Vkfl Szo i ®8o C Biological control of two-spotted spider mites using phytoseiid predators. Part I

Modelling the predator-prey interaction at the individual level

M.W. Sabelis

NN08201,880 M. W. Sabeljs

Biological control of two-spotted spider mites using phytoseiid predators. Part I

Modelling the predator-prey interaction at the individual level

Proefschrift terverkrijgin g van degraa d van doctor ind e landbouwwetenschappen, op gezagva n derecto rmagnificus , dr. C.C.Oosterlee , hoogleraar ind eveeteeltwetenschap , inhe topenbaa r teverdedige n opvrijda g 19 februari 1982 des namiddags tevie r uur ind e aula van deLandbouwhogeschoo l te Wageningen CURRICULUMVITA E

Mouringh Willem Sabelis werd geboreno p 14me i 1950t eHaarlem .Hi j volgde de middelbare school te Den Helder enbehaald ehe tdiplom a Gymnasium-B in 1969.Daarn a studeerdehi j aand eLandbouwhogeschoo l teWageningen .Hi j koos dePlanteziektenkund e als studierichting,waarbi jhe t accent lag op deento ­ mologische en oecologische aspecten van ditvakgebied .D e doctoraalstudie omvatte de hoofdvakken Entomologie en Theoretische Teeltkunde. De inhoud hiervan werd bepaald doorzij nbelangstellin g voor debiologisch e bestrij­ dingva nplagen :analys eva nprooipreferenti e bijpredatoren , populatiedyna­ miek van roof- en fruitspintmijten, populatiegroei van mijten in relatie tot hetmicroklimaa t in een appelboomgaard en bemonstering van mijten in boomgaarden.Zij nbegeleider sware nR .Rabbinge ,J . Goudriaan (beidenwerk ­ zaam aan de Landbouwhogeschool) en M. van de Vrie (Proefstation voor de fruitteelt te Wilhelminadorp). Hij behaalde zijn ingenieursdiploma in september 1975e nkree gkor tdaarn ad e gelegenheid om een promotie-onderzoek tedoe nbi jd evakgroe p Theoretische Teeltkunde.Me tdi tonderzoe k werdbe ­ oogd meer inzicht tekrijge n ind emogelijkhede nvoo rbestrijdin g vankas - spintmijten met behulp van roofmijten. Het onderzoekwa s experimenteel en modelmatige nwer d daarombegelei d doortwe epromotoren :prof.dr . J. deWild e enprof.dr.ir .C.T .d eWit .Bovendie nwa she tgerich to p depraktij k vand e sierteelt.Vandaa r dat er werd samengewerkt metM .va nd eVrie , toegepast entomoloog aan het Proefstation voor de Bloemisterij teAalsmeer . Vanwege zijn deelname aan hetbestuurlij kwer k ind eHogeschoolraa d werd zijnaan ­ stelling met een half jaarverlengd .He tpraktisch e deelva nhe t onderzoek werd afgesloten in april 1979.I nseptembe rva n datzelfde jaar trad hij in dienstva nd evakgroe pDieroecologi eva nd eLandbouwhogeschool , aanvankelijk als wetenschappelijk ambtenaar intijdelijk e dienst,late r alswetenschap ­ pelijkmedewerker . Indez eperiod everzorgd e hij een aantal dieroecologische practica,alsmed ehe tonderwij s ind emethodisch e aspectenva n deDieroeco ­ logie. Bovendien deed hij -i n samenwerking met studenten -onderzoe k aan dedispersi eva nroof -e nspintmijten .Naas tdez ewerkzaamhede n schreef hij ditproefschrift . STELLINGEN

1. De van Holling's Type-2 afwijkende vormen van functionele responsies - zoals die tot nu toe bij roofmijt-spintmijt interacties werden vastgesteld - zijn waarschijnlijk het gevolg van een onrealistische experimentele opzet. Daarom is het vooralsnog niet nodig om deze afwijkende responsies in beschou­ wing te nemen bij het construeren van populatiemodellen van roof- en spint- mijten.

Mori, H. & D.A. Chant (1966a). Canadian Journal of Zoology 44: 483-491. Mori, H. (1969). Proceedings of the 2nd International Congress of Acarology, Sutton-Bonnington, England. Sandness, J.N. & J.A. McMurtry (1972). Canadian Entomologist 104: 461-470. Taylor, R.J. (1981). The American Naturalist 118: 102-109. Dit proefschrift.

2. De resultaten van Cock's prooipreferentie-analyse bij de roofmijt Phyto- seiulus persimilis kunnen worden verklaard door de relatie tussen de voedings toestand van de roofmijt en de relatieve vangsnelheden gemeten in predatie- experimenten met 'monocultures' van de prooistadia.

Cock, M.J.W. (1978). Journal of Animal Ecology 47: 805-816. Dit proefschrift

3. Omdat de roofmijten uit gerefereerd onderzoek in staat blijken te zijn om spintmijtaggregaties op enige afstand te ruiken (Sabelis et al., in prep.) is de hypothese dat deze roofmijten 'op de tast' naar hun prooimijten zoeken, niet langer houdbaar. De verwerping van deze hypothese heeft belangrijke consequenties voor de constructie van populatiemodellen van roofmijt-spint­ mijt interacties.

Mori, H. & D.A. Chant (1966a). Canadian Journal of Zoology 44: 483-491. Fransz, H.G. (1974). Simulation Monographs, Pudoc, Wageningen. Rabbinge, R. (1976). Simulation Monographs, Pudoc, Wageningen. Fuyita, K., T. Inoue & A. Takafuji (1979). Researches of Population Ecology 21: 105-119.

4. Het is onjuist om de laboratorium-toets op waardplantresistentie tegen spintmijten te beperken tot een bepaling van de netto-reproductie (sensu Birch, 1948). Een aanvullende meting van de duur van de ei-tot-ei periode is nodig en kan van doorslaggevende betekenis zijn voor de waarde van de intrinsieke groeisnelheid (sensu Birch, 1948), welke een betere maatstaf is voor het effect van de resistentie op populatie-niveau dan de netto-repro­ ductie.

Tulisalo, U. (1972). Annales Entomologici Fennici 38: 60-64. De Ponti, O.M.B. (1977). Euphytica 26: 641-654. Birch, L.C. (1948). Journal of Animal Ecology 17: 15-26. CURRICULUMVITA E

Mouringh Willem Sabelis werd geboren op1 4me i 1950t eHaarlem .Hi j volgde de middelbare school te Den Helder enbehaald ehe tdiplom a Gymnasium-B in 1969.Daarn a studeerdehi j aand eLandbouwhogeschoo l teWageningen .Hi j koos dePlanteziektenkund e alsstudierichting ,waarbi jhe taccen t lago p deento ­ mologische en oecologische aspecten van dit vakgebied.D e doctoraalstudie omvatte de hoofdvakken Entomologie en Theoretische Teeltkunde. De inhoud hiervan werd bepaald doorzij nbelangstellin g voor debiologisch e bestrij­ dingva nplagen :analys eva nprooipreferenti e bijpredatoren , populatiedyna­ miek van roof- en fruitspintmijten, populatiegroei van mijten in relatie tot hetmicroklimaa t in een appelboomgaard en bemonstering van mijten in boomgaarden.Zij nbegeleider s warenR .Rabbinge ,J .Goudriaa n (beidenwerk ­ zaam aan de Landbouwhogeschool) en M. van de Vrie (Proefstation voor de fruitteelt te Wilhelminadorp). Hij behaalde zijn ingenieursdiploma in september 1975e nkree gkor tdaarn ad egelegenhei d omee n promotie-onderzoek tedoe nbi jd evakgroe pTheoretisch e Teeltkunde.Me tdi tonderzoe k werdbe ­ oogd meer inzicht tekrijge n ind emogelijkhede nvoo rbestrijdin g vankas - spintmijtenme t behulp van roofmijten. Het onderzoekwa s experimenteel en modelmatig enwer d daarombegelei d doortwe epromotoren :prof.dr . J. deWild e enprof.dr.ir .C.T .d eWit .Bovendie nwa she tgerich to pd epraktij k vand e sierteelt. Vandaar dat er werd samengewerkt metM .va n deVrie , toegepast entomoloog aan het Proefstation voor de Bloemisterij teAalsmeer . Vanwege zijn deelname aan hetbestuurlij kwer k ind eHogeschoolraa d werd zijnaan ­ stelling met een half jaarverlengd .He tpraktisch e deelva nhe t onderzoek werd afgesloten in april1979 .I nseptembe rva n datzelfde jaar trad hij in dienstva nd evakgroe pDieroecologi e vand eLandbouwhogeschool , aanvankelijk als wetenschappelijk ambtenaar intijdelijk e dienst,late r alswetenschap ­ pelijkmedewerker . Indez eperiod everzorgd e hij eenaanta l dieroecologische practica,alsmed ehe tonderwij s ind emethodisch e aspectenva n deDieroeco ­ logie. Bovendien deed hij -i n samenwerking met studenten -onderzoe k aan dedispersi eva nroof -e nspintmijten .Naas tdez ewerkzaamhede n schreef hij ditproefschrift . 5. Voor de evaluatie vannatuurlijk e vijandenme tbetrekkin g totbiologisch e bestrijding vanplage n is een systeemanalytischewerkwijz e onontbeerlijk. Op dezemanie r kand ekuns t een kundeworden .

Lenteren,J.C .va n (1980).Evaluatio no fcontro lcapabilitie so fnatura lenemies :doe sar t havet obecom e science?Netherland s Journalo fZoolog y 30(2):369-381 .

6. Het is omnatuurwetenschappelijk e redenen onjuist om de tot-nu-toe ge­ bruikelijke bestrijdingsmiddelen en de biorationele bestrijdingsmiddelen (EPA,Federa l Register, 14me i 1979)aa ndezelfd e toelatingseisen teonder ­ werpen. Om dezelfde redenen dienen de toelatingseisen teworde n aangepast aand e diverse klassenva nbiorationel e bestrijdingsmiddelen.

7. In die gevallen waar een milieuvriendelijke -veela l op kleine schaal toepasbare -gewasbeschermingsmethod e beschikbaar is,dien t als aanvulling op het toelatingsbeleid voor bestrijdingsmiddelen overwogen te worden om het gebruik van het milieubelastende breedwerkende pesticide te 'sturen' door een heffing op de produktie en het gebruik van ditmiddel .He t geld dat uit deze heffingword tverkregen ,ka n danworde n gebruiktte r stimule­ ringva n eenmilieuvriendelijke r gewasbescherming.

8. Gezien de behoefte aan Bodembiologische expertise bij het beheer van landbouwgronden wordt het hoog tijd dat er aan de Landbouwhogeschool een curriculum wordt ontwikkeld voor deBodembiologie .Tusse n devakgroepe n die zich nu reeds met oecologisch bodemonderzoek bezighouden, dient hiertoe samenwerking en afstemming vanprioriteite n tot stand te komen. Uitbreiding vand e onderzoeksinspanning op ditvrijwe l braakliggende terreinva nweten ­ schap isgewenst .

9. Het grote aantal adviesraden van de overheid bevordert de onderlinge competentiestrijd hetgeen tot onnodige verlenging van procedures leidt. Deze gangva n zaken is fnuikend voor een democratische besluitvorming.

10. De roofmijt Phytoseiulus persimilis isméé rwaar dda nhaa rgewich ti n goud.

Proefschriftva nM.W .Sabeli s Biological controlo ftwo-spotte d spidermite s usingphytoseii d predators Wageningen, 19februar i 1982 Biological control of two-spotted spidermite s using phytoseiid predators PartI Agricultural Research Reports 910 M. W. Sabelis

Department of Theoretical Production Ecology, Department of Entomology, Agricultural University, Wageningen

Biological control of two-spotted spider mites using phytoseiid predators. Part I

Modelling the predator-prey interaction at the individual level

Centre for Agricultural Publishing and Documentation

Wageningen - 1981 Abstract

Sabelis,M.W . (1981).Biologica l control oftwo-spotte d spidermite s using phytoseiid predators.Par t1 :Modellin g thepredator-pre y interactiona tth eindividua llevel .Agric . Res.Rep . (Versl.landbouwk .Onderz.) ,910 ,ISB N9 022 0077 66 , (vi)+ 24 2p. ,4 2figs ,7 2 tables,Eng .an dDutc hsummaries ,1 0App. ,25 3refs . Alsot ob euse da sDoctora lthesis ,Wageningen . Thesearchin gbehaviou ro findividua lpredator so ffou rphytoseii d species (Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens, Metaseiulus occidentalis) isinvesti ­ gatedi nrelatio nt oth etwo-spotte dspide rmit e (Tetranychus urticae), whichinfest sgreen ­ house roses.Especiall y therol e ofspider-mit ewebbin g inth epredator-pre yrelatio ni s studied.Webbin g interfereswit hsearching ,decreasin gth erat eo fencounte rpe runi tpre y density.Lo wwalkin gspeed san dactivit yi nwebbin gensur etha tth epredato ri srarel ydis ­ turbed aftercontac twit hothe rmites .Webbin g alsopositivel y influences searching,a s spidermite saggregat ewithi nth ewebbe darea :pre ydensity ,define dher ea sth enumbe ro f preype r squarecentimetr e ofwebbe d leafarea ,i shigh ,a si sth erat eo fencounte rwit h prey.Th eabilit yt ocaptur ea pre yafte rtarsa lcontac tdepend so nth efoo dconten to fth e gut,th eprey-stag e and,i ntw o specificcases ,th ewebbing ;th esucces srati oo f P. per­ similis increasedo na webbe dsubstrate ,tha to f A. potentillae decreased. Modelst osimulat e rateo fprédatio no nth ebasi so fth edynamic so fth emotivationa l statean dth estat edependen trat eo fsuccessfu lencounte rar eproposed .Th efoo dconten t ofth egu ti schose na sa nindicato ro fth emotivationa lstate .A stochasti cqueuein gmode l simulatesprédatio n asaccuratel y asa Mont e Carlomode l ora compoun dsimulatio nmodel . Thequeuein gmode l ispreferre dbecaus eo fit seconomi cus eo fcompute rtim ean dth erela ­ tivelyfe wvariable sused .Th emode lwa svalidate d inprédatio nexperiments . Systemsanalysi sshowe dtha tth eeffec to ftemperatur eo nth erat eo fprédatio ni slarge ­ lydetermine db y itsrelatio nwit hth erelativ erat eo ffoo dconversio nint oeg gbiomas s andno tb ybehavioura lchange srelate dt otemperature .Also ,i twa sshow ntha twebbin gha s animportan t influence onth eprédatio nrate .A ne wmode l forth eanalysi so fprey-stag e preferencei sproposed . Predators invade thewebbe dlea fare aafte rcontac twit hth esil kstrands ,irrespectiv e ofth epresenc eo fprey .Th eresidenc etim ei nth epre ycolon yi sdetermine db ypre ydensity . Simulationo fexperimentall ydefine dwalkin gbehaviou rshow stha tpredator sremai ni nprof ­ itablepre ypatche sb yturnin ga tth eedg eo fth ewebbe dlea farea .However ,whe npredato r density increases,th e tendencyt oleav eth epre ycolon yals oincreases ,eve na thig hpre y densities.Onl y A. potentillae avoidedth ewebbe dlea farea ,preferrin gth ethickes tpart s ofth elea frib so rothe rprotecte dplace so nth eplant . A surveyo freference son'lif ehistor ydat ai spresented ;emphasi si sgive nt oth erol e offood ,temperatur ean drelativ ehumidity .Experiment sb yth eautho rsho wtha tovipositio n history ofpredator y femalesi sa majo rfacto ri ndeterminin gth eactua lrat eo ffoo dcon ­ version intoeg gbiomass ;an dtha tth eeg g stageo fth epredator s isver yvulnerabl et o relativehumiditie sbelo w 70%,thoug hth eévapotranspiratio no fth eplan tan dth ehygro ­ scopicpropertie s ofth ewebbin gbuffe r thist osom eextent .A sth ejuvenil emortalit yo f thephytosend s increases above30°C ,an dtha to fth etwo-spotte dspide rmite sabov e35°C , spider-mitecontro la ttemperature sabov e30° Ci sno teffective . The fourphytoseii d species areranke d onthei r capacities fornumerica lincreas ean d prédation: P. persimilis, A. bibens, M. occidentalis and A. potentillae. On capacity to surviveo nalternativ e foodsthe y areranked : A. potentillae, A. bibens, M. occidentalis and P. persimilis. Sometrial swit halternativ e foodsuppl ydi dno timprov esurviva lrate s establishedfo rprevailin ggreenhous econditions . Therat eo fincreas eo fth ewebbe dare ape rindividua lspide rmit ei squantifie db yex ­ periment.Thi sknowledg ewil lenabl econtinuou smonitorin go fth epre ydensit ydurin gsimula ­ tionso fth epredator-pre yinteraction so nth epopulatio nlevel . Freedescriptors :biologica l control,natura l enemies,Phytoseiidae ,Tetranychidae ,webs , searchingbehaviour ,pre y stagepreference ,prédation ,dispersal ,deterministi c simulation models,stochasti csimulatio nmodels ,lif ehistory .

ISBN9 022 0077 66

Thisrepor twil l alsob euse d as adoctora l thesis for graduation as Doctor ind eLandbouwwetenschappe n atth eAgricultura l University, Wageningen,th eNetherlands .

© Centre forAgricultura l Publishing andDocumentation ,Wageningen ,1981 .

Nopar to fthi sboo kma yb e reproduced orpublishe d in any form,b yprint , photoprint,microfil m oran yothe rmean swithou twritte npermissio n from thepublisher . Contents

1 INTRODUCTION 1 1.1 Control of spider-mite outbreaks 1 1.2 Description of thepredator-pre y system 2 1.3 Extrapolation from laboratory to greenhouse 6 1.4 Modelling of thepredator-pre y system 10

2 BIONOMICS OFPRE YAN DPREDATO R 13 2.1 Tetranychid prey 13 2.1.1 Development andmortalit y 15 2.1.2 Reproduction and life span 20 2.1.3 Sex ratio 27 2.1.4 Weight loss, waterbalanc e and growthbudge t 29 2.1.5 Role ofwebbin g 32 2.1.6 Webproductio n and colony growth 33 2.2 Phytoseiid predators 39 2.2.1 Development andmortalit y 42 2.2.2 Sex ratio 51 2.2.3 Adult life span and fecundity 56 2.2.4 Prédationcapacit y 62 2.2.5 Starvation and survival 65 2.2.6 Cannibalism 65 2.2.7 Alternative food supply 68

3 PREDATION,REPRODUCTIO N AND RESIDENCE TIME INA PREY COLONY 71 3.1 Dynamics of themotivationa l state 74 3.1.1 Ingestion 75 3.1.2 Gutemptyin g 80 3.1.3 Nutritive quality ofth epre y stages 89 3.2 Rate of successful encounter 90 3.2.1 Width ofth e searching path 92 3.2.2 Walking velocity 94 3.2.3 Distance ofpre y detection 100 3.2.4 Walking pattern 104 3.2.5 Walking activity 115 3.2.6 Coincidence inth ewebbe d space 118 3.2.7 Success ratio 121 3.2.8 Handling time 133 3.2.9 Disturbance 135 137 3.3 Prédation 138 3.3.1 Models ofprédatio n I49 3.3.2 Preydensit y 152 3.3.3 Webbing 155 3.3.4 Temperature 3.3.5 Agean dovipositio nhistor y 1 T6 4 3.3.6 Predator density -1£ C 3.3.7 Preystag epreferenc e 17 0 3.4 Rateo fdepartur e i/u 3.4.1 Walkingbehaviou r 170 3.4.2 Preydensit y 173 3.4.3 Predator density 176 4 THEUS EO FEXPERIMENTA LAN DTHEORETICA L RESULTS INDYNAMI C POPULATIONMODEL S 178 4.1 Unvalidated assumptions I78 4.2 Missinginput s 180 4.3 Impacto findividua l characteristics atth e population

level 182

SUMMARY 185

SAMENVATTING 192

ACKNOWLEDGEMENTS 199

APPENDICES A Modelo freproductio n inrelatio nt o food intake 200 B Timeserie s analysis 202 C Maximum Likelihood estimationo fth eparameter s ofth e Tukey distribution 206 D Modelo fwalkin gbehaviou r 208 E Deterministicmode lo fth eprédatio nproces s 210 F MonteCarl o simulationo fth eprédatio nproces s 212 G Matrixalgebraic solutiono fth eQueuein gequation s 214 H Queueingmode l ofth eprédatio nproces s 216 I Queueingmode l ofprédatio ni na mixtur e ofpre y stages 220 J Listo fabbreviation suse d incompute rprogram s 224 REFERENCES 226 1 Introduction

1.1 CONTROL OF SPIDER-MITE OUTBREAKS

Spider Mites (Acarina: Tetranychidae)ar e acontinuou s potential danger to many food and ornamental crops. Their high reproductive potential and rapid development form thebasi s for ahig h capacity ofpopulatio n increase. Hence the outbreaks can develop even shortly after pesticide treatment. Moreover, they appear to develop resistance toman y chemicals that initially gave effective control (Helle& va n deVrie , 1974). This results in aviciou s circle ofpesticid e development and resistance.Therefor e alternative control strategies need to be developed. Apart from supervised control strategies there are fourmajo r alternatives: - plantbreedin g for resistance to spidermite s (e.g.d e Ponti, 1977a). genetic control strategies to reduce the fertility of female spider mites by the introduction of sterilized males (Nelson, 1968; Nelson & Stafford, 1972) or males with chromosomal rearrangements (van Zon & Overmeer, 1972;Overmee r &va nZon , 1973). to displace the endemic spider-mite population by amit e strain thati s not resistant to certain pesticides or very sensitive to extreme tempera­ tures, which can be easily brought about ingreenhouse s (Feldmann et al., 1981). control by a fungal epidemic in the mite population (Shagunina,1977 ; Gerson et al., 1979). control bypredator s (e.g.Huffake r et al., 1970). The choice of aspecifi c method or acombinatio n ofmethod s dependsver y much on agricultural practice and the demands of the grower/consumer with regard to the product. The present study aims to elucidate thepotentia l role ofsom epredator y mites (Acarina:Phytoseiidae ) forth e control ofth e two-spotted spider mite, Tetranychus urticae (Acarina: Tetranychidae),b y systems analysis so thatne w options for integrated pestmanagemen t mayb e developed and compared with alternative control strategies.Th e results of these studies aredescribe d in two subsequentAgricultura l Research Reports concerning investigations in the laboratory (Part 1) and the greenhouse (Part2) . 1.2 DESCRIPTION OFTH EPREDATOR-PRE Y SYSTEM

Thetwo-spotte d spidermite , Tetranychus urticae Koch, is aseriou s pest inth egreenhous e culture of ornamental roses.Sinc e 1967,dienochlo r [per- chlorobi(cyclopenta-2,4-dienyl)] hasbee nuse d forchemica l control ofthi s spider mite in ornamental crops. Because pesticide resistance may evolve (McEnroe& Lakocy , 1969), alternative methods ofcro pprotectio nhav e tob e investigated. It is desirable to replace chemical spraying by biological control. Encouraged by the successful use of Phytoseiulus persimilis asa controlling agento fth etwo-spotte d spidermit e ingreenhous e cucumbers in the 'Westland' districto f theNetherland s (Bravenboer, 1963;Woets , 1976), some rose growers started to use thispredator y mitewit h reasonable suc­ cess (van de Vrie,persona l communication).A s incucumbers ,th e predators areintroduce d ateac h spidermit e outbreak. Thismetho d ofspider-mit e controlwil l onlyb e accepted by the majority ofth egrower s ifi tca nb e achievedwit hn odecreas e inros eproductio n or quality and if it costs no more than treatment withchemica lpesticides . Moreover,becaus e rosebushe s areexploite d for 5-7 years,th eus e ofpred ­ atory mites would be especially attractive if long-term control could be achievedwit h only afe winitia lpredato r introductions.Thes e requirements canno tb eme ta syet ,s otha ta critica l evaluation ofth eus eo f predatory mites is necessary. That evaluation should include assessmento fth e eco­ nomic-damage level and quantification of the potential forcontro l by the predatorymites .Th e economic-damage level isbein g studiedb yva n deVrie , an entomologist at the Research Station forFloricultur e inAalsmeer , The Netherlands. Studies on thepotentia l forcontro lb ypredator y mites,don e uponva nd eVrie' ssuggestion ,ar eth etopi c ofthi sreport . The substrate of Tetranychus consists of leaflets, shoots,bushe s and hedges (Fig. 1).Th e rose shoots thatris e above thehedge s are harvested at an early stage of flowering. Because quality roses have tob e free of

Fig. 1. Greenhouse culture of ornamental roses. Cross section of rose hedges separated by walking paths. Dotted line indicates the boundary between the 'maintenance' leaves and the leaves of the rose shoots that willb eharvested . • •*-.-->:•' ••--•--... ^ - •• A&M

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Fig'. 2. Scanning electronmicrograp h (magnification 50x )o f theoviposi - tion female of Tetranychus urticae. any damage,th e leaves of these shoots shouldb e carefully protected against spider-mite infestation. On theothe r hand, iti s acceptable forth e hedge beneath the economically importantpar t tob e slightly damaged. Adult females (Fig. 2)ar e the founders ofth e spider-mite aggregations on the underside of the leaves, which are frequently located near to an edge or a rib ofth e leaves.Th e juveniles (egg,larva ,protonymph , deuto- nymph and the different moulting stages) and the adults live in self- produced webbing. The pre-ovipositional females disperse after mating to other leaves,wher e theybegi n new colonies.Th epopulatio n growth and dis­ persal apparently result incompac t foci of infestation.Th e upwarddispers ­ al out of the hedge leads to colonization of theuppe r leaves of the rose shoots. This must be prevented by one or more introductions of predatory mites. The mites feed on the leaf parenchyma,whic h causes spots that reduce the immaculate appearance required of quality roses.Losse s causedb ymit e feed­ ing are more serious therefore than in other greenhouse crops, like the cucumber or Gerbera, where the fruits or the flowers are sold andno t the leaves, so that only the photosynthetic function of the leaves iso fcon ­ cern. Clearly,predator y mitesmus tpreven t theupwar d dispersal of theplant - Phytoseiulus persimilis.

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tf

* • ^^*-ta.^>-

D. Metaseiulus occidentalis feeding mites from thehedg eb ycontrollin gth epre ypopulatio n withinth e hedge. Phytoseiid mites feed onal lstage so fth espide rmit e anddeposi t their eggs inth espide r mites' webbing. Thesequenc e of developmental stagesi ssimila rt otha to fth espide rmites ,bu tmuc h less time formoult ­ ing from onestag et oth eothe ri srequired . Similart ospide rmites ,onl y female adult phytoseiids disperse,an donl y aftermating .However , incon ­ trastt othei r prey theyd ono tdispers epredominantl y inth epre-oviposi - tion phase,bu trathe r during their whole adulthood. Howth etetranychi d and phytoseiid females disperse from colonyt ocolony , leaflett oleaflet , shoott oshoo to rhedg et ohedge ,an dth efactor s that induce their disper­ salar emajo r topicso fthi sreport . Because thetim e needed forth espider-mit epopulatio nt odoubl e varies between only2- 4days , theirnumerica l increasei srathe r explosive.Henc e thetiming ,th edos ean dth epotentia l forcontro lb yth ephytoseii d species usedi so fcrucia l importance,th emor es obecaus e -i ncontras tt oimmedi ­ ate exterminationb yacaricid e spraying- th epre y numbers keep increasing for some time after predator release.Th eincreas e ofcolonize d areaan d thetim e lapsebetwee npredato r releasean ddeclin e inpre y numbers willb e treated inPar t2 o fthi s Agricultural Research Report (tob epublished) . These problems areinvestigate d forfou r phytoseiid species: Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens and Metaseiulus occi- dentalis (Fig.3) . Because aspider-mit e outbreak cannotb eeasil y detected init searl y stagesb ya grower ,th epossibilit y ofleavin g this taskt oth epredator s was investigated. Special attention wastherefor e givent oth eabilit yo f the predator tosearc h forscarc e prey aggregations,t owithstan d starva­ tionan dt osurviv eo nalternativ e foodi nperiod so fspider-mit e scarcity. Although thefou r phytoseiid species studied aremor eo rles s specialized predatorso ftetranychids ,ther ear econspicuou s differences inthei r diet­ aryrange .Thes ear etreate d inPar t1 .Th eproble m ofchoosin ga favourabl e combinationo fpredator y capacity anddietar y range forth econtro l oftwo - spotted spider mites inth egreenhous e cultureo fornamenta l roses willb e treatedi nPar t2 .

1.3 EXTRAPOLATION FROM LABORATORYT OGREENHOUS E

Experiments inwhic h predatory mites areintroduce d into greenhousest o 1970^°or" " miteS^ ln S°me CaS6Sbee nSUCCeSSfu l <*rf**ere tal ., ZL °bSerVatl0nS in the henhouse (population estimates,assessmen to f predator-prey ratios anddistributions ) andlaborator y experiments (life tables, prédation rates,mutua l interference among predators, effectso f Ïor!ermirCrOWding )Wlt hSeVera ltetran *chid «* Phytoseiidspecie shav e IL" ""f" the UnderStandin* °fth e *»aging capacity ofth epre y and thecontrollin g potentialo fth epredators , iti stemptin gt oextrapo - late laboratory observations to the practical greenhouse situation, but such extrapolations need tob evalidated . Thisproble m canbes tb e tackled bymodellin g thepredator-pre y system, computing thepopulatio n fluctuations with the model and comparing the resultswit h data gathered in thegreen ­ house. Such astud yma yprovid e interesting startingpoint s for further research in an iterative process of evaluation and design.Mayb epractica l results will follow, but it is not suggested that this method will give rise to fully reliable control methods by itself; large-scale validation underdif ­ ferent conditions generally takes an excessive amount of time and models cannot approach the complexity of biological systems, if only because of the limited capacity of computers. Nevertheless attempts tovalidat e con­ cepts ofbiologica l systems need encouragement asthe y lead to abette rin ­ sight into the use of biological control agents in an agro-ecosystem. Examples of suchvalidation s canb e found in themodellin g studies ofFrans z (1974: Tetranychus urticae - Netaseiulus occidentalis), Rabbinge (1976: Panonychus ulmi - Amblyseius potentillae), Wollkind& Loga n (1978: Tetrany­ chus mcdanieli - Netaseiulus occidentalis) andDove re tal . (1979: Panony- chus ulmi - Amblyseius fallacis). Themode l ofFrans z (1974)i sbase d on acomponen t analysis of thepred ­ atory behaviour of Metaseiulus occidentalis: itsimulate s the rate ofpré ­ dation onpre y eggs andpre ymale s distributed over asmal lbean-lea fdisc . Rabbinge (1976)an dWollkin d & Logan (1978)base d theirpopulatio nmode l of the predator-prey interaction on measurements at the individual level of life history traits and the rate of prédation. By using small leaf-discs the interaction surface is easily defined andpre y density canb e directly assessed as long asth epre y israndoml y distributed over the disc. Inthi s way variables like the rate of prédation and the rate ofreproductio n by thepredato r weremeasure d inrelatio n to the density ofth eprey . The latter authors simulated the predator-prey interactions in larger ecosystems (e.g. the orchard)b y simple extrapolation ofth e measurements on the leaf-discs to the surface of theecosystem , e.g.

5 prey eggs _ 5-1012 eggs 1 cm2 1-1012 cm2 This assumes that the prey is randomly distributed and thatth e predator searches forpre y in arando m fashion.Bu t the distribution of tetranychids in the field aswel l as in the greenhouse crops isgenerall y clustered (e.g. Crofte t al., 1976)an d asi ti s likely thatpredator s tend to aggregate at prey colonies, it isrelevan t to include these aspects forth e understand­ ingo f thepopulatio n fluctuations ofpredato r andprey . Dover et al. (1979)recognize d thisproblem . They directly monitored the result of the dispersal process in thepractica l situation ofth e orchard by counting thenumbe ro fpre ymite san dpredator ymite so neac h leafo fa representative sampleo fleaves .Thes emit e countswer e used tocreat e sepa­ rate frequencydistribution s forpredato ran dprey .A nappropriat e two-para­ meter model,th enegativ e binomial distribution, wasuse d fordescriptio n ofth efrequencies .B yassumin g theindependenc eo fth epredato r andpre y distributions, their descriptive models were related toeac h otheri na jointprobabilit y function.Thi s functionwa suse di na predator-pre y model to account forpredator s occupying leavesa tbelow-mea no rabove-mea npre y densities.However ,thi s implies thateac h leafha sth esam e probabilityo f containinga give n number predators, irrespective ofth enumbe r ofprey . Whether orno tthi s istrue , itremain s difficult tounderstan d howth e -presumabl y prey-density related- prédatio n anddispersa l give riset oa dispersiontha tca nb edescribe db ya negativ ebinomia l function.Moreover , by representing thepredator-pre y distributionb yfrequenc ydistributions , theposition so fth ecolonie san dth eleave swit h respectt oeac h otherar e notconsidered ,s otha tth espatia lmosai co fpredato ran dpre y coloniesi s eliminateda sa naspec to fpredator-pre y interaction. None ofth eabov e models include thedispersa l mechanisms ofpredato r andpre yi nrelatio nt oth eheterogeneit yo fth eenvironment .Thes e factors canaffec tth epersistenc eo fpre yan dpredato rpopulation s ina necosystem , asshow nb yHuffake r (1958)i na nexperimenta l studyo fth einteractio nbe ­ tweena predator ymit e (Metaseiulus occidentalis) anda spide rmit e (Eotetra- nychus sexmaculatus) inartificia l universes differingi ncomplexity H. e constructed anenvironmen t ofinterconnecte d oranges thatwer e suitablea s a food source forth eprey . Some days afterth eintroductio no fth espide r miteso nthei r substrate,th epredator s were released. They exterminated thespide rmite swithi na month .Apparentl yth epredator s were ablet ocove r thewhol e substratei nsearc ho fprey .However ,whe n thesewalkin g predators wereprevente d from dispersing,usin gvaselin ebarriers ,an dpre y dispersal by ballooning- was stimulated with low-velocity aircurrents , preyan d predator survived forsi xmonth s inthi s artificial ecosystem. Therefore more detailed modelling andexperimentatio n areneede d toelucidat eth e e dlSPerSal heter geneity in the Ind prey ^ ° Populationdynamic so fpredato r

enceTfT ^ ^ * *' ***** **° aCCOUat' ™ f°r «»**•' theinflu ­ denit von eT rOSe"CrOP heter°*eneit*' «» *«ecto fP^ y andpredato r spentirr" 6 timS° thf e Predat°rl na ^ COl°^ «d thetim e nede dI nwh 'Tl ^ ^^ ** ** *Mt°n- In *^°» * ^el is thepre dt , ^^ meChaniSmS "" ^^^ incorporatedan d Tlx l H Prey diStribUti0nS "e **»«*" inspace .Bu tsuc ha com - smpli : les??"3 a l0t °fCOmPUtin g tlme- " W°Uld be desi"^ tous ea 1 e S S t COnSUming m0del HOWeVer is pr ri s t a t e T" importanc- < " e o -fdispersat possiblie tomak ei ;::;: -™i™ :is™h ~*» ~ - y models.I t is known thatth emode l proposedb yDove re tal . (1979), inwhic h fieldmeasure d dispersion parameters of thenegativ ebino ­ mial account for the degree of coincidence betweenpredato r andpre y give results that differ considerably from simulations that dono ttak e disper­ sion into account. Because this difference ismor e ademonstratio n ofth e static structure of their model than aproo f ofth e importance of the low degree of coincidence between predator and prey, it shows once more the need for further research onthi smatter . Another aspect of the distribution of Tetranychus spp.tha t isno tcon ­ sidered in most studies of the functional response and in the modelling study ofWollkin d &Loga n (1978), is that these spider mites aggregate with­ in structures of self-made webbing, in contrast to Panonychus spp.,whic h predominantly spin 'lifelines' made of silk strands.A s the predator-prey interaction takes place only where there are aggregations,pre y abundance should be quantified as the number ofmite spe r webbed leafarea , instead of per total leaf area. Moreover, webbing may play an important role in searching and prédation, as indicated by experiments ofMcMurtr y & Johnson (1968), Fransz (1974), Takafuji & Chant (1976)an d Schmidt (1976). Still other factors may contribute to the lack of conformity between laboratory and greenhouse experiments,e.g . effects of spider-mite crowding during hostplant exploitation and availability ofalternat e food sources in periods of prey scarcity.A final difference between laboratory and green­ house conditions can be found in their microclimates. First, temperature plays a very important role in the population dynamics of poikilotherm arthropods. For example, aris e in temperature enhances development, stimu­ lates reproduction and increases food consumption. Although a greenhouse, in, say, Aalsmeer may seem a well-regulated climatic environment, this is only partially true.A s a consequence of the variability of the outdoor climate and despite of the 'between limits' regulation of the glasshouse climate, temperatures rangebetwee n 10°C and 33°C.Becaus e ofthi svariabi ­ lity, temperature has tob emeasure d toenabl e validation of predator-prey models, which incorporate several temperature-dependent variables.Howeve r this raises a problem with respect to themicroclimati c detail needed. As rose leaves are rather dark objects, leaftemperatur e may differ from the air temperature, depending on the amount of incident (hedge-penetrating) radiation. Due to the small size of themite s (<1mm )thei r environmental temperature will be determined to an important extent by the leaf. Goudriaan (1977)ha s presented asimulatio nmode l thatcalculate s the leaf temperature distribution in acanop y on thebasi s ofth eweathe r conditions above thecanopy , the crop geometry, theoptica l properties of the leaf and the behaviour of the leaf stomata.Thi smode l canb e coupled to amode l of arthropod growth (Rabbinge, 1976). Even correction for interception of radi­ ation by the structural elements of agreenhous e canb emade , as shownb y Kozai et al. (1978). Unlike the leaf temperature, the humidity near to the leaf cannot be computedo rdirectl y measured. Moreover, tetranychid webbing coversth e underside ofth elea fan dthi sma yinterfere-wit hth emicroclimat e (Hazan et al., 1975b). This problem canb eeliminate dt osom e extentb yusin g webbed leaveso fintac tplant si ncontrolle d humidity cabinetsi nlaborator y experiments.Th eextrapolatio no fthes emeasurement st oth egreenhous e situ­ ationca nb eaccomplishe dvi aintra-cro p humidity profiles, which canb e calculated fromth eabove-cro pweathe r conditionsusin gGoudriaan' smodel . Althoughth eabove-cro p weather conditions would havet ob emeasure d con­ tinuously, other data forth emodel , sucha sth egeometrical ,optica lan d physiologicalpropertie so fth eleaves ,woul d onlyhav et ob emeasure d once forintra-cro pextrapolation .

1.4 MODELLINGO FTH EPREDATOR-PRE Y SYSTEM

Inmodellin ga comple x systemi ti sadvisabl et odistinguis h onlytw o levelso fcausa ldept h (vanKeulen , 1975). Thereforeth estud y describeid n tworeport s attemptst oexplai nth epopulatio n fluctuationso fpredato ran d

prey ln thegreenhous e (Part2 )o nth ebasi so flaborator y experimentas t the individual level (Part 1).Th elif e history parameters (development, reproduction,mortalit y andse xratio ;Par t1 Chapte r2 )an dth epredator - preyinteractio n (prédationan ddispersa lbehaviour ;Par t1 Chapte r3 )wer e measuredb ystudyin g individualmite si nth elaboratory .Th edat a obtained werefe dint oa mode l thatcompute spopulatio n growthan dgenerate s disper­ sionpattern si nspac e (Part2) . Theseextrapolation st oth epopulatio n levelwer evalidate db ycompariso n withactua lpopulatio n experimentsi nth egreenhouse .Fro mth ediscrepancies , indications were derived forimprovin g themodel .Additiona l measurements ZILT T the m°delling and validationprocedur e repeated.Thi s working In a!" i a frameW°rk f°r thS eValUation <*th ephytoseii dpredators , pecLs henhouse cultureo fornamenta l roses.Thes e phytoseiid eve andt h "^^ ** *"* ^^ «*«*»«* °nth eindividua l calcontro l "*"* ** ***'* diff—s °nth e finalobjective , 'biolog- ica control-,wa sevaluate d withmode l calculations describedi nPar t2 .

in Predat0r Prey relati ns a Howve r Somr % " ^^ ^ ^^ ° " »»"old. varYZ'es TJT " ^ ^^ ^^ BO" Connectionsbetwee n B bMla The StrUCt f Ihe c:Jpre dt ^ ^ "* "^ " - - ° P r Y SyStem WSS SUbdiVided int f0Ur leVel lÏve concer ns T2 : , ° - The first S at somepre y -sityTnT;:?:^::I;:::^::;;~>J: Tt

io«.l .ft. l.L, "tt. I InCOrp0rati"' <*« *»»ic, of th« „otiv.t- *~. >»r:i:°^~™ i~:

10 porating this adds another dimension to thepredator-pre y system (Level3) . Finally the prey aggregate in colonies. As new colonies are founded, the predators may move from one colony to the other.Thi s emphasizes the final level of complexity, the dispersal of thepredato r (Level4) . These four levels are recognizable inth epopulatio n model as submodels that simulate the relative rate of successful encounter at some level of the motivational state, the rate of prédation at some level of the prey density, the population growthpe rpre y colony, the rate ofdepartur e from thepre y colony and the redistribution of the dispersing mites over thesub ­ strate (e.g.pre y colonies in case of thepredato r and leaf surface incas e of the prey). After validating all submodels separately, predictions were obtained from the entire model, which were themselves again validated by experiment. The model is of the state-variable type (Forrester, 1961); state and rate variables are distinguished andmathematica l expressions are given to calculate the value of each rate variable from the state of the system. Examples of state variables areth enumbe r ofeggs , themotivationa l state ofth epredator , etc.Th e rate ofeg g development, the oviposition rate and the prédation rate are examples of some of the ratevariables .Th e state variables are updated by rectilinear integration over asufficientl y short time interval:

Y Y + RY At t+At = t '

RY =Y t-RRY

t =tim e (e.g.day ) At= time interval of integration Y = statevariabl e (e.g.number ) RY =rat evariabl e (e.g.numbe rpe r day) RRY= relative rate (e.g.day " ) Unfortunately integrationmethod s thatcontinuousl y adjustth e time inter­ val of integration onth ebasi s of some accuracy criterion (e.g.Runge-Kutta / Simpson)canno tb e used inth epopulatio nprogram . Themetho d for thesimu ­ lation ofdispersio n in developmental time (the 'boxcar'method ; Goudriaan, 1973) requires the useo fretilinea r integration,becaus e someo fth e rate variables involve adivisio nb yA t (=discontinuou s emptying of a 'boxcar'; deWi t& Goudriaa n 1978,p .20) .Therefor e the sizeo f the time interval of integration has tob eprefixed . As arul e of thumb itha s tob e smaller than 20% of the time constant of the integrationproces s (Ferrari 1978,p .26) . The inverse of the timeconstan t equalspar t of the rateR Y that isindepen ­ dent of Y. For the simple integration above the time constant equals the inverse ofRRY . When the model consists of a system ofintegrals ,th e time constant of this system isgoverne d by the integrationwit h the smallest time constant, to evaluate a number of natural enemies for the biological control of arthropod pests. Because the time constants of different processes treated ina simulatio n model often differ considerably, the computing effort is inefficient for the integration of the slowprocesses .Thi sproble m will be encountered in Part2 wit hrespec tt oth eadaptatio n ofth emotivationa l state of the pre­ datort oa continuall y changingpre y abundance intim e and space.Numerica l integration of difference equations over short time intervals is applied because ofth ecomple x character ofth e interactions.Fo rexample , the rate ofsuccessfu lencounte r ofth epredato rwit h itspre y and thepreferenc e of thepredato r for the different stages of the prey depends on its feeding history. Moreover, temperature influences several rate variables and it variescontinuousl ydurin gpopulatio n growth inth e greenhouse.Th e addition of non-linear terms to the differential equations oftenprevent s solution by analytical techniques.Numerica l methods are the only solution in that case.Evenwhe n the system consists of only linear differential equations, thelarg enumbe ro fthes eequation s necessitates theus e ofnumerica l tech­ niques (seee.g .Hal l& Da y 1977,p .10) . Theus eo frando mnumber s tosimulat e the stochastic character of avari ­ ablei sno tnecessaril y implied.Mos tpart s ofth emode l havea deterministi c character.Howeve rther ear esom e situations inwhic h the stochastic nature of avariabl e is absolutely basic toth eprope rmodellin g of theprocess . Fransz (1974)demonstrate d that even when one is only interested inmea n values, deterministic models of the prédation process can lead to results differentfro mthos eo fstochasti c modelswhe nnon-linea r relations between the rate and state variables of the model are involved. Inth emode lde ­ scribed in this report Monte Carlo procedures are applied to simulate the predatory mites'walkin g behaviour (Part 1, Subsection3.2.4 )an d capture events (Part1 ,Subsectio n 3.3.1). Because ofth e large amounto f replicates needed to obtain areasonabl e estimate ofth emea n rateo fprédatio n these inefficientMont e Carlo procedureswer e replaced bymor e economical alter­ natives whenever possible. For example,th eMont e Carlo simulations of the prédationproces s were compared with several alternative models that are based ona large r set of assumptions butar emuc hmor e efficient in terms

LJoTT eff°rt (e-9- COmPOUn

The framework of a model of arthropod population growth consists of stage-specific rates of development and survival, and age (orstate )spe ­ cific rates of reproduction, sex ratio in the offspring and senescence. Such life-history frameworks canb emodelle d forbot hpre y andpredato r and subsequently Coupled by prey stage-specific prédation rates of each stage ofth epredato r (Part2) . Rates of prédation will depend onpre y abundance,which ,therefore ,ha s tob e quantified.Th e interference between Tetranychus spp.an d theirpred ­ ators takes place on those parts of the leaf area that are covered with webbing, since all stages ofth e spidermit e are aggregated there.T oquan ­ tifypre y abundance therefore, iti smor e logical to definepre y density as the number of prey per square centimetre of webbed leaf,rathe r thanpe r leaf area, as Wollkind & Logan (1978) did. The size of the webbed area changes during population growth, as do the prey numbers. Therefore both the rate of population increase and the rate of increase of webbed leaf area shouldb emeasure d to calculate thepre y density inth ecompute r simu­ lation model. In this chapter acomplet e picture isgive n ofth e life his­ tories,webbin g activity and stage-specific rateso fprédation , as affected by arthropod related factors (stageo f development, ageo f the adult, etc.) and environmental factors (temperature,relativ e humidity and food supply). Thesemeasurement s arepar t ofth e inputt o thepopulatio nmodel s presented and validated in Part2 ,bu tthe y are alsobasi c to the structure ofthes e models. Inth e finalpar to f this chapter the ability ofth epredato r to survive periods of spider-mite scarcity and to recover from starvation aredeter ­ mined. This is important in assessingpossibl e alternative foods formain ­ taining a predator population in a greenhouse crop in absence of spider mites.

2.1 TETRANYCHID PREY

The life history traits of Tetranychus urticae on rose (Rosa canina 'Sonia', grafted on Rosa indica 'Manetti') are discussed in Subsections 2.1.1 - 2.1.3. Although much life history data are available from litera­ ture, new measurements were made because variation due to differences in mite strain (e.g.Leh r& Smith, 1957), hostplan t (e.g.Dabrowsk i &Marczak , 1972) and even cultivar involved (e.g. Bengston, 1970;Tulisalo , 1971;d e

13 Ponti, 1978)ca nb econsiderable . Thestrai n of Tetranychus urticae used throughout this investigation originated from a culture maintained atth e Research Station ofFloricultur e atAalsmeer , where itwa scollecte d from greenhouse roses and reared forsevera l generations onbean s (Phaseolus vulgaris, 'Stamkievitsboon'). Jesiotr& Suski (1976,1979 )foun d adifferenc e inreproductiv e poten­ tial between mites fedo nbean s andthos e fedo nros e 'Baccara'. Afte r transfer ofth emit epopulatio n from roset obea no rvic e versa thesedif ­ ferenceswer eobserve d overa perio do fmor e thanon egeneration ,whic hma y suggest adaptation ofth epopulatio n toth ene whos tplan t through selec­ tion. Because itwa smor epractica lt ocultivat eth espide rmite s onbean s thano nroses ,i nadditio nt oros e 'Sonia'th ebea n 'Noord-Hollandse Bruine' isals oconsidere da sa hos tplant . The food turnover of Tetranychus urticae isconsidere d toenabl e compa­ risono fth econversio nefficiencie so fth eplant-feedin g spider mitesan d themite-feedin g predatory mites (Subsection 2.1.4). Furthermore,th erol e ofth ewebbin g isdiscussed , especially inrelatio nt oth ephytoseii d pre­ dators (Subsection 2.1.5). Thewe bproductio n andth egrowt ho fth ewebbe d area isquantifie d toenabl e thecalculatio n ofpre y density (Subsection 2.1.6).

The following aspectso fth ebionomic s ofTetranychida e willb ediscuss ­ edonl ybriefly :

Food quality of the host plant for the parenchym feeding spider mite The foodqualit yo fth ehos tplant ,a saffecte db yplan tnutrition , iscon ­ sidered tob econstan t under practical circumstances ofcultivation .Fo r example, theN , P and K levels ofros e leaves aremostl y within 10%o f their mean levels (Arnold Bik,persona l communication), which isa smal l variation relativet othei r effecto nth ereproductio n of Tetranychus urti- cae (Rodriguez, 1964).

Fertilization status of prey and predator Femaleso ftetranychi dan dphyto ­ seiid species sampled inth efiel dar erarel y unfertilized. Potter (1976a, ia'tl)an aBlommer s& Arendon k /icna\v-„,. - Phenomenon. ' ^ S6Veral exPla^tions forthi s

eratUre In the !rnrntar "* "^"^ ^^ henhousecultur eo f relt v! h r0^;.temPer— -nnally range between lo-can d33°C , while 2ItziTs t:: rnge between 45% and 9o%-The- «»*» - *-• - " V 4°, l0Cati0nS SP~ad over the rose-growing area ofTh e Netherlands (vanRi 3ssel,persona lcommunication) .

Wind and rain Glasshouse structures nullifv Pff„„f * • nuiiityeffect so fwin d andrain .

14 To restrict the amount ofwor k involved inthi s study, several aspects that influence thepredator-pre y system havebee npurposel y neglected, des­ pite their importance forth eeffectivenes s ofcontrol :

Implications of chemical spraying The toxic effects ofsevera l compounds tobot hpredato r andpre y arebein g studiedb yva nd eVri e (Research Station ofFloriculture ,Aalsmeer )an dva nZo n (University ofAmsterdam , Amsterdam).

Diapause, as a means to survive the winterperiod Theinductio na swel la s the termination ofth ediapaus eo fth etwo-spotte d spidermit e andth ephy - toseiid predator depend onphoto-period , temperature andth eavailabilit y of food. Inadditio nt oth eliteratur e reviewed byva nd eVri ee t al. (1972) andMcMurtr ye tal . (1970), thefollowin g references represent currentknowl ­ edgeo nthi stopic : -Tetranuchus urticae: Geispits etal. , 1971,-Hussey,1972 ;Frenc h& Ludlam , 1973;Hell e& Overmeer , 1973;Fritzsch e &Lehman ,1975 ;Veerman , 1977a,b. -Phytoseiidae: Sapozhnikova, 1964;Bocze k et al., 1970;Ho y& Flaherty, 1970; Wysoki & Swirski, 1971;Knisle y & Swift, 1971;Roc k et al.,1971 ; Croft, 1971;Hoy ,1975a,b ; Simova, 1976;Hamamur ae tal. ,1976b .

2. 1, 1 Development and mortality

The rate of development andjuvenil emortalit y wasmeasure d ina seria l thermal cabinet at constant temperatures of 13,15 ,20 ,25 ,3 0an d35°C ; the relative humidity ranged between 55%a t 35°C and 85%a t15°C .Th e leaves of the host plant were placed upside downo na we tspong e floating in aplasti c box filled with water.Thes e leaveswer e covered withwater - soaked tissue paper that hadbee n perforated at regular distances witha leaf puncher. In thatwa ycircula r parts ofleave swer e obtained thatwer e surrounded bywe ttissue ,whic h acted asa barrie r foral lstage s ofspide r mites.Th ejustificatio n forth eus eo fdetache d leafculture s in life-table studies was given by Rodriguez (1953), de Ponti (1977b) andDabrowsk i & Bielak (1978). The eggs, used tostar tth eexperiments ,wer e deposited within aone-hou r period. The subsequent progress in development andth ejuvenil e mortality were observed atinterval s ofeigh thour s atal ltemperatures .Th e transfer to fresh leaves, which is necessary to eliminate effects of diminishing food quality was carried outa t leastever y3 days,bu tonl yi fth emite s were ina mobil estage . To study the effecto falternatin g temperatures ondevelopment , someo f the experimental boxeswer e transferred atdail y intervals from 10°Ct o20° C and vice versa inon e series, and in another series from 25t o35°C .Th e developmental time from thedepositio n ofth eeg gunti l first reproduction ('egg-to-egg' development) is plotted inFig .4 .Th e rate of development

15 FEMALE(EGG TO EGG) RATEO F DEVELOPMENTAL TIME EGG-TO-EGG (DAYS) DEVELOPMENT (DAY" 1-0.02 n =1 5 36 n =1 1

32

28 h 0.15

2U

20H h 0.1

16

12H

Y 0.05

10 15 20 25 30 35 TEMPERATURE (°C)

S Standard deViati nS (± n= nUmber f • gg-to eaTd T ° ' ° replicate.) of ( lat c nltanH Pmental tlmeS °f *'"»**«» "««• on bean (o) and rose temPeratUreS The ' e t - **"» "»"~ t the rate of ,gg-to-

ah;enerrphen deVel°Pmental ^ **«*• Nearly on temperature (15-35-C). a general phenomenon in Tetranychidae. AStudent' s t-te<,t- fnr- • f two means and an F-test fnr „ «uaent s t-test for comparison of not reveal siJ^ . comParis°n of their respective variances did ^ZlLlZlll , &nC&S betWeen deVel°P-ntal time at the above ontZToTZT9 temPeratUreS (10-20°C and 25-3B°C) and that simulated S temperat ling tech! ^e (Pa;t rt ,r ""^ — <^ !) and amodel - may he c^sfder d as re t ^ ^ ^"^ ^ "te °f ^elopment n 1 tantaneOUSly t0 a Chan e This was also foun;j;:t % r * - temperature. -> - reiran^:^-^^:^^^ ulmi (Rabbinge,

16 Table 1. The effecto falternatin g temperatures on 'egg-to-egg1 developmen­ tal time (hours)o f females of Tetranychus urticae.

Interpolation3 Simulation Observation n Temperature alternation

193.7 15.0 196.2 14.4 198.1 12.4 28 25-35°C 663.8 55.5 671.9 51.0 677.8 48.1 24 10-20°C

a.Developmenta l time (=DR )estimate d by linear interpolation from the

measurements obtained atconstan t temperatures e.g. [(DR1Q + DR2_)/2]~ . b. Simulated by thepopulatio nmode l presented inPar t 2o f this Agricultural Research Report (tob epublished )usin gmeasurement s obtained at constant temperatures.

InTabl e 2th edevelopmenta l times aregive npe r stage and sex.Th e rel­ ative length of the different stages as apar t of the total egg-to-eggde ­ velopmental period israthe r constant, irrespective ofth e temperature: egg 39%, larva 9.5%, protochrysalis 8%,protonymp h 7%,deutochrysali s 8%,deu - tonymph 8.5%, teleiochrysalis 11%an dpre-ovipositio n female 9%. Although the rate of development is strongly affected by temperature, mortality remains constant ata low level (about 10%fro m egg to adult)i n the range 15-30°C (Table 3).Outsid e this temperature rangemortalit y in­ creases, as was also found by Mori (1961), Stenseth (1965) and Nickel (1960). Assuming that ateac hmomen t during the developmental period acon ­ stant proportion of the mites die from anon-predato r cause,th e relative rate ofmortalit y canb e computed asfollows :

-ln(N1./N ) RRM = 1—2_ =-ln(M)-D R t RRM =th erelativ e rate ofmortalit y (day- )

Nfc = thenumbe r ofmite s attim e t t = the developmental period (day) DR = rate ofdevelopmen t (day" ) M = mortality The stage-specific mortalities are incorporated in the population models presented inPar t2 b yusin g these relativerates . Several studies have shown that both low and extremely high humidity causes an increase in juvenilemortalit y and retards development (Boudreaux, 1958; Ferro & Chapman, 1979;Harriso n & Smith, 1961;Haza ne t al., 1973;

17 Table 2. Femalean dmal edevelopmenta l time (hours)o f Tetranychus urticae.

Temperature Stageo fdevelopmen t Total n (°C) E L PC PN DC DN TC PF

M o M 0 M o M a M a M a M a M a M a Females 13 648 24 11 15 342 18 90 14 70 9 61 10 65 9 73 13 85 9 84 21 870 38 15 20 160 4 36 6 31 4 27 6 29 5 34 5 40 5 41 8 398 21 22 25 103 2 24 9 21 4 17 6 21 5 23 4 31 6 21 5 261 14 31 30 68 5 17 5 14 5 13 5 15 8 14 6 20 6 15 4 176 13 24 35 56 3 15 2 11 4 11 4 11 4 19 7 17 4 14 5 154 16 18

Males 13 640 21 12 15 341 14 106 31 69 7 52 10 68 11 50 7 80 6 _ _ 766 45 11 20 161 1 34 3 33 5 24 5 30 5 26 6 38 4 _ _ 346 12 14 25 104 2 19 4 24 5 14 4 21 6 16 5 27 4 _ _ 225 7 7 30 71 4 14 5 13 5 12 4 13 4 11 4 17 3 _ _ 151 11 11 35 59 2 11 4 12 4 10 4 13 6 12 6 16 7 - - 133 9 9

E =eg g DC= deutochrysali s n =numbe r of replicates L =larv a DN= deutonymp h PC= protochrysali sT C teleiochrysalis PN= protonymp h PF preovipositional female

Table 3. Mortality(% ) in thedevelopmenta l stages of Tetranychus urticae.

Temperature Stageo fdevelopmen t (°C) Total

PC PN DC DN TC PF

10 15.6 12.5 38.4 15 6.1 190 1.4 1.0 1.0 0.0 2.2 11.3 154 20 6.3 1.1 0.0 1.3 0.0 0.0 25 4.3 9.6 181 1.9 0.0 0.0 0.0 1.0 9.3 144 30 6.6 1.4 1-2 0.0 1.0 0.0 35 10.1 10.8 100 4.1 0.0 2.9 1.0 2.1 24.4 144

Abbreviations areexplaine d inTabl e2 .

18 McEnroe,1963 ;Nickel ,1960) .Howeve rth erang eo fhumiditie sfo rwhic hde ­ velopment isno taffecte ddiffer sfro mstud yt ostudy .Haza nfoun doptima l conditions for Tetranychus cinnabarinus ata relativ ehumidit yo f38% ,bu t Harrison& Smit hfoun dlittl edifference si neg gdevelopmen to f Tetranychus urticae inth erang e50-90% ,an dshowe dtha tth eeg gmortalit ya t100 %rel ­ ativehumidit yoccurre d only after6 day so fexposure .Becaus esuc hhig h humidities occur foronl y shortperiod sunde r greenhouse conditions (van Rijssel,Researc hStatio no fFloriculture ,Aalsmeer ;persona lcommunication ) thiseffec ti srule dou ta sa facto ro fimportance .Moreover ,a nexperimen t carried outfo ra mor erealisti c rangeo fhumiditie s (50%,75 %an d85 %a t 23°C)di dno trevea lan ydifferenc ei ndevelopmen to rmortalit y (Table 4). Apossibl e explanation forth eabsenc eo fan yreactio ni stha tthes eexpe ­ rimentswer e carried outo nwebbe dleave stha twer econnecte dt oa par to f their shoot,for ,a spostulate db yHaza ne tal . (1975b),bot hwebbin gan d defaecationb yth espide rmit eand ,probabl ymos timportan to fall ,évapo ­ transpirationb y thelea fma y acta sa buffe rt ochange si nhumidity .Fo r thisreaso nhumidit yi sno timportan tunde rth egreenhous econdition s(rel ­ ativehumidit y45-90% )i nTh eNetherlands . Tostud yth eeffect so ftransferrin gspide rmite sfro mbea nt orose ,si ­ multaneous experiments onbot hhos tplant swer e carried out.Th eresult s aregive ni nFig .4 .A t-tes tfo rcompariso no fmean san dF-tes tfo rcompa ­ risono fvariance s didno trevea l significantdifference sa tth e5 %leve l between development onbea n androse .T ochec k ifthi sconclusio nals o holds aftergeneration so ffeedin go nth esam ehos tplant ,anothe rcompar ­ ison was made aftera six-mont hculturin gperiod .Th eresult s (Table9 ) showtha ti ncontras tt oth eresult so fJesiot r& Susk i (1976)wit hbea n and rose 'Baccara', the presentcultivar so fbea nan d rose 'Sonia'ar e interchangeablehos tplant swit hrespec tt odevelopmenta ltime . Butfo ron eexceptio n(Marie ,1951) ,dat afro mliteratur eabou tdevelop ­ mentaltim eo nsevera lbea ncultivar sar ei nclos eagreemen t(Gasser ,1951 ; Husseye tal. ,1957 ;Bravenboer ,1959 ;Fritzsche ,1959 ;Nickel ,1960 ;Susk i

Table 4. Theeffec to frelativ ehumidit y (T= 23°C )o nfemal e'egg-to-egg ' developmental time of Tetranychus urticae.

Humidity (%) Developmentaltim e(hours )

45-50 286 17 44 70-75 289 19 52 85-90 292 21 48

19 & Badowska,1975 ;Shi he tal. ,1976 ;Saito ,1979b ;Feldmann , 1981). Compar­ able data about developmental timeo ngreenhous e rosesar eno t available. As fordevelopmenta l time, juvenile mortalityma ydiffe r withth eplan t specieso rcultiva r (Dabrowski& Marczak , 1972). Tulisalo (1969) found differencesi njuvenil e mortalitybetwee n cultures growno ndifferen t cul- tivarso fcucumber ,althoug hth erat eo fdevelopmen tdi dno tdiffe r signif­ icantly.However ,i nth e study describedi nthi s report juvenile mortality was verylo wo nbot h host plants (beanan drose) , which corresponds with theresult sgive ni nth eabove-mentione d literature,excep tfo rShi he tal. , whoreporte da rathe rhig hmortalit y (30%). Ofth evas tnumbe ro fstudie so nnutritio ni nAcarina ,onl y thato fSusk i & Badowska (1975)concerne dth einfluenc eo fNP Ksuppl yo nth erat eo f devel­ opmentan dth ejuvenil emortality .Th erelation s they establishedar e com­ plex.I ti ssufficien tt omentio nher e thatth enutritiona l ranges usedi n theexperiment s caused changesi nth erat eo fdevelopmen tan djuvenil emor ­ tality thatwer e within 15%o fmea nvalues .Howeve rth enutritiona l range was probably larger thantha tfoun di npractica l agriculture.Th enutrien t compositiono fth elea fma yals ob eaffecte db yit sageing ;n oexperimenta l evidence ofa neffec to nth erat e ofdevelopmen t wasfound , however (Table10) . During mite-colony growthth eegg san djuvenile s arelef t strandedi n already exploited leaf areas.Th eyoun g mites areno ta sactiv ea s the mature mites,whic hma ycaus emortalit y additionalt otha tmeasure di nth e previousexperiments ,wher eth emite swer e cultivated individuallyo nfres h leaves.Wrensc h& Youn g (1978)measure da marke d reductioni nrat eo f devel­ opmentan d survivala thig h spider-mite densities.However ,a sthe y confined themite st oa lea f disc,th eimportanc eo fintraspecifi c competitionfo r food stillha st ob edemonstrated . Spidermite sar eabl et ocontro l their density (numbero fmite spe rsquar e centimetrewebbe d leaf area)partl yb y increasingth ewebbe d areaan dpartl yb ydispersal .T odecid ewhethe r these factorsnee dt ob estudie di nmor e detail,a greenhous e experimento npopu ­ lation growthwa scarrie dou tan dth enumerica l resultswer e compared with simulationso fth esam eexperiment ,whic hneglec t effectso fintraspecifi c competition.Thi s experimentwil lb ediscusse di nPar t2

2.1.2 Reproductionand life span

rlmentS n thS te f re roduction a siIn ° " ° P -nd ageing were carried out using X P tal d6Sign that d6SCribed in the sZctTon 2 TTr ^ P«vi-B subsection sZ d for e*ach ; T' ^^ ^°™hs Cl°se *o their final moult were MaleS Were intr dUCed t0 gUarantee 171 on of the f T ° *—"ate inse- r m v d .t eÏÏhtT "" eCl°Si°n- ^ ™**' °f ^ ^ «»'- -

by unnatural causes, e.g. drowning in the water-soaked tis-

20 NUMBERO F EGGS(DAY" 1 35°C

AGE CLASSES

Fig. 5. Rate ofreproductio n of Tetranychus urticae inrelatio n to female age class and temperature. The histogram visualizes the descriptive power of the intra-age class regressions. Length ofeac h age class at different temperatures: 3.5 day at 15°C; 2.5 day at20°C ;2. 0 day at25°C ; 1.25 day at30°C ;1. 0 day at35°C .

sue (5-10%). Because both reproduction andmortalit y appeared todepen d on age, the data were classified in age periods forming equal parts of the maximum life span.Thi smaximu m longevity ofth e femalewa s estimated via a least-squares estimate ofth e 97-99%poin t ofth e cumulative frequency dis­ tribution of life spans,plotte d onprobabilit y paper ofth e Gaussian dis­ tribution. From this linear relation themortalit y per age classwa s esti­ mated. This mortality togetherwit h the duration of theclassifie d agepe ­ riods was used to calculate therelativ e rateo fmortality . Thisclassifi ­ cation approach requires some degree ofintra-clas s constancy of therela ­ tive rate variables involved. For this reason the maximum life span was divided in 18 ageclasses ,precede d by apre-ovipositio n period.Th edura ­ tiono fth e ageperiod s and the age-dependent rate ofreproductio n inrela ­ tion to temperature are given in Fig. 5. Itappeare d that the intra-class rate of reproduction in the initial 10 ageclasse s depends on temperature

21 SLOPE (EGG S •DAY"-"C" 1) 1.0-,

"I I I—l—I—I—I—I—I—I—I—I—I—l—l—I—I—I 1 23456789 10 11 12 13 U 15 161 7 18

AGE CLASSES Fig. 6. Slope of the oviposition rate (eggs-day" -°c" )i n relation to theag eclass .Slop e= ovipositio n rate/(temperature - 10°C).

Table 5. Potential andne t fecundity of Tetranychus urticae in relationt o temperature.

Temperature (°c) Fecundity

potentiala netb

range

10 31.2 28.6 9.8 48 6- 44 15 98.0 84.2 36.6 43 35-170 20 146.2 129.9 53.3 42 43-272 25 160.8 129.7 48.9 45 41-237 30 135.3 119.5 33.7 38 40-185 35 135.4 120.6 38.6 39 40-177

10-20 101.1 87.5 28.8 41 35-157 25-35 148.3 123.9 40.8 38 43-205

22 in a linear fashion over the whole temperature range from 15°C to 35°C. This enabled amor e concise description via the slopes ofth e linearregres ­ sion lines,whic h cross the x axis close to 10°C. These tangents of the angle of inclination are plotted in Fig. 6 and their descriptive power is visualized by the histograms in the original graph of the age-specific rates of oviposition (Fig.5) . In Table 5 the mean egg production per female is given as ane t (=fe ­ male mortality included) and a potential (= female mortality excluded) fecundity, which shows thatmortalit y causes only a 10-20%decreas e of the fecundity relative to thepotential .Fecundit y appears tob e unaffected by temperature over a rather large range (20-35°C). Howeverbelo w 20°C itde ­ creases,bein g 70%a t 15°C and 20%a t11°C . The mean and maximum life-spans depend on temperature in a much more gradual way, asca nb e seeni nTabl e 6an d Fig. 5.Becaus e thepost-oviposi - tionperio d is absent orver y short,th e adult life-span is only subdivided in apre-ovipositio n period and apost-ovipositio n period. Aswit h reproduction, survival may depend on temperature and ageing, i.e. the age relative to the maximum life-span.Therefor e the relative rate of mortality was determined foreac h age class and atal l experimental temper­ atures. From simulations ofpopulatio n growth (Part 2), itappear s that the numerical effects of thetemperatur e dependency couldb eneglecte d aswel l (12-35°C). For this reason the relative rateswer e smoothed outb y repeated simulation of the above survival andreproductio n experiment until anaccept ­ able overall fit was found.Thes e fittedvalue s are given inTabl e 7.The y demonstrate thatth e relative rate ofmortalit y depends onth e age relative toth emaximu m life-span.

Table 6. The length ofth epreovipositio n and oviposition period (days)o f Tetranychus urticae.

Temperature Preoviposition period Oviposition period (°C) range

10 25.00 - 20 100 - 48 28- 15 3.49 0.87 15 39.3 14.5 43 12-67 20 1.70 0.32 22 26.5 8.1 42 13-44 25 0.89 0.20 31 21.8 8.8 45 8-48 30 0.61 0.16 24 11.6 3.2 38 8-20 35 0.60 0.20 18 10.6 2.6 39 6-16

10-20 3.05 0.91 22 40.6 10.0 41 16-59 25-35 0.55 0.11 28 13.4 5.1 38 6-31

23 Table 7. Thesmoothe destimate so fth erelativ emortalit yrat e (day") o f Tetranychus urticae inrelatio nt oth eag eclas so fth eadul tfemale .

Femaleag eclas s

1-5 6 7 8 9 10 11 12 13 14 15 16 171 8

0.0 0.0020.0 20.0 50.0 50.0 70.1 0 0.100.1 00.1 00.1 5 0.15 0.30 0.50

Table 8. The effect of humidity (T= 23°C) onne t fecundity and oviposi- tion period of Tetranychus urticae.

Relative humidity (%) Net fecundity Oviposition period (days) n

45--50 130. .1 44. .0 23, .1 9, .2 26 70- -75 129, .8 45, .1 23, .6 7, .9 34 85- -90 122, .4 38, .2 22 .4 7, .1 30

The effecto fhumidit yo nth e rate ofreproductio nwa s analysedb y Boudreaux (1958),Nicke l (I960)an dHaza ne tal . (1973).Th eovipositio n ratei smaxima lfo rrelativ ehumiditie sbelo w 90%, themaximu mdependin go n temperature and thespecie s involved;Haza ne t al. (1973)foun doptima l valuesa trelativ ehumiditie so f22-38% .Abov e90 %relativ ehumidit yth e ovipositioni slowest .A s argued inth epreviou s subsection thehumidit y neart oa webbe dlea fwil lprobabl ydiffe rfro mth eenvironmenta lrelativ e humiditya tth esam etemperatur edu et oévapotranspiratio no fth elea fan d laclt10% „theSPlde rmite -T °StUd yth e6ffeC to fth e *»"ity*- fferin* strate Jlh T"* "^ "^ ^oductionwa smeasure do nthi ssub - for L J ^ l6VelS

rost-sont and"?6 °' ^^^ £*™^ wasmeasure d alsoo nbot h cTew t h pi::rm r '"°°^^ Bruine- (Table 9). Thesetrial s were 0n .itesculUvate titivatead for for"si xmonth ^s o nros^^ e Roi-v^ , +• *- ** .» ^ ™« ««»"tedwit h -sono fmean san dvariances ,respectTvel v ,, *""' '" C°mPa" res ectl ferencesa tth e5- /i evPl ^ P vely,di dno trevea lsignifican tdif - W.level .Therefor ei ti sprobabl etha tthes eparticula r 24 Table 9. The effect ofth eculturin gperio d on some life-history traits of Tetranychus urticae (T= 25°C) .

Phase of Female 'egg-to-egg1 Net fecundity Oviposition period culturing developmental time (days) (hours)

n M n M directly after 31 261 14 45 129.748. 9 45 21.8 8.8 transfer toros e after a6-mont h 42 266 16 40 132.147. 3 40 21.5 8.1 period of culturing onros e ('Sonia') continuously cultured 15 270 21 41 133.4 50.8 41 22.2 9.2 onbea n('Noord - Hollandse Bruine')

cultivars of bean and rose are interchangeable hostplant swit h respect to the life-traits studied. Comparison of these results on rose with data from the literature on bean shows similar fecundity levels (Bravenboer, 1959;Leh r& Smith, 1957 (Massachusets strain); van deBun d &Helle , 1960;Watson , 1964 (old leaves); Suski & Badowska, 1975; Shih et al., 1976; Saito, 1979b;Feldmann , 1981) with only a few lower values (Gasser, 1951 - 68 eggs; Lehr& Smith, 1957 (Canterbury strain) - 107 eggs; Fritzsche, 1959 - 57-80 eggs)an d higher values (Watson, 1964) (young leaves).A t otherhos tplant s fecundity levels similar to thepresen tresult sma yb e obtained,bu tmostl y lower levels are reported. Insevera l cases thechemica l compositiono fth eplan tha sbee n shown to correlate withmit e fecundity.Accordin g toJesiot r& Suski (1974)fecundit y of the two-spotted spidermit e is lower onros e 'Baccara'tha n on anumbe r ofothe r rose cultivars.Howeve rDabrowsk i & Bielak (1978),wh o studied nu­ tritional correlations with mite reproduction in4 cultivars ofbot horna ­ mental roses, were not able to explain this result; theyonl y found some correlation with the content of glutamic acid. Furthermore, they found a positive correlationwit h the totalnitroge n content and total freeendoge - neous amino acids.Accordin g to the reviewb y Suski& Badowska (1975)th e effect of nitrogen is often positive, but the results withpotassiu m and phosphorus are far from conclusive.Susk i et al. (1975)stat e thatth eex ­ treme conditions produced in the nutritional solutions in the laboratory are rarely met in practice today and therefore theeffect s onmit erepro -

25 auctionreporte dca nb eignored .Moreover ,th erol eo fadaptatio no fa mit e population tomodifie d nutritional conditions,a sindicate db yth eresult s of Jesiotr& Suski (1974),i svirtuall y overlooked inth elaborator y expe­ riments, where generally instantaneous, instead ofdelaye d responses (>1 generations)t onutritiona l changesar emeasured . Because inpractica l rose culture today more orles sconstan tNP Klevel sar emaintained , andbecaus e thegeneti cmake-u po fth egreenhous e populations seemst ob erathe r stable, which indicates minor exchange with outdoor mitepopulation s (Overmeere t al., 1975),i tma yno tb efa rfro m realityt oconside rth enutritiona l con­ ditions asa constan t ora nimplici t 'noise' factor. This assumptioni s supportedb yth efac t that inpractic e NPKlevel s of 'Sonia' rose leaves (3.10%N ,0.28 %K ,2.20 %P )ar elargel ywithi n10 %o fthei r mean values,s o thati nmos tcase s fecundityvarie swithi n11 %o fit smea n level (Rodriguez, 1964). Rabbinge (1976)cam et oth ever y same conclusion forth efruit-tre e redspide rmite ,whic h infestsDutc h appleorchards . Besides fertilizer doses,th enutrien t compositionma yals ob einfluence d byth eag eo fth elea fo rb yseasona l changes (e.g.Storms , 1969; Dabrowski, 1976). However theag eo f 'Sonia' leaves isprobabl y noto fimportance : femalespide rmite splace do ngree n leavesa tth etop ,middl e orlowe r part ofa ros e bushproduce d asimila r amounto fegg s (Table 10).Besides , yel­ lowing leavesar edroppe d rather soonan dthes e senescent leaves aresimpl y lefto ravoide db yth espide rmites .Seasona l changes infoo d quality were notstudied . Food quantity isaffecte db yfeedin go fth espide r mites.Th eavailabl e leafparenchy m decreases during population growth untilth ehos t planti s exhausted.Th eoveral l damagema yexcee dth edirec t damage donet oth ehos t

inflUenCe f1Sa f age n S me oTrltZnui Tetranychus T urticae. ° ° ° ^"history traits (T= 25'C,

Leafnumber , n pom=i counted fromth e Ztlo . • "* *""""** 0viP°siti- Period topo fa flowerin g developmental ^ rose shoot (hours)

M c M ô M CT 2- 4thlea f 30 258 14 131.1 46.4 22.1 8.9 12-14thlea f 25 269 19 126.8 40.9 21.8 9.1 20-24thlea f 21 262 13 124.6 55.1 20.9 9.8

26 plant by the piercing ofth e leafcells .Possibl y the quality of available food dropped by indirect causes.Anyway ,mit e feeding activity does affect the food, as shown by a number of researchers (Davis, 1952; Bravenboer, 1959;Tulisalo , 1970;Rasmy , 1972;Wrensc h &Young , 1975). To decide whether these factors need tob e studied inmor e detail,a populatio n experiment in the greenhouse was compared with population simulation, excluding density dependent factors (Part 2). Inthi sway , ifth e simulations fitunde rcir ­ cumstances of free growth (unlimited food supply), the critical level of plant exploitation may be found abovewhic h intraspecific competition acts upon thepopulatio n growth of Tetranychus urticae.

2.1.3 Sex ratio

The two-spotted spidermit e Tetranychus urticae is anarrhenotokou s par- thenogenetic species: unmated femalesproduc e onlyhaploi d eggs,whic hde ­ velop into males,wherea s mated females produce both haploid and diploid eggs, which develop into males and females, respectively. Mating takes place immediately after the las moult of the female. Supply of sperm is organized very efficiently dueto : the guarding and defendingbehaviou r of themale s (Potter et al.,1976a , 1978) the role of pheromones, tactile stimuli and web (Cone et al.,1971ab , 1972; Penman& Cone,1972 ,1974 ;Rege v & Cone,1975 , 1976) a shorter developmental time of themale s relative to the females (Sub­ section2.1.1 ) a lower tendency ofth emale s to disperse relative totha to f thepreovi - position females (Part 2) the presence of an overdose of males relative to thenumbe r ofteleio - chrysalids near the ecdysis (Potter, 1978;Functiona l sex ratio). The insemination atth e firstmatin g appears tob e the effective one (Helle, 1967; Overmeer, 1972;Wrensc h &Young , 1978). According toBoudreau x (1963)th eproportio n of females in the offspring of asingl e female israthe rvariable , sotha tther e isn o fixed sexratio . He states, that the sex ratio in the offspring ofeac h female depends on the amount of sperm received during mating. ThoughOvermee r (1972)demon ­ strated the possibility of such a relationb y artificial coitus interrup­ tions, it is still not clear if these interruptions occur under natural conditions. Moreover, Potter & Wrensch (1978) summarize some mechanisms thatma y lead to resistance of themale s to disturbanceb y othermales . Although the sex ratio inth eoffsprin g of asingl e female is subject to variation, this need nott ob e true forth e sex ratio inth eoffsprin g ofa population of spider mites.Overmee r (1967)an d Overmeer &Harriso n (1969) found that the ratio of the total number of fertilized eggs against those thatescap e fertilization israthe r fixed over alarg e number of subsequent

27 generations.The y suggesttha tse xrati o is an inherited property of apop ­ ulation, i.e. strain specific.Mitchel l (1972) attempted to verify this genetic hypotheses. He found similar indications and suggested that the variability of the sex ratio would appear to be a genetic polymorphism. BothMitchel l andOvermee r& Harriso n found inthei r experiments amaterna l effect on the inheritance of the sex ratio.Althoug h the selective forces that cause fixation of the sex ratio of amit e population have neverbee n demonstrated, there are some indications of strain-specific sex ratios (Lehr & Smith, 1957;Overmee r & Harrison,1967 ;Mitchell , 1973;Feldmann , 1979) and itwil l be considered as such in this study. Nevertheless all datahav eon easpec ti ncommon :th epreponderanc e of females among theoff ­ spring.Thi sca nb esee n inth e studies justmentione d and also inthos eo f Gasser (1951),Davi s (1961), Iglinsky (1951), Laing (1969), Overmeer (1967, 1972),Haza ne tal . (1973). The proportion of female progeny was therefore measured again in the present strain of Tetranychus urticae. The eggs,produce d in the reproduc­ tion experiments at 25°C,wer e allowed todevelo p untilmaturity , whenth e sexo fth eindividual s canb e registrated conveniently. To study apossibl e relation between the sex ratio and the ageo fth eparenta l female the eggs were grouped according toth eag eclas s ofthei rmothe r (timeperiod s of2 days). Because the number of eggs produced during the final 8 age classes werelow ,du et oa lo wrat eo freproductio n and survival of theparents ,a n extranumbe ro f femaleswa s grown simultaneously with the reproductionexpe ­ rimentst oincreas eth enumbe r of 'old female'egg s for sex ratio assessment. From the results (Table 11) it appears that the sex ratio increased from 0.55 in Class 1t o0.7 5 inClas s2 and starting from Class 6graduall yde ­ creasedt o0.5 1 again.Thi s change inth e sex ratiowit h age canb e attrib- vill :ntrinSlCally gating actors, because themortalit y duringde - l P sT' TV"8 than 10%- " WaS generally found ««* the first egg deposited tends to be unfertilized more frequently (e.g.Overmeer , 1972). T^jzrziT.Ti ;":ringo fTetranuchus Mcae agains tth eag e

Ageclas snumbe r Proportion females Number ofegg s Number of inprogen y parental females 1 0.55 2-3 197 0.74 125 4- 6 320 0.75 118 7- 9 228 0.70 112 10-14 479 0.63 96 15-18 302 0.51 72 178 65

28 The subsequent increase of the sex ratio was also foundb yNicke l (1960), Hazane t al. (1973)an dPotte r& Wrensc h (1978). Feldmann (1981)reporte d a response of the sex ratio to the age ofth e female,tha twa s qualitatively similar to that found inth epresen twork . Because sex is determined by the fertilization process,contro l ofth e sex ratio as found in hymenopterous parasitic wasps may be expected.Be ­ cause females are larger than males (6:1;Tabl e 12),an dbecaus e females require much food for egg production, sex determination has an important bearing on the rate ofplan t exploitation.A t some specified degree ofin ­ festation itma yb emor e efficient toproduc e less diploiid eggs (= females) in view of their chances toreac hmaturity . Inthi s respectth e results of Wrensch & Young (1978) should be noted.The y found aneffec to f depletion of the food resource onth e sex ratio thatcoul db e ascribed to anintrin ­ sically operating mechanism in the female parent.Th e relative importance of this aspect for thepopulatio n growth of the spidermite s is determined by comparison of simulated and experimentally determined population growth (Part2) .

2.1.4 Weight loss, water balance and growth budget

Because theweigh t increase during development and the rate of foodcon ­ version into egg biomass play a central role inth e quantitative analysis ofth epredator-pre y relation, it isworthwhil e topoin t out the differences in this respect between the parenchym-sucking Tetranychidae and themite - sucking Phytoseiidae.Th eweigh twa smeasure d atdifferen t stages of devel-

Table 12. Weight increase of Tetranuchus urticae duringdevelopment .

Stage of development Liveweigh t (ug)

â/Vn egg 1.2 - 20 (group) larva 1.6 - 20 (group) protochrysalis 1.5 - 20 (group) protonymph 3.7 0.2 25 deutochrysalis 3.5 0.2 10 deutonymph9 10.9 0.5 18 deutonymph<* 3.4 0.2 20 teleiochrysalis 9 11.0 0.4 20 teleiochrysalis a 3.5 0.2 20 adult female in oviposition phase 24.1 0.8 40 adultmal e 3.9 0.1 28

29 opmentwit ha Cah nelectrobalance .Th eresult s (Table12 )ar ei nclos eagree ­ mentwit h thoseo fMitchel l (1973)an dThurlin g (1980), both obtainedfo r Tetranychus cinnabarinus. Thetwenty-fol d increasei nweight , fromeg gt o ovipositingfemale ,take splac eprimaril yi nth edeutonymp h stage (30%)an d thepreovipositio n stage (55%). This relative distributiono fth eweigh t overth edevelopmenta l stages appearst ob ever y similart otha to f Phyto- seiidae (Subsection2.2.1 ,Tabl e 18).Spide rmite s disperset oothe r leaves inth ebeginnin go fth epreovipositio n phase after fertilization. Inthi s waycolonizin g femalesdispers ebefor e theyhav e attained half theirmatur e weight.B ydelayin ghal fo rmor eo fthei rgrowt han dthei r full reproduction effortunti l after dispersalt one wfoo dresource s these mites reducede ­ mandso nthei r original location,wher e juveniles,male s andparenta lfe ­ malesremai nhavin ga muc hlowe rtendenc yt odispers e (Part 2). The feeding physiologyo fspide r mitesi scharacterize db yth elarg e guantitieso fplan t fluid passing the digestive system. McEnroe (1961, 1963), studying theactivel y feeding femaleb ya radioactiv e tracertech ­ -3 nique, estimateda ningestio nrat e equalt o6x io Ml per3 0minute san d 3 a simultaneous defecation rateo f5x io" Mi per 30minutes .Thi s implies thata namoun to fflui dequivalen tt o20-25 %o fth efemal eweigh ti s passing thegu ta t3 0minut e intervals.Lieserin g (i960)counte d thenumbe ro fpa - renchym cellspuncture d andemptied . Hisestimatio no fth eingestio nrat e amountst o10 0parenchy m cellspe r5 minutes, which , assuming thecel li s spherical with radius 0.01mm ,implie sa ningestio nra to f5 „ 1pe rhour . Eliminationo fth elarg equantitie so fwate r ingestedi nthi swa yi saccom ­ plished viaa bypas s system that shuntsexces s fluids fromth eoesophagu s withCtiYrt0 thS hindgUt- ^ thlS WSy ^^icular digestionma yprocee d without theadde d burdeno fprocessin g andtransportin g excess liquid (McEnroe, 1963). Large volumeso fwate r canb epasse d rapidly throughth e sr'tÏ rT T and eXCreted With°Ut reqUirin* «ergy *>r -electiveab - How mo? SP°rt t0 thS traCheal SySt6m for excretion.Als o substances gutfro mr Tght (methYleneblU e SOlUti0n)* aSS Btraightt oth e hind- rete dt othe 0eS°fr S- "^ & C°11<>idal ^^ °fCong ore di sdi - m 9 - - Bekke~r (1956- -)* suppose*•£ d - showed that these freTlT "" ***** ^^ WieSmann (1968) especiallychloroph y V^ ^ ^^ d^s, particlesan d legations o^,^^^*«** -to ballso fexcrement , U sha ed aboutth ecommo nnam e»two-spotte d sni7 ~ P ** lumen have brought the bodywall .Upo nexcretio n ^ mite"' *" t0 the tranaparancyo f PeUetS COntain large amount ofplan t "1 , " ""^ ""^ " *

Nasser,1951 , McEnroe iT^s^" ""* ^^ ^^ ^> another typeo ffaece s n»„'K 1^Sering' 1960>- Apart from these solid faeces 6 •i- t» theblac k pellets an , P^er™ »* «" ****** equali n spider mite eggs, butevaporat es oquickl y 30 thatonl y aver y small solid fraction containing nitrogeneous waste products (McEnroe, 1961), remains:th e "whitepellets" .Anothe r means of eliminating large quantities of water istha tvi a tracheal evaporation.B y sealing the tracheal openings and by cyanide treatments,McEnro e (1961)showe d that an important part of weight loss canb e attributed to tracheal transpiration. Blauvelt (1945) showed the structural basis for the control of tracheal transpiration via the peritremes, which are located dorsally just behind the gnathosoma inthi sprostigmati dmite .Th e role ofcuticula r evaporation is very limited (McEnroe, 1961), probably because of alipi d layer inth e cuticle (Gibbs& Morrison , 1959). As expected of a plant-feeding arthropod, the conversion of ingested plant liquid into eggbiomas s is accomplished with low efficiency.A crude estimate ofth econversio n efficiency hasbee n obtained from the following: - The size of a fresh faecal pellet approximates that ofa n egg, so that their respectiveweight s will notdiffe rver ymuc h (approximately 1|jg )(ow n observation). The rate ofovipositio n isequa l to 75%o f the rate ofdefecatio n (rela­ tivehumidit y = 60-80%) (Hazane t al., 1973, 1975). The weight loss during the first hour of food deprivation isequa l to 1.2 pg at I = 30°C and arelativ e humidity = 15-20% (McEnroe, 1961). This mayb e considered as anestimat e ofth e tracheal transpiration rate. - Oviposition and defecation atT =30° C (and relative humidity = 15-20%) takes place at 2 and 1.5 hour intervals,respectivel y (Hazane t al., 1973, 1975), so that the weight loss via tracheal transpiration equals thatvi a ovipositionplu s defecation. The weight loss via oviposition therefore contributes to 3/7 x 1/2 =ca . 20% of the total weight loss. In the steady state (fluid intake =tota l weight loss), the conversion efficiency of ingested fluid to eggmas s is equal to approximately 20%,whic h contrasts with thato fth ephytoseii d fe­ males (Section 3.1).Becaus e mature females of this family lose most of their weightvi a eggproduction , Phytoseiidae canconver t the ingested con­ tent of the spider mite to egg biomass with an efficiency of about70% . This difference may be explained by a relatively higher degree of water conservation inth ePhytoseiidae , as indicated by thepresenc e of Malphighian tubules and a colon (Akimov & Starovir, 1975), andb y a lowproportio n of indigestable constituents. In spidermite s thephysiologica l effort is not directed to recycling ofwater ,bu t rather toeliminatin g it,a s indicated by thepresenc e ofth e combined hindgut and excretory organ (Blauvelt, 1945). Moreover, large amount of solid food residue areeliminated , as indicated by the "blackpellets" .

31 2.1.5 Role of webbing

Tetranychid species differ withrespec tt othei rmod e ofwe bformation . Panonychus spp.us eth esilke nstrand spredominantl y indispersa l (Fleschner etal. , 1956) . They spinthread sb ywhic h they lower themselves froma lea f until they arepicke d upb yai rcurrents .Sait o (1979) found thatth e fe­ maleso f Panonychus citri spinwhil ewalking ,bu tappea rt oavoi d theirow n threads,whic h merely serve as 'lifelines'. Apart from itssimila rus ei n dispersal, Tetranychus spp.us eth esilke n strands asmateria l forbuildin g structures ofwebbing , within which allstage s find aplac e tolive .Th e adult stageso fthes e species walk upon, ino runde rth ewebs , whilefo r example Oligonychus ununguis mostly lives under awebbin g cover (Saito, 1979). Thestructur e ofthes es ocalle d colonies differs among themember s of the Tetranychus species. Colonies of Tetranychus atlanticus are more compact andhav e agreate r profusion ofwebbin g than thoseo fmos t other species (Leigh, 1963). Tetranychus desertorum produces colonies similart o the latter species (Nickel,1960) ,bu t Tetranychus pacificus produces only a looseo rdisperse d typeo fcolony ,wit hrelativel y little webbing. Tetra­ nychus urticae produces colonies with anintermediat e amount ofwebbin g (Leigh, 1963).O nth eothe rhan dth efor man ddensit yo fth ewe bdepend so n thehos tplan tinvolve d (hairs,ribs , smoothness) (vand eVri ee tal. , 1972). Several functions have been ascribedt oth ewebbin g (Gerson, 1979).Th e silkserve sa sballoonin g threadsi naeria l dispersal,a sa lifelin e indis ­ persalb ywalkin gan da sa carrie ro fse xpheromones .Th ewebbin gma yindi ­ cate thestat e ofdepletio no ffoo d resources andi tma yb ea prerequisit e forth econditionin g ofsocia l interactions.Th ewebbin g isuse d inintra - specificmatin g competition betweenmale san di ninterspecifi c competition

againstothe r non-spinning phytophagous mites. The webbingcove rma yals o ZUS lnffenCe °nth e ^oclimate, forinstanc e viath ehygroscopi c itZZT « fibr°in Silk StrandS- M0—< " Protectsth einhab - naturalT '^ ^ C°nditions' *™ Pesticidesan da tleas tsom e eS In thlS the P! dt r Dr ;; ; '*"* *^ «* "**ing on the acarine m theare l Cti°n ^ ^^ "* onlybecaus eth ewebbin gde ­ in™^ ; ™ :rr ;r er mites and theref°re sh°uid -used t0 be Ve imPOr tantcu ei nth efla Z lh ^^ * ^^ * ^ ' The roleo fw T " °f* * ***»«*" predators. —hidÎ^^^^^TcS" .£ T" ^ " "* (1966)stat etha t Ambluseius A• * **' McMurtry & Johnson another direction „h aiùxsci sometimes backed awayan dproceede di n Wh they walked over it !^ ^ ^ "**" ««' -eas **othe rcase s Afe wtime sthi spredatoTwT s^ "^ "^ (Wi^^™ sPP->unharmed , SerVed lns d gainedacces st oth ep r M i e thewebbin g structures having & J hnS n r6P rt that nicus wasl ess hinderedb vt-T" ? ° ° ° ^>^eius ^°" ed bY the Webbln^ ««1 ^lyseius chilenensis immedi- atelycrawle dbetwee nth estrand so fwebbing .A negativ einfluenc eo fweb ­ bingo nprédatio nb yPhytoseiida eha sbee nreporte dfo rth eadul tfemale s of Amblyseius longispinosus (Mori, 1969), A. largoensis (Sandness& McMurtry, 1970, 1972), Typhlodromus caudiglans (Putman, 1962), T. pyri (McMurtrye t al.,1970 )an dfo rth elarva eo f T. tiliae (Dosse,1956) ;th eadult so fth e latter species seemedno tt ob e affected.Howeve rothe rPhytoseiida esee m tob e attracted toth ewebbin g andundisturbe db yth esilk .Thes einclud e Amblyseius fallacis, Phytoseiulus persimilis and Metaseiulus occidentalis (Putman & Herne, 1966;Huffake r et al.,1969 ;McMurtr y etal. ,1970) . Schmidt(1976 )measure da nincrease drat eo fprédatio nb y Phytoseiulus per­ similis duet oth ewebbing .Sh efound ,tha tweb sarreste dth epredato rmor e thanpre yegg so rexuviae ,an dsuggested ,tha tthi sarrestmen twa sbase do n tactile stimuli.Thes e observations correspondwit h thoseo fTakafuj i & Chant (1976), who observed that Phytoseiulus persimilis, asoppose dt o Iphiseius degenerans, consistentlydistribute ditsel fove rth esilk-covere d leaves,an dth eadul tfemale sinvariabl ydeposite dthei regg si nth ewebbing . Fransz (1974,p .99-100 )conclude dtha twebbin ghinder s Metaseiulus occiden­ talis sufficientlyt oaffec tth eprédatio nrate .H eobserve dsevera lbehav ­ ioural changeso f Metaseiulus occidentalis inrespons et owebbin gproduce d byth emale so f Tetranychus urticae (decreaseo fwalkin gactivity ,walkin g velocity,coincidenc e ofpre y andpredato r andhandlin gtim ewit hrespec t toth epre ymales) .H estate dtha ti fthi sspecie si scommo ni nspide rmit e colonies,i ti smor edu et oth eeffec to ftrappin gan da hig hreproductio n ratei nth epresenc eo fmuc hfoo dtha nb yattraction .Thes efinding sstimu ­ latedth einvestigation sdiscusse di nthi srepor to nth erol eo fwebbin gi n thepredator-pre yinteractio n (Chapter3) .

2. 1. 6 Web production and colony growth

Tetranychus spp.produc e silkstrand s (0.03-0.06|j mdiameter )b ywa yo f a glandular system,whic hopen s ina hollo whai ra tth eto po fth epedi - palps (Mills,1973 ;Albert i& Storch ,1974) .Th estrand sar estretche dbe ­ tweenth ecurve dlea fedge ,th elea frib san dth elea fsurface .Whe npowder ­ ed withtalc ,th ewebbin gbecome svisible . Itappear s tob echaoticall y structured excepttha ti ttend st o form acompact ,coheren tcove rwit ha more-or-lessobviou sborder .T oquantif ywe bproductio na fixe damoun to f fluorescent powder was dispersed over the webbed area, aspropose db y Fransz (1974,p .24) .Som eo fth efluorescen tparticle sstic kt oth esil k strands,bu tth emajorit y fallont oth elea fsurface .Th enumbe ro ffluo ­ rescentparticle sstuc kt oth esil kstrand sca nb ecounte dusin ga binocula r microscopean da UV-lam pfo rillumination .Thes ecount sma yserv ea sa rel ­ ativemeasur eo fth eamoun to fwebbing ,becaus ethe yindicat eth elengt ho f thesil kstrands .Th ewebbin gdensit yi squantifie db yth enumbe ro finter ­ cepted particles per squarecentimetr e oflea farea .T ostandardiz eth e

33 GUN WITH ,--'C02 PRESSURE

TURN TABLE

Fig. 7. Apparatus used for spraying fluor escent particles over the webbed rose leaves.

method of powder disDercrai i-u„ t ,,

1 t »Uo„ tiz. ,na ptevent cl o'tt^g » * -«««tor to obtain particles of - Theamoun to fDowdo r it ™„x• »alancet oobtai nI numbero 7arLlTT ' "^ ^ * "** ^^ M Uttle variation - Theparticle s are dispersed ^ " fungal spore dispersal overa "f^ aPPar&tUS originally designedfo r ofth einfectio n Th» • ****' aimin9 ata unifor m distribution "• lne experimental desicm i= „ • - Allmeasurement s arema d • Sn ln Figure 7' webbing, produced atT- 6 SlmUltaneouslY witha standar d measuremento f anda relativ e humidity= 75% ,t odetec t 34 variations inth eexperimenta l procedure andt oenabl e correction forthes e variations ifnecessary . These standard treatments were allwithi n 15%o f their overall mean, so thatth eexperimenta l procedurewa sconsidere d tob ereliable . Hazan et al. (1974)quantifie d thewe bproductio n of Tetranychus cinna- barinus ina comparable way.The y used the fraction ofth etota l faecal- pelletproductio n anchored toth esil k threads asa measur e forwe bproduc ­ tion. Saito (1977a)develope d adifferen t approacht oth eproblem .H econ ­ structed a grid of1 m mmes h from thin (50um )nylo n threads andplace d it on the leaves. Themite s produced webbing over the leaf-grid system.Th e mites were subsequently removed andth egri dwa slifte d withth ewe bthread s attached. The amount ofwebbin g wasmeasure d using dark-field microscopy. To date no comparison ofthes etw omethod sha sbee nreporte d inth eliter ­ ature. The experiments onwe b production were carried outa t three constant temperature levels (T= 15,23 ,29°C) ; the relative humiditywa s75% .I n another series of experiments measurements were made at three humidity levels (relative humidity = 45-50, 70-75 and 85-90%) andon e constant temperature (T= 23°C). AWeis s GrowthCabine t (typeZ K220 0E/+ 4 JU-P-S), located atth e Institute of Plant Protection Research,Wageningen , served asa climat e room (T= x ± 0.25°C ; relative humidity =y ± 2.5%) . Single preoviposition females were transferred toros e leaves thatwer e still connected toa 5 c msectio no fthei r shoot.Thes e femaleswer e allowed to produce eggs andwe b during aperio d equal toth emea n incubation time ofth eeggs . Each experiment ata certai n combination ofT an dR Hwa srepli ­ cated at least 15 times.Th e results aregive ni nTable s 13an d14 .Thes e show that web production is stimulated by increasing temperature buti s only slightly affectedb ychange s inhumidit y withinth erang e 50-85%. From

Table 13. Rate ofincreas eo fare awebbe db y Tetranychus urticae.

Temperature (°C) Relative humidity (%) Rateo fincreas eo fwebbe d area (cm2-day-1-9_1)

13 70-75 0.016 0.005 20 16 70-75 0.057 0.014 16 23 45-50 0.167 0.039 21 23 70-75 0.157 0.046 18 23 85-90 0.129 0.043 19 29 70-75 0.218 0.032 12

35 Table 14. Webproductio no fyoun g females of Tetranychus urticae, asindi ­ catedb yth einterceptio no ffluorescen tparticles .

Temperature (°C) Relativehumidit y (%) Rate ofwe b production (particles-day -9 )

13 70-75 8 3 20 16 70-75 26 8 16 23 45-50 72 14 21 23 70-75 63 11 18 23 85-90 54 9 19 29 70-75 102 19 12

the same experiments the daily expansion ofth ewebbe d areawa s measured. Sincewebbin gbecam evisibl e afterpowderin gwit h fluorescents andUV-illu - mmation, the circumference ofth ecolon y could be drawn on graphicpaper . The rare case ofa singl e strand stretched over apar t of uncolonized leaf wasneglected .A sca nb esee n fromTable s 13 and 14,th e ratio of thedail y increaseo fparticl e interception and thato fth ewebbe d area is aboutcon ­ stant, so that apparently the web production is largely used for lateral expansiono fth ewebbe d areaove rth e leafsurface .Thi s does notmea n that thewebbxn gi sdistribute d uniformly over thewebbe d area.Th ewebbin gden - itywa s mapped crudely and some characteristic cases are given in Figure the LT"3 thSt the l0WSr denSltieS a" f°Und in »»11 stripsnea rt o

In a subsequent

Fig. 8. Growth of the webbed area on the underside of a rose leaflet and a schematic representation of areas ofhigh ,moderat e and low density ofwebbing . LeafA untilD represent increasing stages ofcolonization .

the food sourcewa s almostexhauste d andth emite swer ebecomin g increasing­ ly active, probably in search of food. There is an explosive increase in the amounto fwebbin g due toth eincreas e inwalkin g activity. Saito (1977a) also noticed a high correlation between thewalkin g activity andwebbing. His observations clearly show that the spider mites continually produce threads while walking. Because silk secretion isprobabl y notcontinuous , continuous threadproductio n isprobabl y due to theeffec t of silkcoagulat ­ ingb y stretch.

37 NUMBER OF PARTICLES PER 1It, CM -LEA F AREA

300-

260-

220-

180-

160-

120- II T I I 80- Tl T 40-

i I l v— 1 'V •0 1 2 3 4 13 25 TIME (DAYS) PERIOD A PERIODB PERIODC

17. 9. webbing intensity, as indicated by the density of intercepted en PartiCleS ln dlfferent Peri ds of PerlTa \ ' ° »Pi*»' »ite colonization, adult V , femaleS Pr°dUCe eg9S Snd Webbin5' abundant food. Period B: untU 17V Pr°dUCe 1SSS SggS' SggS °f Period A are etched and developed until the deutonymph stage, moderate food availability. Period C: all stages source T^ '""**' °f ** ^ ^ration caused exhaustion of the food source, walking activity is increased.

thiflL t?!th S inCrSaSe °fth e Webbed ™ * -y * questioned, _ how ofth e LLt ? the aCtUal l6af areS damaged b*th e Piling andsuckin g silyb vyth e "T 0111The1 mitS inJUryellY tW0 SPy°UntSg — leth— «aghnb darkedetecte greed n u cu ticll Zr " ° ° ^ — - ^ " is infested onol d ' "^ ^^^ °*whic h sideo fth elea f probably because t^T^ .leaV6S^ ^ SP°tS 3re mUch less recognizable,

ecei development.Therefore ,u s• ved thatdamag e ina nearl y stageo f Y Ung r SS leaves measured easilyb yquant ifi t. ° ° ' thedamage d area canb e Theresult so fthes equantitati v^ diameterSan dth enumb « ofspots . Pr6Sente d Tabl e 15 and Were tained simultaneously withth er „"" *» ^ reproductl section 2.1.1. AS with r d °n experiments discussedi n Sub- P he rate at hich the leaves,i s dependent on te ;;e;;tt";;d th ; »**« damage P f female S ider mite Baker& conell( 1963) measur eJd t "" T ° * * *> - visible injuryo fsoybea n leaves damaged 38 Table 15. Daily leaf injury (mm2-day~ •$" )o n soybean3 and rose (4-5th leaf from top of flowering plant), causedb y feeding of adult female spider mites.

Temperature (°C ) Soybean Rose ('Sonia'), age class of the adult female leaf from leaf from upperpar t lowerpar t 2-3 8-10 11-18

15 0.6 0.2 20 0.9 0.3 24 0.5 0.33 25 1.2 0.4 0.1 26 0.66 0.41 30 1.4 0.5 32.5 0.85 0.74 35 1.7 0.6 a. Data fromBake r &Conel l (1963), using females of Tetranychus atlanticus (ageunknown) . b. Present study, n= 10-20.

by spidermit e femaleso f Tetranychus atlanticus. Their dataar eals o given in Table 15. They did not standardize the age ofth e spidermit e females explicitly, which makes exact comparison difficult due to age-released changes in the rate of food ingestion.Nevertheless , the conclusionma y be drawn that both results indicate arat eo flea f damagemor e thante n times smaller than the rate ofcolon ygrowth .Thi s suggests thata larg epar t of the leaf covered withwebbin g isstil l available forjuvenil e foodrequire ­ ments, as long as the colony is allowed to expand freely.Afte r complete colonization ofth e leaf, food scarcityma y sooner or laterbecom e apparent.

2.2 PHYTOSEIID PREDATORS

In this section the bionomics of fourphytoseii d species are discussed that are generally considered to be specialized on tetranychid prey (McMurtrye t al., 1970). Thesepredator sare :

Phytoseiulus persimilis Athias-Henriot 1957 This species was obtained from the culture of the firm ofKopper t (Berkel en Rodenrijs, The Netherlands),wher e itwa s fedwit h Tetranychus urticae. Dosse (1958) originally obtained specimens from Chile.Kennet t& Caltagi -

39 rone (1968)showe d that the Chilean population readily hybridizes witha Sicilianpopulation ,whic h isconsidere d tob e endemic (Ragusa, 1977). Many records from otherMediterranea n countries are available (seee.g . McMurtry, 1977). This predator has been introduced in North American and European glasshouses to control spider-mite outbreaks.Th e resultshav ebee nsatis ­ factory (Hussey& Scopes, 1977).

Metaseiulus occidental is (Nesbitt,1951 ) This species was obtained from the culture ofKüchlei n (Agricultural Uni­ versity,Wageningen) ,whic horiginate d onth e culture ofBravenboe r (Glass­ houseCrop sResearc h& Experimenta l Station,Naaldwijk) . According toHoyin g& Crof t (1977)thi spopulatio n isconspecifi c withpopu ­ lations inhabiting citrus orchards in the western part of NorthAmerica , wherei ti sconsidere d tob e asuccessfu l predator of Tetranychus mcdanieli and, to a lesser extent, Panonychus ulmi (Hoyt & Caltagirone, 1971). The name of the genus (Metaseiulus instead of Typhlodromus) is adopted from Schuster& Pritchar d (1963).

Amblyseius bibens Blommers, 1973 This species was obtained from the culture ofva n Zon& Blommer s (Amster­ dam, The Netherlands), where itwa s fed on Tetranychus urticae. Blommers (1973)collecte d specimens in Madagascar. He reports this predator tob e successfuli ncontrollin g Tetranychus neocaledonicus and Tetranychus urti­ cae populations in the greenhouse (Blommers & van Etten, 1975;Blommers , 1976).

Amblyseius potentillae (Garman, 1958) This species was obtained fromth ecultur e ofva n deVri e (Wilhelminadorp, The Netherlands), where itwa s fed on Tetranychus urticae. The culture did not succeed on mite-infested bean plants,bu t was successful when mites were brushed off the leaves and offered to the predators (van de Vrie, personal communication; own observations).Van de Vrie collected specimens in the south-west part of The Netherlands (Serooskerke). Here iti scon ­ sideredt ob e aneffectiv epredato r of Panonychus ulmi, togetherwit h other predatory mites like Typhlodromus pyri and Amblyseius finlandicus (vand e Vrie, 1972;McMurtr y & van de Vrie, 1973;Rabbinge , 1976). Boczek et al. (1970)recorde d this species also in Central European orchards.Recently , McMurtry (1977) collected specimens in Southern Italy and showed that a stock from apple in The Netherlands was reproductively compatible witha stock fromcitru s in Italy (McMurtry et al., 1976).

Thepurpos e ofthi sstud yo fphytoseii dpredator s is threefold: - to analyse interspecific differences indevelopment , abioticmortality , fecundity and sex ratio inrelatio n totemperature ,humidit y andpre yden -

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41 sity(Subsectio n2.2.1-2.2.3) . - toquantif y therelativ e contributiono fth edifferen t juvenilean d adultstage so fth epredato rt oth epre yconsumptio n achievedi na whol e life-span(Subsectio n2.2.4) . - toestimat eth eeffect so fdrinkin gwater ,cannibalis mand ,whe ntetra - nychidfoo di slacking ,non-tetranychi dfoo dconsumptio no nphytoseii dsur ­ vival,an dt odetermin ethei rabilit yt orecove rfro mstarvatio n(Subsec ­ tions2.2.5-2.2.7) .

2.2.1 Developmentand mortality

Datao ndevelopmenta ltim ean dmortalit ysee mt ob eavailabl e (Table16 ) insufficien tquantities .Howeve rman yresult sar econtradictory ,whic hma y bedu et odifference si nstrain so rexperimenta lmethods ,e.g .result so f Bravenboer& Doss eo nth edevelopmenta l timeo fPhytoseiulus persimilis (Bravenboer& Dosse ;Tabl e1 an dFigur e 1),result so fTanigosh ie tal . (1977)an dPruszynsk i& Con e(1973 )o nth edevelopmenta ltim eo f Metaseiulus occidentalis, andresult so fMcMurtr y(1977 )an dRabbing e (1976)o nth ede ­ velopmental timeo fAmblyseius potentillae. Becauseo fthes e differences interspecificcomparison swer emad esimultaneuousl ybetwee nfou rphytoseii d species.Thi stria lwa scarrie dou ta tthre etemperatur e levels< T= 15, 20, 30°c;relativ ehumidit y= 70% ;photoperio d= 1 6hours) .A tth estar t femaleswer eallowe dt ooviposi tfo rtw ohour sa tT= 20°C .Th eegg sob ­ tainedi nthi swa ywer eimmediatel ytransporte dt oth eclimati ccabinet . Afterhatchin gth elarva ewer epu tseparatel yi nHunge r cages (Fig. 10), IhroLh TT" SUPPlled With SbUndant Pre*

FILTER PAPER

GLASS PLATE

Fig. 10. Design ofth eMunge rcag e used inth e studyo f Phytoseiidae.

temperature regime.Thi s difference ispossibl y related toth e climatic ori­ gin ofthes e species.On e common traito fth e rate ofdevelopmen t among the Phytoseiidae studied is thatthe y develop faster than theirprey : Tetrany- chus urticae - rate = 0.0067x (T-11.0) (day- ).Moultin g causes only a very short interruption in the food searching activity of phytoseiids. Tetranychid development is characterized by distinct moulting stages ofa duration similar to thato fth eprecedin g feeding stage.Thi s causes anin ­ terruption of feeding and hence a retardation of development. From this point of view it is worthwhile to note that theegg-to-eg g developmental periods of predator and prey equal each other, ifth emoultin g stages are excluded from the computation of developmental time.Th e relativecontri ­ bution of the hatching, intermoultan dpreovipositio n periods toth e total egg-to-egg period is aboutth e same for alltemperature s and for all species studied; on average 34%o fth e egg-to-eggperio d isspen t inth e eggstage , 12% in the larva stage, 15.5%i nth eprotonymp h stage,16.5 %i nth edeuto - nymph stage and 22%i n the preoviposition stage (Table 17).Th e standard deviation and the mean of the developmental periods were estimated froma plot of the cumulative frequency distribution ofdevelopmenta l periods on probability paper of theGaussia n distribution.Th e8-hou robservatio nin ­ terval was taken as a class unit. The estimated standard deviations were 7-12%o fth eestimate d mean developmental time. InTabl e 16th e proportional differencesbetwee n thepresen tmeasurement s and those found inth elitera -

43 RATE0F"E6G-T0-EG6 " DEVELOPMENT(DA Y -1, 0.25-1

0.20H -4

0.15-

0.10-

0.05-

~1 ' I I • 1 ! 15 20 25 30 35 TEMPERATURE(°C )

Zl' "I* fte °fegg 't0"egg developmento ffou rphytoseii d species andth e tw- p 0tted spider mitei nrelatio nt otemperature ,o ,Ptytoseiulus persi- "«*!;*' ^1VSeiUS blbw" +' ^^eius patenting A, Metaseiulus occi- tW _SP tted Spider mite standarstandarl'deTTTd deviatio- 'n (Tn= 30-50) ° . ° ' Tetranychus urticae; 1,

ri mmr the d3ta ln the literatU TZt7er^ T« - concerned egg-to- P !d was add d °f egg"t0_egg Peri°dS' the 1Sngth °f ^ developmental tion inth e dat , aCC°rdinglY- ThiS ^^ demonstrates the large varia­ m e lite ure compared to the data is :;te dt to s°t rarn r «* **• — EventhoughZr\ SP6ClflCness ^ experimental methods. n ent reiated uneariy to the -e i nri r ofttirtTh *; —- give riset oresult s thaTT Y' flUCtuatin9 temperaturesma y -on.Howeve r^^I^T^ r f°r^ ^ "^ considereda sreactin g • «. rate of developmentma yb e reacting instantaneous!v i-^, u neouslyt oachang ei ntemperatur e (Aia&iy- Table 17. Stage-specific developmental timeso ffou rphytoseii dspecies .

Species Temperature Mean developmental time (days) (°C) egg larva proto- deuto- preoviposition nymph nymph female

Phytoseiulus 15 8.6 3.0 3.9 4.1 5.6 persimilis Amblyseius 15 6.8 2.4 3.3 3.4 4.2 potentillae Amblyseius 15 9.2 3.2 4.3 4.5 5.8 bibens Metaseiulus 15 9.8 3.6 4.4 4.9 6.6 occidentalis Phytoseiulus 20 3.1 1.1 1.4 1.6 1.9 persimilis Amblyseius 3.2 1.1 1.4 1.5 2.0 potentillae 20 Amblyseius 3.5 1.3 1.6 1.8 2.3 bibens 20 Metaseiulus 4.4 1.7 2.0 2.4 3.1 occidentalis 20 Phytoseiulus 30 1.7 0.6 0.8 0.8 1.1 persimilis Amblyseius 30 1.6 0.7 0.8 0.8 1.1 potentillae Amblyseius 30 1.7 0.7 0.8 0.8 1.1 bibens Metaseiulus 30 1.7 0.8 0.9 1.0 1.3 occidentalis

seius potentillae). Begljarow (1967), Ushekov& Begljaro w (1968)an d Stenseth (1979)showe d thatdevelopmenta l time is also affected by relativehumidity .Onl ya sligh t increasei ndevelopmenta l timewa s observed by these authorswhe n the rel­ ativehumidit y was increased from40 %t o 70%.Th e tendency togai nwate rb y increased prédationa tlo w humidity may account for this reduced effect (Begljarow, 1967; Pruszynski, 1977). Accordingt oBegljarow , development almost stops atrelativ e humidities of 25-35%. In the present experiments,mortalit y during developmentwa sa slo aw s in Tetranychus urticae. Atal l temperatures 87-94%o fth e eggs reached maturity, independento fth e species involved (RRM= -ln(0.9)x DR ; RRM= relative rate ofmortality ;D R= 'egg-to-eg gdevelopmenta l rate). In another experiment the effecto fextrem e temperatures was investigated for Phyto­ seiulus persimilis and Metaseiulus occidentalis; afive-da yperio do fth e

45 eggsa tT = 10° Cdi dno talte rth epercentag eo fegg sreachin gmaturit yi n asubsequen tperio da tT = 20° Can drelativ ehumidit y= 70% .A tT = 35° C andrelativ ehumidit y= 75 %th epre-adul tmortalit yros et o24% .Accordin g toHamamur ae tal . (1978)th eegg so f Phytoseiulus persimilis failedt o hatchafte rstorag eperiod so fmor etha n6 day sa ttemperature sbelo w10°C , butth eadul tfemale swer eabl et osurviv ean dt oremai nreproductiv eafte r 25da ystorag ewithou tfood ,afte r5 0da ystorag ewit hhone yan dafte r7 0 daystorag ewit hspide rmites ,whe nrelativ ehumidit ywa ssufficientl yhigh . According toBegljaro w (1967)th emortalit y inth eeg g stagedepend s verymuc ho nth ehumidit ylevel .A ta relativ ehumidit yo f50 %th eegg so f Phytoseiulus appearedt oshrive la tal ltemperature sbetwee n13° Can d37°C . Ata relativ ehumidit yo f60 %hatchin go fth eegg swa ssuccessfu lbelo wT = 30°C,bu tabov ethi stemperatur eleve la relativ ehumidit yo f80 %wa snec ­ essaryfo rsuccessfu lhatching .Larvae ,nymph san dadult swer eles saffect ­ edb yhumidity ,probabl ydu et oa compensator ymoistur esuppl ythroug hin ­ creasedprédatio na tdecreasin ghumidities .The ycoul ddevelo pnormall ya t relativehumidit y= 50% ,bu ta t25-35 %stoppe d (Begljarow,1967) .A numbe r ofauthor sconfirme dth efac ttha tth eeg gstag eo f Phytoseiulus persimilis isrelativel yvulnerabl et orelativ ehumiditie sbelo w70 %(Usheko ve tal. ,

1968; Hamamurae tal. , 1978; Pralavorio etal. , 1979;Stenseth ,1979) .A similartyp eo fvulnerabilit ywa sfoun db yMcMurtr ye tal . (1976)fo r Ambly seius potentillae. AnItalia nstoc ko fthi sspecie sappeare dt ob emor ere ­ sistantt olo whumiditie stha na Dutc hstoc k(50 %mortalit yo fth eegg sa t relativehumiditie so fapproximatel y55 %an d70% , forth erespectiv estocks) . McMurtrye tal .stat etha tthes eresult sar econsisten twit hth eclimati c todr v 'he.St0CkSM d that the «**stag ei sprobabl yth emos tvulnerabl e todr yconditions :th emobil estage sca nobtai nmoistur efro mthei rfoo do r rimoU m0re/aV0Urable (-cro)climate.However ,althoug hth eeg gitsel f potHn th ? 1S deP°Sited bY the adUlt f6male '"**« -tcharacteristi c

and most ^ "*"* *° ** ^ **"> ' °^ Cl°se t0 ^ leaf t£ webbinos t ?°rtant Wlth re9ard t0 the ^oseiidae - ^stion "i n alllÎ Z Z Pr0dUCed bY thelr Pre^ AS Ported byKaza ne tal . VJ-^'3;,th ehygroscopi cpropertie sn f+->, ~f u • climatei nth ewebbin gstructur e the T f "^ StrandS' ^ miCr°' rationo fth elea fan d ƒ ""' the SU^ of moisturevi aevapotranspi - maybuffe rth e^ h^ ^I TÏ ^^ * "» »"' ""*

Becauseth ehenhous e climate is suc^hT ^^^ 40%an d70 %d ooccu rrathe rfrequentl y 1 ^^ hnmiditieS betWe6n buffersth eeffec to fh 'd' Y'th e extent to whichth emicrohabita t velopmentwer eplace d ^LZl^T^ ^l "*"*"" '" ^ "" - Plantwit hwebbin gan dmite s (J„ !COntrolled -^vironmentroom : - uncovered „unger cagewithou t l ^^ ^ ^ substrate). weaves,webbin gan dspide rmite s (=Perspe x

46 Fig. 12. Plant system used in the study ofclimati c effects onlif e history. and were allowed to oviposit for one day. In thisway ,th eegg swer e not deposited in an artificial way,bu t according to theovipositio n behaviour ofth e femalepredator .Afte r removal ofth e ovipositing females thehatch ­ ing success ofth epredato r eggswa s recorded during the following six days. The results (Fig.13 )sho w thati ncompariso nwit h the artificial substrate the combination ofplant ,webbin g and spidermite s exerts apositiv e influ­ ence on the hatching success.Unde r theclimati c regime ofth e greenhouse culture of ornamental roses (relativehumidit y > 50%)n odetrimenta l effects are tob e expected because thehatchin g success declines forrelativ e humid­ itiesbelo w 50%,eve n athig htemperatures .Th e results concerning the arti­ ficial substrate correspond with reports ofsimila r investigations (Ushekov

47 PHYTOSEIULUS PERSIMILIS AMBLYSEIUS POTENTILLAE HATCHING SUCCESS (%) T=20°C T=30°C T=20°C T=30°C 100-i o^°^•oo fi^o O' o 80 / ? ySf

60

40

20-^

0J o' a' i—i— -,—r 405 06 07 0 405 06 07 0 405 06 07 0 405 06 0 70 RELATIVEHUMIDIT Y(% )

rig. 13. Hatchingsucces so fth eegg so ftw ophytoseii dspecie s( o= Phyto-

seiulus persimilis and+ = Amblyseius potentillae) inrelatio nt orelativ e

hunudityan dt oth esubstrate . ,web bed bean leaves (Fig.12) ; ••••- uncoveredMunge rcage s(Fig . 10).

etal. ,1968 ;Pruszynski ,1977 ; Pralavorioe tal. ,1979 ;McMurtry ,1977) . Those concerningth e'natural - substratecorrespon dwit hth eresult so f Stenseth(1979) ,wh ouse dth eappropriat eexperimenta lprocedur ea ttw oex ­ tremehumiditie s (relativehumidit y= 80 %an d40%) . Thereport so fjuvenil emortalit ya thig htemperature s( T>30°C )ar e numerous.Bravenboe r& DOSS P MQR9\ e (1962) dl *Ad no* t *. nf Dh + ., reporta nincreas ei nmortalit y S aUVenil6S T= 3 Can d 35 C;H a et 1976a) founda Tl ^ °° ° — «*• < fun da hlg h mortalityo fP hytoseiulus Persimilis attemperature s above att « rOW r68)M dBÖh m(1970 )° bSerVedl0 W^^ y of the eggs yeve nai r tT 3°°C" * ^^ ^ «™* *ver yhig hmortal - report so fi n = mllarly f°r MetaSe 33 c^(pruszynsk s occiäenflis.i& thereari973 e high

m a;":~x 9 z r 10° T — Ch ' Theinterpretati o o't h J: X: *' ^' °* ^^ '* = >"'. specificationo fth . Very difficult, boththroug hlac ko f experiments strLT™" " •^'^ ^ "* M °f "**>*** ^ *» indicatea nincrease "a " 7- ^T" " ™' '^ <" "* aDd high hum criticalhumidit yleve ] h0i .- idity,bu tth e «easingtemperature s seTZl ^^ ^^ ±8 "±8ed *" ^ detrimentaleffect scai ^ H '1968 K Pr°bablv the rapid°nse to f cannotb eprevente db yhig hhumiditie swhe ntemperatur e 48 Table 18. Stage-specific freshweight s (ug)o f fourphytoseii dspecies .

Predator Egga Larva Proto- Deuto- Male Female a species nymph ^b nymph ,b9

Phytoseiulus 4.5-4.8 4.0-4.8 5.2-6.7 9.7-10.9 5.4-6.7 24.1-28.9 persimilis Ambluseius 2.9-3.3 15.1-17.9 potentillae Amblyseius 2.0-2.4 10.1-12.? bibens Metaseiulus 1.8-2.1 1.8-2.2 2.3-2.9 3.1-3.9 2.5-3.0 8.0-10.4 occidentalis

a. Number ofreplicate s -20 . b. Number ofreplicate s =5 .

exceeds 32°C. Measurements of the weight increase during development are given in Table 18. The males attain their final weight level ina nearl y stage of development: the protonymph stage. The females obtain almost 60%o f their weight increase during thepreovipositio n period. Themaximu m difference in weightbetwee n females sampled fromwell-fe d cultures ato rbefor eoviposi - tion almost corresponds with theweigh t ofa negg .Thi s isbecaus e one egg ata tim e (=th e terminal oocyte)i s absorbingvitellogeni c materials.Afte r attaining its final size and fertilization the egg will be deposited and thenex t egg inth e 'queue'wil l startgrowing .Th e adultovipositin g female weighs 4-5 times more than the original egg mass, arati o thathold s for all species studied. Furthermore, itappear s thatthoug h the relative weight increase isconstan t forth e species studied, absoluteweigh t levels differ considerably. As shown in Fig.3 , Metaseiulus occidentalis isth e smallest phytoseiid of the four studied. Relative to this species the ovipositing females of Phutoseiulus persimilis contain 2-3 timesmor ebiomass , Ambly- seius potentillae 1.5-2 timesmor e and Ambluseius bibens 1.1-1.3time smore . The effect of food supply onth e rate ofdevelopmen t is demonstrated in Table 19,whic h presents some unpublished data of Küchlein and data from the literature (van de Vrie, 1973;Takafuj i & Chant, 1976). The critical level of food supply,belo w which development is retarded andmortalit yin ­ creases, is about 1-2 »g perday .Fro m the interspecific and stage-specific weightdistributions , iti sobviou stha tth eeffect s aremor epronounce d in the larger-sized phytoseiid species and in the preoviposition phase, in which relative to theothe r stages alarg eweigh t increase has tooccu r in a short time span.Th e larvae ofal l species inquestio n are ablet omoul t

49 Table 19k. The influence of the density ofth epre y on the developmental time of Metaseiulus occidentalis. Leaf area = 5cm 2; daily replacemento f thepre yconsumed ;T = 27°C .Source :Küchlei n (tob e published).

Prey (eggs)Developmenta l time (days) number egg n larva n protonymph n deutonymph n egg to adult

1 1.7 44 1.16 37 1.94 32 1.26 27 6.06 2 1.72 69 0.98 65 1.26 57 1.02 51 4.98 4 - 0.97 76 1.00 73 1.00 73 4.67 25 1.61 74 1.01 69 1.01 67 0.93 67 4.56 50 1.81 99 0.90 90 0.89 82 0.95 75 4.55

Table 19B. The influence of prey density on the developmental time of Phutoseiulus persimilis. n = 10-14; paper area = 4 cm2; daily replacement of the prey consumed; T = 25°C. Source: Takafuji & chant (1976).

Prey (protonymphs) Developmental time (days) number larva protonymph deutonymph egg to adult

1 0.8 2.8 5.1 8.7 2 0.8 1.2 1.7 3.7 4 0.8 1.2 1.2 3.2 20 0.8 1.2 1.2 3.2

Prey (adult9 ) Preoviposition number

1 5.5 2 4.1 4 2.9 8 2.0 16 1.5 32 1.4

intoth enex tnympha l stagewithou tan v „ * „ .' f of development, butmoulting fJ 2 ^ "* "^ «* retardationo reguirefoo dconsumption ,whe npre yegg s are^ T ^^ "^ ^ similis and Metaseiulus occidental* abundance Phutoseiulus per- occidentals consume 15 and 8 eggs, respectively, 50 Table 19C. The influence ofpre y density onth edevelopmenta l time (days) of Amblyseius potentillae. n = 11-13; cage area = approx. 20 cm2; daily replacement ofth epre y consumed;T =23°C .Source :va n deVri e (1973).

Prey (larvae) Developmental period Preoviposition period number (eggt o adult) high 6 (5-6.5) 2 (1.5- 3.5) 10 6 (5-6.5) 2 (1.5- 3.5) 4 8 (7-9.5) 4 (3.5- 5.5) 2 12 (10-18) 8 (7.0-10.5)

duringnympha l development (Subsection 2.2.4). These quantities of foodre ­ quired are constant at all temperatures, which suggests a fixed amounto f food needed to mature. However, phytoseiids are able to mature on 66%o f the food quantity described previously (own observation). Although their bodies were flattened under conditions oflo w food supply, theywer e still able to moult into the next stage despite their obviously hungry state. Apparently development allows forsom e flexibility with respect to the food requirements in thenympha l stages.

2. 2.2 Sex ratio

For four phytoseiids, egg production commences only after copulation (McMurtry et al., 1970; Schulten et al., 1978;persona l observation).Al ­ though karyological evidence indicates that males arehaploi d and females diploid (Wysoki & Swirski, 1968; Blommers & Blommers-Schlösser, 1975; Oliver, 1977), bothmale s and femalesprobabl y result from diploid eggs, as has been shown by genetic means forth ecas eo f Amblyseius bibens, Phyto- seiulus persimilis (Helle,1978 )an d Metaseiulus occidentalis (Hoy,1979) . Apparently the haploid condition ofth emale s iscause d by the loss and/or heterochromatization of half of the chromosomes. Thus parahaploidy, not arrhenotoky, as found inth e spidermites ,i sth egeneti c system (Hoy, 1979). The probability that aneg gbecome s amal e or afemal e canb e estimated from the sex ratio (9/(9 +d ) in a large sample taken from eggs lainb y randomly selected phytoseiid parents.Se x distinction ismos t conveniently made in the adult phase: females are larger thanmales .Th eproportio n of females canthu sb e assessed inth e group ofadult semergin g from alabora ­ tory ab ovo cultivation.Thi sproportio n equals the sex ratio ifth erela ­ tive rate of juvenile mortality of both sexes areth e same. InTabl e 20a data survey is given for 'laboratory' sexratio s ofth e fourPhytoseiidae . Although the sample size of the parental females is generally small, it

51 Table 20. Sex ratio in the progeny of fourphytoseii d species accordingt o references inth eliterature .

Predator Temperature Sexrati oNumbe r Number of Reference species (°C) 9/(9+ <*) ofegg s parental females

Phytoseiulus 23 0.89 954 Amano & Chant,197 8 persimilis 25 0.86 816 11 Schulten et al.,197 8 25 0.84 930 13 Hamamura et al.,197 6 25 0.82 400 100 Takafuji & Chant,19 7 15-28 0.804 245 20 Laing, 1968 22-27 0.79 247 20 Kennett et al.,196 8

Metaseiulus 18 0.66 50 Tanigoshi etal. , occidentalis 1977 0.70 50 Tanigoshi etal. , 21 1977 0.64 50 24 Tanigoshi etal. , 1977 0.68 50 27 Tanigoshi etal. , 1977 0.68 29 50 Tanigoshi etal. , 1977 0.62 32 50 Tanigoshi etal. , 1977 0.60 35 50 Tanigoshi etal. , 1977 24 0.53 43 Lee& Davis , 1968 22.5 0.63 620 60 Croft &McMurtry , 1972 22.5 0.55 179 20 Croft& McMurtry, 1972 15-28 0.71 Laing, 1969 25.5 0.62 Sharmaa, 1966 Amblyseius 29 0.83 360 bibens 54 Blommers, 1976

Amblyseius 15-30 0.69 238 potentiliae 85 Rabbinge, 1976

a-Ph.D .thesis ,refer^ H i- • referred tol n croft& McMurtr y (i972). 52 seems justified toconclud e that for all four species the sex ratiogeneral ­ lyexceed s 50%an d that there areinterspecifi c differences.Th e sex ratios of Amblyseius potentillae and Metaseiulus occidentalis arearoun d66% ,whil e thoseo f Phytoseiulus persimilis and Amblyseius bibens areclos et o83% . Based onbot h laboratory sexratio s and sex ratios observed inth e field, the sex ratio may be considered constant, although a few exceptions are noteworthy: - Tanigoshi et al. (1977) established a slight decrease of the sex ratio of Metaseiulus occidentalis attemperature s exceeding30°C . Dyer & Swift (1979) found that short-term variations in sex ratio were related to meteorological changes,particularl y humidity, temperature and wind speed. The reason isno tye tclear . - Amano & Chant (1978)observe d thatth e sex ratio of Phytoseiulus persi­ milis was constantwit h age,excep t for ahighe r proportion ofmal e progeny atth e onset ofreproduction . - Amano & Chant (1978) found that the sex ratio was independent of the feeding history of the female as ajuvenile ,bu t incompariso nwit h well- fed females temporary food deprivation in the adult stage gaveris e toa decrease ofth e sex ratio inth e subsequent offspring. The causes of the deviating 'laboratory' sex ratiosma y be due tobot h differences inmortalit y among the sexes and the sexdeterminatio nprocess . The 'field' sex ratios are also influenced by the shorter life spano fth e males, differential susceptibility to detrimental factors,etc . There seems to be no reason why adult females should notmat e shortly afteremergence : - The eggs are deposited inpre y aggregations,s otha temergin gmale s and females arei nclos evicinity . - The tendency to disperse is low in all stages relative to that inth e fertilized females (Section 3.4).Th e foodrequirement s fordevelopmen t are very low and even flexible to acertai n extent (seeSubsectio n 2.2.1), so that the aggregation of the juvenile, male and virgin female phytoseiids hasn o severe effect onpre y availability andwhe npre ybecome s scarce,th e strongest individuals can survive and develop bywa y ofcannibalis m (Sub­ section 2.2.6). - The sex-attracting cues areprobabl y only effective over short distances (Rock et al., 1976; Hoy & Smilanick, 1979)an d theproportio no fmale s in theoffsprin g is always less than50% . - Severe starvation is notdetrimenta l toth ewillingnes s tomat e (Ragusa & Swirski, 1977;Blommer s et al-, 1979). A single mating is sufficient to achievemaxima l fecundity inth e case of Phytoseiulus persimilis (Schulten et al., 1978;Aman o & Chant, 1978). HoweverHamamur a et al. (1976a)found , thatthos e females thatha d deposited less than4 3 eggs, restarted tooviposi t after thereintroductio no f amal e onda y 33 since firstoviposition . Surprisingly the sex ratioo fth e 'second'

53 Table 22. Surveyo fth eliteratur eo nfecundit y (numbero feggs )an do n life-spano fsom ephytoseii dpredators .

Species Temperature Potential Net Reference (°C) fecundity fecundity

Phytoseiulus 81.2 -105 Begljarow& Hlopceva ,196 5 (A) persimilis 75.0 -8 7 51.8 -6 3 53.5 38 14-101 Laing,196 8 (B) 43.8 23.3 10 -7 8 McClanahan,196 8 (C) 53.5 20.7 12 -8 7 62.0 Kamath,196 8 (D) 25-26 59.0 Böhm,196 6 (E) 22-27 56.1 20 Kennett& Caltagirone ,196 8 (F) 22-27 64.7 20 74.5 Plotnikov& sadkowskij ,197 2(G) : 23 71.9 15.3 10 Amano& chant ,197 7 (H) 25 79.5 25.2 30 Takafuji & Chant,197 6 (I) 25 71.5 20.4 23-93 Hamamurae tal. , 1976a(J ) 17 65.5 12 51-79 Pruszynski,197 7 (K) 21 73.1 12 60-85 26 74.1 66-87 78.0 52-93 70.9 42-91 (eggsa sfood ) 57.9 36-89 (larvaea sfood ) 25 74.2 59-98 Schultene tal. , 1978 (L) 20 78.8 16 12-95 Fernando,197 7 (M) 5 0 14 Pralavorio,197 9 (N) 5-12 16.8 21 10 31.0 25 20 80.2 30 16.4

Ajnblyseius 10 9.0 10 Rabbinge,197 6(O ) 15 potentillae 20.0 10 20 27.8 38 25 29.1 30 16.0

Amblyseius 22 65.0 63.2 54 Blommers,197 6 (P) bibens 25 64.1 60.1 54 29 63.7 63.6 54 a 39.5 20 Schultene tal. , 1978 (S)

Netaseiulus 24 33.7 51 occidentalis 15-28 21-56 Lee& Davis ,196 8 (R) 34.0 25 22.5 14-53 Laing,196 9 (s) 33.8 80 24 Croft& McMurtry ,197 2 (T) 37 30 18.5 Croft,197 2(U ) 33.8 10 25 13-55 Pruszynski& Cone ,197 3 (V) 35.2 12 30 21-54 28.2 12 18 17-48 21.9 50 21 Tanigoshie tal. , 1976 (W) 28.1 50 24 29.6 50 27 33.1 29 28.2 32 33.4 35 27.8 44.0 Küchlein(t ob epublished )(X ) Femalesha dmate donl y,

54 Table 21. Continued.

Ref. Preoviposition Oviposition Postoviposition Female period period period longevity

22 21 19 32.6

15.1 - 20 - - - - 18.6 - 20 - - - - ±21 ------1.3 0,3 16 23.3 5.5 10 - 0.. 7 0.8 10 25.1 5.. 7 10 - 1.5 0.5 30 21.6 6.0 30 - 13.. 1 7.7 30 36.2 9.. 3 30 - 1.3 17.2 4.8 13 - - - - 49.0 11,. 1 13 - 33.6 - 12 26-38 - - - 56.3 - 12 23-9 2 26.3 - 12 22-37 - - - 54.1 - 12 19-9 3 18.8 - 12 16-23 - - - 38.2 - 12 15-5 B 33.8 - 18 25-48 - - - 77.9 - IS 49-123 24.3 - 19 13-33 - - - 51.1 - 19 15-138 23.1 - 12 12-36 - - - 37.5 - 12 19-128 10-15 ------37.1• 8.8 16 6-44 22.. 7 11.3 11 50.9 17. 0 19 10-7 2 ------52 - 14 - 43 ------65 - 21 - 44 - 25 - - - - 68 - 25 - 30 - 24 - - - - 45 - 24 - 5.5 - 25 - - - - 9 - 25 -

7.4 1.1 4.0 1.0 22.2 11.8 4-41 8.0 35 0-28 34.2 1.9 0.9 15.1 8.5 6-28 7.6 8 0-28 24.6 2.9 0.8 13.4 7.8 2-44 10.8 37 0-45 27.1

-4 6 -2 8 -2 3

1.3 1-2 38.7 51 21-56 3.2 2.5-4.0 25 7-25 20.2 18 10-30 1.5 80 27-41 30 16-29 2.8 10 2-3 27.1 10 15-39 1.2 12 1-1.5 14.3 12 10-18 1 12 0.8-1.3 10.9 12 7-15 4.1 50 17.6 50 - 2.7 16.0 50 - 2.4 13.9 50 - 2.4 13.4 so - 1.3 50 11.5 50 - 1.1 50 11.4 50 - 1.5 50 9.5 50 - 27.1 13.86 7 1-2

55 broodha ddecrease dt o76% . Amblyseius bibens (Schultene tal. , 1978), Meta- seiulus occidentalis (Küchlein,persona lcommunication )an d Amblyseius po- tentillae deposit only about2/ 3o fthei rtota leg gpotentia l foronl yon e mating.Henc emor etha non ematin gi srequire dt omaximiz e reproduction.

2.2.3 Adult life span and fecundity

Fromth eliteratur e datai nTabl e2 1o nphytoseii d longevity andfecun ­ ditya tvariou stemperature san dhig hpre y density,i tfollow s that: Interspecific differencesi nfemal e longevityar eabsent ,bu tth especies - specific fecundities decrease inth efollowin g order: Phytoseiulus persi- milis (approx.70) , Amblyseius bibens (approx.60) , Metaseiulus occidentalis (approx.35) , Amblyseius potentillae (approx. 30). - Strain specific fecunditiesma yb epresent ,a sindicate db yth ediffe ­ rences between theDutc h straino f Phytoseiulus persimilis (Pruszynski, 1977; Schultene tal. , 1978)an dth eothers .A similar indicationca nb e foundb ycompariso no fth edat ao fKüchlei nan dth eNort hAmerica n reports for Metaseiulus occidentalis. - Netfecundit yi s70-97 %o fth epotentia l fecundity (femalemortalit yex ­ cluded). The oviposition period isshortene db yincreasin g temperatures. Female longevityi sles s affected asth epostpositio n periodi srathe rvaria - ble. Fecundityi sprobabl y maximali nth etemperatur e rangeo f17-28°C .Onl y a fewdat aar eavailabl ea ttemperature sbelo w 17°C,bu ta decreas e is ex­ pected.A ttemperature s above 28°C sucha decreas e will eventually occur also,bu tth ecritica l temperaturei sno tknown .

P ete theSe rSSUltS inters eci sJlT ,l P fic comparisonsa tlo w(1 2an d15°C ) andhig h (30an d33°C )temperature sar enecessary .Thes e reproductionexpe ­ rimentswer e carried outi nHunge r cages with ample supplyo fpre y (eggs n larvae) and high relative humidity (relative humidity = 85%). Atth e guentlTth ?ed f6male "* *" ^ ~" "* ^ eachcag ean d fe9g S deP Sited WaS rSCOrded liaciZUTe 22)) indicat ind T e that° except fnr° i^hi • ^^ *» «suits upper iHmHi- -i K Amblyseius potentillae thecritica l upper limit is above 3i°r TI, I-I T *.+. C3Se the limit is tween2 5an d ^r I ^ somewherebe - 5 ha considered reiative to their .axiLi ,:::: t -t: :;r:rin r' r amongth especie s fecundity below I7°cwa salmos t equal Several authors have establisheda decreas ei n ^ . athumiditie sbelo w65° LOWbb /, IWrt , urease m therat eo freproductio n • * (Ustchekowe ta l "IQGA. BQ -i• ,• ; 1977; Pralavorio I97

«nt.o nintac tplants ,s otha tth eef fect of ^ ^.^ ^ ^~ bufferin ***° fth eplan twa sno t includedi nth l '^ * «pac- level.Elativ e humidityi scri t J" " ^ "^^ hUmidity 56 c ±ow 50^'a s experimentso nth esensi - Table 22. Netfecundit y (number ofeggs )o ffou r phytoseiid speciesa t someextrem e temperatures.

Species T= 12° C T= 15° C T= 30° C T= 33° C

Phytoseiulus 20.27. 2 15 40.915. 22 5 62.819. 22 5 60.814. 32 5 persimilis Amblyseius 13.45. 2 20 48.216. 42 0 60.816. 32 0 58.814. 12 0 bibens Netaseiulus 9.42. 8 20 30.112. 41 8 41.311. 02 0 44.012. 72 0 occidentalis Amblyseius 10.23. 3 15 22.5 9.81 5 21.413. 22 5 16.5 7.72 5 potentillae tivity ofhatchin g success tohumidit y indicate.Therefor e iti sassume d thatn odetrimenta l effects ofhumidit y aret ob eexpecte dunde rth ecli ­ maticregim e occurring forth egreenhous e cultureo fornamenta l roses. The rate of food conversion into eggbiomas si sver yhigh .Ovipositin g phytoseiid females have adail yeg gbiomas sproductio nequa lt ohal fthei r maximum body weight, which istake n tob ethei rmea nweigh tjus tprio rt o egg laying. Moreover, although thefecundit y ofphytoseiid s is2- 4time s lower than that ofth espide r mites, thebiomas s ofegg sproduce dma yb e equal (Amblyseius bibens) oreve ntw otime slarge r {Phytoseiulus persimilis). Because ofth ehig h production ofeg gbiomas s thesuppl yo fpre ywil lb e very importantt othes epredator si nrealizin gthei rreproductiv epotential . The effect ofpre yeg gdensit yo nth elif e spanan dne tfecundit yo f Meta­ seiulus occidentalis isgive n inTabl e 23an dFig .14 .Th emea n lifespa n is double ata pre y densityo f1- 2egg spe r5 cm 2lea fdisc ,replacin gth e prey eatenb yth epredato r ordie d from other causesa tdail yintervals . Thecumulativ e numbero fegg sproduce dpe rlivin g femalei splotte d against time elapsed since thelas tmoul t ofth efemal efo rvariou s levelso fth e prey density. Theultimat enumbe ro fegg sproduce d (=potentia l fecundity) decreased from74 %a t4 pre y eggspe r5 cm 2 to44 %a t2 pre y eggspe r5 cm 2 andnex tt o10 %a t1 pre yeg gpe r5 cm 2. The rate ofreproductio n doesno tdepen do nth eag eo fth efemale ,bu t rathero nth enumbe ro fegg s alreadydeposited : - Virgin females retain theabilit yt oproduc eegg sal lthei r life.Thei r agea tfertilizatio n doesno tinfluenc eth esubsequen trat eo freproductio n north ese xrati o (Schultene tal. , 1978). - Adult female Phytoseiidae retain their ability toproduc ea norma leg g number after anyperio d offoo d deprivation,unles sprevente db ydeat ho r old age( >5 0 days). SeeTabl e2 4an dBlommer se tal . (1979). Ashiharae t 57 Table 23. Theinfluenc eo fpre ydensit yo nfemal e longevity of Netaseiulus occidentalis. T= 27°C ;relativ ehumidit y= 60-80% ; daily replenishmento f thepre yconsumed .Source :Küchlei n(t ob epublished) .

Prey (egg)densit y Life-span (days)

(number/5cm 2) M 5 n

0

1- 2 56.8 27.1 19 4- 10 41.1 13.1 37 25- 50 26.8 13.7 51 75-150 27.5 14.0 16

CUMULATIVE NUMBERO F NUMBERO F PREYEGG S EGGSPRODUCE D PERAREN A (5CM 2)

100 Fig. 14. TIME(DAYS ! *eta lusZ^ZVll'T^l dSnSity °nth e "*~ti.l ^cundityo f Seiu identalzs. (Data fromKüchlein ,t ob epublished ) al. (1978) similarly found thai-i->,« > PtVtoseiulus ers ^ Tl^T^ "^^ °f femal6S ^ ona die to fhoney P. imilis had »untamed afterbein g reared for3 5day s - Reproduction stops after deposition „f unfavourable conditions delay III I *SPSClfie d numbe^ °* "M", if onth eresultin g sub-optimall evelItuTh ^ " ^ ^^ " ^^ thecritica lag eo f5 0 daysi s fecundity isrealize d orunti l therat eo freproductio na tthe^r^ ' SitUati°nS the"fore occur inwhic ! femalei slarge runde r «,,K / ° ** (bUt *5 °days ) a9es ofth epredator y under sub-optimal conditions thanunde r optimal conditions 58 Table 24. The influence ofth e starvationhistor y onsubsequen t fecundity of fourphytoseii d species.

Species Starvation history Net fecundity

temper- food presence |j ature deprivation0 of (°C) period (days) water

Phytoseiulus 20 5 no 66.4 11.8 20 persimilis 7 no 62.4 14.2 18 10 yes 69.6 15.4 26 20 yes 66.4 13.7 16 30 2 no 60.1 9.4 12

Amblyseius 20 28.2 8.1 18 potentillae

Amblyseius 20 54.2 10.0 18 bibens

Netaseiulus 20 no 40.8 11.4 18 occidentalis

a. Food deprivationwa sbegu n afterdepositio n of1- 3 eggspe rfemale .

at the same age. Examples of thisphenomeno n areth erat eo f reproduction of Amblyseius bibens at low temperatures (Fig. 15),tha t of Metaseiulus occidentalis at low prey densities (Fig. 14)an d thato fth e same species atunfavourabl e predator densities (Küchlein, 1966). Just before reaching the specified levelo feg gproductio n adeclin e in the rate of oviposition takesplace .Consequentl y the rateo f reproduction is not related to the female age ina fixedway ,bu t depends on theovipo ­ sition history, which becomes relevant after amajo rpar to f theegg s has been deposited. For this reason it makesmor e sense to studyth einterre ­ lations between the availability ofprey ,o n theon ehand , and thesearch ­ ingbehaviou r and conversionphysiolog y onth e other,han d (Chapter 3),tha n toestablis h age-related reproductioncurve sunde r allkind so fconditions . The reproduction curves presented here only serve tovalidat e concepts of theunderlyin g processes (Section3. 1 and Subsection 3.3.5), rather thant o be used directly inth epopulatio nmodels .However ,th edat ao f thepoten ­ tial fecundity are actually used inthes emodel s to specify themaximu m egg depositpe rphytoseii d female. The data concerning the life spanmeasure d at favourable feedingcondi ­ tions are remodelled before use in simulation. The maximum life span is

59 CUMULATIVE NUMBER OF EGGS PER FEMALE 70-,

T=22°C

TIME(DAYS ) Fig. seiu* IS.hi* CumulativS enumbe ro fegg 6ggsproduce S producedpe d rPe livinrlivin g femalg femaleo fe o fAmblyAmbH ns atdiffer^r.1 -t™^„ ^ , at d lf nttemPerStUr el6Vel S f r le f00d atT T-29 29 ,2 25an 5d22° TCar eobtaine dfro mBlommer « * s° (1976) -P . °^

Zti7Tl°l "'tmea n llfe SPan- ThlS time SP- isobtaine dvi aa least - squaresestimat eo fth e97-QQ» /T^-;»,* .* • a cumul oflif esnan ,m *«.. ° ative frequencydistributio n Fromthi s iL °nPr0babilit ^ P«P« ofth eGaussia ndistribution . —fort^na fZ^^^CXgda l 6qUatl°n ^ "^ ^"" *" "° "*f™ "^^ ^can "b ^eestimate d icaleffect so fth .* Populationgrowt h(Par t2) ,tha tth enumer ­ us reasonth e ^IT^* ^«dency couldb eneglecte da swell .Fo r availablesurviva lan d^ "^ ^ Sm°°thed b*repeate dsimulatio no fth e 1 8 aCœPtabl6 VeraU fitwa sfound .Th efit^CLT^" ^ ^ ^ ° dependencyo nth erelativ ea . giV6n ln Table 25- Theysho wa clea r span). S age (l-e- the agerelativ et oth emaximu mlif e

60 Table 25. The smoothed estimates of the relative rate of mortality (day- ) of four phytoseiid species in relation to the age class of the adult female.

Species Female age classa

123456789 10

Phutoseiulus 0.004 0.009 0.017 0.042 0.053 0.108 0.170 0.220 0.220 0.320 persimilis Amblyrseius 0.006 0.010 0.019 0.038 0.064 0.090 0.150 0.190 0.230 0.320 potentillae Amblyseius 0.004 0.008 0.020 0.035 0.071 0.094 0.140 0.220 0.280 0.420 bibens Metaseiulus 0.008 0.014 0.014 0.029 0.032 0.042 0.073 0.083 0.112 0.250 occidentalis

a. See Table 27.

Table 26. The effecto fpre y supplyo nth erelativ erat eo f femalemortalit y (day-1)o f Metaseiulus occidentalis.T =27°C ;relativ ehumidit y = 60-80%. Source:Küchlei n (tob e published).

Prey density Female age class (number ofegg s — ~~ per 5 cm2 leaf) 123456789 10

1-2 0 0 0.010 0.010 0.010 0.010 0.018 0.021 0.0260.03 0 4- 10 0 0.0040.00 40.01 4 0.014 0.016 0.0400.05 00.14 9 0.209 25-150 0.0040.01 3 0.017 0.0260.04 20.04 30.08 80.09 80.10 1 0.153 a.Se eTabl e27 .

Table 27. Smoothed estimates of the duration ofa n ageclas s in relation totemperature .

Temperature Duration (°C) of an age class (days)

15 9.0 20 7.0 25 6.0 30 4.5 35 3.3

61 Theeffec to fth epre y supplyo n survival is incorporated in thepopula ­ tionmode lb yappropriat e modificationo fth e relative rate of-mortality , forwhic h the residence time per ageclas s ishel d constant.B y modelling in thiswa ya lo wpre y supplyonl ycause s additional mortality, whileth e survivors are not affected inan ywa yb ythei r feeding history. Theobser ­ vations on the recovery of starvation (Table2 4an d Section 3.1) support this approach.Dat a on the relative rate of mortality are given inTabl e 26, but only forth ecas eo f Metaseiulvs occidentalis at 27°C. Inth esim ­ ulationso fpopulatio ngrowt h these datawer e extrapolated to othertemper ­ aturelevel san duse d forth e fourphytoseii d species.

2.2.4 Prédation capacity

The reproducing female determines the prédation capacityo fth e four Phytoseiidaei nthi s study: developmental timei sshor t comparedt oth e ovipositionperiod ,th ese x ratio favours females,an d their food intakei E considerablebecaus e themea neg gbiomas sproduce d per day ishig h compared to thebod y weight ofa matur e female. Therefore, the young ovipositing female was chosen forth e detailed study ofth epredator y behaviour ofth e fourPhytoseiidae .T osuppor t this choice with quantitative argumentsth e prédation capacityo fa nindividua l predator over its whole life spani s estimated and the contributiono fth e reproducing female to this capacity is assessed. Such anestimat e canb e obtained by taking 'snapshots' ofth e rateo fprédatio nwhil e development and ageingproceeds , andb y integrate the rate ofprédatio nmultiplie d by the fractiono fsurvivin g predators overth ephytoseii d lifespan . The measurementso fstage-specifi c prédation are presented in Fig.16 . Except forthos eo f Metaseiulus occidentalis the larvaewer e notpredaciou s as confirmedb ydirec t observationo fth e larval behaviour. The nymphs, males and postposition females were much lessvoraciou s than the young d3Tr femaleS- SimUltaneoUS measurements ofth e reproduction ratein - forli t 7Proximately 70%o fth e biomass of prey killed is utilized 17ns IT, egg Pr0dUCti0n; f°r exa"^< a female of Pnytoseiulus persi- «2» consumed6. 6 eggspe reg gdeposited ,whic h correspondst oth e resul« of 10 TsZa T al' <1978> mSaSUred at diffSrent temperatures in the range g and the' T the f°0d COntent °fa Prey e^ wei*s approximately1 to w xL" T°SeiUlUS W6ighS 4'7 "*'th e utilization ratio eguals to n/0. Thusa rouq hestimat er, fi-v , whole oviposition period can be obt "T ^ *"* **" ^^ «"^ ^ utiliZation ratio.Furtllor e th ^ ** ^ ^^ "* ^ y kilied during the othel — - - computerr;^:; ~:;:hr t P f the rates and the appropriate mMn * ° ^age-specific prédation -ing into acclnî^pXb^^ ^ '^ ^^ "^ female or a male (SubsectL7^" Z\Z T^ dSVel°PS ^ " •<••£) and that it may die from some abiotic RATE OF PREDATION (PREY EGGS DAY"1) 25-

22H

16H

13H

7H

» A» H 0 g d* ç d1 E L PN DN AM PF AF1 AF2 PREDATORSTAG E Fig. 16. Stagespecifi crate so fprédatio no fthre ephytoseii dspecie sfo r T= 20° C andR H= 75% .o , Phytoseiulus persimilis; •, Ambluseius bibens; A, Netaseiulus occidentalis. Preyeg gdensit y= 30-6 0eggs/cm* ;webbe dare a 4-11 cm2;numbe ro freplicate s =20-30 .E ,egg ;L ,larva ;PN ,protonymph ; DN,deutonymph ;AM ,adul tmale ;PF ,preovipositio nfemale ;AFI ,ovipositio n female;AF2 ,postovipositio nfemale . cause (Subsections 2.2.1 and 2.2.3), acrud eestimat eo fth eprédatio n capacityo fa nindividua lpredato rca nb emad efo reac hphytoseii dspecies . Thefollowin goveral lprédatio ncapacitie s (onegg san dlarvae )wer efound : - Phytoseiulus persimilis about55 0pre yitem seac ho f1 p g - Ambluseius bibens about20 0pre yitem seac ho f1 M 9 - Ambluseius potentillae about15 0pre yitem seac ho f1 p g - Metaseiulus occidentalis about10 0pre yitem seac ho f1 pg . Theprédatio ncapacit y dependso nth esiz eo fth ephytoseii dspecies :a largerspecie sproduce s largeregg sand ,thus ,require smor efoo dfo reg g growthetc .Thi si sonl ymodifie db yinterspecifi cdifference si nfecundit y

63 WEIGHT (jug) 28-,T

25H -EGG DEPOSITION IS CEASED 22H

19H

16H

13H

1(H

lu >>... i t

—r 0 2 6 TIMEO FFOO DDEPRIVATIO N(DAYS ]

Fig. 17. Weightdecreas edurin gth estarvatio no ffou rphytoseii dspecies , startingwit hyoun gwell-fe dfemale si nth einitia lphas eo fthei roviposi - tionperiod .T = 20° can dR H= 60-80% .o , Phytoseiulus persixilis; ., Amblr setus blbens; +w^to, potentillae; ki Metaseiulus occidentalis; dry-weightlevels; !, standar ddeviatio n( n= 20).

"L7 beain°'" 1S dem°nStrated b*« - Prédationcapacit yo f Mtlyseius oT^oZ*s-7&T t0 that °f AmblVSeiUS '»tentiii.e.Th econtributio n and 7oyTZ t0 th6Se Predati°n Capacities -»ount-t o84 ,80 , DO ana b0/orespectively .Becau^ Pn fI-V, J femalesthes ewer echose n V -Portantrol eo fth eovipositin g chingbehaviou r(Cha Pter3 ) »*—"^ Terences i»P« ysear -

64 2. 2. 5 Starvation and survival

After depletion of their food source Phytoseiidae are able to survive for some time. When well-fed young females were placed in a Munger cage without any food or water, oviposition initially continued utilizing the food ingested before the start of the experiment, but itcease swithi n1 day after one or -les s frequently -tw o eggs hadbee n deposited. Because the weight of an egg corresponds to 20%o f thematur e femaleweight ,th e initialweigh t declinewa sver y steep,a sillustrate d by the electrobalance measurements of the femaleweigh t during food deprivation (Fig.17) .Afte r egg deposition had ceased, the weight decreased steadily, but much more slowly. Some of the predators were able to withstand severe dehydration. Theirbod y weight approached dryweight ,bu t they did notdie .A s discussed in Subsection 2.2.3, these starving females areabl e to recover andsubse ­ quently oviposit as well as they didbefor e starvation.Th e rates ofsur ­ vival during these and other starvation experiments are summarized inTabl e 28 as the 90, 50 and 5%point s ofth e survival curve.Larva e develop into protonymphswithou t any food,bu t afterthi smoul tthe yrequir e food tode ­ velop into the nextnympha lstage . Two factors are very important with respect to the rate of survival. First, dehydration is enhanced by anincreas e oftemperature .Second , high humidity and drinking water enables prolonged survival. The role ofbot h factors is demonstrated inTabl e 28usin g additional data from thelitera ­ ture. Because inros e culture themea ntemperatur e is about20° C andbecaus e water spraying takesplac e frequently, itma yb eexpecte d that Phytoseiidae areabl e to survive for 2-3 weeks after theexterminatio n ofthei rpre y and inth e absence of alternative,non-tetranychi d food supply. Whether non-tetranychid food sourcesprovid e amean s tosurviv e duringa longerperio d inth e greenhouse culture ofornamenta l roses,wil lb e treated inth e remaining subsections ofthi schapter .

2- 2. 6 Cannibalism

When other food resources are lacking,th e adult female and occasionally the nymphal stages of the Phytoseiidae are reported to feed onthei r own young, mainly eggs and larvae.Th e tendency towards cannibalism may differ from species to species and even from population to population. Croft & McMurtry (1972)observe d cannibalism among four strains of Metaseiulus occi- dentalis originating from differentpart s ofth eU.S.A . They foundsignifi ­ cantdifference s inth e extent ofth ecannibalisti c behaviour. Laing (1969) reported thatwhe n several ofeac h stageo f Metaseiulus wereplace d together ina cell , the adults fed on immature stages,bu tno to neac h other.H e also observed thatnymph s of Metaseiulus could be reared tomaturit y onegg s and larvaeo f the same species.Howeve r theresultan t adults laid only fewegg s

65 co co 01 r- 01 oi 10 en 10 p p P P P «a 10 p P P p (0 P> ^ M u o P a) o o M 0»- r^ u M u M P ft p fi o 0 01 01 O 0 0 oi ft a rH rH o o (0 10 O) (V a a a ft ft u U (V (V IV 1) 11 •H u Ä X n o 10 10 u fl n M u u u u fi o P P 01 Ü1 il i> n u P p M M P P p p a 3 o C fi c IV m (0 i« •a a) a) 1 oo CM fi a ^ r- CM 01 3 i rH CM O is in in f> 'M 0M 'M O p (0 Ol co r^ m ai IV C0 rH p o • i 01 H mr - n (0 in CO m S -a X! P S« CM o i Cl u Ol CS •C •P I I I I C m m oo o o O tu r> H CM 10 O p m rH 10 * OM in CM fi •H I <* oo a m i0 oi co st1 oo i co oo 3 E in • i i i Ol •H co I I i I I I I in oo CM Ol CO CO •rjt p U co t- 00 CM M (V m m p in •p p m i (0 OM (0 (0 Oil S* I co CO CO H S I co t> a o N I I I p in e œ <( oo en CM •H 3 f- 10 CM r- i0 CM G O (0 o £ a a P 5« «3 o •H o i OM CM CM 10 lO a S Ui ' I I •f> lO CM CM •H in i I 0M H H m m i I I I I •p m in rH rH to

m •p m m E CM 'M (U O o i u o CM oo 10 Ol Ol o »H CM CM CM 0M 0M o O CM CO O O Ol Ol •P OM OM p o CM CM CM OM CM OM OM 10 IV -Ö u Oi 11 'M (0 u < < Pu Es £ b, 2 u a J3 H < < < < PH < Cu (0 fi 01 "' a a u >-H 01 0] >*H 01 'M 00 3-M 3 "H c OM q » 'M "H U "rH *H IS 0 p u 3 -u p -u o «. 0. 11 Ü *! O < CM 66 andha d shorter life spans. Inth e straino f Metaseiulus occidentalis reared by Küchlein, only very occasionally didhungr y females succeed inpiercin g the egg chorion. This corresponds with observationsb y Bravenboer (1959). Amblyseius bibens mayb ecompare dwit h Metaseiulus occidentalis inthi sre ­ spect. According to our own observations Amblyseius potentillae becomes cannibalistic to some extent after 1-2 dayso f food deprivation atT =20°C . Itma y then feed primarily onegg s andlarvae . Dosse (1958)wa s firstt orepor tcannibalis m in Phytoseiulus persimilis. The extent of cannibalism is relatively high inthi s species:1 2hour s of food deprivation at T = 20°C induced cannibalism of eggs; longer periods led to feedingo n the larval andnympha l stages. Ina starvatio n experiment with only an initial supply of 30 freshpredato r eggs, the longevity of female Phytoseiulus persimilis did not exceed the mean value measured in presence of free water in anyo fth e 20replicates .A s expected, thewell - fed females deposited one ortw oegg s during the firstday ,bu tonl yocca ­ sionally did egg deposition occurdurin g thenex ttw o days.Afte r 3-4 days most of the eggs had hatched. During the subsequent period thewate r and food content of the larvae and nymphs decreased exponentially withtime , until death, as shown for example in Fig. 17.Therefor e the food supply decreased drastically during theexperiment . Because the acarine predator-prey interaction frequently leads torapi d local extermination of the prey, the aboveexperimen t represents a fairly realistic situation and itma y thereforeb econclude d thati nth e longru n theeffec to fcannibalis m on female longevitydoe sno texcee d the effecto f water supply. Under the present glasshouse conditions iti sreasonabl e to assume the continuous availability of freewater ,whic h thus determines the Predator capacity to survive irrespective of cannibalism. However, under drycondition s cannibalism mayprovid e amean s forth e strongest individuals tosurviv e for some time,whe nn o other food itemsar eavailable . Cannibalistic behaviour mayb e favouredb ynatura l selection,whe ndiffe ­ rentgeneration s ofth epredato r areconfronte d attime swit h temporary food scarcity. Such a situation canb e inducedb y ahig hpredator y andreproduc ­ tivecapacit y of thephytoseii d itself. Itwil lb e shown inPar t2 thatth e capacity of Phytoseiidae indeed leads toloca l extermination ofpre y clus­ ters. Ifneithe r alternative food norwate r sources are available,canniba - iism can be expected. It is not surprising, therefore, that especially Phytoseiulus persimilis is the most cannibalistic of the species studied he re, for the individual weight and thevoracit y ofthi s species arerela ­ tively high and, as will be discussed in Subsection 2.2.7,thi s predator feeds itself exclusively withTetranychidae .

67 2.2.7 Alternative food supply

ThePhytoseiida econtai nman ydivers eform swit hrespec tt othei rfeedin g habits (McMurtrye tal. ,1970) .Som especie ssee mt ob especialize dpreda ­ torso fTetranychida e andsho wn otendenc yt oreproduc eo nothe rtype so f food. Phutoseiulus persimilis issuc ha species .Althoug hth eothe rspecie s studiedcoul dcertainl yb eranke da sspecialize dpredator so fTetranychidae , theirdietar yrang ei sno trestricte d tothi skin d ofprey ,bu tinclude s otherplant-inhabitin gmites ,youn gstage so fvariou sinsect san dsom enon - animalfoods ,lik epollen san dfungi .Abrie frevie wo fth eliteratur eil ­ lustratesth einterspecifi cdifference so fa numbe ro fPhytoseiidae : - Phutoseiulus persimilis isver ydependen to nth eavailabilit yo fTetra ­ nychidae (Dosse,1958 ;Chant ,1961 ;Ashihar a etal. , 1978). Accordingt o Mori& Chan t (1966)th eadditio no fnutritiv esubstance ssuc ha ssucrose , glucose,pollen ,hone yan dfis hmeal so fvariou skind st oth edrinkin gwate r didno tsignificantl y increase longevity compared toth eeffec to fwate r drinkingalone .Ashihar ae tal . (1978)als odemonstrated ,tha t Phutoseiulus persimilis didno treproduc e onhone y orpolle n (strawberry, castor,re d pine),bu tmea nadul tlongevit ywa sincrease dt o4 5day sb ynutritiona lsub ­ stancessuc ha sfres hhone yo ra 10 %sucros e solution,a scompare dt o1 2 dayswit honl ywate ravailable .Lain g(1968 )report stha tstrawberr ypolle n didno tpromot elongevit yo rdevelopmen to f Phutoseiulus, comparedt ospe ­ cimenskep twithou tfood .Similarly ,McMurtr y (1977)foun dtha tpolle no f Hymenocyclus croceus wasno ta nacceptabl e foodfo rthi sspecies ,i ncon - trastt osom eothe rPhytoseiidae . - Metaseiulus occidentals hasbee nobserve d to feed,develo pan drepro ­

duceo ntarsonemid s (Huffaker& Kennett,1956 ;Flaherty , 1967), tydeiids

(Flaherty& Hoy,1971) , Brevipalpus phoenicis, thripsan dsom ecrawle rspe ­

cies(swirsk i *Dorzia ,1969) .Accordin gt oFlahert y& Hoy (1971), Metasei- C Uld n0t rSaCh adUlth 0d nCa t folia7 T. ° ° ° ^ Pollen (rupha lati- 197 Jin18" imP°rtant f°0d f°r *»"*">*» -^sci (Kennette tal. , bubüonltonl yvwhe w hn Tetranychida TT (1968) erePwer °erteabsen d feSdint g °nthl S P°llen »? the ad«ltS< predator LllT r *^ ^ P°UenS teSted as food f°r this 0 S m e iiOMCeae O en!ieTth ep red a°t o rr " *'"**"*" •™ " ™» «" "" thebes tfoo dsubstTt't e MasT ^ ^ malntain "»"*"**«• Pollenwa s lencoul db econtint ' T °*° ftM S Predat0r delusivelyo npol - - ^lyseius po e,! ./e iTl ^ '" "^ "»» * *«• Aculus SPP. inth e eXDer ** "* "*«*««» "adily on apple pollen and ting are the expTrJT ? ^ ^"^^ <1971>" Specially interes- ^llphoraZsZnZT MCMUrtry (1977)' WhiCh lndicated th- P°"- °f For a diet ofonl y ^1^ ^ " ^^ °f «»"« ^es was present, only pollen, hefoun d a lower rate of reproduction (about

68 two-thirds the normal rate)an d alonge rpreovipositio nperio d than foronl y Tetranychidae. Not allpollen s are accepted as foodb yPhytoseiidae .Fo rexample ,cotto n pollen was rejected as foodb y Metaseiulus occidentalis (Swirski &Dorzia , 1976) and Amblyseius bibens (Blommers, 1976), possiblybecaus e of its size (75-100 |jm)(Kennet t et al., 1979). Inman y othercase s iti spresume d that the negative responses to certain pollens are related to the chemical or physical nature of their waxy orresinou s exine (Kennette t al., 1979). Several authors state thathoneyde w canmerel y serve topromot e survival, but allows little reproduction (Huffaker& Kennett ,1956 ;Chan t& Fleschner , 32 1960; McMurtry& Scriven, 1964,1965) . Ina nexperimen t inwhic h a Psolu ­ tionwa smixe d with bee honey andoffere d asdroplet s tohungr y young females 32 of the phytoseiid species inhunge r cages,th edegre eo f P ingestionwa s measured with the aid of-th e Cherenkov-method.Th eresult s indicated that Amblyseius potentillae was farmor e ablet o ingestth ehone y (500-2000 counts per minute) than the other species, evenwhe nthes ewer e starved forlon g periods (Amblyseius bibens 100-200 countspe rminute ; Metaseiulus occiden­ talis 50-100 counts per minute; Phytoseiulus persimilis 0-50 counts per minute). From the review ofth e literature thedegre e ofspecialis m on tetranychid Preyca nb e derived using thepreferenc e forth edifferen tpollen s relative totetranychi d prey as acriterion .A s statedbefore , Phytoseiulus persimi­ lis ishighl y specialized ontetranychi d prey,whic h isals otru e for Meta­ seiulus occidentalis and Amblyseius bibens butespeciall y the latter species isabl e to rely onnon-anima l foodwhe ntetranychid s are absent. Amblyseius Potentillae, however, seems toaccep tbot hpolle n and tetranychidswhe nof ­ fered simultaneously. The original criterion thus leads toa sequenc e that corresponds with thatobtaine d fromth e32 P ingestionexperiments . The short survey above indicates differences inth e dietary range that may be important forthei r survival andreproductio n ina natura lhabitat . Itma y be important too inth egreenhous e cultureo fornamenta l roses,bu t thehairles s rose-leaves are less suitable aspolle n gathering centres and, besides, other plant feeding arthropod orhoneyde w are absentand/o runde ­ sirable, itwa s therefore presumed, thatunde rth egreenhous e conditions to be investigated, the effects ofa n alternative food supplywil l notexcee d that of simple water supply to an important extent. Thispresumptio nwa s confirmed by release experiments with the fourphytoseii d species. Fifty young ovipositing females were released on a group of five potted rose bushes upon which 1-2 gram of fresh Vicia pollensha dbee n scattered. The roses were sprayed daily with water. Therat eo fsurviva lwa smeasure d in twoways :b y direct inspection ofth e leaves;and ,i fthi smetho d indicated !ownumber s ofpredators ,b y inspectingmit e infestedbea n leaflets 10hour s after being pinned on to the rose leaves (10 leafletspe r bush). Ifbot h checks rendered negative results,th epredator swer eassume d tob eabsent .

69 Table 29. Survivalo fyoun g phytoseiid femaleso ffou r specieso nros e bushes scatteredwit hpollen .T = 17-22°C ;relativ e humidity= 60-80% .

Species Numbero fpredator s found Numbero fpredator s found bydirec tinspectio no f by trappingi nmit e colonies leaves onbea n leavespinne d ontoth e rose leaves

Numbero fday s afterreleas e Number ofday s after rele

10 15 21 29 29

Phytoseiulus 21 13 2 persimilis 0 0 Amblyseius 33 27 potentillae 6 0 0 Amblyseius 43 bibens 36 8 0 1 Metaseiulus 45 29 occidentalis 3 0 0

t0 n0t Slgnificant ZZ29TTÎ- ^ ^ P—ted byth epolle n treatment 6XPeCted under water suliv, ^ **"*** cl imat ^e (T=i7^^ 22 c; reiati conditionty 6 8s o%)f -i r: mi;zzTis d - ° -— • °- ° - the survival^/, 1, ^^ effeCtS °fth e Pollen treatmento n Se2US Heuse dpel t Dl," "*""' ^ " * ^ ^Perature (T= 28°C). termit T h ^ Tt'"T ^ ^ ^^ *°™*«" »^ ~ plants were covlr TI P°PUlation ™ theseplants .Consequentl y these r 8 webbing which may a ponen ;:L; n : ntie ;:;^:::^ ' -™ - — however,trea tthi s aspect "^ leaV6S- ™S ^^ d°SS n0t' nen^rth^ririorT011"."maintain the -— »»•*•*« — ut al ubstances the survivai f the -st speLaîLed h s i: ;::r ; ' ° ™ ^-^~^^^r^^-'spraying 10% .ucro..^^. ^"h """'""1978)^ "**- ** ^«^ **-

70 3 Prédation, reproduction and residence time in a prey colony

As argued inChapte r 2 theprédatio ncapacit y ofphytoseii d predators is largely determined by the high rate of foodconversio ndurin g theoviposi - tionperiod ; under favourable conditionsphytoseii d females are able topro ­ duce an egg biomass per day equal tothei row nweight .Th e rate ofrepro ­ duction will therefore depend on the searching efficiency ofth epredato r and the availability of theprey . Itwa soutlined ,moreover , thatpreviou s reproductive success (i.e. the number of eggs already deposited) ismor e important in determining future reproductive food demands than ageing. Apparently, among Phytoseiidae there is a tendency todeposi t a specified number of eggs. Because the availability ofpre y isno tuniforml ydistri ­ buted in space, the food demands of the ovipositing female may lead to moving from colony to colony insearc h ofa satisfactor y supply ofpre y and aminimize d level ofinterferenc e withothe r conspecific females. The availability of the two-spotted spider mite is restricted to the plant area covered bywebbing .Th ewebbe d area isgenerall y situated atth e lower side of the leaves and is arbitrarily subdivided inunit s surrounded by uncolonized parts of the leaf. These so called colonies attain their maximal sizewhe n theundersid e ofth e leafi scompletel ywebbed . During the residence of thepredato r ina certai ncolony ,pre yconsump ­ tion will lessen the local supply of prey until the predator leaves the colony, because of the lower level ofpre y availability. Insearc h ofne w Prey colonies, the predators tend to aggregate atcolonie swit hhig hpre y supply, but this aggregative responsema yb e counteracted bymutua l inter­ ference among the predators, which enhances thetendenc y todispers e from thecolony , independent of the localpre y supply.Moreover ,mutua l interfe­ rence can lead to a decreased rate of reproduction, asshow nb yKüchlei n (1966). In this chapter the relation between onth eon ehan dpre y and predator density inth e colony and, on theother ,th erat e ofprédation , reproduction and departure is analysed. This analysis isconfine d to the level of afe ­ malepredato r foraging in acolon y ofspide rmites .Thos e aspects of forag­ ing behaviour that takeplac e after departure from acolon y aretreate d in Part 2o f thisAgricultura l ResearchReport ,a swel l asth e aspects concern­ ingpopulatio n growth. The analysis is carried outb yvalidatio n ofconceptua l models ofpreda ­ tory behaviour. A prédation model is constructed that is based on random searching periods between successive encounters with prey items and ona

71 relationbetwee nth emotivationa lstat eo fth epredator s (Section3.1 )an d thepre ydensit yrelate drat eo fsuccessfu lcaptur e (Section 3.2). Thein ­ dicatoro fth emotivationa lstat eo fth epredato ri schose nt ob eth efoo d contento fit sgut .Accordin gt oAkimo v& Starovi r (1978)th egu twall so f phytoseiids aremarkedl yextensible ,compare dt oothe rgamasids .Neverthe ­ lessther eha st ob e amaximu m load,whethe rthi si scause db ya limite d extensibility ofth ebod yo rgu twalls ,o rb ya negativ efeedbac kt ofeed ­ ingvi agu to rbod ywal lstretc hreceptors ,a sfoun di n Phormia regina by Gelperin (1971)an dBeize r (1979).Becaus e ingestion,maxima lgu tconten t andgu temptyin gma yb equantifie db yus eo fth eelectrobalance ,th efoo d contento fth egu tca nb erelate dt obehavioura lcomponent sb yobservatio n ofth epredator ybehaviou r andsimultaneou scalculatio n ofth e amounto f foodpresen ti nth egut . Thebehavioura l componentsneede dt ocalculat eth erat eo fencounte ra t anyleve lo fth emotivationa lstat ean dpre ydensit yar ea sfollows : - widtho fth esearchin gpat h(cm ) - distanceo fpre ydetectio n(cm ) - walkingspee d(cm/s ) - walkingpatter n - walkingactivit y (%) - coincidencebetwee npre yan dpredato ri nth ewebbe dspac e - successrati o (%) -handling andfeedin gtim e(s) . behaviour10118 betWeen thS m0tivational -täteo fth epredato ran dthes e (TÎV!r Urf '°mPOnentS a" »•«*- asimulatio nmode lo fth egueuein gtyp e tob et' h •CUrrY& DeMiChele' 1977>< -hereth epredato ri sconsidere d 0 faCllitY iie thedentiStl an dth e "i:whoL v ir";™ ^: n?v' te- ' re —-' —P« y<* ^h-eclient- **> —<, - in ann,-v, , 'digestion,absorptio nan degestion') . iS rat o ne" T^t ^ "eenpredatorandprey^ ^^^ ^^ rthe^ calculateth e ttpey: ::", r ° «*°**»«*****» i-nepre ycolon y (Sections3 2 an d^ a i„ „«-v .x .• abovecomponent so fwalkin abeHa v °fmeaSurement s °fth e trationo ft-h . ^ behaviour.Vide oequipmen tenable dth eregis - lklng ttern ir/n dt L ;j;u r ' **«*« » ««*t omeasur eth ewalkin gveloc - y dlStribUti n f fiLd LP SL T ° ° ^*s - walkingdirectio nafte ra assumpttr :;:\:T™:z~ srwalking behaviour °n basis °f the calculatiothepreviou nsoste fth pwite rat te f '„aucocorrelatlon "^ ^"8fa eing^ fraccounte °m the erectiod for.Th noe f the defined frequencydistriwTo PredatorT T^re" ^ ^^ ^ ^"mentally effecto frecrossin at h aUtocor"P y encounterserve st oestimat eth e calculation nr JL'* J*™' Searche«lationd h S being accounted for.Th e culationo fth erat i n* /"" ^^ Y thepredator .Th ecal - e f dePartUrS from roleo fpatc h spec" fic° thecolon yserve st oelucidat eth e PeClflC CU6S ln the intracolonyresidenc etim eo fth epre -

72 Apart from fundamental ecological interest inanalyzin g the foragingbe ­ haviour, there are more reasons toundertak e adetaile d component analysis instead of direct measurement ofth eresultin g rateo fprédation .Extrapo ­ lation of the measured prey consumption to the population level is only allowed if themotivatio n ofth epredato r is ina stead y state during these measurements of the rate ofprédation , aswel l asdurin gpopulatio n growth ofpredato r and prey.Rabbing e (1976)solve d the firstproble m by allowing thepredato r to adapt itsmotivationa l statet o aconstan tpre y densitybe ­ fore measurement of the rate of prédation.Pre y densitywa s kept constant by replacement of the prey captured (ordie d from other causes)a t1 5mi n intervals.Howeve r prey replacement isessentiall y impossible inth ewebbe d colony, because mite transfer with the aid of a brush candamag e thewe b structure and can disturb thepredato rbein g sensitive tomovement s ofth e web. Numerical simulation ofth eprédatio no nth ebasi s ofa componen tana ­ lysis may provide a means to keep tracko fa changin gpre ydensit y andt o estimateprédatio n atconstan tpre y density.Wit h respectt oth eextrapola ­ tion of prédation measurements to the level ofpopulatio n growth -th e second problem -Rabbing e (1976)assume d instantaneous equilibration ofth e phytoseiid motivation to any change in prey density. This assumption is tested inPar t 2 of thisAgricultura l ResearchRepor tb yusin g asimulatio n model of population growth and dispersal ofpre y andpredato r thatca nac ­ count fornon-stead y states ofth emotivation . Finally, the component analysiswa sundertake n tostud y therol e ofweb ­ bing in the acarinepredator-pre y interaction. Inmos to fth ereporte dex ­ periments webbing was either not included ori twa s distributed ina nunrea ­ listic way due to the flat and artificial substrates (paper,plastic )o r due to the stage of the prey,whic hproduce d awe b different from thato f the adult female.Althoug h female-produced webbingha s aver ychaoti c struc­ ture, it can be considered as acoheren tuni t (Figure 8),whic h should be distinguished from the uncolonized parts of the leafi nacarin epredator - Preystudies . Actually some unexpected types of functional response of phytoseiid Predators to the density ofthei rpre ywer e attributed"t oclumpe d distribu­ tions ofwebbin g in space (Mori,1969 ;Fransz ,1974) . Other deviating forms °fth e functional response were attributed todisturbanc e of feedingpreda ­ tors by active prey, resulting in an attack on theinterferin g prey, that bumped into it (Sandness &McMurtry , 1972), or attributed tocontac tdistur ­ bance, decreasing the number of successful captures (Mori& Chant , 1966). Küchlein (to be published) found a second rise ofth e functional response °f Metaseiulus occidentalis athig hpre yeg gdensities .Probabl y thispheno ­ menonwa s not related to the food satiation level ofth epredator ,bu trath ­ er to a contact stimulus. However it may be questioned whether the above behavioural factors operate in the webbed area. Preliminary observations indicated thatbot h predator andpre ywer e less active inth epre y colonies

73 anddisturbanc eo fth epredato rwa srarel yobserved .Furthermore ,webbin g maychang eprédatio nsimpl yb ysurfac eenlargemen to rb yinducin gspecifi c changesi nth epredator ybehaviour ,a sdiscusse di nSubsectio n2.1.6 .There ­ foredetaile dobservatio no fprédatio nwa spreferred .

3.1 DYNAMICSO FTH EMOTIVATIONA LSTAT E

Byassumin gth efoo dconten to fth egu tt ob eth emai nindicato ro fth e motivationalstat eo fth epredator ,th edynamic so fth epredator ymotivatio n canb esimulate db yintegratio no fth erat eo fingestio n (Subsection3.3.1 ) andth erat eo fgu temptyin g (Subsection3.1.2) .Thi ssimpl econcep tallow s thecalculatio no fth emotivationa lstat edurin gobservatio no fth epreda ­ torybehaviour ,s otha tpredator ymotivatio nan dbehavioura lcomponent sca n berelate dt oeac hothe r(Sectio n3.2) .Thes erelation sar euse di ntur ni n theprédatio nmodel st ocalculat eth erat eo fprédatio n (Section3.3) . Validationo fthi styp eo fprédatio nmodel sdi dno tresul ti narejectio n ofth econcep t (Holling,1966 ;Nakamura , 1974;Fransz ,1974) .Howeve rth e postulateno fon eintervenin gvariable ,indicatin g thehunge rdrive ,ma y toosimpl ea hypothesi st oaccoun tfo ral lhunge rrelate dbehaviour .Fo r examplei tma yb equestioned ,whethe rth emotivationa lstat eadapt sitsel f instantaneouslyt oa chang ei nth efoo dconten to fth egut .m otherword s wheth3 "faln leVel °f9U t filling indUœ the same -archingbehaviour , lara^ T aChleVed ViS ingeStion or S»temptyin gstartin gfro mlo wo r argeamount so ffoo di nth egu trespectively .Thi sproble mi sconsidere d probZ °CCaS10nS " thlS ChaPter (f°r 6Xample ^section 3.2.7).Anothe r for I" nS the gUallty °fth e f°0d- The «i-t«ce <*"Pecifi chunger s BecaLe H' SU93rS " "^ ^ ^ ^ *"^ bl°" f1^ (Deth±er' ^)' S P llenS f rtetran?rr ^ ^ ^ "* ™ ° < ^-ydewan dwate rapar t ZTnTZTT Md bSCaUSe thS deVel°P^tal stageso fth espide rmit e rL vn ti nd ; """ ^ ^^ t0 the *«**<*, dietcompositio nma yb e IguantiL;111119 ^ m°tiVati°nal State <*th epredato r Howevera de - UnderStandin g f compLTo n forr ° ^ -tabolic consequenceso fdie t abS 10n SyntheSis and notye tex ist T ' allocationo ffoo delement sdoe s -d""f "wint PhySi01— —• - -e timebein gth e 6 6 5 19 assu ing - quality of the ^ Lodi: :; :;:,:;: ;?: ".^" : const assumptioni scriticize do ni- h K ant.I nSubsectio n3.1. 3thi s ^^t^-:\z;:~r*-etcompositio n J££.% Z^^ ^^ an'™treate * *d° in th e »rti„.a tal ldevel opmental stages £ -£ t T^™" °' ^^^ = 75%). Femaledeutonymph swer ecollecte d~ £Z t'n " ^^ ^ transferred t0 otherleave swit habundan tfoo d( T 20o" , ^^ "" the y moulte aftersuppl yo f males whenth .V , * d and copulated •Whe nth efemal epredator sha ddeposite dthei rfirs t 74 eggs, they were ready for experimentation. Subsequently, whenever these predators were deprived of food,car ewa stake nt ous e only satiatedpreda ­ torsb y sampling them immediately aftera nactua l feedingperiod .Nex tthe y werepu t individually inMunge rcage s (Figure 10)fo rdifferen t timeinter ­ vals and at different temperatures,dependin go nth eparticula r purpose of theexperiment .Unles s stated otherwise,th e femalepredator s never exceeded theag e of 10 days asa nadult .

3.1.1 Ingestion

After asuccessfu l capture thepredato r starts ingesting thepre ycontent , themovement s of the ingested fluid beingvisibl e through its transparant bodywall . Presumably praedigestive fluidsar einjecte d for extra-intestinal digestion (Akimov& Starovir, 1975). The amounto f food ingested dependso n thefollowin g factors: - the amount of food thatca nb e ingestedb y oneo rmor epredator s froma singlepre y stage (the ingestable food contento fth eprey ) - the suction force inrelatio n toth ephytoseii d species involved andth e fluidity ofth e food (theingestio n constant) - the difference between themaximu m foodconten tan dth e actual foodcon ­ tento f the guto f thepredato r (thesatiatio n deficito fth e gut) - the sum of theperiod s inwhic h themout hpart s ofth epredato r arein ­ truding thebod y of thepre y (thefeedin gtime ,Subsectio n 3.2.8). As a first approximation ofth e ingestable food contento fth epre y one

Table 30. The ingestable food content of the developmental stages of Tetranychus urticae.

Preystag e Weight increase (ug)afte r feeding Freshweigh tminu s dryweight 3 Metaseiulus Amblyseius Phytoseiulus occidentalis potentillae persimilis

e99 1.0 0.2 30 0.8 1.3 larva !.1 0.2 24 1.1 0.2 12 2.7 Protonymph - 2.3 0.3 14 7.3 0.5 21 8.6 deutonymph? 2.9 0.2 16 5.1 0.3 30 raale _ _ 2.5 0.2 27 2.4 0.3 17 2.7 female 2.8 0.4 18 4.9 0.4 16 7.8 0.5 29 17.9

According to the data ofMitchel l (1973).

75 couldmeasur eth edifferenc ebetwee nth e freshan dth edr yweight so fth e differentpre ystages .Thes eestimation s canb eobtaine dfro mth ewor ko f Mitchell (1973).A mor eprecis emetho di st ocompar eth eweight so fa nini ­ tiallyhungr ypredato r (2day s starvation atT= 20°C )befor e andafte r feedingo na certai npre ystage .Th eresult so fbot htype so fmeasurement s aregive ni nTabl e30 ,whic hshow scorrespondenc eonl ywit hrespec tt oth e smallpre ystages .Becaus eth eamoun to ffoo dingeste d fromth eadul tfemal e preyincrease dwit hth ebod ysiz eo fth ephytoseii dspecies ,on ema ysuppos e theingestabl e foodconten to fthi sstag et ob emuc hhigher .I na nexperi ­ mentwit hfemale so f Phytoseiulus persimilis and Tetranychus urticae the totalweigh to ffoo dconsume db y threehungr ypredator s from onesingl e preyamounte dt o16. 6ug ,whic hresul tclosel y approximates theestimat e basedo nth edifferenc ebetwee nth efres han ddr yweigh to fth eprey .Appa ­ rentlyth eamoun to ffoo di nth efemal epre yexceed sth emaxima lfoo dcon ­ tento fth ephytoseii dgut .I tca ntherefor eb econcluded ,tha tth eingest ­ ablepre yconten tpe rsingl epredato ri slimite db ybot hpre ysiz ean dgu t size Inanothe rserie so fexperiment s ingestionwa smeasure di nrelatio nt o feeding time.B yinterruptio n of feeding after fixed time intervalsth e amounto ffoo dingeste db ya hungr ypredato rca nb emonitore dwit hth eai d ofth efollowin gmethods .Th efirs tmetho di st omeasur eth eweigh to fth e predatorbefor e and aftera predetermine d feedingperiod .Howeve rthi s

methodi sno treliable ,whe n theweigh tdifference s arebelo w0. 5M ,a s e.g.m theeg gstage .I ntha tcas eanothe rmetho dwa sapplie dusin g32 P- abelledprey .Th espide rmite swer elabelle db yfeedin gdurin g1 2hour so n abea nleaf ,previousl ypu twit h itsste mi na 32 P solution (1mCi )fo r1 ay. Radioactiveegg swer eobtaine dfro mradioactiv efemales .Th elabelle d Pe ywa soffere dt oa nunlabele d femalepredator ,bein gdeprive do ffoo d at T = 2 C SlnCe satiation amoi,n/T - °° - Fransz (1974)assumed , thatth e HowevL°f r 10aCtiVitY ln thS PrSy WaS P«»°rtionalt oit sfoo dcontent , U th0r SeXperiment s prirL / 1 ' Seated sucha hig hvariabilit yamon g 7Jt thi °feXaCtl Y the Same Sge and labelled °nth esam ebea nlea f TeZoTslTTr1 S i3n2Valid- ThlS variabilityma yb edu et oth eunhomo - 121Z acti^t T °f P ln thS leaf °rt 0 individ^ differencesi n the 32 £Z^*r^zza^enedPre v * " ^?rr?' ^"^ when ^tioth ne experimentr —^swit —h P * Present in the indl J ey ITZ °' ^ ^ »*"«*** ***«? were brought into « r6aSOn the exPl°iter and its victim subsets ; r:isSr:; 1"3 after a—***** —*• & weredissolve di l10 "l w ^ ZeT^ V ^ ^ "* ^ "^ counter,whic hdir^i o SW6r e brou9ht intoa radioactivit y ofth eCherenko dlrSCtlvmetho y regiSted Th« V P-^aaiationemittanc eo f ^P bymea r or„. .' _ " theß-radiatio nemitt.n ^„ f32 p ^ meanS counteddurin gl o XlÎ' ** ^^ by the "* -leculeswer e ng minutesan dnex tcorrecte dfo rth emea nnumbe ro fcoun t 76 registrated invial s containing only water.Th eproportio no fth etota l radioactivity ingestedb yth epredato r canb ecompute d from these counts and this indicates theleve lo fingestion .Th eshape so fth eingestio n curves obtainedb yth eabov emethod s were invariablyo fth esaturatio n type. Therefore thefollowin g formulawa sadequat e fordescriptio no fth efractio n ingested relative tomaxima l (i.e. uninterrupted) ingestion:

RRFI tim e Fraction ingested= 1- e ~ ' RRFI= relativ e rateo ffoo d intake (time-)

In this formula RRFI represents theresultan to fth esuctio n force (or ingestion constant)o fth epredato r andth eviscosit yo fth epre y content. Thevalu eo fthi s ingestion constantca nb eestimate d fromth eslop eo fth e linear regressiono fln(l-FI )o ntime . These estimates aregive ni nTabl e 31. Apparently theingestio n constantsd ono tdiffe rver ymuc hbetwee nth e species studied. However,on eexceptio nmus tb enote di n caseo f Amblyseius potentillae attemptingt oinges t theconten to fth etetranychi d egg. For some reason this predator hasdifficultie s inpuncturin g theeg gchorion , as suggested bydirec t observationo fth epredator y behaviour. Küchlein (personal communication)measure da muc h lower rateo freproductio n ofthi s predator:i fegg so f Tetranychus urticae instea do flarva ewer e offered asprey . This result corresponds with themeasurement so fingestio n that indicated noabsolut e barriert oingestion ,bu tsom ehindranc e when compar-

Table 31. Theingestio n constants RRFI (min") o ffou rphytoseii d species inrelatio nt oth estag eo fth eprey .

Predator Egg Larva Proto- Deuto- Male Female species nymph nymph?

pnpnMnMnMnMn

Metaseiulus 1.9 27 1.11 0 - 0.111 0 0.71 2 0.071 8 °ccidentalis Atälyseius 1.8 12- -- -- "" "" bibens Anblyseius 0.25 2 0.8 9 0.62 6 0.31 4 0.42 1 0.152 4 Potentillae Phytoseiulus 1.8 38 - - 0.9 37 0.4 30 - 0.051 1 Persimilis NB-Th ecorrelatio n coefficients varybetwee n0.8 4an d0.91 ;th eintercept s areno ttabulate da sthe yar eclos et o zero.

77 ed with theothe rphytoseii d species.Anothe r conclusionca nb edraw nfro m the measurements inTabl e 31wit h respectt oth eeffec to fth epre y stage onth eabilit y toinges t itscontent ; themor e development proceeds,th e more difficulti ti sfo rth epredato rt osuc kth epre y content. Thisma yb e causedb yth einterna l structureo fth ebod y being very compartimentalized inth eadul t femalephase .Anothe r explanationma yb efoun d inrelatio nt o the time required forextra-intestina l digestion ofsoli d structures. De­ spite these differences inth emeasure d ingestion constants itca nb estated , that90 %o fth eoveral l ingestionpe rpre y takes place duringth einitia l 20%o fth epre y stage specific feeding timeso fth edifferen t predator spe­ cies (Subsection 3.2.8). Because thefeedin g times arerathe r shortand , therefore, also theperio d needed for90 %foo d intake,i ti sno tfa rfro m realityt oconside rth eingestio nproces s asa nimmediat e swallowingo fth e food content ofth eprey . This concepti sa prerequisit e forth equeuein g approacho fth eprédatio nprocess ,t ob ediscusse d inSubsectio n 3.3.1. Several times observations indicated, that even small prey wereno t consumed completely, asals o reportedb yLe e& Davi s (1968), Fransz (1974) andRabbing e (1976). Rabbinge presented indirect evidence forthi sphenome ­ non.B yassumin g that ingestionb yth epredato r equals itsgu temptyin go n the average ata constan t prey density,h eestimate d theprey-utilizatio n from thisequatio n aftermeasuremen t ofth erat eo fprédatio nan dgu tempty ­ ing.Thes e indirect estimations pointed toth eimportanc e ofpartia l inges­ tiono fth epre y content. Direct proofwa sgive nb yth efollowin g experi­ ments, using theelectrobalance . Females of PHytoseiulus persimilis were Til ° f0°d f°r dlfferent periods st-ting from full satiationan d subsequentlya femal e of Tetranyctus urtiaae wasoffere d asprey .Th edif ­ ferencem theweigh to fth epredato r beforean dafte r feeding weremeasure d with theelectrobalanc e andth eresult s arep lotted inFig .18 .A simila r

INGESTION(ju g) 9n

i i 1 1 2U 28 32 36 40 U i.8 TIME OF FOOD DEPRIVATION (HOUR S ;

feMl 'iii^'fromlemaleVof ^/T^ ^ ^ «» <*^"seiulus Per- Urticae a deprivation (T =2 "ci ± ^^ "er different periods of food \L ^C).l= standard deviation.

78 FRACTION OF P-LABELED EGG INGESTED 1.0- txt II«r:

0.5-

r 1 1 1 0 12 A 6 TIMEO FFOO D DEPRIVATION(HOUR ) 32 Fig. 19. Proportion of radioactivity ingested from a P-labelledeg go f Tetranychus urticae by individual young females of Metaseiulus occidentales after differentperiod s of fooddeprivatio n (T= 20°C).

32 experimentwa s done with females of Metaseiulus occidentalis and P-label­ ledegg s of Tetranychus urticae (Fig.19) .Bot h experiments demonstrate the occurrence of partial ingestion.Moreove r theshap eo fth e ingestion curve is of the saturation type instead ofsigmoid ,whic h suggests that thepre ­ datortend s to empty itspre y as far asallowe db y thesatiatio n deficito f itsgu to r the food content ofit sprey . As discussed before, the amounto f food inth e adult female spidermit e largely exceeds the phytoseiid gut volume. Inthi swa y anestimat e ofth e gutvolum ewa s already available.Howeve r asecon d estimatewa sneeded ,be ­ cause the apparent gut volume may depend onth epre y stage involved.Thi s was accomplished by allowinghungr yphytoseii d females (2day s fooddepriva ­ tion at T = 20°C) to feed on eggs and larvae instead of feeding on adult female prey until they were satiated. Satiationwa sdefine db yth eoccur ­ renceo f at least 10 successive contactso fth epredato rwit h itspre ywith ­ out subsequent attack. The weight difference between the predator before and after feeding until satiationwa smeasure d using theelectrobalanc e to estimate the apparent gut volume in case of small prey stages.Predator s unable to achieve satiationwithi n twohour swer ediscarde d topreven tover - estimation of thevolum e due togu temptyin gb y absorptiono regestion .Th e results indicated only asligh tinfluenc e ofth epre y stage onth e estimated 9utvolume, as shown in Table 32.Therefor e this aspectwa sneglecte d in further analyses for the sake ofsimplicity .Moreove r theresult s indicate that the interspecific differences ingu tvolum e areproportiona l to their size, as expected. Insummary , the ingestionproces s canb econsidere d asa n immediate swal-

79 Table 32. Theapparen tgu tvolum eo ffou rphytoseii d species,estimate dfro mth eweigh tincreas eo fhungr y femalepredator safte rfeedin go negg san dlarva eo f Tetra.nych.us vrticae untilsatiation .

Phytoseiidspecie s Weightincreas e(|jg ) n

Metaseiulus occidentalis 3.2 0.2 25 Amblyseius bibens 3.3 0.2 15 Amblyseius potentillae 5.2 0.4 32 Phytoseiulus persimilis 8.1 0.4 38

able1 PreY'Th S am°Unt °f f°0d COnSUmed is determinedb yth eavail - ofbot hf T gUt °rth e f0°d C°ntent °fth e *«*' deP-dingo nwhic h gestion 1S thS SmallSr °ne-T °lnlCUd e this asPect thepreviou sin ­ gestionformul aca nb eextende da sfollows :

T|^= 1 - e "RRFT-FT IF and IF= min(SDG ,FCP )

FT =feedin gtim e 1 =ingeste dfoo d

SDG I le f0°d COntent °fth e PrSy P« P«^tor SDG -satiatio ilTT ndefici to fth egu t

FCP =ingestabl ef oodconten to fth epre y

3.1.2 Gut emptying

amounto fC O tored,, . J, Predatorswer e 'drugged'b ya sligh t Nextthe ywer ebrought ^^ lr BObllity andweighe dusin ga nelectrobalance . abundantnumber so feaasl l ^"l 3rea' COnsistin9° *a pre ycolon ywit h untilsatiatio n JteT maleS'Wher e th^ were ^™* tofee d toleav epre yunharme d &üeT^^ """^ ^ SUCCessful stackspredator sten d 10successiv e failures'o f^ ^ ^^ "^ ^ predators' fron tlegs .Whe n reC rded the deredt ob esatiated .T o prevL ""* ° ' P^datorwa sconsi - togu temptying ,thi sserie^If ^° VereStimationo f the foodconsumed ,du e interval.Predator s ~m,-i^ ° SVentS had to take Placewithi na shor ttim e reguirxngmor etha ntw ohour s( T =20 oC)t o acnieve

80 satiation were therefore not considered. After an anaesthetic, the final weighto f thepredato r wasmeasure d and theweigh tincreas e afterth e hunger period inquestio n could be calculated. Theresult s of these experiments are shown inFigur e 20 foryoun g females of Phytoseiulus persimilis, at three different temperatures. Inagreemen t withHollin g (1966)an d Green (1965), theresult s showtha t thegu t isemp ­ tiedi na nexponentia l fashion:

RRGE FE= 1- e- *time

FE = fraction emptied RRGE= relativ e rate of gut emptying (time ) Moreover, temperature is an important factor influencing the rate ofgu t emptying. The RRGE values estimated fromth emeasurement s were almosti na straight line when plotted against temperature (RRGE in day" = 0.21 x (temperature - 11°C). Moreover these estimates showtha tth eingestio ncon ­ stant is much larger than the relative rate of gutemptyin gviz .70-270 0 perda y compared to 1-4 per day. Although this experimental procedure did produce some useful results, there were some problems in applying it for all thespecie s inquestion . Weighing of the individuals before and after feedingwa s ratherdifficult , because they were easily disturbed by the manipulations during transport causing a delay in the achievement of full satiation. Besides, the time Period allowed for the achievement of satiationmad ei tnecessar y to dis­ card almost 60%o f the replicates from the final results.Therefor e some alternatives were applied. The firstmetho dwa s toomi tth eweighin gproce -

WEIGHTO FFOO D CONSUMED(ju g) 9-,

I 1 1 1 1 1 1 1 r i i ' 0 t, 8 12 16 20 2/. 28 32 36 UQ U 48 TIMEO FFOO DDEPRIVATIO N(HOURS ) fiÇf- 20. weight of the food consumed until satiationb yyoun g females of Phytoseiulus persimilis after differentperiod s offoo d deprivation and at threetemperatur e levels, o,T =25°C ;A ,T = 20°C ;a ,T =15°C ; = standard deviation. 81 durean dt ofee dth epredato rmerel ywit heggs .A simpl eenumeratio no fth e numbero fegg sconsume dan dth edat ao nth eingestabl efoo dconten tprovide d awa yt oestimat eth eingestio nunti lsatiation ,thereb yneglectin gpartia l ingestion.Althoug hth eprocedur ewa smuc hmor esimple ,th e criterionfo r fullsatiatio nremaine da centra lproble mt oobtainin greplicate seasily . Thereforeanothe rmetho dwa sdeveloped ,base do nth eenerg yexpenditur ei n thephytosen dphysiology . Asdiscusse di nSubsectio n2.2.3 ,th ephytoseii d femalei scapabl eo f

producinga dai ly eggmas sequa lt ohe row nweight .Obviousl yth eleve lo f energyconversio ni sguit ehig hi nth eovipositio nphase .Therefor ei tma y isclf T Ï tte rSte °fabsor Ption of digestedfoo dint oth ehaemolymp h d fre roductio and 21 { nT4) *°absorptio *" "* °n fP amin acid- sAccordingt oTrehern e(1967 , el ;r : z r ° ° «* •»*«• *«» ** **^~ appear to V ^ Vertebrate int-tine in that these substances do not centrât^ T"*** ** ^^ ^^ tr™S*0^ »-hanisms against con- ITri 2 TtS- Wlth reSPeCt t0 Upids' the- -e also no valid a ~ ZZJTT^™^across the gut wa11' as — * andt or euî t r' 1 ^^tioa appearst ob elinke dt owate rmovement s duet oth e L T T C°nCentration gradientsdevelope dacros sth egu twal l beth eresul t f "^ ^ ^ haemo1» ^hesewate rmovement sca n is andarthropods are capabie f perfo in tic work (Be ge i^:r ° - ^ — abs r tion against cn " ^ ° P «* ** stores may even occur HOWv r c;:; en tra tlon gradients between the gut fiuid «* *» *-»*»*>• ^^rr^oT t e m h ^ ™dby diffusive ab~ induced by srores teins and Bmn ». • - Arapi d conversion of amino acids to pro- ar ldeS c0;: ntration g^dt t *° ^^^ *" tend to maintain a steep b the elements are ut ! ? ^^ ^ ^ ^ ' ^ — ^orbed food tion „m: z:z:n::g formation andfue i ^ ^ »*• °f ab^- CMe fa hi tU f energy.Hudso n )f ^^ *" " ° * — ° storesi sgreatlv ' „T eX*mPle' *" BhOWa that the del-eryo fgu t night.simTlari 7 ZVl ^^ "*«» «^ture. « forexampl e thebloo dÄI^^T 1 °fWatS r m0lSCUleS *- tbe <"«•>•»*in - waterlos sfro mth e^ ^ "TZ "^ "" *" » "^ <° isver yprobabl etha t Z t transP"ationan doviposition .Therefor ei t transpiration,an do fcour « Y related to egg formationan d course,vjc eversa . 0 bly d minate the ratS f *r -e;tseletf Tti:;an?;T; ° ° ^ -«**»* indicatesom edegre eo frecycli n o "tUbUl6 S (Akim°V & Starovir' 1975) tureo fth etwo-spotte dsüi d ^ °f^ W&ter' as °PPosedt oth e gutstruc - theegestio nrat eo nbasi sof^s^T f ^ Z-1^- *^ "*""*»° f quencyo fdefaecation so fas f h faeces dropletsan dth efre - ofth eegestio nconstan ttha ti^Ü f f^" ^toSeiüi«s resultedi navalu e

S/o0 fth erelativ erat eo fgu temptying . Based onth e above,tentativ e reasoning, therelativ e rateo f absorption (RRA)ca n be estimated from thebalanc ebetwee n ingestion andweigh t loss. Under conditions of abundant food thegu twil l approach satiation, andbe ­ causeth e gutvolum e ismeasure d (Subsection 3.1.1), RRA canb e fitted such that the rate of absorption compensates the weight loss occurring under these circumstances.Th eweigh t lossdu et oeg gproductio nca nb e estimated fromth e specific weight ofth ephytoseii d egg andth emeasure d rate ofovi - position. As well, an approximation of theweigh tlos sdu e to respiration andtranspiratio n canb e obtained fromth eweigh tdecrease smeasure d inth e starvation experiments presented inSubsectio n 2.2.6.Th e estimation ofth e relative rate of absorption iscarrie d outwit h asimulatio nmode l inwhic h RRA isth e only unknownparameter ,whil e theoutpu tconsist s ofth e rateo f oviposition. The structure of the model is based on the principle that arthropods avoid gluttony, sotha tther ema yb e anoptima l bodyweigh t above

W TERMINAL E OOCYTE I G H T fT R] R E A S N P S 1 P R L 1 A y ^RESORPTION R T 0 A 1 T 0 S 1 N 0 S N

PREY GUT 7 I E G N E G S E T S PREDATOR I T 0 I N 0 N

Pig. 21. Flow diagram ofphytoseii d energyexpenditure ,relatin g ingestion to oviposition.

83 whichth eabsorbe d food isspen to neg g formation andbelo wwhic h iti sspen t oncompensatio n ofweigh t lossdu et orespiratio n and transpiration.Becaus e the terminal oocyte absorbs the major part ofth e lipoproteins andwater , egg production canb e simulated by extrusion of the egg, ifth e specific weight of the phytoseiid egg is achieved. A flow diagram of this simple concept of the relationbetwee n ingestion and reproduction ispresente di n Fig.21 ;th eprogra m isliste d inAppendi xA .Wit h thismodel ,th erelativ e rateo fabsorptio n canb e fitted such thatth erat e of ovipositioncalculat ­ ed by themode l correspondswit htha tmeasure d experimentally. Theexperi ­ mentalvalue s ofth eovipositio n (Fig.22 )wer emeasure d at severaltemper ­ aturesi na colon ywit h abundantnumber so fpre y eggs foryoun g femalepre ­ datorso f Phytoseiulus persimilis and Metaseiulus occidentalis. Theoviposi ­ tiondat aconcernin g Amblyseius bibens and Amblyseius potentillae wereob ­ tained from Blommers (1976)an d Rabbinge (1976). The results arepresente d inTabl e33 .Thes e showtha t Metaseiulus occidentalis and Amblyseius bibens resemble Phytoseiulus persimilis greatlywit h respect to the estimatedval ­ ueso fRRA ,bu ttha t Amblyseius potentillae has amuc h lower level ofenerg y conversion, because of its lower rate of egg production. Moreover, for Phytoseiulus persimilis itca nb e concluded thatth e RRA estimates obtained by the present curve fitting procedure correspond very closely with the estimates of RRGE (= RRA) obtained by adequate use of the electrobalance. This correspondence may justify further use ofth eRR A values obtainedfo r theothe rphytoseii d speciesb y thecurv e fittingprocedure . Because these model estimations of RRA were obtained from reproduction

OVIPOSITIONRAT E (EGGS-DAY"1) 6

25 30 . TEMPERATURE(°C ) iTJlztioT* !"° VipOSition °f »o»ng females of fourphytoseii d species (n = HT . LTPeratUre (SbUndant f00d)- °< ^oseiulus persimilis

25),+ . Amblyseius potentiUae (Rabbinge/ 1976)

84 Table 33. Indirect estimations atdifferen t temperatures ofth erelativ e rate ofabsorptio n (day- ),base d onth eweigh t balance ofa phytoseii d female (seeFigur e22) .

Predator species Temperature(°C )

13 15 18 20 22 25 26 29 30 32

Phytoseiulus - 0.86 1.50 1.98 - 3.08 3.33 3.87 - 3.99 persimilis Ambluseius 0.31 - 1.32 - 1.86 2.55 - 3.33 - 3.88 bibens Metaseiulus - 0.72 1.33 1.62 - 2.54 2.55 3.15 - 3.21 occidentalis Ambluseius - 0.76 - 1.26 - 2.10 - - 1.52- potentillae Relative rate of- 0.45 0.68 0.78 - 1.01 - - 1.46- colour decrease A. potentillae (Rabbinge,1976 ) Relative rateof ------10.44- - - gutemptyin go f #• occidentalis (Fransz,1974 )

experiments forabundan t food supply,i ti sworthwhil et ocompar eth erat e ofovipositio n calculatedb yth emode l forlowe r levelso ffoo d supplywit h those measured inmatchin g experiments.Th emode l usesth eRR Avalu e esti­ mated atabundan t food supply andth erat e ofprédatio nmeasure d atsub - optimal levels of food supply, butth erat e ofovipositio ni scalculate d forlowe r food supply levels forcompariso nwit hth emeasure d reproduction. Twocomparison s concerning Metaseiulus occidentalis and Amblyseius poten- tillae arepresente d inTable s 34an d35 .Th eresult s showa clos ecorre ­ spondence between the calculated andmeasure d oviposition, which demon­ strates theusefulnes s ofth eestimate d RRAvalues .Apparentl yth egu ti s emptied ina nexponentia l fashion,a swa sals o foundb ydirec t measurement for Phutoseiulus persimilis. Inth esimulatio n model,th etim e requiredfo r transport, synthesis, utilization andallocatio no fth eabsorbe d gut-stores ^ theacarin e body isno tconsidered , because itwa sassume d that each molecule absorbed wasmatche db ysimultaneou s utilizationo fanothe rmole ­ ne. This assumptionwa steste d intw oexperiment s concerningth ereactio n °fth ereproductio n onsudde n changes infoo d supply.Th efirs t experiment consistedo fth emeasuremen t ofth enumerica l responseo f Metaseiulus occi- «entalis to sudden changes inpre y eggdensity , using twolevel so ffoo d s«PPly, both giving rise tosom e level ofreproduction . Themeasurement s ca"ied outb yKüchlei n were compared with matching simulations basedo n

85 Table 34. Simulated and measured rates ofovipositio n fordifferen t food regimes for young females of Amblyseius potentillae. The relative rateo f gut emptying is estimatedb y fitting itsvalu e in themode l such toobtai n an oviposition rate of 0.85 (or 2.26) eggspe r day at an average levelo f 95% gutfilling .

Temperature Coloration ofth e Measured rate of Simulated rate of a (°C) thegu t (expressed oviposition oviposition incolou runit s (eggs/day) (eggs/day) ranging from 0-7)

15 1.2 0.16 0 .00 2.0 0.12 0 .08 3.1 0.26 0 .22 4.0 0.27 0 .35 5.0 0.49 0 .49 5.9 0.68 0 .66 6.8 1.00 0. .85

25 1.2 0.00 0. .00 2.0 0.64 0. .22 3.0 0.83 0. .56 3.9 1.16 1. .00 5.0 1.33 1. ,47 6.0 1.65 1. .90 6.8 2.25 2. 26 a.Dat a fromRabbing e (1976).

the functional response atth e givenpre y densities (Table 36).Bot hmode l and experiment indicate the adjustment of the rate of oviposition toth e newfoo d levelwithi n oneday .Th e initially larger reproduction rate after ng hi9h t0 l0W eg9 d6nSity Wil1 theref TesT \T °- be caused by the ITtZ , T 9Ut St0reS and by the 6ggS alrea<* developed near toovipo ­ sition. similar but opposite reasons apply to the oviposition response ments 1? ^ ^ t0 Mgh ^ densitv- * another series ofexperi - Ïme -au! H aSSUmPti°n WaS tested * measurementan d simulation ofth e privation L "^ ^ Pr°dUCti°n '*" "^^ P«*"* of foodde - " reSUltS' PreSentSd in Table 37, demonstrate that the female h a reC Ver fr0m the (3 days f 0 0dƒ ° **«*«i°«" effects of severe starvation 1011 = 25 C) bef0re 1-ri;:; simlar: one?™' :— ::\::r:\::°-* ^ * " ^ (i977)Productio fonrwa -"-*s restarted» . valid forshorte rperiods ^o fsC;:^ 10118 ^^ ^ ±S ^

86 Table 35. Simulated and measured rates of oviposition at different prey egg densities for young females of Metaseiulus occidental is.

Preydensit y Measured rate of Simulated rateo f ... a (eggs/cm2) oviposition oviposition (eggs/day) (eggs/day)

0.2 0.1 0.1 0.4 0.4 0.4 0.8 0.9 1.0 5.0 2.3 2.5 10.0 3.2 3.3 20.0 3.4 3.5 30.0 3.5 3.6

a. Data from Küchlein (personal communication); T = 25-27°C; leaf area = 5 cm2; daily replacement of eggs consumed. The rate of prédation was not measured in the same experiment but in a similar experiment by Küchlein, presented in Table 57.

Table 36. The oviposition response of Metasei ulus occidentalis to sudden changes in prey egg density.

Simulatedrat eo f Female age (in. days ) Prey egg Measured rateo f ... a startiii g from final density oviposition oviposition moult (eggs/cm2) (eggs/day) (eggs/day)

3 10.0 3.3 3.3 4 10.0 2.6 3.4 5 10.0 3.0 3.3 6 0.4 1.7 1.5 7 0.4 0.4 0.6 0.5 8 0.4 0.5 0.4 9 0.4 0.55 0.4 10 0.4 0.3 0.4 11 0.4 0.4 12 0.4 0.4 0.3 13 1.5 10.0 1.3 14 3.3 10.0 3.2 15 3.3 10.0 3.2 16 3.3 10.0 3.1

2 a 5 cm ; - UnPUblished data from Küchlein; T = 25-27°C; leaf area 87 aily replacement of the prey eggs consumed. Table 37. Thetim e required forth eproductio n ofth efirs teg gafte r differentperiod so ffoo ddeprivation .T= 25°C ;hig h densityo fpre y eggs.

Predator species Period of food Time required forth e production deprivation (days) of the first egg (hours)

n measured simulated

Phytoseiulus 0 30 6.2 6.2 persimilis 1 30 11.3 10.7 3 30 13.5 14.2 6 16 18.2 15.4

Metaseiulus 0 15 6.3 occidentalis 6.0 1 15 9.4 7.9 3 30 18.6 10.9 6 15 27.2 11.7

Amblyseius 0 33 6.3 6.0 bibens" 2 29 12 10.2 4 26 12-24 11.4 6 15 12-24 11.8

a.Dat a fromBlommer s (1977).

Comparisono fth edat aobtaine do nRRG E(o r RRA)value s with thosegive n in literature reveals many discrepancies.A close r examinationi sneeded , therefore,o fth emethod s adoptedb yth edifferen t authors (Fransz, 1974; Rabbxnge, 1976). Fransz estimated RRGEb ya fittin g procedure relatedt o the observed predatory behaviour, insteado ft oth econversio nphysiology - He simulatedth epredator y activitiesi na par to fhi sbehavioura l observa­ tionsusin gth erelation sbetwee nth efoo d contento fth egu tan dth e beha- InaToI C°TTtS eStlmated fr°m the °therPar t °fth e observations,select - related ,"1 ^^ ** ^ ** ^^ C°nStant- This °r0Cedure «** behaviour &" ^ °f** ** " ^^ that enabled predictiono fth e sTZa int h° ne,rrt° fth S° bSerVati°-» thebasi so fth ebehaviou rob - tI t ; Part' SUCh S Pr°CedUre d0SS not' h-ever, guaranteae Rabbi" ;°n;f mGE' beCaUSS there »y »* «re thanon eLlution . ratioTo,U 7 a m°re direCt meth°d baSSd « ^ Prey-inducedgu t colo- "^L^Ti^T"'thecoloratio nbein gvisibl ethroug hit s ent in the ^^^^^^ ^ » ^rotenoids ^ Prédation, .though Rabbinge Lj^'J^^^ ^ ^^

88 correlated state variable, itma y give anestimat e ofth erelativ e rateo f gutemptyin g (RRGE). However, iti squestionabl ewhethe r therat eo fabsorp ­ tiono f other metabolically more important food elements, likeproteins , lipids and sugars, equal to that of the carotenoids.Anyway , theresult s obtainedb y Rabbinge and Fransz (Table33 )diffe r largely fromthos eo fthi s report.

3.1.3 Nutritive quality of the prey stages

There is some evidence that food quality depends on the developmental stageo fth epre y consumed. Because 60-70%o fth eingeste d food isutilize d inth eproductio n of egg mass, effects of food qualityma yb e determined fromth e rate of reproduction of aparticula r prey stage,i.e . ina pre y monoculture. However these kind of experiments aredifficul tt o interpret whenth e prey stages have no equal capture probability, which is due to prey-stage preference of the predator or the escaping capacities of the prey stages. In otherwords ,eg gproductio nma yb e loweredmerel yb y ade ­ crease in the food weight consumed, instead ofprey-stag e foodquality .A s willb e shown in Subsection 3.2.7,adul t femalepre yru nmuc h lessris ka t being captured than any other stage.Especiall y thispre y stagegive sris e to a lower rate of reproduction when offered abundantly in monoculture (Metaseiulus occidentalism. Croft &McMurtry ,1972 ;Croft ,1972 ;Pruszynsk i &Cone ,1973 ) (Phytoseiulus persimilis: Shehata,1973 ;Begljaro w& Hlopceva , 1965).Therefore , to analysewhethe r the lowrat eo freproductio n isdu et o alo wrat e ofprédatio n or tonutritiv e quality,measurement s ofprédatio n inmonoculture s of prey stages can be supplied to themode lpresente d in Appendix A and subsequently the reproduction ofth epredato r canb esimu ­ lated assuming that 1p g of food ingested from anypre y stageha sth esam e nutritivequalit y as 1M g eggmass . Inthi swa y indicationswer e found that spidermit e females aspre y give rise toa lowe rrat eo freproductio nmainl y becausethe y are captured less easily andhenc econsume d less frequently. Another approach is to compare reproduction rates inhig hdensit ymono ­ cultures of different prey stages thathav ebee nmeasure d atsimila r rates °fPrédation .Fo r example, Croft& McMurtr y (1972)use d Metaseiulus occiden- t'lis and measured a rate of prédation of about 10pre ype rda y forbot h eggmonoculture s and nymph-male cultures,whil e the appropriate rates of «productionha d arati o of3:2 . Similarly,Blommer s (1976)use d Amblyseius bl^ns and measured corresponding rates ofprédatio n for eggs andmales , whileth ematchin g reproduction had arati oo f4:3 .Pruszynsk i &Con e (1973) used Metaseiulus occidental and measured a higher rate of predatxono n e93s then on nymphs. However the rates ofreproductio nwer e equalo reve n rgheri ncas e of nymphs as food. °fcourse , under more natural conditions ofpopulatio n growth the age distribution of the prey mites will neverresembl e theextrem e ofa mono - 89 culture ofa specific agegrou p ofth emites .Althoug hth eproportion so f the different agegroup s inth epopulatio n arerathe r variable,ther ei s alwaysa mixtur eo fyoun gan dol dstage sdu et oth econtinuou s reproductive efforto fth eadul t females.Th eauthor' s experiments indicate thateve n slightsupplie so fegg st omonoculture so fpreovipositiona l females resulted ina maxima l rateo freproduction ; additiono f1 0egg st o3 0postovipositio n femaleso na lea fdis co f5 cm *raise dth ereproductio no f Metaseiulus occi­ dental's from 2.7egg spe rda yt o3. 6egg s perda y( n= 18 ,T = 27°C). Shehata (1973)foun d similarresult sfo r Phx/toseiulus persimilis. Therefore foodqualit yi sno tconsidere d inth emodel s presented.

3.2 RATEO FSUCCESSFU L ENCOUNTER

Inth epreviou s section (3.1), methods toquantif yth edynamic so fth e foodconten to fth egu twer ediscussed . Inthi s sectionth ebehavioura lcom ­ ponents, such aswalking ,resting , attackingan dfeeding ,ar edescribe di n relation toth e food contento fth egut .Thes e components aremeasure d during continuous observations ofth epredator ybehaviou ran dsubsequentl y relatedt oth efoo dconten to fth egu ta scompute d fromth erat eo fgu temp ­ tying (Subsection3.1.2 )an dth eobserve d time serieso fingestions .A tth e starto fth eexperiment s femalepredator s areintroduce d thatar estandard ­ izedwit hrespec tt oag e(3-1 0days) , feedinghistor yan dadaptatio nt oth e experimental arena (6hours) . Thecomputatio n ofth estat e dependentrat e ofsuccessfu lencounte ri sgive nb yth efollowin g formula forth etota ltim e spentpe rsuccessfu lencounte ri nsearching ,handlin gan dfeeding :

RSE ~ (RE-COIN-SR)

RSE =rat eo fsuccessfu l encounter (time-1) FT =feedin gan dhandlin gtim e (time) RE -rat eo fencounte r (time-1) COIN= coincidenc ei nth ewebbe d space(% ) SR -succes srati o (%)

h r a 0 & lth ±tS is preyp y aelLt-ectioe ctiondistanc ndTsT e (Subsection^ ** ^'« q^ •>* i ^- , „ ^ determinedb yth e j ofbot hpredato ran dp rey (sill I 3.2.3)an dth ewalkin g speed rections ofth eTi - ^section 3.2.2). Assuming thatth ewalkin gdi - followllgformul a "" "^^ ln**«*«*. Skellam (195B)derive dth e RE= 2- d• v • D prey IZVJIZLT^Z^ (M-^-> - -f « thedistanc eo f vectorso fpredato r V ""^ " ***resulta ^ velocityo fth espee d predatoran dpre yan di ti sgive nby : v'= v 2 2 pre+ v y v Prey+^predato r" ^prey-predato r— *

90 6represent sth eangl e between themomentar y directionso fpredato ran dprey . Takingexpectation s we get:

2 2 2 ,. sinceƒ co s 6=0 Ev = Ev pre+y Ev predator' i Mori& Chan t (1966) suggestth eabsenc eo fan yfor mo fremot e sensingi n phytoseiid predators. However, itma yb etha t thewe bthread s influence searching by acting asa warnin g signal forth epre y orb ydrawin gth e attentiono fth epredato r to active prey. These hypotheses areteste di n Subsections3.2. 1an d3.2. 3b ycomparin gth eresult so fa nactua l experiment concerningth erat e ofencounte r anda calculatio no fthi s rateb ymean so f Skellam's formula, where thepre y detection distancei stake nt ob eequa l toth esu mo fth eradi i ofth ecircumference s ofpre yan dpredator . Within apre y colony thephytoseii d predators display aver y tortuous walkingpattern . This mayhav etw oconsequences .Th erat eo fencounte rma y bedepresse d by revisiting areas already exploited.O nth eothe r hand,th e residence time ofth epredato r ina pre y colonyma yb eincrease db ythi s behaviour;fo rth eopposit e case,a straigh tpath ,a shorte r residence time willoccur , provided thepredato r does nottur nwhe n arrivinga tth eedg e ofth ecolony .Th eanalysi s ofbot hth e'recrossing 'phenomeno nan dth efac ­ torsinvolve d inth eresidenc e timei scarrie dou tb yobservatio nan dsimu ­ lationo fth ewalkin g behaviour (Subsection3.2. 4an dSectio n3.4) . The rate ofencounte r isals o determinedb yth ewalkin g activityo fth e mites (Subsection 3.2.5). Iti sdefine da sth epercentag eo fth eobservatio n timetha tth emit e spends walking.Assumin g thatth eactivit yo fbot hpreda ­ toran dpre y isindependen t ofth emomentar y activityo fthei r neighbouring mites,th erat e ofencounte r canb ecompute d byaddin git ssub-estimate s thatpertai n to three combinations ofpredato ran dpre y activity (walk- Walk,wal k- rest , rest- walk): \ 2 act act RRE,„, = 2- (r + r • \/vv + v 2 ' prey ' pred (r prey WW * prey pred) pred

RRE 3C ed WR = 2-(r + rpred> vpred • d-^rey' ' V WK v prey act &ct RRERW = 2-(r + Ved' V ' prey ' ^- pre^ KW l prey prey RE = (*™m + RREWR + RBERW> ' °prey RRE -relativ e rate ofencounte r (RE/Dprey) r =radiu so fth ecircumferenc e ofa mit e(cm ) act- _ - activity (%) ™» formula ofSkella m presented here isrestricte d toth ecas eo fa aeneous and two-dimensional surface. Itca nb eeasil y extended toa th -e-dimensional space/ as in tne web. However thedistributio no fth e Wit^ andthei r walking behaviour inth eheterogeneou s webstructur e 91 such thatth eprobabilit yo fa visi ti sno tth esam e forever y locationi n the vertical plane ofth ewebbe d space.Therefor e thecoincidenc e inspac e (Subsection3.2.6 )i sintroduce d asa factor ,whic h accounts forth epheno ­ menon that predator andpre y maypas s over andunde r each other.I nthi s wayth epotentia lnumbe ro fencounter so na two-dimensiona l leaf surfacei s correctedt oobtai nth enumbe ro frea l contactsi nth ewebbing . Notal lencounter s resulti nprédation .Th egreate r andstronge rth epre y stage,th emor e difficulti ti sfo rth epredato rt ocaptur eth eprey .More ­ over, themotivationa l state ofth epredator , asindicate d byth efoo d contento fit sgut ,ma ydetermin eit schance so fseizin g prey. Thereforeth e rate ofencounte r hast ob emultiplie d byth esucces s ratio (Subsection 3.2.7)t oobtai n anestimat e ofth erat eo fsuccessfu l encounter.Finall y the time spent handlingan dfeedin gth epre y after successful attack (Sub­ section 3.2.8)ha st ob esupplemente dt oth etim e spent searchingpe rsuc ­ cessfully capturedpre y item. Inthi swa yth etota l time spentpe rsuccess ­ fulencounte r (1/RSE)i sobtained .

3. 2.1 Width of the searching path

The circumference ofa predator ymit ei sno tfull y determinedb ytakin g the distance between thetip s ofth elatera l forean dhin d projectionso f the mite. Iti sals o related tobehaviou r that enlargesth eare a covered (Fig.23) .I nthi srespec ttw obehavioura l components canb edistinguished :

WIDTHO F WIDTH OF THEBOD Y THE SEARCHING PATH ( ) r

l<\

r-r+- i i i i r- i—i—i—i—r-i—r-T- . 5 mm- A * CA A A - A i A

i r~i—i—i—| n i i—i- T—r—i 'i "T"' r-i—i—n—i—i i i—r~i—r—i m I r~

™^ Tth° f the Searchin9 Path determined bybod y andfron tleg - movement ofa phytoseii dpredator .A , tarsio fleg s 2, 3an d4 ;A ,tarsu s ofbol v 1 arTS indiCate leg"movement<- straightlin e represents position ay-axis.Exgh tsuccessiv ephase so ff orward locomotionar egiven .

92 first,th e frequent turning ofth ebod y from onesid et oth eother ;second , asuperimpose d fast ambushing with the front legs, resembling theus e of antennaei nhymènopterou sparasiti cwasps .T omeasur e these actionssepara ­ telya vide o equipment (camera,recorde r andmonitor) , connected to abino ­ cularmicroscope , was used, thus offering the facility to fixth emovin g image. Theobservation s indicated that anincreas e ofth ewalkin g speed results ina decreas e of the lateral reach ofth epredator y female.Whe nth epreda ­ tori sdisturbe d by something thewalkin g speed isrelativel y high (Subsec­ tion3.2.2 )an d the lateral reach almost equals the breadtho fa restin g mite. In a state of complete restth e frontleg s aredraw nu p close toit s mouthparts, which causes the length tob e equal toth elengt ho fth esoma . Spidermites ,wit h their rigid shufflingwa yo fwalking ,d ono tsho wan yo f thesecharacteristics . Themeasurement s of the lateral and distal reacho fundisturbe d female predators in different states ofactivit y arepresente d inTabl e38 .Thos e ofth e spider mites are given in Table 39,relate d to the developmental stage, itma y be concluded thatexcep t forth erestin g stateo fth epreda ­ tors, the breadth of themite s isver y near tothei rlength ,s otha ti ti s notunrealisti c for simulation purposes toconceiv emite s ascircula r units witha diamete r equal tohal f the sum ofth erea l lengthan dbreadth .Thes e measurements will be used in calculations with Skellam's formula forth e rateo f encounter, for which the distance ofpre ydetectio n isassume d to beequa lt o the sum of the radii ofpredato r andpre y (Subsection 3.2.3).

7aWe 38. The lateral reach and thedista l length ofth e femaleso ffou r Phytoseiid species (n= 20) .

Predator State Length (mm) Breadth (mm) Diameter (mm) p à (length+ breadth)/ 2 species M °

phytoseiulus walking 0.98 0.147 0.84 0.068 0.91 Persimilis 0.020 0.565 resting 0.71 0.040 0.42 0.040 0.76 walking 0.81 0.038 0.71 Potentiliae 0.027 0.56 resting 0.69 0.034 0.43

0.020 0.605 walking 0.65 0.037 0.56 oibens 0.029 0.46 resting 0.62 0.030 0.30

eta 0.018 0.57 "Met.seiulus walking 0.62 0.033 0.52 0.028 0.445 resting 0.62 0.031 0.27

93 Table 39. Length andbreadt ho fth e developmental stageso f Tetranychus urticae (n= 10).

Developmental stage Length (mm) Breadth (mm) Diameter (mm) - M â M â (length+ breadth)/ 2

egg 0.137 0.007 0.137 0.007 0.137 larva 0.307 0.017 0.219 0.017 0.263 protonymph 0.411 0.040 0.272 0.035 0.342 deutonymph? 0.539 0.040 0.362 0.048 0.451 male 0.592 0.032 0.376 0.044 0.484 preoviposition female 0.749 0.077 0.443 0.082 0.596 oviposition female 0.779 0.061 0.534 0.061 0.657

3.2.2 Walking velocity

The walking velocity wasmeasure da sth e displacement along thetrac k peruni to ftime .Thes ewalkin g trackswer e registered with thevide oequip ­ ment showni nFig .24 .Thi s experimental setu pprovide da nalmos tperpen ­ dicular projectiono fth epath swit ha magnificatio no fabou t8 times .Al ­ thoughth eexperimenta l leaveswer e selectedo nthei r flatness,th ewalkin g tracksnea rt oth eedg eo fth elea fwer e incorrectly projectedo nth escree n due tn thecurvatio no fth e leaf and therefore discarded.T opreven tan y possible orientationb yth emite so na surroundin g unequal lightdistribu ­ tion,th eexperimenta l leafwa s enclosedi na n'opal ' Perspex cylinder, which diffused the lateral incoming light.Th eligh t distributionwa smea ­ suredwit ha seleniu m unitconnecte dt oa nampère-meter .Th eradiatio n flux variedbetwee n2 an d2. 3Wat tpe rm *nea rth eleaf . The walking time wasmeasure d simultaneouslyb ymean so fa sto pwatch ; each1 0secon d periodwa smarke do nth edrawing so fth ewalkin gpaths . The walking activityo fth emite s was frequently interruptedb yshor to rlon g stops.Thos e stopstha tlaste d less than1 secon d couldno tb e separatedb y observers from thewalking-tim e registration duet olag si nreactio ntime . From these measurements ofwalkin g timean ddisplacement ,th emea n walking speed wascomputed .A nattemp twa sals omad et ocharacteriz e thevariatio n inwalkin g speedb ycomputin g thevarianc eo fth evelocitie si nth earbi - trary 10-secondperiods .

vaJon Tin9 Vel°City WaS StUdi6d ln relati°n t0 the Periodo ffoo ddepri - SoTlt 'webbing and the side of the leaf- T° ^ythese rela' walkLJth Very lmP°rtant t0 dlStinguish ^tween edge-oriente b d walks and re": ££.£^iToVT e inspection of leaf-edge-relate' J""^ ^ d structure^ s~ an~d the ^regula r

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97 *: o returno fth emit etoward sth elea fedg eafte rloosin gcontac twit hit . A fewtime sth emite slos tcontac twit hth eedg ean ddi dno treturn .O nthos e occasionsthe ywer eswayin gt oan d fro;t oth eautho rthe yappeare dt ob e disoriented. Onlyth ewalkin gpath so nth elea fsurface ,i.e .no tedge - oriented,ar euse di nth etreatmen to fwalkin gvelocity .Th eedge-oriente d walkwil lb ediscusse di nrelatio nt oth etim espen toutsid eth epre yaggre ­ gationsfPar t 7\- Thewalkin gbehaviou rca nb estrongl yinfluence db yexperimenta lmanipu - lation.Fo rexample ,disturbance sca nb eobserve dafte rth epredator ymigh t aredisplace db ya brush .T oillustrat eth eeffec to nth ewalkin gspee dsom e measurementswer e made ofth ewalkin gbehaviou r ofdisturbe dpredators ; thesear egive ni nTabl e40 .Disturbanc ediminishe swithi ntw ohours .There ­ foreth ebehavioura lobservation so fpredator swer euse donl yafte ra rest ­ ingperio do fsom elengt h( >5 min.) ,s otha tth epredato rstarte dwalkin g spontaneously. Theeffec to fth estarvatio nperio do nth ewalkin gspee do fth epredator s isprobabl yrathe rcomplicate d (Table40) .whe nstarve dfo rtw oconsecutiv e studio "Wh °le daY'th eWSlkin gSpee d °fa1 1fou rPhytoseii dspecie s studied increased byles stha n 30%.However ,whe n A^lyseius titens was creall *"J**0** °fleS S than * **y. thewalkin g speed initiallyin - meLured ™bBeQUently f°ll0Wed * *urease . The latter effectwa sals o (tob e ,TT dneSS & MCMUrtry (1972) f°r ^^eius largoensis. Küchlein ty/actlvt /d) f°Und indirSCt 6VidenCe f°r an in— - -Ikingveloc - thTprev ,7 the CaSe °f Met*S^s occi.entalis atlo wdensitie so f thepre y(fro m3 egg spe r5 cm *t o1 eg gpe r! 0«»a, . Observation^0"te "*eratu™ °nth e displacemento ffemal ephytoseiid s (= wakZ ) 7* Walklng SPeed X fraCti°n °f« * observationtim espen t bY EVerS n (1979) Snd Penman & Cha coneu dd ITT ° P— <"80).Everso n e diSPla f e ce bytem D r — ° ^oseiulus persiffliiiswa s L influ- y P e n b th a gl3SS SUbStrate Chapln obta ; ° ° "°* *bea nleaf .Penma n* of1 5"» e ! Slmilar 6VidenCe f°r «**"*"*>* occidentals inth erang e IVdeer " t hUmidity = ?5%)'bU t beloW 15°C displacementwa sclear - of TetTnTl' """ *" ^ ^^ ^ these au^ors forth ecas e fsIa^oT UrtICae- ThS rSSUltS °fth S PrSSent *™y <™>le40 )indicat e ki incLLi "r™ r - — - - ~s .tt^.™ . dityleve li , J Accordingt oPenma n& chapma n (1980)th ehumi - seiuluTU« ƒf 1110"lmP °rtanCe for th*displacemen to ffemale so f Meta- seiulus occzdentalxs and Tetranychus urticae theApre0dUa9torrP:ratUre^ ^ "^ '^^ °*th e-Ikin g velocityo f WaS min r COmPared t0 that fth e poit[ onno fth e ,\ ° g speedo fth °e fou BLucturr phyt ean iidd specie s :tudie: w:; ^r r «c rr °- downward-facingsid eo fth eit. " ruZT^^• ^ ^ ^^ ^ ^ leafshowe d thatth S , Turningexperiment swit hth eexperimenta l thatthi sresul twa sno tcause db yth etextur edifference sbe - 98 t&SMrçr if

1

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Fi g- M- A.Bac k view of a femalepredato r (Amblyseius potentillae) resting next to a leaf mid-rib (magnification: 90x ) . B.Detai l ofth etarsu so f the hindleg (magnification: 6000x )show ni nA .Notic e thepositio n ofth e Cla"s and the swab-like empodium and comparewit hth epositio no fth ecla w re»nantsan d the empodial hairs ofth e spidermites ,show ni nFigur e26 .

99 tweenth euppe r and lowercuticle ,bu tprobabl y by gravitational force.Thi s phenomenonma yb e related toth e adhesivepropertie s ofth e swab-likeempo - dium and the claws of phytoseiid mites (Fig. 25),becaus e their walking speed was not reduced when walking on the mid-rib ofth e downward-facing sideo fth eros e leaf.Th ewalkin g speed ofth e spidermite s was notinflu ­ encedb yth epositio no fth e leaf,possibl y because they are always attached toth eleaf ,a swe b threads are continuously produced during walking (Saito, 1977a). Artificial trembling of the leaf caused the spider mites andth e predators to lose contactwit h the leaf surface,bu t itwa s often observed that the two-spotted spider mites crawled along its web thread up toth e surface after thismanipulation . Bothspide rmite s andpredator y mites walkedmor e slowly in awebbe den ­ vironment (Tables4 0 and41 )i fcompare d with theirwalkin g velocity onth e upward-facing side ofth eros e leaf.Eve n aver y lowwebbin g density caused thepredator y mites to slow down.Th ewe b structures were inspected inten­ sively with their front legs. Once apassag e through these structureswa s detected a forward movement was made. Presumably the long dorsal setae pointing backwards on the pear shaped phytoseiid body serve as awedg ei n the sticky web during forward locomotion. Sandness & McMurtry (1972)re ­ ported that the stickiness and thephysica l presence of several strandso f webbing impeded theprogres s of Amblyseius largoensis. Inth epresen tstud y itwa sobserve d a fewtime s that females of Amblyseius potentillae stuckt o thewe bwit hthei r dorsalplate .A n explanation forthi s fact couldb efoun d in the absence of long setae onth e dorsum of Amblyseius potentillae, the longer setae being positioned near the edgeo fth e dorsal plate. Itma yb e worthwhile toreconside r acarinepredator-pre y relations from this pointo f view. When mites are in the webbing the influence of gravity can bene ­ glected. Likewise,th e effecto ftemperatur e on thewalkin g velocity wasno t significant formite smovin g inth ewebbing . Surprisingly the same ruleap ­ plies toth e interspecific differences.Thi s implies thatth ewalkin gveloc ­ ityi sno tresponsibl e for any interspecific difference in the intra-colony rateo fprédation ,bu t itma yb e relevant inth e specific capacity ofinter - colonydispersa l (Part2) .

3.2. 3 Distance of prey detection

As statedb yMor i& chan t (1966), initial contact of Phytoseiulus persi- milis with itspre y appears tob ematte r ofchance .Th epre y mites areap ­ parently first detected by contact with the anterior tarsi of the front legs which are extended in front ofth ebody .Afte r contact thepredato r usuallymove s closer toth epre y andpalpate s itwit h itspedipalp s before penetrating the mite's soma. On the basis ofbehavioura l observations and scanningelectro nmicrograph s ofth e setae onth epedipalp s and the anterior

legs IJackso n (1973,i 974)suggest s thatmechanoreceptio n andcon - 100 mmmmmmm )\ 1 ')

k-

•U-' < •

Fi? • 26. Tarsus of amal e of Tetranychus urticae (magnification: 6000x) . Noti=e the position of the empodial hairs on the webbing strand and the

^ition of the four claw remnants (tctp« ovuXoi, four fingers) aside of this strand.

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102 tact chemoreception is involved at both tarsal and palpal contact with the prey. However web may interfere with searching by providing a warning signal to the prey or by drawing the attention of the predator to active prey. Therefore a distinct validation of Skellam's model is needed. To accomplish this, estimates of the rate of encounter were compared with the results of an experiment where the encounters between predator and prey were scored on a time scale. Hungry predators (0.5 days food deprivation, T = 20°C) were used to ensure reaction to the presence of prey, if any. The experiments were made in the presence and absence of web. The effect of the mobility of the prey was also investigated, using eggs and females of Tetranychus urti-

Table 42. Measured and simulated rates of encounter between female phytoseiid predators and a mobile (female) or immobile (egg) stage of Tetranychus urticae in absence or presence of webbing.

Predator Prey stage Webbing Rate of encounter (number/min) Total observation species and density simulated measured time

Phytoseiulus 4 eggs absent 3.26 3.35 32 Persimilis per cm* Anblyseius 36 eggs absent 16.3 18.9 21 Potentillae per cm* 96 2 eggs absent 0.91 1.08 per cm2 160 0.25 eggs absent 0.12 0.14 per cm2 1.10 86 Vetaseiulus 4 egss absent 1.13 °ccidentalis per cm2

222 Ph present 0.47 0.57 ytoseiulus 4 eas9s PersinUis per ^2 0.36 245 AMlyseius 4 eaas present 0.32 »tentiii.e per9cm2 250 tetaseiulus 4 eaas present 0.30 0.34 Mentalis pe^cm2

h 92 > 9toseivlu a 1.73 s 10 ç present 1.76 Pei~simiii s per cm2 Ambit a 1.24 110 jyseius in o present 1.37 82 ^seiulus 10 oa present 1.34 1.25 Mentalis per'cm2

The walking activity of the female spider mite - 4%.

103 cae as prey. The activity ofth e female spidermit ewa s registered andac ­ counted for in thecalculatio n ofth e rate ofencounter . The femalepreda ­ tors, however, were only observed when they were active. Care was taken that the mites were accustomed to the experimental leaf,whic h wasplace d onwe tcotto nwoo l to keep the leaf fresh andpreven t themite s from leaving the leafsurface .Th e arenawa smarke db y asquar e onth e ocular of abino ­ cularmicroscope . Itwa s smaller thanth e rose leaf to avoid any edgeeffect . Therein theegg s (immobile category)wer e spread equidistantly. Inthi swa y unnecessary variation in the results as aconsequenc e of the casualoccur ­ rence of clusters of eggs were prevented. Forth emobil e femalepre ythi s wasobviousl yno tpossible .Th eprojectio n of the ocular square on thelea f surface resulted in an imaginary arena of4 cm2. A female predator wasal ­ lowed to traverse this arena and the number of contacts during the time spent in the arenawer e scored. On awebbe d substrate encounters wereals o scored when the projections of prey and predator on the horizontal leaf plane overlapped. The mean rate of encounter was calculated as thetota l numbero fencounter s scored dividedb y the cumulative time spentwalkin gi n thearena . InTabl e 42 themeasure d rates ofencounte r are given together withth e estimates according to Skellam's formula. From these results itca nb econ ­ cluded that the contribution ofolfactio n orwe b (=th e difference between the measured and the calculated rate)wa s always less than 20%o f thecal ­ culated rate.Fo regg s asprey , all differences between simulation andmea ­ surement disappear when the diameter ofth e simulated egg is doubled.Thi s suggests that the eggs are scented fromnea rby . Incas e thepre y isa mo ­ bile female, the measured rate turns out to be consistently smallertha n the calculated rate.A n explanation for this small but consistentdiffe ­ rence may be found in the warning action of webvibration s caused byth e predator. The overall conclusion istha tth e influence of olfactory or otherstimu ­ liemergin g from thewe b is low, sotha t iti s allowed tous e the formulao f Skellam for the calculation ofth e rate ofencounter .Thi smean s thatpre ­ datorypreferenc e for apre y stageo r the escaping capacity of thepre yma y forcomputationa l purposesb e considered to arise at themomen t ofcontact .

3.2.4 Walking pattern

The walking pattern of the predator affects the rate of encounterwit h prey m twoways . Inth e firstplac e itdetermine s the time spent in apre y colony.Whe nth eedg eo fth ecolon y does not influence thewalkin g behaviour of the predator, a straight path causes the residence time tob eminima l andth edistanc ebetwee n starting andmomentar y position (=linea rdisplace ­ ment) to be maximal. The more tortuous thewalkin gbehaviour , the smaller the linear displacement andthu s the longer the residence time of thepre -

104 datori na pre y colony. Of course,th e transitiono fcolonize d leafsurfac e touncolonize d parts of theplan tma y induce theretur no fa predato rwhe n itarrive s atthi s edge.However , such amechanis m hasno tbee nreporte ds o farwit hrespec t to Phytoseiidae. Inth esecon d place, aver y tortuouswalkin gpatter nma ycaus e adepres ­ siono fth erat e of encounter ifth epredato r devours thepre y itemsencoun ­ tered;th e predator may stay too long ona spo tpreviousl y occupiedb yde ­ voured prey. Predatory mites walk tortuously when searching inwebbin g (Fig.27) .Therefore , the walking paths being available fromth emeasure ­ mentso fth ewalkin g velocity (Subsection 3.2.2), itwa sworthwhil e toana ­ lyseth e effect of thewalkin g pattern onth eresidenc e timeo fa predato r ina pre y colony and on the rate of encounterbetwee npredato r andprey . Forthi spurpos e asimulatio nmode l ofth ewalkin gbehaviou rwa sconstructed . Thewalkin gbehaviou r of an individual animal canb e simulated asfollows . Eachtim einterval ,whic h is equal to thequotien to fste psiz ean dwalkin g velocity, the animal makes a forward movement with a change indirectio n overa fixed distance. This angular deviation is chosen atrando m froma distribution of changes in walking direction (-n, +n) obtained from the walkingpath s registered on video equipment. These angulardeviation s are found in principle by determination of the angle between two successive directions after a linear step of a fixed length (Fig.28) .Th eshap eo f thefrequenc y distribution strongly depends on themagnitud eo fth estep . 'Advancingwit h seven-league boots' the distributiontend st oth eGaussia n

FINISH J V— START

H^U

W* V- Walking path of a female predator (Päytoseiulus persimlis) on a Webb ^ leaf area.

105 Fig. 28. Determination of three consecutive angular deviations (A s-2' As-1' As} after pacing linear distanceso ffixe d length. or uniform-type, while fora smal l stepth etendenc y istoward sa Student - typedistribution .T ojustif y comparisono fdifferen t distributions measured and tofulfil l therequirement s ofa naccurat e description ofth ewalkin g paths,a ste p size isselecte d ofhal fth eaverag e lengtho fth emite s( = 0.04 cm), whichcorrespond st oabou t2 time sth este p lengtho fadul tmites . Correlationbetwee n successive changesi nwalking direction canb eaccounte d forb ya naut oregressio nmodel :

A A + A + s=V s-l

^s- directiona l changea tste p numbers X•.s= rando m processt oobtai n angular deviations froma frequenc y distribution, corrected forautocorrelation s o. •0 1 m autoregressioncoefficients m =orde ro fth eproces s The first-order auto regressive processi sthen :

AsVl'V = l+ Xs

The procedures to obtain and to interpret the values of the auto correlation correl^entS' *° CalCUlate the aut° regression coefficients from the auto ZlliT°n H ientS' and flnally t0 aetexmlae the order of the process are explained in Appendix B. theF°frreCZrehTiVe ^^^^ <* the results it is useful to describe Studentt•:::: ^^~;;r:r d tribUti0nS by theitor m0mentSbein " H~™ -< - -th —e Gaussiaiiitynan .d »etail so fth emeasure d distributions.Th eTuke ydistri - 106 butionwa schose ndu et oit sflexibilit yi nthi srespect .Th emathematica l formo fthi sinverse ,symmetric ,continuou san dcumulativ edistributio nis :

X =u + 0- Y s r p

107 P(%) 50 <

bU A^QTZ "ö^TTs" J -V L5? <^N-

QC. ^2g

Qfi

99.5 -

QQ ft - qq q - 99 95 -

QQ QQ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 : ANGLE DEVIATION RAD)

x=o.u a=0.8 X=0.U a=0.2

X=0.85 a=0.034 8

UNIT=DISPLACEMEN T AFTER 25 STEPS

Fig. 29. Relation between the shape of the frequency distribution of angular deviations andth e actual walking path. Two differently scaled Gaussian distributions and another distribution with a longer tailar e plotted on probability paper ofth eGaussia n distribution. The matching Simulations ofwalkin g paths areshow n below andth e computer program is listed inAppendi x D.

108 trackwit h fixed linear steps andb y subsequentdeterminatio n ofth e angular deviationbetwee n successive directions (Fig.28) .A tth een do feac hpat h thecollecte d angles were ordered into afrequenc y distribution (-n, +n) . Thisprocedur e and the subsequent estimationo fth eTuke yparameters ,aut o regression and correlation coefficients,plu s afina ltes to nth egoodnes s offit ,wer e executed with the aid of a computerprogra m constructed for thispurpos e (Ruardij, 1981). The paths canb e supplied toth eprogra m in thefor m of aserie s ofx, y coordinates via anx- y tabletconnecte d toth e computer.Th e distances between those coordinates areinevitabl y subjectt o irregularities due to human inaccuracy. Therefore aninterpolatio nmetho d (Splineo r Aitken-Lagrange) operate s inth eprogra m toobtai na continuou s walkingpat h along which the fixed step sizeca nb epaced .Overshoo tprob ­ lemswit h the interpolation at sharp turns inth ewalkin gpath s aresolve d initially by interpolation over smaller parts of thewalkin g track and ultimately by simple linear interpolation. The program was tested ina serieso fexperiment s with straight and circularwalkin gpaths . Thewalkin g tracks analyzed in this paragraph originate from solitary mites,walkin g on explicitly defined substrates. Ifth eeffec to fcontac t betweenpredato r and preywa s studied, thiswa s accomplishedb yputtin gth e Preyclos e to apredato r and subsequently removing itafte rth eoccurrenc e ofth edesire d action.T o obtain awebbe d areawithou tan yprey ,bot hmale s andpreovipositiona l femaleswer epu to n afres h leaf,fro mwhic hthe ywer e discarded after about 2 days topreven t eggdeposition .Th eresult s ofth e analysiso fthes e walking paths arepresente d inTable s4 3 and44 .T oge ta betterestimatio n of the correlationbetwee n successive angulardeviations , °nlyth e longest walking paths were used. Inmos tcase sth eaut ocorrela ­ tionsshowe d a low level of correlation, if any. Whensignifican tvalue s occurred (| 0 |> 2/VN; N = total number of steps), thesenormall y indicated afirst-orde r auto regressive process. The irregular pattern ofpositiv e andnegativ e values also supports the conclusion, that the mites do not showa n autocorrelated walk. The evaluationo fth edifferen ttreatment si s facilitatedb y tabulating the linear displacementafte r20 0ste punit s next t°th evalue s of the Tukey parameters andth eaut ocorrelations .Fro m these displacements it can be concluded thatth eeffec to fth estarvatio nperio d is rather small, even incombinatio nwit hpreviou s contactwit hprey .How - ev*r, thesubstrat e appeared tob ever y important,a swa s alsoth ecas efo r th*walkin gvelocity . The tortuosity ofth ewalkin gpath s inth ewebbin gi s «pressed by an increase in the value of the scaleparamete ra ,whic hi n ***cause s the decrease inth e estimated linear displacement.The »P°«*« » 0f thepredato r on the upper orundersid e ofth e leafdoe sno taffec tth e dikingpattern , although thewalkin g speedwa s severelyreduce do nth esid e fa'ingdownward . Consequently three regions canb edistinguishe d onth e Wlthrespec t to thewalkin g speed and thewalkin gpattern : * theuppersid e of the leaf,th emid-ri b onth eundersid e ofth e leaf

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en m r> t-~ ai r- in co oi in cs m cs co cs r-l Ol •* co KD Ol o o o cs o i-l O o o o o o O o o o I I I I I i i

r-l u u 0) 0> Ol 01 01 73 m ft T3 •H X! ft- g a a P w o. c 3 3 >i 3 3 +j Dl •H C Ul •H C co g •Q (U •p a o o ö 2 S> •cH s G Ö T3 0 C H O ,0 0 «H •H P «H (0 0 •>H 00 00 CO CO 11 M cs cs g cs cs I •H a CO (U o * 00 00 H T3 CS <* * cs cs to Ol 3 W IJ i-H W 3 "-I 3-H U •H f-l •H i-S 0 CU-N 0) 'H •p W +J w e (0 ui q Cu M T3 "-s -. 43 -P jq 0) U a o cd ,Q 3 0. the stem: fastan d straightwalk ,predominantl y edge-oriented - theundersid e ofth elea fexcludin g themid-rib : slow and straightwal k - thewebbe d areao fth e leaf:slo w and tortuous walk. Evidently theresidenc e timeo fth e femalepredato r per unitwebbe d areai s promoted relative to that per unit of any other plant area.Thi s tendency becomes even more obvious when the data onwalkin g activity atth eabove - plantregion s (Subsection3.2.5 )ar e considered. Itma y be questioned whether the presence or abundance ofpre y inth e webbed area has an additional arresting effect onth e femalephytoseiids . Forexample ,severa l arthropodpredator s andparasitoid s change theirwalk ­ ing pattern from straightt otortuou s after contactwit h apre y item,pre ­ sumably to increase the probability of a subsequent capture of patchily distributed prey (Hassell, 1976,p . 50-55). Besided, thewalkin g speedan d walking activityma ydecreas ewhe npredator s arrive atloca l patches ofprey . Finally, there may be somepatch-specifi c signal causing the return ofth e predator when it arrives at the edge ofth e colony. To elucidate therol e ofth e above factors inth ecausatio n ofth e residence time thewalkin gbe ­ haviour is also measured in colonies withpre y and experimentally defined residence times are compared with estimates, based on simulations ofth e walkingbehaviour ,whic h assume the absence of specific returns of thepre ­ dator, when arrived atth eedg eo f thecolony .Bot hmeasurement s andsimu ­ lations'ar ediscusse d inSubsectio n 3.4.1. Togiv e agenera l ideao fth e sensitivity of the linear displacementfo r the parameters of the Tukey distribution and the auto regressioncoeffi -

MEANLINEA RDISPLACEMEN T

*=-0. 1

X=-0.85

0 100 200 500 ' ^00 NUMBERO FSTEP S Fig. 30. Mean linear displacement, expressed in step units, in relation toth enumbe ro fstep smove d atdifferen t levels ofX (a= 0.2) .

112 MEAN LINEAR DISPLACEMENT

200-

180-

160-

U0-

120-

100-1

80-

60-

40

20

I 1 1 1 1 I I I 0 0.1 0.2 0.3 0Â 0.5 0.6 0.7 0.8 a(RAD ) Fig. 31. Mean linear displacement after 200steps , expressed inste p units,i nrelatio n toth escal eparamete ra a tdifferen t levelso fth eshap e parameter X.

cients,thre e graphs aregive nbase do nth emea nvalue so fa serie so f100 0 Montecarl o simulations. Ineac h graphth emea nchang ei nwalkin g direction

ischose n tob eZ ero andth evalue so fX ar ethos eo fth eapproximat e uni- *>» (X= 1),norma l (X= 0.14 )an dStuden t (A= -0-85 )distributio n sup- Pliedwit h onerealisti c intermediate (K =0.1) .I nth efirs tgrap h (Fig. 30)th enumbe r ofstep s takenb yth eanima lar evarie da ta consta n eve <*th escal e parameter. Therelatio n between thelinea r displacementan d thedistanc e walked appears tob enon-linear .Thi s resulti sexpiate do

basis0 fth eprobabilit y toretur nt oth eorigina lposition .Afte ron e P thisprobabilit y iso fcours e equalt ozero .Eac h successive step,«1 1_ - «easeth eprobabilit y ofreturn , dependingo nth etortuosit yo fthewalkin g

Pattern.However , bymovin g away from theorigina l ^^J°^%ahle. Possiblereturnin g paths become morean d-r e compe x nd u ^^ Jnothe rwords ,th eprobabilit y ofleavin ga circula renv i

»ithenl argement of the circle. with respectt oth eothe rgraphs ^onl yth e ^near displacement after 200step s isgiven .Th esecon d graph (Fig. J

*°ws an exponential increase ofth elinea r displacement

-lueso f thescal eparameter .Seemingl ysmal l -/^^^^Hisplacement. meterca nthu shav ever yimportan tconsequence sfo rth eli n ** thirdgrap h (Pig.32 )show sth eeffec to fpositiv ean d «^J^ «*th efirst-orde raut oregressio ncoefficient . ^^J^^^T

-se« correctiQn Qf sharp turns inth e walkin^^»^1.11, less opposite turn.A sca nb esee n fromth egraph sthi s 113 MEANLINEA R DISPLACEMENT 200-

-0.75

Fig. 32. Mean linear displacement, expressed inste p units, inrelatio nt o the first-order auto regression coefficient a atdifferen t levels of X( a =0.2) .

promotes thelinea r displacement. Positive correlations, however, intensify the turnings instead ofcorrectin g them, thus causing a decrease of the linear displacement. From these simulations itca nb econcluded , that within the range ofmeasure d parameter values (-0.4< X < 0.14; 0.1< a < 0.6; -0.2 < a <0.2 )th evalu e ofth escal e parameter ismos t decisive forth e linear displacement, subsequently followed byth eshap e parameter, while the autoregression coefficients areo fmino r importance. The above method tosimulat e thewalkin g behaviour ofa nindividua l ani­ mal canb eextende d forth ecas e oftw oo rmor e animals encountering each other. Then theanimal s arerepresente d bycircle s andeac h time stepi s considered tob eequa l toth equotien t ofth este p size andth ewalkin g velocity ofth efastes t animal. Foreac h time step theposition s of the circles aretrace d andne wencounter s registered ifth edistanc e between the centres ofth ecircle s issmalle r than half thesu mo fthei r diameters. Such amode l isliste d inAppendi x Dfo rth esimpl e case ofimmobil e prey and equidistant distributions ofth e prey items. This model isuse d toexa ­ mineth eeffec to ta tortuou s path onth erat e ofencounter . Imagine anare a so large that even a straight path ofth epredato r starting atth ecentr e n r Ult ln 9 C nfr0ntation !auL s°t ,T ° "ithth eedge .Th epre yegg sar esprea d I'3! and 6Ver* « —d byth ewalkin gpat ho fth epredato ri s affect; T °fth S lar9e arSa the nUmbSr °f «** removals will hardly affectth h e value ofth eoveral l prey density. A tortuous path byth epreda -

114 torma y give rise, however, toa frequent recrossing ofa sub-are a previous­ ly freed ofprey , sotha t a prediction ofth e rate ofencounte r with the aido f Skellam's formula results ina noverestimatio n due toit s dependency on the overall prey density. Ona webbe d substrate predatory mites exhibit a tortuous walk, independent ofth epresenc e ofpre y (Subsection 3.4.1). Therefore a simulation experiment was done ata pre y density of4 eggs/cm2 overa 100 0 step walking track. The simulated mean rate ofencounte r after 100 replicates appeared tob eequa l to81 %o fth e Skellam's estimate.O f course, aparto fth e eggs andth e moulting stages, the mobility ofth e other prey stages lower theprobabilit y onloca l depressions inthei r density. Simulations forth ecas e ofmobil e larvae resulted ina nestimat e equalt o 94%o f the Skellam's estimate, sotha t the effect ofa tortuou s walk onth e rateo fencounte r ina pre y colony mayb econsidere d tob ever y small.

3.2.5 Walking activity

The walking activity ofth e predator refers toth e fraction ofth e obser­ vation time the animal spends walking. The walking and resting periods were measured partly with the aid ofth e video-equipment described inSubsectio n 3-2.2, and partly with the aid ofa binocula r microscope. During the conti­ nuous observations thestar t anden do fth e walking periods were recorded ona tim e scale. Theactivit y isno t computed asth e quotient ofth e total walking period andth eobservatio n time since once amit e starts walking, walking during thenex t time unit isver y probable. Therefore to reduce these correlations, theactivit y isconceive d asa Bernoulli ! variable( 0 °r 1)th evalu e ofwhic h isdetermine d atrando m moments during the obser­ vations within thedesire d limits ofth e relative food content ofth e gut. The number ofdetermination s ofth e Bernoulli! variable needed toattai na specified accuracy atth e 5%level , were calculated with the binomial sam­ pling formula (a= 0.05; d= 0.04 x y/ZdZ&q?: Pr(|p-P|> d> =a • >Th e re~ suits are presented inTabl e 45. ••*•** Theexistenc e of interspecificdifference si nth eleve lo factivit ybe - c°»eclea rb y comparison ofth e activitylevel sunde rwebbe dan d ™bbed circumstances.Th eactivit yo f Phytoseiulvs persimilis decreasesdu et o e factorweb ,almos tirrespectiv e ofth epresenc eo fprey .I n «j«*^^ activityo f Metaseiulus occidentalis seemst ob eunaffecte d y e 19 *»an dth esam eapplie st o A^lyseius titens. but* ^ •'•""" "9?7).

-ntlyie SS activefo rabundan tpre ysuppl yi nth ewebbin g( B- - ?>• A —

Predator Timeperio do f Activity (%) species food deprivation (hours) substrate

leafwit h leafwithou t artificial webbing webbing substrates

Phytoseiulus 0 (+ prey) 8 68 75 persimilis 24 9 30h 48 16 120 12

Amblyseius 0 (+ prey) 19 14 potentillae 24 17 10 48 16

Metaseiulus 0 (+ prey) 36 39C, 52d occidentalis 48 43 120 41

Amblyseius 0 (+ prey) 46e bibens 82 6 66€ 12 82 30 97 56 94 120 48 144 29 168 34

Tetranychus urticae females 4 72 males 5 65-80h juveniles 4

a.Takafuj i& chan t (1977);T = 25° Can dR H= 75-90% b.Mor i& Chan t (1966);T = 23° Can dR H= 76%. c Küchlein(t ob epublished) ; T= 27° can d m =70 % d. Fransz (1974);T = 27° Can dR H= 70 % e.Blommer s (1977);T = 28° Can dR H= 7 °o%

116 ciesmove d actively in thewebbing , noeffectiv e displacementwa smade , On rareoccasion sth epredato r evenbecam e stuck inth ewebbin gwit hit sdorsum , presumably due to a lack of long dorsal setae inth ecentr eo fit sdorsa l plate.Unde r circumstances of abundant foodth espide rmite sar emuc hles s activei nth e webbing than any predator speciesstudied .Thi si sprobabl y duet othei r predominant feeding activities. When the food sourcebecam e exhausted,th e activity of all stages increased, leadingt oa stee pincreas e ofth ewebbin g density asmeasure d inSubsectio n2.1.6 . Thewalkin g activity of the predators was unaffected after starvation periodso fmor e than one day. However Amblyseius bibens showed adefinit e increase in activity after starvation periods of0. 5 dayso rmore .Sever e starvation induced a lower level of activity in this predator.Hungr y femaleso f all phytoseiid species were very sensitive to contact.Whe na femalespide r mite was used to bump against thebac k of thepredator sa drasticincreas e of the activity occurred duringth esubsequen ttw ohours . Satiatedfemale swer e almost unaffectedb y these actions.Fro mthes eobser ­ vationsi tca nb e concluded that the relationship betweenth ehunge rstatu s andth eactivit y is indirectly expressed bywa yo fdisturbance . Asfoun d for thewalkin g speed (Subsection 2.2.2), theeffec to fth etem ­ peratureo nth ewalkin g activity ofth epredator s iso flittl eo rn oimpor ­ tance,especiall y when the predators are studied in the webbed areao fa Preycolon y (Table 46).Spide r mites, however, are probably activated y increasingtemperatures . This canb e derived fromth e facttha tth erat eo «ebproductio n (Subsection 2.1.6)i s increased by increasingtemperature , incontras tt oth ewalkin g speed, which isonl y little affected inth erang e of15-30° C (Penman & Chapman, 1980;ow nobservation) . Mori& chant (1966) studied the effect of humidity onth e activlt* femaleso f Phytoseiulus persimilis ando f Tetranychus urticae. Thea c °fbot hpre y and predator was reducedb y increasinghumidit ylevel s ed -er,althoug h the qualitative effects ofhumidit ywer eclearl y ^^ ' «* extrapolation of their results to the plant substrate isno tallo w *» toth eus e of an artificial substrate.Moreove r thereaction s ofpred a col ny toran dpre y may be different in thewebbin g ofa pre y ° - ^^ an APartfro m its effect onth emea n activity, thesubstrat ea «fluence on the activity rhythm. In the webbed area therestin gp

Tab^ 46. The activity (%) of femalephytoseiid s residing lna pre ycolony , in relation to the temperaturelevel .

15°C 20°C 29°C

taseiulus occidentalis 38 36 41 ^Vtoseiulus persimilis 10 8 12

117 are frequently alternated with walking periods, while on anunwebbe dsub ­ strate these activities weremuc h less fragmented; inth e latter casewal ­ king periods and resting periods were longer than those for webbed sub­ strates.Thi s factan dth e findings discussed in Subsection 3.2.3 justifya modelling approach based onrando m inter-arrival times ofth epredato rbe ­ tweenit sencounter swit hpre yitems . Iti so fimportanc e tostres s that the factors discussed inthi ssubsec ­ tion do not determine the activity in a fixed way. For example, theleve l of starvation does notdetermin e the activity level,bu t rather determines theleve lo freceptivit y tostimuli .Also ,th e substrate does notdetermin e the level of activity nor the walking speed; hungry phytoseiidpredators , when disturbed artificially, can walk very fast in the webbingstructure . Disturbance by artificial means orb ybumpin g against anothermit e areno t the only stimuli evoking bursts of walking activity. For example,whe na predatory female leaves apre y colony onhe r own accord (Section 3.4)an d thusleave sth ewebbin g andenter s theunwebbe d part of the leaf,th ewalk ­ ing activity and thewalkin g speed ishig h during the firsthou r andtend s tostabiliz etoward sth eactivit y levels given inTabl e45 .

3.2. 6 Coincidence in the webbed space

The three-dimensional structure of the webbing may cause the predator andit spre yt opas sabov e andbelo w each other.Assumin g the occurrenceo f themite s to beequall yprobabl e ateac hpositio n in the webbing, thefor ­ mula of Skellam canb e easily extended to the three-dimensional caseb y taking themite s asspherica lunit s andb ymeasurin g the depth ofth eweb - ing. However, avertica l section through thewebbin g will certainlysho w that the spxdermite s are clustered near to the leaf surface duet othei r predominant feeding activities.Moreover , the eggs of the spidermite sar e or the ma:orpar t located in the lower layer of the webbing near toth e toward^f06" DUe t0 thlS hetsr°9eneity anextensio n of Skellam's formula ina th three-dln>ensional casewoul d bemuc h too complicated, yetleav - unconsidPeCUllaratleS ^ ^ Walkin5 behaviour of both predator andpre y two Til Sred" ThlS Pr°blem can fae solved more easily by multiplying the tweenrn nal f°rmUla °fSkeUa m with the factiono frea lcontact sbe - the leaf f *** *"* °Ut° f* U coinciding perpendicular projectionso n witha bi n I"' The measurement «fthi s fractionwa s done by observation tionabove 0" f miCr°SC°pe maintained continuously in aperpendicula rposi " Predat r The specifieda „ at* ° -5x ™*beei r of observations needed to attaina •-pC^r(. -r05 r • - <«^- - aidof *» «**? this way a rouahL ' = ^ * ^n* > = -)• In counterdu eJ \l "" °btained °*th ereductio n of the rateo fen -

webbmg forthre ediff erent phases incolon y growth:

118 - Phase 1 The webbing intensity brought aboutb y femalespide rmite sin ­ creasesrapidl y inth e initial colonizationperiod ,bu ti tlevel sof fafte r lesstha na da y as lateral expansion ofth ewe bbecome spredominant . - Phase 2 After hatching of the eggs, the juveniles contribute to the productiono fweb . - Phase 3 When the newbor n juveniles havematured , thefoo ddemand sin ­ creaseexponentially , so that ultimately the food source will becomeex ­ hausted, causing an increase of the walking activity of all stages and, thus,a nincreas e in thewebbin g intensity. Themeasurement s of the coincidence inthes ethre ephase sar epresente d inTabl e47 .Thes e results show thatth erat eo fencounte r isbein greduce d bya facto ro f45-55 % as aconsequenc e ofth eheterogeneit y ofth ewebbing , and,tha tthi s result is,surprisingly , independento fth epredato rspecie s andth epre y stage involved. Amor e expected resultwa sth edecreas eo fth e coincidence at the increased webbing intensity onth ehighl yinfeste dros e leaf.Durin g a part of these experiments the activity statuso fpredato r andpre y was taken into account (walk-walk,walk-rest ,rest-walk) .Th e re-

Table 47. Coincidence in the webbed spacebetwee n femalephytoseiid san d different stages of their prey at three phases of colony <3rov^h^ 12hours ; n= 350-600 ;pre y density =20-6 0mites/cm? ; adaptationperio d-">•>> • T= 20°C .

Predator Prey stage Coincidence(% ) sPecies colony growth colonygrowt h colonygrowt h phase 1 Phase 2 Phase3

33.0 Phytoseiulus eggs 47.3 43.4 Persimilis 28.2 juveniles 48.3 females 56.2 49.0

Anblyseius eggs 50.1 Potentiliae juveniles females 43.2

Anblyseius eggs 47.8 bibens 46.3 juveniles females 55.0

Met 52.2 *seiulus eggs 49.1 occidental is 46.1 24.3 juveniles 55.8 females 43.8

119 Table 48. Coincidence inth ewebbe d space between female phytoseiidsan d mobile stageso fthei rpre ya tthre e different combinations ofth eactivit y ofth epredato ran dtha to fth eprey . Prey density =20-4 0 mites/cm2; adaptationperio d= 1 2hours ;T = 20°C .

Predator Prey stage Coincidence (%) foractivit y combinations species (predator-prey)

walk-•walk walk-•res;t b rest-walk

Phutoseiulus larvae 45.5 48.0 52.5 persimilis females 47.5 45.0 49.4

Metaseiulus males 47.2 51.1 44.0 occidentalis females 50.2 49.5 48.4 a.Numbe ro freplicate spe rrati o= 100-150 . b. Numbero freplicate spe rrati o= 200-400 . c.Numbe ro freplicate spe rrati o= 150-300 .

suits, presented inTabl e 48,d ono tsho w effects ofquantitativ eimpor ­ tance.A similar conclusionwa sdraw n from measurements ofth ecoincidenc e usinghungr ypredator s (Table 49). itma ytherefor e bestated , that- excep t for exhaustion ofth efoo d source ofth espide r mites -webbin g actsa sa constant 'labyrinth'i nth epredator-pre y interaction atth ecolon ylevel - Itma yb eworthwhil e topoin t outth edifferenc e between thepresen t definition ofth ecoincidenc e inspac e andtha t of Fransz (1974). Fransz measured thesam e catalogueo fbehavioura l components of Metaseiulus occi­ dentalis oncircula r leafdisc so fth eLim a bean. Inadditio nh erecognize d theproble mo fspatia l heterogeneity incomputin g therat e ofencounte rbe ­ tweenpredato ran dpre yo nthes e discs.Th espatia l heterogeneity iscause d hereb yth erib s andth eedg eo fth elea f disc. Since predators prefert o walknea rt othes e structures inabsenc e ofwebbing , asmalle r leafare ai s scannedb yth epredator .Moreover , according toth eexperimenta l designo f the functionalrespons e (Küchlein,t ob epublished ; Fransz, 1974),th e eg*> were placed outside theribbe d areaan da tsom e distance ofth elea fedge - Forthes ereason sth eedg e oriented walk causes aspatia l heterogeneityre -

ultrngl n a reductiono fth erat eo fencounte r between predator and P^ cL benCd?ng the Pr°blem ^ this Wa*< the coincidence onth elea f di-" wasr ermineddireCtl Y^ WSS d°ne* «- author,instea do fi***** * Ïentwat " FranS2 (1974)- ™S Was accomplished bymeasurin g theti * llZlZTl 7the ribsan d neart oth e ed9- °f the ieaf disc'bein9Z Parently wasted time with respect toth etim e available forsearchin g t* 120 Table 49. Coincidence inth ewebbe d space between hungryfemal ephytoseiid s andegg so f Tetranychus Urticas, n= 150-250 ;pre y density= 20-6 0 mites/cm2; adaptationperio d= 0. 1hour ; timeo ffoo d depriv­ ation= 2 days ; observation period= 1- 2hour spe r predator;T= 20°C .

Predatorspecie s Coincidence(% )

Phytoseiuluspersimilis 46.6 Metaseiulus occidentalis 44.0

preyeggs . Inthi swa yi twa sfoun d that58 %o fth esearchin g time (133min ­ utes)i sbein g spent inefficiently. This resultca nb ecompare dwit h Fransz's indirectmethod , using Küchlein'sbehavioura l observationso nth eleaf^discs . Hemeasure da walkin g speed of0.4 7mm/ san da walkin g activityo f39 %i n presence ofpre y eggs.H eals o measured thenumbe r ofencounter s during 6-hourtim eperiod s atsevera l densitieso fth epre y eggso nth elea fdisc s andfoun da linea r relation betweenth enumbe ro fencounter san dth enumbe r ofpre y eggs onth e5 cm 2 leaf discs,th etangen tbein g equalt o2.236 . thespatia lheterogeneit y weret ob ediscarded ,th etangen tcompute d accor­ dingt oth eSkella m formula onth ebasi so fKuchlein- s behavi™ra^^ tionswoul d be equalt o5.5 4 (encounters per5 cm 2 per6 hou rpe r estimate ang e n t dividingbot h thedirectl y measured tangentb yth e \; T h e 'rate estimateo fth ecoincidenc e isobtained , which amountst o40.2/ o; ^^ ofencounte ri sthu s reducedb y60% ,whic h approximatesth eorigi n estimate closely.

3.2.7 Success ratio •,! „ (trichobothria)o f Afterdetectio no fapre ywit hit s™ * «^^^ subsequently thefron t legs thepredato rma ymov e closet oit scapt i

"- -iliary mouth parts arepushe d through the integument^JP J^

••«while inspecting thepre y withit spedipalps .Whe n* * attack ^ngswa snotice d during thebehavioura l ^^^Z encounter. w« scored, while tarsal contact ledt oth eregistratio no f T<* fractiono fsuccessfu l attacksou to fth etota lnumbe r fen cunt es

^rtherreferre d to as the success ratio.Thi s <*^°* ^M™' th *to fth ecoincidenc ei nth ewebbe d space,whic hred u estimate ornate ofth erat e ofencounte r between circularitem s ^ <*th erat eo ftarsa l contact.Howeve ro na nunweb > d1 .f , J Wal*ingpredator s inspectth eare a covered less intensively 121 ping front legs, which may laed to a failure to detect a smallpre ystag e located inthei rwalkin gpath . Intha tcas e another factor shouldb edefined , onetha texpresse sth etippin g intensitywithi n the area covered byth epre ­ dator'scircumference .Anothe r complication ariseswhe n thepre y encounters a resting predator atth eback . Inth ewebbing , this type ofprey-predato r contactgenerall y results instimulatio n ofth e locomotory activity,bu to n anunwebbe d substrate this sometimes caused aquic k turnb y ahungr ypreda ­ tor and a subsequent attack on theprey .Thi s apparent enlargemento fth e width ofperceptio nb yth ehungr y females canb e accounted forb ymultiply ­ ingth erat eo fencounte rbetwee n activepre y and the resting predatorwit h a factor,rangin g from 0.5 (noturn )t o 1. (turn). At the start ofth econtinuou s observations of the predatorybehaviour , femalepredator swer euse d thatha dbee n deprived of food for differentpe ­ riods since satiation. By transferring thepredator s from theMunge rcage s to the experimental arena with a brush severe disturbance would havebee n brought about very frequently. To prevent this artefact the predatory females were transferred on a leaflet, whichwa s placed previously inth e hunger cage as a refuge for thepredators . Inthi s way thepredator swer e allowed toente rth eexperimenta l arenao nthei r own accord. Theexperimenta l arenaconsiste d ofa pre y colony founded after aprece ­ ding infection of female spidermite s ona ros e leaf of an intactplan ti n the greenhouse. These leaves were cut off and placed upside down onwe t cotton wool in a petri dish. In another series of experiments unwebbed leaves were used stillconnecte d to apar to f their shoot.Th e shootswer e put in a test-tube filled with wet cotton wool and closed byplasticine . This leafsyste m formed aneasil y turnable unit.Th e prey items wereoffere d one by one toth epredator ,excep t forth epre y eggs, which were deposited by female spider mites and subsequently freed ofwebbin g and femalesusin g abrush . During the observations the behavioural elements were scored ina tim e scale. These time series of observations were analyzed afterwards bycom ­ puting the food contento fth ephytoseii d gut in aparalle l time serieso n basis of the observed ingestion history of the individual phytoseiid females and the physiological variables measured in Section 3.1.B ydivid ­ ing the gut content in 20 classes of food contents the encounters between predator and prey and the eventual successful attacks among theseencoun ­ ters were ordered in relation to the level of the food content ofth e Phytoseiid gut. The number of encounters needed to determine the class specific success ratio with apredefine d accuracy at the 5%leve l was^om- puted using the binomial sampling formula (a= 0.05- d = 0.1 x y/ldM^)' remn'tY/ * = °* ' ^ ^"^ °fobse ^ations per food content classwer e hiïorv of ° aCMeVe the desired —acy bymanipulatin g the deprivation over the S^artln9Predato r and the subsequent observation time.More -

er, the normal- prey densities in thepre y colonies happen tob equit e

122 high,e.g .th e egg density ranged from 20-60 eggspe r cm2 webbed leafarea . Thereforeman y observations canb e obtained ina reasonabl y shorttim espan . Mosto fth e observations were made at T = 20°C with colonies containing onlypre yegg s or only larvae andnumph so ronl y females oronl ymales .Som e observationswer e done atT = 15°C andT = 29° C incolonie s containingonl y eggs. Theresult s are presented in Table 50Awit h respectt oth ewebbe dsub ­ stratean d in Table 50B with respect to the unwebbed substrate.Smoothe d curvesar e drawn in Fig. 33 to accentuate themai ncharacteristics .Thes e revealconspicuou s interspecific differences among the phytoseiid species studied,whe n comparing the success ratios on webbed and weblessleaves . Thefacto r webbing induces alowe r level of success forth ecas eo f Ambly- seius potentillae, favours Phytoseiulus persimilis andhardl y affects Ambly- seius bibens and Metaseiulus occidentalis. With respectt oth eprey-stag e preference, the success ratio curves resemble eachothe r ina qualitativ e sense.Becaus e the ability ofth epre y toescap e from anattac ko fth epre ­ datorincrease s with itsmobilit y and its strength,egg sar eeasie rt ocap ­ turetha nlarvae ,etc. ; female spidermite s areth emos tdifficul tstag et o capture. In a quantitative respect, the prey-stage related successratio - curves differ among the phytoseiid species studied. For each predator specieso n its most favourable substrate,th e interspecific differencesi n successrati o levels suggest arelatio nbetwee nth ebod y sizeo fth epreda ­ toran d its predatory success. However, ifth e foodconten to fth egu ti s «pressed in weight units instead of fractions ofth emaximu m levelo fgu t filing, the relation of the success ratio with the satiationdefici to f thegu tdoe s reveal the samebu t lessconspicuou s interspecificdifferences . Somenote s on the predatory behaviour underlying the measured success «tios should be made. The adverse effects of webbing on the success of üfilvseius potentillae may notb e surprising duet oth e foregoingnote so n therestricte d mobility of this species inth ewebbin g (Subsection 3.2.2). Theeffec t of webbing on the success of Phytoseiulus persimilzs, however, needsfurthe r explanation. On an unwebbed substrate thispredato r species "alksfas t and spends more time inwalking .Whe na femal epredato r ofthi s secies bumps into a female spider mite,i tturn sbac k andrun s awaywit h a*increase dwalkin g speed,whic h indicates disturbance.Mor i& Chan t (1966) "Ported the very same effect. They found only5 successfu l stacks among 480 contacts between Phytoseiulus females and Tetranychus females.A tth e si <*o fth e leaf facing downward, where thewalkin g speed islowe rbu twher e diking activity is still high compared totha ti nwebbing ,thes eeffect s "** observed to the same extent.Apparentl y thewebbe d environment,wher e bot*Predato r and prey walk slowly, offers amor e favourable substrate,fo r P^atory activity of this species, disturbance being a rare Phenomenon Section 3.2.9). With respect to the success ratio againstegg sdistur - bai *e was never observed, so that other factors operate causing

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100 METASEIULUS OCCIDENTALS AMBLYSEIUS BIBENS

II I I —r~V' I I

PHYTOSEIULUS PERSIMILIS

0 102 03 0 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

RELATIVE FOOD CONTENT OFTH E GUT (%l Fig- 33. Smoothed curves of the success ratio in relation to ther e a ^ food content of thegu t for four phytoseiid species on small prey stage^ (E, eggs; L, larvae) andadul t females (AF); , predatory behaviour an unwebbed leaf; , predatory behaviour on a webbed leaf.

at unwel decreaseBMd succesSUCCesss oof Phytoseiulus persimilis against this stage " Phytoseiulus persimilis against this stage at ui fre- substrates. Al-t-h™,,^ 4- _ ,_*-4 -• substrates. Although tarsal contact occurred, the females left the e, gently unharmed without showing a rejective reaction, like running a« ^ For some reason their sensitivity in detecting the presence of the prtf inabSenCe f Webbin p bexHnt ° 9- °ssibly the inspection of the si*««.... _- :ti"n ing intensified in the diversely structured webbing, ensure oi a prey bv spvor=i that öeverai stated can be-- ^ w Phuto • consecutive contacts. Anyhow' it can 1 eiulus persimilis is very much web oriented, being less adap

126 capturea pre ywhe ndispersin gfro mwebbe dare at owebbe darea ,withi nwhic h successi sensured .Th edisturbanc edescribe dabov ewa sals oobserve dwhe n afemal eo f Amblyseius potentillae bumpedagains ta nactivel ywalkin gfemal e of Tetranychus urticae atth esid eo fth elea ffacin gupward .Th ebehavioura l reactionswer ever y similart o Phytoseiulus persimilis exceptfo rth efac t thathungr y femaleswer eusuall yno tdisturbe dbu treacte dmor efrequentl y byattac kupo ncontact . Incontras tt o Phytoseiulus persimilis, thedis ­ turbedreaction swer e almostabsen twhe nth e female-femalecontact swer e observeda tth esid e ofth elea f facingdownward ,wher ewalkin gspee di s low.i tma yb e stated thatth esucces srati odepend so nth ewalkin gspee d ofbot hpredato ran dpre yan dbecaus eth ewalkin gspee dvarie swit hth etyp e andth epositio n ofth esubstrat e (Subsection3.2.2) ,th esucces srati oi s relatedt othes easpect stoo .Fro mthi spoin to fvie wi ti sconceivabl etha t thesmall-size dphytoseii dspecies ,lik e Metaseiulus occidentalis and Ambly- seius bibens, are lessaffecte dwit hrespec tt othei rsucces sratio ,bein g relativelysluggis han dles ssensitiv et odisturbanc e (Subsection3.2.2) . Apartfro mth einfluenc eo fth ewalkin gspeed ,als oth elocomotor yacti ­ vityo fbot hpredato ran dpre yma yaffec tth esucces sratio .Th eintensit y ofattac kstimul i emanatedb yth epre yma yvar ywit hth epre y ^^^-^ walkingpre ymit ema yevok epursui tb yth epredator .Thi seffec tma ya sw e becounteracte d by agreate rchanc eo fescape .Furthermor eth ereactio no t anactiv epredato r toactiv epre yma ydiffe rfro mtha to fa ninactiv epre ­ dator.Fo rthes e reasonsi tma yb eworthwhil et odifferentiat eth esucces s ratiowit hrespec tt oth estat eo factivit yo fth eattacke ran dth e atta^ Theelaboratio no fthi sbehavioura laspec ti sdon efo rth ecas eo fpre ym a jj J„Tahi p51 .sho wtha t andfemale s(preoviposition) .Th eresults ,presente di nTabl e o±, *. ,+--i^ Fransz(1974) ,measurin g thedifference sar esmal lan dfa rfro msystematic .Frans zii * thesucces srati oo f Metaseiulus occidentalis againstpre ymales ,simiJ ^ Y foundsmal l differences between the success ratioso factiv epr ea o gainstactive/inactiv epre ymale s (SRWW=0.03 8an dSRW R= 0 034 ) butth e /cow— n 026 ). Buttni s restingpredato r seemed toreac tles saggressiv e(SRR W- u . differencei sth econsequenc eo fhi sdefinitio no fth esucces sr a , busseso nth esuccessfulnes so fmutua lcontacts ,whethe r *** *™ ^ encountered frontally, laterally orposteriorly . Inth eprese n ^^ successfulnesswa smeasure d inrelatio nt otarsa lcontact .Thi s ismor elogi cfro ma behavioura lpoin to fview ,becaus eth e P«<^£»»le «»t detectsth epre ywit hth etarsa eo fhe rfrontie r A W^ b-P-g againstth ebac k ofa femal epredato rusuall yevoke dlocomotor yac tvatio n - thepredator ,rathe rtha nattac kstimuli . ™^J^£?Z~~ hunterswit ha restin gpredato rar erelate dt oth eactiv iy *<* 3.2.5,an dth efrequenc yo ftarsa lcontac tafte r ^^^^^ «easured separately. The lattervariable ,adequatel ycalle d 'turning',wil lb ediscusse dbelo wi nthi ssubsection . *>elucidat ewhethe r thetemperatur eaffect sth esucces sratio , 127 fi U 0 OJ 4) -H a) n P u e ra X3 3 fi o r- es o c- •P c -H m co oo es r- »x> ra m o m C/l co CO co t- LT> P u '-H m ra M g H P "H u) -M oi +J 4-1 01 CJ G •H fi H ni ra 3 1 4-1 ra es cr> co <* * H >i ra X 0 0) § Cl H a. H os co t- co un i> M T) ra ra C/l co co co r- in a m 3 M e XI 3 0) XI II 'M >1 H (LI il 01 W M •* * es üi a X0I - 3 -H 5 en r-i in m en g U - •Q ' 5 o C B ra os t- o H co in •P O 0 10 co en co r- LD O N -H < > C -P •H n ra ra fi ai H -ri ra *U] ^• " I0 d) u A: u .n 3 H o CM es o •H H w ra PS u ra x 'H g « es »xi co es es 1) S ri i-i OJ n co t- io ^ es a i ra •H 'M Kl p 3 S U] 1 •M G •a i> * W 0 •H U r-H Is -H •H 10 (U P (1) - 3 a, -H in * o io a) W P ra g 0 Ul II to 0 os o r- co H co p ai Ü1 CD [- UO * H >-a4 -Ha £ 1 S 3 > a x •M 0 r-l •* u m m ra o M H ^ rH H Û. > Uî co r- * if N ^o ras ram i a) M X 0 4) H 0 H (0 3 ra 3 ra S ~ ,, os •p os os IÛ in es M o 'M -ri W co 0 > 4J •H c; m 5Q^ +0° O° "Ö 'M i u m >, o 0 ra un r-~ <* en in 0 0) o 0 0) g H OS »XI * es o o C M ra co = 1 0 3 E rat i r/p r •H "•H 0 0 4-1 3 >, W P -H ra "M (U w nj p C 11 M • T) •H CU m0 0) «h « a 4-> U 14 •4J es <* r- es in 3 a u 0 D ra 1 M m m os es in H H o 4-1 u s: > 1 Ul CO ra 0) 0 .* X) £ ra i-4 •o 3 H ra m 0 C 4-1 3« 0 ra 0 ra 1 'M 1*4 •O • H 0 4-1 0 il -1 4-1 -H ra m XJ ^ «O H 0) > +J 4-1 X3 M '1 c 3 4) 4-1 m Öl 3 II ra pi o o o o o fi H co in c— ai Ö S H G 0) '«iii

Table xs

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128 experiments were carried out at T = 15 and 29°Cusin gpre ycolonie swit h eggsonly .Th e results arepresente d inTabl e 52.The y indicateth eabsenc e ofan ytemperatur e effect. On the basis ofthi spreliminar y resulti twa s supposed that the food content of the gut determines the probability of success,whil e the temperature related rateo fgu temptyin gdetermine sth e dynamics of the success ratio. This simple hypothesis is tested in some prédationan d simulation experiments presented inSubsectio n3.3.4 . Thesuccess-rati o curves presented inthi s reportresembl e thoseobtaine d byFrans z (1974: Netaseiulus occidentalis vs eggso fmale so f Tetranychus urticae atT = 25°C)an d by Rabbinge (1976: Amblyseius potentillae andlar ­ vaeo f Panonychus ulmi atT = 18°C). Thepresen tresult s invariably showed asucces s ratio of about 90%a ta low levelo fgu tfilling ;thi swa sals o foundb yRabbing e (1976)an d corresponds with the indirectly estimatedsuc ­ cessratio s of Küchlein (tob e published). However the success ratios;mea ­ suredb yFrans z differed largely, being always lesstha n 50%.Crof t (19 h studyingth epredator y behaviour of Metaseiulus occidentalis inrelatio n^ o Tetranychus pacificus, measured the success ratio in a different way. measured the percentage of successful capture bypredator s after twoc tactswit h a particular prey. In thepresen twor k anencounte rwa sscor e

Table 52. Success ratios (%) ofyoun g females oftw o Phytoseiid species in relation to thetemperature . Eggsa sprey ;webbe d leaf substrate.

Relative food content 15°C 29°c ofth egu t MO PP M0 PP

77.5 - 70.4 — 91.4 - 82.3 - 86.2 - 80.1 — 30.1 - 30.8 — 19.4 - 23.0 — 13.8 - 14.7 — 9.0 9.8 - — _ - - 76.5 71. .4 - 47. .3 - 50.1 28.0 31. .1 - 6.7 - 6 .2 -

Mo= Metaseiulus occidentalis. = Phytoseiulus persimilis. 129 once tarsalcontac twa snoticed ,whethe ri twa ssucceede db ymor epalpation s ontha tparticula rpre yite mo rnot .Th enex t encounterwa sno tscore dunti l after thepredato rha dlef tth eprey .Anothe r difference withCroft' swor k istha th ewithdre wth epre y aftera predato rha dcapture d aparticula rpre y stage andha dassume dth efeedin g position. Inthi swa yth epredator sob ­ tained little,i fany , food,s otha tthe y couldb euse d again afterfurthe r starvation.A final differencei stha tencounter s resulting isdisturbanc e were excluded from thecomputatio n ofth esucces s ratio. Croft observed that direct frontal approaches ofth epredato r toth eadul t femalepre y nearly always resulted ina navoidanc e response byth epredator s at all starvation times, andthes e were notcounted ,whil e they were includedi n the present experiments.Fo rthes e reasonsth eresult so fbot h studiesar e not comparable, except forth efac ttha th efoun d90 %succes s ratiosafte r 1 daystarvation ,whic hcorrespond swit hth eauthor' sresults . Theeffec to fa les sintensiv e inspectiono fth eare a coveredb yth epre ­ dator wasstudie d simultaneously during thebehavioura l observations.A s discussedbefor ethi saspec to fsearchin g shouldb einvestigate d separately atth eunwebbe d substratebu tno ta tth ewebbe d substrate,becaus ei ti s implicitt oth edefinitio no fth ecoincidenc e inth ewebbe d space.Th eob ­ servations indicate that smallprey ,e.g .egg s andlarvae ,wer e onlyover ­ lookedb yth epredator y females ofth elarg e species whenwalkin ga tth e sideo fth elea ffacin gupward . Itwa sestimate d that Phytoseiulus persimi- lis missed about30 %o fth eegg s inthei r walking path,whil e Amblyseius potentillae missed less than10% .O nth eundersid e ofth elea fthes elarg e predators walk more slowlyan dhenc e inspect theirwalkin g pathsmuc hmor e thoroughly.Th eothe rtw ophytoseii d species (Metaseiulus occidental!* and Amblyseius bibens) walk relatively sloweran dar esmal l sized,s otha tan y prey stagelocate di nthei rwalkin gpat hi sdetected . An encounter ofa mobil e prey withth ebac ko fth epredato r resulteda few times ina tur no fth epredato r towardsth eencounterin g preys otha t tarsal contact occurred afternon-tarsa l contact.Thi sphenomeno nwa sver y rarely observed inth ewebbing ,probabl ydu et oth erestricte d mobilityo n thissubstrate . Amblyseius potentillae, inparticular , showed aturnin gre ­ sponse onunwebbe d substrates, m Table5 3th erelativ e frequencyo fturn s towards prey females encountering thebac k of Amblyseius potentillae (?) are given. Iti sclearl y demonstrated, thatth ewidt ho ftarsa lperceptio n is enlargedb yprolonge d starvation. Apart fromth eturnin g reactionsth e predator also reactedb yforwar d locomotion asa consequence ofth e en­ counter.Th erelativ e frequencyo fthi sbehavioura l reactioni sals ogive n xnTabl e 53.Thi svariable ,too ,appear st odepen d onth etim eo ffoo dde ­ privation.Afte rth epre yi spuncture db yth epredato r asucces si srecorded , theTV!"' * S°0n after' H0WeVer< * "»y* -questione d whether feeding W talitv fr reSUltS ln thS dSath °fth e Prey. Hoyt (1970)studie dth emor ­ tality 0fdifferen tpre y stageso fth eMcDanie l spider mite aftershor tpe -

130 Table 53. The relative frequency of turning of a female predator (Amblyseius potentillae) towards a female prey encountering the back of the predator. T = 20°C; each value is based on a minimum of 170 encounters.

Relative food content Relative frequency of Relative frequency of of the gut, ordered turning activations in classes

0- 20 0.64 0.29 20- 30 0.21 0.64 30- 40 0.05 0.22 80- 90 0.02 0.04 90-100 0.00 0.01

riods of feeding by females of Metaseiulus occident.Us. These investigations revealed that a high percentage of eggs and larvae of the prey are £""* after being fed on for 5-30 seconds. Feeding periods of 30-120 secondscaused a high percentage of mortality among the nymphs and 5 minute *«^ » adult female spider mites resulted in only 40% mortality, ™*£B^*g reduced oviposition by the surviving females. Van de Vne ( found 50% mortality among adult females of Panonychus *™ ***^J^ ling periods of M*lyseius potentillae. He reported that this ™^*™ „^ =forwards . A comparison oi established within one day and did not increase afterwards. F sent behavioural observations (Subsection 3.2.8) snow a very small part of the total feeding period except for the rare an attack of a satiated female predator on a female spider mite^ ^ ^ ^ Apparently the probability of a successful capture^ isre a ^ content of the gut. However, there are two exceptions to x lrt 1 which set limits to the applicability of this ™ "°' J ^''pregent ex_ starved predators can respond differently to those use in^ ^ ^^ ^ ^

Periments, which are starved for no longer than 2 days, a indicated dehydrated state, Aml>lVseius potentillae is very aggress ^ ^ ^ ^ by the increase of the success ratio against female^ spi ^

food contents in its gut. One meal on a female spider ***™ Q£ & ^_ ** to be filled completely, so that the «*«^ P^ ^

«ssful capture is expected to be very low, acco a appeared t0 maintain However, severely starved females (6 days at T ^^ ^^ ^^ second a high success ratio after their first meal, an ^ ^ ^ ^^ Qf m^al the success ratio was higher than expecte « measurements foof«-dj • i „ac verv low acLui."-"'3 ingested after the first meal was vexy 131 Table 54. The success ratio (%) ofyoun g and hungry femaleso f Ambluseius potentillae against adult femaleso f Tetranychus urticae. T= 20°C ; observationtim emaximu m 6hour spe r individual; eachvalu e isbase do na minimu m of20 0encounters .

Prédationhistor y Starvation periods

2 days 6day s

firstsucces s 32.5 33.8 second success 1.2 29.4 third success - 8.4 fourthsucces s - 1.0

of the female weight,s otha tthi spredator y behaviour is inducedb yothe r motivationalvariable s thanth e acquired amount of food. Presumably theper ­ sistence of aggressiveness iscause db y the relaxation time ofth epnys i logical processes, leading torecover y ofth emetaboli c imbalance. Inc trastt o Amblyseius potentillae, severestarvatio no f Metaseiulus occiden- talis ledt oa lowe rsucces srati p than found after 2 days fooddeprivation . This effectwa s clearly related tothei r loss of strength, as indicated Y thedecreas e inwalkin gvelocit y and their sluggish reactions.Bot hth e creased anddecrease d aggressiveness after severe starvation areno tuni q for the species mentioned,bu twer e observed more frequently inthes epa r ticularcases .Apar tfro m this lower limit to the applicability ofth efo o conceptther e isals oa nuppe r limit caused by high rates of encounterw i prey.Küchlei n (tob e published) found a second rise of the rate ofeg g prédationb y Metaseiulus occidentalis above the density of 30 eggspe r cm2- Because the femalepredator s arecertainl y well fed atthes edensities , this 'Vi lV phenomenonca nno tb erelate dt oth e food content of their gutbu tposs i tosom e stimulus resulting from frequentcontac twit h prey. These examples clearly demonstrate the limitations of food consumption asa nindicato ro fth ehunge r level.Nevertheless ,wit h respect toth eran g ofcondition s relevant inth egreenhous e theus e of food consumption isac ­ ceptable; for,th e lower limitwil lb e only relevant after exterminationo thepre ypopulatio n andth euppe r limit at frequentpre y contact is V^obab not metwithi n therang eo fprevailin gpre y densities.Althoug h theeffe< * offrequen tcontac twa s assessed ata seemingl y realistic egg densityo f ^ eggspe rcm? ,i tshoul db e stressed that the rate of egg encounter is »th^ highi nthes eexperiment s duet oth e absence ofwebbing . Inth e caseo f« e seiulus occidentalis thedifferenc e inrat e of encounter betweenwebbe da n 132 unwebbedsubstrate si sapproximatel y proportionalt oth edifferenc ei nwalk ­ ingvelocit ys otha tth ecritica l eggdensit yi na we bamount st o4 0 x 0.47/0.18= approximatel y 100egg spe rcm? .Suc hhig hpre ydensitie swer e nevermeasure d innatura l colonies growno ngreenhous e roses,eve nwit h respectt oal lstages .Thes e densities ranged between20-6 0pre y itemspe r cm?an doccasionall y densities upt o8 0mite spe rcm ?wer eobserved . For thesereason si ti sallowe dt oappl y thesimpl econcep to ffoo dconsumptio n forth epurpos e intended.

3.2.8 Handling time

The time spent handling acapture d prey wasals o measured duringth e continuous observations ofth epredator y behaviouran d subsequently itwa s relatedt oth efoo d contento fth egu t accordingt oth emetho ddescribe di n thepreviou s subsection. Thehandlin g time consistso fsevera lactivities , likepalpating , piercing, feeding, 'guarding'an dretur n feeding.Hungr y predators feed almost immediately after contact withthei rprey ,bu twel l fedpredator s spendmor e timei ninitia lpalpatin gan dpiercing .Feedin gi s frequently interrupted fora shor t period andsubsequentl y continuedo n otherpart so fth eprey , especially whenth epre yi sa deutonymp ho ra n adult,A fe wtime s thepredator y female seemingly leftit scaptive , but subsequently returned towards thepre yan dstarte dt ofee dagain .A tothe r occasionsth epredato rwa sobserve d tosi tan dwai t nextt oit scaptiv e duringa handlin g period, cleaning itsextremitie s inth e meantime . The actualfeedin gperio d during handling amountst o90 %i nth eyoun g stageso f thepre yan d60-70 %whe n feedingo nmatur eprey . Themea nhandlin g timesa tdifferen t levelso fgu tfillin gar e tabu^d inTabl e5 5i nrelatio nt oth edevelopmenta l stageo fth eprey .I tca n e concluded thatth ehandlin g time increases withdevelopmenta l P™*»"1"1 <*th epre y andwit h theperio do ffoo ddeprivation .Th elatte reffec t

alsofoun db yPutma n (1962), Sandness& McMurtry (1972)an dFrans ,(1974 > Somepeculiaritie s concerning thespecie s studiedma yb enotice d Axbly «**.« Potentiate spends little timei nth ehandlin go fspide rmite ,egg. .

*s^cusse d before, this iB due to this species having someP '> » ^ Pacing theeg gchorio n (Subsection 3.1.1).Th emajorit yo fth e feed g

tempts fail, but successfui feedingswer eobserve dto oan d Periodswer e equalt othos e observedi nth eothe r species. *«""^JJ -e harmedb yth epiercin g attempts,th etim e^ - ^^ as a handlin gperio d despiteth eabsenc eo f W'*™-™*"**^ tne st«died ingestth econten to fth eegg swithou tan yproble m inpiercin g ^ chorion. Pnvtoseiulus persimilis requires lesstim ei nemptyin g thjg

^n *etaseiulus occidentalis and Mtblyseius bibens. ^ ^^ ^cies spend equal amountso ftim ei nhandlin gth eothe r stages prey.

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134 3. 2.9 Disturbance

Inth eacarin e predator-prey system, disturbance showsitsel fi nsevera l ways: - asa decreas e in the probability ona successfu l capture,e.g . incas e offronta l encounters between a female predator and a female prey,bot h walkingo na nunwebbed , upward-facingsubstrat e (Subsection3.2.7 ) - asa n increase inwalkin g speed, e.g. after frontal contactbetwee nac ­ tiveadult s - asa nincreas e inwalkin g activity, e.g. aftercontac tbetwee n arestin g predator and an active stage of thepre yresultin g inreactivatio no fth e former(Subsectio n 3.2.5) - asa decreas e in thewidt h ofperception , e.g. aftercontac tavoidance , lateral inspection by the antennae-like frontlegs (Subsection 3.2.1)de ­ creases,resultin g in adecrease d widtho f 'antennal'perceptio n - asa decreas e inth e handling time,e.g . feedingpredator sbein ginter ­ ruptedb ypre y bumping into thepredato r (Mori,1969 ) - asa nincreas e inth e success ratio of feedingpredators ,e.g . theprey , bumping into the predator, is immediately attacked (Haynes & Sisojevic, 1966;Sandnes s &McMurtry , 1972;Hoyt , 1970). Theeffect s of the above types ofdisturbanc e onth e functionalrespons e ofphytoseii dpredator s topre y density areconsidere d tob ever y important byvariou s authors. Mori & Chant (1966) attributed the domeshap eo fth e functional response of Phytoseiulus persimilis to contact disturbance o feedingpredator s by the numerous female prey.Sandnes s& McMurtr y (1972, founda secon d rise of the rate ofprédatio na tpre ydensitie so f1 0female s jr„i 4-t- rkso fth efeedin g Percm2 . This effect was attributed to successful attacks o a x a ^^ Predatorso nth epre y occasionallybumpin g intothem .Hoy t (1970)sug g , thatthi s »two flies in one blow» principle will increase the *^°l efficiency in reducing preypopulation s athig hdensities .Lain g S

-rson (1979) showed that the rate of ^^^^^^^ ^strate was only a fraction oftha to nth e «**£«.! ^

<*thei rprevailin g feeding activities.O na ^J ^ low walking b*eve nmor e conspicuous due to low coincidence inth eweb b g, -d andlo wwalkin g activity.Henc e itma yb e q—^£££?«* Terences in the webbing are vigorous enough to cause 135 P O. 3 0> U U u 01 «J p £1 c Is 3 W •O 3 0) P &U> a 3 H

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136 whether these disturbances occur frequently at thepre y densities prevailing in the greenhouse crop. This question was studied by recording the walking behaviour andth e encounters in prey colonies, grown on greenhouse roses and containing a lot of mobile stages. Two types of colonies were selected: - colonies with 20-40 nymphal and male stages percm 2, plus a few females - colonies with eggs and10-1 5 females per cm2. One predatory female of Metaseiulus occidentales or Phytoseiulus persi- milis was released on each leaf andth e observations started half a day later. Theresult s arepresente d in Table 56. It can be concluded that for both phytoseiid species and both types of prey colonies, disturbance during feeding is a rare phenomenon and thewalkin g speed and walking activity of both predator andpre y areunaltere d when compared to thedat a obtained in colonies containing few, or even no, mobile mites. When a female preyen ­ countered a feeding predator, thepredato r mostly continued feeding and in the rare case of feeding interruption thepre y captive was already sucked dry, while attack on the disturber was observed only once. Disturbance phe­ nomena may occur upon exhaustion of theplan t food source, causing the spi­ der mites to increase their locomotory activity in search of fresh food. However this situation was notstudie d because it implies an infestation by spider mites that surpasses an economically acceptable damage level.

3.3 PREDATION

Theprédatio nwil lb emodelle d forth ecas eo fa predato rwhos egu tfil ­ lingdetermine s therelativ e rateo fsuccessfu l attack (-RS Efo rD prey Thedynamic s ofth efoo d contento fth egu ti ssimulate db yintegratio no f therat eo ffoo d intake andth erat eo fgu temptyin g over shorttim einter ­ vals.B yassumin g that each predator ina serie so fsimultaneous ' P^*1^ experiments consumes uninterrupted bysearchin gperiod san da tte sam ^ squiresth esam e portion offood , foragingwoul db econceive da sa determ »ticprocess .Howeve r therando m distributiono fth epre yan dth eundir -e tedsearchin g behaviour ofth epredato r give riset osequence s otf«*£* «* searching periods that aresubjec t tostochasti c variation. Fort h reasoneac h predator goes througha uniqu e time serieso f f^J^ » thata ton emomen t duringth eprédatio nproces s each *«afferen t amount of food init sgut .Therefor e stochasticmo d1 ^o f the Prédationproces s arediscusse d andsubsequentl y compared with deterministic Vogues toelucidat e theeffec to fth eunderlyin gconcepts . After selection ofth emos t adequatemode l fromth eabov ep on to fv *-rie s ofprédatio n experiments onbot h webbed andunwebb • •^£

-e discussed and compared withappropriat e ^**™£.£££ it is »»-«red inputs andth econcept s underlying thatmodel . S«^*

:r:Ued that themajorit y ofth e-^ ^ i^^ - ^ 0rzer opre y density, ata standar d temperaturean di n 137 studying solitary predators only. This raises the problem of how to extra­ polate those measurements to intermediate prey densities, other temperatures, age periods and predator densities? Hence a concept of the relation between reproduction and prédation is proposed on the basis of experiments previ­ ously discussed in Subsections 2.2.3 and 3.1.2, which enables extrapolation in a simple way. Some validations of this concept are presented. Finally, there is the similar problem of extrapolating measurements of 'monoculture' success ratios to 'mixed cultures' of prey stages. This is discussed on the basis of the behaviour measurements described in Section 3.2 and of the available references pertaining to prey-stage preference of phytoseiid predators.

3. 3.1 Models of prédation

Ensuing from the behavioural component analysis (Section 3.2), prédation is determined by the food content of the phytoseiid gut, which in turn de­ pends on food intake and gut emptying (Section 3.1). In CSMP notation, the dynamics of such a system can be simulated by the following numerical inte­ gration: FCG = INTGRL (IFCG, RFI - RGE) RGE = RRGE * FCG (I)FCG = (initial) food content of the gut (pg) RGE = rate of gut emptying (pg-day-1) RRGE = relative rate of gut emptying (day-1) RFI = rate of food intake ((jg-day-1) Because of the small time constant of the ingestion process and the short duration of the handling period needed for 90% of the ultimate food intake, ingestion may be conceived as an immediate swallow of the prey content, the size of the portion being limited by the satiation deficit of the gut (Sub­ section 3.1.1):

RFI = AMIN1(SDG/DELT, RSE * FCP) SDG = GUTC - FCG

SDG = satiation deficit of the gut (Mg)

GUTC = gut content (Mg)

FCP = food content of the prey (Mg) 1 RSE = rate of successful encounter (prey day" ) havJ T6 °f SUCCeSSful «counter can be computed from the measured be­ havioural components and prey density: RSE = l./TSC

TSC =F T + 1/(RRE , COIN ^ SR ^ DpREY)

II' I fm*S*^ P- successfulcaptur e(day ) T -beding-tim e(day ) RRE = atxverat eo fencounte r= RE/DPRE Y (day"1) 138 SR =succes s ratio (%) COIN= coincidenc e inspac e (%) Severalo fthes e behavioural components positively influenceth erat eo f successful encounter atlo wlevel so fgu tfilling .Fo rexample ,th esucces s ratioincrease s ifth efoo d content ofth egu tdecrease s (Fig.34) .A ta constant density ofth eprey , soonero rlate rth erat eo ffoo d intakewil l becomeequa lt oth erat e ofgu temptying . Thenth efoo d contento fth e gut, andconsequentl y therat eo fprédation , attaina constan t levelan dth epré ­ dationproces s enters astead y state. However,a sa consequenc e ofprédatio npre y density decreases unless each preykille db yth epredato r (orb yothe r causes)i sreplace d immediatelyb y afres h one. Because immediate replacement isgenerall y impracticable,th e rateo fprédatio n intha t case isno tassesse d ata stead y state,du et oa changingpre y density. Incas eo ffixe d time delayso fpre y replacementth e fluctuation ofth epre y density canb emonitore d duringth esimulatio ni n thefollowin gway : DPREY= INTGR L (IDPREY, (-RSE/AREA)+ (REPL* ( IDPREY-DPREY)/DELT )) REPL =IMPUL S (0.,REPDEL ) (I)DPREY = (initial) densityo fth epre y (prey/cm2) AREA =experimenta l leaf area(cm 2) REPL =replacemen t action (0o r1 ) REPDEL= tim e delay ofpre y replacement(day ) The fluctuation inpre y density canb edampe db yenlargemen to fth eex ­ perimental leaf area andb yshortenin g ofth etim e delayo fpre yreplacement .

REUWV E FOOD CONTENT SUCCESS =?AT10 OFT HE GUT (%) % ) 100-, r-100

BU- - ÖU

60- - 60

40- - 40

20- - 20

- 0 -tff 1 i 1 1 1 ' 1 ' i 0 42 48 6 2 18 24 30 36 TIME(HOUR )

"* *. Graphic display ofth emai n counteracting ^^^IZL Nation foryoun gfemal e Metzseiulus occiäent.lis andegg s °*™»^_ ü ^-e.Gu t emptyLg given by dotted line,an dsucces s ratio gxvenb y to9ram. 139 Adequate manipulation of these measures can approximate a steady stateo f theprédatio nproces swithi n the limits ofpracticability . The above type ofsimulatio n (Appendix E)i s called deterministic,becaus e each moment in theprédatio nproces s allows for only onepossibl e stateo f the system.Th epredator s areconsidere d tob e identical foragers,eac hcon ­ suming the same portiono f 'crumbs' of thepre y 'cake'.Moreover ,consump ­ tion takes place uninterrupted by searching periods,whil e the sizeo fth e food portions vary in time due to the dynamics of the satiation levelo f the predator. Itgoe s without saying thatth e actualprédatio nproces si s quite different from thispicture .Th e random distribution of thepre yan d the undirected searching behaviour of the predator cause the searching periods to be variable and bounded by discrete feeding periods, so that each predator has a different amount of food in its gut at one instant during the prédationprocess . Therefore it may be worthwhile to consider stochasticmodel s thattak e into account the instantaneous variation ofth e motivational state. Monte Carlo simulation of the predatory behaviour may serve as afirs t illustration ofa stochasti c model. Ina mit e colony the searching behaviour of the predator and thespatia ldistributio n ofth epre y are approximately random, sotha tth e inter-encounter periodswil l be random too. Inthi scas e the inter-encounter periods, as well as the inter-attack periods (Fransz, 1974), meetth econdition s ofa Poisso nprocess .Th eprobabilit y ofn osuc ­ cessful attacks isthe nequa l toEX P (-RSE* TIME) , so that in asufficient ­ ly short interval (=BELT ) atmos ton e singlepre y canb e attacked.Henc e theprobabilit y ofa captur e inDEL T isequa lto : PRC= 1 .- EXP(-RS E *DELT ) PRC= probabilit y ona captur e The capture events can be obtained from a comparison between PRC and random drawings at consecutive time intervals from aunifor m distribution, ranging from 0t o1 :

RDRAW =RNDGEN(U ) INCONU = 3 CATCH = INSW(PRC- RDRAW , 0. ,1 . ) U =startin gvalu eo fth e random number generator (RNDGEN) RDRAW =rando m drawing from aunifor m distribution ranging from 0t o1

CATCH =indicato r ofa catch event (0o r 1) When CATCH equals zero, the predator is searching; CATCH = 1denote sa catchevent , m thiswa y sequential time intervals of searching aresimula - thé'in nte"UPtl°nS f°r ^gestion are simulated asdiscret e moments,s otha t lows °n Statement °f«deterministi c »»«telca nb e modified as fol-

RFI =CATC H *AMINKSDG , FCP)/DELT

140 Thusfoo d intake takes place asa nimmediat e swallowingo fth efoo dcon ­ tento fth epre y during atim e intervali nwhic hCATC Hhappen st oequa l1 . Anexampl e ofsuc h a simulation ispresente d inFig .35 ,whic hshow sth e courseo fth efoo d contento fth egu tdurin ga foragin gperiod . Fromrando m draws fora serie so fDELTs ,th efeedin ghistor yo fa nindi ­ vidualpredato rca nb esimulated .T oobtai na naccurat e estimateo fth emea n numbero fpre y attacked, alarg e numbero frerun sar erequired ,e.g .a tleas t 100,whic hmake s Monte Carlo simulationa computer-tim econsumin gprocedure . Theprogra mi sliste d inAppendi xF . The above formulation ofa stochasti c prédationproces sca nb eextende d insevera l ways. Thecaptur e eventan dsimultaneou s swallowingo fth epre y contentca nb e replacedb ya nexplici t feedingperio dan da dynami cinges ­ tionproces s (e.g.Fransz , 1974;i ncontras tt oFransz' smodel ,th efeedin g

CUMULATIVE RELATIVEFOO D NUMBER OF CONTENTO FTH E CAPTURES GUT(% ) ir 10 100-, \

i \ i \ \\ ! \ h 7 i \ ' i \! \ i

h 5 50

h 3

0 48 U TIME (HOURS)

Fig. ». or.phiPhicc reputatiorepresentationn oo,f «th- e P^^^^o^T.Z'ZlliTToTd -ten^ t M°nte carlo me thods (Appendix F). The Ramies o ^ ^ ^^ er G °f the gut is given by" the dotted line. The cumulative^^ ^ £edgLtor

**ing the period of prédation is given by the' «^«^ .ngests prey eggs aseiulus occidentalis) starts at full saL A after random searching periods. 141 time in the model discussed above was only considered aswast e timewit h respect to the time available for searching). Another extension canb eac ­ complished by coupling the model of thewalkin gbehaviou r ofpredato r and prey to the above prédation model,whic h isespeciall y attractive incas e ofnon-rando m distribution ofth epre y (Subsection 3.2.4). Intha tcas eth e rateo fencounte r (RE= RR E *DPREY )i s replaced by simulation of thewalk ­ ing behaviour of the predator (and prey)a ta certai n distribution ofth e prey.A tth emomen to fa simulate d encounter the occurrence of a successful attack canthe nb e determined by the same type ofMont e Carlo procedurebu t where theprobabilit y ofa captur e (=PRC )equal s theproduc t of thecoinci ­ dence in space and the success ratio (=COI N *SR) .However , becauseimme ­ diate swallow of the prey content isno t far from reality, and theintra - colony distribution of the prey is close tobein g random, both extensions were considered tob e irrelevant toth epresen tproblem . Besides,th emino r effect of 're-crossing areas already visited by the predator1 canb eac ­ counted forb y simple correction ifnecessar y (Subsection 3.2.4). By confining the simulation problem in thiswa y the computer-timecon ­ suming Monte Carlo simulations can be replaced by ones based ongueuein g theory (Saaty, 1963).Taylo r (1976)an d Curry& DeMichel e (1977)recognize d the analogy between a queue of clients,waitin g tob e treated by theden ­ tist and the 'queue'o fingeste dpre y 'waiting' in the gut tob e digested, resorbed and egested by the predator. The treatment time is equal toth e time needed for digestion, resorption and egestion ofth emas s equivalent toon eprey , referred toa s 'gut-emptying time'.Th e gut content is divided in^classes, also equivalent to the mass ofon eprey .A t full satiation( = N class)n o successful captures can take place, while the rate of gut emptying equals zero in case of an empty gut (= zero class). Based ona Poisson distribution of thesearchin gperiod s and anexponentia l distribu­ tion of the 'gut-emptying time', a seto fN+ l difference equations canb e derived by computing the shortinterva l changes inth e relative frequencies

(=P n(t))o f predators at each satiation classn (0< n« N).Fo r asmal l time incrementDEL T atmos ton epre y canb e encountered, so thatp n(t+DELT) can be computed fromP n(t)b y summationo fth e following transitionproba ­ bilities: - theprobabilit y tocaptur e and ingeston epre ymas s without simultaneous resorption ofa mas s equivalent toon eprey , causing an increase of thefoo d contento fth egu t fromclas sn- 1t on theprobabilit y tocaptur e and simultaneously resorb themas s equivalent to one prey, resulting in the absence of a change inth e food contento f thegu t (=n )

- theprobabilit y ofn ocaptur e and no resorption, resulting in a constant level m the foodconten to fth egu t (=n )

the probability of no capture and onepre ymas s resorbed, causing ade ­ crease ofth e food contento fth egu t from classn +l ton .

142 Theprobabilit yo fa captur eo fon epre y massca nb efoun d fromth efol ­ lowingformul a (CSMP notationi sno tuse di nal lsubsequen t formulas): ? ) PRC=1 - exp(-RS E* DELT )= 1- ( 1-RS E*DEL T+ -* T\ " Neglecting theterm s involving DELT2, this formula canb esimplified :

PRC= RS E* DEL T BecauseRS Edepend s onth eamoun t offoo di nth egut ,thi s formulaca nb e rewrittenb yaddin gth esuffi xn ,whic h indicatesth e satiationclass :

PRCn= RSE n* DEL T andPRC N= RSE N= 0 Theprobabilit y ofth eresorptio no fon epre ymas s ingestedca nb ecom ­ putedi nth esam ewa yafte r calculation ofth etim eneede dt oresor bth e massequivalen t toon epre ya tdifferen t levelso fth efoo dconten to fth e gut( 0

PRE^ = RGE1 * DELT and PRE« = 0 n n u

RGEln = l/TGEl and RGE1Q = 0

TGEln = ln(n/(n-ONE))/RRGE for (1

" Pn(t) * PRE * PRCn

" Pn(t) * (1 - pREn) * (1 - PRCn)

" Pn+1(t) * PRE * (1 - PRCn) o f small DELT, so that 2 Again, the terms involving DELT drop outi n case o ^ g. 3imu- the distribution of the predators over the satiation claSSeS star- lated by recursive use of the following set of difference equations, ting from anyinitia l distribution of Pn(t=0): Pn(t+DELT) =p (t) * (1 - (RSEn+RGEln) * DELT) + ... ^ SE p l(t) * RGEln+1 * DELT + p^tt) R n-l n+l^ n+1 pRED) is equal to The expected number of prey killed per time interval .i ^^ ^ ^^ the amount of food consumed in DELT, which canb e compu e f <-vio satiation ievGj.=, c- rence between the successive distributions of ttie ^j. the amount of food resorbed from the gut during time in

N N DELT ^+DELT) * RGEln * PRED = z ( (t+DELT) - pn(t)) + Z n Pn

dPn p (t+DELT)- p (t ) pA(t) = dt^= Li m — DËLT = ° n dt DELT-0 DELT Theequation s obtainedca nb erearrange d asfollows : RGEl *p -RSE *p =RGEl *p -RS E n+1 n+1 n n n n 'n-1 pn-l

Because P(J(t)= RGE1 1 * p± - RSEQ * pQ =o ,th erigh than d sideo fth e re­ arranged equationi sequa lt ozer oa tconsecutiv e valueso fn (n= 1,2,3,... ] Thisresult si nth efollowin g simple equation, showing thatp isproportio ­ n nalt op n_i:

RSE RGE1 n-l *P n-1= n *P n

After selection ofa narbitrar y starting valueo fp Q, thevalue so fp n (n= 1,2,3,... )ca nb ecompute d consecutively with this equation. Subsequent

rescalingo fth ep n values suchtha t I p = iproduce s thesteady-stat e n=0 n distribution ofth epredator s over thesatiatio n classes.I nthi s special case theformul a ofth enumbe ro fpre y killed duringDEL T (=PRED )reduce s toth eter m thatcompute sth eamoun to ffoo d resorbed duringDELT : N PRED= 1 p *RGE 1 *DEL T n=0 n n

Thus iti spossibl e tocomput e directly therat e ofprédatio na tsteady - statecondition s insteado fb ynumerica l integration over small timeincre ­ ments. Moreover, aslon ga spre y densityi skep tconstan ti nsom eway ,th e number ofpre y killedca nals ob ecompute d overan ytim e interval starting from anyinitia l distributiono fth esatiatio n levels (=p (t=0)). Thisi s doneb ymatri x algebra, asi sshow ni nAppendi xG .However" ,whe nth epre y density ischangin gi ntime ,an dconsequentl yRS Etoo ,th ese to fdifferenc e equations representingth equeuein gproces sca nonl yb esolve db ynumerica l integration over small time increments (=DELT) . m theforegoin gdiscus ­ siono fth equeuein g approachi twa sassume d thatth egu tconten t couldb e divided into classes equivalentt oth emas so fon eprey .However ,a sshow n in ^section 3.1.1, thepredator y mite does ingestth epre y contentpar ­ tially when thesatiatio n defecito fth egu ti ssmalle r thanth efoo d con- strucln !rey'Thl S aSPeCt Can bS inClUded in the *»«•*»*-de lb ycon - onepre v r tl0n ClaSS6S 6qUiValent to. onl y a fraction ofth emas so f Y (e.g.0. 5 Mg). Then the amount Qf foQd ingested by ^ predator

144 mayexcee d theamoun to ffoo d equivalentt oon eclas san dca nb eexpresse d interm so fclas s units: ENLARG= NCLASS/GUT C f =min(FC P *ENLARG ,N - n ) (SDG =N - n ) ENLARG= facto r accounting forth eenlargemen to fth egu tsiz e (andpre y size)du et osubdivisio n insatiatio n classes (Nclass) f =foo d intake ofa successfu l predatora tsatiatio nleve ln , expressed inclas s units (=INTEGERS ) Inthi swa yingestio n isrepresente d asa discret e jumpove rf classes , sotha tth eter m inth equeuein g equations thatrepresent sth eingestio no f onepre yite mu pt ostat en i sequa lt oRSE n_f *P n_f (f< n« N-l), instead ofRSE n_1 *p Themaximu m satiation levelca nthu sb eattaine dvi acom ­ plete a'ndpartia l ingestion ofth epre y content,i.e .startin g fromeac h classi nth erang e ofN- ft oN-l .I ntha t caseth eingestio nter mo fth e queueingformul ai sequa l to T* RSEn *p .A sa consequenc eo fpartia l n=N-f ingestionth eexpecte d number ofpre y killed during DELT isno tequa lt o theamoun to f food consumed. Itca ntherefor e onlyb ecompute d fromth e termi nth edifferenc e equations that accounts forth esuccessfu lcaptures : N PRED= 1 p (t)* RS E *DEL T n=0 n n j_• « ie cimilar to that Thecomputatio no fth esteady-stat e distribution,p n, issi m ofth ecomplet e ingestion ofth epre y content.Startin g froma narbitrar y 0t valueo fp 0, thevalu e of ç± canb esolve d from P'0 =

RSEQ* p 0 +RGE1 1 *p x =0

** *= lf2f3 N_x the valueo fP n+1 canb esolve d consecutively from dfipn dT= 0

- (RSEn+ RGEV *p n + RGEln+i *p n+1 =0 _0 ! f< n . < N-l) + RSE P (RSEn+ RGEl n)* P n +RGEl n+1 *P n+1 n-f n-f

Sequent rescaling ofth ecompute d pn values suchtha tthei rsu m ^.^ r ^lts inth e steady.state distributiono fth epredators ,o Cl —s (= }.Again , when RSE or RGEl vary duringth e proce- '°l«tiono fth edifferenc e equations isth eonl ymetho d thatca ^ ^.^^

Whenonl y discrete changes inth efoo d contento fth eg ^^ tQ Whe ther these aredu et o food intakeo rgu temptying ,i t ^ searching ex Pressthes e changes interm so fprobabilities, s otn a ^^ Because tlm stochaStl C ean dth egu temptyin g time aresubjec tt o and the random ofth erando m distribution ofth epre y within thec oo n respect Sea^hing behaviour ofth epredato r this seemst ob eobviou s 145 to the searching times between captures. Then the catch events occurb ya Poisson process and the probability of one or more captures is given by 1 - exp(-RSE * t).Thi s quantity is a cumulative distribution from which by differentiation, one obtains the exponential density function RSE * exp(-RSE * t) for the distribution of times between captures with mean 1/RSE and variance 1/RSE .Howeve r with respect to the gut emptying time stochastic variation seems much less obvious.Eac h gut content class isemptie d with aprobabilit y ofRGE 1 *DEL T during a small time increment: p(t +DELT )= (1- RGE 1 *DELT )* p(t ) Hence dP(t)_ . p(t+DELT)- v(t) dt ~ Llm —DFFT ^~^ ~ - RGE1 * P(t) DELT->0 DELT This differential equationha s the solution p(t)= c *exp(-RGE l *t ) Since each gutconten t classwil l be emptied sooner or later it follows that 00 ƒ c *exp(-RGE l *t )d t= 1 0

Hence c= RGE1 .Thu s the gutemptyin g time is described by the negativeex ­ ponential distribution with density RGE1 * exp(-RGEl * t).Th e mean gut emptying time therefore equals 1/RGE1, and the variance is 1/RGE12. From this it can be seen that because RGE1 depends on thenumbe r of satiation classes distinguished (= n), the stochastic variation in gut emptying time canb e reduced by dividing the gutconten t intomor e (but smaller) satiation classes. In case ofa ninfinit e number of satiation classes theproces s of gut emptying is completely deterministic (variance =0). If onewant s to reduce the variance, the effecto fenlargin g the number of satiation clas­ ses isgoverne d by the law ofdiminishin g returns. Simulations indicate that the introduction of stochastic variation of the gut emptying time hardly affected the end results. Even the modification of the distribution from negative exponential to constant, uniform or normal proved tob e ofmino r importance in a series of Monte Carlo simulations. This result was also established by Curry & DeMichele (1977). Therefore it may be stated that the choice for the class size (orth e number of satiation classes)mainl y depends onth e accuracy one iswillin g to sacrifice indescribin g therela ­ tionbetwee n RSEn andn .Te nt o twenty satiation classes proved tob esuffi ­ cientwit hrespec t to the descriptive power. The reclassing principle shown in the queueing equations was used by Fransz (1974)i na mor e extended form.H e also distinguished satiation clas­ ses (- n) and appropriate relative frequencies ofpredator s (=p (t)),bu t he additionally recorded themea n satiation level within each ola«. Accor­ ding to the queueing approach the satiation level is only expressed indis -

146 crete class units and food intake and gut emptying are accounted for by the probability of discrete jumps from one class (n-f or n+1 resp.) to the other (=n) . The reclassing method applied by Fransz is more complicated. Within each satiation class the mean food content of the gut is monitored by inte­ grating the food intake and gut emptying. When this integration results in asatiatio n level outside the class boundaries, both relative frequency and themea n food content of the gut are transferred to the appropriate satiat­ ion class. After all reclassings, which are needed after a time step of in­ tegration, a weighted mean of the class-specific food content of the gut and of the matching relative frequencies of predators is computed. Due to this reclassing principle, called Compound simulation by Fransz, the process of gut emptying can be simulated in a deterministic way, while searching conserves its stochastic character. However, as stated before, Monte Carlo simulations have shown that the estimated prédation is almost unaffected by the stochasticity of the gut-emptying time, whether uniform, exponential or Gaussian distributions were used. Therefore for reasons of economy the re­ classing principle of the queueing approach is to be preferred since it is based on one instead of two variables per class. A realistic aspect of the Compound model (Fransz, 1974) is that the in­ gestion can be integrated over small time increments instead of being re- Presented by discrete jumps in the satiation level. Fransz accomplished this fcy splitting each satiation class into 2 subclasses: one with predators handling a prey and one with predators searching for prey. Each subclass is *aain split into a fraction of predators continuing the same occupation (idling or searching) and a complementary fraction shifting from handling t° searching (= abandoning the captive) or vice versa (= catching the prey,. «thin the handling subclasses ingestion can be monitored by numerical i - oration. However one may ask whether this realistic detail is necessary. *» *ort period needed to achieve 90%o f the ultimate food intake during «* total handling period and the high suction force of the ingestingr pre-_

**or may justify a concept of .«diate swallow'. To establish any P- ble effect of the underlying concepts of food acquisition, the follow g "«*" are compared for the case of a young female predator <*£^

°^ntalis) hunting for eggs of the two-spotted spider mite (retr-ayc*» "rticae):

Deterministic model (Appendix E) Monte carlo model (Appendix F)

* Cueing model (Appendix H) this study). impound model (Fransz, 1974; input adapted to resui ^ ^ Both the Monte Carlo model and the Compound model are able separate -o Muriner the handling peixu" par*te recording of the ingestion process during discussed ^al integration procedures required to accomplish this F I -nsz (1974). As dLussed before, the ^terministi mod i th6 c °ncePt of continuous feeding by identical predators, 147 RATE OF EG6 CONSUMPTION ( DAY"') 16-,

PREYEG GDENSIT Y(CM" 2) Fig. 36. Comparisonbetwee n fourdifferen tmodel so fth eprédatio nproces s foryoun gfemale so f Metaseiulus occidentalis andegg so f Tetranychus urti- cae (T= 27°C). (Coincidence inspac ei sno tconsidered) . ,Compoun d simulation; ,Queuein gapproach ; ,Deterministi c simulation;1 themea nan dstandar d deviationo f10 0Mont e Carlo simulations.

model is based onth econcep to fimmediat e swallowingo fth epre ycontent . The resultso fth esimulation swit h these fourmodel s aregive ni nFig .36 . Both theCompoun d model andth eQueuein g model give prédationrate s that fall within theconfidenc e limits ofthos e obtained from theMont e Carlo simulations. Itma ytherefor eb econclude d that inth epresen tmodel so f the acarine predator-prey system detailed representation ofth eingestio n process is superfluous andca nb ereplace db yimmediat e swallowing ofth e prey.Th edeterministi cmode lproduce s consistently lowervalue s ofth epré ­ dationtha nal lothe rmodel spresented .A sdiscusse db yFrans z (1974), this difference iscause db yth ecurvilinearit yo fth erelatio nbetwee nth esati ­ ationleve lan dsevera l componentso fth esearchin gbehaviou r (e.g.succes s

Forth eremainde r ofth esimulation s theQueuein g model ispreferred , becauseo fit stractabl emathematica l properties,parsimon y with respectt o Morel .f VariableS and relatively economic demandso ncompute r time, which T QUeUeln9m0de l Can be Pr°S~ed asa comprehensiv e subroutine, ToZJ, fC0UPle d t0 the m0del °fth S Predator-prey interactions onth e population level (Part2) . 148 13.2 Prey density

It should be stressed that the majority of data concerning the predatory behaviour (Section 3.2) were obtained at high prey density or in complete absence of the prey. For this reason it is necessary to validate simulations of the rate of prédation at intermediate prey densities. The relation be­ tween the rate of prédation and prey density should be determined at stan­ dardized initial conditions (standard age, sex, feeding history, temperature, relative humidity and prey distribution), as well as at steady-state condi­ tions during the experimental period. These conditions imply that: - the motivational state of the predator is independent of its initial level and oscillates around a stable level - the prey density remains constant, despite prédation, by immediate re­ placement of the prey killed and by ruling out the possibility of reproduc­ ing or developing into a next stage. However immediate replacement of the prey killed (or moulted) is frequently impractical, in contrast to scheduled replacement. In the latter case, prey density fluctuations depend on the time interval of prey replacement. Con­ sequently the mean motivational state is destabilized. The fluctuation of the prey density can be damped by shortening the replacement interval and enlarging the experimental area, provided the initial prey density is kept at the same level by adequate increases in the number of prey. Due to the actuating prey density the rate of prédation will be underestimated rela­ tive to that obtained at a constant density. The degree of underestimation at several values of the replacement inter- val and of the experimental area are given in Figures 37 and 38 for a spe- ci*l case studied by Küchlein (young female predator of Netaseiulus occi- ****lis, eggs of Tetranychus urticae as prey, unwebbed substrate, T = 25-27°C). As the density initially established declines, the underestima­ tes become more and more severe at all schedules of prey replacement. This is a consequence of the curvilinear shape of the functional response c^e: the effect of a unit change of the prey density on the rate of pr - dati°n becomes more and more severe as the initial prey density^f "^ Tt* actional response, measured by Küchlein (to be P^^ *£ Requirements: the experimental leaf area was large (5 cm*), the inte ;al <* Prey replacement was short (0.5 hour) and the predators were stand- 12ed ^fore use and adapted to their experimental environment for se **•• The leaf discs were put on water-soaked cotton xn . PetriJU- , 1Ch largely prevented dispersal of the predator from ^fj^^

I; pimentai time alloted (. hours). *. ^£^£^* 1 SimUlati0n S ^hlr:-U1 ^ . r^rrrlrlt However .t lowerpre y each other in the range 5-30 prey eggs per cm'. «"- a fa ;::^ ** .^.t* PMtim «— ** -«««- ^ „i Dr dator and Aviation may be explained by a lower coir 149 RELATIVE UNDERESTIMATION!^ 1.0

PREYEG GDENSIT Y(CM "

Fig. 37. Influence of the prey replacement interval on prey consumption relative toth erat eo fstead y stateprédation . Experimental conditionsar e takensimila r tothos ei nKüchlei n (tob epublished )excep t for theexperi ­ mental area (=1 cm 2; comparewit h Fig.38) .

RELATIVE UNDERESTIMATION (%) 1.0

1 5 10 PREYEG GDENSIT Y(CM" 2)

Fig. 38. influenceo fth esiz eo fth eexperimenta l area atconstan t initiai litial prey density onth erat eo fprédatio nsimulate d under conditions of a12-hou r prey-replacement schedule.Th eunderestimatio n of thepre y consumptionrela ­ tivet oth esimulate d rateo fstead y stateprédatio n isplotte d againstth e initial prey-egg density. Experimental conditions are similar to thosei n Küchlein (tob epublished) . 150 ie in o co <* es in co o d es co in co in o H CM <* in M in r- o es r- H es es es co co co

C o •H +J 10 TJ 01 H a •o

id H 3 incsmocsHin^coooicscoin a cot^oir-ics^int^csint^ocsr- •H HHCSCSCSCOCOCO CO o o o o c 0 •H 4J 10 Ol es es en t- V t-~i^r~r~coooooo H Ol iß ^ 0) (0 0) ' H co m r- H CS a a 0 3 w n e o •H o H lu 0) ft 10 T3 4-1 ^ 01 3 •H O o o co 3 o o o o co o m I •P * r~ o o o o r- £sssss^° 10 CS CS H H CS

151 prey, causedb y an increased tendency towards anedg e oriented walk (=dis ­ persal). Possibly the ribs and edge ofth e leaf are frequented more often in this range of low prey densities than indicated by themeasurement s at high prey densities (Subsection 3.2.6). Atver y lowpre y densities thesi ­ mulatedprédatio nbecome s equal and subsequently lower than the actualmea ­ surements. As discussed by Küchlein (to be published), themeasure d prédationre ­ veals two particular phenomena at the extremes of the prey density range under investigation. Firstly the eggconsumptio n does not decreaseprogres ­ sively below a food supply of8 egg spe r disc,bu t rather ittend s tosta ­ bilize despite the decreasing prey supply. Küchlein argues that probably the searching behaviour isstimulate d by increased walking speed and acti­ vity, assuming prey isdetecte d attarsa l contact (Subsection 3.2.3). Such a behavioural response was observed for Amblyseius bibens, apredato rre ­ sembling Metaseiulus occidentalis invariou s respects.Henc e it isinteres ­ ting to include thesebehavioura lmeasuremen t inth e input for anothersimu ­ lation experiment. The agreement between simulated andmeasure dprédatio n is somewhatimproved ,bu t aful l explanation ofth e sigmoid prédationcurv e is stillno t achieved. The secondpeculiarit y ofth e functional response curve shows up athig h prey-egg density. Comparison between simulation and measurement revealsa second riseo fth emeasure dprédation .Thi s difference may indicate another motivational component, which is not related to the amount of food inth e gut; the piercing ofth eeg gchorio nma yb e stimulated by frequent contact withpre y eggs.Th equestio n ariseswhethe r this level of contact frequency operates under more realistic circumstances. The prey density of 40egg s per cmz is certainly relevant under field conditions.Howeve r the rateo f contact atthi sdensit ywil lb eprobabl y toohig h due to the absence ofweb ­ bing in these experiments. The difference between simulation andmeasure ­ ments athig hprey-eg g densityma yb e caused aswel l by changes in thewal ­ king pattern related to the eggs which were distributed in groups ofte n eggs to easify counting;th epredato rma yb e arrested by the high eggden ­ sity inth e egggroups .

3. 3. 3 Webbing

The webbing produced by the spidermit e causes the relative rate ofen ­ counterbetwee npredato r andpre y (=RE/DPREY )t ob e reduced by a factor1 0 to 100.Thi sreductio n isdu e toth edecreas e of thewalkin g speed, thewalk ­ ing activity and the coincidencebetwee npredato r andpre y in thewebbing . Moreover, webbing can induce drastic changes in the success ratio (Subsec­ tion 3.2.7).Therefor e distinctvalidatio n ofth emode l and its behavioural inputdat a isneede d forth ecas e ofa substrat e covered with webbing. Includingth ewebbin g factor causes several experimental problems.First ,

152 prey replenishment turns out to be an impracticable procedure. Contact be­ tween the brush and the web threads frequently results in activation of the predator, which is sensitive to movements of the web threads. The web struc­ ture may be harmed, too, by these manipulations. Besides, positioning and settlement of the eggs by a brush may differ from the natural egg deposition of the female spider mite. For these reasons the measurement of steady-state prédation is hardly possible. Simulation accounting for non-steady state conditions is the only way out then. To enable these simulations the experi­ ments were started with fully satiated female predators and a specified ini­ tial density of prey eggs in the colony. According to Fig. 39 the underesti­ mation of the rate of prédation can be kept within certain limits by enlarg­ ing the webbed area, shortening of the experimental period and omitting the study of prédation at low prey densities. Another problem is raised by the dispersal tendency of the predators. Leaf discs surrounded by a water barrier proved to be a satisfactory substrate for Metaseiulus occidentalis. However the leaf disc-water barrier system proved to be insufficient for the case of Phytoseiulus persimilis; when the prey density is low, this predator is frequently observed to disperse from the discs and to drown in the water. The best solution is therefore to use natural colonies formed on the plant and to omit the study of prédation at the range of low prey densities, which

RELATIVE UNDERESTIMATION (%) 1.0-,

PREY EGG DENSITY (CM" fi?. 39 Influence of the size of the webbed area at constat! in ^^^ Sens «* on the rate of prédation simulated under conditio ^^^ ^ Prey-repi . underestimation of acement schedule The • plotted against the 1Ve t0 , the simulated rate of steady state prédation is P-— -» = ^ ^^ Dltial prey-egg density. No prey-replacement; experimental per = 2°°C; RH = 70%. 153 giveris et ohig hdispersa l tendency ofth epredator s (see Subsection 3.4.2). At the start ofth eexperiment s rose leaves connected to a 5-10 cmpar t ofthei r shootwer e cutoff .Subsequentl y the leaf systems were placed ina water filled test tube. Young female spidermite s were allowed toproduc e egg colonies on these leaves during 2day s atT =25°C .Nex t the leafsys ­ tems were transferred to aroo m kepta ta lowe r temperature (T= 20°C),t o postpone hatching. After removal of the colonyfounders thewebbe d areawa s measured and the appropriate number ofegg swer e counted ateac hreplicate . The sizeo fth ewebbe d area should exceed 4 cm2, so that an extreme rateo f prédationo f2 0egg spe r 10hour swoul d cause adecreas e of only 5unit so f thepre ydensity .Th e eggdensit y should match some specified levels(14-15 , 30-40o r 50-60), otherwise thesehav e tob e adjusted by crushing thesurplu s eggs with a thinneedle .On eyoun g and satiated femalepredato r wastrans ­ ported to the upperside ofeac h leaf system ona nexcise d part of itsori ­ ginal leaf. This procedure disturbs the predator less. Thepredator s left the excised leaf parts and entered the egg colonies within anhour .Thei r position in the colonywa splotte d foreac h leaf system. During thesubse ­ quent 10 hours thecolonie swer e continuously observed oneb y one.Th ede ­ partures of the predators during this period were registered (Subsection 3.4.2),bu tthes ewer eno tuse d in further calculations of the rate ofpré ­ dation. The results are presented in Table 58, together with simulations formatchin g conditions.A t allpre y densities tested, the simulationscor ­ respondwit hth emeasurement s forbot hphytoseii d species studied. Because most studies ofphytoseii d prédation inth epas t have neglected the factor webbing, it may be worthwhile to comment onthei r reliability

Table 58. Prédation inpre y colonieswit h spidermit e eggs. Webbed area= 4-11 cm2; nopre y replacement;experimenta l period = 10hours ; temperature 20°C;R H= 70% .

Predator species Number of Range ofpre y Measured prédation Simulated replicates egg densities during 10hour s prédation

Phytoseiulus 22 40-60 9.59 3.10 8.92 persimilis 48 25-35 7.79 2.49 7.96 20 10-15 6.71 2.12 6.50

Metaseiulus 27 40-60 3.51 1.48 3.67 occidentalis 29 25-35 3.34 1.13 3.23 26 10-15 2.31 1.04 2.4 2

154 for the purpose of extrapolation to thepopulatio n level.Accordin g toth e datapresente d in Tables 57 and 58 the rate of prédation of Metaseiulus occidentalis is lower on awebbe d substrate (0.36egg spe r hourv s 0.55 eggs perhour) . Behavioural measurements and simulations indicate thatthi sdif ­ ference is explained largely by the difference inwalkin g speed, associated withthes e substrates.Beside s itshoul db e recognized thatth e coincidence between predator and prey eggs onth ebea nlea fdisc suse db yKüchlei n (to bepublished ) accidentally corresponds withtha t inth ewebbe d space.Thu s itma y be stated thatth e artificial edge ofth e leafdisc s contributes to theconcealmen t ofth erea l differences between thesubstrates . Another example of the importance ofth e substrate is found inth ecas e of Phytoseiulus persimilis, which shows drasticbehavioura l changes inre ­ sponse towebbing. Th e relative rate ofencounte r decreasesb y afacto r 100 asa consequenc e ofth ewebbing ,bu tth e success ratio isincreased . Simula­ tions based on these behavioural data show that the rate ofprédatio no n the webbed substrate exceeds thato nth ebar e leafdis cb y afacto r 1.5-2. Apparently the effect on the success ratio overrules thato nth e relative rateo fencounter . Schmidt (1976), whomeasure d theprédatio no fthi sphyto - seiid on bare andwebbe d leaves,foun d aver y similar difference.Th edat a ofTakafuj i & Chant (1976)an d Laing (1968), obtained onunwebbe d substrates, are therefore likely to be underestimations of the prédation rate.Lain g found aprédatio n rateo f 14egg spe r day atT =20°C ,whic h is substantially lowertha n that found inthi spresen t studyb y directmeasuremen t andsimu ­ lation, i.e. 23 eggs per day. Takafuji & Chant found arat eo fprédatio n equal to 20-22 eggspe r day atT =25°C ,whic h contrastswit h themeasure ­ mentsan d simulations atthi s temperaturepresente d inTabl e 58 (i.e.abou t 30egg spe rday) . The female predators of Amblyseius potentillae showed acompletel ydif ­ ferent response to the presence of webbing. The webbed areaso nth e leaf system were frequently avoided.Th epredator s apparentlypreferre d tosta y neart oth e thickestpart s ofth erib s ori nan ycavit y thatca nb edistin ­ guished on the stem.Muc h less frequently thanth eothe rphytoseii d species studied, they entered themit e colonies,wher e theprobabilit y ofcapturin g PreY (= success ratio) is less (Subsection 3.2.7). Thisprobabl y explains the failure of Amblyseius potentillae to control thepopulatio n growtho f Tetranychus urticae, as found ina populatio n experimentdescribe d inPar t2 . These examples undoubtedly prove the importance ofth e factorwebbin g inth e quantitative assessmento fth eprédatio ncapacit y ofphytoseii dpredators .

3.3.4 Temperature

Most of thebehavioura l observations (Section3.2 )wer e carried out atT =20?c ,s o thatthes emeasurement s shouldb e repeated forothe rtemperatures . However the few additional experiments carried outa tothe rtemperatures ,

155 indicated ratherunimportan teffect s onth e searchingbehaviour .Temperatur e does exert a strong influence, however, onth e food conversion physiology of the Phytoseiidae (Subsection 3.1.2). Itma yb e assumed, therefore,tha t the searching behaviour isrelate d toth e food content of the guti na wa y independent of temperature, while the temperature-related dynamics ofth e food conversion determine therat e ofprédation . Inothe rwords ,th erela ­ tionbetwee n the relativerat eo fgu temptyin g and temperature mayexplai n the effect of thetemperatur e onth erat e ofprédation . This assumptioni s evaluated ina numbe r ofsimulation s and experiments concerning therat eo f prédation at different levels of the temperature and high density ofth e prey. These are presented in Tables 59, 60, 61, 62 and 63.An y measured prédationrate ,deviatin g from the simulations based on the aboveassumption , may indicatebehavioura l changes,associate d with the temperature.Fo rexam ­ pleth ewalkin g speed,th ewalkin g activity orth e ability to capture apre y may be decreased bytemperature s lower than 20°C. Intheor y it ispossibl e thatcounteractin g effects ofth etemperatur e neutralize each other, sotha t theresultin g rateo fprédatio ndoe s notdeviat e from the simulation.Howeve i iti sno tlikel ytha tth e temperature has apositiv e effect on onebehaviour a component and anegativ e effecto n another. Iti smor e likely, thatth eef ­ fecto ftemperatur e onth e searchingbehaviou r shows one consistenttendency , if any. In that case an evaluation, as outlined above,ma y be apowerfu l tool inlocalizin g relevant areaso f further research onth e searchingbeha ­ viourunderlyin g the functional response atdifferen t levels oftemperature . In Table 59 the simulated and measured egg consumption of Netaseiulus

Table 59. Therat eo fprédatio no ftw ophytoseii d species (young females) atthre elevel s ofth etemperatur e and high density of thepre y inth e webbed area.Pre yeg gdensit y =40-6 0eggs/cm 2;webbe d area =4-1 1 cm2;n o preyreplacement ;experimenta l period = 10hours ;young , satiated female predators.

Predator species Number of Temperature Measured prédation Simulated replicates (°C) during 10hour s prédation

Phutoseiulus 31 15 5.16 1.44 4.71 persimilis 22 20 9.59 3.10 8.92 35 25 12.16 2.72 12.58

Netaseiulus 27 15 2.07 1.12 2.19 occidentalis 27 20 3.51 1.48 3.67 22 25 4.57 1.41 4.92

156 Table 60. The rate of prédation of Metaseiulus occidentalis atdifferen t levelso ftemperatur e andhig hdensit y ofth eprey .Numbe r ofpre y eggspe r leafdis c = 100;lea f area = 5cm 2; unwebbed substrate;th epre y eggs killed werereplace d after one day= adaptationperio d ofth epredator ; subsequent periodo f 1da y = experimental period.

Number of Temperature Egg consumption Simulated replicates (°C) perda y egg consumption

71 15 4.73 2.95 5.23 76 21 10.09 5.94 9.82 64 26 13.16 - 13.57 68 33 14.87 6.30 15.30

a.Unpublishe d data fromKüchlein .

Table 61. The rate ofprédatio no f Amblyseius bibens atdifferen t levels ofth e temperature andhig hpre y density.Pre y eggnumbe r =40 ;lea fare a= 4.5 cm2; unwebbed substrate;th epre y eggskille dwer e replaced afteron e day= adaptatio nperio d ofth epredator ;subsequen tperio d of1 da y =expe ­ rimentalperiod ; eggs of Tetranychus neocaledonicus.

Number of Temperature Egg consumption Simulated egg consumption replicates (°C) perda y

32 18 4.4 1.8 7.5 21 22 9.7 1.8 10.3 30 25 13.4 2.2 13.5 16.6 25 28 17.2 1.7 18.9 37 31 21.2 2.3

a.Dat a fromBlommer s (1976).

occidentalis and Phytoseiulus persimilis isgive n forthre edifferen t levels oftemperatur e andhig hpre y density.Thes e experimentswer eearne d outo n webbed leaves according to theprocedur e discussed (Subsection 3.3.3). There is a striking correspondence between the simulated andmeasure dprédation , which indicates the absence ofrelevan t effects ofth etemperature .Th e same

157 Table 62. The rate of prédation of Amblyseius potentillae at different levels oftemperatur e and atdifferen t densities of the larvae of Panonychus ulmi. Leaf area = 3.8 cm2 (or7. 6 cm2); unwebbed apple leafo f 'GoldenDelicious' ;interva l ofpre y replacement = 15minute s (T= 25°C )o r 1 hour (T = 15°C); experimental period = 1 day;predator s are adaptedt o the environmental circumstances forsevera l hours.

Number of Temperature Number ofpre y Prey consumption Simulated prey replicates (°c) per leafdis c per dayc consumption

16 15 0.5 1.7 1.45 3.32 24 1 2.7 1.15 4.29 10 5 9.9 6.2 7.46

2 18 1 6.0 - 6.11 8 2 7.7 10.1 7.91 8 5 9.7 10.2 10.94 5 10 12.0 7.6 13.57 4 25 19.4 11.4 16.94

20 25 1 13.4 9.1 9.43 12 5 23.0 13.1 17.81 8 10 24.0 3.9 21.90

Data fromRabbing e (1976).

conclusion can be drawn from a similar analysis of the experiments of Küchlein with Metaseiulus occidentalis over a broad range of temperatures (Table 60).O n the contrary the analysis of Blommers's experiments with Amblysezus bibens reveal aneffec to f thetemperatur e (Table 61);th esimu ­ lations at low temperature result in anoverestimat e ofprédation , those athig h temperature result ina nunderestimatio n of theprédation .Apparent ­ lyth e searchingbehaviou r of Amblyseius bibens is stimulated by hightemper . ature, while it is less effective at low temperature. Another indication for such a role of the temperature can be obtained from an analysis of Rabbinge's(1976 )dat aconcernin g Amblyseius potentillae and Panonychus ulmi as prey (Tables 62 and 63).Assumin g that the fruit-tree red spidermit e and the two-spotted spider mite are identical asprey , the functionalre ­ sponse of Amblyseius potentillae to the density of the larvae and adult thHr i, theSPlde rmlt e areSimulated - Comparison between the dataan d simulations again shows atendenc y to overestimate theprédatio n atlo w

158 Table 63. The rate ofprédatio no f Amblyseius potentillae at different levelso ftemperatur e and atdifferen t densities ofth e adult females of Panonychus ulmi (eggs of Panonychus ulmi were not consumed). Leaf area= 3.8 cm2 (or 7.6 cm2); unwebbed leafo f 'GoldenDelicious' ;interva l ofpre y replacement = 15minute s (T= 25°C )o r 1hou r (T= 15°C); experimental period= 1day ;predator s are adapted toth e environmental circumstances forsevera lhours .

Numbero f Temperature Number ofpre y Prey consumption Simulated prey replicates (°C) per leafdis c perday " consumption

16 15 0.5 0.91 1.03 0.70 24 1 1.17 0.43 1.03 11 5 1.09 1.62 2.42

20 25 1 2.55 3.12 1.89 12 5 6.99 3.60 4.47 8 10 6.38 5.18 6.55 a.Dat a from Rabbinge (1976). temperature (15°C) and to underestimate at high temperature <25°C),whil e there is correspondence at intermediate temperature (18°C). indeed there are some directmeasurement s ofth e searchingbehaviou r that indicate that it is affected by temperature,thoug honl y slightly. Forexam ­ ple, the walking speed increases somewhat for an increase in temperature (Subsection 3.2.2). It is quitepossibl e thatth ewalkin g activity oreve n the ability to capture a prey are affected too.Howeve rbefor e suggesting the need of further experimentation it shouldb e stressed thatth e effect of the temperature on the walking speed, aswel l astha to nth epredator y searching behaviour, was studied onunwebbe d substrates facingupward .Fo r webbed substrates, which are theusua l substrate foran ypredato r foraging on the two-spotted spider mite, similar analyses showed that temperature hadn o effect onpredator y searching behaviour.Thi sresul tcorrespond swit h the assessment of onlymino r effects ofth etemperatur e onth e temperature on the walking speed inth ewebbe d area (Subsection 3.2.2). Inadditio ni n the case of the fruit-tree red spider mite, which does not produce web aggregates, it is more careful to study the effect oftemperatur e onth e searching behaviour atth e sideo fth e leaf facing downwards,becaus e there the walking speed of Phytoseiidae is reduced to 15-25% ofvalue s forth e upperside of the leaf and the effect of temperature onth ewalkin g speed mayconsequentl y besmall . 159 3.3.5 Age and oviposition history

So faronl y young females, aged 3-8 days after their finalmoult ,hav e beenconsidere d inthi s chapter.Becaus e thepopulatio nmode l ofth epreda ­ tor-prey interaction includes prédationa tal lphase s ofageing , thebeha ­ vioural study ofth ephytoseiid s should beextende d accordingly.However , before doingso ,th enee d forfurthe r experimentation isconsidered . Itma y be assumed tentatively that the ability tocaptur e apre y successfullyi s constantwit h agei ncontras tt oth econversio n of food (digestion,resorp ­ tion, synthesis and allocation). Inothe rwords ,th erelativ e rateo fsuc ­

cessful encounter (=RSE n, ifDPRE Y= 1 ,0 « n« N)ar econstan t duringth e whole period of female adulthood,bu tth erelativ e rate ofgu temptyin g( = RRGE) isvariabl e in this respect. Inthi s case anychang e inth erat eo f prédation during the adult period is thought tob e causedb y achang ei n the intrinsic food utilization of thepredato r apart from changes inth e prey density. Ifthi s conception is true,i ti ssufficien t tomeasur eth e behavioural components aton e specific ageperiod , while the agerelate d changes inth e relative rateo fgu temptyin g canb eestimate d from there ­ production curves,presente d or referred to inSubsectio n 2.2.3,wit hth e aid ofth emode l ofmas s expenditure inth ephytoseii d body (Subsection 3.3.2). These assertions willno wb eevaluate d against experimental obser­ vation.

The assumption thatRSE n isconstan twit h ageca nb eevaluate db ycompa ­ risono fth eobserve d prédationrat eo ffemale s ofdifferen t ages thathav e the same level offoo dconversion . This isachieve db ycomparin g thepréda ­ tiono fnon-ovipositin g females ofdifferen t ages: - unmatedyoun g females (2-4day s after final moult) - unmatedol dfemale s (about3 0day s after final moult) - 'young'postovipositio n females (25-35 days after final moult) - 'old'post-ovipositio n females (45-55 days after final moult). These females aresuppose d tohav e thesam e levelo ffoo d conversionbe ­ cause theirweight s areapproximatel y equal andth esynthesi s ofprotoplas m only serves to replace oldprotoplas m ('non-growing system'). Inadditio n to direct measurement, prédationca nals ob esimulate d (Subsection 3.3.1). The relative rates of successful encounter (=RS E, i fDPRE Y= 1 , 0 < n 4 N) areobtaine d fromth e3- 8da y females (Section".2 )an dusin g themode l ofphytoseii d mass expenditure (Subsection3.3.1 )unde r conditions ofsatia ­ tion, avalu e ofRRG Eca nb efitte d such thatth eweigh t lossb ytranspira ­ tion and respiration (=f reshweigh tminu s food content ofth egut ,multi ­ pliedb yth erelativ e rateo fweigh t loss; seeSubsectio n 2.2.5 andSectio n 3.1)ar e compensated byresorptio n offoo d from thegu tstore .Th esimula ­ tionso fth erat eo fprédatio no nbasi s ofthes e inputdat a correspond with thevalue s obtainedwit hunmate d young andol dfemale s andth e 'young'post ­ oviposition females (Table 64).Th eprédatio no fth e -old'post-ovipositio n

160 T3 fi Ol 0 pi •H (0 •p rH (0 3 T3 O) m •sH M M P. fi 0 >1 •H XI in •P l/> (0 0a i •o *—>1* •H m ai ai (0 •P T3 •H <* o u Ifl M-l a M O o 4) T3 •Oo) •aH m rH ft ai o uP en 0> H in Ol •p 10 Ifl (0 0> 10 >1 o m 01 CD 0 4a) (0 E w a 1H •0 co fi 0 >1 •H Lfl •P x> m Ifl ^-N fi0 i -0 >1 •H in IV (0 P CN •0 •H uP. Ifl M-t 0 0 T3 n4) •o 4) •aH m r-t M a 4) 0 3 (0 0> H m Oi P 10 Ifl m Oi u E >1 co O) a> 0 41 as » S a i 0 •H xi •P w 10 .-»* 0) >i H -ma (8 (0 M T3 •0 a(U rH a M-l 0 •a 4^> Ifl Mu a neu >1 3 [0 •P Ifl M Oi -0 ai 01 mg co CM 1) 4> o in S w 32 m 01

C 1 0 •H X) P Ifl (0 ^~s 11 T) >1 r-l (U (0 (0 T3. M •0 S H 1) 0 a M M-l T) (U Ifl 0 a. •0 >i u (U (0 3 m p T3 en r~ (0 Oi (0 H 10 Oi ë sl< 41 <1* O «tf a> fi H E •^ 3 M

Ifl w 3 IQ -H "H Ifl w 3 -H 3 'H 3 ^ (0 •H "-H •H 3 -P 4) 'H 4) •r-4 fi 0 m Ifl S Ifl tfl 4) 4) P 41 üi C W "0 •H 0 'H (0 +J Ifl r-H CO H! -M •a 0 Ül>s >Q •Q •U 0 4) 41 •C 4) s "H 41 U u a G< 0. •^ •Q S 0 fc u 161 females is somewhat lower thanth e others,whic h indicates a slighteffec t due to ageing. However this effect can alsob e left out in simulations of the interactionbetwee npredato r andpre ypopulations ,becaus e the fraction ofth e females reaching thisphas e of adulthood (50days )i s small,anyway . For this reason the simulations onth epopulatio n level have beenbase do n the assumption ofsearchin g ability,whic h is constantwit hage . The second assertion ofa variabl e relative rate ofgu t emptying (RRGE) with age is thereforeprobabl y true,becaus e the reproduction has acurvi ­ linear relation with age (Subsection 2.2.3). The relation of RRGE toag e appears to have a flexible character due to the strong tendency amongth e Phytoseiidae to achieve the deposition of aspecifie d number of eggs,for , as argued in Subsection 2.2.3, the rate of reproduction does not dependo n age, but rather on thenumbe r of eggs already deposited. Becausereproduc ­ tiondepend s onth e delivery of gut stores,reproductio n canb emodelle db y relating the relative rate of gut emptying to the oviposition history of the predatory female (=th eproportio n ofth epotentia l fecundity thatha s been realized). InSubsectio n 3.1.2 itha sbee n shown that directmeasuremen t ofth eRRG E corresponds with its indirect estimation by amode l ofth ephy - toseiidmas s expenditure.Therefor e thismode l hasbee nuse d for theappro ­ priaterate s ofreproductio n to estimate RRGE for several 'history'classes . These estimates weremad e forth e case of ample food supply, so that aswel l asth erat eo freproduction , the food content ofth e gut is known.Thu sth e relative rate of gut emptying canb e fitted inth emas s expendituremodel . For sufficient description ofth e changes inth e food conversion, theovipo ­ sitionhistor y shouldb e divided into at least fourepisode s (classes)wit h respectt oth e realized parto fth epotentia l fecundity: - less than 60%o fth e eggs deposited - 60-85%o fth eegg s deposited - 85-100%o fth eegg s deposited - all eggs deposited (=post-ovipositio n period). The appropriate values ofth e relative rate ofgu temptyin g are giveni n Table 65.Thes e estimates were obtained from the reproduction curvespre ­ sented orreferre d to in Subsection 2.2.3,whic hwer e obtained at conditions ofabundan t food supply.Th eestimate s were evaluated atlo wprey-eg gdensi ­ ties for the caseo f Metaseiulus occidentalis, using data of itsreproduc ­ tionhistor y (Küchlein, tob epublished )an d simulations ofth e eggconsump ­ tion at the appropriate conditions (prédationwa s notmeasure d inth e same experiment). Because estimates ofprédatio n atal lprey-eg g densities were available andth eRRG Evalue s ofeac hhistor y classwer e estimated fromth e reproduction curve ata hig hpre y density (150egg spe r 5 cm*), therat eo f reproduction at lower prey-egg densities were simulated with themode lo f mass expenditure, and subsequently theestimate d andmeasure d reproduction curves were compared (Fig. 40).Th e agreement was quite satisfactory for the period 0-50 days, but when the age of thepredato r exceeded 50 days,

162 0) 1 H M 0) U« u u u a 01 0u 0 0 0 •o ms 01 m \0 (0 o •H •p M CO M CO co H 3 i 1 1 1 •0 (8 m <* W 0 •H w o 4J •H ! m r-l öl 0 u •oH< >1 •cH u >1 0> 0 •p 4-> •p •* •* •* oi 10 O O* O o a 0 •H s41 —• , CM J3 O » O • O • o•

Ü V r-l • h« 1 >1 X >1 M 01 (8 0 •0 4-1 •>H CwM 01 4-1 *^»- •H (B jo M si H Ol PH CO U O u o o o U II iJ 0 o W «H G U V U —' H 01 >1 1 01 a M O ro G 0 0 r-l 0 4-1 U •H 10 r-l . 4-> •H 1 >1 (0 Xi >i M r-4 (0 O 0> C •o 4-1 U 0 to •ri •H T) 01 4-1 X! . 01 •H w •a 43 04 a* « 01 •P 10 •o 01 M o 01 •H 0 o 01 ij O 01 •H r-l 01 0) 0 ra M « CU 1-1 o. r-l >1 0 01 u H *—, >1 4-1 Ä H 01 4-> •r( U •p >1 10 4J •H •0 U (8 •H •O ß 01 C 0 rH Ä T3 G 3 •H 0 3 ü •P r-l , fi 01 W 1 3 u >1 01 'M 'M 01 0 >i M 01 M-l 0 01 itJ 0 1« r-l ft) •0 4-1 ra 10 J3 01 r-\ <-\ra •H G 0, •H ra •H 4-1 0 W •H 4-1 •H V4 CM a in O c C4 4-1 0) 4J 3 O M CV] G Oc) •P (0 O J 0 H 4J

80 90 100 TIME(DAYS )

Fig. 40. Cumulative reproduction inrelatio nt oag ean dovipositio n history of Metaseiulus occidentalis atdifferen t levels ofprey-eg g density. Measured data ofKüchlei n (tob epublished ) ( )an dsimulate d values ( )• Unwebbed leaf disc; area 5 cm2;dail y replacement ofegg s consumed; T =25-27°C ;R H= 70%. reproduction stopped, irrespective ofth eovipositio n history. Because rela­ tively fewfemale s reach this period ofadulthood , this aspectma yb eignore d m simulations ofth einteractio n between predator andpre y populations. Unfortunately, such evaluations ofth eestimate d values ofRRG E couldno t be carried outfo rth eothe r predator species because oflac k ofreproduc ­ tion-history data atlo wpre y densities andfo rth ewhol e life-spano f phytoseiid females.

3. 3. 6 Predator density

When predators aggregate incolonie s with a high prey density, iti s likely that they will encounter each other while searching forprey . This contactma yi ntur n lead toa nincrease d tendency toward dispersal (Subsec­ tion 3.4.3)or ,i fth epredator s areconfine d toth epre y colony, toa de ­ creased prey consumption.Th elatte r case willb econsidere d below. Küchlein (1966)observe d adecreas e inth erat eo freproductio n of Meta­ seiulus occidentalis atpredato r densities exceeding onefemal e perlea f disc. Fernando (1977) found adecreas eo fth erat eo fprédatio nb yfemale s of Phvtoseiulus persimilis. Because the ingested food isutilize d toa great extent ineg gproduction , reproduction decreases when prey consump­ tion decreases. A decline inth erat e ofpre y consumption canb ecause db ya decreas e

164 in: - therat e of contactwit hpre y items (i.e.RRE ) - thereceptivit y to contactwit hpre y (i.e.Succes s ratio) - therat e of food conversion (i.e.RRGE) . Because the timepredator s spend incontac twit h each other isneglegible , and the walking speed and activity remain unchanged after mutual contact (ownobservation ; Küchlein,persona l communication),th e time available for prey searching remains nearly unchanged, at realistic predator densities andtherefor e the firstpossibilit y canb e cancelled. The latter twoexpla ­ nations are difficult to illustrate by experiment. Itma yb e hypothesized thatth e reproduction site inth e acarine functions as a 'sink'wit h respect toth enee d for food and thatthi s 'sink'i scontrolle d by theneurophysio - logical state of thepredator .Mutua l contactbetwee npredator y femalesma y affect that state and hence the need of food for egg production. Ifth e prey-capture ability isno t affectedb ypreviou s contact,th edecrease d rate ofpre y consumption isth e simple resulto fa decrease d rateo f foodconver ­ sion. This is a simple mechanism because itrequire s only achang e inth e relative rate of gut emptying instead ofchange s inth e success ratios at several levels of gut filling. For the time being this explanation ispursue d andhenc e theeffec to f interference among femalepredator s canb emodelle db y estimating RRGE from the reproduction curves at different levels ofpredato r density, measured byKüchlei n (1966)fo rth e case of Metaseiulus occidentalis. This estimation is again made with the model of the mass expenditure (Subsection 3.1.2), assuming that the success ratio isunaffecte db ymutua l interference.Eve n ifthi s tentative conception turns outt ob ebiologicall y invalid afterwards, it is still a very easy way ofimitatin g theobserve d effects ofpredato r density onth e rate ofprédation . The estimated values ofRRG E aregive ni n Table 66 for different phases in the ovipositionhistor y ofth epredator y mites.

3.3. 7 Prey stage preference

If prey stage preference is not expressed until the momento f contact with a prey stage,i tca nb e defined quantitatively by the<"««*»« " ^ tween the success ratios related to the differentpre y stages (Subsection 3.2.7). Preference thus defined includes the defensive measures taken by theprey , and thepalabilit y ofth eprey ,a swel l asth e ^^essiveness nd attackingmeasure s takenb y thepredator .Th e successratio shav e I.en «. sured in -monocultures' of each prey stage (Subsection3.2.7 ) *»••*£ are suitable for extrapolation to 'mixed cultures' ofpre y stagesi fth e actual success ratio isno t alteredb y experiences at ^'^^ Preystages, an d ifthi s ratioi sdetermine d merelyb y thea cu . «ount of food inth e gut,whic h isth eresul to f 'past' ingestion and past

165 CD XI w P ta rd 73 r-l a U m r-T >1 >i 1 M u >1 0 o rd p p •0 to 10 >-• -H •H £ Xi O S-i (C lu ^0 ^0 Ö OJ 0 0 os m o o o o •H •M •ri U] 0 a Ü •H m >O to to m rd xl r-l •P u ». . H~ >1 Oi 5-S 1 ^ >1 0 •rai ro- rd P >i •0 to —• -H P u X! o- ^ U in in in s a Ü U o o er. r> ai 3 K 0 P - « XI m CM CM •P rO II in U w H (0 (1) r-l u -r>i W• --•" •P -N r-l >1 rd "S 1 M r-l ni >1 O CD -u rd -P U q T> U] 0 « 0 C 0 (U « <« CD 10 S 3. P "H 0) S CD X) "M 10 CD roH •H a « r-l 0 t< to rd •H -tJ Ul CU •P 1 (U 1 1 U Ol p •o CD CD >1 0 •r-l a Xl 10 rd -P 3 P rd TJ tO Ö u 0 >— -H 3 CD tH Xi - ,- o m w in in U CD 'M X! U M CM lO CM 1 «u O CD O -H •H P •P rd M P a •P P -H •rt CD O S« a 0. m •H o •H *0• u U U U-l o > <& o 0 M V "ö co rH O p P CD 0 •O ia I P (0 X! I - T3 siono ffood . Under this assumption theprédatio ni nmixe dpopulation so fpre y stages canb esimulate d onth ebasi so fbehavioura l inputdat ameasure d inpopula ­ tionso fon estag ea ta time .Th eQueuein gmode lca nb eadapte dt oth ecas e ofmixe d populationsb yextendin gth e'ingestion 'ter mi nth ese to fdiffe ­ rence equations, which relate p (t+DELT)t op (t)(Subsectio n 3.3.1).Th e food level no fth egu tca nb earrive d atb yingestio n from several lower levels duet oth edifferen t food contentso fth epre y stages (=FC P; s = 1,2, .... s = prey stages labeled byenumeration) , which areswallowe d immediately after capture.Th esiz eo fth efoo d intakedepend so nth efoo d contento fth epre y stagean dth esatiatio n deficito fth egu t( = N-n).

f^= min(FCP S *ENLARG ,N-n )

Henceth eprobabilit y toreac h staten vi apre y capturean dsubsequen tin ­ gestionconsist so fth esu mo fth eprobabilitie so neac h- pre y stagespeci ­ fic- ingestio n (=FCP S), which arrivesa tstat en :

S <; S S S I = i RSE *p *DEL T (f= FCP *ENLARG ;N- n> FC P) n n-f *n-f s=l At full satiation itincludes ,furthermore ,th esu mo fth eprobabilité so n eachpossibl e partial ingestion,whic h arrivesa tN : S N-l s,

I.T= 2 2 RSE *p *DEL T (f= FCP "* ENLARG ;N- n^ FCP) N s=ln=N- f n n

Thecomplet e seto fdifferenc e equationsi sthen :

Pn(t+DELT)=p (t)* ( I RSE^+ RGEl n)* DEL T+ P n+1(t)* RGEl n+1 *DEL T+ I n s=l

PN(t+DELT)=p (t)* RGE1 N *DEL T+ I N Theexpecte d amounto ffoo d consumedpe rtim e intervalDEL T (=CONS )ca nb e computed from thedifferenc e between thesuccessiv e distributions ofth e satiation levels, plus theamoun to ffoo d resorbedo regeste d fromth egu t duringDELT :

N N

CONS = 1I ((pVip (t+DELT (t+DELTv ))- P - np(t)n(t))+ )2 + 1 Pn(t+DELT) * RGEln * DELT n=„=0n nn n n=n=0 0 The expected number ofeac h prey stage killed duringDEL Tca nb ecompute d from theproduc t ofth erelativ e frequencieso fpredator sa tth edifferen t satiation levels andth eappropriat e prey stage specific rateo fsuccessfu l capture:

167 N PREDs =I RSE"* DEL T Pn(t) n n=0

Thestead ystat edistributio no fth epredator sove rth esatiatio nclasse s (=p )ca nb ecompute d ina wa yanalogou st otha tdiscusse di nSubsectio n 3.3.1.I ncas eRGE 1an dRS Ear evaryin gdurin gth eprocess ,numerica lsolu ­ tiono fth ese to fdifferenc eequation si sth eonl ywa yout . Withth eai do fthi smode l extensioni ti spossibl et oextrapolat eth e inputdat ameasure di n 'moncultures'o fth epre ystage st oth ecas eo fmixe d populationso fpre ystages .Thi sapproac hca nb evalidate dusin gexperimenta l datao fRabbing e (1976).H eoffere d 10spide rmite so ftw odistinc tpre y stages (larvaan dadul tfemale )t oa youn gfemal e Amblyseius potentillae. The prey stages were offered indifferen tproportion s (8:2,5:5 ,2:8) , whichwer emaintaine db yreplacin gth epre ykille d (ormoulted )afte rin -

PREDFEMAL E PREDLARV A 10

0.050. 1 D FEMALE D LARVA Fig. 41. Measurements (Rabbinge, 1976; Experimental area = 5 cm*; interval of prey replacement = 1 hour; T = 25°C) andsimulation s (this report)o f prey-stage specific prédation inmixe d populations oftw opre y stages (lar­ vaean dadul tfemal eo f Panonychus ulmi). Thequotien to fth epre ystag e specificprédatio nrate si splotte dagains tth equotien to fth erespectiv e densitieso fth epre ystages ,bot ho na logarithmi cscale .Measure dvalue s (•)•a t 3 prey stage combinations: 2 9+ 8 larvae; 5 ?+ 5 larvae ; M+2 larVae" Stations ( )a t3 overal lpre ydensities : prey female+ Dlarvae~ WAREA ,wher eARE Aequal s5 ,5 0o r50 0cm 2

168 RELATIVEFOO DCONTEN TO FTH EGU T 1.0-

FEMALE LARVA 5 2 0 PREYSTAG ECOMBINATIO N

Fig- 42. Simulated mean level of the gut filling at three overall prey densities, consisting of different combinations of larvae and females. Thisplo t fits to the simulation experiments presented inFig .41 .

spections at short time intervals (1 hour). By assuming, that the prey stages in question resemble the two-spotted spider mite in theirrol e as prey, these experiments can be simulated onbasi so fth ebehavioura l data of this Agricultural ResearchReport .Th e results arepresente d inFigure s 41 and 42 as a plot of the quotient ofth epre y stage specificprédatio n rates against the quotient ofth e respective densities ofthes epre y stages (2:8, 5:5, 8:2).Th e simulations agree with the experimental data ifth e larvae constitute halfo rmor e ofth epre ypopulation .Whe nth e adult female Preys form the majority, however, the prédation of this particular stage seems to be favoured in comparison toit s simulatedprédation . Presumably thiseffec t is causedb y adisturbin g effecto fsom econtact sbetwee n adult female predators and the large-sized female prey. The contact caused the predator tob e less attentive inlocalizin g the small sized larvalprey . The success ratio curves presented in Subsection 3.2.7 show thatpre y stage preference is strongly related to the size of the prey. Moreover these data suggest, that the preferences tend to vanish asth esatiatio n level of thepredato r decreases.Thi s effecti sdemonstrate d inFig .4 2wit h theai d of simulations atlowe r levels ofth epre ydensit y (=enlargin gth e experimental area). At a prey density of0. 2 (=10/5 0cm *) th elarva ear e captured more successfully than atth edensit y of2 (=10/ 5 cm), decrease to thever y low density of 0.02 (=10/50 0cm* )tend st orende rth e Predator less fussywit h respect tobot hpre y stages.Henc ei ti sshow ntha t

169 preference could be far from a stablephenomenon . For this reason theus e of descriptive formulas of the functional response curve - like the Disc equation (Cock, 1977)o r other equations (Rabbinge, 1976)- in analyzing preference isdiscouraged : fussiness ofth epredato r is likely to dependo n the food contento fth e gut (orth e availability of the prey).

3.4 RATEO FDEPARTUR E

So farth epredator y behaviour hasbee n considered isolated from anyten ­ dencyt o leaveth epre y colony.B y staying in acolony ,prédatio ndecrease d the food supply of the predatory female and, also,it sprogeny . Therefore departure to other colonies is likely tooccu r sooner or later.Moreover , aspredator s aggregate incolonie s withhig hpre y density, it isincreasing ­ ly likely that theywil l detecteac h otherwhil e searching forprey ,whic h may leadt o anincrease d tendency toward dispersal.Thi s section dealswit h the quantitative assessment of the rate of departure in relation topre y supply and interference between phytoseiid females, butbefor e discussing these measurements the walking behaviour of the predator and the sizeo f the colonized area on residence time in a colony is investigated. Duet o its apparent avoidance of the webbed area Amblyseius potentillae hasbee n excluded from themeasurements .

3.4.1 Walking behaviour

As discussed inSubsectio n 3.2.4, iti spossibl e to simulate thewalkin g behaviour and the linear displacement,base d on analysis ofmeasure d walking tracks.Thi s simulation technique couldb e used to estimate the rate ofde ­ parture, assuming theedg e ofth e colonized area exerts no influence onth e walking pattern. Before turning to such simulations it shouldb e recalled thatth ewalkin gpath s ofSubsectio n 3.2.4 were measured in absence ofpre y or otherpredators .Therefor e iti snecessar y to ascertain whether thewal ­ kingpatter n ismodifie d by theirpresence .Th e observations were madewit h thevide o equipment,describe d in Subsection 3.2.4,t o copy thewalkin gpaths . Thepath swer e registered for1 o r4 predator y femaleswalkin g inside afres h prey colony (eggs and females). Theparameter s of theexperimentall y defined frequency distributions ofangula r deviations were used to estimate thelin ­ eardisplacemen t after20 0steps .Thes e estimates,togethe r with thewalkin g speed and activity, are given in Table 67.The y canb e compared withth e results of Subsections 3.2.2 and 3.2.5. This clearly demonstrates thatth e walkingpatter n isno taffecte db ypre y orpredato r density, nor thewalkin g speed and activity. Thus the rate of departure is independent ofpre yo r predator density, if iti stru e thatwhe n thepredator s arrive atth eedg e ofa colon y theymak e nodistinc t decision to leave or stay. Totes tthi shypothesis ,simulation s of the rate ofdepartur e were compared

170 Table 67. Walkingbehaviou ro ffemale so ftw ophytoseii dspecie si n presencean dabsenc eo fpre yan dpredator si nth ewebbe darea .

Walking Simulatedlinea r Predator Prey Numbero f Walking activity displacementafte r species density predators speed (number/ (mm/s) (%) 200step s(numbe r cm2) ofsteps )

Phytoseiulus 0 1 0.19 12 45 persimilis 20-60 1 0.19 8 43 20-60 4 0.20 9 44

Metaseiulus 0 1 0.18 40 32 occidentalis 20-60 1 0.20 36 29 20-60 4 0.20 38 29 withmeasurement so fth eactua lrat eo fdepartur efro ma colony .Thre ekind s ofcolonie swer eused : - small webbed areas withoutprey , foundedb ymale s andpreovipositio n females , - large webbed areas withoutprey ,founde db ymale s andpreovipositio n females ,. _ , - largewebbe d areaswit hpre yegg sonly ,founde db yovipositin gfemales , whichwer eremove dbefor eth eexperiment . Sucha colon ywa slocate do non eleafle to fa compose dlea fan dt opro ­ videa nalternativ e residence forth epredator ,on eo rmor eo fth eothe r leafletswer e alsocolonize dwit hTyp e3 colonies .On efemal epredato rwa s ade ate f releasedo nth euppersid eo fa leafle tcontainin gth e ^ ^ ° ^ed onyAfte rth epredato rinvade dth ecolony ,th eresidenc etim e bycontinuou s observation (i.e.1 4hour spe rday )ove ra pen ^ of3 days . Thedeparture swer e scored after *<^^^^l^.teZtn afterdiscover yo fth epredato rm oneo fth ealternativ e distancewalke d toreac hth eedg eo fa circula r ^^^^2 100Mont eCarl o simulations ofth ewalkin gpattern ,an dthi ses tmat ewa s convertedint oth eresidenc etim eusin gth ewalkin gspeed , *»"££?££ vity and ifpre ywa spresent ,th efeedin gtime .Th eresidenc etime sest i matedtom^erimlally defined ^^^TZ^ZT

isdetermine db yth elo wwalkin gvelocity ,th elo w» al*in*a ^ £ .„. tortuouswalk .Probabl ysurfac eenlargement ,walkin g ^^^^^ creasedfrequenc yo ftactil eprobin gbefor eadvancemen t- theh eteroge web strucJTe areth efactor sdeterminin gth eresidenc etim em the 171 Table 68. Residencetim eo fyoun g femaleso ftw ophytoseii dspecie si na colonywit han dwithou tprey .T = 20°C ;R H= 70% .

Predator Webbed Prey Measured Simulated species area density residence residence (cm2) (number/cm2)tim e(hour ) time(hour )

Phytoseiulus 3-5 0 0.46 0.2 22 0.52 persimilis 15-25 0 1.60 0.8 32 2.56 15-25 20-60 47.5 17.2 36 2.76a

Metaseiulus 3-5 0 0.36 0.1 28 0.19 occidentalis 15-25 0 0.58 0.3 17 0.66 15-25 20-60 53.4 21.3 24 0.86a

a.Mea nhandlin gtim einclude di nsimulatin gth eresidenc etime .

areawhe npre yi sabsent .Th epresenc eo fkairomone spresumabl yassociate d withth esil k (Hislope tal. ,1978 ;Ho y& Smilanick ,1981 )doe sno tarres t thepredator smor etha nwa sexpecte d fromth emeasurement so fth ewalkin g behaviouri nth ecentra l areao fth ecolony .Howeve rth ekairomona lcue s mayoperat ea sstimul it oente rth ewebbe darea .Indeed ,direc tobservatio n ofth ecolony-invadin gbehaviou rindicate da neviden treactio nupo ncontac t withth esilk ;female so f Phytoseiulus persimilis, Metaseiulus occidentalis and Amblyseius Mbens, walkingo nth euppersid eo fth elea ffrequentl yalon g eedg e(Par t2 )invariabl yturne dt oth eundersid eo fth elea fafte rcon - actwit hsil kstrand sa tth elea fedge .Thi sapparen tinvadin gbehaviou r was^independento fth epresenc eo fpre yi nth ewebbe darea . ea cua lrat eo fdepartur ei npresenc eo fpre ywa smuc hlowe rtha nex ­ pected fromth esimulation so fth ewalkin gbehaviour :th epredator sstaye d forel' f°r SeVeral dayS inStead of thefe whour spredicted .There ­ 036 that thS Predat rs are ab atth ee r T " ° ^ toretur nwhe nthe yarriv e abundant p „ COl°nY ^ that this behaviouralreactio ndepend so npre y ortnHr e "*" * **"*** ±S & "">«^^an t *»ctortha ncolon y•* , webbedove rr CleS "* ^^ Sized when theros eleafle ti s completely 3 and even at betweensu ,, ^^ °^ thismaximu mth etim einterval s vTsZZn T 6d9e arriValS a- °fs -l- magnitudea sth etim einter - twelnI:! ::JZ:::- Theref°re — —^ *" «* changever y persalmechanis m arriV&1S' S°th& t ^ is allowed toconceiv eth edi- - ofturn C t LaIdPred°minantlyPrey —^ty dependent.Direc tobserva ^ theedg ewa strie dtoo ,bu tthi sapproac happeare dt ob eham - 172 peredb y the long observation times necessary toobtai n asufficien tnumbe r ofregistration s and by the inability to find ausefu l criterion forth e 'edge of the colony'. Anyway, the fewresult s ofthes e direct observations wereno t in contradiction withthos e ofth e indirectanalysis . As for colony invasion, the behaviour at evasion from thepre y colony wasobserve d tob e characteristic; theevadin gpredator s tended todecreas e thelikelihoo d of returning into the samewebbe d areab ymovin g toth e leaf edge on the upperside of the leafo rt oth emai nri bo fth eros e leaf,b y increasing the walking speed, by initially spending much time inwalkin g andpresumabl y alsob y atemporar y lowerresponsivenes s tocontac twit hth e silkstrands .Th e latter suggestion isbase d onobservation s of justevade d predators recrossing their path along the edge of the colonized leafan d contacting the silk strandswithou t subsequentinvasion .

3.4.2 Prey density

Quantitative assessment of the rateo fdepartur e shouldb edon e atcon ­ stant density of theprey .Howeve r replacemento fth epre yconsume d isim ­ practicable due to the presence of webbing inth ecolony .A sdiscusse d in Subsection 3.3.3, the prey density can be kept within acceptable limits despiteprédatio nb y enlargement ofth ecolonize d areaan db y shortening of theexperimenta l period. Onth e otherhand ,thes emeasure s shouldb e adapted insuc h awa y thatdispersa l cantak eplac e atth eprope r time.Fo rquanti ­ tative assessment of the rate of departure the followingdesig nprove d to be practicable. The most voracious phytoseiid canconsum e amaximu m of1 6 eggs in 10 hours, so that prey density decreases less than4 unit s ifth e webbed area exceeds 4 cm*. Based on this tentative calculation itwa s decided to classify thepre y density ingroup so f5 units .Becaus e therat e ofprédatio n approaches itsmaximu m atpre ydensitie s above2 0egg spe rc m, the classes were enlarged inthi s rangeo ffoo d supply.Accordin g tothes e conditions, two or more colonies were grown on a rose leaf.Th e female spider mites were removed and the egg densities adjusted to the proper density class bypiercin g the surplus eggswit h aneedle ,i fnecessary .Th e colonized rose leaves were leftconnecte d to a1 0c mpar to fthei rshoot s which were placed in water-filled test-tubes kepti na rack .On ewell-fe d Predator female was transported to each leafsyste m ona n^" * £'^* itsorigina l hostplant.Th epredator s succeeded ininvadin gth e freshcolony within an hour. Subsequently thedeparture s ofth epredator s bynake d eye inspection ofbot h sideso fth eleaflets .»»P ^ £^ generallymove d to theuppersid e ofth e leaf,wher ethe ywer e„» 1y ietec

ted. ln some cases dispersal was indirectly assessed by detect-of the Predator in one of the alternative colonies.I nthes ecase sthe yprobac y dispersed along themid-ri b onth eundersid e ofth eleaves . The numbers of predators thatstaye d inth ecolon y longertha n1 0 173 Table 69. Rateo fdepartur eb yyoun gfemal ephytoseiid sfro ma colon yi n relationt opre ydensity .T = 20°C ;R H= 70% ;webbe dare a= 4-1 1cm 2.

Predator Prey Simulated Numbero fpredator s in Relative species density relative thecolon y rateo f 2 (number/cm ) gutfillin g U,GJhJCLl.UUJ- v -1 (%) atth e start after 10hour s (hour ) Nt=0 Nt=10

Phytoseiulus 40-60 92 24 24 0 persimilis 25-35 91 51 48 0.006 10-15 88 38 20 0.064 5-10 85 41 6 0.192 0-5 <8 1 32 0 0.868

Metaseiulus 40-60 92 45 ' 44 0.002 occidentales 25-35 90 32 29 0.010 10-15 87 36 16 0.081 0-5 <8 0 19 0 0.977

Amblifseius 30-40 91 30 30 0 bibens 10-15 88 30 14 0.076 0-5 <8 1 29 0 0.792

aregive ni nTabl e6 9i nrelatio nt oth edensit yo fth eprey .Becaus eth e fractiono fresidin gpredator sdecrease di na nexponentia lfashion ,th edis ­ persaltendenc yca nb echaracterize db yth erelativ erat eo fdepartur eac ­ cordingt oth efollowin gformula :

-ln(Nt/N0) RRD

RRD= relativ erat eo fdepartur e(hou r )

Nt =numbe ro fpredator sresidin gi nth ecolon ya ttim et (hours) . Ifpossible ,th eRR Dvalue swer ecompute dfro mth etim eelapse dunti l50 % ofth epredator sha dlef tth ecolonies .T oprovid esom einsigh ti nth emea n levelo fgu tfillin ga tth edifferen tdensit yclasses ,simulate dvalue so f therelativ efoo dconten to fth egu tar egiven . Theresult sdemonstrat eth edependenc yo fth erat eo fdepartur eo nprey - egg density while interspecific differences seemt ob eabsent .A spre y densitydecreases ,th erat eo fdepartur eincreases .Thi seffec tcanno tpos ­ siblyb eexplaine db ya decrease d timeexpenditur ei nfeedin gactivities . Evenfo rth eextrem ecas eo f1 6eg gcapture si nth e1 0hou rperio d (Phyto­ ne seiulus persimilis), the total feeding time would amount to 1 hour.Th e residence times aretherefor e predominantly determinedb yth ewalkin gbeha ­ viour at the edge ofth e colony, as argued inth epreviou s subsection. Finally it is a glaring fact, that atth e density of 10-15egg spe rcm * half the initial number ofpredator sha dlef t their colony after1 0hours , although their gut fillingwa sstil l rather high accordingt oth ecomputa ­ tions. This high rate of departure mayb edu et oth eabsenc eo ffemal e spider mites inth e experiments. Hence the experiment hasbee n repeated forth e prey density of 10-14egg s and 0.5 femalepe rcm* .Despit eth einevitabl e ovipositionb yth efemal e spidermite sprey-eg g density remained withinth e limits indicated. The results (Table 70)sho w thatth eadditiona l presence ofth e female spider mites didno t alter the rateo fdeparture .Henc ei t may be supposed, thatpre y density isth egovernin g factori nth erealiza ­ tiono fth eresidenc e timeo fth efemal epredators . Evidently there isa stron g tendency toforag e atdensitie s above2 0egg s per cm*. Natural selectionma yhav e favoured thisdispersa lbehaviou r asa consequenceo fth eachievemen to fa large rprogeny ,bu tthi s simplifiedex ­ planation isno tclear , aslon ga sth eenerg y expenditure involved inreach ­ ingothe rmor e favourable food areas isno tknown . Itma ya swel l havebee n evolved as an anticipation onth e survival chances of theirprogeny .Th e experiments, discussed in Subsection 2.2.1, demonstrate, that development was retarded andmortalit y was increased below a food supplyo f1- 2egg s perday .Howeve r theassessmen to fjuvenil e dispersal yielded only someac ­ cidental departures at this critical rateo ffoo d supplyan deve n«nfertx - lized femalesha da lo wtendenc y todispers e (Table 71).Becaus e thedensit y ofphytoseii d eggsca nris e aboveth eleve lo f1 eg gpe rcm *colonize d area

Table 70. Rate ofdepartur eb yyoun g femalephytoseiid s froma pre y colony containing eggs and females.T = 20°C; RH = 70%;webbe d area= 6-1 0c m; 10-14eggs/cm * and0. 5 female spidermite/cm* . _^^_____

colony Relative rateo f Number ofpredator s inth e prey Predator departure (hour") species atth e start after 10 hours N Nt=0 t=10 0.063 Phytoseiulus 30 16 persimilis 0.060 Metaseiulus 42 23 occidentales 0.050 Amblyseius 28 17 bibens

175 Table 71. Rate ofdepartur e from apre y colonyb y juveniles andunfertil ­ ized females of two phytoseiid species. T =20°C ;R H = 70%;webbe d area= 4-11 cm2; prey egg density = 1-3 eggs/cm2.

Predator Predator stage Number of predators in the colony species of development at the start after 10hour s

N N t=•0 t=10

Phytoseiulus larva 51 49 persimilis protonymph 24 23 deutonymph 41 39 unfertilized female 37 35

Metaseiulus larva 10 10 occidentalis protonymph 28 26 deutonymph 43 41 unfertilized female 32 30

(Part 2),i t isno tunrealisti c to suppose aprofitabl e effect of the dis­ persalbehaviou r ofth e adult femalepredator s onth e developmental prospects ofthei r lessmigrator y juvenileprogeny .Thi s questionwil l be investigated furtherb y sensitivity analysis ofth epopulatio nmode l with respect toth e relative rateo fdepartur e (Part2) .

3.4.3 Predator density

Küchlein (1966)measure d an increased tendency ofyoun g females of Meta­ seiulus occidentalis todispers e from theexperimenta l leaf discswhe nmor e than one predator waspresen tpe r area;predator s leaving the disc drowned in the water-soaked cotton surrounding the disc.Küchlei n stated thatth e data on migration tendency thus obtained are of arbitrary value as longa s a similar study ofth edispersa l on an actualplan t is lacking.A nexperi ­ mentt oprovid e this informationwil l nowb e described. The experimental procedure differs from that discussed in thepreviou s subsection inth e following respects.One ,tw o or four females of Metaseiulus occidentalis were released on the leaf system instead ofonl y one.Becaus e the predators were allowed to invade the colony on their own accord, the colonies were frequently occupied by a lowernumbe r ofpredator s thanre ­ leased onth e leaf.Onl y colonies thatcontaine d adequate (1,2 ,4 )number s ofpredator swer e selected.Th e departures were assessed at consecutive time intervals of 4 hours by detection of thepredato r inon e of the alternate colonies on the other leaflets of the rose leaf.Whe n apredato r leftth e

176 Table 72. The relative rate of departure ofyoun g females of Metaseiulus occidentalis related topredato r density. T= 25°C ;R H= 65% .

Initialnumbe r The range Relative rate ofdepartur e (hour" ) ofpredator s ofpre y egg — — • invaded in the densities first afteron e aftertw o afterthre e colony assessment departure departures departures

4 10-20 0.202 0, .113 0.074 0.039 2 0.033 0. .017 1 0.027 -

4 20-40 0.133 0. .096 0.048 0.022 2 0.016 0. .010 1 0.028 -

colony it was removed to prevent re-invasions;th eobservation swer econ ­ tinued for the remainingpredator s until allwer egon eo runti l theexperi ­ mental period, of 24 hours, had elapsed. This experimental procedurewa s carried out attw o levels ofpre y density: 10-20egg spe rcm * and20-4 0egg s per cm*. The predator densities werebiase d duet ovariatio n inth ewebbe d areas per colony (p= 6.2 cm*, S - 3.1;range :3-1 4 cm*), but thisvariat ­ ionwa s present foreac h level ofpredato r release.Th evalue s ofth erela ­ tive rate of departure, each computed from an initial amounto fa tleas t 100predators , are given inTabl e 72.A spredato rdensit y decreases during theexperimen t as aconsequenc eo fth e departures from thepre y colony the relative rate of departure was computed for each 4-hourperio d thereby classifying the replicates with respect to the predator density at^th e start of these periods. In this way itwa spossibl e tocalculat ethe ^Re ­ values after one, two or three departures incas e fourpredator swer ein i tially present in the prey colony and, similarly, after one departure casetw opredator swer e initially inth ecolony . Evidently there is atendenc y to avoidpredato r agrégationeve nfo rhig h prey densities. This can be recognized from the data m two ™^*Bt' the relative rate of departure increases fora nincreas e in *»^£ predators initiallypresen t inth ecolony . Second,-" ^ ^ ^ by aperio d with alowe rvalu e ofth erelativ erat e °*<*^'^£ dencies are very similar at both levels ofpre ydensity .A ls o t** *>- dispersal atth e lower density rangeconfirm sth e in^£££.«- previous subsection. For some reason (e.g.difference si n P tribution ofpre y densitieswithi nth eclas srang e theRH Dvalu e after the onepredato r release arehighe rtha nthos e stated subsection.

177 4 The useo f experimental and theoretical results in dynamicpopulatio n models

Theprecedin g chapters of thisAgricultura l Research Report describe the modelling of an acarine predator-prey interaction atth e individual level and themeasurement s ofth e inputdat aneede d for thatmodelling; four spe­ cies of phytoseiid predators were studied in relation to theirprey ,th e two-spotted spider mite, which feeds on greenhouse roses. The results of these laboratory studies atth e individual level are tob e used for themo ­ delling of the predator-prey interaction at the population level in the greenhouse. Because of this extrapolation to the population level it is worthwhile torealiz e which assumptions underlying theprédatio nmodel s are still unvalidated, andwhic h inputdat a are stillmissing. In addition,som e important questions arise that arebase d onth e available experimental evi­ dence at the individual level;thes ewil l have tob e solved by experiments and simulations at the population level. Theunvalidate d assumptions,th e missing inputs and the questions that relate to the population level are considered in this chapter,preparin g thewa y forPar t 2 (tob e published) of this report, whichdeal s with themodellin g ofth epredator-pre y inter­ action atth epopulatio nlevel .

4.1 UNVALIDATED ASSUMPTIONS

InChapte r 3,model s havebee ndevelope d forth e simulation of thewalk ­ ing behaviour and the rate of prédationo fphytoseiids .Thes e models were used for the analysis ofth epredator-pre y system atth e individual level. The results are to be used in the population models presented inPar t2 . Someo f the assumptions underlying thesemodel s arebase d onmeagr eexperi ­ mental evidence;other shav e no empiricalbasi s atall . Though the Queueing model ofth eprédatio nproces s proved tob e asgoo d as or even better than other prédation models and successfully simulated the rate of prédationunde rvariou s conditions (Section 3.3), it shouldb e remembered thati trest s on fourbasi c assumptions,eac h ofwhic h needssepa ­ ratevalidation . First,a Poisso ndistributio n is assumed for thenumbe ro f prey capturespe runi ttim e ata certai n level ofth emotivationa l stateo f the predators. Second, the food content ofth e gut is assumed to determine the state dependent rate of successful encounter, whether this state is achieved by previous gutemptyin g orb y previous ingestion of food.Third , iti s assumed thatth e food quality ofpre y is the same for allpre ystages . This assumption is implicitly made since the flow of ingested food ismerel y

178 treated interm s ofweight . Some attempts have been madet ovalidat eth e assumptionb yconsiderin g theavailabl e datao fprédatio nan dreproductio n ratesi nmonoculture s ofdivers epre y stages,bu t theydi dno tprovid ean y decisive evidence (Subsection 3.1.3). Fourth,th emode lo fth eprédatio n processi sbase d onth eassumptio n thatth estat edependen t success ratios measuredi n'monocultures 'o feac hpre y stagear eals o applicablei n'mixe d cultures'o fsevera l prey stages (Subsection 3.3.7); theprobabilit yo fa preycaptur e afterpre y detectionmerel y dependso nth eleve lo fgu tfillin g andpas t experience incapturin g other prey stagesi sonl yregistere dvi a changes inth eleve lo fgu tfilling .Thi s assumptioni sno trefute db yth e available experimental evidence, butmor evalidatio nexperiment sar estil l needed. Another point forcommen t isth econcep to ffoo d conversion,whic hi s basict oth epopulatio n modelo fth e predator-prey interaction.Th epresen t statuso fth esystem s analysis pointst oth eimportan trol eo fth erelativ e rateo ffoo d conversioni ndeterminin gth erat eo fprédatio na tvariou stem ­ peratures, different oviposition histories,an dpre y andpredato r densities (Section 3.3).Th eincreas ei nth erat eo fprédatio nwit h increasingtemper ­ aturei sdetermine d notb ytemperature-relate d changesi nth esearchin gbe ­ haviour,bu tb yth eeffec to fth etemperatur eo nth erelativ e rateo ffoo d conversion intoeg gbiomass .Th erelativ e rateo ffoo d conversioni sshow n to depend onth enumbe r ofegg s already depositedb yth e femalepredator , i.e. itsovipositio n history. However, only circumstantial evidencewa s given forth eassumptio n thatth edecreas eo fth erat eo fprédatio na tin ­ creasing predator density iscause db ya decreas ei nth erelativ e rateo f foodconversion ,an dno tb ybehavioura l changeso fth e predators aftermutua l contact,no rb yth etim ewaste d forpre y searching uponmutua l contactbe - tweenth epredators .Furthermor ei tshoul db erecalle d thatth efoo dconten t ofth egu ti sno ta goo d indicatoro fth emotivationa l statewhe nth epre ­ datori sseverel y starved (Subsection 3.1.2 and3.2.7 ) Simulationso fexperimentall y defined walkingbehaviou rwer e «™V£ todetermin eth eeffec to frecrossin g areas already searchedb yth epredato r on searching efficiency, andt oestimat e theresidenc e timei na circu l webbed area underth eassumptio n thatth eedg eo fth ewebbe d areaexert sn o effecto nwalkin gbehaviour .Thes e simulation experimentssho wthatt h tor tuous walk ofth epredator y mites inth epre y colony leas t oa n Prax mately20 %decreas ei nth erat eo fencounte rwit h immobilepre y «^section 3.2.4?,an dtha tth epredato r cannotsta yi na V"^ 1' *"\*^e: turning atth eedg eo fth ewebbe d ™™J£^^^ZZ~ b thewalkin g paths simulatedo nth e »» °'^^ ^ lodness o£ fit,

.eters( M, a,x an d% ) wereno t ^^^ inJtin^ish^ from though with thenake d eyeth esimulate dpath swe r ^ ^ ^^

the paths originally measured.Th eaut o regres describe the charac- Processwa sth ebes t availablemode lt ocomprehensivel y

179 teristic properties of thewalkin g pattern (Subsection 3.2.4).Anyway ,th e simulated level of recrossing is low and is hardly affected by even20 % changes inth eparamete r values.Moreover , long residence times in aprofi ­ table prey patch are best explained by theedge-turnin g strategy; without theedg e effect simulated residence times equal to those determined experi­ mentally could onlyb eobtaine d forextrem e types ofwalkin gbehaviou r that differ largely from the measurements at naked eye inspection. Hencepre y density predominantly determines the relative rate of departure of the predator from the prey colonies thatwil lb e generated by themode l atth e population level.

4.2 MISSING INPUTS

InChapter s 2an d 3experiment s with individual mites havebee n described that servet omeasur e ratevariable s forus e inpopulatio n models.Fo r some cases the seto f inputs is incomplete, orth e results cannotb e used inth e population models without making new assumptions,whic h in turnnee d sepa­ ratevalidation .T o gain insight into these limitations it isworthwhil e to look atthes e aspects inmor edetail . The possibility of maintaining apredato rpopulatio n inperiod s ofpre y scarcity inth egreenhous e iso fconsiderabl e practical importance;i twoul d be convenient if thepredator s residing inth e crop are able todetec tne w spider mite infestations in due time forcontro l ofth emit epest .Litera ­ ture data and some additional experiments haveprovide d some insightint o the survival chances ofth epredator y mites inth e greenhouse.Whe npre yi s scarce in the greenhouse rose crop, the availability ofwate r seems tob e mostimportan t for the survival ofth ephytoseiid s (Subsection 2.2.5).Can ­ nibalism provides only a limited means for survival, as itdepend s onth e survival ofothe rpredators ,an d asth e food andmois t content of thesepre ­ dators decreases exponentially with the length of food deprivation (Subsec­ tion 2.2.6). The supply ofpolle n onth eros eplant s didno t improve survival in comparison to the supply ofwate r only (Subsection 2.2.7). However,be ­ cause only one level ofpolle n supply was tried, no decisive,practica l in­ formation canb e giveno nth epossibilit y ofmaintainin g apredato rpopula ­ tion in the rose crop.Anyway , the amount of pollen originating from the flowering roses inth egreenhous e is insufficient inthi s respect.A thighe r levels of pollen supply, especially Amblyseius bibens may perform better, asshow nb yBlommer s (1976)i n small scaleexperiments . By extrapolating data onindividua l lifehistorie s measured atconstan t temperatures to the greenhouse situation, an important assumption ismad e that has been only partially validated. The rate of development, the rate ofreproduction , therat eo fmortality , the rate ofwebbin g and therat eo f prédationwer emeasure d atconstan t temperature levels inth e range 10-35°C Ofcourse ,temperatur ewil l fluctuate inth e greenhouse albeitwithi n limits

180 (10-35°C). The effect of variable temperature regimes on these rateswa s investigated for the two-spotted spider mite, but hardly at all for the phytoseiids considered in this report.Bu tbecaus e thepopulatio nmode l pre­ sented inPar t 2 isbase d onth e assumption thatbirth ,deat h andprédatio n processes react instantaneously to changes in temperature, validation of thisassumptio n is still needed forth ephytoseiids . Though the prey supply to the predators has been quantified insuc ha way that prey density and prey number can be computed in the population model (Part 2),th e level of food supply toth e spidermite s hasno tbee n considered. Some arguments havebee n givent oconside r thenutritiona l value ofth ehos tplan t as aconstan t forspide rmite s infesting greenhouse roses (Section 2.1). However, incontras t toth e food quality ofth e roseleaves , food quantity can be affected by feeding of the spidermite s themselves. Theavailabl e leafparenchy mdecrease s duringpopulatio n growth ofth e spider mitesunti l thehos tplan t isexhauste d asa food source,o r the growerap ­ plies pesticides. Also, the juvenile spidermite s are leftstrande d inal ­ ready exploited areas, because they are less ablet odisperse .A s the life historyvariable s havebee nmeasure d forindividua l spidermite s andplent y of fresh plant food, an important gap in the experimentsma yb epresent . Therefore, to decide ifthes e factorsnee d tob e studied inmor e detail,a greenhouse experiment on population growth of the spider mites should be carried out and the numerical results shouldb ecompare dwit h simulations thatneglec t the effects ofcompetitio n for food among theindividua l spider mites. Thispopulatio n experiment and the adherentsimulation s willb e dis­ cussed inPar t2 . Another subject that is important in the interpretation of theresult s ofpopulatio n simulations is the determination ofth e sexratio .Althoug h the sex ratio ofth eprogen y candepen d onarthropod-relate d factors,suc h asth e age of the spider-mite •mother' .(Subsectio n 2.1.3), iti sassume d to bea fixe d ratio thatdoe s not alter inrespons e toenvironmenta lconditions . Butthi s is an assumptionmad ebecaus e oflac ko fexperimenta l data,rathe r thana well-establishe d foundation forpopulatio nmodelling . Controlo fth e fertilization process and hence these x ratio inrespons e to environmental conditions may play a role in arthropods reproducingb y arrhenotoky This possibility should be taken into consideration when interpreting the sex ratios simulated andmeasure d atth epopulatio n level (Part2 >- An important statevariabl e inth epopulatio nmode lo fth e P~dat°r"^ interaction is thepre y density. Inthi srepor tth epre ydensit y as the number of prey per square centimetre of webbed leafarea ,becaus e two-spotted spider mites only inhabitthos epart so f bywebbing .Durin gpopulatio n growthno tonl yd opre ynumber s ™^Z'dT- alsoth e extent ofth ewebbe d area.Therefore , forcalculatio n ofpre yde n -ity for simulations at the population level,lif ehistor ycompo nn t as well as the rate of increase ofwebbe d leafarea ,hav ebee nmeasure d 181 individual level (Section 2.1).Th e rate of increase of webbed leaf area can depend on the host plant species thati s colonized by the two-spotted spidermite .Fo r example,th ewebbin g cover on Limabea n is less aggregated thano nrose ,an dth ewebbin g iseve nmor e spread outo n leaves ofGerbera . Presumably the hairiness of the leaves isa n important factor inthi s res­ pect. The rate of colonization estimated inthi s study onros e 'Sonia'i s therefore by no means generally applicable and should be determined for otherplants . Bydistinguishin g webbed leaf areas fromunwebbe d leaf areas iti sneces ­ sary to assess which factors determine theresidenc e time of the predators inside andoutsid e thewebbe d area.Th e residence time of individualpreda ­ tors in the webbed area of apre y colonyha sbee n studied inthi sreport , but their residence timeoutsid e thewebbe d area isa n aspect thatha sno t yet been considered fully at the individual level.Som e details havebee n discussed inSubsectio n 3.2.4 and 3.4. Itwa s found thatth epredator y mites walk along the leaf edge or a rib, invading thepre y colony aftermakin g tarsal contact with the silk strands attached to the leaf edge or rib. Aablifseius potentillae behaved differently. Thisphytoseii d predator tends to avoid the webbed leaf area andprefer s to staynex t to the thickpart s of the main rib of a rose leaf or atothe rprotecte d spots onth eplant . More knowledge isrequire d on the question ofho w apredator y mite searches forne wpre ypatches ,especiall y how thesearchin g is influenced by themod e ofplan t orcro p colonization by the two-spotted spidermites .Thes e aspects willb e discussed inPar t2 o fth eAgricultura l ResearchReport .

4.3 IMPACTO F INDIVIDUAL CHARACTERISTICSA TTH E POPULATION LEVEL

Themeasuremen t ofmit epropertie s atth e individual level can sometimes be sufficient for the evaluation of their impacto nth epopulatio nlevel . For example, hatching of phytoseiid eggs fails forrelativ e humidities of 30-60%, but the spidermit e eggs areno taffecte d inthi s range.Henc e egg mortality isprobabl y ake y factor in the failure ofphytoseiid s to control thepopulatio n growth ofth e two-spotted spidermite s at lowhumidities .I n other cases, the measurement ofmit epropertie s atth e individual leveli s notsufficien t forth eevaluatio n ofthei r relative importance atth epopu ­ lation level.Fo rexample ,wha t isth e importance of a 10%shorte r develop­ mental time relative to a10 %ris e of the rate ofreproduction ? Bothdevel ­ opmental time and reproduction affectth e rate ofpopulatio n increase,bu t their relative effect cannotb e determined without the help of aquantita ­ tive tool, sucha sa mathematica lmode l ofth epopulatio n growth.Th eeval ­ uation ofsuc heffect s iseve nmor e difficultwhe n their relative importance has to be assessed forinteractin g populations ofpredato r andprey .Henc e the evaluation ofth e interspecific differences in life histories is deferred toPar t2 ,wher e thepredator-pre y interaction ismodelle d atth e population

182 level. Because several processes inth epredator-pre y system interactwit h each other, and several ratevariable s depend in anon-linea r way on statevaria ­ bles, it is often not possible event odescrib e the consequences ofinpu t datameasure d atth e individual level forth e interaction atth e population level, let alone to indicate their relative importance. The role dynamic simulationma ypla y inthi s respect is further illustrated inthre eexamples . Example 1 - the role of webbing in prédation Thesearchin gbehaviou ro f individual female predators has been studied in the webbed leafarea ,a s wella so nunwebbe d leaves (Section 3.2). Webbing interferes generally with searching by decreasing the rate of encounter per unit prey density (the relative rate of encounter), as aconsequenc eo fa reductio n inth ewalkin g speed, the walking activity and the coincidence betweenpredato r andpre y inth ewebbe d space.Th e relative rate of successful encounterwa s affected byth ewebbin g indifferen tways , however,dependin g onth ephytoseii d spe­ cies involved: the success ratio of Phytoseiulus persimilis increases in thepresenc e of webbing; the success ratios of Amblyseius bibens and Meta- seiulus occidentalis are unaffected by the webbing;bu tth e success ratio of Amblyseius potentillae decreases (Subsection 3.2.7). Iti sshow nb ysimu ­ lation of the prédation rate on basis of these behavioural data,an dth e dynamics of the gut filling, that the increase of the success ratio of Phytoseiulus persimilis inth ewebbin gmor e thancompensate s forth ereduc ­ tion of the relative rate ofencounte r inth ewebbing ,resultin g ina nin ­ crease in the rate of prédation in a prey colony (Subsection 3.3.3). The factor webbing may therefore be important for futurestudie s ofth einter ­ action between phytoseiid predators and the two-spotted spider mite, but the relative importance of the substrate-related differences inprédatio n rateha s yet tob e demonstrated atth epopulatio n level (Part2) . Example 2 - prey-stage preference of the phytoseiid predators Thepro ­ bability of capturing a prey depends verymuc ho nth epre y stage involved (Subsection 3.2.7): eggs areeasie r tocaptur e thanlarvae ,larva e aremor e easy to capture thannymph s and theadul t female spidermite s areth emos t difficult to capture.Thes eprey-stag e specific differences insucces s ratio may mean that the diet of thepredato r largelyconsist so fth eyoun gpre y stages and that the reproductive spider mite females are allowed to continue the reproductionproces s forsom etime .Henc eth eexterminatio n of the prey population may be postponed due to the initialconcentratio n of thepredator s onth eyoun gpre y stages.O nth eothe rhand ,th eadul tfemal e spidermite s dono t live foreve r and eachconsumptio no fa femal ejuvenil e Prevents the development ofa reproductiv e female.Therefor e thehypothesi s thatpredator s keep 'layinghens ' shouldb e evaluatedb ydynami c simulation ofth epredator-pre y interaction atth epopulatio n level (Part 2). example 3 - dispersal of the predator from colony to colony ^J^ • '4-v,v,-i«v . nrpvdensities ,thi stendenc y Predators tend to stay incolonie swit hhig hpre y densities 183 can lead to predator aggregation in theprofitabl e prey patches,whic h in turn leads to adecrease d rate ofprédatio n (and thus reproduction), or to predator dispersal from thepre ypatc h (Section 3.4).Wha t effect thismod e ofpre ypatc hexploitatio n has on thepopulatio n level is an important ques­ tiontha tma yb e solvedb y dynamic simulation ofpopulatio n growth and dis­ persal. Forthes e simulations,wher e predators maymov e from onepre y colony to the other, possibly differing in prey density, and where prey density continually changes in time,i ti snecessar y to account forth e non-steady state of the prédation process. The Queueingmode l developed inChapte r3 offers that facility and, moreover, it canb e easily coupled to apopula ­ tionmode l inth e formo f asubroutine .

184 Summary

The two-spotted spidermite , Tetranychus urticae (Acarina:Tetranychidae) , is amajo r pest of many food and ornamental crops. Inth egreenhous e cul­ tureo fornamenta l roses,a nacaricide ,calle d dienochlor [perchlorobi(cyclo- penta-2,4-dienyl)] is used to control it. For environmental reasons iti s desirable to replace chemical spraying with abette r alternative. This Agricultural Research Report describes investigations into thepossibilit y ofbiologica l control oftwo-spotte d spidermite s ingreenhous e roseswit h predatory mites (Acarina: Phytoseiidae). Biological control hasbee nsuc ­ cessful in the greenhouse culture ofcucumbers , forexample . In greenhouse roses, however, much less damage can be tolerated because the ornamental value of their flowers and leaves determines theeconomi cvalu e ofth ecrop . This quality demand applies especially to theros e shoots thatgro w above the rose hedge, which are cut off ata beginnin g stageo f flowering;mor e damage can be tolerated in the rose hedge itself. Spidermite s should be controlled in such awa y thatdamag e toth eyoun g rose shoots isminimized . Two-spotted spider mites are able to double their number inth e short period of 2-4 days. Even after the release ofth epredator ymite s thepopu ­ lation of spider mites will increase initially.Onl y after sometim ewil l itdecrease .Henc e iti s important toestimat e theminimu m number ofpreda ­ torst ob e released for acceptable mitecontrol .Th econtro l ofnewl ydevel ­ oped infestations will depend onth e abilityo fth ephytoseiid s to survive periods of prey scarcity. Because phytoseiid species can differ inthei r ability to survive or reproduce onalternativ e food, andi nthei rprédatio n capacity, four species arecompare dwit h eachother ,i.e . Phytoseiulus per- similis, Ajnblyseius potentillae, Amblyseius bibens, Metaseiulus occidentals. The potential role ofthes epredator ymite s forth econtro l ofth etwo - spotted spidermite s hasbee n investigatedb y systems analysis,i.e .b ymo ­ delling and experimentation. Inthi sAgricultura l ResearchReport ,experi ­ ments and models atth e individual level areconsidered . InPar t2 o fthi s report (to be published) the results ofthes eexperiment s andmodel swil l be used in a new model tosimulat epopulatio n growtho fbot hpredato ran d Prey; simulations with thispopulatio nmode lwil lb ecompare dwit hpopula ­ tion experiments in thegreenhouse .Afte rvalidatio nth emode l canb euse d forcalculatio n ofth eminimu m release ofpredator ymite s ata certai nstag e ofpes t development. These estimates may then be transformed intosimpl e rules of thumb. ,„,. _ For a systems approach it is necessary toquantif y thepre y supply (in 185 particular, two-spotted spider mites)t oth epredator y mites in thegreen ­ house. Because the spider mite numbers increasewit h time,th e properties oftetranychid s were investigated thatdetermin e the rate ofpopulatio nin ­ crease, i.e. thedevelopmenta l time,age-dependen t reproduction and thepro ­ portion of females inth eprogen y (Subsections 2.1.1-2.1.3). Environmental temperature influences the rate ofdevelopmen t and reproduction ofPoikilo ­ thermie arthropods. Itwa s showntha tth e relationbetwee n temperature and these rates is linear inth e range 12-35°C;unde r greenhouse conditions rel­ ativehumidit y isno timportant .Furthermore , itwa s shown thatth e rateo f reproduction and the proportion ofth eprogen y thatar e females depends on the age of the reproductive female. With respect to thequantificatio n of the prey supply to the predators, it isals o important to distinguish the stages ofdevelopment ,becaus e each stagerun s different risks ofbein gcap ­ tured by the predatory mites.Henc e the rate ofmortalit y and development were measured for each developmental stage, sotha t inpopulatio n simula­ tions thepre y supply canb e subdivided perpre y stage. The prey supply toth epredato r is also determined by themea n distance between prey items, i.e. thepre y density. Two-spotted spidermite s havea strong tendency to aggregate.The y construct labyrinths of silk strands on the lower side of the leaf, starting from the leafedg e or ari b and dis­ persing over the leafsurface . Inth ewebs , the eggs are deposited andde ­ velop into adults. The preoviposition females are inseminated immediately afterth e lastmoul t and subsequently disperse, frequently to otherleaves , where they form new colonies.Henc e colonization isa nessentia l aspecto f the prey supply to thepredator .Th epredator y mite has to invade theweb ­ bing tocaptur e itsprey .Therefor e thepre y supply isdefine d asth e number of spider mites per square centimetre webbed leaf area.Consequently , the rate of increase of webbed area was quantified by experiment (Subsection 2.1.6). On thebasi s ofth emeasure d rateo fwebbin g and themeasure d life- history components, apopulatio n model can be constructed that simulates prey numbers and prey density inth ecours e ofth epredator-pre y interaction (Part2) . Inth egreenhous e culture ofornamenta l roses,foo d substances other than spider mites are rare.Henc e the survival of the predators inperiod so f prey scarcity will depend on cannibalism and abiotic factors,suc h asth e availability of water, temperature and relative humidity. In contrast to the otherphytoseii d species studied, Amblyseius potentillae and Amblyseius bibens can reproduce when feeding onpollen , so thatth e addition ofthes e plant substances may lead to themaintenanc e of thepredato r population in thegreenhous e crop.Experiment s indicate that the amounts ofpolle n required areprobabl y high (Subsection 2.2.7). Honey and sucrose solutions can improve the rate ofpredato r survival to a significant extent.T o date thepossibil ­ ityo fmaintainin g apredato r population in aros e crop without spidermite s has still notbee n demonstrated.

186 Population growth of the predatory mites will depend on thenumbe r of spidermite s inth ewebbe d leaf area and the temperature and relative humi­ dity there (Subsections 2.2.1-2.2.3).A s forth e spidermites ,th e rate of development and the rate ofreproductio n are linearly related totemperature . However,whe n temperature rises above 30°C andrelativ ehumidit y dropsbelo w 70%, juvenile mortality becomes high.A s the spidermite s aremuc h less vul­ nerable to temperatures in the range 30-35°C and humidities inth e range 40-70%, these conditions arecritica l forthei r controlb ypredator ymites . The four phytoseiid species studied differedwit h respectt o developmental time, size of progeny and proportion of females in theprogeny .However , allphytoseii d species matured ina shorte r time-span,bu t laid fewer eggs than the two-spotted spidermites .Th e relative importance ofthes ediffe ­ rences can not be determined without thehel p ofa quantitativ e tool, such as a population simulationmodel .Th e evaluation ofthes edifference s will thereforeb e treated inPar t2 o fthi sAgricutlura l ReseachReport . Whenpre y supply is sufficient,youn gphytoseii d females utilize approxi­ mately 70%o f the ingested food foreg gproduction . Inaddition ,th erat e ofovipositio n is sohig htha tth ereproducin g females determine thepréda ­ tion capacity of the phytoseiids. The rate at which the ingested food is utilized for eggproductio n ofne wprotoplas m was found tob emainl y depen­ dento n the individual ovipositionhistory ,tha ti st osa yo nth enumbe r of eggs already deposited by the female predator; female predators tend to achievepotentia l fecundity almostirrespectiv e ofthei r age.Henc e there ­ productive females represent themos tvoraciou s stageo fth epredator ymites , and they decide where andwhe n theegg s aredeposited .Fo rthi s reasonth e searching behaviour of the female predators was studied in anattemp tt o relate prey supply to prédation and, consequently, reproduction (Chapter 3). For a study of the searching behaviour iti simportan tt o characterize the motivational state of the predator. Sinceth erat eo f food conversion is high, it makes sense tous e the food contento fth egu ta sa nindicato r of the motivational state ofth epredator .Th edynamic s ofth egu tfillin g can be computed when ingestion, resorption andegestio nar equantifie d by experiment. By weighing hungry predators before and after food "take the foodconten t of the differentpre y stages,th egu tconten tan d the foodde ­ ficit of the gutwer emeasure d (Section3.1) .Likewise ,i twa spossibl e to quantify the rate of ingestion and the rate of gut emptying. These data wereuse d in amode l of food conversiontha ti sbase d onth eassumptio ntha t the surplus of the resorbed food substances is used for egg P«***^ (Fig. 21). This modelwa s tested, forexampl eb y computing the timeneeded for a hungry female to produce anegg .Th ecalculation swer ecorrec ti na broad range of food deprivationperiods ,bu tafte r a ^»^°*J*J°* ^privation a period ofrecover ywa snecessar ybefor e thefemal erestarte d eggproduction . 187 The food conversion model (AppendixA )wa s used for the analysis ofth e observations of the predatory behaviour. Young femalepredator s belonging to four differeftt species of Phytoseiidae were deprived of food forsom e specified pefiod, starting from astat e of satiation, and thenplace d ina prey colony, Theif behaviour was recorded ahd the dynamics of the gut fil­ ling computed. Thus iti spossibl e tofelat eWalkin g velocity, walkingac ­ tivity, Walking pattern, success ratio and feeding time to the estimated level of food ihth edu to fth e femalepredato r (Section3.2) . This experiment was cätfied out on two substrates:webbe d leaf andun - webbed leaf. Itwa stherefor epossibl e to assess the role ofwebbin g inth e searching behaviour of thepredator y mites. Inth ewebbin g the rate ofen ­ counterpe rUhi tpre ydensit ywa s found to be lower,becaus e predatorymites , as well as spidermites ,mov e slowly ohthi s substrate and spend lesstim e in walking". The slow advancement ofth emite sprevent s bumping of onemit e into another, so thatdisturbanc e of thepredato r is afar ephenomenon .O n an unwebbed substfa'te disturbance is important, as is reported by several authors. The coincidehce betweenpredato r andpre y ahd hence also therat e of encounter ate lowered as a consequence of the labyrinth formedb y the webbing: predator and pfey may move over andunde r each otherwithou ten ­ countering one another. The predatory mites probably search atrando m and locate theirpfe y after contactwit h the tafsi of their front legs (Subsec­ tion 3.2.3). Mowever, notever y encounter leads to asuccessfu l attack.I t Was showntha tth e successrati o depends ofith e gut filling of thepredator , the.pre y stage ahd,.ihtw o specific cases,o h the substtate: in the webbing the success fätio of Phytoseiulus persimilis increases ahd thato f Amblyseiu* potentillae decreases (Subsection3.2.7 ,frig. 337 . The results ofthi sbehavioura lcomponen t analysis were used in apréda ­ tion,mode l derived ftorngUeUeihg 1theor y (Section 3.3).Thi s theory hasbee n used ih.problem s concerning'waitihd-lihe s ofcustomer s and service facili­ ties. Consider, forexample , aqueu e ofpatiefit si h adentist' s waiting-room'. The patients feptesent the prey, the dentist represents the predator and the waiting-toom represents the dut of the pfedator. The rate of patient arrivals thewaiting-roo m isequivalen t to the rate ofprédation ; thetim e heeded to help the patient is equivalent to the time needed to emptyth e gut of the predator by the amounto fon eprey .A smor e patients enterth e waiting-room, the dehtist will shorten theconsultin g timepe rpatien tan d itbecome s increasingly probable thatnewl y arrived patients will refuset o wait and decide to returh at ahothettime .Analogou s to this example,th e rate ofgu temptyin g increases with ah increasing level of gut filling,and , simultaneously, themotivatio n ofth epfedato r to attack itspre ydecreases , while the probability ofpfe y escaping incfeases.Èot h tendencies werede ­ monstrated byexperiment . • A stochastic qùeueihgmode l canb e derived ifon e assumes thatth enumbe r of successful attacksb y apredato rwit h acertai n level of gut filling fits

108 aPoisso ndistributio n andtha tth egu temptyin gtim epe ringeste dpre yi s distributed according toth enegativ eexponentia ldistribution .Thi smode l wascompare d with adeterministi cmodel ,a Compoun dsimulatio nmode lan da MonteCarl osimulatio nmode lo fth eprédatio nproces s (AppendicesE-H) .Th e Queueingmode l ispreferre dbecaus eo fit seconomi c useo fcompute rtim e andbecaus e ituse sa minimu mnumbe ro fvariable swithou tlosin gprecisio n (Subsection3.3.1) . TheQueuein gmode lwa svalidate d ina serie so fprédatio nexperiment s carriedou to nwebbe d andunwebbe d leaves (Subsections3.3. 2 and3.3.3) . Therat eo fencounte rpe runi tpre ydensit yi slowere db yth epresenc eo f webbing,whic h results in a decreased rateo fprédatio nfo r Amblyseivs Mbens and Metaseiulus occidental!*. Opposedt othi sdecreas ei nsearchin g ability,th epre ydensit yi nth ewebbe dare ai shig h (20-60mite spe rsquar e centimeter ofwebbe d leafarea) .S oth erat eo fencounte rbetwee npredato r andpre yturn sou tt ob ehigh ,anyway .Accordin gt oth esimulations , Phyto- seiulus persimilis and Amblyseius potentillae are affectedb y the webbing ina simila rway ,bu tth eprobabilit yo fthes epredator scapturin ga pre y after tarsal contact (success ratio)i sstrongl y influenced. Amblyseius potentillae hasa lowe rsucces srati oi nth ewebbin gtha no nunwebbe dleaves , andthi sresult s ina nextr adecreas eo fth erat eo fsuccessfu lattac k In contrast, Phytoseiulus persimilis• •- ,• hau,,s-a =highe H-inbp rrsucces succes ssx ratia oi nth ewebbing , whichmor e thancompensate s forth edecreas eo fth esearchin gabilit y( = therat eo fencounte rpe runi tpre ydensity) :th erat eo fprédatio nm the preycolon y ishighe rtha no nunwebbe dleave swit hth esam enumbe ro fpre y

Per f re Sy;te ms analysis ofth eprédatio nproces s atdifferen tlevel so fth e temperatureshow stha tth eeffec to ftemperatur eo nth erat eo ffoodco n version determines therat eo fprédatio n (Subsection3.3.4) . Be^ural changesrelate dt otemperatur e ^.^^^XZZ^^^ creaseo f the rateo fprédatio nwit hte.perature .Pre s I rateo f reproduction atincrease d predator« - -° <='«"»J decreasei nth erat .o ffoo dconversio» .• » no *-£^ „^ behaviouro rb ya nincreas eo fth etim ewasteo . y achieve Predators ,Subsection3.3.e> .Becaus e «ale ^'^'^"J^ theirpotentia l fecundity,i ti ssuppose dtha tth er . a..el la sth er,t .o freproductio ni sno tdependen to n« • ™ ^ hero fegg s depositedh yth efe.al e(subsectio n 3^5). rateo f foodutilisatio nfo reg ,product" »i sprohaM * ^ factori ndefinin g therat eo fprédatio n a» ea y^ ^^

canprobac yh econsidere d- ^^J*^.» ,„\e .„^.dcultures . Finally theQueuein g»ode l»a s« toMe preferencefo reac h ofpre y stages «Subsection3.3. 7an d»p . •• ™ ^ ^^ ^ „„„

specificpre ystag ei sdeter.in.d ^th e„ y ^ ^^ Bhott measured in 'monocultures'o fthes epre y 189 that spider-mite eggs are easier to capture than larvae, that larvae are easier to capture than nymphs and that the adult female spidermite s are the most difficult to seize. Moreover, they show thatth e differencesbe ­ tween success ratios ofth e differentpre y stagesbecom e smaller as thegu t fillingo fth epredato r decreases:th epredato r is less fussy as itshunge r increases. Simulation and measurement of prédation in mixed cultures of larvae and adult females of thepre y suggest thatth e 'monoculture' success ratios sufficiently describe theprobabilit y ofcaptur e under these circum­ stances.Mor evalidatio n experiments areneeded , however. The residence time of a predator in apre y colony ismainl y determined by thepre y density (Subsections 3.4.1 and 3.4.2). This iseviden t from the comparison of the residence time of predators in webbed areas with and withoutprey .Analysi s of thewalkin gpatter n of thepredator y mites inth e webbing and, based upon this analysis, simulation of the residence timei n the webbed area shows that the tortuous walkingpat h of thepredato r does not explain the length of the residence time inth epre y colony. Theexperi ­ mentally measured residence times inpre y colonies canonl y be achievedb y the predator when it turns back atth e edge of thecolony .Th e simulation ofth ewalkin g behaviour of thepredato r shows that itcome s in contactwit h the edge frequently enough toreac t adequately to adecreasin g prey supply. When female predators stay incolonie s ofhig hpre y density,predato rden ­ sityma y increase there. Itwa s shownb y experimenttha t an increase ofth e predator density leads to a shorter residence time despite the ample supply of prey (Subsection 3.4.3). Hence predator andpre y density are themajo r factors determining the residence time of the predatory mites in a prey colony. In distinguishing webbed leaf areas on theplan t from unwebbed ones, it isno t sufficient todetermin e only the factors thatregulat e the residence time inth epre y colony. Iti s alsonecessar y to find the factors thatdeter ­ mine howmuc h time isspen toutsid e thepre y colonies:ho w does apredator y mite search forne wpre y colonies? Of course,thi s is also an aspect ofth e analysis atth e individual level,bu t itwil lb e discussed inPar t 2o fthi s report in relation to the colonization of the plant by the spidermites . Some details, however, havebee n discussed in Subsection 3.2.4 and Section 3.4. It was found that the predatory mites walk along the leaf edge ora rib and that they invade the prey colony aftermaking'tarsa l contactwit h the silk strands attached to the leafedg e or therib . Amblyseius potentil- lae behaves very different inthi s respect.Thi sphytoseii d predator tends to avoid the webbed leaf area andprefer s to staynea r to the thick parts of the main rib of a rose leaf or otherprotecte d 'holes and corners'o n theplant . The measurements at the individual level give rise to questions which canb e solved onlyb y simulation and experimentation atth epopulatio n level (Chapter 4).A n example isth emeasuremen t of the rate of departure ofth e

190 predator from a prey colony atdifferen tpre y andpredato r densities.Wha t isth e role ofthi s dispersal mechanism inth epopulatio n dynamics ofpre ­ dator and prey?A s thenumbe r ofmite s andth ecolonizatio npatter n arecon ­ tinuously subject to change,dynami c simulation incombinatio nwit hpopula ­ tionexperiment s inth egreenhous ema yprovid e the answer.Thi s systemsap ­ proach may also be useful indetectin gmissin g knowledgeo nth e individual levelo fth epredator-pre y interaction. Forexample ,th erat eo fdevelopmen t andreproductio n ofth e spidermite swer emeasure d forampl esuppl yo ffood . Because the spider mites feed on the contents ofth elea fparenchym , food quality may decrease andpossibl y the life-history variables areaffected . Ifthi s is so,simulate d population growthwil l exceedth emeasure dpopula ­ tiongrowt h inth e greenhouse.Populatio nmodel s canthu sb euse dt oeluci ­ date the role of certain measured properties of predator andpre y andt o determine which experiments atth e individual levelma y stillb enecessar y toimprov e theexistin gpopulatio n models.

191 Samenvatting

De kasspintmijt, Tetranychus urticae (Acarina:Tetranychidae) , vormtee n belangrijke plaag inee n grootaanta lvoedings - en siergewassen. Ind esier ­ teelt onder glas wordt het kasspint chemisch bestreden metbehul p vanee n gechloreerde koolwaterstofverbinding die bekend is onder de naam Pentac. Het is wenselijk om dezebestrijdingsmethod e tevervange n door eenmilieu ­ vriendelijk alternatief. Mijn onderzoek is erop gericht om mogelijkheden voor biologische bestrijding van het kasspint met behulp van roofmijten (Acarina: Phytoseiidae) te onderzoeken, en wel in de teelt van kasrozen. Deze methode wordt reeds met succes toegepast in de komkommerteelt en andere teelten van kasgroenten.He tproblee m van de toepassing ind e teelt van kasrozen is echter, dat hier veel minder zuigschade van het kasspint kanworde ngetolereerd , omdathe tbla d sierwaarde heeft.Dez e hogekwaliteits ­ eis geldt voor de rozenscheuten diebove n de rozenheg uitgroeien en inee n vroeg stadium van debloe i worden afgesneden enverhandeld . Veel meer schade kan worden getolereerd ind e rozenheg; hetkasspin t zal daar zodanig onder

controle gehoudenmoete nworden ,da t de jonge seheuLenz u MJ.u .uogeiijK ,,ua*s ondervinden.

Depopulati e vanhe tkasspin t kanzic h ind e korteperiod e van 2-4 dagen verdubbelen. Ook na het loslaten van de roofmijten zal depopulatiegroe i van het kasspint nogwe l evendoorgaa n alvorens het aantal spintmijtenza l dalen. Daarom is hetva nbelan g om tewete n hoeveel roofmijten bij eenbe ­ paalde spintaantasting minimaal moeten worden uitgezet om eengewens tbe - stnjdingsresultaatt everkrijgen . Ofd epredatorpopulati e na onderdrukking van de plaagontwikkeling ook op eigen krachtnieu w opkomende spinthaarden de baas zal kunnen zijn,hang t afva n haarvermoge n omperiode n vanprooi - schaarste te overleven. De bepaling van ditvermoge n is daarom vanbelan g voor het inzicht inintroductiestrategieë n van roofmijten. Omdatverschil ­ lende roofmijtspeciesverschillend e combinaties vanpredatie - enoverlevings - capaciteit bezitten, zijn eenvierta l soorten roofmijten met elkaarverge ­ leken, nl. Phytoseiulus persimilis, Amïlyseius potentillae, Amblyseius bibens en Metaseiulus occidentalis. Voor de oplossing van bovenstaande problematiek werd een systeemanaly- tische aanpak gekozen,d.w.z .combinati e vanmode l enexperiment . InDee l1 van het rapport werden experimenten enmodelle n op het individu-niveaube ­ sproken, inDee l 2 (in voorbereiding) zullen de resultaten van deze indi­ vidu-experimentene nd e gevalideerde individu-modellenworde nbetrokke n bij deconstructi e van eennieu w simulatiemodel,da td epopulatiegroe i vanpre -

192 datore nproo i intijc je nruimt eberekent - peberekeninge nme t41 tpopu}.atie - modelzulle nvergeleke nworde nme tpopulatie-experimente ni n4 ekas .Pa sn a gebleken bruikbaarheid zal ditmode l kunnendiene nvoo rberekenin gva nhe t minimale aantajlo s te }atenpredatore nbi jee nbepaald e spintaantasting,e n eenbepaal d wensenpakket van de tuinder.Weich t kunnendez eschattingen - danvoo r depraktij kvertaal d wordeni nvuistregels . Voor de systeemanalytische benadering ishe tvereis t omhe tvoedselaan ­ bodvoo r de roofmijtent equantificeren ,t ebeginne nbi j dekasspintmijten . omdat het aantal spintmijtenverander t ind etij4 ,werde n eerst4* eeigen ­ schappenva nd eparencjiymzuigend espintmijte n oncjerzocjit,4i e bepalend zijn voord e snelheid'vanpopulatiegroei ,t eweten :d eontwikkelings4uur , deleef - tijdsafhankelijj^e repro4uctie en 4egeslachtsverhoudin g inhe tnakomeling ­ schap (paragraaf2.l' .1-2-1.3) .p eomgevingstemperatuu r speeltee nbelangrij ­ ke rol bij 4e ontwikkelijigs- en reprodpctiesnefheidva n 4eze koudbloedige arthropoden. De relatie tussen de temperatuur en4ez evariabele nblee k in grote trekken lineair tezij ntusse n 12°Ce n35°C .On4e rkasomstandighede p speelde de luchtvochtighei4gee nbelangrijk e ro^.D ereppductiesne;hei d en de geslachtsverhouding van het nakomelingschap pieken sterk af te hangen vand e leeftijdva n hetrepro4uctiev e vrouwtje.D e leeftij4va nd ejuveniel e spintmijt is ook van behang voor 4e kwantificeripg van hetvoe4se;aanbo d voord e rovers,'omdat'dedivers eontwikkelingsstadi aee nster kverschillend e kans lopen om doop'een'roofmiitt eworde ngevangen .Daaro m wer44 «ontwikke - lingsduur en de mortaliteitva nel kontwikkelingsstadiu m experimenteelbe ­ paald, zodathe tvoedselaanbo d ind e simulatieva nd epredator-proo i xnter- actie op populatie-niveau kan worden gedifferentieerd naarontwikkeling* - stadium. , Het voedselaanbod voor depredato rword too kbepaal d doord egemiddeld e onderlinge afstand tussen de prooi-individuen, m.a.w. de prooidichtheid. Spintmijten vertonen een sterke neiging tot aggregatie.Z1 3 huizenm een labyrinth van spinseldraden dat zij construeren aan de onderkantvar.he t blad,beginnen d langsd ebladran d ofd ehoofdner fe nva nd ^ «*»£V over het hele blad. Indez e spinselsworde nd eeiere ngeleg de ngr o end e juvenielen op.D e preovipositievrouwtjesworde nonmiddellij k« * 1^££ vervelling bevrucht door de mannetjes enverhuize nda nveela lnaa rander e bladen Vaar een nieuwe spintkolonie wordt gesticht. »™J^ is dusee nessentiee l aspectva nhe tvoedselaanbo d van e P^£££< mijt spintmijtenwi lbemachtigen ,za ldez ed espinsel s m Daarom werd het prooiaanbod voor de predator gedefinieerd alshe t antal spintmijten per cm* bespinseld bladoppervlak en -™g^" - waarmee individuele spintmijtenbedrage n aand e *°»^£L ^ oppervlak, experimenteel bepaald (paragraaf 2.1.6). « P resultaten en de bepalingva nd eeigenschappe ndi ed eP°P U^ ._ len, zal een model wordengeconstrueer d datd eprooiaantalle n

193 Naast spintmijten komen er in de teelt van kasrozen nauwelijks andere prooien of andersoortig voedsel voor. De overleving van depredatore nbi j afwezigheid van spintmijte nza l dus afhangenva n demogelijkhei d totkanni ­ balisme en abiotische factoren, zoals debeschikbaarhei d vanwater ,tempe ­ ratuur en luchtvochtigheid (paragraaf 2.2.5 en 2.2.6). Integenstellin g tot de andere onderzochte soorten kunnen Amblyseius potentillae en Amblyseius bibens reproduceren met pollen als voedsel, zodat toevoeging hiervan zou kunnen leiden tot handhaving van een predatorpopulatie. Debenodigd e hoe­ veelheden zullen waarschijnlijk groot zijn (paragraaf 2.2.7). Honing of sucrose-oplossingen kunnen de overlevingskansen van roofmijten aanmerkelijk vergroten. De mogelijkheden om in een rozengewas zonder spintmijten een predatorpopulatie te handhaven zijn nog niet aangetoond, maar vergroting van de overlevingskansen van een bestaande predatorpopulatie lijkt prak­ tisch realiseerbaar. De populatiegroei van de roofmijten zal afhangenva nhe t aantalspint - mijten dat zich op het bespinselde bladoppervlak bevindt,maa r tevensva n de temperatuur en de relatieve luchtvochtigheid (paragraaf 2.2.1-2.2.3). Ook bij roofmijten is de ontwikkelingssnelheid en de reproductiesnelheid lineair gerelateerd aan de temperatuur. Echter temperaturenbove n 30°Ce n vochtighedenbenede n 70%veroorzake n eenhog emortalitei t onder de juveniele roofmijten. Omdat spintmijten veel minder kwetsbaar zijnbi j temperaturen tussen3 0e n35° C enbi j lage luchtvochtigheden (40-70%), zijndez e omstan­ digheden inhe tkasklimaa t kritiekvoo r debeheersin g van spintmijtenplagen m.b.v. roofmijten.D evie r onderzochte soorten roofmijten vertoondenonder ­ ling verschillen in ontwikkelingsduur, grootte van hetnakomelingscha p en de geslachtsverouding hiervan. Zij ontwikkelden zichechte r allemaal snel­ lerda nd espintmijten ,maa r legdenminde reieren .D e consequenties vandez e verschillen zijnmoeilij k te overzienzonde r gebruik temake nva n computer­ modellenva nd epredator-proo i interactie oppopulatie-niveau . De evaluatie van dezeverschille n zal daarom inDeel "2 va n ditrappor tworde n behandeld. Als het prooiaanbod voldoende groot is, kunnen jonge roofmijtvrouwtjes ongeveer 70%va n hetopgenome nvoedse l besteden aand e aanmaakva neieren . De eiproduktie is zohoog , dathe tvoornamelij k de reproduktieve vrouwtjes zijndi e depredatiecapacitei t van deroofmijte n bepalen (paragraaf 2.2.4). De snelheid waarmee het voedsel wordt gebruikt voor de aanmaak van nieuw protoplasma bleek in hoofdzaak af te hangen van de ovipositiehistorie, d.w.z. het aantal reeds gelegde eitjes;roofmijtvrouwtje s lijken te 'stre­ ven' naar volledige realisatie van depotentiël e eiproduktie.D e reproduk­ tieve roofmijtvrouwtjes zijn dus het meest vraatzuchtig enzi jbepale n in welke kolonies de eierenworde ngedeponeerd . Daarom werd het zoekgedrag van deze roofmijtvrouwtjes bestudeerd inee npogin g omhe tprooiaanbo d terela ­ teren aand epredati e end e daaruit resulterende reproduktie (Hoofdstuk3) . Bij debestuderin g vanhe tzoekgedra g ishe tva nbelan g om demotivatie ­ toestand van de predator te karakteriseren. Gezien dehog e snelheid vand e

194 voedselconversie ligt hetvoo rd ehan do md evoedselinhou dva nd edar mal s indicator voor demotivatietoestan d tekiezen .D edynamie kva nd edarmvul ­ lingka nworde n berekend alsd eingestie ,resorpti ee negesti e experimen­ teel kunnen worden gekwantificeerd. Ditblee k mogelijkme tbehul pva nee n elektrobalans,waarme ehe tgewich tva nindividuel e mijtenka nworde nbepaald . Doormetin gva nhe tgewich tva nee ngehongerd e roofmijtvoo re nn avoedsel - opname kond evoedselinhou d vand everschillend e prooistadia,d emaximal e darmvulling enhe tverzadigingsdefici t wordenbepaal d (paragraaf 3.1).Oo k washe tmogelij k omd eingestiesnelhei de nd esnelhei dwaarme ehe tvoedse l uitd edar m verdwijnt, tebepalen . Deze kwantitatieve gegevenswerde nge ­ bruikti nee nmode lva nd evoedselconversie ,da ti sgebaseer do pd eaannam e dathe tsurplu sva nd egeresorbeerd evoedingsstoffe nword t gebruiktvoo rd e aanmaakva neiere n (Figuur 21).Di tmode lwer do pbruikbaarhei d getestdoo r bijvoorbeeld uitt e rekenen hoeveel tijd eengehonger d roofmijtvrouwt3e nodigheef to mwee ree ne it eproduceren ,e ndi tt evergelijke nme texperi ­ menteelbepaald e tijdsperioden.D eberekeninge nbleke n juistt ezi 3n inee n breed trajectva nhongerperioden ,maa rn aee nbepaald ehongerperiod everoor ­ zaaktevoedseldeprivati e effectendi eo mee nherstelperiod evroege n alvorens hetvrouwtj e weerto teiprodukti eko novergaan .

Hetmode lva nd evoedselconversi e (AppendixA )wer d gebruiktbi 3 deana ­ lyseva nd egedragswaarnemingen . Jongevrouwelijk e predatorendi evana fver ­ zadigde toestand waren gehongerd vooree nbepaald eperiode ,werde nbi 3ee n prooikolonie geplaatst.He tgedra gva nd epredato rwer d geobserveerd end e dynamiek vand edarmvullin g werd berekend. Opdez ewijz eko nd el°Qp.nel - heid,d eloopactiviteit ,he tlooppatroon ,d ekan so pprooivangs te nd eduu r van devoedingsperiod e worden gerelateerd aanhe tgeschatt e voedselmveau ind edar mva nd epredato r ^^^^ predatorspecies werduitge - Dit experiment over hetgedra gva n v voerd op twee substraten: bespinseld blad enonbespinsel d blad. Op^ wijze kond ero lva nhe tspinse l bijhe t ^^^^ ^.Je^L ^ ,. vcoi hlee kd eontmoetingssnelhei dpe reennei a leek de wordenvastgesteld . Inhe tspin^ spintmijten ziche r 1 Prooidichtheid lager tezi 3n, «^ J™ *lope nbesteden . DeZe tragever ­ langzaam voortbewegene noo kminde r ti3daa n1 P zodat ver_ Plaatsingvoorkom t heftige^f^^J^ storingva nd eroofmi 3t,zoalsveelv u * tussen predator en substraat, nauwelijks meer optreedt. Decoi n labyrinth- prooi endu soo kd eontmoetingssnelhei d wordenje^ag d ^ structuur vanhe tspinsel , immerspredato r en prooi kunnen ^

elkaar doorlopen zonder datonderlin g contact ^^ ^ eeR prooi

zoeken waarschijnlijk opd etas t£« ^ potenpaar hebbenontdekt ,ka n met de zintUlgen °Pd S achter nietel kcontac tleid tto tee nsuccesvoll e een aanvalworde n ingezet.Echte r ^ ^ ^ darmVullingva nd e prooivangst. De succes ratio bleek cht van de pr0oi en,i ntwe e predator,he tontwikkelingsstadiu m enhe tgesla c 195 bijzondere gevallen,va nhe t substraat;i nhe t spinsel neemtd e succesrati o van Phytoseiulus persimilis sterktoe ,terwij ldi eva n Amblyseius potentil- lae danjuis tster k afneemt (paragraaf3.2.7 ,Figuu r33) . Op basis van deze gedragscomponentenanalyse werd eenpredatiemode l ont­ worpenme tgebruikmakin g vanwachttijdtheori e (paragraaf 3.3). peze theorie wordt veel gebruikt bij de analyse van dienstverleningsprocessen,bijvoor ­ beeld debehandelin g vanpatiënte n ophe t spreekuur van een arts.D epatiën ­ tenzij nn u deprooien , de arts isd epredator , end ewachtkame r is dedar m van de predator. De snelheid waarmee zichnieuw epatiënte n aanmelden eni n de wachtkamer gaan zitten is equivalent met de predatiesnelheid; detij d die benodigd is voor de behandeling van de patiënt is equivalent aan de tijd die de predator nodig heeft om eenproo i tevertere n enhe t verteerde voedsel in de haemolymphe op te nemen. Naarmate er meer patiënten in de wachtkamer zitten, zal de arts depatiënte n sneller behandelen en naarmate dewachtkame r voller is,za l er eengroter e kans zijnda td enieuw-aankomen ­ depatiënte nva n eenbehandelin g afzien.Analoo g aan ditvoorbeel d neemtd e snelheidva nvoedselresorpti e toeme ttoenemend e darmvulling, terwijldaar ­ mee de motivatie om nog een prooi tevange n afneemt.Beid e tendenzen zijn experimenteel aangetoond- Aangenomen dat het aantal prooivangsten per tijdseenheid een poisson- verdeling heeftbi jee nbepaal d niveauva n dedarmvullin g enda td eresorp - tietijd per prooi een negatief exponentiële verdeling heeft,ka n een sto­ chastischwachttijdmode l worden afgeleid.Di tmode lwer d vergeleken metee n deterministisch model,ee n Compound-simulatiemodele n eenMont e Carlo-simu- latiemodel van het predatieproces (Appendix E-H).Dez e vergelijking viel uit inhe tvoordee l vanhe twachttijdmodel , omdatdez eminde r rekentijdver ­ bruikt en spaarzaam is in het gebruik vanvariabele n zonder datd eessen ­ tiesverlore n gaan (paragraaf 3.3.1). Het wachttijdmodel werd opbruikbaarhei d getesti n een serievalidatie - experimenten, uitgevoerd op bespinselde en onbespinselde substraten (para­ graaf 3.3.2 en 3.3.3). Het bleek dat de ontmoetingssnelheid per eenheid prooidichtheid wordt verlaagd door de aanwezigheid van spinsel en datdi t effect resulteert in een verlaagde predatiesnelheid bij Amblyseius bibens en Metaseiulus occidental is. Tegenover deze daling inhe tzoekvermoge n staat echter dehog eprooidichthei d die ind e spinselaggregaten wordt aangetroffen (20-60 individuen per cm2 bespinseld blad), zodat de ontmoetingssnelheid tussenpredato r enproo i tochno ghoo g is.D e overige twee onderzochte roof- mijtenspecies bleken deze effecten ook te ondervinden, maar deze species worden door het bespinselde substraat tevens beinvloed voor watbetref td e kans om een prooi te vangen na tarsaal contact (succes ratio). Amblyseius potentillae heeft een lagere succes ratio op hetbespinseld e blad, hetgeen deverlagin gva nhe tzoekvermoge n meer dan alleen compenseert:d epredatie ­ snelheid in de prooikolonie ishoge r dan op onbespinselde bladeren metde ­ zelfdehoeveelhei dprooi .

196 Systeemanalyse van depredati e bijverschillend e temperaturen leerde dat het effect van de temperatuur op de voedselconversiesnelheid bepalend is voor de vraatsnelheid (paragraaf 3.3.4). Gedragsveranderingen ten gevolge van de temperatuur bleken dus van veel minder belang. Vermoedelijkword t óókd everlaagd e reproduktie bijhoger epredatordichthede n veroorzaakt door eenverlagin g van devoedselconversiesnelhei d ennie tdoo rveranderinge n in het zoekgedrag of door tijdverspilling bij onderling contact tussenroof - mijten (paragraaf 3.3.6). Omdatroofmijtvrouwtje s strevennaa r derealisa ­ tieva n depotentiël e eiproduktie isd evoedselconversiesnelhei d evenals de reproduktiesnelheid niet afhankelijk van de leeftijd maar van het aantal reeds door haar gelegde eieren (paragraaf 3.3.5).He tgebrui k van voedsel voor de eiproduktie bleek bij deze predatoren centraal te staan ind ebe ­ paling van de predatiesnelheid, terwijl hetvermoge no mprooie nt ebemach ­ tigen als een substraat gebondenconstant eblee k tekunne nworde nbeschouwd . Hetwachttijdmode l werd tenslotteuitgebrei d voorhe tgeva l datmeerder e prooistadia met elk eenverschillend e voedselinhoud aanwezig zijn (paragraaf 3.3.7; Appendix I).D e predatie van eenbepaal dprooistadiu m wordt inhe t model bepaald door succes ratios, die gemetenware n in 'monoculturen'va n prooistadia. Uit deze metingenblee k datspinteiere nee nmakkelijke rproo i vormen dan larven, larvenee nmakkelijke rproo ivorme nda nnymphen ,e nda t deadult e spintvrouwtjes verreweghe tmoeilijks t tebemachtige n zijn.Boven ­ dienblee k dat deverschille n inprooivangkanse nvoo rd everschillend e sta­ diakleine rworde nnaarmat e de darmvullingva nd epredato r lager is:d epre ­ datorword tminde r kieskeurig naarmate zijmee rhonge rheeft .Simulati e van depredati e in een 'mengcultuur' suggereerde dat de 'monocultuur' succes ratios ook onder deze omstandighedend eprooivangkan skunne nweergeven .Ech ­ ter,e rmoete n nogvee lmee rvalidatie-experimente nworde nuitgevoerd . De duur van het verblijf in eenprooikoloni e wordtvoora lbepaal d door deprooidichthei d (paragraaf 3.4.1 en 3.4.2).Di tblee kui td e vergeli^ng vand everblijfsduu rva npredatore n inspinsel sme te nzonde rprooie n Ana­ lyse van het looppatroon endaaro p gebaseerde simulatiesva nd everbi dfs - duur leerde,da the tkronkelig e looppadva nd epredato r geenverklarin g kan geven voor de duur van het verblijf in deprooikolonie .D e •*«"«*•£ vastgestelde verblijfsduur in een prooikolonie kan alleenworde n ***** indien depredato r bij deran dva nd ekoloni eomkeert .Volgen s van het loopgedrag komtd epredato rvaa kgenoe gbi jd e kolon.er^om^e. tekunne n reageren opverlagin gva nhe tprooiaanbod .Doo r at ™£££Z_ tjesblijve n litten ind ekolonie sme thog eprooidichthei d zal^d epredato r dichtheid ter plekke toenemen.Experimentee l werd ^^™£^ van de predator—d leidt tot een kortere verb^^^ ;:;—;~z?— ÏZ - « .^ vand e^~ ^oTrdat er onderscheid werd gemaakt tussen gekoloniseerd blad en ongeko- 197 loniseerd blad is het niet alleen nodig om de factoren tebepale n died e verblijfsduur in de kolonie regelen,maa r ook de factorendi ebepale nhoe ­ veel tijd een predator buiten de kolonies doorbrengt,m.a.w .ho e zoektee n roofmijt naar nieuwe prooikolonies? Dit is natuurlijk ook een aspectva n het gedrag op het individu-niveau, maar hetza l inDee l 2va n dit rapport wordenbehandel d insamenhan gme t dekolonisati e van deplan t door despint - mijten. Wèl is in Deel 1 reeds besproken (paragraaf 3.4 en3.3.4 )da td e roofmijtenlang s debladran d ofee nner f lopen enee nkoloni e binnendringen na tarsaal contactme td e spinseldraden. Amblyseius potentillae vormthier ­ opee nuitzondering .Dez e roofmijtheef td eneigin g om debespinseld e blad­ delen te mijden en zit bij voorkeur naastd edikk e delenva n de hoofdnerf of in anderebeschermd e hoekjes op deplant . De metingen op het individu-niveau kunnen aanleiding geven tot vragen die slechts door simulatie en experimenten oppopulatie-nivea u kunnenwor ­ den opgelost.Den kbijvoorbeel d aand emetinge nva nhe tvertre k van depre ­ dator uit een prooikolonie bijverschillend e prooi-e n predatordichtheden. Welke rol speelt ditdispersie-proce s ind epopulatiedynamie k vanpredato r enprooi ?Doorda td everanderinge n ind e aantallen enhe t kolonisatiepatroon continuplaatsvinden , zou dynamische simulatie incombinati e metpopulatie ­ experimenten een oplossing kunnen leveren. Ook hetbelan gva n ontbrekende experimentele gegevens ophe t individu-niveau kunnenworde n opgespoord. Denk bijvoorbeeld aan het feit dat de ontwikkelingsduur end ereprodukti e zijn gemeten aan individuele spintmijten bij een overmaat aanvoedsel .Doorda t de spintmijten het bladparenchym leegzuigen zal de kwaliteitva nhe tbla d achteruitgaan en mogelijk zullen de groei-variabelendaardoo rworde nbein - vloed. Wanneer dit een rol speelt,da nzoude n simulaties van depopulatie - groeiva nd e spintmijten eengroter e aantalstoename tezie n geven danpopu ­ latie-experimenten in de kas.Dez e voorbeelden laten zien hoe populatie- modellen kunnen worden gebruikto mhe tbelan gva nbepaald e karakteristieke eigenschappen vanproo i ofpredato r voor depopulatiedynamie k tedemonstre ­ rene n omnieuw emetinge n ophe t individu-niveau terechtvaardigen . Opdez e wijze zijnee n aantalvrage n geformuleerd inHoofdstu k 4,di eopgelos tzou ­ denkunne nworde ndoo rcombinati e van simulatie enexperimen t oppopulatie ­ niveau.D ebeantwoordin g vandez evrage n zal inDee l 2plaatsvinden .

198 Acknowledgements

Thanks are due to all thosewh o helpedm ewit hm yresearc h and thisbook . Ofsome , Ishoul d liket omak e specialmention : - my promotor, CT. deWit , for his inspiration during the research and forth e critical reading ofth edraft s ofth emanuscript . - my co-promotor, J. deWilde , forconstructiv e comments onth ephysiolog ­ ical and acarological parts ofth emanuscript . - M.va n deVri e for suggesting the project, for introducing me to the practice of greenhouse culture and forreadin gth emanuscript . - R.Rabbing e for initiating the project and for his comments on the manuscript. - J.H. Küchlein forreadin g thethir d chapter and forgenerousl y providing mewit h some ofhi s data onprédatio nan dreproductio n of Metaseiulus occi- dentalis (Table 19,23 ,26 ,35 ,36 ,5 7an d 60;Fig .14) . - the students that participated inth eproject :P .Ruardi j forconstruc ­ ting acompute r program forth e analysis ofwalkin gpattern s andT .Rennen , T.D. Keja, D. Adhidarma, Q. deRanit z and R.J. Klei for theirpar t inth e observations ofth epredator ybehaviour . - M.A.J,va nMontfor t andA .Otte n forsuggestin g theus eo fth eTuke y dis­ tribution and forothe radvice . - W.j. Tigges andH . Snellen forth econtinuou s supplyo f Metaseiulus occi­ dental's andA.Q . van Zon for astartin gcultur e of Ambluseius bibens. - J.P.W.Noordin k forhi shel pwit h radioactivetechniques . - F. Thiel forassistanc e with scanningElectro nMicroscopy . - S.G. Wever andW.C.Th .Middelplaat s fordrawin g thefigures . - Mrs.W.M . Laoh-Gieskes fortypin g themanuscript .

199 APPENDIXA MODELO FREPRODUCTIO N INRELATIO NT OFOO D INTAKE

TITLE REPRODUCTION INRELATIO N TOPOO D INTAKE TITLE DETERMINISTIC SIMULATION OFTH EPOO D CONVERSION TITLE DISCRETE FEEDING SCHEDULE INITIAL DELX=1./DELT ************************************************************************ *** INPUT DATA *** METASEIULUS OCCIDENTALS *** PARAM GUTC=3.3,0PTFW=2.2,DRYW=2.7,EGG=1 . 9 ************************************************************************ *** RELATIVE RATES *** RRRES =(TEMP-11.)*0.195 RREG =(TEMP-11.)*0.01 RRWLOS=(TEMP-11.)*0.04 PARAM TEMP =26. #*•******•**»**************»********#********»*•******»****•************ *** INITIAL CONDITIONS *** PARAM FDEPRT=0. IFRW =OPTFW *EXP(-RRWLOS*FDEPRT) IFCG =GUTC *EXP(-RRRES *FDEPRT) IREP =0. DYNAMIC ************************************************************************ *** STATE VARIABLES *** WEIGHT=FRESHW +DRYW +PCGUT FRESHW=INTGRL(IFRW,RRESW-RWLOSS) PCGUT =INTGRL(IFCG,RFI-RRES-REG) REPR0D=INTGRL(IREP,RRESR-PU8H*BGG*DELX) NEGG =INTGRL(0.,PUSH*DELX) PUSH =INSW(REPR0D-EGG,0.,1. ) FOOD =INTGRL(IFCG,RPI ) FAECES=INTGRL(0. ,REG ) MTBOL =INTGRL(0. .RREStf) ***RAT E VARIABLES *** RFI =AMIN1(GUTC-FCGUT,PREY)*PULS*DELX RRES =RRRES »PCGUT RRESR =INSW(PRESHW-OPTPW,0.,RRE3) RRESW =INSW(PRESHW-OPTPW,RRES,0.) REG =RREG *FCGUT RWL0S3=RRWL0S*FRESHW i***********************************.****.*.**^.****^^^^,^**************** *** FEEDING SCHEDULE *** PARAM PERI0D=1. PULS =IMPULS(0.,PERIOD) PARAM PREY =1.

200 ***OUTPU T STATEMENTS *** PHINT POOD,FAECES,MTBOL,FCGUT,FHESHW,WEIGHT,REPROD,NEGG TIMER FINTIM=50.,OUTDEL=2.,PRDEL=2.,DELT=0.05 METHOD REGT END STOP ENDJOB

201 APPENDIXB TIMESERIE SANALYSI S

Sequential changeso fwalkin gdirection sma yb ecorrelated .Thi sca nb e analysedi ntw oways : - Markovchai nanalysi swit hregar dt oth esig no fth echange si nwalkin g direction; - Autocorrelatio n analysiswit hregar d toth esig nan dth emagnitud eo f changesi nwalkin gdirection .

Markov chain analysis

Ifa sig no fa nelemen ti na tim eserie sdepend so nth esign so fpreced ­ ingelements ,a Marko vmode lma yb eadequate .Th ecas emos tcommonl ytreate d isth e firstorde rMarko vmodel ,fo rwhic honl yth elas telemen ti na tim e seriesinfluence sth echoic eo fa ne welement :

Prob(As= i | As_1= j, k, )= Prob( A A j) Ji s-2 s-1= forpositiv eo rnegativ ej ,i ,k Thisi scalle da transitio nprobabilit yfro mj t oi .Fou rtransitio nproba ­ bilitiesar epossible :p ,p ,p andp Supposew ewan tt otes tth enul lhypothesi stha ta directio nchoic epro ­ cessha sorde r zero (nofeedbac k atall )agains tth ealternativ etha tth e order ison e (aninfluenc eo fonl yth elas telement) .The ni ti susefu lt o orderth esequence si nth efollowin gcontingenc ytables :

For N^+l the point indi­ -s^tO + - total cates that the first ele­ from "--^ ment in a sequence can be + N N N either + or -; the second ++ +- +. element must be a +. Simi­ - N N N -+ _. larly for N the first element in a sequence must total N N N .+ ._ be a +, the second may be + or -, and so on. Underth enul lhypothesis ,p equal sN.../ N( i= + o r -). Accordingt oAnder ­ son& Goodma n(1957 )th efollowin gChi-squar estatisti capplies :

(»iH.-S-Nj.)2^ (N^-d-p)-^,)- H =^ i=-,+ p-N, (l-p)-N,

202 If this zero-order testreveal s dependency, itma yb easke di fth epro ­ cess is of order oneo r higher. Thenul l hypothesis of order =1 ca nb e tested against the alternative oforde r =2 wit hth eai do fth efollowin g contingency tables:

vtO + - .to + - from\ from\

-+ N N N N -++ -+- -+

++ N N +- N N ~ +++ ++- +-+ + According toAnderso n& Goodman ,thes e tablesma yb etreate d ascontingenc y tables again.Th esu mo fth ex ? statisticsha sth e *\ distribution underth e nullhypothesis .

Auto correlation analysis

Correlation between successive observations ina seriesi scalle d auto correlation (seee.g . Chattfield, 1975). Theaut ocorrelatio n coefficient is calculated with theai do fth ecovarianc e coefficient c^, whichb yana ­ logywit hth eususa l covariance formulai sdefine das :

C 1 A A ) (A A) k = nf"" '< s" • s+k" ' s-1 This is called the auto covariance atla gk , inwhic hs i sth enumbe ro f theelemen t inth eseries .Th eaut ocorrelatio ncoefficien t pk isestimate d asth equotien to fc R andth evarianc ea A (-ck=Qj.

r, =^ ,fo rk = 1 ,2 man dm <

suppose thatV A2 An areindependen tan didenticall y distributed random variables with an arbitrary mean, then itca nb eshow n (Kendall6 Stuart, 1966,chapte r48 )that :

E(rk) s -1/n and var(rk) =1/n , and that r„ is asymptotically normally distributed.Afte rplottin go fth e r.value s againstk , approximate 95%confidenc e limitscar,.b edraw, ,a t

-1/n ± lA/n -t nn^= "1/n ±2/Vn .Value so fr R thatfal loutsid e thl ills are^gnificantly different fromzer oa tth e« level For thepurpos eo fsimulatio na multipl e regressionmode li s ^^ account for correlation between successive ranges in walking*~^ (1< s< n).Thi sproces sca nb edescribe db yth eaut oregressio nequation . A s •- - - a +a -A +X„ . wheref(X g)= * =0 . A u + A*_s == a,-A

203 A isno tregresse d on independent variables but onpas tvalue s ofA s- Hence the term auto regression; m is the so-called order of the auto regressive .... are the auto regression orpar - process.Th e coefficients o;.,,a_ . a m tial auto correlation coefficients andX is determined by apurel y random process. To obtain a series X ,whic h is freed of correlation, the auto regression equation is rewritten as

Xs = "s - («->J1, "s-1 ' "2 "s-2 As-2 + m "s-m)* Theparameter s M, a, and A.o f theTuke ydistributio n mayb e estimated again onthi s corrected series X. s Now tworelate d questions remain tob e answered: How to determine theorde r m ofth e process? How can we estimate the auto regression coefficients from the autocor ­ relations? The order of the process is indicated by the range ofvalue s ofr . or a,, which are significantly different from zero (i.e. outside the range ± 2/Vn). The relation between a and r can be obtained by multiplying the auto regression equationwit hA . andb y calculating expectations: . n-k a. n-k a n-k + —5L ( . ) -^in-k— I .(Ax s -A s-k.) ' + n-k 2 ,Av s-mA s-k' s=l H=k-^«Vl-Vks= l » s=l for2?> k, this equationma yb e simplified with the aid ofth e formula for the auto covariance coefficient

a c + + c , l- k-l a m• k-m

Ifth e auto covariance coefficientc k isdivide d by thevarianc e â'i (=cQ), we obtain theYule-Walke r equations:

a r + + r , l' k-l a m• k-m

Because rk is equal tor_ k> them unknown auto regression coefficients can be solved out of ase to fm Yule-Walke r equations. Inmatrix-notatio n these equations are:

m-l\ m-2

m-3

m-1r m-2r m-3

204 Note, that for a firstorde r autoregressiv eprocess ,th e auto correlation coefficients decrease exponentiallywit h k: rk =

205 APPENDIX C MAXIMUM LIKELIHOOD ESTIMATION OFTH E PARAMETERS OF THE TUKEY DISTRIBUTION

Theprocedur e toestimat e theparameter s u , a andÀ ofth eTuke ydistri ­ bution consists of aroug h estimation ofthes eparameter s to obtain starting values, and asubsequen tmaximizatio n of the likelihood function to optimize theparamete r estimates (vanMontfor t& Otten , 1976).

Starting values

Estimate approximate values ofX forth e 10%,30% ,70% ,90 %point s of themeasure d cumulative frequency distribution.Wit h these estimations, K„ canb e solved from the following equationb yNewton-Raphso n iteration:

X0.7 "X 0 3 (0-7^° -0.3 A°)- (0.3A° -0.7 A°) 0.7A°- 0.3 A° X0 9" X 0.1 (O-9*0 -0.1 A°)- (0.1A° -0.9 A°) 0.9A°- 0.1 A°

The 50%poin to fth ecumulativ e frequency distribution,X Q 5, serves asa startingvalu e for Mo - The starting value ofa 0 canno wb e obtained from equation:

A A Xog =M o +a o-(0.9 °- 0.1 °)/Ao

Iterative optimization procedure

Thisprocedur e isbase d onNewton-Raphso n iterationwit h theLog-Likeli ­ hood function: A\ /A.N + (-L")-1-L' V„,, \a/, K+l "K K = iterative step number L = ln(L*) (theLog-Likelihoo d function) c L* =n^p i i (theLikelihoo d function) i = 1,2 , ,c c =numbe r of frequency classes i^ = frequency inclas si p.^ =probabilit y inclas si 2n, =N

206 Wheng . isdefine d asth eclas sboundary , theLog-Likelihoo d functionca n be computed asfollows :

c g M L =I n.•I n f:V(aaïi+i" )- ^(sp ) i=l i A

f Yp =f x

and P= ^

2 ÔL2 6L2 ÔL L" 6L 6M ôuôA. Ô(JÔ|J ôuôa

ÔL 6L2 ÔL2 6L2 <5a| ôaôX ôaôp ôcjôa

It is possible that -L" has a negative eigenvalue in the beginning of the iterative procedure. Therefore van Montfort & Otten (1977)propos e a repara- meterization to reduce this inconvenience. This is done by replacement of a e by s for P(K=1) = = 0.731 = CT-YP(K=D r^" A.

The iteration process can be stopped when LR - LR_1 or L' o] - I M K+l is sufficiently small. A x^.3 test (c = number of frequency classes) is used to test the fit of the Tukey model to the measured frequency data. A confidence interval for the parameters can be constructed on the basis of the covariance matrix

1 (-L")- 1 N

207 APPENDIX D MODEL OF WALKING BEHAVIOUR

TITLE TORTUOUS WALK + PREDATION / DIMENSION C(100,100) FIXED U,I,J,K,X,Y INITIAL DELX =1./DELT INCON U =1 PARAH UNIT =.5

*** PROPERTIES OF PREY AND PREDATOR *** SPEED =0.018*60. DIAH1 =0.091 DIAM2 =0.013 RADIUS=0.5*(DIAM1+DIAM2)/UNIT PARAH LABDA=-0.85,SIGMA=0.2,MU=0. NOSORT *#* «A******************************************************** *** REGULAR DISTRIBUTION OF THE PREY *** DO 1 1=1,99 DO 1 J=1,99 C(I,J)=1. 1 CONTINUE DYNAMIC ********************************************************** ***NON-AUTOCORRELATE DWAL K *** P =RMDGEN(U) A =MU+SIGMA*(P**LABDA-(1.-P)**LABDA)/LABDA DIR =INTGRL(0.,A*DELX) CSDR =COS(DIR) SNDR =SIN(DIR) X1 =INTCRL(50.,CSDR/UNIT) Y1 =INTGRL(50.,SNDR/UNIT) NOSORT ***

***REGISTRATIO N OFPREDATOR-PRE Y ENCOUNTERS *** DO3 1=1, 7 DO3 J-1, 7 X -X1-4+I Y =Y1-4+J IF (C(X.Y).EQ.O.)G OT O3 DIST =SQRT((X-X1)**2+(Y-Y1)**2) IF (DIST.GT.RADIUS)G OT O3 URITE(6,100)X, Y 100 F0RKAT(1X,2(F3.0,1X)) C(X,Y)=0. SUM =SUM+1. 3 CONTINUE SORT CLOCK=TIME/SPEE D

208 ******************************************************** ***OUTPU TSTATEMENT S *** PRINTSUM,CLOC K TIRER FIHTIM=100.,PHDEL=1.,0UTI>EL=0.O4,DELT=0.0 4 METHODREC T FINISHX1=0.5,X1=99.5,Y1=0.5,Y1=99. 5 INTERACTIVE OUTPUTX1(50.,70.),Ï1(50.,70. ) LABELPHÏTOSEIULU SPERSIMILI 5 PAGEXYPLO T END STOP ENDJOB

209 APPENDIXE DETERMINISTIC MODEL OFTH EPREDATIO N PROCESS

TITLE FUNCTIONAL RESPONSE OPA PREDATOR TO THE DENSITY OP ITS PREY TITLE DETERMINISTIC APPROACH TITLEYOUN G FEMALE PREDATOR OFMETASEIULU S OCCIDENTALS VERSUS TITLE EGGS OF TETRANYCHUS URTICAE

»»»»•»»»»»»•»»»•#*»***»#»***#**#»»*#*#*****#************************** *** PHYSIOLOGICAL AND BEHAVIOURAL INPUT VARIABLES *** PARAM GUTCON=3-3 PARAM FCPREY=1. INCON IFCG =2.95 PARAM TEMP =26. RRGE =(TEMP - 11. )* 0.19 5 PARAM DMPREY=0.013 PARAM DMPRED=0.057 DM =DMPREY +DMPRE D PARAM VLPREY=0. PARAM ACPREY=0. PARAM COIN =0.42 VLPRED=APGEN(VLPT,FCG/GUTCON) ACPRED=APGEN(ACPT,FCG/GUTCON ) SR =AFGEN(SRT ,FCG/GUTCON) FT =AFGEN(FTT ,FCG/GUTCON) FUNCTION VLPT=0.,0.047,1.,0.047 FUNCTION ACPT=0.,0.39,1.,0.39 FUNCTION FTT =0.,.009,.1,.007,.2,.006,.3,.005,.4,.004,1.,.00 4 FUNCTION SRT =0.,.558,.05,.936,.1,.854,.2,.273,•3,.217,.4,.152, ... .5,.083,.6,.103,.7,.0469,.8, .02 17,.9,.007,.98,0.,1.1,0 . ***

*** COMPUTATION OF THERAT EO F SUCCESSFUL ENCOUNTER *** RREWW =DM *SQRT(VLPREY**2 +VLPRED**2)*ACPREY*ACPRE D RREWR =DM *VLPRE D *ACPRE D * (1.- ACPREY ) RRERW =DM *VLPRE Y *ACPRE Y* (1.- ACPRED ) RSA =(RREWW +RREW R +RRERW )* DPRE Y * COIN * SR * 86400. TSC =FT + (1./AMAX1(RSA.1.E-5)) RSE =1./TSC CUMPRD=INTGRL(0.,RSE) ***

*** DYNAMICS OF THEFOO D CONTENT OF THEGU T *•* FCG =INTGRL(IFCG, RFI - RGB ) RGE =RRGE * FCG RPI =AMIN1(SDG/DELT,RSE »FCPREY) SDG =AMAX1(0.,GUTC0N -FCG ) *** *** FLUCTUATION OF THE PREYDENSIT Y INRELATIO N TO *** THE TIME INTERVAL OF PREY REPLACEMENT ***

210 DPREY =INTGRL(IDPREY,(-RSE/AREA)+ (REP I* (IDPREY-DPREY)/DELT) ) PARAM NPREY=125. PARAM AREA =5. IDPREY=NPREY/AREA REPL =IMPULS(0.,REPDEL) REPDEL=0.5/24. *** ****•*******#***************#*»*****•*•»*#*»*******»****##*****•****#*#» *** OUTPUT STATEMENTS *** PRINT CUMPRD, FCG, DPRE Y TIMER FINTIM=0.25,PRDEL=0.01,DELT=0.001 METHOD RECT **» H*********************************************************************** END STOP ENDJOB

211 APPENDIX F MONTE CARLO SIMULATION OFTH E PREDATION PROCESS

TITLE FUNCTIONAL RESPONSE OP A PREDATOR TO THE DENSITY OP ITS PREY TITLE MONTE CARLO APPROACH TITLE YOUNG FEMALE PREDATOR OF METASEIULUS OCCIDENTALIS VERSUS TITLE EGGS OF TETRANYCHUS URTICAE ********************************************************************** *** PHYSIOLOGICAL AND BEHAVIOURAL INPUT VARIABLES *** PARAM GUTC0N=3.3 PARAM IFCP =1. INCON IFCG =2.95- PARAM TEMP =26. RRFI =1.8*60.*24. RRGE =(TEMP - 11.) * 0.195 PARAM DMPREY=0.013 PARAM DMPRED=0.057 DM =DMPREY +DMPRE D PARAM VLPREY=0. PARAM ACPREY=0. PARAM COIN =0.42 VLPRED=APGEN(VLPT,FCG/GUTCON) ACPRED=AFGEN(A CPT,FCG/GUTCON ) SR =AFGEN(SRT ,FCG/GUTCON) FT =AFGEN(FTT ,FCG/GUTCON) FUNCTION VLPT=0.,0.047,1.,0.047 FUNCTION ACPT=0.,0.39,1-.0.39 FUNCTION FTT =0.,.009,.1,-007,.2,.006,.3,-005,.4,.004,1.,.004 FUNCTION SRT =0.,.558,.05,-936,.1,.854,.2,.273,-3,.217,.4,.152, ... .5,.083,.6,.103,.7,.0469,.8,.0217,.9,.007,.98,0. ,1.1,0 . *** ****************************************************************** *** ENGAGEMENT OF THE PREDATOR *** FIXED HANDLE HANDLE= 0.5 + INTGRL(0.,(CATCH-ABAND)/DELT) SEARCH=1. -HANDL E HTIM =INTGRL(0.,RHTIM) RHTIM =FT*CATCH/DEL T -INSW(DELT-HTIM,1.,HTIM/DELT ) ABAND =INSW(-HTIM,0.,1.)* HANDL E

*** COMPUTATION OF THERAT E OF SUCCESSFUL ENCOUNTER »*» RREWW =DM *SQRT(VLPREY**2 +VLPRED**2)*ACPREY*ACPRE D RREWR =DM *VLPRE D *ACPRE D * (1.- ACPREY ) RRERW =DM *VLPRE Y *ACPRE Y * (1. - ACPRED) RSE =(RREWW +RREW R +RRERW ) DPREY *COI N * SR * 86400. PRC =1.- EXP(-RSE*DELT ) RDRAW =RNDGEN(TELLER*200.) CATCH =INSW(PRC -RDRA W ,0. ,1.) * SEARCH CUMPRD=INTGRL(0.,CATCH*INTERV/DELT) INTERV=INSW(TIME-ADAPT,0.,1.) PARAM ADAPT =0.1

212 fr****************************************w********#«**«*«*****«»»»*#*** *** DYNAMICS OF THE POOD CONTENT OP THEGU T *** PCG =INTGRL(IFCG, RPI- RG E ) RGE =RRGE *PC G RPI =AM1N1(SDG,FCPREY)*HANDLE*RRFI SDG =AMAX1(O.,GUTC0N -PCG ) PCPREY=INTGRL(0.,CATCH*(IPCP-PCPREY)/DELT -RP I ) APCG =INTGRL(0.,FCG/DELT/NUM*IMPULS(ADAPT,PERIOD)) NUM =(PINTIM-ADAPT)/PERIOD PARAM PERI0D=O.O5

*** FLUCTUATION OP THE PREY DENSITY INRELATIO N TO *** THE TIME INTERVAL OP PREY REPLACEMENT DPREY =INTGRL(IDPREY,((-CATCH/AREA)+REPL*(IDPREY-DPREY))/DELT) PARAM NPREY =125. PARAM AREA =5. IDPREY=NPREY/AREA REPL =IMPULS(0.,REPDEL) REPDEL=0.5/24. *** ******»•*»*»••**»»#**»•******•*********»**»**»*•*»********»*•*****»***»* *** OUTPUT STATEMENTS *»* TIMER FINTIM=0.25,PRDEL=0.01,DELT=0.001 METHOD RECT TERMINAL PARAM NREP =100. INCON MPRED=0.,MFCG=0. INCON SPRED=0.,SFCG=0. INCON VPRED=0.,VFCG=0. INCON TELLER=0. MPRED =MPRED+CUMPRD/NREP MFCG =MFCG +AFC G /NREP SPRED =SPRED+CUMPRD*CUMPRD SPCG =SFCG +AFC G *AFC G TELLER=TELLER+1. IF (TELLER.GE.NREP)G O TO1 CALL RERUN GO TO2 1 VPRED =(SPRED-NREP*MPRED*MPRED)/(NREP-11.) VFCG =(3FCG -NREP*MFCG*MFCG)/(NREP-1. ) WRITE(6,100)IDPRE Y 100 F0RMAT(11H DENSITY = ,F8.0) WRITE(6,101)REPDE L 101 FORMAT(23H REPLACEMENT INDAY S = ,F8.4) WRITE(6,102) 102 FORMAT(25H MPRED,VPRED ,MFCG , VFCG) WRITE(6,103)MPRED,VPRED,MFCG,VFC G 103 F0RMAT(2(4X,2(F8.4,4X))) 2 CONTINUE III********************************************************************* END STOP ENDJOB

213 APPENDIX G MATRIXALGEBRAI C SOLUTION OFTH EQUEUEIN G EQUATIONS

Under conditions of constantRS E andRGE 1 thequeuein g equations canb e solved as follows: LetA b e thematri x ofth e coefficients inth e queueing equations

rl-RSE0 RGE^ 0

RSEQ 1-RSE1-RGE11 RGE12

RSE, 1-RSE2-RGE12 RGE13 0 A = RSE„

RGE1N-1 0 RSE^ 1-RSE^-RGE^ RGE1-N, RSE 1-RGE1. N-l

Letp b e avecto r ofth e stateprobabilities ,p ,i nth e queueing equations

/P0(t)

P2(t) P(t) =1

PN(t) /

When R stand for a square matrix of eigenvectors arranged in columns, then a matrix Q can be obtained with the eigenvalues of A (= q )ranke d on its diagonal

/Sn 0 0 *1 °

Q = R_1-A-R =

I0 ° %•

214 The distribution ofp (t)ca nno wb e calculated as follows n

p(t)= e A,t-p(0)= R-(e R 'A'R)-R_1-p(0)= R-e 6't-R~1-p(0)

/eV1.

»Q-t

e^N •' The solution of this seto fequation s isrepresente d byß nn + q.-t Pn^= Ko ]=1 Pnj n = 1, 2,3 , N q is negative

ß0 = equilibrium coefficients

Thenumbe r ofpre y killed during atim e spant (=CUMPRD t)ca nb e foundb y integration ofth eprédatio nequatio n N , N dPRED PREDI = LimPRE D = t =2 n-p (t)+ 1 RGEln-pn(t) DELT*0 dt n=0 n-0

N N t CUMPRD.<_ = I n-p (t)+ 1 (RGE1 •ƒP n(u)du) t n=0 n=0 0 t SJ" p (u)du =ß -t+ ^ , 1 - .(l-e-^l-t)+ i.p^-d-e-V* )+ • • 0 n n0 nl q2-„ 2

215 APPENDIX H QUEUEINGMODE LO F THE PREDATION PROCESS

TITLE FUNCTIONAL RESPONSE OP A PREDATOR TO THE DENSITY OP ITS PREY TITLE QUEUEING APPROACH TITLE YOUNG FEMALE PREDATOR OF METASEIULUS OCCIDENTALIS VERSUS TITLE EGGS OF TETRANYCHUS URTICAE STORAGE PST(22),PTD(22) FIXED NCL INITIAL *********************************************************************** *** ENUMERATION OF THE FOOD CONTENT CLASSES OF THEGU T *** 1 2 3 4 5 I 192 0 21 22 =N C *** 1 2 3 4 N 18 192 0 =NC L *** 0 1 2 3 171 8 19 =NCLAS S *** NC =22 NL =NC-1 NCL=20 NCLASS =19 *** **•»*********»****#***»•»**#*#*******»•*»*********»#*#»»*»•****»**•****# *** COMPUTATION OF THEFLUCTUATIO N OF PREY DENSITY INRELATIO N TO *** THE TIME INTERVAL OF PREY REPLACEMENT *** PARAM AREA =5. PARAM NPREY =(.1,.25,1.,2.,3-,4.,6.,8.,12.,32.,50.,75.,100.,125•,200.) IDPREY=NPREY/AREA DPREY =IDPREY DELX =1./DELT REPDEL=0.5/24. PARAM TEMP =26. RRGE =(TEMP-11.)*0.195 MDPREY=0. MFCG=0 . CUMPRD=0. DYNAMIC REPL =IMPULS(0.,REPDEL) NOSORT CALL PREDA(RRGE,DPREY,PRED,FOOD,PCG) DPREY =DPREY -(PRED /AREA)+REPL*(IDPREY -DPREY ) IP (TIME.LT.DELT)G O TO 5 CUMPRD=CUMPRD+ PRED MDPREY=MDPREY+(DPREY*DELT/FINTIM) MFCG =MPCG +(FCG »DELT/FINTIM) *** ••••A**********»»**»«»«»»**»**»**»*****»»*******»****,****************** *** OUTPUT STATEMENTS *** IF (TIME.LT.PINTIM)G O TO 5 WRITS(6,111)CUMPR D .MDPREY ,MFCG 111 F0RMAT(2X,3(2X,F6.3,2X)) * DO 5IG=1,NC L * GUTCON =IG * WRITE(6,112)GUTCON,PST(IG+ 1),PTD(IG+ 1) * 112 F0RMAT(2X,3(2X,P8.4,2X)) 5 CONTINUE

216 SORT TIMER FINTIM=.25,PRDEL=.25,DELT=.001 *** •****•»*»»*»****»***»**»•**•«.**«»**»»*#****»*»»»**•*«***•**»»******.**• END STOP SUBROUTINE PREDA(RRGEMP,DS , $ PN,FI,GT) COMMON C*************************»*******»***»******«**#********************* C** PHYSIOLOGICAL AND BEHAVIOURAL INPUT DATA C** DIMENSION RSE(22),RS1(22) DIMENSION 3R(20) ,FT(20) DIMENSION PT(22),RGE1(22 ) DIMENSION VL(20) ,AC(20) DATA VL/20*.047/ DATA AC/20*.39/ DATA SR/.936,.936,.854,.273,-245,-217,.185,.152,.128,.103, $ .093,.083,.065,.047,.034,.0217,.014,.007,.0035,0./ DATA PT/2*.009,2*.007,2*.006,4*.005,10*.004/ PCP =1. GUTC =3-333 ENLARG=NCLASS/GUTC DMPREY=0.013 DMPRED=0.057 DM =DMPRED+DMPREY VLPREY=0. ACPREY=0. COIN =0.42 C*** c»****«*•**#*•*»»*******•********************»***********************»** C*** COMPUTATION OP THERAT EO P SUCCESSFUL ENCOUNTER AND C*** THE INVERSE OP THETIM ENEEDE D TORESOR B AND EGEST C*** THEMAS S EQUIVALENT TO THE CLASS-SPECIFIC PART OF THEPRE Y

DO 51 N=1,NCL I=N+1 RGE1(l)=-RRGEMP/AL0G((N-.99)/N) RREWW =DM*SQRT(VL(N)*VL(N)+VLPREY*VLPREY)*AC(N)*ACPREY RREWR =DM*VL(N)*AC(N)*(1.-ACPREY) RRERW =DM*VLPREY*AC PREY*(1.-AC(N))*0.5 RSA =(RREWW+RREWR+RRERW)*DS*SR(N)*C0IN*864OO. TSC =(FT(N))+(1./(AMAX1(RSA,1.E-5))) RSE(I) =1./TSC P3T(I) =0. 51 CONTINUE RGE1(1 )=0. RGE1(NC)=1 . RGE1(2 )=0. RSE(1) =0. RSE(NL)=0. RSE(NC)=0. c*»***»**»»*»»*»,»»**»»»»*»««**»»*************************************** C*** COMPUTATION OF THE STEADY STATEDISTRIBUTIO N OF C*** THEPOO D CONTENT OP THEGU T C*** PST(1)=0 . PST(NC)=0. PST(2) =1. SUMST =0. DO 52N=1,NC L I=N+1 PCPREY =AMIN1(NL-2.,FCP*ENLARG)

217 11 =MAX1(I-FCPREY.1. ) PST(I+1)=(-PST(l1)*RSS(I1)+PST(I)*(RSE(l)+RGE1(I)))/RGE1(1+1 ) SUMST =SUMST+PST(I) 52 CONTINUE DO 53N=1,NC L I=N+1 PST(I)=P3T(I)/SUMS T 53 CONTINUE C*** C***********»»*************•**»*#***»**#*•************»***************** C*** INITIALIZATION OF THE FREQUENCY DISTRIBUTION OF C*** FOOD CONTENT OF THEGU T C*** PT(1 )=0 . PT(NC)=0 . DO 54N=1,NC L I=N+1 PT(I) =PTD(I) IF (TIME.LE.DELT)PT(I )= PST(I) RS1(I)=0 . 54 CONTINUE C*** C*************»*******»*#******»******»****•*•*••****»* #*•••******#**•«•* * C*** COMPUTATION OF THERAT E OF PREDATION AND THE FOOD INTAKE C*** ACCOUNTING FOR PARTIAL INGESTION PN=0 . FI=0 . IP =FCP*ENLARG 11 =MAX0(NCL-IP+1,2 ) DO 55 N=I1,NCL I=N+1 PART =RSE(I)*PT(I)*DELT RS1(NL)=RS 1(ND+PART/DEL T PN =PN+PART FI =FI+PART*(NL-I) 55 CONTINUE 12=MINO(NCL,IP ) DO 56N=I2,NC L I=N+1 WHOLiOLE= =RSE(I-IP)*PT(I-IP)*DELF T RS51(I)=RS1(I)+WH0LE/DEL1 T PN =PN+WHOLE FI =FI+WHOLE*IP 56 CONTINUE C***

C*** COMPUTATION OF THE FREQUENCY DISTRIBUTION OF FCGUT C*** AT TIME +DEL T C*** SUM =0. DO 57N=1,HC L I=N+1 RS1(I)=(RS1(I )+RGE1(1+1)*PT(1+1))»DEL T PTD(l) = PT(I)*(1.-(RSE(I)+RGE1(I))*DELT)+RS1(I) SUM =SUM + PTD(I) 57 CONTINUE GT =0. GUT =0. DO 58 N=1,NCL I=N+1 PTD(I) =PTD(I) /SUM G =N-.5 GUT =GUT+PTD(I)»G/ENLAR G GT =GT +PST(I) *G/ENLARG

218 58 CONTINUE C***

RETURN END ENDJOB

219 APPENDIX I QUEUEINGMODE LO FPREDATIO N INA MIXTURE OF PREY STAGES

TITLEFUNCTIONA L RESPONSE OF APREDATO R TO TITLE THE DENSITY OF AMIXTUR E OF PREY STAGES TITLE QUEUEING APPROACH TITLE YOUNG FEMALE PREDATOR OF METASEIULUS OCCIDENTALIS VERSUS TITLE ALL PREY STAGES OF TETRANYCHUS URTICAE TITLEEGG,LARVA,PROTO -AN D DEUTONYMPH C.Q. CHRYSALES.MALE AND FEMALE STORAGE DSI(10),DS(10),PST(22),PTD(22),PN(10) FIXEDNCL.NS T INITIAL NCL=20 NST=9 ***

*»•*#*******#***•*»********»****•»***•»*»»*«*****»************************ *** COMPUTATION OF THEFLUCTUATIO N OF THE DENSITIES OF SEVERAL ***PRE Y STAGES INRELATIO N TO THE TIME INTERVAL OF PREY REPLACEMENT ** * INCON RP=0.,WP=0.,SP=0. NOSORT DO 1IS=1,NST+ 1 DSI(IS)=0. DS(IS)=0 . PN(IS)=0 . 1 CONTINUE PARAM AREA =5. PARAM NPREY =(0.,2.,5-,8.,10.) DSI(2)=NPREY/ARE A DSI(9)=(10.-NPREY)/ARE A DO 2IG=1,NCL+ 2 PTD(IG)=0. 2 CONTINUE SORT DELX =1./DELT REPDEL=12./24. PARAM TEMP =25. RRGE =(TEMP-11.)*0.16 DYNAMIC REPL =IMPULS(0.,REPDEL) NOSORT CALL PRED(RRGE,RP,WP,FCG) DO 4 IS=2,9,7 îfMîl =2,S IS)-(PN(IS)/AREA)+REPL*(DSI(IS)-DS(IS)) PN(IS) =PN(IS)*DELX ***

*** OUTPUT STATEMENTS *** IF (TIME.LT.DBLT)G O TO 4 WRITE(6,111)PN(IS),DS(IS),FC G 111 F0RMAT(2X,3(2X,F8.4,2X)) 4 CONTINUE PERC=PN(9)/(PN(2)+N0T(PN(2))) WRITE(6,110)PER C 110 F0RMAT(2X,1(2X.F8.4,2X)) * DO 5IG=1,NC L * GUTCON =IG

220 * IP (TIME.LT.DELT)G O TO5 * WRITE(6,112)GUTC0N,PST(IG+1),PTD(IG+1 ) •112 F0RMAT(2X,3(2X,F8.4,2X)) * 5 CONTINUE SORT TIMER FINTIM=.001,PRDEL=.001,DELT=.001 END PARAM AREA=50. END PARAM AREA=500. END STOP SUBROUTINE PRED(RRGEMP, S REPR,WEIGHT,GUT) COMMON C*********#***»**^************»*********#*#**********»#*****•• •****«* » C*** PHYSIOLOGICAL AND BEHAVIOURAL INPUT DATA

DIMENSION PT(22),RGE1(22) DIMENSION RS(22,10),RS1(22) DIMENSION PY(9),SR(20,9),PT(10,9) DIMENSION DM(10),VP(20),VL(10),AC(10) DATA PY/1.,1.3,1.1,2.3,2.5,2.7,8.6,2.7,18./ DATA DM/.013,2*.026,3*.034,-045,-084,.065,0.076/ DATA VL/O.,.004,0.,.007,0.,.01,.01,.02,.02 ,.068 / DATA VP/5*0.035,5*0.08,5*0.075,5*0.068/ DATA AC/0.,.04,0.,.04,0.,.04,.04,.04,.04,.14/ DATA SR/20*0., $ .774,.908,.883,.884,.880,.880,.861 ,.861 , .728, .728, $ .741 ,.741 ,.679,.679,.541,.541,.452,.307,.110,0., $ 20*0., $ 20*0., $ 20*0., $ 20*0., $ 20*0., S 20*0., 5 .325,.325,.302,.115,.115,.03,.08,.07,.07,.06, $ . 06 , . 06, . 06, . 06, . 06,. 05, . 05, . 04, . 02,0. / DATA FT/1 0*0., $ 8.6,6.3,6.3,5.4,5.8,5.3,5.1,6.0,4.3,2.5, $ .011 ,.011,.009,-008,.007,-006,.005,.005,.005,.005, $ .015,.013,.011,.011,.010,.010,.009,.008,.003,.008, $ .01 5,.013,-011,.011,.010,.010,.009,.008,.008,.008, $ .01 5,.013,.011,.011,.010,.010,.009,.008,.008,.003, S .024,.021,.020,-020,.019,.014,.010,.009,.009,.009, $ .027,-023,.023,.023,.023,.022,.020,.020,.018,.015, S .040,.032,.031,.027,-026,.021,.021,.019,.019,.019/ NL=NCL+1 NC=NCL+2 MP=NST+1 GUTC =5.2 ENLARG =(NCL-1.)/GUT C GUTM =21. OPTW =4.5 EGG =3.2 DLT =DELT DO 50 M=1,NST PN(M) =0. RS(1,M)=0. RS(NC,M)=0. 50 CONTINUE DO 51 N=1,NCL I=N+1 PST(I) =0. RS(I,MP)=0. 51 CONTINUE C*** 221 (J*********************************************************************** C*** COMPUTATION OP THE RATE OP SUCCESSPUL ENCOUNTER AND C*** THE INVERSE OF THE TIME NEEDED TO RESORB AND EGEST C***TH E MASS EQUIVALENT TO THECLASS-SPECIFI C PART OP THE PREY C*** DO 52N=1,HC L I=N+1 RGE1(I)=-RRGEMP/ALOG((N-.99)/N) DO 52M=1,KS T AC2 =0.013*(TEMP-11,9)*AC(M)/0.1094 AC1 =AC(MP) ENCAA =(DM(MP)+DM(M))*SQRT(VP(H)*VP(N)+VL(M)*VL(M))*AC1*AC2 ENCAR =(DM(MP)+DM(H))*VP(N)*AC1*( 1.-AC2 ) ENCRA =(DM(KP)+DM(M))*VL(M)*AC2*(1.-AC1)*0.33 RSE =(ENCAA+ENCAR+ENCRA)*DS(M)*SR(N,M)*86400. TSC =(FT(1/2,11)/86400.)+(1./(AMAX1(R3E.1.E-5))) RS(I,M)=1./TSC RS(NL,M)=0. RS(I,MP)=RS(I,MP)+RS(I,M) 52 CONTINUE RGE1(1 )=0. RGE1(NC)=1. RGE1(2)=0 . C***

C*** COMPUTATION OP THE STEADY STATE DISTRIBUTION OF C***TH E FOOD CONTENTS OF THEGU T C*** SUMST =0. PST(1)=0 . PST(2) =1. DO 54N=1,NC L I=N+1 RS1(I)=0 . DO 53M=1,NS T PREY =AMIN1(GUTM-2.,PY(M)*ENLARG) 11 =MAX 1(I-PREY.1. ) RS(1,M)=0. RS1(I)=RS1(I)+PST(I1)*RS(I1,M ) RS(NL,M)=0. 53 CONTINUE RGE1(2)=0 . P3T(I+1)=(-RS1(I)+PST(I)*(RS(I,MP)+RGE1(I)))/RGE1(1+1) SUMST =SUMST+PST(I) 54 CONTINUE ,D O 55N=1,NC L I=N+1 PST(I)=PST(I)/SUMS T 55 CONTINUE c**************»************************»****«**#«*#»*#»***********#**** 0*** INITIALIZATION OP THEFREQUENC Y DISTRIBUTION OF C*** POOD CONTENTS OP THE GUT PT(1 )=0 . PT(NC)=0 . DO 56N=1,NC L I=N+1 PT(I) =PTD(I) IP (TIME.LE.DLT) PT(I)= PST(I) RS1(I)=0 . 56 CONTINUE C***

C***COMPUTATIO N OF THERAT E OF PREDATION

222 DO 58N=1,NC L I=N+1 DO 58M=1,NS T PREY =AMIN1(GUTM-2.,PY(M)*ENLARG) 12 =MINI(GUTM-PREY+N.GUTM ) 11 =MAX1( I -PREY ,1.) WHOLE =RS(I1,M)*PT(I1)*DLT PART =RS(I2,M)*PT(I2)*DLT RS1(I)=RS1(I )+WHOLE/DL T R31(NL)=RS1(NL)+PART /DLT PN(M) =PN(N) +PART+WHOLE 58 CONTINUE

C*** COMPUTATION OF THE FREQUENCY DISTRIBUTION OFFCGU T C*** AT TIME +DEL T

RGE =0. SUM =0. DO 59N=1,NC L I=N+1 DIG =RGE1(1+1)*PT(I+1) RGE =RGE+DIG/ENLARG RGE1(2)=0. PTD(I)=PT(I)*(1.-(RS(I,MP)+RGE1(I))*DLT)+(RS1(I)+DIG)*DL T SUM =SUM +PTD(I) 59 CONTINUE GT =0. GUT =0. DO 60N=1,NC L I=N+1 PTD(I) =PTD(I)/SUM G =N-.5 GUT =GUT+PTD(I)*G/ENLARG GT =GT +PST(I)*G/ENLARG 60 CONTINUE c*********************************************************************** C***REPRODUCTIO N IN RELATION TOFOO D INTAKE IF (TIME.EQ.DLT)FRESHW=OPT W WEIGHT =AMIN1(0PTW,FRESHW) FRESHW =FRESHW+(RGE-(TEMP-11.)*(GUT*0.01+WEIGHT*0.04))*DLT PROD =AMAX1(0.,FRESHW-OPTW) FRESHW =FRESHW-PROD REPR =REPR+(PROD/EGG)

RETURN END ENDJOB

223 APPENDIX J LISTO FABBREVIATION S USED INCOMPUTE R PROGRAMS

A = angular deviation ABAND = abandoning the captured prey AC- = activity ADAPT = adaptationperio d allotted to the predator CATCH = catching apre y item COIN = coincidence in space D- = density DIST = distance betweenpredato r and prey DM- = diameter ENLARG = factor accounting for the enlargement of the gut size FC- = food content FDEPRT = timeperio d of food deprivation -FI = food intake FINTIM = finishing time of the simulation FT = feeding time -G = gut -GE = gut emptying GUTC(ON) = gut content H- =handlin g HANDLE =handlin g acapture d prey I- = initial M- =mea n N- = number OPT- = optimum PART =partia l ingestion (vs.WHOLE ) PN =prédatio nrat e PRC =probabilit y of apre y capture PST = steady state probability PT =p(t ) PTD =p( t +DELT ) PY = food content ofth epre y R- = rate RDRAW =rando m drawing using therando m number generator -REP = replicates REPDEL =tim e delay ofpre y replacement REPR = reproduction -RES = resorption

224 RR- = relative rate RSA =rat e of successful attack (excluding feeding time) RSE = rateo f successful encounter (including feeding time) -RW =predato r is resting andpre y iswalkin g S- = sum SD = satiation deficit SEARCH = searching forpre y SR- = success ratio TEMP = temperature TSC = time spentpe r successful capture V- =varianc e VL- =velocit y VP =velocit y ofth epredato r -W =weigh t WHOLE = complete ingestion ofth epre y content -WR =predato r iswalkin g andpre y isrestin g -WW =predato r andpre y arewalkin g

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