependence oncro pdevelopmenta l stageha sbee nshow nb yAnkersmi t & Dijk- man(unpublishe d data;se eTabl e3 )an dWat t& Dixon (1981). Multipleregres sion analysis using the sampling results from two wheat fields near Norwich studied in 1977 was used to determine the relationship between the proportion of alates developing, aphid density and crop developmental stage. As theduratio no f thealatifor m fourth instarwa sassume d tob e 1.5time sth e length of theapterou s fourth, thenumbe r of thelatte rwa smultiplie d by 1.5 to compensate for this. The number of alatiform fourths was then expressed asa percentageo f thetota l numbero f fourth instaraphid spresent .Thi swa suse da s the dependent variable. Aphid density (TOTDEN)i neac hfield wa splotte d against physiological time on the x axis, with a threshold temperature of -3.6 °C. Crop developmental stage (GSTAGE) was also plotted against accumulated D°, using 6 °C as the threshold temperature. Thealatifor m fourth instarnymph srecorde di nth e field were born, on average, 186 D° previously in terms of aphid development and HOD0 in terms of crop development. The difference in time is due to the dif ferent threshold temperatures. Thus the aphid density and the crop develop mental stagea t thebirt h of theseaphid swer eestimated . Thesevalue swer ethe n used as the independent variables in the multiple regression: %ALATE = 2.603 x TOTDEN + 0.847 x GSTAGE - 27.189 for which r2 = 0.96. Bothindependen tvariable sar esignifican t (Table4) ;thi si ssupporte d by field observations of Ankersmit (personal communication), Rabbinge et al. (1979) and Watt &Dixo n (1981), which show that even for years when aphid density was low a high proportion of alatiform nymphs was produced as the crop ripened. Table 4. Regression coefficients of the multiple regression relating the proportion of nymphs developingint oalata et oth enumbe ro faphid spe rtille ran d cropdevelopmenta l stage. Coefficient S.E. t-value Averagenumbe ro f aphidspe rtille r 2.603 0.340 7.659** Cropdevelopmenta l stage 0.847 0.339 2.501* Constant -27.189 15.956 -1.704 N.S. *p < 0.05; **p < 0.001;N.S . = not significant. 26 (temperature) Figure 12. Relational diagram for reproduction and morph determination of cereal aphids. 3.2.4 Physiologicalprocesses The submodel The most widelyuse d system for a time scale in insect population modelsi s that of physiological time based on accumulated H° or D° above a threshold (Hughes, 1962). This approach is not used here, instead each hour, develop ment, survivalan d reproduction of theaphids ,predato r consumption (see Sub section 3.3.3.)an d crop development (seeSectio n 3.4) arecalculated , basedo n the prevailing number of H°. In this approach a real-time scalei sused ,whic h makesi teasie rt otes tth evalidit yo fth emodel' spredictions .Thu si ti ssimila rt o the approach used in other monographs on simulation (e.g. Rabbinge, 1976; Barlow &Dixon , 1980). Initially,th etim eo fsunris e(t oth eneares tinteger )i scalculate d asthi si sth e time when temperature is at a minimum. The actual time depends on the latitudeo f thesit ean d theda ynumbe r (timeo f year).Hourl ytemperature sar e calculatedb yfitting a sin ecurv ethroug h theminimu man dmaximu m(a t 1400h ) temperaturesfo reac hday .A naverag eove reac hhou ri scalculate d(AMTEMP ) by linear interpolation between the temperatures at the start and end of the hour. For calculating aphid development thisaverag etemperatur e isconverte d to H° (HRDEG) byth eadditio n of 3.6 over thetemperatur e range 10.0° Ct o 22.5 °C.Ove rthi srang eo f temperatures therelationshi pbetwee ndevelopmen t ratean dtemperatur ei s linearan di ti s assumedtha tth eaphid' sreactio nt otem perature changei sinstantaneou s (Rabbingee tal. , 1979).Fo r averagetempera turesles stha n 10° Cbu t greater than5. 0 °Cth enumbe r H° isreduce dlinearl y 27 towardszero ,whil ebelo w 5.0 °Cth enumbe ro f H° isse ta t0.1 ,i.e . aver ylo w value.Thu sfo rtemperature sbelo w 10°C ,developmen t isles stha ntha t predic tedb ylinea rextrapolation . Between22. 5an d25. 0° Cth enumbe ro fH °i sse ta t a constant 26.1;abov e 25.0 °C but less than 30.0 °C it is reduced linearlyto wards0.1 ;a t30. 0° Can dabov ei ti sse ta t0.1 . Thiscircumvent sth eassumptio n made in calculating physiological time, alinea r relationship over awid erang e of temperatures, which would result at the temperature extremes in predicted developmental rates greater than those observed. Longevities and development times are measured in H°, so that survival rates, for eachhou r canb ecalculate d assuming aconstan t ratethroughou tth e aphid'slife-span . Thesetw ovariable sar etemperatur edependen tan dar ecalcu latedusin gAMTEM P + 3.6rathe rtha nHRDEG .Thu sa tlo wan dhig h tempe ratures aphids continue to die, but development is veryslow . Reproductive rates are measured in nymphs H0_1 adult"1, but this process hasa differen t relationshipwit htemperatur etha ndevelopmen t andAMTEM P + 3.6 isuse dinstea d of HRDEG. Below 10.0° Can dabov e30. 0 °Creproduc tion stops. Between 10.0an d20. 0 °Creproductio n increases, butbetwee n20. 0 and30. 0 °Ci tdecrease slinearly . Reproduction alsodepend so nth eadul t morph and the crop developmental stage (see Subsection 3.2.3). Thedat a The calculation of the time of sunrise follows that used by Rabbinge et al. (1979), but with time as an integer in hours rather than as a real number.Th e algorithmuse dt ocalculat ehourl ytemperatures , usingth eminimu man dmaxi mumvalues , isa nadaptatio no f thatuse db yCarte r(1978 )an dRabbing ee tal . (1979). The number of H° is calculated by adding 3.6 to the mean hourlytempera ture. The adjustments made to the number of H° at thetemperatur e extremes are partly based on Dean's results (1974b) and partly established by trial and error.Th eadjustment s toth enumbe ro f H° usedt ocalculat ereproductio nar e also based on Dean's results (1974b)an d estimates of what ishappenin g atth e temperature extremes (i.e. below 10° C orabov e2 5 °C). It would beusefu l to knowth eeffec t of thesetemperatur eextremes , especiallywhethe rther ei sa la g in the resumption of development and reproduction when conditions become more favourable. 3.2.5 Adaptation of the modelfor othercereal aphidspecies The same model structure used for S. avenae can be applied to othercerea l aphid species, i.e. M. dirhodum and R. padi, providing the aphid parameters 28 and variables arechanged . This has been done for M. dirhodum using biologi cal characteristics derived from the laboratory studies of Dean (1973a, 1974b) and Ankersmit (personal communication). The predicted population growth is in good agreement with that observed in different years and different places (Rabbinge & Marinissen, 1981. Internal Report, Department of Theoretical Production Ecology, Agricultural University, Wageningen). Whenth emode l isinitiate d withsuctio ntra pcatche sth econcentratio n factor determining thenumbe ro f aphids colonizing acro pneed st ob echanged . There is little information on the flight behaviour of M. dirhodum and R. padi. The concentration factors for the two species would havet o bedetermine d bycom paring predicted and observed numbers of alates. Their threshold temperature for development, and hence development times, are different (e.g. for M. dir hodum it is -2.2. °C), as arethei r reproductive rates and their dependence on temperature and crop developmental stage (Vereijken, 1979;Watt , 1979). Sur vivalrate san dthei rinteraction swit htemperatur e andcro pdevelopmenta l stage are also likely to vary for each species. Finally, although morph determination is dependent on aphid density (Dixon &Glen , 1971;Elkhider , 1979), the crop developmental stage is also likely to be important and to differ in its effect for each species. Thusalthoug h thestructur eo f themode l needno tb echanged , thebiolog y of each aphid and their response to changes in their environment will have to be determined. 3.3 Natural enemies 3.3.1 Introduction Threelevel s of approach canb eadopte d when simulating theeffect s of natu ral enemies: empirical, simplified interaction and complex interaction. Thena turalenemie s included inthi sstud yar ecoccinellids , parasitoids and fungi. Coc- cinellids are the most common predators in cereal fields in Norfolk (Carter et al., 1980) although in other parts of Europe syrphids may also be numerous, e.g. the Netherlands (Rabbinge et al., 1979). The submodel for coccinellids is basedo na simplifie d interaction, whereastha t forth ecombine deffect s ofpara sitoids and fungi is empirical. The numbers of coccinellids, recorded in the field, areuse d to calculate the number of aphids eaten per hour while themor tality due to parasitoids and fungi, estimated from field counts of mummified and diseased aphids, Isuse d directly in themodel . At present the different spe cieso f naturalenemie sar elumpe dtogether . Account willb etake no f theeffect s of individual species as more information becomes available. The effects of polyphagous predators are ignored because their searching and consumption rates are unknown. Much of the detailed laboratory information on thesepre - 29 dators is not suitable for usei n themodel . 3.3.2 Parasitoids and diseases The submodel The effects of these organisms are included within the main aphid model, operatingafte r thefourt h instar aphidshav ebee nupdate d butbefor e thealate s emigrate. If PARNO equals one or if there are no parasitoids or diseasethe n this submodel is omitted. Thetota l number of susceptibleadults ,TOTFAD , iscalculate d bysummin g the numbers in the first ageclas so f the apterous, ADULTS(1) ,an d thealate , ALATED,adults .Th enumbe rdyin gpe rmillio ntiller si sPARSIT ,th eproduc t of thetota l number of aphids, TOTDEN x 106,an d themortalit y factor. The numbers of alate (PARAL) and apterous (PARALD) adults killed are calcu lated, assuming both morphs are equally vulnerable to parasitoids or disease. These are then substracted from their respective age classes. The number of aphids killed byparasitoid s and diseasesever y2 4h i sTOTPAR . Thedat a Verylittl e research has beendon eo n thepopulatio n dynamics of theparasi toids and fungi of cereal aphids. Asa large number of species isinvolve d this component isver ycomplicated . Astud yo f theirinteraction swit hcerea laphid s would result inmor erealisti cmodels . Counting the number of mummies and diseased aphids in the field under estimates the mortality caused by parasitoids and entomophagous fungi (McLean, 1980), and to correct for this the results should be multiplied arbi trarilyb y2 befor e theyar euse di nth emodel .Powel l(1980 )ha sshow ntha tpar t of theexplanatio n is that aphidsparasitize d byToxares deltiger mummif y ono r in thesoi lan d soar eno t recorded inth etille rsearches . Toge ta naccurat eestimat eo fth eproportio n of aphidsparasitize d ordisease d on each sampling occasion it is necessary to have counts of (a) live healthy aphids,(b) live ,bu t parasitized or diseased aphidsan d (c)dead , mummified or diseased aphids. Then the percentage mortality is: b + C x 100 a + b +c Unfortunately mortalitydu et oparasitoid san ddiseas ei s recordedi nth efiel d as numbers of mummified and diseased aphids. The proportion of the total 30 population parasitized or diseased is used to calculate the number of newly moulted adults that died each hour. This is an over-simplification but thesub model cannot be made more realistic until more is known about thebiolog y of the parasitoids and diseases. 3.3.3 Coccinellids The submodel The number of aphids in each instar is converted to aphid units (AU) using the following transformation: an aphid unit is equivalent to 1.0 adult, 1.5 fourth instar, 2.0 thirdinstar , 3.5 secondinsta ro r5. 0first insta raphid s(Lowe , 1974). Thetransformatio n is based on sizedifference s of the various instars. A moreaccurat e method would also takeint o account the 'attractiveness' of each instar, capture efficiency and prey utilization (Rabbinge, 1976) but this infor mation is not available for coccinellids feeding on S. avenae.Th e aphid units aresumme d togiv eth etota lAFIDUN , andth enumbe ro f aphidunit smad eu p of thefirst thre einstars ,ONYAFD .Th epredato rsubroutine , PREDTR, canb e omitted if necessary, i.e. if there aren o predators present or if the temperature is less than 15 °C or greater than 30 °C. If PREDTR iscalled , thevalu e of ONYAFD ischecked . If there aren o aphids present in the first three instars (young aphids) then the first part of the sub routine is skipped. If ONYAFD is not equal to zero then the proportion of the total number of aphid units that areyoun g aphids iscalculated , PERPRE. The numbero f aphidunit skille db yal lpredato rinstars ,TOTNY , iscalculate d from (a) the consumption ratesi n aphid units per H° for each larval instaro fCocci- nella7-punctata given in Table 5, and (b) the numbers of larvae in each instar and the number of H° for that instar, assuming the predator has an activity temperature threshold of -3.6 °C. As the fourth instar and adult beetles also Table 5. Consumptionrate so fcoccinelli dlarva e at2 0° C whenfe dexces saphid s inth e laboratory. Coccinellid instar Aphids eaten No (3rdinstar )d- 1 AU d"1 AUOi0)-1 I 4 2.0 0.0053 II 13 6.5 0.0172 III 21 10.5 0.0278 IV 36 18.0 0.0477 AfterMcLea n (1980). 31 eat fourth instar and adult aphids, the number of aphid units made upo f the first threeinstar si sreduce db yPERPRE .The nth eproportion so f young aphids killed, PRDFC, and surviving, 'PRDFAC, arecalculated . Ifther ear en oyoun g aphidspresen tthe n fourth instaran dadul t coccinellids preyonl yo n fourth instaran dadul t aphids.Th enumbe ro f aphidunit skilled , TOTADC, is calculated and TOTNY is set to zero and PRDFAC to unity. If therear eyoun gaphid spresen tthe nTOTAD Cwil lb elowe ra sth efourt hinsta r and adult beetleswil l alsopre y on these. Theproportion s of fourth instaran d adult aphids killed, PRDAD, and surviving, PRDADC, are calculated. Total predation, TOTCON\ is'TOTNY ' + TOTADC Controli sthe nreturne dt o the mainprogram . If ALOWAF (switch variable) equals one and ONYAFD or ADUAFU (= AFIDU N - ONYFAD) are less then 3.0 aphid units, then PRDFAC and PRDADC, respectively, increaselinearl y asaphi d density declines.Thi smean s that at low aphid densities coccinellids are not consuming aphids at themaxi mumrate . Thenumbe ri neac hinsta rag eclas si sreduce db yth eappropriat eamount ,a s are the totals for each instar. A new total aphid density is calculated and TOTCON is summed over 24 h, from 1300t o 1200th e following day, to give daily consumption, DAYCON. Thedat a Thedail y consumption of C. 7-punctata larvae, fed anexces s of thirdinsta r aphidsa t2 0 °Ci nth elaboratory , hasbee ndetermine d byMcLea n(1980) .Th e results are presented in Table 5. The numbers of aphids were converted into aphidunit s(AU) ,a soutline dabove .Thes eexperiment swer edon eunde rcondi tionso f constanttemperatur ean dda ylength ,an di twa sassume dtha tth ecocci nellids only fed during the day. Thehourl y consumption ratei sthu stota lcon sumption divided by 16 (i.e. hours of daylight), or in AU H0-1, hourly con sumption divided by23.6 . Coccinellid searching behaviour is dependent on temperature (McLean, 1980). Inth emode ln oaphid sar eeate ni fth eaverag ehourl ytemperatur ei s less than 15° Co rgreate rtha n3 0°C .Th ethreshol daphi ddensit yi s3 AU per tiller (a 'guestimate'), below which predation is linearly reduced. There is no infor mation on either theeffect s of temperature extremes orlo w aphid densities on coccinellid searchingbehaviour . 3.4 Crop The submodel The major objective of the present study is the explanation of cereal aphid population growth. Therefore, detailed crop growth and development processes are not strictly relevant, but as cereal aphid population growth is dependent on the crop developmental stage (see Chapter 2 and Section 3.2), it is included (Vereijken, 1979; Watt, 1979a). At the end of each day the crop developmental stage, GSTAGE, is updated. The number of D° is calculated using an algorithm developed by Frazer &Gil bert (1976) with a developmental threshold temperature of 6 °C. The develop mental stage is calculated using a polynomial equation, based on the accumu lated number of D°, designated TOT. Rabbinge et al. (1979) used an alternative approach. Crop developmental rate, expressed in decimal units, is linear up to flowering and again after flowe ring but with adifferen t slope and intercept. Before flowering therelationshi p is Y = 0.0007 X - 0.002 for which Y = developmental rate and X is temperature. crop development stage 90 300 400 500 accumulated daydegree s above 6° C Figure 13. Relationship between wheat development stage and cumulative daydegree s above 6 °C in thefield (1977) . w Afterflowering th erelationshi pi s Y = 0.0012*-0.01 The latter formula implies that in the period between flowering and end of kernelfilling, late-milky-rip e (crop developmental stage 77) 850 °C havebee n accumulated at 10°C . The introduction of a new developmental scale, which is calibrated to give linearity overth ewhol erang eo f cropdevelopmenta l stages, could result inth e development of asingl erelationship . Thedat a The field results from 1977, from three sites in Norfolk, were used to cal culate the polynomial equation used inpredictin g cropdevelopment . Fieldob servations were carried out at least weekly, and usually twice a week after flowering. Theresultin g equation (seeFigur e 13) is: GSTAGE = 0.173 X TOT - 0.00)125 (TOT)2 + 26.336 for whichr 1 = 0.97, n = 48. 14 4 Results 4.1 Comparison of model output with observed results 4.1.1 Validation Verification and validation are terms that are loosely used in simulation studies. Inthi smonograp h verification is'testin gt ose etha t thecompute rpro grami n fact operates on input data inth eintende d way*(Loomi se tal. , 1979). Validation isth eproces so fcomparin gth emodel' sprediction swit hreality .Th e cerealaphi d model for S.avenaeha sbee nthoroughl y verified, bybuilt-i ncom puter checks and detailed examination of the program. The simplest means of validation, and probably the most widely used, isa subjective comparison of model predictions with results obtained fromfield surveys,ideall yove ra numbe ro f yearsan di ndifferen t locations.Carte r(1978 ) has criticized many of theearl y insect population modellers for their failure to validate their models.Ten g et al. (1980)us ebot h a subjective comparison and twostatistica ltest st ovalidat ethei rmodel ,whic hsimulate sth edevelopmen to f a barley leaf rust epidemic.Th efirst tes t isa linear regression analysis of field resultsagains tmode lpredictions .However ,a sth epoint sar ei na tim eserie si ti s not possible to assign significance levels (Barlow &Dixon , 1980).On ewa yt o overcome this problem is to compare the observed peak densities, or their timing, with model predictions. These points are independent and the correla tioncoefficien t andth eresult so f the/ test so nth eslop e(shoul db eone )an dth e intercept(zero )o fth erelationshi pgiv ea stringen ttes to faccurac yo fth emodel . Theonl yproble m withthi sapproac h isa practica lon e - eachpoin t represents a season's samplingo f onefield. Ten ge tal .(1980 )als ous eth enon-parametri c Smirnov test to determinewhethe r therei sa significant difference betweenth e observedan dpredicte dvalue sa tth epoin twher eth etw ocurve sdiffe r most. Al though this test is less stringent than regression analysis, as it is only testing significance at onepoint , itdoe sno t suffer thedrawback so f timeserie s regres sionanalysis .However , whenth eincidenc eo f adiseas eo rpes ti slo wth ediver gencebetwee n observed and predicted resultsmigh t beto o small for thetes tt o be meaningful (Teng et al., 1980). In this study a subjective comparison of population trends and a regression analysiso fth eobserve d andpredicte d population peaksar euse dt ovalidat eth e model. 1€ 4.1.2 Model predictions Crop submodel A comparison of the predictions of the crop development model with field observations (U.K., 1976-1980; the Netherlands, 1976-1979) shows reasonable agreement (Figure 14a-n). The rate at which the crop ripened in the U.K. was overestimated in 1979 (Figure 14f) probably because the wet summer slowed down crop development. At present the effect of rain on crop development is notinclude di nth emodel . Asth eU.K .field result s for 1977(Figur e 14 c,d)wer e used to construct the crop development model they are included for reference only. It is not always easy to determine the crop developmental stage, asi t can vary within afield an d in particular it is difficult to recognize stages within the milky-ripe stage (stage 73-79), which can be prolonged. This is serious because asth egrai nripen sth esurviva l andreproductiv e ratesan dmorp hdeterminatio n of the aphid change dramatically and these are primarily responsible for the decline in aphid numbers. crop development stage 90, • =observe d 80 or predicted 70 60 50 40,P-^# 1 30;•••••••• J i i i 1 1 1 L• 3 0 ^y•—• — • J•••• 1 1 L • JU••••••• - 30«- J L J• L •• 19 26 2 7/,- 7/. 7 /, 7% % 21 3a 7, 14/ n 7 26, 2, 97/ 16, 23 / y30/ 7, 14, 19, 26, 2/ % 16/ 23 , /30 , 1. 14, 90-5 5 6 6 4 \ 4 n n h s 4 4 e 4 4 i 4 4 4 4 4 940 4 4 'i 90r 90r f / o 80- 80- ° V •80 o ° / -o"5 70 _^* 70 - .' o 70 o / X 60r - 60 60 50 50 - t 50 40 •/ 40. / 40 30 • • • L J 1 L 30 J L ' ' ' '30 J i- J L ]9/r 26/c \ \ \ 2\ 3 **£ crop development stage 100 100 90 - g 90 80 80 s 70 70 /o /o So 60 60 -S 50 50 • 1 1.1 /.ft TIII to 2 2 2 13/ 2 3 1 2 100 r %X \ \ \ \ % 7 mr\ \ % h V7 *V7 h 90 90 o ?-V** 80 /: 80 ./o / i^O o ,—' 70 70 - s*" s 60 60 50 50 v 40. J I I I I I L 40 J i i t i i 27, 3, 107 17y 24/ 1/ 8/ 15/ 22/ 26. 3, 10, 17, 24, 31/ 1. 14/ 21, 75 i ;6 4 i 77 77 77 x7 % n n n n n % 78 i 8 date crop development stage 90r W 90 r 90 r m o 80 80 '"80 A' S* 70 70 70 /. / 60 60 y 60 /. /• 50 50 50 / 40 40 40 30L £ J I L I • i I I L 301—« • ' ' ' 1 ' 29, 5/ 12/ 19/ 26, 3, 10, 17, 24, 5/ 12/ 19/ 26, 3, 10, 29/ 5/ 12/ 19/ 26, 3/ '6 ^ 76 't> n n '5 76 76 '6 76 77 75 4 76 76 76 n n n n 90r n 80 o o ^.•- 70 / 60 / 50 40 30L i • t » 13, 20/ 27/ 4/ 11/ 18/ 25/ % i i 76 n n n n date 17 aphids per filler 100 Field 1 • Field results 90 - o Reduced predation x Maximum predafion 80 70 60 50 40 30 \ o 20 of/ X °x/ 10 \ \ 1 i i n 26/5 2/6 9/6 16/6 23/6 30/6 7/7 date Figure 15. Observed and predicted trends in numbers of aphids per tiller of wheat(cv . Maris Huntsman), Field 1,Norwic h 1976. Aphid submodel The results collected during 1976-1980fro m fields near Norwich, inth e U.K., are used in the subjective comparison with model predictions. Two winter- wheatfields nea r Norwich wereintensivel y sampled in 1976,1977an d 1980,an d one field in 1978 and 1979. The field results from Wageningen 1976-1979, and results collected from other parts of the U.K. in 1979an d 1980ar e used in the regression method for validation described in Subsection 4.1.1. As the results varied between years and regions they are a rigid test of the accuracy of the model's predictions. For 1976,th e model predicts an earlierrise i naphi d numbers and higher peak levels of abundance than those observed in the fields sampled near Norwich (Figures 15an d 16).Thi s might reflect our poor understanding of the effects of the coccinellids and parasitoids, which werecommo n in 1976.Th e processes in corporated in the submodel for predation affect the predictions. Predators arc aphids per tiller 100 Field 2 • Field results 90 o Reduced predation x Maximum predation °° 80 o o 70- .x o x 60- o 50 40 30 20 10 0 iQQQQ0**?000 26/5 2/6 9/6 16/6 23/6 30/6 7/7 date Figure 16. Observed and predicted trendsi nnumber so f aphidspe rtille r of wheat(cv . MarisHuntsman) , Field2 , Norwich1976 . assumed either to eat the maximum number of aphids possible each day, irres pectiveo f aphiddensity ;o rthei rconsumptio n is reduced linearlya taphi ddensi tiesles stha n threeaphi d unitspe rtille r(Subsectio n3.3.3) .Maximu mconsump tion by the coccinellids, independent of aphid density, gives a better prediction of theaphi d population trendstha n doesreducin gpredatio n at lowaphi ddensi ties. This means that either coccinellids are efficient at finding aphids at low densities or some other factor is missing from the model. As the instar and morph of the aphids were not recorded in 1976i t isdifficul t to account for the difference between observed and predicted population trends. Thepredicte d population curvesfo r thetw ofields sample d in 1977ar esimila r tothos eobserve d(Figure s 17 and 18).Th edifferenc e inaphi d numbersbetwee n the fields, due to a slight difference in crop developmental stage, is accurately predicted. Asa further test of theaccurac y of the model's predictions thenum bersi nspecifi c instarsca nb ecompare d withthos eobserved . Thisindicate s that the model is giving an acceptable representation of what is happening in the ^fl aphids per filler 100 90 • Field result's o Simulation predictions 80- 70 60 50 40 30 20 10 - leoocffff^0 i 16/6 23/6 30/6 7/7 AUI1 21/7 28/7 date Figure 17. Observed and predicted trendsi nnumber so f aphidspe rtille r of wheat(cv . MarisFreeman) ,Norwic h1977 . field (Figures 19an d 20). Thenumbe r of adultaptera ei sslightl y underestimated (Figure20 ) - thus they probably livelonge r than allowed for in themodel . In creasei nth etim efo r whichadul t apteraesurviv ewoul d havet ob ecompensate d for by a decrease in the survival rate of the nymphs. Carter (1978) has shown, however, that doubling adult longevity, from 7 to 14days , at 20 °C, only in creasesth epea k density by30 %an d doesno t affect thedat eo f thepeak . Adult longevity needst o bedetermine d under natural conditions.Th enumber s of im migrant alatesobserve d inth efiel d andthos epredicte d byth emodel ,initialize d with data from suction traps, weresimila r until theen d of June. From July on wards the numbers of alates are underestimated (Figure 20).Alatifor m fourth instar nymphsar euncommo n atthi stim e(whe nimmigratio n ceasesi nth emodel ) and henceth eincreas ei nth enumbe r of alatesi sdu et ocontinue d immigration. When a further five days of immigration are included in the model the predic tiono f alatesi sclose rt oth eobserve d butther ei slittl eeffec t onth epea k density reached. This is because at this time alates represent less than 10% of the total adult population. 40 aphids per tiller 100h 90 • Field results o Simulationprediction s 80- 70 60- 50- 40 30 20 10 0 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 18. Observed and predicted trendsi nnumber so f aphidspe rtille ro f wheat(cv . MarisHuntsman) , Norwich1977 . The predictions for 1978 overestimate the peak density by more than three times: 17.2pe r tiller rather than 5.0 (Figure21) . However, the shape of thepo pulation curve is accurately predicted. The numbers in all instars are overesti mated (Figures 22an d 23).Th e low temperatures and high rainfall in thesum mer of 1978migh t have reduced the survival rates of nymphs and adults in the fieldbelo w that included in the model. Natural enemies were uncommon and had little impact on aphid population build-up, although it is possible that the effects of Entomophthora spp. were underestimated. In 1979S. avenaewa s rare, although M. dirhodum wasver ycommon . Asi n 1978 only a few alate S. avenae colonized cereals, and they arrived late in the season (Walters, 1982)an d hence aphid population development was retarded. The peak density predicted is half that observed (Figure 24), probably because the predicted crop development is too quick. A slower ripening of the crop in themode l for 1979give saphi d populations that arei ngoo d agreement with the observed populations (Rabbinge& Marinissen, unpublished results).Thi sillus - aphids per tiller 100 i ± 9/6 16/6 23/6 30/6 7/7 14/7 21/7 28/7 o o o 16/6 23/6 30/6 7/7 14/7 21/7 28/7 9/6 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 19. Observed(• ) andpredicte d(o ) trendsi n numberso f(a )first to thir dinstar ; (b)apterifor m fourth instar;an d(c )alatifor m fourth instaraphid spe rtille ro fwhea t(cv . MarisHuntsman) , Norwich1977 . trates howimportan t theaphid-hos t interaction isi naphi d population dynamics. For 1980, the model predicts greater numbers of aphids than those observed (Figures 25 and 26). Predation, as in 1976, was important in reducing aphid population levels.Th e model does predict thedifferenc e between thetw o fields - i.e. aphids achieved a higher density in the field of cv. Maris Huntsman. Weather conditions during June, especiallynea r the end, wereadvers e as rain fall was high: over 40 mm of rain fell on 30 June. This probably reduced the population growth rate. Linear regression analysiso f therelationshi pbetwee n predicted and observed peak numbers, for theabov eresult san d thosefro m other locations,reveal stha t the model predictions are reasonably accurate (Figure 27). However;th e 1980 Englishfield results ,othe r than thosefo r Norwich, aremuc h lowertha npredic ted, as populations declined after flowering. This was due to predators and parasitoids andadvers eweathe rconditions .Thes eresult swer eomitte d from the 42 aphids per tiller T Ir "J. V* I 16/6" 23/6 30/6 7/7 K/7 21/7x 28/7 0.20r b xr o Standard immigration Q161— x extended immigration 0.12 0.08 0.04 3^^°°^' 26/5 2/6 9/6 16/6 23/6 30/6 7/7 date Figure 20. Observed(• ) andpredicte d(o ) trendsi nnumber so f(a )apterou sadult ; and (b)alat eadul t aphidspe rtille r of wheat (cv.Mari sHuntsman) , Norwich1977 . regression analysis although they are presented in Figure 27. When more is known about the effects of natural enemies it ishope d to improve thepredicti ons. S. avenae at Rothamsted in 1979achieve d lowpea k densities - lesstha n 1.0 Pertiller . The predicted peaks wereals o low - lesstha n 2.0pe r tiller, although on a log scale this difference is marked. If these 1979 Rothamsted results are omitted from the regression analysis the relationship (see Figure 27)i s Y = 0.74 X + 0.25 43 for which r = 0.86, p < 0.001, n = 13. The slope is not significantly different from 1.0 or the intercept from zero. When the 1979Rothamste d results areinclude d the relationship (see Figure27 ) is: Y = 1.20 X - 0.53 for which r = 0.87, p < 0.001, n = 16. Theslop e isno t significantly different from 1.0, but the intercept isjus t signifi cantly less than zero. With theexceptio n of theyear swhe naphid swer erar ean dwhe n naturalene mies were particularly important, the model gives predictions that are in close agreement with observed results from a number of different localities. Thusal though some processes need further clarification the model is reasonably accu rate. aphids pertille r 20 18 o 16 - o o 14- 12 - 10 8 0 22/6 29/6 6/7 13/7 20/7 27/7 3/8 10/8 date Figure 21. Observed ( • ) and predicted (o ) trendsi n numberso f aphidspe rtille ro f wheat (cv. MarisHuntsman) , Norwich1978 . AA 20 aphids per tiller 110, oo „ 1.0 WO o o 90 4 _L ^jgPSH-H 15/6 22/6 29/6 6/7 13/7 20/7 27/7 3/8 10/8 80 12 - o 70 28 - o O o 60 o° 2.1- 50 20 40 16 o o o 30 12 o 20 08 10 04 f 0 0 1—1 1 _L 22/6 29/6 6/7 13/7 20/7 27/7 3/810/ 8 15/6 22/6 29/6 6/7 13/7 20/7 27/7 3/8 10/8 date Figure 22. Observed(• ) andpredicte d(o ) trendsi nnumber so f(a )first t othir dinstar ; (b) fourth instar; and (c) fourth instar alatiform aphids per tiller of wheat (cv.Mari s Huntsman), Norwich1978 . 4.2 Sensitivity analysis 4.2.1 Introduction During and after the construction of a model the importance of its compo nents can be assessed using sensitivity analysis. Carter & Rabbinge (1980) de scribetw oform s of sensitivityanalysis :fine , and coarse.Fin ei swher esmal lpo sitive and negative changes are made to individual components to estimate the level of accuracy needed to obtain reliable results. The size of the changes de pends on the accuracy of the components. Those that vary little can only be changed slightly, i.e. within the confidence intervals, whereas those that vary greatly require testing over a considerable range of values, but again within the confidence intervals. When a small change in a component results in a large change in the prediction!a super-proportional response, then the value of that component has to be known accurately. Such changes may also alter the form of the response, i.e. do the changes result in a symmetrical or asymmetrical change in the form of the predictions? In coarsesensitivit y analysisth ecompo - 45 aphids per tiller 2.0 1.8 1.6 1.4 o o 1.2 o o 1.0 0.8 0.6 0A .oP °o° 0.2 H •rtA^/' fr^gOOOQjpOOPOOOyd&* 15/6 22/6 29/6 6/7 13/7 20/7 27/7 3/8 v10/8 date Figure 23. Observed (• )an d predicted (o) trendsi n numbers of apterousadul t aphids per tiller of wheat (cv. Maris Huntsman), Norwich 1978. aphids per tiller 10 8 4- 2- 28/6 5/7 12/7. 19/7 26/7 2/8 9/8 date Figure 24. Observed ( • ) and predicted ( o ) trends in numbers of aphids per tiller of wheat (cv. Maris Huntsman), Norwich 1979. 46 aphids per tiller 140 U .Field © Simulationwithou t naturalenemie s x Simulation with predators 120 • Simulationwit hpredators•parasitoid s 0 100 o 80 o 60 X X 40 o X 20 o X * o X /^"A* 1276 26/610/724/7 7/8 date Figure 25. Observed ( • ) and predicted ( o ) trends in numbers of aphids per tiller of wheat (cv. Maris Freeman), Norwich 1980. aphids per tiller 140 • Field 0 Simulationwithou tnatura lenemie s x Simulationwit h predators 120 • Simulationwit h predators• parasitoid s 0 o 100 o x X 80 X o 60 ¥ 40 x / \ \_* o \ 20 o x / \ X ItWfammmm 12/6 26/6 10/7 24/7 7/8 date Figure 26. Observed ( • )and predicted ( o ) trends in numbers of aphids per tiller of wheat (cv. Maris Huntsman), Norwich 1980. 47 observed peak density (Ig nospe r 28h 24 2.0 16 1.2 0.8 0.4 0.4 0.8 1.2 1.6 2.0 24 2.8 predicted peak density (Ig nospe r tiller) -04 -0.8 -12 -1.6 -2.0 Figure 27. Relationship between predicted and observed peak densities of S. avenae. Linea i sY = 0.74X + 0.25;Lin eb i sY = 1.20X - 0.53.Value sbetwee nparenthese s areomitte d from regressionanalysis . nent isomitted . This isdon e to assessth e importance of the component and to determine its overall effect in the system. The effects of small changes to temperature (daily minimum and maximum values + or - 1°C) , the initial crop developmental stage (+ or - 2), instar length (+ or - 20%), survivalrat e( + or - 6%, alarge rchang ewoul d resulti n some instances in survival rates exceeding 100%!), reproductive rate (+ or -20%), immigration (+ or -20%), parasitism and disease(4 - or - 20%)an d morph determination (+ or -20%) were assessed. Coarse sensitivity analysis wascarrie d out on morph determination, for which it wasassume d all nymphs bora would develop into apterous adults. Removal of parasitism and disease t+Q aphids pertille r 100 • standard temperature x 90 o +1°C x -1°C ..••. 80 70 60 o -o° ° 50 o°° o X o o 40 t X • o o o 30 • X « o o • o 20 o * o . o X o 10 o * o • o # * X ~1° ^xX 0 i t** ** i i , i °Q, ^6- 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 28. The effect on predicted cereal aphid population trends of small changes in daily minimum and maximum temperatures. has very little effect in the years studied (Carter, 1978, unpublished). As the pre dictions for 1977 were close to the observed values, the data of that year were chosen for the sensitivity analysis. As predation was negligible in 1977i t was not included in the sensitivity analysis. 4.2.2. Fine sensitivity analysis Temperature A reduction of 1 °C in the daily minimum and maximum temperatures leads to a delay in the date of the peak aphid density of six days, but results in an in crease in its size; 153.7 aphids per tiller instead of 87.9 (Figure 28). An increase of 1° C leads to an earlier - by one day - and lower - 57.0aphid s per tiller - 49 aphids per tiller 120 • standord crop development stage 110 o Initial crop development stage +2 x Initial crop development stage -2 X*w 100 X X 90 .• *. X 80 X 70 oo O .x O O 60 • X o 50 o#* o 40 X ft o 30 ft Ox ft OX 20 ft ft ox ox 10 6x ft 6 t T* ' ' ' I Qo- 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 29. Theeffec t onpredicte dcerea laphi dpopulatio ntrend so fsmal lchange si nth e initial cropdevelopmenta lstage . peak. Thereaso n for thisi sth edifferentia l effect of temperature oncro pdevel opment and aphid population growth. Lowtemperature sslo wdow ncro pdevel opment more than aphid population growth, thus the aphids have more time for reproduction whileth ecro p isoptimal . Therelationshi p iscomple x because not only is the response in peak size asymmetrical but so is its timing. A small change in temperature hasa largeeffect , which indicates that it isa n important factor. Initial crop developmental stage Changing the initial crop developmental stage affects the size of the peak population densityan d therespons ei ssymmetrica l (Figure29) . Inpreviou ssen - 50 sitivityanalyse schangin gth einitia lcro pdevelopmenta l stageresulte di na chang e inth etimin g of the peak density aswel l asit s size (Carter, 1978;Carte r & Rab- binge, 1980). Themajo rdifferenc e betweenth emodel s theyuse dan dthi son ei s that crop development is represented by a polynomial equation rather than linearregression .Th elinea rregressio nmode lwa sles sreliabl edurin gth ecritica l milky-ripe stage. However, another model using two linear regressions, onebe fore and one after flowering gave reasonable results (Rabbinge et. a!., 1979). The influence of factors other than temperature on crop development need to be studied and a new relationship produced. Instar length Alterations toth elengt h of nymphalan dadul t instarsb y + or -20% havea dramatic influence on aphid population growth (Figure 30). An increase inin - star length, which extends the pre-reproductive period and adult longevity, de laysth epea k densityb yeigh t daysan dreduce si t from 87.9t o 60aphid spe rtil - aphids per filler 200 • standard duration 180 o x 1.2 x x x0. 8 * 160 X 140 X 120h x x 100k v ••••• X • 80h * X * 60 0G°0 x • oooooco0 . o o o X • . o 40 x •. o x 0 o v .o • o 20 . o X X x»~ o •n ° \ m x. ° 0l 1— ...*&&T X •JOT 0 I | I*xxx-i- 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 30. The effect on predicted cereal aphid population trends of small changesi n aphidinsta rduration . 51 ler(33 % decrease). An equivalent decrease ininsta r length bringsth etimin g of the peak forward two days and increases its size to 180aphid s per tiller(105 % increase).Thi si sa nexampl eo f asuper-proportiona l andasymmetrica l response. Therefore, instar length needs to be known accurately as it has an important andcomple x effect on thesystem . Rabbingee tal . (1979)hav erepeate d someo f Dean's work (1974b) using wheat plants and obtained similar development times. They haveals o shown thatth eaphid' s response to temperaturechang ei s instantaneous. However, the duration of the fourth instar alatiform nymph at different temperatures and the effect of different cropdevelopmenta l stages on aphid development still need to be determined. Survival rate Changes to the survival rateso f thenympha l andadul t instars have no effect on the general shape or timing of the population curve, but have a large effect on the size of the peak density (Figure 31). The response is super-proportional aphids per tiller 60 x» o o* X 50 • Q.X X 40 • • X x o o 30 o X •x o o • x 20 .* °.« i ox ,, 10 M. © • g - n •••••••T * _l— 1 1 1 I 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 31. Theeffec t on predicted cereal aphid population trends of small changesi n aphidsurviva lrates . 52 andsymmetrical ; a6 %chang eresult si na 20 % changei nth epea k aphidpopu lationdensity . Thussurviva l ratesnee d tob eknow naccuratel yeve nthoug h iti s extremely difficult to measurethe m in the field. Few attempts have beenmad e to determine the effects of high winds ortorrentia l rain on aphid survival. The model can be used to obtain estimates, although changing survival ratest oim proveth eprediction , aproces scalle dcalibration , reduces thegenera l usefulness of the model. Some examples of calibration are described by Loomis et al. (1979).The ysho wtha tcalibratio n canbecom ea sophisticate d curve-fitting rou tine.Therefor e calibrationshoul db eomitte do ruse dwit hcare ,otherwis ea nex planatory model may degenerate into a descriptive model. Reproductive rate Changes in the reproductive rate, aswit h survival rate, have no effect on the timing of the peak density, only on its size (Figure 32). The response is super- proportional (Subsection 4.2.1) and asymmetrical as an increase in the repro ductiverat elead s to agreate rabsolut e change(5 1% increase) inth epea k densi ty than a decrease in the reproductive rate (41% decrease). This means that the reproductive rate needs to be known accurately. Reproductive rate varies with the nutritional status of the host plant, its developmental stage, the age of the aphid and temperature, but these effects have not been determined for wheat. The information available is for other cereals, e.g. effect of host stage of oats aphids per tiller 140 • standard reproductive rate o x 1.2 oooQ x x08 „ ° 120 o 100 • •••• 80 o • o 60 °. .o o XXXXXXXs ox C*x #o ° • X i- # 40 o • x x x *° X x 20 ° • xX * 3°v h. aaSfifP^ - 9 0 i»i..Mimx | ij L 1 X 16/6 23/6 30/6 111 14/7 21/7 28/7 date Figure 32. The effect on predicted cereal aphid population trends of small changesi n aphidreproductiv erates . 53 on aphid fecundity (Watt, 1979a) and temperature on fecundity of aphids reared on barley (Dean, 1974b). Similar information isneede d for different varieties of wheat. Immigration As in previous sensitivity analyses (Carter, 1978; Carter & Rabbinge, 1980), when populations are initiated by immigrant alates in early summer, changes in the number of immigrants have a proportional and symmetrical effect on the size of the aphid peak (Figure 33). The timing of the peak is affected only in the simulation where immigration was reduced, but the shapes of the population curves are very similar. Thus the level of immigration has a 1:1 effect on the size of the peak density over the range of changes made, and need not be determined as accurately as the survival, developmental and reproductive rates, which have aphids perfille r 110 standard immigration rate 100 o x1 2 oo° o x x 0.8 o ° 90 •• o # 80 h # o o xxxx * 70 xx x 0 x. o*x x 60 o X o#x 50h * 40 # o X X 30 - °*x o o»x J 20 - o#x o X o-x ox 10h Q°* °-x xx o *» 0 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 33. The effect on predicted cereal aphid population trends of small changes in aphid immigration rates. KA a super-proportional effect on the peak density. Nevertheless theleve l of immi gration is an important component of the system. Alate determination Changing theproportio n of nymphstha t developint oalat eadult saffect s not only the size of thepea k but also itstimin g (Figure 34).A n increase inth epro portion leads to a lower peak (79.3 aphids per tiller) two days earlier than the standard simulation (87.4 aphids per tiller); a decrease leads to a higher peak (99.0) two days later. The response is sub-proportional and slightly asymmetri cal but this is probably due to the asymmetrical nature of the change. In the standard simulation, if the proportion is greater than 0.83, a 20% increase in the sensitivity analysis simulation resultsi na proportio n greater than 1.0.Thu s atproportion sgreate rtha n0.8 3 theresultin gpercentag echang ei sles stha n20% . The conclusion is that it is not important to know the proportion of alate aphids per filler 100 x**xx • standard proportion X X : o x 1.2 alate < 90 - x x 08 X < X • 80 .< *»o ' X o o • 70 o x X • o • 60 o X o • X • o 50 o • X X • o o • 40 - X X 6 o 30 - s i . x 20 — ° X • • o x • o• . 10 - • • o . • o o 4.•••••!* i i n 1 I 1 16/6 23/6 30/6 7/7 14/7 21/7 28/7 date Figure 34. Theeffec t onpredicte dcerea laphi dpopulatio ntrend so fsmal lchange si nth e proportion of alatiform nymphs induced. nymphs accurately, although the increase in the proportion of alatiform nymphs at the end of the season and the subsequent emigration of the alates is an important factor contributing to the aphid crash. Parasitism Similar to previous sensitivity analyses, changing the rate of parasitism has very little effect on either the timing or size of the peak density. It seems likely that therat e of parasitism would havet o behig h early on inth eseaso n to havea significant effect on aphid population increase, and this has not been observed in Norfolk or generally in the Netherlands over the period 1976 to 1980. How- aphids per tiller o 480 o 440 400 • withalate s o withoutalate s 360 320 280 o o 240 o 200 o o 160 o o o o 120 o 80 o •••••• o. • 40 o» 9* Sf9 0 17/6 24/6 1/7 8/7 15/7 22/7 29/7 date Figure 35. Theeffec t on predicted cereal aphid population trendso f omitting alate de termination. everther ear eexception st othi spatter ni nsom eplace si nth eNetherlands .Ther e therat eo f parasitism washig h earlyi nth eseaso nan dth epopulatio n growth of the cereal aphids was reduced and resulted in lower aphid peaks (Rabbinge et al., to be published). 4.2.3 Coarsesensitivity analysis Alate determination If the production of alate adults, which emigrate from the crop, is omitted this causes a dramatic change in the population development of the aphids (Figure 35). Instead of the aphid population peaking in mid-July, during the milky-ripe stage (stage 73-79), it continues increasing and peaks during the doughy-ripe stage (stage 83-89). As intra-specific competition is not incorpora tedi nth emode l theeffec t of removing morphdeterminatio n from thesyste mi s amplified, nevertheless thecontinue d increasei naphi dnumber sindicate stha ti t isa nimportan t component indeterminin g thetimin g of theaphi dcrash .Thi si s agenera l feature of cereal aphidpopulatio n dynamicsi nsevera lplace si nEurop e (Watt & Dixon, 1981;Ankersmi t et al., to bepublished ) where natural enemies are not very numerous and have not exerted an important influence on thean nual aphid population increase over the period 1976-1980. *7 5 General discussion 5.1 Simulation results 5.1.1 Validation Although thecro p development submodel ispurel y descriptive itgive sa rea sonable fitt ofield observation s fora numbe ro fdifferen t cerealvarietie si ndif ferent localities over a number of years. If new varieties, with markedly diffe rent development patterns, e.g. aver y short flowering period, were introduced then this would have tob eallowe d fori nth emodel . Theeffec t of rainfallan d soil type oncro p development could also beincorporated , buta tpresen t thisi s not thought to be necessary. The model for S. avenae gives predictions that aresimila r to field observa tions, except for 1980, when insom e localities aphid populations declined after flowering. At present it is not possible to explain whypopulatio n growthwa s slow or why the peaks occurred earlier and at lower levels than predicted in 1980. Whether natural enemies canregulat e aphid population growth, and un der what conditions, is unknown and more work is needed before deciding whether they canb euse d inth ebiologica l control of cereal aphids. The outbreaks in 1976an d 1977 were accurately described byth emodel ,al though theweathe r conditions inth esummer so f thosetw o yearswer ever ydif ferent. Thesumme ro f 1976wa smuc h warmer than that of 1977, with amea n June temperature of 16.7° Ccompare d to 12.3° Ci n 1977. Mayan dJul ytem peratures were also higher in 1976(11. 8 °Can d 18.0°C ,respectively ) thani n 1977 (10.1 °Can d 15.5 °C).Rainfal l wasvariabl e within andbetwee n the two summers. InJun e 1976an d July 1977i twa sver ylo w (9.3 mman d3. 0mm ,res pectively). Itcoul d beargue d that lowrainfal l isconduciv e toaphi d outbreaks, because much of the aphid population development occurred in these two months. In 1980, however, high rainfall inJun e (96.4 mm)an d July (51.5 mm) did notpreven t S. avenaefro m reaching outbreak levels nearNorwich . In197 8 and 1979th e low densities of S. avenaeo n wheat were reasonably accurately predicted. Theywer eth eresul to f alat ecolonizatio n bya fe walat eimmigrants . In 1980th e predictions for the Norwich area were reasonably accurate, al though thepredicte d peak densities andpopulatio n growth were toohigh .Fo r other areas, further south, and partso f theNetherlands , natural enemies,espe - fO daily coccinellids, werecommone r earlyo ni nth eseaso nan dpossibl ysuppresse d the aphid populations, preventing an outbreak. To test this, more information is needed on theinteractio n between aphids and natural enemies and morespe cifically with coccinellids and syrphids. Regression analysis of observed and predicted peak densities is amor estrin gent test of the model's predictions than qualitative comparisons of observed and predicted aphid densities insuccessiv e samples. Thislatte rtechniqu e isuse ful, however, especially whenth e observed population trend and simulatedpre dictions diverge, because it indicates at what stage the model is wrong. This is especially truei f thenumber so f aphidspresen ti nspecifi c instarsar ecompared . 5.1.2 Sensitivityanalysis Omitting alate determination from the model reveals that when aphid popu lations reach high levels of abundance it is mainly the increasing proportion of aphids that develop into alateadult san demigrat e from thecro ptha tcause sth e aphidcras ha tth een do f theseason .Thi ssupport sth esuggestio n thati nth eab sence of natural enemies the induction of alates, together with the lowerrepro ductivean dsurviva l rateso f theaphids , determineth edeclin ei naphi dnumber s (Rabbinge et al., 1979; Vereijken, 1979; Watt, 1979; Watt &Dixon , 1981). The fine sensitivity analysis reveals the level of importance of the different aphid components. Changing the instar length orsurviva l or reproductive rates results ina super-proportiona l response. Therefore theeffec t of changes inhos t plant quality, temperature and other extrinsic variables on these aphid compo nents must be accurately determined. Much of the data used in the model are not for S. avenaereare do n wheat, butth esimulatio n predictions indicatethes e values are not unreasonable and are acceptable until more accurate values are available. Thevalue so f othercomponents , sucha simmigratio nan dalat edeter mination, have less effect on aphid abundance. Changing the proportion of aphids developing into alatae results in a sub-proportional response, which is surprising as this component is important in determining the decline in aphid numbers at the end of the season. It is likely, however, that by changing the relationship between alate determination and crop developmental stage agreate r response might occur (Rabbinge et al., 1979). Extrinsic variables, like temperature and initial crop developmental stage, affect thesiz eo f thepea kaphi ddensity , andtemperatur eth etimin go f thepea k density. A lower temperature somewhat surprisingly leads to a higher peak density but at a later date. This is a consequence of the differential effect of temperature on aphid and plant development (see Rabbinge etal. , 1979),whic h is further complicated by the action of natural enemies. At lower temperatures aphids are present for longer periods of time, so that natural enemies might 59 exert a greater influence on aphid population development (see Vickerman & Wratten, 1979). The earlier (in terms of crop developmental stage) the aphids arrive, thehighe rth epea k densitythe yachiev ea sthe yhav emor etim et oincreas e in numbers. The effect of the crop developmental stage on alate settling be haviour isunknown , which isa serious gap inou r knowledgeo f theearl y phase of aphid population development. 5.2 Simple decision models 5.2.1 Introduction Carter& Dewar(1981 )hav ereviewe d someo f thesimpl edecisio nmodel stha t have been developed in an attempt to forecast cereal aphid outbreaks. Suter& Keller (1977) and Vickerman (1977) found that a cold spring was usually fol lowed by a cereal aphid outbreak. Mild springs are thought to allow the build up of natural enemies early in the year, which then prevent rapid population development of cereal aphids in summer. Cold springs suppress the build-upo f natural enemy populations by keeping alternative-prey species scarce without significantly reducing the numbers of cereal aphids. Vickerman (1977) presented several significant relationships between peak aphid populations on cereals in West Sussex insumme r and temperature in March and April,e.g . betweenpea k density and Ig(n + 1)Apri l air frost days. However, in Norfolk in 1978, the expected cereal aphid outbreak did not occur because very few S. avenae colo nized cerealswherea s in 1980,i n Norfolk, an outbreak occurred contrary toth e prediction asth e natural enemies did not arrivei nth ecerea lcrop searl y enough or insufficien t numbers to reducesignificantl y aphid population growth. When natural enemies or aphids are scarce the severity of the weather in spring isun likely to have a marked effect on the subsequent cereal aphid build-up.There fore the relationship proposed by Vickerman does not apply every year. It might, however, beusefu l in our present state of understanding as an indicator of potential cereal aphid outbreaks. RautapM's (1976) study of forty fields of spring-sown cereals over seven years revealed significant relationships between the peak aphid density of R. padi and the numbers present three, seven and 10 days after the first aphids werefound . Hewa sals oabl et o show that morecoccinelli d larvaewer epresen t in fields with high densities of R. padi, although there was no correlation be tween either the numbers of first or second generation coccinellid adults and aphid density. However, therewa sa relationship between thepea k aphid popu lation and the number of aphids per coccinellid adult ten days after the first aphids were found. The fewer aphids per coccinellid the lower the resulting peak. Similar relationships were also found for aphids and syrphid larvae al though the latter weregenerall y lesscommo n than coccinellids.Thu s RautapM was able to predict early in a season the future aphid population trend. 60 Whalon & Smilowitz(197$ )develope da mode l forth epopulatio n build-upo f the peach potato aphid, Myzus persicae, which was used to make short-term predictions of population growth. They assumed exponential population growth dependent on temperature, using data collected in the field from 1975- 1977. In 1978, however, their model gave inaccurate predictions. Indeed, early inth eseaso n theyha dt oupdat eth esimulatio n predictionst oth evalue sobserve d in the field, otherwise the model would have seriously underestimated popula tiondevelopment ! Adjusting simulationprediction si nthi swa ymake sth esimu lation model redundant. 5.2.2 Attempts at cerealaphid population prediction in1980 Three approaches wereuse d to predictcerea l aphidpopulatio n development: one based on short-term predictions, i.e. three days in advance; and the other two on predicting the peak aphid density. Data were collected from various BURY SI. .STOWMMKET EDMUNDS x • HEXTON X.MORIHFARM^Tv.-. 80K M 50 MILES Figure 36. Locationo f the sitessample di n198 0 (• ) andth eRothamste dInsec t Survey suction trapsi nEnglan dan dWale s( x ). 61 placesi nEnglan d (Figure 36): (i)Nort h Farm (near Worthing, Sussex), Hexton (Bedfordshire), Rothamsted (Hertfordshire) and Brooms Barn (Suffolk); (ii) Stowmarket (Suffolk); and (iii)Norwic h (Norfolk). Theresult s from (i)an d(ii ) wereuse di nal lthre epredictio n methods, thosefro m (iii)wer euse d onlyt opre dict peak populations. Method 1 The short-term prediction is based on a simplified version of the complex simulation model presented here.Thre ebasi cchange swer emade :th einitializa tionprocedur ewa saltere d toallo wfo r theintroductio n of aphid instarsi naddi tion to alates; step length was increased to two hours (which only had a minor effect on aphid population build-up);an d natural enemieswer eno t considered. Field observations weremad eonc eo rtwic ea week .Three-da ytemperatur epre dictions and general weather conditions wereobtaine d from the Meteorological Office at Bracknell, Berkshire. The model's predictions were sent to thefield workers within two days. Method 2 Significant relationships were obtained when peak densities were plotted against thecorrespondin g aphid densitiesa t different specific crop developmen talstage sfo r datacollecte d inNorfol k anda t Wageningen, theNetherlands ;th e later the crop developmental stage the more significant the correlation (Figure 37). This method is similar to that of RautapM (1976). lg nos at peak 20 cropdevelopmen tstag e 51• cropdevelopmen tstag e 65* 0 Q2 0.4 06 08 10 12 14 1.6 1.8 2.0 22 2.4 2.6 2.8 3.0 3.2 3.4 lg nos per 100 tillers Figure 37. Relationship between the peak cereal aphid densities achieved and cereal aphid numbersa t (a)flowering an d (b)ea remergence ,Norwic h and Wageningen1976 - 1978. 62 Crop developmental stage 59 Y = 0.35 X + 0.71 for whichr = 0.87, n = 10,p = 0.0)1 65 y = 0.50* + 0.17 for whichr = 0.92, n = 10,p < 0.0)1 and where y isl gaphi d numbers per tiller at peak and X lgaphi d numbers per lO) tillers at the particular crop developmental stage. Method 3 This method isbase d on that of Whalon &Smilowit z(1979) ,bu t isaddition ally corrected for crop development. In the simulation model, crop develop ment isdetermine d byaccumulate d daydegree s(abov e6 °C )an d asimila r rela tionship can beobtaine d for aphid population development assuming exponen tial growth (Figure38) : Y = 0.0223X + 1.7715 for which r = 0.95, n = 36,p < 0.0)1, and where Y isI naphi d numbers per lO) tillers and X is accumulated day degrees. In nos per 100 tillers 1O0i 9.0 8.0 7.0 6.0 5.0 40 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 32034 0 accumulated day degrees above6° C Figure 38. Relationshipbetwee nth enatura llogarith mo fth enumber so fS. avenaeper 100 tillersan d theaccumulate d daydegree sabov e6 °C . 63 The assumption of exponential growth agrees with the observed results. Thus,knowin gth eaphi ddensit ya tan yparticula rcro pdevelopmenta lstag ean d assumingtha t thepea k densityoccur sa t cropdevelopmenta l stage75 , iti s pos sible to predict the size of the peak population. A three-dimensional diagram hasbee ndevelope d for thispurpos e(Figur e39) . Asimila rmetho dt othi si suse d inth esupervise dpes tan ddiseas econtro lprogra m(EPIPRE )i nth eNetherland s (Rabbinge& Carter, inpress) .I nthi sprogram ,farmer s samplefield susin gsim pleprocedure s(Rabbing e& Mantel , 1981)an dth eresult sar euse dt opredic tth e peak density of aphids.Thi spea k densityi suse dt oestimat eyiel dlos san dhel p decidewhethe r sprayingi sjustified . Thisdecisio ni sbase do na profit-cos t ana lysistha t takes into account thecost s of spraying, labour needed, etc.(Zadok s et al., in press).Thi s supervised control system isru n for about 500farmer s in theNetherland san dma yhel pt olowe rpesticid eusag ean dt oincreas eprofit sa s thecost so fwhea tcultivatio n arelowere d(Rijsdijk , Rabbinge& Zadoks ,1981) . predicted (In nos per tiller) SO 7T 70 75 crop development stage Figure 39. Therelationshi p between predicted peak population, observed aphidnum bersan dcro pdevelopmenta l stage. 5.2.3 Results and discussion Unfortunately, aphid population development in eastern England (Figure 36), except near Norwich, was not as predicted by any of the three methods. Population growth was always much slower arid the peaks lower and earlier than predicted. This was probably due to a combination of adverse weather conditions and theactio n of natural enemies,tw o factors that areno t included in the models used for forecasting. The peak density was accurately predicted for one of thefields sample d in Norfolk, but for anotherfield th eobserve dpea kwa shighe rtha ntha tpredicte d by either of the Methods 1an d 2 (Figures 39 and 40). This discrepancy was probably due to the extended ripening period of the crop, which allowed the aphid populations more time to increase. 5.3 Future prospects These attempts at forecasting cereal aphid outbreaks have revealed many gaps in our knowledge of the cereal aphid system. To define the extent of the system relevant to a warning scheme,a newapproac h isproposed . The frame work of thisapproac h described inFigur e4 1i ssimila r to theschem epropose d byDedryve r (unpublished). Thelif e cycleso f theaphids , their natural enemies and thecro par estudie d simultaneously and theinteraction s between them are emphasised. It is unlikely that this schematic diagram includes all the relevant components in the system. It does, however, include the factors currently thought to berelevan t and howthos e factors interact and affect thelikelihoo d of an outbreak. Thetim eo f sowingaffect s aphid population build-up, evenwhe n aphids do not overwinter onth ecrop .Th erelationshi pi spoorl yunderstoo d buti tma yb e a consequenceo f earlier sowing, whichresult si nmor eadvance d cropdevelop ment, and, therefore, lesstim e for theaphid s to colonizean d increasei nnum berso n thecrop sth e following spring and summer (sensitivity analysisi nSub section 4.2.2). A reservoir of aphids and natural enemies will develop when aphids overwinter on early-sown crops. The ratio between the two, and the mildness of spring weather, willdetermin ewhethe r theaphid swil lreac hhighe r levelstha no nlate-sow ncrops .A stud yo f overwintering aphids,aphi d eggsan d natural enemies isdifficul t because they are usually present at very lowdensi ties. In spring, cereal aphids, which colonize cereal fields, may be attacked by largenumber so f specieso f natural enemies.Man yo f theseorganism swil lals o havemigrate d into cerealcrop s from habitats wherealternativ e preyma yhav e been numerous. If these natural enemies arrive early enough and in sufficient 65 aphid nos per tiller 1000 Figure 40. Weeklypredicte d peakpopulation s(• , O)an dobserve d populationtrend s (•, •) and peak populations predicted from aphid numbers at the end of flowering (*, +) intw owinte rwhea tfields, respectively , near Norwich,1980 . numbers, then depending on the number and time of arrival of the immigrant aphids, they might prevent an aphid outbreak. The outcome willals o be affec ted by weather conditions and the level of resistance of the cereal crop to aphids. •m Foreac hcerea laphi d speciesan d localityi ti slikel ytha t different partso f the system will be more or less important. Using this framework facilitates the development of effective warning and management schemes on a field tofield basis,a sfo r EPIPRE. Thesimulatio n modelso f population growth for thedif ferent aphid species, including interactions with their natural enemies and 66 (EARLY SOWN) Figure 41. Schematicdiagra mo fth e seasonalchange si n the structureo fth e cerealaphi d ecosystemfo r usei npredictin gcerea laphi doutbreaks . weather,wil lcontinu et ob e usedt oimprov eunderstandin go f the system. How ever, because of the complexity of thesemodel s it isunlikel y that they willb e used for prediction. It is more likely that the simpler and more easily applied summary modelsan d decision rulesbase d on theinsigh t gained from thecom plex models will beuse d for management and warning programmes. Acknowledgements We are grateful to Gert Ankersmit, Herman Dijkman, Geoff. 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Annalso fApplie d Biology85:319-331 . Zadoks,J.C. , T.T. Chang& C.F .Konzak , 1974. Adecima lcod efo r thegrowt hstage so f cereals. Eucarpia Bulletin 7, 11pp . Zuniga, F. &H . Suzuki, 1976.Ecologica l and economic problems created by aphids in Latin America. Outlook on Agriculture 8:311-319 . 72 Appendix A Program listing of thepopulatio n model of theEnglis h grain aphid (Sitobion avenae) CA POPULATIO N MODEL OFSITOBIO N AVENAE ONUINTERUHEA T C C THIS MODEL SIMULATES THEPOPULATIO N GROWTH OFS AVENA E TAKING INTO C ACCOUNT THEEFFEC T OFPREDATORS , PARASITES ANDTH EHOS T PLANT. C c C*******1 INITIALISATION************ C C C VARIABLE NAMES UILL BEEXPLAINE D ASTHE Y APPEAR INTH EPROGRA M C REAL NEUNY,NUNY,LAT,MXTT,MNTT DIMENSION PRED(250,5),PARA<250),HRDALD(750),ALATAD(750), 1HRDAD(750),ADULTS(750),FNyMPH(200),HRDFN(200),ALFN<200), 2HRDALF(200),TNYMPH 4HRDSN(150>,ALSN(150),HRDALS(150),IMM<200),MNTT(250>f 5MXTK250).DAYL<250 ).IRISE<250),RISE(250),TEMP(24), 6AMTEMP(24),HRDEG(24) C C ZERO ALLINSTAR S NOSAN DAGE S STATING UITH THEADULT S C DO 11*1,75 0 HRDALD(I)=0.0 ALATAD(I)=0.0 HRDAD(I)=0.0 ADULTSU)=0.0 1 CONTINUE C C NOU THEFOURT H INSTAR, APTERAE THEN ALATIFOPrt r. DO 2 1=1,200 FNYMPHU)=0.0 HRDFN(I)=0.0 ALFNU)=0.0 HRDALF(I)=0.0 2 CONTINUE C C NOUTH EOTHE R INSTARS C DO3 1=1,150 TNYhPH(I)=0.0 HRDTN(I)=0.0 ALTN(I)=0.0 HRDALT(I)=0.0 SNYflPH(I)=0.0 HRDSN(I)=0.0 ALSN(I)=0.0 HRDALS(I)=0.0 PNYNPHU>=0.0 HRDPN(I)=0.0 ALPN(I)=0.0 73 nnvnki \ A r —v • v 3 CONTINUE C C 2ER0 ALL INSTAR TOTALS C T0TADR=0.0 T0TAD*0.0 T0TALA=0.0 TQTFQR=0.0 T0TALF=0.0 T0TTHI=0.0 T0TALT=0.0 T0TSEC=0.0 T0TALS=0.0 T0TFIR=0.0 T0TALP=0.0 C C ZERO PREDATOR AND PARASITE ARRAYS C DO 4 1=1,250 DO 5 J=1,5 PRED(I,J)=0.0 5 CONTINUE 4 CONTINUE DO 6 1=1,250 PARA(I)=0.0 6 CONTINUE C TOTCON=0.0 PRDFAC=1.0 PRDADC=1.0 DAYCON=0.0 TOTPAR=0.0 C C C>M*MM*»2.. ..DATA INPUT****************** C C C THE FIRST TUO, THREE DIGIT INTEGER NOS ARE THE START AND FINISH C DAY, DAY 1 IS JAN 1ST. C C READ(1.7)ISTART,IFINIS 7 F0RHAK2I3) C C NOU THE SENSITIVITY ANALYSIS FACTORS, SEN1=TErtP*/-1 OR 0. CSEN2=GSTAGE+/-2. SEN3=INSTAR LENGTHX 1.0.8,1.2, SEN4=SURVIVAL C X .94,1.06.1, SEN5=REPR0DUCTI0N * 1.2,0.8,1, SEN6=IrtrtIGRATI0N C * 1.2,0.8.1. SEN7= PREDATION * 1.2,0.8,1, SEN9= PARASIUSrt C *1.2.0.8.1, SEN9= ALATE NYHPHS* 1.7.0.8.1. C READ(1.13)SEN1,SEN2,SEN3,SEN4,SEN5,SEN6,SEN7fSEN9.SEN9 13 F0R1AK9F5.2) C C C NOU THE TErtPERATURE DATA, ALL THE NAXIflUrt DAILY TEHPS,STARTING C AT DAY ISTART-1 AND FINISHING IFINIS. THEN THE PlNlrtUfllEflP S C STARTING AT DAY ISTART AND FINISHING DAT IFInlS+l. C ONE REAL NUfl&ER PEP LINE C 74 READU,?>rtXTT(I) 9 F0RMAT(F10.2> C C SENSITIVITY ANALYSIS C MXTTU)=NXTT 75 C SKIP LINE C 19 CONTINUE C IF(PARNO.EQ.1.0)GO TO2 1 C C NOUTH E PARASITES FIRST, START AND FINISH DAYS C READ(1,22)IPARA,IPAFIN 22 FORMAH2I3) C C NOW THE MATRIX, 5NO SPE R LINEf EACH THE HOURLY MORTALITY FORON E C DAY C READ(1,23HPARA(I),I= IPARA,IPAFIN ) 23 F0RHAK5F10.4) 21 CONTINUE C C THIS FINISHES DATA INPUT C C C AS THEMODE L ISUPDATE D HOURLY TEMPS HAVE TO BE CALCULATED C HOURLY, BUT FIRST THE TIME OF SUNRISE IS CALCULATED(IRISE) C PI=3.1415927 RAD=PI/180.0 CONV=RAD*LAT C DO 1234 IDArY=ISTART,IFINIS*1 DEC=-23.4*C0S(PI*UDAYY+10.173)/182.621> SSIN=SIN(CONV)*SIN(RAD*DEC) CCOS=COS 76 2YH/2.0 lF 22.0 IF(IT.EQ.IRISE(IT'AYY>)1FrtPUr»-=rtNUMn«.Yt> IK H 6T iftiSF(iriAYn.AN[«.n.ir.M>rF.MP(IT)--((r.n7(n.Arr?-nNnUli 1AYY))M-C0S(PI*UT-IR]SE(IDAYY)l/M4-IRISE(I0AYY)n)»/2.nf.:n<(T«I ?F iA > Y> •n r >TI C 21»A / r >) /"2. 0 i: lFiIT.E0.14)T£fi^ C NOU FOR THE 4TH INSTAR AHTERAE C SURN=10** 79 lUirHl'-HLHICUTHUULIOl I/ C THEPROCEDUR E ISSKIPPE D IFTHI S ZERO IF(TOTFAD.EQ.O.O)GO TO543 2 IF(1DAYY.LT.IPARA)G0 TO543 2 IFUDAYY.GT.IPAFIN)GO TO543 2 CNO UTH ENUMBER S DYING ARECALCULATE D PARSIT=t000000.0*TOTDEN+PARA(IDAYY)*SEN8 IF(PARS1T.GT.T0TFAB)PARSIT=T0TFAB CNO UTH ENUMBER S OFALATE S ANDAPTERA E KILLED ARECALCULATE D PARAL=ALATEO*PARSIT/TOTfAD PARALD=ADULTS(1)*PARSIT/TOTFAD GO TO543 3 5432 PARAL=0.0 PARALD*0.0 5433 ALATED=ALATED-PARAL ADULTS<1)=ADULTSU>-PARALD IF(IT.EQ.13)TOTPAR=0.0 T0TPAR=T0TPAR+((PARAL+PARALD)/1000000.0) 28 CONTINUE C C ACCOUNT ISNO UHAD E OF EMIGRATION C IF(IT.E0.13)TOTALE=0.0 ALTEM=ALATED/1000000.0 ALATEM=ALATED ALATED=0.0 TOTALE=TOTALE+ALTEH C C NOU THE 3RD INSTAR APT IF(T0TTHI.EQ.0.O)GO TO 118 TOTTHI=0.0 FNYMPH(1)=0.0 IF(.N0T.(TNYMPH(150).EQ.0.0))G0 TO 1001 DO 117 J=1,149 1=151-J IF(TNYhPH(I-1).E0.0.0)60 TO 117 TNYnPH(I)^TNT«PH(I-1)*SURN HRDTNU)=HRDTN(I-1 )+HRDEGUT) TNTHPH(I-1)=0.0 HRDfN(I-1)=0.0 IF 80 * f 1int4M b I «« r i * ALFN(1)=AIFN(1)*ALTN 81 HRDPN(I-1)=0.0 IF(HRDPNU).LT.1234.97*SEN3)G0 TO 21? SNYMPH11)*SNYMPH(1HPNYMPHU) PNYHPHU)=0.0 HRDPN(I>=0.0 HRDSNU)=0.0 219 TOTFIR=TOTFIR*PNYMPH(I) 125 CONTINUE 126 CONTINUE C C NOU FINALLY THE ALATE 1STS IF(TOTALP.EQ.O.O)GO TO 123 TOTALP=0.0 ALSN(1)=0.0 IF(.NOT.(ALPN(150).EQ.O.0))GO TO 1001 DO 127 J=1,149 I=151-J IF(ALPN(I-1).E0.0.0)G0 TO 127 ALPNU) =ALPN(I-n*SURAL N HRDALP(I)=HRDALP(I-1)+HRDEG(IT) ALPN(I-1>=0.0 HRDALP(I-1)=0.0 IF(HR0ALP(I).LT.1234.97*SEN3)GO TO 220 ALSN(1>=ALSN<1)+ALPN(I) ALPN(I)=0.0 HRDALP(I)=0.0 HRDALS(1)=0.0 220 TOTALP=TOTALP+ALPN 83 716 PRBFAC=1.0 PRDABC=1.0 715 IF(PRDFAC.EQ.1.0.AND.PRBADC.£Q.1.0)G0 TO999 8 C REDUCE NOSI NEAC H INSTAR BECAUSE OFPREDATIO N DO 7171=1,20 0 FNYMPH(1)=FNYMPHU)*PRDA»C ALFN(I)=ALFN(I)*PRDADC 717 CONTINUE DO 719 1=1,150 TNYrtPH(I)=TNYf)PH 85 9995 F0RHAT(20F7.2) URITE<2,9994) 9994 FORHATdOH rtIN TEflPS//) URITE(2,9993)(NNTT 86 Definitions of variables used in model Variable Description Unit ADULTS(N) Number of apterous aphids per million tillers 1 AFIDUN Aphid units in number per tiller 1 ALATAD(N) Number of alate adult aphids per million tillers 1 ALATE Proportion of newly born aphid nymph that will develop 1 into alates ALATED Numbero f recentlymoulte dalat eemigran taphid spe rmil lion tillers 1 ALATEM Equivalent to ALATED 1 ALATIM Immigration rate of alate aphids per million tillers d-1 1 ALFEC Reproductive rate of alate adult aphids: nymphs alate" arbitrar Ho-l unit ALFN(N) Number of fourth instar alatiform aphid nymphs permil lion tillers 1 ALOWAF Switch variable for inclusion exclusion of aphid density threshold with predation ALPN(N) Number of first-instar alatiform aphid nymphspe r million tillers ALSN(N) Number of second-instar alatiform aphid nymphs permil lion tillers 1 ALTEM Number of emigrant alateaphid spe rtille r 1 ALTIM Numbero f immigrant alateaphid s pertille r 1 ALTN(N) Numbero f third-instaralatifor m aphid nymphspe rmillio n 1 tillers AMTEMP(N) Meantemperature s (timeinterva l lh) DAYCON Consumption rateo f coccinellids inaphi dunit s d~* DAYL(N) Daylengt h h DD Dailyphysiologica l timeunit s for cropdevelopment : D° arbitral-) unit FEC Reproductive rate of apterous adult aphids in nymphsar > tera^H0-1 ^ arbitral") unit FNYMPH(N) Number of fourth-instar apteriform aphid nymphs per million tillers 1 GSTAGE Crop developmental stage (decimal code) arbitral-) unit HRDAD(N) Physiological age of apterous adult aphids: H° HRDALD(N) Physiological age of alate adult aphids: H° tt >» HRDALF(N) Physiological age of fourth-instar alatiform aphid nymphs: H° HRDALP(N) Physiological ageo ffirst-instar alatifor maphi dnymphs :H ° if »» 8' Variable Description Unit HRDALS(N) Physiological age of second-instar alatiform aphid nymphs: H° »» HRDALT(N) Physiological age of third-instar alatiform aphid nymphs: H° HRDEG(N) Physiological time: H°, each hour HRDFN(N) Physiological age of fourth-instar apteriform aphid nymphs: H° HRDPN (N) Physiological ageo f first-instar apteriform aphidnymphs : H° HRDSN(N) Physiological age of second-instar apteriform aphid nymphs: H° HRDTN(N) Physiological age of third-instar apteriform aphid nymphs: H° iDAYY Day number: 1Januar y = Day1 [FINIS Day number at end of simulation iMFINI Day number at end of aphid immigration tMM(N) Number of alate adult aphids caught in a 12.2 m suction trap -l [MSTAR Day number at start of aphid immigration [NCONF Concentration factor for aphidssettlin gi na cro pi nexces s of random settling (PARA Day number at start of parasitism and disease [PAFIN Day number at end of parasitism and disease [PRED Day number at start of predation (PRFIN Day number at end of predation (RISE(N) Time of sunrise, as anintege r [START Day number at start of simulation LAT Latitude of site degrees of angle MNTT(N) Minimum temperature (time inverval 1 d) °C MXTT(N) Maximum temperature (time interval 1 d) °C NEWNY Numbero f newlybor naphi dnymph swit hapterou smoth ers per million tillers 1 NWNY Number of newly born aphid nymphs with alate mothers per million tillers 1 ONYAFD Number of aphid units in first threeaphi d instars permil lion tillers 1 PARA(N) Number of aphids dying from parasitism and disease per tiller, constant over theda y h"1 PARAL Number of newly moulted alate adult aphids dying from parasitism and disease permillio n tillers h-1 PARALD Number of newly moulted apterous adult aphids dying from parasitism and disease permillio n tillers h"1 PARNO Switch variable for inclusion orexclusio n of mortalitydu e to parasitism and disease PARSIT Numbero f newlymoulte d adult aphidsdyin g fromparasi - 8 Q O Variable Description Unit tism and disease permillio n tillers h~» PERAD Number of apterous adult aphids pertille r 1 PERADR Number of reproductively mature apterous adult aphids pertille r PERALA Number of alateadul t aphids pertille r PERALF Numbero f fourth-instar alatiform aphid nymphspe rtille r PERALP Number offirst-instar alatifor m aphid nymphs per tiller PERALS Numbero f second-instar alatiform aphidnymph spe rtille r PERALT Number of third-instar alatiform aphid nymphs per tiller PERF Numbero f fourth-instar apteriform aphidnymph spe rtille r PERP Number offirst-instar apterifor m aphid nymphs pertille r PERS Numbero fsecond-insta rapterifor m aphidnymph spe rtille r PERT Number of third-instar apteriform aphid nymphs pertille r PNYMPH(N) Number offirst-instar apterifor m aphid nymphs per mil lion tillers 1 PRDADC Proportion of fourth-instar and adult aphids surviving predation h"1 PRDFAC Proportion of the first three aphid instars surviving pre 1 dation h- 1 PRED(Nlt Na) Number of coecinellids, in individual instars pertille r PREDNO Switch variable for inclusion orexclusio n of mortalitydu e tocoecinellid s RISE(N) Time of sunrise 1 SARTA Survival rateo f alate adult aphids h- SNYMPH(N) Densityo fsecond-insta rapterifor m aphidnymph spe rmil 1 lion tillers h-» SURALN Survival rateo f alatiform aphid nymphs h-> SURN Survival rateo f apteriform aphid nymphs SURT arbitrar Longevity of apterous adult aphids « unit SURTA Survival rate of apterous adult aphids 1 SURTAL Longevity of alate adult aphids h" arbitrar TAYPAL Taylor-Palmer randomdepositio n factor: number of alate unit adult aphids settling atrando m permillio n tillerspe ralat e ina suction trap d-» TEMP(N) Temperature each hour °C THRESH Crop development threshold temperature °C TILERS Number of tillers m-2 TNYMPH(N) Number of third-instar apteriform aphid nymphs permil lion tillers 1 TOT Accumulated physiological time units for crop develop arbitrar ment unit TOTAD Number of apterous adult aphids permillio n tillers 1 TOTADR Number of reproductively mature apterous adult aphids per million tillers 1 8 Variable Description Unit TOTALA Number of aiatcadul t aphidspe rmillio ntiller s TOTALE Numbero f alateadul t emigrant aphids pertille r TOTALF Number of fourth-instar alatiform aphid nymphspe rmil liontiller s TOTALP Numbero ffirst-instar alatifor m aphidnymph spe rmillio n tillers TOTALS Numbero f second-instaralatifor m aphid nymphspe rmil liontiller s TOTALT Number of third-instar alatiform aphid nymphs per mil liontiller s TOTCON Number of aphid unitsconsume d by coccineilids h-1 TOTDEN Number of aphidspe rtille r TOTFAD Number of newlymoulte d adult aphids per million tillers TOTFIR Number of first-instar apteriform aphid nymphs permil lion tillers TOTFOR Number of fourth-instar apteriform aphid nymphs per million tillers TOTPAR Calculated number of newly moulted adult aphids dying ! from parasitism and diseasepe r tiller d" TOTSEC Number of second-instar apteriform aphid nymphs per milliontiller s TOTTHI Number of third-instar apteriform aphid nymphspe rmil liontiller s TOTYN Number of aphids inth efirst thre einstar s pertille r Predator subroutine Variable Description Unit ADFAU Number of aphid units in fourth-instar and adult aphids pertille r 1 Number of aphid unitspe rtille r 1 ONY Numbero f aphid unitsi nfirst thre eaphi d instarspe rtille r 1 PERPRE Proportion of aphid unitsi nfirst thre eaphi d instars — PRDAD Proportiono faphi dunit si nfourt h instaran dadul taphid s dying from predation h"1 PRDADC Proportiono faphi dunit si nfourt h instaran dadul taphid s survivingpredatio n h"*1 PRDFAC Proportion of aphid units infirst thre eaphi d instarssur vivingpredatio n h"1 PRDFC Proportion of aphidunit si nfirs t threeaphi d instarsdyin g from predation " h~l PREDCNpNj) Numbero f cocdnellids,i nindividua linstar spe rtille r 1 TEMP Meanhourl ytemperatur e °C TOTADC Number of aphid units in fourth instar and adult aphids consumed bycoccineilid s pertille r h~ l jPU Variable Description Unit TOTNY Number of aphid units in first three instars consumed by coccinellldspe rtille r h~ l 91 The large area of land devoted to cereal crops, with nearly 40% of all arable land under wheat, and the apparent increase in the incidence of cerealpest san ddisease sove rth elas ttwent yyear sjustif y astud yo fcerea l pests. In terms of hectarage wheat is one of the most important crops in the world and any loss of yield caused by pests has serious consequences, both locally and world-wide. In Great Britain cereal aphids were not considered as important pests until 1968, when they reached very high levels on wheat. It was shown that cereal aphids can cause considerable losses of yield in someyears . Their abundance, however, varies from year to year and from place to place. For an effective advisory service knowledge of loss of yield relative to aphid densityan dth egrowt ho faphi dpopulation so ncereal sar eneeded . This book deals with the latter. To predict cereal aphid outbreaks it is necessaryt o understand whatcause sth espatia lan d temporal differences in abundance. D udoc Waneningen ISBN9 022 0080 4 5