Biological Control of Two-Spotted Spider Mites Using Phytoseiid Predators

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). Biological control of two-spotted spider mites using phytoseiid predators. Part 1: Modelling the predator-prey interaction at the individual level. Agric. Res. Rep. (Versl. landbouwk. Onderz.), 910, ISBN 90 220 0776 6, (vi)+ 242 p., 42 figs, 72 tables, Eng. and Dutch summaries, 10App. , 253 refs. Also to be used as Doctoral thesis,Wageningen .

The searching behaviour of individual predators of four phytoseiid species (Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens, Metaseiulus occidentalis) isinvesti gated in relation to the two-spotted spider mite {Tetranychus urticae), which infests green house roses. Especially the role of spider-mite webbing in the predator-prey relation is studied. Webbing interferes with searching, decreasing the rate of encounter per unit prey density. Low walking speeds and activity inwebbin g ensure that the predator is rarely dis turbed after contact with other mites. Webbing also positively influences searching, as spider mites aggregate within the webbed area: prey density, defined here as the number of prey per square centimetre of webbed leaf area, is high, as is the rate of encounter with prey. The ability to capture apre y after tarsal contact depends on the food content of the gut, the prey-stage and, in two specific cases, the webbing; the success ratio of P. per similis increased on awebbe d substrate, that ofA . potentillae decreased. Models to simulate rate of prédation on the basis of the dynamics of the motivational state and the state dependent rate of successful encounter are proposed. The food content of the gut is chosen as an indicator of the motivational state.A stochastic gueueing model simulates prédation as accurately as a Monte Carlo model or a compound simulationmodel . The queueing model ispreferre d because of its economic use of computer time and the rela tively fewvariable s used. The model was validated inprédatio n experiments. Systems analysis showed that the effect of temperature on the rate of prédation is large ly determined by its relation with the relative rate of food conversion into egg biomass and not by behavioural changes related to temperature. Also, itwa s shown that webbing has an important influence on the prédation rate. A new model for the analysis of prey-stage preference is proposed. Predators invade the webbed leaf area after contact with the silk strands, irrespective of the presence of prey. The residence time in the prey colony is determined by prey density. Simulation of experimentally defined walking behaviour shows thatpredator s remain inprof itable prey patches by turning at the edge of the webbed leaf area. However, when predator density increases, the tendency to leave the prey colony also increases, even at high prey densities. Only A. potentillae avoided the webbed leaf area, preferring the thickest parts of the leaf ribs or other protected places on the plant. A survey of references on life history data is presented; emphasis is given to the role of food, temperature and relative humidity. Experiments by the author show that oviposition history of predatory females is amajo r factor in determining the actual rate of food con version into egg biomass; and that the egg stage of the predators is very vulnerable to relative humidities below 70%, though the évapotranspiration of the plant and the hygro scopic properties of the webbing buffer this to some extent. As the juvenile mortality of the phytoseiids increases above 30°C, and that of the two-spotted spider mites above 35°C, spider-mite control at temperatures above 30°C is not effective. The four phytoseiid species are ranked on their capacities for numerical increase and prédation: P. persimilis, A. bibens, M. occidentalis and A. potentillae. Oncapacit yt o survive on alternative foods they are ranked: A. potentillae, A. bibens, M. occidentalis and P. persimilis. Some trials with alternative food supply did not improve survival rates established forprevailin g greenhouse conditions. The rate of increase of the webbed area per individual spider mite is quantified by ex periment. This knowledge will enable continuous monitoring of the prey density during simula tions of the predator-prey interactions on the population level.

Free descriptors: biological control, natural enemies, Phytoseiidae, Tetranychidae, webs, searching behaviour, prey stage preference, prédation, dispersal, deterministic simulation models, stochastic simulation models, life history.

ISBN 9022 0 07766

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

Nopar t ofthi sboo kma yb e reproduced orpublishe d inan y form,b yprint , photoprint,microfil m or any othermean s withoutwritte npermissio n from thepublisher . Contents

1 INTRODUCTION 1 1.1 Control ofspider-mit e outbreaks 1 1.2 Description ofth epredator-pre y system 2 1.3 Extrapolation from laboratory togreenhous e 6 1.4 Modelling ofth epredator-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 Sexrati o 27 2.1.4 Weight loss,wate rbalanc e andgrowt hbudge t 29 2.1.5 Roleo fwebbin g 32 2.1.6 Webproductio n andcolon y growth 33 2.2 Phytoseiidpredator s 39 2.2.1 Development andmortalit y 42 2.2.2 Sexrati o 51 2.2.3 Adult life spanan d 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 NAN DRESIDENC E TIME INA PRE YCOLON Y 71 3.1 Dynamics ofth emotivationa l state 74 3.1.1 Ingestion 75 3.1.2 Gutemptyin g j 80 3.1.3 Nutritive guality ofth epre y stages j 89 3.2 Rate ofsuccessfu l encounter | 90 3.2.1 Widtho fth esearchin gpat h 92 3.2.2 Walkingvelocit y 94 3.2.3 Distance ofpre y detection 100 3.2.4 Walkingpatter n 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 3.3 Prédation 137 3.3.1 Models ofprédatio n 138 3.3.2 Prey density 149 3.3.3 Webbing 152 3.3.4 Temperature 155 3.3.5 Age andovipositio n history 160 3.3.6 Predator density 164 3.3.7 Prey stagepreferenc e 165 3.4 Rateo fdepartur e 170 3.4.1 Walkingbehaviou r 170 3.4.2 Prey density 173 3.4.3 Predator density 176

4 THEUS E OFEXPERIMENTA L AND THEORETICAL RESULTS INDYNAMI C POPULATION MODELS 178 4.1 Unvalidated assumptions 178 4.2 Missing inputs 180 4.3 Impacto f individual characteristics atth e population level 182

SUMMARY 185

SAMENVATTING 192

ACKNOWLEDGEMENTS 199

APPENDICES A Model of reproduction inrelatio n to food intake 200 B Time series analysis 202 C Maximum Likelihood estimation ofth eparameter s ofth eTuke y distribution 206 D Model ofwalkin gbehaviou r 208 E Deterministic model ofth eprédatio nproces s 210 F Monte Carlo simulation ofth eprédatio nproces s 212 G Matrixalgebraic solution ofth eQueuein g equations 214 H Queueingmode l ofth eprédatio nproces s 216 I Queueingmode l ofprédatio n ina mixtur e ofpre y stages 220 J Listo f abbreviations used incompute rprogram s 224

REFERENCES 226 1 Introduction

1.1 CONTROL OFSPIDER-MIT E OUTBREAKS

Spider Mites (Acarina: Tetranychidae)ar e acontinuou spotentia l danger to many food and ornamental crops. Their high reproductive potential and rapid development form thebasi s fora hig hcapacit y ofpopulatio nincrease . Hence the outbreaks can develop even shortly after pesticide treatment. Moreover,the yappea rt odevelo presistanc e toman ychemical s thatinitiall y gaveeffectiv e control (Helle& va n deVrie , 1974). This results ina viciou s circleo fpesticid e development andresistance .Therefor e alternativecontro l strategies need to be developed. Apart from supervised control strategies there are fourmajo ralternatives : - plantbreedin g forresistanc e to spidermite s (e.g.d ePonti , 1977a). geneticcontro l strategies , to reduce the fertility of female spider mites by the introductiono f sterilized males (Nelson, 1968; Nelson & Stafford, 1972)o rmale s with chromosomal rearrangements (van Zon & Overmeer, 1972;Overmee r& va nZon , 1973). to displace the endemic spider-mitepopulatio nb ya mit estrai ntha ti s not resistant to certain pesticides or very sensitive toextrem etempera tures, which can be easily brought abouti ngreenhouse s (Feldmanne t al., 1981). control by a fungal epidemic in the mite population (Shagunina,1977 ; Gersone t al., 1979). controlb ypredator s (e.g.Huffake re t al., 1970). Thechoic eo fa specifi cmetho d or acombinatio n ofmethod sdepend sver y much on agricultural practice and the demands ofth egrower/consume r with regard to the product. The present study aims to elucidate thejpotentia l roleo fsom epredator ymite s (Acarina:Phytoseiidae ) forth econtro l ofth e two-spotted spider mite, Tetranychus urticae (Acarina: Tetranychidae),b y systems analysis so thatne woption s for integrated pestmanagemen tma yb e developed and compared with alternative control strategies.Th eresult so f these studies aredescribe d intw osubsequen tAgricultura l Research Reports concerning investigations in the laboratory (Part 1) and the greenhouse (Part2) . 1.2 DESCRIPTION OFTH EPREDATOR-PRE Y SYSTEM

The two-spotted spidermite , Tetrangchus urticae Koch,i s aseriou s pest inth e greenhouse culture ofornamenta l roses.Sinc e 1967,dienochlo r [perchlorobi(cyclopenta-2,4-dienyl)]ha sbee nuse d forchemica l control ofthi s spider mite in ornamental crops. Because pesticide resistance may evolve (McEnroe& Lakocy, 1969), alternative methods ofcro pprotectio n have tob e investigated. It is desirable to replace chemical spraying by biological control. Encouraged by the successful use of Phgtoseiulus persimilis asa controlling agent ofth etwo-spotte d spidermit e ingreenhous e cucumbers in the 'Westland'distric t ofth eNetherland s (Bravenboer, 1963;Woets , 1976), some rose growers started to use thispredator ymit ewit h reasonable suc cess (van de Vrie,persona l communication).A s incucumbers ,th epredator s areintroduce d ateac h spidermit e outbreak. Thismetho d of spider-mite controlwil l onlyb e acceptedb y themajorit y ofth e growers if itca nb e achievedwit hn odecreas e inros eproductio n or quality and if it costs no more than treatment with chemicalpesticides . 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 couldb e achieved with only a fewinitia l predator introductions.Thes e requirements canno tb eme t asyet ,s otha t acritica l evaluation of theus e ofpredator y mites is necessary. That evaluation should include assessment ofth e eco nomic-damage level and quantification of the potential forcontro lb y the predatory mites.Th e economic-damage level isbein g studiedb yva nd eVrie , an entomologist at the Research Station forFloricultur e inAalsmeer ,Th e Netherlands. Studies on thepotentia l forcontro lb ypredator y mites,don e uponva nd eVrie' s suggestion, areth e topic ofthi sreport . The substrate of Tetrangchus 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 freeo f

Fig. l. 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 e harvested. Fig. 2. Scanning electronmicrograp h (magnification 50x )o fth eoviposi - tion femaleo f Tetranychus urticae. anydamage ,th e leaves ofthes e shoots shouldb ecarefull yprotecte d against spider-mite infestation. On theothe rhand , iti sacceptabl e forth ehedg e beneath theeconomicall y importantpar tt ob e slightly damaged. Adult females (Fig. 2)ar eth e founders ofth e spider-mite aggregations on the underside of the leaves,whic h are frequently located near to an edge or a ribo fth 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 nne wcolonies .Th epopulatio n growth and dis persal apparently resulti ncompac t focio finfestation .Th eupwar ddispers al out of the hedge leads tocolonizatio n ofth euppe r leaveso fth eros e shoots. This must be prevented by one or more introductionso fpredator y mites. The mites feed on the leaf parenchyma,whic h causes spotstha treduc eth e immaculate appearance required ofqualit yroses .Losse scause db ymit e feed ing are more serious therefore than in other greenhouse crops, like the cucumber or Gerbera, where the fruits orth e flowers aresol d andno tth e leaves, so that only the photosynthetic functiono fth eleave s iso fcon cern. Clearly,predator ymite smus tpreven tth eupwar d dispersal ofth eplant - A. Phytoseiulus persimilis.

B. Amblyseius potentillae.

Fig. 3. Scanning electronmicrograph s (magnification5 0x )o fovipositin g females of four phytoseiid species. C. Amblyseius bibens.

D. Metaseiulus occidentalis feeding mites from thehedg eb y controlling thepre ypopulatio nwithi n the hedge. Phytoseiid mites feed on all stages ofth e spidermit e and deposit their eggs in the spider mites'webbing . The sequence of developmental stages issimila r totha to f the spidermites ,bu tmuc h less time formoult ing from one stage toth eothe r isrequired . Similar to spidermites ,onl y female adult phytoseiids disperse,an d only aftermating .However , incon trast to their prey theyd ono tdispers epredominantl y inth epre-oviposi - tion phase, but rather during their whole adulthood. How the tetranychid and phytoseiid females disperse from colony tocolony , leaflett oleaflet , shoott o shooto rhedg et ohedge ,an d the factors that induce theirdisper sal aremajo r topics ofthi sreport . Because the time needed forth e spider-mite population todoubl evarie s between only 2-4 days, theirnumerica l increase israthe r explosive.Henc e thetiming , thedos e andth epotentia l forcontro l by thephytoseii d species used iso fcrucia l importance, themor e sobecaus e -i ncontras tt oimmedi ate extermination by acaricide spraying -th epre ynumber s keep increasing for some time after predator release. The increase of colonized areaan d thetim e lapsebetwee npredato r release and decline inpre ynumber swil lb e treated in Part 2 of this Agricultural ResearchRepor t (tob epublished) . These problems are investigated for four phytoseiid species: Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens and Metaseiulus occidentalis (Fig.3) . Because a spider-mite outbreak cannot be easily detected in itsearl y stages by a grower, the possibility of leaving this task toth e predators was investigated. Special attention was therefore givent oth e ability of the predator to search for scarce prey aggregations,t owithstan d starva tion and to survive on alternative food inperiod s ofspider-mit e scarcity. Although the four phytoseiid species studied aremor e or less specialized predators oftetranychids ,ther e are conspicuous differences inthei rdiet aryrange .Thes e aretreate d inPar t 1.Th eproble m ofchoosin g a favourable combination ofpredator y capacity and dietary range forth econtro l oftwo - spotted spider mites inth e greenhouse culture ofornamenta l roseswil lb e treated inPar t2 .

1.3 EXTRAPOLATION FROM LABORATORY TO GREENHOUSE

Experiments in which predatory mites are introduced into greenhouses to control spider mites have in some casesbee n successful (Huffaker et al., 1970). Observations in the greenhouse (population estimates,assessmen to f predator-prey ratios and distributions) and laboratory experiments (life tables, prédation rates,mutua l interference among predators, effects of spider-mite crowding)wit h several tetranychid andphytoseii d species have formed a basis for the understanding ofth e damaging capacity ofth epre y and the controlling potential ofth epredators . Iti stemptin g toextrapo - 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,computin g thepopulatio n fluctuations with the model and comparing the resultswit hdat agathere d inth egreen house. Sucha stud yma yprovid e interesting startingpoint s for further research in an iterative process of evaluation anddesign .Mayb epractica l results will follow, but it is not suggested that this method will give riset o fully reliable controlmethod sb y itself;large-scal e validationunde rdif ferent conditions generally takes an excessive amount of time andmodel s cannot approach the complexity of biological systems, if only because of the limited capacity of computers. Nevertheless attempts tovalidat econ cepts ofbiologica l systemsnee d encouragement asthe y leadt o abette rin sight into the use of biological control agents in an agro-ecosystem. Examples of suchvalidation s canb e found inth emodellin g studieso fFrans z (1974: Tetranychus urticae - Metaseiulus occidentalis), Rabbinge (1976: Panonychus- ulmi - Amblyseius potentillae), Wollkind& Loga n (1978: Tetrany chus mcdanieli - Metaseiulus occidentalis) andDove re tal .(1979 : Panony chus ulmi - Amblyseius fallacis). Themode l ofFrans z (1974)i sbase d ona componen tanalysi so fth epred atory behaviour of Metaseiulus occidentalis: itsimulate s therit eo fpré dationo npre y eggs andpre ymale s distributed overa smal lbeari-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 ofprédation . By usingsmal l leaf-discs the interaction surface iseasil y defined andpre y density canb e directly assessed aslon g asth epre y israndoml y distributed overth edisc . Inthi s way variables like the rate of prédation and the rateo freproductio nb y thepredato rwer emeasure d inrelatio nt oth edensit y ofth eprey . The latter authors simulated the predator-prey interactionsi nlarge r ecosystems (e.g. the orchard)b y simple extrapolation ofth emeasurement s onth e leaf-discs to the surface ofth eecosystem , e.g.

5pre yegg s 5-1012 eggs 1 cm2 1-1012 cm2 This assumes that the prey is randomly distributed and thatth o predator searches forpre y ina rando m fashion.Bu tth edistributio n oftletranychid sj inth e field aswel l as inth egreenhous e crops isgenerall y clustered (e.g.! Crofte t al., 1976)an d asi ti slikel y thatpredator s tendt o aggregate at' prey colonies, it isrelevan tt o include these aspects forth eunderstand ingo fth epopulatio n fluctuations ofpredato r andprey . Dover et al. (1979)recognize d thisproblem .The ydirectl ymonitore d the result of the dispersal process in thepractica l situationo fth eorchar d by counting the number ofpre ymite s andpredator ymite s oneac h leafo fa representative sample ofleaves .Thes emit e countswer euse d tocreat esepa rate frequency distributions forpredato r andprey .A n appropriate two-para meter model, the negative binomial distribution, was used for description of the frequencies. By assuming the independence ofth epredato r andpre y distributions, their descriptive models were related to each other in a jointprobabilit y function.Thi s functionwa s used ina predator-pre y model to account for predators occupying leaves atbelow-mea n or above-meanpre y densities.However ,thi s implies thateac h leafha s the sameprobabilit y of containing a given number predators, irrespective of the number ofprey . Whether or not this is true, it remains difficult to understand how the -presumabl y prey-density related -prédatio n anddispersa l give rise toa dispersion thatca nb e described by anegativ ebinomia l function.Moreover , by representing the predator-prey distributionb y frequency distributions, theposition s ofth ecolonie s and the leaveswit h respectt oeac h other are notconsidered , sotha tth e spatialmosai c ofpredato r andpre y colonies is eliminated asa n aspect ofpredator-pre y interaction. None of the above models include the dispersal mechanisms ofpredato r andpre y inrelatio n to theheterogeneit y ofth e environment.Thes e factors can affect thepersistenc e ofpre y andpredato rpopulation s ina necosystem , asshow nb yHuffake r (1958)i n anexperimenta l study ofth e interactionbe tween apredator ymit e (Metaseiulus occidental is) and aspide rmit e (Eotetra- nychus sexmaculatus) in artificial universes differing in complexity. He constructed an environment of interconnected oranges thatwer e suitable as a food source forth eprey . Some days after the introduction ofth e spider mites on their substrate, the predators were released. They exterminated the spidermite swithi n amonth .Apparentl y thepredator s were able tocove r thewhol e substrate insearc h ofprey .However ,whe n thesewalkin g predators wereprevente d from dispersing,usin gvaselin ebarriers ,an dpre y dispersal by 'ballooning' was stimulated with low-velocity air currents,pre y and predator survived for six months in this artificial ecosystem. Therefore more detailed modelling and experimentation are needed to elucidate the role of dispersal andheterogeneit y inth epopulatio n dynamics ofpredato r andprey . Factors that have tob e taken into account,ar e forexample :th einflu ence of degree ofrose-cro p heterogeneity, theeffec t ofpre y andpredato r density on theresidenc e time ofth epredato r ina pre y colony and thetim e spent outside the prey colonies by the predators. In addition amode l is needed in which thedispersa l mechanisms are specifically incorporated and thepredato r andpre y distributions are generated inspace .Bu t such acom plexmode l requires alo to fcomputin g time. Itwoul db e desirable tous ea simpler, less time-consuming model. However, it is not possible to make a-priori statements on the relative importance ofdispersa l mechanisms in predator-prey models. It is known that themode lpropose d byDove r et al.

8 (1979), inwhic h fieldmeasure d dispersionparameter s ofth enegativ ebino mial account for the degree of coincidencebetwee npredato r andpre y give results that differ considerably from simulations thatd ono ttak edisper sion into account. Because this difference ismor e ademonstratio n ofth e static structure of their model than aproo f ofth e importanceo fth elo w degree of coincidence between predator and prey, it shows once more the need for furtherresearc ho nthi smatter . Another aspect of thedistributio n of Tetranychus spp.tha ti sno tcon sidered in most studies of the functional response and in the modelling study ofWollkin d &Loga n (1978), istha tthes e spidermite s aggregatewith in structures of self-made webbing, in contrastt o Panonychus spp.,whic h predominantly spin 'lifelines' made of silk strands.A s thepredator-pre y interaction takes place only where there are aggregations,preyiabundanc e should be quantified as the number ofmite spe rwebbe d leafarea ,instea d of per total leaf area. Moreover, webbing may play an important role in searching and prédation, asindicate db yexperiment s ofMcMurtr y& Johnson (1968), Fransz (1974), Takafuji & Chant (1976)an dSchmid t (1976). Still other factors may contribute to the lack of conformity between laboratory andgreenhous e experiments,e.g . effects ofspider-mit e crowding duringhostplan texploitatio n and availability ofalternat e food,sourcesi n periods of prey scarcity.A finaldifferenc ebetwee n laboratory andgreen house conditions can be found in their microclimates. First, temperature plays a very important role in the population dynamics of poikilotherm arthropods.Fo rexample ,a ris e intemperatur e enhances development,stimu lates reproduction and increases food consumption. Although a greenhouse in, say, Aalsmeer may seem awell-regulate d climatic environment,thi si s only partially true.A s a consequence of the variability of the outdoor climate and despite of the 'between limits' regulation of theglasshous e climate, temperatures rangebetwee n 10°Can d 33°C.Becaus e ofthi svariabi lity, temperature has tob emeasure d toenabl evalidatio n ofpredator-pre y models, which incorporate several temperature-dependent variables.Howeve r this raises a problem with respect toth emicroclimati c detailneeded .A s rose leaves are rather dark objects, leaftemperatur ema y differ fromth e air temperature, depending on the amount of incident (hedge-penetrating) radiation. Due to the small size ofth emite s (<1mm )thei r environmental temperature will be determined to an important extent by the leaf. Goudriaan (1977)ha s presented asimulatio nmode l thatcalculatej sth elea f temperature distribution ina canop y onth ebasi s ofth eweather>condition s aboveth ecanopy ,th ecro p geometry, theoptica lpropertie s ofth e leafan d the behaviour of the leafstom ata . Thismode l canb ecouple dt oa mode l of arthropod growth (Rabbinge, 1976). Evencorrectio n forinterceptio n ofradi ation by the structural elements of agreenhous e canb emade ,a sshow nb y Kozai et al. (1978). Unlike the leaf temperature, the humidity near to the leaf cannot be computed or directly measured. Moreover, tetranychid webbing covers the underside of the leaf and this may interfere-wit h themicroclimat e (Hazan et al., 1975b). This problem can be eliminated to some extent by using webbed leaves of intactplant s incontrolle d humidity cabinets in laboratory experiments.Th eextrapolatio n ofthes emeasurement s to thegreenhous e situ ation can be accomplished via intra-crop humidity profiles, which canb e calculated from the above-crop weather conditions usingGoudriaan' smodel . Although the above-crop weather conditions would have tob emeasure dcon tinuously, other data for the model, such asth egeometrical ,optica l and physiological properties of the leaves,woul d onlyhav et ob emeasure d once for intra-crop extrapolation.

1.4 MODELLING OFTH EPREDATOR-PRE Y SYSTEM

In modelling a complex system it is advisable to distinguish onlytw o levels ofcausa l depth (vanKeulen , 1975). Therefore the study described in tworeport s attempts toexplai n thepopulatio n fluctuations ofpredato r and prey in the greenhouse (Part 2) onth ebasi s of laboratory experiments at the individual level (Part 1).Th e life history parameters (development, reproduction, mortality and sex ratio;Par t 1Chapte r 2)an d thepredator - prey interaction (prédationan d dispersal behaviour;Par t 1Chapte r 3)wer e measured by studying individual mites inth e laboratory. The data obtained were fed into amode l thatcompute spopulatio n growth andgenerate s disper sionpattern s inspac e (Part2) . These extrapolations toth epopulatio n levelwer evalidate d by comparison with actualpopulatio n experiments inth egreenhouse .Fro m thediscrepancies , indications were derived for improving the model.Additiona l measurements were taken and themodellin g andvalidatio nprocedur e repeated.Thi sworkin g procedure offered aframewor k for theevaluatio n ofth ephytoseii dpredators , inparticula r for greenhouse culture ofornamenta l roses.Thes e phytoseiid species were compared for each laboratory experiment on the individual level and the impacto fthes e differences onth e final objective, 'biolog ical control',wa s evaluated withmode l calculations described inPar t2 . In the acarine predator-prey system the causal relations aremanifold . However, some parts of the system contain more interconnections between variables than others. These parts are called submodels.Th e structure of the acarinepredator-pre y systemwa s subdivided into four levels.Th e first level concerns the ability ofth epredato r tolocat e itspre y atsom epre y density and ata well-define d motivational state ofth epredato r (Level1) . Motivation isno tconstant ,bu tdepend s onth e feeding history and the food conversion (e.g. Fransz, 1974). Incorporating thedynamic s ofth emotivat ional state leads to the subsequent level ofcomplexit y (Level 2).Du et o prédation, but also reproduction, abiotic mortality, development, etc., prey andpredato r numberswil l change during the interactionperiod ;incor -

10 porating this adds another dimension toth epredator-pre y system (Level3) . Finally the prey aggregate in colonies.A s new colonies are founded,th e predators may move fromon ecolon y toth eother .Thi s emphasizes the final level ofcomplexity , thedispersa l ofth epredato r (Level4) . These four levels arerecognizabl e inth epopulatio nmode l as submodels that simulate the relative rate of successful encounter at some levelo f the motivational state, the rate of prédation at some level of the prey density, the population growthpe rpre ycolony , therat e ofdepartur e from thepre y colony and theredistributio n ofth edispersin gmite s overth esub strate (e.g.pre y colonies incas eo fth epredato r and leafsurfac ei ncas e of the prey). After validating all submodels separately,prediction swer e obtained from the entire model,whic h were themselves again validatedb y experiment. The model is of the state-variable type (Forrester, 1961); state and rate variables are distinguished andmathematica l expressions aregive nt o 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 erat eo feg gdevelopment ,th eovipositio n ratean d the prédation rate are examples of some of the ratevariables .Th e state variables are updated by rectilinear integration over asufficientl yshor t time interval:

Y^.t+A.t = Y . +tRY-A t RY =Y -RRY

t =tim e (e.g.day ) At= tim e interval of integration Y = statevariabl e (e.g.number ) RY =rat evariabl e (e.g.numbe rpe r day) RRY= relativ e rate (e.g.day " ) Unfortunately integrationmethod s thatcontinuousl y adjustth etim einter val ofintegratio n onth ebasi s of someaccurac y criterion (e.g.Runge-Kutta / Simpson)canno tb euse d inth epopulatio nprogram . Themetho d forth esimu lation ofdispersio n indevelopmenta l time (the 'boxcar'method ;Goudriaan , 1973) requires the use ofretilinea r integration,becaus e somed fth erat e variables involve adivisio nb yA t (=discontinuou s emptyingo fa 'boxcar'; deWi t& Goudriaa n 1978,p .20) .Therefor e the sizeo fth etim e (intervalo f integrationha s tob eprefixed .A s arul eo fthum b itha st ob e smaller than 20% of the timeconstan to fth e integrationproces s (Ferrari 1978,p .26) . The inverse ofth etim econstan t equalspar to fth erat eR Ytha ti sindepen dent of Y. For the simple integration above the timeconstan tequal sth e inverse ofRRY . When the model consists of a system ofintegrals ,th etim econstan to f this system isgoverne db y the integrationwit hth esmalles ttim econstant , to evaluate a number of natural enemies for the biological control of arthropodpests . 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 willb e encountered in Part2 wit h respectt o the adaptation ofth emotivationa l state ofth epre dator to acontinuall 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 ,th erat e ofsuccessfu l encounter ofth epredato rwit h itspre y andth epreferenc e of the predator for the different stages of the prey depends on its feeding history. Moreover, temperature influences several rate variables and it varies continuously duringpopulatio n growth inth e greenhouse.Th e addition of non-linear terms to the differential equations oftenprevent s solution by analytical techniques. Numerical methods are the only solution intha t case.Even when the system consists of only linear differential equations, the largenumbe r of these equations necessitates theus eo fnumerica l tech niques (seee.g . Hall& Da y 1977,p .10) . Theus e ofrando m numbers tosimulat e the stochastic character ofa vari able isno tnecessaril y implied.Mos tpart s ofth emode l have adeterministi c character.Howeve r there are some situations inwhic h the stochastic nature of a variable is absolutely basic toth eprope rmodellin g ofth eprocess . Fransz (1974) demonstrated that even when one is only interested inmea n values, deterministic models of the prédation process can lead to results different from thoseo fstochasti c modelswhe nnon-linea r relationsbetwee n 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 , Subsection 3.3.1). Because of the large amounto f replicates needed to obtain areasonabl e estimate ofth emea nrat e ofprédatio nthes e inefficient Monte Carlo procedures were replaced bymor e economical alter natives whenever possible. For example,th eMont e Carlo simulations ofth e prédation process were compared with several alternative models that are based on a larger set of assumptions but aremuc hmor e efficient interm s of computing effort (e.g. compound simulation, Fransz 1974; queueing approach, Curry &DeMichel e 1977). Mathematical formulation of the interacting growthprocesse s forces the investigator to measure the biological components ofth e system insuc ha way that they fitth e contexto fth emodel .Subsequently , the importance of the input data relative to each other can be determined by studying the overall effect of astandar d perturbation of aparamete rvalu e inth emodel . This so called sensitivity analysis gives an indication of the required accuracy of the input data and thus ofth enumbe r of replicates needed to obtain this accuracy at the 5% level (e.g. Cochran 1963,p . 73-77). Both the investigation of therelativ e importance ofth evariable s involved and the assessment of therequire d accuracy ofth e inputsma ymak e it feasible

12 2 Bionomics of prey and predator

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 rateso feac h stage ofth epredato r (Part2) . Rates of prédationwil l depend onpre y abundance,which ,therefore ,ha s tob e quantified. The interferencebetwee n Tetranychus spp.an dthei rpred ators takes place on those parts of the leaf area that are coveredwit h webbing, since all stages ofth espide rmit e areaggregate d there.T oquan tifypre y abundance therefore,i ti smor e logical todefin epre y density as the number of prey per square centimetre of webbed leaf,rathe rtha npe r leaf area, as Wollkind & Logan (1978)did . The size of thewebbe d area changes during population growth, as do the prey numbers.Therefor ebot h the rate of population increase and the rate of increase ofwebbe d leaf area shouldb emeasure d tocalculat e thepre y density inth ecompute rsimu lation model. In this chapter acomplet epictur e isgive no fth e life his tories,webbin g activity and stage-specific rates ofprédation ,a saffecte d by arthropod related factors (stageo fdevelopment , ageo fth e adult,etc. ) andenvironmenta l factors (temperature,relativ e humidity and food supply). Thesemeasurement s arepar to fth e inputt oth epopulatio nmodel spresente d and validated in Part2 ,bu tthe y are alsobasi c toth estructur eo fthes e models. Inth e finalpar to fthi schapte r the ability ofth epredato r to survive periods of spider-mite scarcity and to recover from starvation aredeter mined. This is important inassessin gpossibl e alternative foods formain taining a predator population in a greenhouse crop in absence of spider ' mites.

2.1 TETRANYCHIDPRE Y

The life history traits of Tetranychus urticae on rose (Rosa canina 'Sonia', grafted on Rosa indica 'Manetti')ar e discussed in Subsections 2.1.1 - 2.1.3. Although much life history data areavailabl e fromlitera 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) can be considerable. The strain of Tetranychus urticae used throughout this investigation originated from a culturemaintaine d atth e Research Station of Floriculture at Aalsmeer, where itwa s collected from greenhouse roses and reared for several generations on beans (Phaseolus vulgaris, 'Stamkievitsboon'). Jesiotr & Suski (1976, 1979) found adifferenc e inreproductiv epoten tial between mites fed on beans and those fed on rose 'Baccara'. After transfer of the mitepopulatio n from rose tobea no rvic evers a thesedif ferences were observed over aperio d ofmor e thanon e generation,whic hma y suggest adaptation of the population to thene whos tplan t throughselec tion. Because it wasmor epractica l tocultivat e the spidermite s onbean s thano n roses,i n addition toros e 'Sonia'th ebea n 'Noord-HollandseBruine ' isals o considered as ahos tplant . The food turnover of Tetranychus urticae isconsidere d toenabl ecompa rison of the conversion efficiencies of theplant-feedin g spidermite s and the mite-feeding predatory mites (Subsection 2.1.4). Furthermore, therol e of the webbing isdiscussed , especially inrelatio n to thephytoseii d pre dators (Subsection 2.1.5). Thewe b production andth e growtho f thewebbe d area is quantified to enable the calculation of prey density (Subsection 2.1.6). The following aspects ofth ebionomic s ofTetranychida e willb ediscuss edonl ybriefly :

Food quality of the host plant for the parenchym feeding spider mite The food quality ofth ehos tplant , as affectedb yplan tnutrition , iscon sidered to be constant under practical circumstances of cultivation. For example, the N, P and K levels of rose leaves are mostly within 10%o f their mean levels (Arnold Bik, personal communication),whic h is asmal l variation relative tothei r effect onth ereproductio n of Tetranychus urti cae (Rodriguez, 1964).

Fertilization status of prey and predator Females oftetranychi d andphyto seiid species sampled inth e field arerarel y unfertilized. Potter (1976a, 1978) and Blommers & Arendonk (1979) review several explanations forthi s phenomenon.

Extreme temperature and relative humidity In the greenhouse culture of ornamental roses temperatures normally range between 10°C and 33°C,whil e relative humidities range between 45%an d 90%.Thes e ranges arebase d on measurements at 40 locations spread over the rose-growing area of The Netherlands (vanRijssel ,persona lcommunication) .

Wind and rain Glasshouse structures nullify effects ofwin d andrain .

14 To restrict the amount ofwor k involved inthi sstudy ,severa l aspects thatinfluenc eth epredator-pre y system havebee npurposel yneglected , des pite their importance forth eeffectivenes s ofcontrol :

Implications of chemical spraying Thetoxi c effectso fsevera l compounds tobot hpredato r andpre yar ebein g studiedb yva nd eVri e (Research Station ofFloriculture ,Aalsmeer )an dva nZo n(Universit yo fAmsterdam , Amsterdam).

Diapause, as a means to survive the winterperiod Theinductio na swel la s theterminatio no fth ediapaus eo fth etwo-spotte d spidermit ean dth ephy - toseiid predator depend onphoto-period , temperature andth eavailabilit y of food. Inadditio nt oth eliteratur e reviewedb yva nd eVri ee tal . (1972) andMcMurtr ye tal . (1970),th efollowin g references representcurren tknowl edgeo nthi stopic : -Tetranychus 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 a etal. ,1976b .

2.1.1 Development and mortality

The rate of developmentan djuvenil emortalit ywa smeasure 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 t35° C and85 %a t15°C .Th e leaves ofth ehos t plant were placed upsidedow no na we tspong e floating in aplasti c box filled with water.Thes e leaveswer e coveredwit hwater - soaked tissue paper that hadbee n perforated atregula r distanceswit ha leaf puncher. Intha twa ycircula rpart so fleave swer e obtained thatwer e surroundedb ywe ttissue ,whic h acted asa barrie r foral lstage so fspide r mites.Th ejustificatio n forth eus eo fdetache d leafculture s inlife-tabl e studies was given by Rodriguez (1953), de Ponti (1977b)an dDabrowsk i & Bielak (1978). The eggs,use dt ostar tth eexperiments ,wer e deposited withina one-hou r period. The subsequent progress in development andth ejuvenil emortalit y were observed atinterval so feigh thour sa tal ltemperatures .Th etransfe r to fresh leaves,whic h isnecessar y to eliminate effects of diminishing food quality wascarrie d outa t leastever y3 days ,bu tonl yi fth emite s were ina mobil estage . To study the effecto falternatin g temperatureso ndevelopment , someo f theexperimenta l boxeswer e transferred atdail y intervals from10° Ct o20° C and vice versa inon e series, and in another series from2 5t o35°C .Th e developmental time from thedepositio no fth eeg gunti l firstreproductio n ('egg-to-egg' development) isplotte d inFig .4 .Th e rate of development

15 FEMALE(EGG TO EGG) RATEO F DEVELOPMENTAL TIME EGG-TO-EGG (DAYS) DEVELOPMENT(DAY " •0.02 15 36- I- I- 32

-0.15 28

20 0.1

12-

0.05

I 10 15 20 25 30 35 TEMPERATURE (°C)

Fig. 4. Means and standard deviations (J_ , n = number of replicates) of 'egg-to-egg' developmental times of Tetranychus urticae on bean (o) and rose (•) at constant temperatures. The drawn lines represent the rate of 'egg-to- egg' development.

the inverse of developmental time) depends linearly on temperature (15-35°C), a general phenomenon in Tetranychidae. A Student's t-test for comparison of two means and an F-test for comparison of their respective variances did not reveal significant differences between developmental time at the above mentioned alternating temperatures (10-20°C and 25-35°C) and that simulated on basis of the measurements at constant temperatures (Table 1) and a model ling technique (Part 2) at the 5% level. Therefore the rate of development may be considered as reacting instantaneously to a change in temperature. This was also found for other Tetranychidae, like Panonychus ulmi (Rabbinge, 1976)an d Tetranychus mcdanieli (Tanigoshi et al., 1976).

16 Table 1. Theeffec to falternatin g temperatures on 'egg-to-egg'developmen taltim e (hours)o f females of Tetrangchus 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 ttemperature s e.g. [(DR10 +DR 2Q)/2]~ . b. Simulatedb y thepopulatio nmode lpresente d inPar t2 o fthi sAgricultura l ResearchRepor t (tob epublished )usin gmeasurement s obtained atconstan t temperatures.

InTabl e 2th edevelopmenta l times aregive npe r stagean d sex.Th e rel ative length of thedifferen t stages asa par to fth etota l egg-to-eggde velopmental period israthe rconstant ,irrespectiv e ofth e temperature:eg g 39%, larva 9.5%, protochrysalis 8%,protonymp h 7%,deutochrysali s 8%,deu - tonymph8.5% , teleiochrysalis 11%an dpre-ovipositio n female 9%. Although the rate of development is strongly affected by temperature, mortality remains constant ata lo w level (about10 %fro m eggt oadult )i n| the range 15-30°C (Table 3).Outsid e this temperature rangemortalit yin creases, as was also found by Mori (1961), Stenseth (1965) and Nickel (1960).Assumin g thata teac hmomen tdurin g thedevelopmenta l period acon stant proportion of the mites die from anon-predato r cause,th e relative rateo fmortalit y canb ecompute d asfollows :

-lndT/N ) RRM = -—2_ =-in(M)-D R t RRM =th erelativ e rateo fmortalit y (day- )

Nt =th enumbe ro fmite s attim e t t =th edevelopmenta l period (day) DR =rat e ofdevelopmen t (day- ) M =mortalit y The stage-specific mortalities are incorporated in the population models presented inPar t2 b y usingthes erelativ erates . Several studies have shown that both low and extremely high humidity causes anincreas e injuvenil emortalit y and retards development (Boudreaux, 1958; Ferro & Chapman, 1979;Harriso n & Smith, 1961;Haza ne t al.,1973 ;

17 Table 2. Female andmal e developmental time (hours)o f Tetranychus urticae.

Temperature Stage of development Total n (°C) PC PN DC DN TC PF

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 6402 1 - - - 12 15 341 1410 6 316 9 7 52 10 68 11 50 7 80 6 766 45 11 20 161 1 34 33 3 5 24 5 30 5 26 6 38 4 346 12 14 25 104 2 19 42 4 5 14 4 21 6 16 5 27 4 225 7 7 30 71 4 14 51 3 5 12 4 13 4 11 4 17 3 151 11 11 35 59 2 11 41 2 4 10 4 13 6 12 6 16 7 133 9 9

E =eg g DC = deutochrysalis n =numbe r of replicates L =larv a DN =deutonymp h PC= protochrysali s TC = teleiochrysalis PN= protonymp h PF =preovipositiona l female

Table 3. Mortality (%) inth e developmental stages of Tetranychus urticae.

Temperature Stage of development Total n (°C) PC PN DC DN TC PF

10 15.6 12.5 ------38.4 190 15 6.1 1.4 1.0 1.0 0.0 2.2 0.0 0.0 11.3 154 20 6.3 1.1 0.0 1.3 0.0 0.0 1.0 0.0 9.6 181 25 4.3 1.9 0.0 0.0 0.0 1.0 1.0 1.5 9.3 144 30 6.6 1.4 1.2 0.0 1.0 0.0 0.0 1.0 10.8 100 35 10.1 4.1 0.0 2.9 1.0 2.1 3.0 4.0 24.4 144

Abbreviations areexplaine d inTabl e2 .

18 McEnroe, 1963;Nickel , 1960). However therang eo fhumiditie s forwhic hde velopment is not affected differs from studyt ostudy .Haza n found optimal conditions for Tetranychus cinnabarinus ata relativ ehumidit y of38% ,bu t Harrison& Smith found little differences ineg gdevelopmen to f Tetranychus urticae inth erang e 50-90%, and showed thatth eeg gmortalit y at100 %rel ative humidity occurred only after 6 days of exposure. Because suchhig h humidities occur for only short periods under greenhouse conditions (van Rijssel,Researc h Stationo fFloriculture ,Aalsmeer ;persona l communication) thiseffec ti srule d outa sa facto ro fimportance .Moreover , anexperimen t carried out for amor e realistic rangeo fhumiditie s (50%,75 %an d85 %a t 23°C)di d not reveal anydifferenc e indevelopmen to rmortalit y (Table4) . A possible explanation forth e absenceo fan yreactio n istha tthes eexpe riments were carried outo nwebbe d leaves thatwer econnecte d to apar to f their shoot, for, as postulated by Hazane t al. (1975b),bot hwebbin gan d defaecation by the spidermit e and,probabl ymos timportan t ofall ,évapo transpiration by the leaf may act asa buffe r tochange s inhumidity . For this reasonhumidit y isno t importantunde r thegreenhous e conditions (rel ativehumidit y 45-90%)i nTh eNetherlands . To study theeffect s oftransferrin g spidermite s frombea nt orose ,si multaneous experiments on both host plants were carried out.Th e results aregive ni nFig .4 .A t-test forcompariso no fmean s andF-tes tfo rcompa rison of variances did not reveal significantdifference s atth e 5%leve l between development on bean and rose.T o check if this conclusion also holds after generations of feedingo nth esam ehos tplant ,anothe rcompar ison was made after a six-month culturing period. The results (Table 9) show that in contrast to the results of Jesiotr & Suski (1976)wit hbea n and rose 'Baccara', the present cultivars of bean and rose 'Sonia' are interchangeable hostplant swit hrespec tt odevelopmenta l time. But foron eexceptio n (Marie, 1951), data from literature aboutdevelop mental timeo n severalbea n cultivars arei nclos e agreement (Gasser,1951 ; Hussey et al., 1957;Bravenboer , 1959;Fritzsche , 1959;Nickel ,1960 ;Susk i

Table 4. Theeffec to frelativ ehumidit y (T= 23°C )o n female 'egg-to-egg' developmental timeo f Tetranychus urticae.

Humidity (%) Developmental time (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 time on greenhouse roses areno tavailable . As for developmental time, juvenile mortality may differ with the plant species or cultivar (Dabrowski & Marczak, 1972). Tulisalo (1969) found differences in juvenile mortality between cultures growno ndifferen t cultivars ofcucumber , although therat e ofdevelopmen t didno tdiffe r signif icantly. However, in the study described inthi s report juvenile mortality was very low on both host plants (bean and rose), which corresponds with theresult s given inth e above-mentioned literature,excep t for Shihe t al., who reported arathe rhig hmortalit y (30%). Of thevas tnumbe r of studies onnutritio n inAcarina ,onl y thato fSusk i & Badowska (1975)concerne d the influence ofNP K supply onth e rate ofdevel opment and the juvenilemortality . The relations they established arecom plex. It is sufficient tomentio nher e thatth enutritiona l ranges used in theexperiment s caused changes inth e rate ofdevelopmen t and juvenilemor tality that were within 15%o f meanvalues .Howeve r thenutritiona l range was probably larger thantha t found inpractica l agriculture.Th e nutrient composition ofth e leafma y alsob e affected by its ageing;n o experimental evidence of an effect on the rate of development was found, however (Table10) . During mite-colony growth the eggs and juveniles are left stranded in already exploited leaf areas.Th e young mites are not as active as the mature mites,whic h may causemortalit y additional totha tmeasure d inth e previous experiments,wher e themite swer e cultivated individually on fresh leaves.Wrensc h& Youn g (1978)measure d amarke d reduction inrat e ofdevel opment and survival athig h spider-mite densities.However , asthe y confined the mites to a leaf disc, the importance of intraspecific competition for food still has to be demonstrated. Spidermite s are able tocontro l their density (number of mitespe r squarecentimetr ewebbe d leafarea )partl yb y increasing thewebbe d area andpartl yb y dispersal.T odecid ewhethe r these factors need tob e studied inmor e detail,a greenhous e experiment onpopu lation growth was carried out and thenumerica l resultswer e compared with simulations of the same experiment,whic hneglec teffect s of intraspecific competition.Thi s experimentwil lb e discussed inPar t2 .

2.1.2 Reproduction and life span

Experiments onth e rate ofreproductio n and ageingwer e carried outusin g a similar experimental design astha tdescribe d inth epreviou s subsection (Subsection 2.1.1). Fifty female deutonymphsclos e tothei r finalmoul twer e sampled for each trial.Male swer e introduced toguarante e immediateinse mination ofth e female after eclosion.Th enumbe r ofegg swer e recorded and removed ateight-hou r intervals.Moreover , femalemortalit ywa s registered, ignoring deathsb yunnatura l causes,e.g . drowning inth ewater-soake dtis -

20 NUMBER OF EGGS (DAY"1 35°C

16 18 AGE CLASSES

Fig. 5. Rate ofreproductio n of Tetranychus urticae inrelatio n to female age class and temperature. The histogram visualizes thedescriptiv e power of the intra-age class regressions. Length ofeac h ageclas s atdifferen t temperatures: 3.5 day at 15°C; 2.5 daya t20°C ;2. 0 day at25°C ; 1.25 day at30°C ; 1.0 daya t35°C .

sue (5-10%). Because both reproduction andmortalit y appeared todepen do n age, the data were classified in age periods forming equal parts of the maximum life span.Thi smaximu m longevity ofth e femalewa sestimate dvi aa least-squares estimate ofth e 97-99%poin to fth ecumulativ e frequency dis tribution of life spans,plotte d onprobabilit y paper ofth eGaussia n dis tribution. From this linear relation themortalit ype r ageclas swa s esti mated. This mortality togetherwit h theduratio no fth eclassifie d agepe riods was used tocalculat e therelativ e rateo fmortality .Thi sclassifi cation approach requires somedegre e ofintra-clas sconstanc y ofth erela tive rate variables involved. For this reason themaximu m 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 rateo freproductio n inrela tion to temperature are given in Fig.5 . Itappeare d thatth e intra-class rate of reproduction in the initial 10ag eclasse sdepend s on temperature

21 SLOPE(EGGS-DAY-° C 1.0

l—i—l—l—l—l—l—l—I 0 1 9 101 11 21 3U 151 61 71 8 AGECLASSE S Fig. 6 Slope of the oviposition rate (eggs-day" •° C )i n relation to the ageclass .Slop e =ovipositio n rate/(temperature 10°C).

Table 5. Potential andne t fecundity of Tetranychus urticae inrelatio nt o temperature.

Temperature (°C) Fecundity

potential net

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 a.Potentia l fecundity =tota l number ofegg sproduce d perfemale , excluding age-dependentmortality . b. Net fecundity =tota lnumbe r ofegg sproduce dpe r female, including age-dependentmortality .

22 in a linear fashion over the whole temperature range from 15°C to 35°C. This enabled amor e concise descriptionvi a the slopeso fth elinea rregres sion lines,whic h cross the x axis close to 10°C. These tangents ofth e angle of inclination are plotted in Fig.6 an d theirdescriptiv epowe r is visualized by the histograms in the original graph of the age-specific rateso fovipositio n (Fig.5) . In Table 5 the mean egg production per femalei sgive na sa ne t (=fe male mortality included) and a potential (= female mortality excluded) fecundity, which shows thatmortalit y causes onlya 10-20 %decreas e ofth e fecundity relative to thepotential . Fecundity appearst ob eunaffecte db y temperature over a rather largerang e (20-35°C).Howeve rbelo w20° C itde creases,bein g 70%a t15° C and 20%a t11°C . The mean and maximum life-spans depend on temperature in amuc h more gradualway ,a sca nb e seeni nTabl e 6an dFig .5 .Becaus e thepost-oviposi - tionperio d isabsen to rver y short,th e adultlife-spa n isonl y subdivided ina pre-ovipositio n period and apost-ovipositio nperiod . Aswit hreproduction , survivalma y depend ontemperatur e and ageing, i.e. the age relative to the maximum life-span.Therefor e therelativ e rateo f mortalitywa s determined foreac h ageclas s and atal lexperimenta ltemper atures. From simulations ofpopulatio n growth (Part 2), itappear s thatth e numerical effects of thetemperatur e dependency couldb eneglecte d aswel l (12-35°C). For this reason therelativ erate swer e smoothed outb y repeated simulation ofth e above survival and reproduction experimentunti l anaccept able overall fit was found.Thes e fittedvalue s aregive ni nTabl e 7.The y demonstrate thatth erelativ e rateo fmortalit y depends onth e age relative toth emaximu m life-span.

Table 6. The lengtho fth epreovipositio n andovipositio nperio d (days)o f Tetranychus urticae.

Temperature Preovipositionperio d Ovipositionperio d (°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. The smoothed estimates ofth erelativ emortalit y rate (day- )o f Tetra.nych.us urticae inrelatio n toth e ageclas s ofth e adultfemale .

Female age class

1-5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.0 0.0020.0 2 0.05 0.05 0.07 0.10 0.10 0.10 0.10 0.15 0.15 0.30 0.50

Table 8. Theeffec to fhumidit y (T= 23°C )o nne t fecundity andoviposi - tionperio d 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 effect of humidity on the rate of reproduction was analysed by Boudreaux (1958), Nickel (1960) and Hazan et al. (1973). The oviposition rate ismaxima l forrelativ e humidities below 90%,th emaximu m depending on temperature and the species involved; Hazan et al. (1973) found optimal values at relative humidities of 22-38%. Above 90%relativ e humidity the oviposition is lowest. As argued in the previous subsection the humidity near to a webbed leafwil lprobabl y differ from theenvironmenta l relative humidity at the same temperature due toévapotranspiratio no fth e leafan d defecationb y the spidermite .T o study the effecto fth ehumidit y buffering capacity of the webbed leaves mite reproductionwa smeasure d onthi ssub strate at three humidity levels (relative humidity =50 ,75 ,85 %a t23°C ) for the same experimental design asdiscusse d inSubsectio n 2.1.1.Th ere sults (Table 8) indicate that as for the rate ofdevelopment ,humidit y is ruled out as a factor of importance for the reproduction of Tetranychus urticae within thehumidit y range ofpractica l interest. As with the rate of development, fecundity was measured also on both rose 'Sonia'an dbea n 'Noord-Hollandse Bruine' (Table 9).Thes e trialswer e donewit h spidermite s cultivated previously onbea nan dwer e repeated with mites cultivated for sixmonth s onrose .Bot h t-test andF-tes tfo rcompa risono fmean s andvariances ,respectively , did not reveal significantdif ferences at the 5% level. Therefore it is probable thatthes e particular

24 Table 9. Theeffec to fth eculturin gperio d onsom elife-histor y traitso f Tetranychus urticae (T= 25°C) .

Phase of Female 'egg-to-egg'Ne t fecundity Ovipositionperio d culturing developmental time (days) (hours)

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 ofculturin g onros e('Sonia' ) continuously cultured 15 270 21 41 133.450. 8 41 22.2 9.2 onbea n('Noord - Hollandse Bruine')

cultivars of bean and rose are interchangeable hostplant swit hrespec tt o thelife-trait s studied. Comparison of these results on rose with data from the literature on bean shows similar fecundity levels (Bravenboer, 1959;Leh r& Smith,195 7 (Massachusets strain);va nd eBun 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 - 68eggs ; Lehr& Smith ,195 7 (Canterbury strain) - 107 eggs; Fritzsche, 1959 - 57-80 eggs)an dhighe r values (Watson,1964 )(youn g leaves).A tothe rhos tplant s fecundity levels similar toth epresen tresult sma yb e obtained,bu tmostl y lower levelsar e reported. Insevera l cases thechemica l composition ofth eplan tha sbee n shownt o correlatewit hmit e fecundity.Accordin g toJesiot r& Suski (1974)fecundit y of the two-spotted spidermit e islowe r onros e 'Baccara'tha no na numbe r ofothe rros ecultivars .Howeve rDabrowsk i &Biela k (1978),wh o studiednu tritional correlations with mite reproduction in4 cultivar s ofbot horna mental roses,wer e not able to explain this result; theyonl y found some correlation with the content of glutamic acid. Furthermore, they founda positive correlationwit h thetota lnitroge nconten tan dtota l freeendoge - neous amino acids.Accordin g to the reviewb y Suski& Badowsk a (1975)th e effect of nitrogen is often positive, but the results withpotassiu m and phosphorus are far from conclusive. Suskie t al. (1975)stat etha tth 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 d canb e ignored.Moreover ,th e role of adaptation of amit e population to modified nutritional conditions,a sindicate db y the results of Jesiotr & Suski (1974), isvirtuall y overlooked inth e laboratoryexpe riments, where generally instantaneous, instead of delayed responses (>1 generations)t onutritiona l changes aremeasured . Because inpractica l rose culture today more or lessconstan tNP K levels aremaintained , andbecaus e the geneticmake-u p ofth e greenhousepopulation s seems tob e ratherstable , which indicates minor exchange with outdoor mitepopulation s (Overmeere t al., 1975), itma y notb e far from reality toconside r thenutritiona l con ditions as a constant or an implicit 'noise' factor. This assumption is supported by the fact that in practice NPK levels of 'Sonia'ros e leaves (3.10%N , 0.28%K , 2.20%P )ar e largely within 10%o fthei rmea nvalues ,s o that inmos tcase s fecundity varieswithi n 11%o f itsmea n level (Rodriguez, 1964). Rabbinge (1976) came toth ever y same conclusion forth e fruit-tree red spidermite ,whic h infestsDutc h appleorchards . Besides fertilizer doses,th enutrien t compositionma y alsob e influenced by the ageo f the leafo rb y seasonal changes (e.g.Storms ,1969 ;Dabrowski , 1976). However the age of 'Sonia' leaves is probably not of importance: female spidermite splace d ongree n leaves atth etop ,middl e or lowerpar t of a rose bushproduce d asimila r amounto fegg s (Table 10).Besides ,yel lowing leaves aredroppe d rather soon and these senescent leaves are simply left or avoided byth e spidermites .Seasona l changes in food quality were not studied. Food quantity is affectedb y feeding ofth e spidermites .Th e available leaf parenchym decreases during population growth until thehos tplan ti s exhausted. Theoveral l damagema y exceed the directdamag e done toth ehos t

Table 10. The influence of leaf ageo n some life-history traits (T= 25°C ) of Tetranychus urticae.

Leafnumber , n Female Net fecundity Ovipositionperio d counted fromth e 'egg-to-egg' (days) top of aflowerin g developmental rose shoot (hours)

2-4t h leaf 30 258 14 131.1 46.4 22.1 8.

12-14th leaf 25 269 19 126.8 40.9 21.8 9.1

20-24th leaf 21 262 13 124.6 55.1 20.9 9.i

26 plant by the piercing ofth e leafcells .Possibl y thequalit y of available food dropped by indirectcauses .Anyway ,mit e feeding activitydoe s affect the food, as shown by a number of researchers (Davis, 1952;Bravenboer , 1959;Tulisalo , 1970;Rasmy , 1972;Wrensc h& Young , 1975). Todecid ewhethe r these factorsnee d tob e studied inmor e detail,a populatio n experiment in the greenhouse was compared with population simulation,excludin g density dependent factors (Part 2). Inthi sway , ifth esimulation s fitunde rcir cumstances of free growth (unlimited food supply), the critical levelo f plant exploitation may be found abovewhic h intraspecific competitionact s upon thepopulatio n growth of Tetranychus urticae.

2.1.3 Sex ratio

The two-spotted spidermit e Tetranychus urticae isa narrhenotokou spar - thenogenetic species: unmated femalesproduc e onlyhaploi d eggs,whic hde velop into males,wherea s mated females produce both haploid anddiploi d 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 : theguardin g and defendingbehaviou r ofth emale s (Pottere tal. ,1976a , 1978) the role of pheromones, tactile stimuli and web (Cone etal. ,1971ab , 1972;Penma n& Cone ,1972 ,1974 ;Rege v& Cone ,1975 ,1976 ) a shorter developmental timeo fth emale s relative toth e females (Sub section2.1.1 ) a lower tendency ofth emale s todispers e relative totha to fth epreovi - position females (Part 2) the presence of an overdose of males relative toth enumbe r ofteleio - chrysalids nearth eecdysi s (Potter,1978 ;Functiona l sex ratio). The insemination atth e firstmatin g appears tob eth eeffectiv e one (Helle, 1967; Overmeer, 1972;Wrensc h& Young , 1978). According toBoudreau x (1963)th eproportio n offemale s inth e offspring ofa singl e femalei srathe rvariable ,s otha tther e isn o fixed sexratio . He states, that the sex ratio in the offspring ofeac h femaledepend s on the amount of sperm received during mating.Thoug hOvermee 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 ofth emale s todisturbanc eb y othermales . Although the sex ratio inth eoffsprin g ofa singl e femalei ssubjec tt o variation,thi snee d nott ob etru e forth ese xrati o inth eoffsprin go fa population of spider mites.Overmee r (1967)an dOvermee r &Harriso n (1969) found that the ratio of the totalnumbe r of fertilized eggs againstthose , thatescap e fertilization israthe r fixed over alarg enumbe r of subsequent

27 opmentwit h aCah nelectrobalance .Th e results (Table 12)ar e inclos eagree ment with those of Mitchell (1973)an dThurlin g (1980),bot h obtained for Tetranychus cinnabarinus. The twenty-fold increase in weight, from eggt o ovipositing female,take splac eprimaril y inth edeutonymp h stage (30%)an d the preoviposition stage (55%). This relative distribution of the weight over the developmental stages appears tob ever y similar totha to fPhyto - seiidae (Subsection 2.2.1,Tabl e 18).Spide rmite s disperse toothe r leaves in the beginning of the preoviposition phase after fertilization. Inthi s way colonizing females dispersebefor e theyhav e attained halfthei rmatur e weight.B y delaying halfo rmor e ofthei r growth and their full reproduction effort until after dispersal to new food resources thesemite s reducede mands on their original location, where juveniles,male s andparenta lfe males remainhavin g amuc h lowertendenc y todispers e (Part2) . The feeding physiology of spider mites is characterized by the large quantities of plant fluid passing the digestive system. McEnroe (1961, 1963), studying the actively feeding female by aradioactiv e tracertech - _3 nique, estimated an ingestion rate equal to 6x 10 pipe r 30minute s and _3 a simultaneous defecation rate of5 x io pipe r 30minutes .Thi s implies that anamoun to f fluid equivalent to 20-25%o fth e femaleweigh t ispassin g the gut at 30minut e intervals.Lieserin g (1960)counte d thenumbe r ofpa - renchym cells punctured and emptied. His estimation ofth e ingestion rate amounts to 100 parenchym cells per 5minutes ,which , assuming thecel li s spherical with radius 0.01 mm, implies aningestio n rato f 5p ipe rhour . Elimination ofth e large quantities ofwate r ingested inthi swa y isaccom plished via abypas s system that shunts excess fluids from the oesophagus directly into the hindgut. In this way ventricular digestion mayprocee d without the added burden of processing and transporting excess liquid (McEnroe, 1963). Large volumes of water canb epasse d rapidly throughth e digestive system and excreted without requiring energy for selective ab sorption and transport toth e tracheal system forexcretion .Als o substances oflo wmolecula rweigh t (methyleneblu e solution)pas s straight toth ehind - gut from the oesophagus. However a colloidal solution ofCong o red isdi rected to the midgut (Akimov & Barbanova, 1978). Bekker (1956) supposed that chloroplasts and chlorophyll grains were phagocytized by disengaged epithelial cells, in which the stroma wasbein g digested.Wiesman n (1968) showed that these free-living gut cells accumulated dyes, particles and especially chlorophyll,convertin g themultimatel y intoball s ofexcrement . Aggregations of these food balls in the U-shaped gut lumen have brought about thecommo nnam e "two-spotted spidermite" ,du e toth e transparancy of the body wall. Upon excretion these so called "black pellets" contain a large amount of plant-pigment-related waste products (Blauvelt, 1945; Gasser, 1951;McEnroe ,1961 ;Liesering , 1960). Apart from these solid faeces another type of faeces can be distinguished. These are initially equal in size to the black pellets and spider mite eggs, butevaporat e soquickl y

30 thatonl y aver y small solid fractioncontainin g nitrogeneouswast eproduct s (McEnroe, 1961), remains:th e "whitepellets" .Anothe rmean s of eliminating large quantities of water istha tvi a tracheal evaporation.B y sealingth e tracheal openings and by cyanide treatments,McEnro e (1961)showe d thata n important part ofweigh t lossca nb e attributed totrachea l transpiration. Blauvelt (1945) showed the structural basis for the control of tracheal transpiration via the peritremes, which are located dorsally just behind thegnathosom ai nthi sprostigmati dmite .Th erol eo fcuticula r evaporation is very limited (McEnroe, 1961), probably because ofa lipi d layer inth e cuticle (Gibbs& Morrison , 1959). As expected of aplant-feedin g arthropod, the conversion of ingested plant liquid into eggbiomas s isaccomplishe d with lowefficiency .A crude estimate ofth econversio nefficienc y hasbee nobtaine d fromth e following: The size of a fresh faecal pellet approximates thato fa negg ,s otha t theirrespectiv eweight swil lno tdiffe rver ymuc h (approximately 1 \ig) (own observation). Therat eo fovipositio n isequa l to75 %o fth erat eo fdefecatio n (rela tivehumidit y = 60-80%) (Hazane t al., 1973, 1975). - The weight loss during the first hour of food deprivation isequa lt o 1.2 |jga t T = 30°C and arelativ ehumidit y = 15-20% (McEnroe, 1961). This mayb econsidere d asa nestimat e ofth etrachea l transpirationrate . - Oviposition and defecation atT = 30° C (andrelativ e humidity = 15-20%) takes place at 2an d 1.5 hour intervals,respectivel y (Hazane t al.,1973 , 1975), so that the weight loss viatrachea l 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 j weight loss), the conversion efficiency of ingested fluid to eggmas s is equal toapproximatel y 20%,whic h contrastswit h thato fth ephytoseii d fe-] males (Section 3.1).Becaus e mature females of this family lose most of theirweigh tvi aeg gproduction ,Phytoseiida e canconver tth eingeste d con-| 1 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 , asindicate db yth epresenc eo fMalphighia n tubules and a colon (Akimov & Starovir, 1975), andb y alo wproportio no f indigestable constituents. In spidermite s thephysiologica l efforti sno t directed to recycling ofwater ,bu trathe r toeliminatin g it,a s indicated by thepresenc e ofth ecombine d hindgut andexcretor y 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 with respect tothei rmod eo fwe b formation. Panonychus spp.us e the silken strandspredominantl y indispersa l (Fleschner et al., 1956). They spinthread sb ywhic h they lower themselves from alea f until they are picked up by aircurrents .Sait o (1979)foun d thatth efe males of Panonychus citri spinwhil ewalking ,bu t appear toavoi d their own threads, which merely serve as 'lifelines'. Apart from its similar usei n dispersal, Tetranychus spp.us e the silkenstrand s asmateria l forbuildin g structures of webbing, within which all stages find aplac e to live.Th e adult stages of these species walk upon, in or under thewebs ,whil e for example Oligonychus ununguis mostly lives under a webbing cover (Saito, 1979). The structure ofthes e socalle d colonies differs among themember s of the Tetranychus species. Colonies of Tetranychus atlanticus are more compact and have a greater profusion of webbing than those ofmos tothe r species (Leigh, 1963). Tetranychus desertorum produces colonies similart o the latter species (Nickel, 1960), but Tetranychus pacificus produces only a loose ordisperse d typeo fcolony ,wit h relatively littlewebbing . Tetra nychus urticae produces colonies with an intermediate amount of webbing (Leigh, 1963). Onth e other hand the form and density ofth ewe b depends on thehos tplan t involved (hairs,ribs , smoothness) (vand eVri e et al., 1972). Several functions have been ascribed toth ewebbin g (Gerson, 1979). The silk serves asballoonin g threads inaeria l dispersal,a sa lifelin e indis persalb ywalkin g and as acarrie r ofse xpheromones .Th ewebbin g may indi cate the state ofdepletio n of food resources and itma yb e aprerequisit e for the conditioning of social interactions.Th ewebbin g isuse d inintra - specific mating competition betweenmale s and ininterspecifi c competition against other non-spinning phytophagous mites.Th e webbing coverma y also exert an influence on the microclimate, for instance via the hygroscopic properties of the fibroin silk strands. Moreover, it protects theinhab itants from adverse climatic conditions,som epesticide s and atleas tsom e natural enemies. In this study the effects of webbing on the acarine predator-prey interaction are considered. Notonl ybecaus e thewebbin gde limits the area occupied by the spidermite s and therefore shouldb euse d inquantifyin gpre y density,bu t alsobecaus e itappear s tob e aver y impor tantcu e inth e foragingbehaviou r ofth ephytoseii dpredators . The role of webbing inth e interactionbetwee nphytoseii d predators and tetranychid prey has been studied only a few times.McMurtr y & Johnson (1966)stat e that Amblyseius hibisci sometimesbacke d away andproceede d in another direction when contacting the webbed area,wherea s inothe rcase s they walked over it,leavin g the spidermite s (Oligonychus spp.)unharmed . A fewtime s thispredato rwa s observed inside thewebbin g structures having gained access to theprey .McMurtr y &Johnso n reporttha t Amblyseius limonicus was less hindered by the webbing and Amblyseius chilenensis immedi-

32 ately crawled between the strands ofwebbing .A negativ e influence ofweb bing on prédation by Phytoseiidae has beenreporte d forth eadul t females of Amblyseius longispinosus (Mori, 1969), A. largoensis (Sandness& McMurtry , 1970, 1972), Typhlodromus caudiglans (Putman, 1962), T. pyri (McMurtry et al., 1970)an d forth e larvae of T. tiliae (Dosse,1956) ; the adults ofthe ! latter species seemed not to be affected.Howeve rothe rPhytoseiida e seem to be attracted to the webbing andundisturbe db y the silk.Thes e include Amblyseius fallacis, Phytoseiulus persimilis and Metaseiulus occidentalis (Putman & Heme, 1966; Huffaker et al., 1969;McMurtr y et al., 1970). Schmidt (1976)measure d an increased rateo fprédatio nb y Phytoseiulus per similis due toth ewebbing . She found,tha tweb s arrested thepredato rmor e thanpre y eggs orexuviae ,an d suggested, thatthi s arrestmentwa sbase d on tactile stimuli. These observations correspond with those of Takafuji & Chant (1976), who observed that Phytoseiulus persimilis, as opposed to Iphiseius degenerans, consistently distributed itselfove rth e silk-covered leaves, andth e adultfemale s invariably deposited theiregg s inth ewebbin g Fransz (1974,p .99-100 )conclude d thatwebbin g hinders Metaseiulus occiden talis sufficiently toaffec tth eprédatio nrate .H e observed severalbehav ioural changes of Metaseiulus occidentalis inrespons e towebbin g produced by the males of Tetranychus urticae (decrease ofwalkin g activity, walking velocity, coincidence of prey and predator andhandlin g timewit h respect toth epre y males). He stated thati fthi s species iscommo n inspide rmit e colonies, it is more due toth eeffec to ftrappin g and ahig h reproduction rate inth epresenc e ofmuc h food thanb y attraction.Thes e findingsstimu lated the investigations discussed inthi srepor to nth erol eo fwebbin g in thepredator-pre y interaction (Chapter3) .

2.1.6 Web production and colony growth

Tetranychus spp.produc e silk strands (0.03-0.06 pmdiameter )b ywa yo f a glandular system, which opens in a hollow hair atth eto po fth epedi - palps (Mills, 1973;Albert i & Storch, 1974). The strands arestretche dbe tweenth ecurve d leafedge ,th e leafrib s andth elea fsurface .Whe npowder ed with talc, the webbing becomes visible. It appears to be chaotically structured except that it tends to form a compact, coherentcove rwit ha more-or-less obvious border. To quantify web production a fixed amounto f fluorescent powder was dispersed over the webbed area, aspropose d by Fransz (1974, p. 24).Som e of the fluorescentparticle s stickt oth e silk strands, but the majority fall onto the leafsurface .Th enumbe r offluo rescentparticle s stuck toth e silk strands canb ecounte d using abinocula r microscope and aUV-lam p forillumination .Thes e countsma y serve asa rel ativemeasur e ofth e amounto fwebbing ,becaus e they indicate the lengtho f the silk strands.Th ewebbin g density isquantifie db y thenumbe r ofinter cepted particles"pe r square centimetre of leaf area. To standardize the

33 GUN WITH C02 PRESSURE

TURN TABLE

Fig. 7. Apparatus used for spraying fluorescentparticle s over thewebbe d rose leaves.

method ofpowde r dispersal the followingmeasure swer etaken : The fluorescent powder is kept in a desiccator to obtainparticle s of uniform size andpreven tclotting . The amount of powder (1mg ) is accurately weighed on a Cahn electrobalance toobtai n anumbe r ofparticle s subject tolittl evariation . The particles are dispersed in an apparatus originally designed for fungal spore dispersal over a leaf area,aimin g ata unifor m distribution ofth e infection.Th eexperimenta l design isgive n inFigur e7 . All measurements are made simultaneously with astandar d measurement of webbing, produced at T = 23°C and a relative humidity = 75%,t o detect

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,s o thatth eexperimenta l procedurewa sconsidere d tob ereliable . Hazan et al. (1974)quantifie d thewe bproductio no f Tetranychus cinnabarinus ina comparable way.The y used the fraction ofth etota lfaecal - pelletproductio n anchoredt oth esil kthread sa sa 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 (50pm )nylo nthread san dplace di t on the leaves.Th emite s produced webbing over the leaf-grid system.Th e miteswer e subsequently removed andth egri dwa slifte dwit hth ewe bthread s attached. The amount ofwebbin g wasmeasure d usingdark-fiel d microscopy. To date no comparisono fthes etw omethod sha sbee nreporte di nth eliter ature. The experiments onwe bproductio n 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).A Weis s GrowthCabine t (typeZ K220 0E/+ 4JU-P-S) , located atth e Institute ofPlan t ProtectionResearch ,Wageningen , served asa climat e room (T= x ± 0.25°C ; relativehumidit y= y ± 2.5%) . Single preoviposition females were transferred toros eleave s thatwer e still connected toa 5 c msectio no fthei rshoot .Thes e femaleswer e allowed to produce eggs andwe b during aperio d equalt oth emea n incubation time ofth eeggs .Eac hexperimen t ata certai ncombinatio no fT an dR Hwa srepli cated at least 15 times.Th eresult sar egive ni nTable s 13an d14 .Thes e show that webproductio n is stimulated by increasing temperature buti s only slightly affectedb ychange s inhumidit ywithi nth erang e 50-85%.Fro m

Table 13. Rateo fincreas eo fare awebbe db y Tetranychus urticae.

Temperature (°C) Relativehumidit y (%) Rateo fincreas eo fwebbe d area (cmz-day"1^"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 n ofyoun g females of Tetranychus urticae, asindi catedb y the interception of fluorescentparticles .

Temperature (°C) Relativehumidit y (%) Rateo fwe b production (particles-day" •¥ )

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 smeasured . Sincewebbin gbecam evisibl e afterpowderin gwit h fluorescents andUV-illu - mination, the circumference ofth e colony couldb edraw no ngraphi cpaper . The rare case of asingl e strand stretched over apar to funcolonize d leaf was neglected.A s canb e seen from Tables 13 and 14,th e ratio of thedail y increase ofparticl e interception andtha to fth ewebbe d area is aboutcon stant, so that apparently the web production is largely used for lateral expansion ofth ewebbe d area over the leaf surface.Thi s doesno tmea n that thewebbin g isdistribute d uniformly over thewebbe d area.Th ewebbin gden sity was mapped crudely and some characteristic cases aregive ni nFigur e 8. It appears that the lower densities are found insmal l strips neart o the boundaries of thecolony .However , tosimplif y further analysis itha s been assumed that thewebbin g ina mit e colonyprovide s ahomogeneou ssub strate for predator-prey interaction. This simplification mustb e kepti n mind ininterpretin g results discussed inthi sreport . In a subsequent series of experiments the colonization period wasno t stopped after the elapse of the mean incubation time ofth e eggs,bu tth e females and their offspring were allowed to continue feeding until the leaves were exhausted as a food source. InFigur e 9th echang e inwebbin g density is given forthre e characteristic sub-periods of spider-mitecolo nization of aleaf . Inth e firstperio d only adult femalesproduce d webbing; the density of silk strands per square centimetre of webbed leaf area reached its maximum within ada yo fth e transfer of females toth eexperi mental leaf. In thesecon dperio d themit epopulatio n consists ofal lpos sible stages of development. The webbing density increased only very slightly despite the increase inweb-producin g mites.Thi s reflects apre dominant lateral expansion of the colony. The third period started,whe n

36 HIGH DENSITYO FWEBBIN G HH MODERATEDENSIT YO FWEBBIN G lilijiy LOW DENSITYO FWEBBIN G

Fig. 8. Growth of the webbed area on the underside of a rose leaflet and a schematic representation of areas ofhigh ,moderat e andlo wdensit y ofwebbing .Lea fA unti lD represent increasing stages ofcolonization .

the food sourcewa s almostexhauste d and themite swer ebecomin g increasing ly active, probably in search of food. There is anexplosiv e increase in theamoun to fwebbin g duet oth e increase inwalkin g activity. Saito (1977a) also noticed a high correlation between thewalkin g activity andwebbing .

Hls observations clearly show that the spider mites continually produce threads while walking. Because silk secretion isprobabl yno tcontinuous , continuous threadproductio n isprobabl y duet oth eeffec to fsil kcoagulat ingb y stretch.

37 rone (1968) showed that the Chilean population readily hybridizes witha Sicilianpopulation ,whic h isconsidere d tob e endemic (Ragusa, 1977). Many records from otherMediterranea n countries areavailabl e (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 occidentalis (Nesbitt, 1951) This species was obtained from the culture ofKüchlei n (Agricultural Uni versity, Wageningen),whic h originated onth e culture ofBravenboe r (Glass house Crops Research& 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 , where it isconsidere 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 nZo n& Blommer s (Amster dam, The Netherlands), where it was fed on Tetranychus urticae. Blommers (1973) collected specimens in Madagascar. He reports this predator tob e successful in controlling Tetranychus neocaledonicus and Tetranychus urti cae populations in the greenhouse (Blommers & van Etten, 1975;Blommers , 1976).

Amblyseius potentillae (Garman, 1958) This species was obtained from the culture ofva nd eVri e (Wilhelminadorp, The Netherlands), where itwa s fedo n Tetranychus urticae. The culturedi d not succeed on mite-infested bean plants, but was successful when mites were brushed off the leaves and offered to the predators (van deVrie , personal communication; own observations).Van de Vrie collected specimens in the south-west part of The Netherlands (Serooskerke). Here iti scon sidered tob 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) recorded 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 from citrus in Italy (McMurtry et al., 1976).

Thepurpos e ofthi s study ofphytoseii d predators isthreefold : to analyse interspecific differences indevelopment , abioticmortality , fecundity and sex ratio inrelatio n totemperature ,humidit y andpre yden -

40 H + ft« 0) + G a>) o 0 •a • o rH •H H •P + + 1 + 0fi •«H > 10 + 1 o •p CM ai + + xi CM ai X + CM u ai o + o o m co rH + en CM c CM rH + CM 1 1 s a> + + 4-> in + u CM + V >—u . fi41 t-t O 1 + in in 4) •H + 1 CM M •o ai 1 M o. + + MH (0 o. • o CO 00 0 1-1 "t1f H • • •0 asi 1 1 m ai H CM •P r-t •rci 3 'M CM CM tfl a> 10 lO (V •o en . Oi 01 •-I M ai p C ai ai rH r- rH r-^ •. « o M ta tn » r~ * oo ai •. XI •H ai ta (0 co P 01 iO >i P •P P 0 0 00 te C rH rH• en ai H oc i-l • •ri Ifl p u u io ai 10 (0 rH u 10 10 10 S -H (0 en rH X! r» P 01 H r- t-- rH 01 oi rH C) r- •P H 3 01 p ai ai 01 TJ a>i vO 00 CJi fi10 a> U*) ai ?; ai rH •H rH -•-* •, 0) Tf ai u H 10 io .. 01 H X! ~ -H lO 0 -H H a ai ^ ai iH en 01 lï fi10 - u 10 10 > 01 r M •H * ». •. (0 10 P O rH o •H rH 0 •fi •H a 10 XI 10 H m XI ai >1 (0 -ri ai H (0 •n •a «0 u p oi (0 Oi M M a •. gtt >i ai •s a) •§ u rO 3 C 3 ai >fii o •P ai & * >. c g O H XI 0 01 rH ai 3 (0 01 •n 10 m (0 0 e tn oi 01 p N ru •fiH M () u >XI > tu g c rH •-H 10 c c (0 «H 01 •ri X) 3 g •0 3 10 10 10 ri •H 01 o A! H 10 mfi ai •Hfi 0 3 ?; 0 M C• ai O M EH M (D :,^0 10 ai 0 10 ai fi10 p ai 10 M M (c0 •3 0 i-i 0) •0 w eu > OJ u ai H i* M en j J U H S « •ri « "-' -' s 1 fc en m (Il •>H H 3 w M 41 H •O "•H W -P 0 C aie; 0. P O •u <0 m M •-H 41 rs !». 0) afi> a •C ai ." 0 S 0 •sS '"^H P s O w u. u. * 0 •^ w. <-

41 sity (Subsection 2.2.1-2.2.3). to quantify therelativ e contribution ofth e different juvenilean d adult stageso fth e predatort oth e prey consumption achievedi nawhol e life-span (Subsection 2.2.4). to estimateth eeffect so fdrinkin g water,cannibalis m and,whe ntetra - nychid foodi slacking ,non-tetranychi d food consumptiono nphytoseii d sur vival,an dt odetermin e their abilityt orecove r from starvation (Subsec tions 2.2.5-2.2.7).

2.2.1 Developmentand mortality

Datao ndevelopmenta l time andmortalit y seemt ob eavailabl e (Table16 ) insufficien t quantities.Howeve rman y results arecontradictory , whichma y bedu et odifference si nstrain so rexperimenta l methods,e.g . resultso f Bravenboer &Doss e onth e developmental timeo f Phytoseiulus persimilis (Bravenboer& Dosse ; Table1 an dFigur e 1),result so fTanigosh ie tal . (1977)an dPruszynsk i& Con e (1973)o nth e developmental timeo f Metaseiulus occidentalis, and resultso fMcMurtr y (1977)an dRabbing e (1976)o nth ede velopmental timeo f Amblyseius potentillae. Becauseo fthes e differences interspecific comparisons weremad e simultaneuouslybetwee n fourphytoseii d species. This trial was carried outa tthre e temperature levels( T=15 , 20, 30°C; relative humidity= 70% ;photoperio d= 1 6hours) .A tth e start females were allowedt ooviposi t for two hoursa tT= 20°C .Th eegg sob tainedi nthi s way were immediately transportedt oth eclimati c cabinet. After hatching the larvae were put separately inMunge r cages (Fig.10) , where they were supplied with abundant prey (eggs, larvaean dfemales) , throughout their development. Thepresenc eo fexuvia ewa suse da sa crite rium for previous moulting.Th eskin s were discarded after detection.A t the preoviposition phaseo fth e females, twomale swer e addedpe r caget o ensure fertilization.Th eexperimen twa s stopped after all females hadde posited their first egg.I nthi swa yth e progressi ndevelopmen twa sre corded every8 hour swit ha tleas t3 0replicates .Th eresult s arepresente d in Fig.1 1a sth e inverseo fth etim e elapsed between egg sampling andth e depositiono fth e firsteg gb yth e grownu pfemal e (therat eo f'egg-to-egg ' development).Th einterspecifi c differencesi nth e rateo fdevelopmen t are summarizedi nlinea requation s relating the rateo fdevelopmen tt oth etem perature( T= 15-30°C) : Phytoseiulus persimilis - rate= 0.01 1x (T-ll.2 )(day -) Amblyseius bibens - rate= 0.01 1x (T-ll.5 )(day -) Amblyseius potentillae - rate= 0.01 0x (T-11.0 )(day -) Metaseiulus occidentalis - rate= 0.00 8x (T-11.0 ) (day") Phytoseiulus persimilis developssomewha tfaste rtha n Amblyseius bibens, butmuc hfaste rtha n Metaseiulus occidentalis. Amblyseius potentillae devel opeda sfas ta sPhytoseiulus , but appearedt ob ebette r adaptedt oth e lower

42 FILTER PAPER

GLASS PLATE

Fig. 10. Designo fth eMunge r cageuse d inth e studyo f Phytoseiidae.

temperature regime.Thi s difference ispossibl y related toth eclimati c ori gino fthes e species.On ecommo n traito fth erat eo fdevelopmen t amongth e Phytoseiidae studied is thatthe ydevelo p fastertha nthei rprey : Tetrany- chus urticae - rate = 0.0067x (T-11.0) (day" ).Moultin g causes only a very short interruption in the food searching activity ofphytoseiids . Tetranychid development is characterized by distinct moulting stages ofa duration similar totha to fth eprecedin g feeding stage.Thi scause s anin terruption of feeding and hence a retardation of development. From this point of view it is worthwhile to note that the egg-to-egg developmental periods of predator and prey equal eachother ,i fth emoultin g stages are excluded from the computation of developmental time.Th erelativ econtri bution of the hatching, intermoult andpreovipositio nperiod st oth etota l egg-to-eggperio d isabou tth e same foral ltemperature s and foral l species studied; on average 34%o fth eegg-to-eg gperio d isspen ti nth eeg gstage , 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 periodswer e estimated froma plot of the cumulative frequency distribution ofdevelopmenta l periodso n probability paper of theGaussia ndistribution .Th e8-hou robservatio nin terval was taken as a class unit. The estimated standard deviationswer e 7-12%o fth eestimate dmea n developmental time. InTabl e 16th eproportiona l differencesbetwee n thepresen tmeasurement s andthos e found inth elitera -

43 RATEOF"EGG-TO-EGG " DEVELOPMENT(DAY" 1) 0.25-1

0.20-

t 0.15-

Ä 0.10-

0.05-

I I I I I 15 20 25 30 35 TEMPERATURE(°C )

Fig. 11. Rateo fegg-to-eg g developmento ffou rphytoseii d species andth e two-spotted spider mitei nrelatio nt otemperature ,o ,Phytoseiulus persimilis; •,Amblyseius bibens; +, Amblyseius potentillae; A, Metaseiulusocci - dentalis; ,th etwo-spotte d spider mite, Tetranychus urticae; _L, standard deviation( n= 30-50) .

turear esummarized . Whenever the datai nth e literature concerned egg-to- adultperiod s insteado fegg-to-eg g periods,th e lengtho fth e developmental period was adjusted accordingly. This survey demonstrates the largevaria tioni nth e data from the literature compared toth e datao fthi s study. Thisma yb edu et ostrai n specificness and/or experimentalmethods . Even thoughth erat eo fdevelopmen ti srelate d linearlyt oth etempera turei nth e rangeo finteres ti nthi s study, fluctuating temperaturesma y give riset oresult s that deviate from thatexpecte d for the linearrela tion. However Rabbinge (1976) showed that the rateo fdevelopmen tma yb e considered asreactin g instantaneously toa chang ei ntemperatur e (Ambly-

44 Table 17. Stage-specific developmental timeso ffou rphytoseii d species.

Species Temperature Meandevelopmenta l 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 20 3.2 1.1 1.4 1.5 2.0 potentillae Amblyseius 20 3.5 1.3 1.6 1.8 2.3 bibens Metaseiulus 20 4.4 1.7 2.0 2.4 3.1 occidentalis 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 dStenset h (1979)showe d thatdevelopmenta l timei sals o affectedb yrelativ ehumidity .Onl ya sligh t increase indevelopmenta l timewa sobserve db ythes e authorswhe nth erel ativehumidit ywa sincrease d from40 %t o70% .Th etendenc yt ogai nwate rb y increased prédation atlo whumidit y mayaccoun t forthi s reduced effect (Begljarow, 1967;Pruszynski , 1977). According toBegljarow , development almost stopsa trelativ ehumiditie so f25-35% . Inth epresen t experiments, mortality during developmentwa sa slo wa s in Tetranychus urticae. Atal ltemperature s 87-94% ofth eegg s reached maturity, independent ofth especie s involved (RRN= -ln(0.9 )x DR ;RR M= relative rateo fmortality ;D R= 'egg-to-eggdevelopmenta l rate). Inanothe r experiment theeffec t ofextrem e temperatures wasinvestigate d for Phyto seiulus persimilis and Metaseiulus occidentalis; afive-da yperio do fth e

45 eggs at T =10° C did not alterth epercentag e ofegg s reachingmaturit y in a subsequent period at T = 20°C and relative humidity =70% .A tT = 35° C and relative humidity =75 %th epre-adul tmortalit y roset o24% .Accordin g to Hamamura et al. (1978) the eggs of Phytoseiulus persimilis failed to hatch after storageperiod s ofmor e than 6day s attemperature s below10°C , but the adult femaleswer e able to survive and toremai n reproductive after 25 day storage without food, after 50da y storagewit hhone y and after7 0 day storagewit h spidermites ,whe nrelativ e humidity was sufficientlyhigh . According to Begljarow (1967) the mortality in the egg stage depends very much on thehumidit y level.A t arelativ e humidity of50 %th e eggso f Phytoseiulus appeared to shrivel at all temperatures between 13°C and37°C . Ata relativ ehumidit y of60 %hatchin g ofth eegg swa s successful belowT = 30°C, but above thistemperatur e level arelativ e humidity of80 %wa snec essary for successful hatching. Larvae,nymph s and adultswer e lessaffect ed by humidity, probably due to acompensator y moisture supply throughin creased prédation at decreasing humidities.The y could develop normally at relative humidity = 50%,bu t at25-35 %stoppe d (Begljarow, 1967). Anumbe r ofauthor s confirmed the facttha t theeg gstag e of Phytoseiulus persimilis is relatively vulnerable torelativ e humidities below 70%(Usheko ve t al., 1968; Hamamura et al., 1978; Pralavorio et al., 1979; Stenseth, 1979). A similar type ofvulnerabilit y was foundb yMcMurtr y et al. (1976)fo r Ambly- seius potentillae. An Italian stock of this species appeared tob emor ere sistant to low humidities than aDutc h stock (50%mortalit y ofth eegg s at relative humidities of approximately 55%an d 70%,fo rth erespectiv e stocks). McMurtry et al. state that these results areconsisten twit h the climatic origin of the stocks and thatth e egg stage isprobabl y themos tvulnerabl e todr y conditions:th emobil e stages canobtai nmoistur e from their foodo r move to amor e favourable (micro)climate.However , although theeg g itself isimmobile ,i ti sdeposite d byth e adult femalepredato r at characteristic spots on the leaf (e.g. stuck toth e leafhairs) , often close toth e leaf ribs and -mos t important with regard toth ePhytoseiida e inquestio n -i n thewebbin g structureproduce d by theirprey .A spostulate d byHaza ne t al. (1975), the hygroscopic properties ofth e fibroin silk strands,th emicro climate in the webbing structure,th e supply ofmoistur e viaévapotranspi ration of the leaf and,t o asmalle r extent,defecatio nb y the spidermit e maybuffe r the lowhumidit y levels inth eplan tenvironment . Because the greenhouse climate is suchtha trelativ e humidities between 40% and 70%d ooccu rrathe r frequently, theexten tt owhic h themicrohabita t buffers the effecto fhumidit y was investigated. Two substrates foreg gde velopmentwer eplace d simultaneously ina controlled-environmen troom : plantwit hwebbin g andmite s (eggs and adults) (Fig.12) ; uncovered Munger cagewithou t leaves,webbin g and spidermite s (=Perspe x substrate). Subsequently, well-fed female predators were released onthes e substrates

46 Fig. 12. Plantsyste m used inth estud yo fclimati c effectso nlif ehistory . and were allowed to oviposit for one day. In thisway ,th eegg swer eno t deposited in an artificial way,bu taccordin g toth eovipositio nbehaviou r ofth e femalepredator .Afte r removal ofth eovipositin g femalesth ehatch ingsucces s ofth epredato r eggswa s recorded duringth e following sixdays . Theresult s (Fig.13 )sho w that incompariso nwit hth eartificia l substrate thecombinatio n ofplant ,webbin g and spidermite sexert s apositiv einflu ence on the hatching success. Under theclimati c regime ofth egreenhous e cultureo fornamenta l roses (relativehumidit y >50% )n odetrimenta l effects aret ob e expectedbecaus e thehatchin g success declines forrelativ ehumid itiesbelo w 50%,eve n athig h temperatures.Th eresult s concerning thearti ficial substrate correspondwit h 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

o / ,+—.^ -+ S 0 S^/\/^+ t 80- /

60-

20- .0 0 .+ 0' a' +'' 1 1 1 1 t-î' ,r - 405 0 607 0 40 50 607 0 40 50 607 0 40 50 607 0 RELATIVEHUMIDIT Y( % )

Fig. 13. Hatching success of theegg s oftw ophytoseii d species (o= Phyto- seiulus persimilis and += Amblyseius potentillae) inrelatio n to relative humidity and to the substrate. ,webbe d bean leaves (Fig. 12);•••• , uncoveredMunge rcage s (Fig.10) . et al., 1968;Pruszynski , 1977;Pralavori o et al., 1979;McMurtry , 1977). Those concerning the 'natural' substrate correspond with the results of Stenseth (1979), who used the appropriate experimental procedure attw oex tremehumiditie s (relative humidity =80 %an d40%) . The reports of juvenile mortality at high temperatures (T >30°C )ar e numerous.Bravenboe r& Doss e (1962)di d notrepor t an increase inmortalit y of Phytoseiulus juveniles at T = 30°C and 35°C; Hamamura et al. (1976a) found a high mortality of Phytoseiulus persimilis at temperatures above 30°C; Begljarow (1968) and Böhm (1970) observed lowviabilit y of theegg s at temperatures above 30°C andMcClanaha n (1968)foun d aver y highmortal ity even at T = 30°C. Similarly for Metaseiulus occidentalis, there are reports of increasing mortality above 33°C (Pruszynski &Con e 1973,hig h mortality atT = 35°C ;Tanigosh i et al. 1975,100 %mortalit y atT = 38.4°C). The interpretation ofthes e results isver y difficult,bot h through lacko f specification of the environmental humidity and lack ofuniformit y inth e experimental substrates. The experiments described in this study did not indicate an increase in mortality at T = 30°C andhig hhumidity , butth e critical humidity level, belowwhic hmortalit y increases,i sraise db yin creasing temperatures (see Begljarow, 1968). Probably the rapid onset of detrimental effects cannotb eprevente d by highhumiditie s when temperature

48 Table 18. Stage-specific freshweight s ([ig) of fourphytoseii dspecies .

Predator Egg Larva Proto- Deuto- Male Female species nymph ,_b nymph,_ 9b

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 Amblyseius 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.Th e males attain their final weight level ina nearl y stageo f development: the protonymph stage.Th e females obtain almost60 %o fthei r weight increase during thepreovipositio nperiod .Th emaximu m difference in weightbetwee n females sampled fromwell-fe d cultures ato rbefor eoviposi - tion almost corresponds withth eweigh to fa negg .Thi s isbecaus e oneeg g ata tim e (=th etermina l oocyte)i sabsorbin gvitellogeni cmaterials .Afte r attaining its final size and fertilization the egg will be deposited and thenex teg g 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,i tappear s thatthoug h therelativ eweigh t increase isconstan t forth e species studied, absoluteweigh tlevel s differ considerably. As shown inFig .3 , Metaseiulus occidentalis isth e smallest phytoseiid of the four studied. Relative to this species the ovipositing females of Phytoseiulus persimilis contain 2-3 timesmor ebiomass , Ambly seius potentillae 1.5-2 timesmor e and Amblyseius bibens 1.1-1.3time smore . The effect of food supplyo nth e rateo fdevelopmen t isdemonstrate d 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 levelo f food supply,belo wwhic hdevelopmen t isretarde d andmortalit yin creases, isabou t 1-2 |jgpe rday .Fro m the interspecific and stage-specific weightdistributions , iti sobviou s that theeffect s aremor epronounce d in the larger-sized phytoseiid species and in the preoviposition phase, in which relative to the other stages alarg eweigh tincreas eha st ooccu ri n a short time span.Th e larvaeo fal l species inquestio n areabl et omoul t

49 Table 19A. The influence of the density ofth epre y onth e developmental time of Metaseiulus occidentalis. Leaf area =5 cm 2; daily replacement of thepre y consumed; T= 27°C . Source:Küchlei n (tob epublished) .

Prey (eggs)Developmenta l time (days) number egg n larvan protonymph n deutonymph n eggt o 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 Phytoseiulus persimilis. n = 10-14; paper area= 4 cm 2; daily replacement ofth epre y consumed; T= 25°C .Source :Takafuj i &Chan t (1976).

Prey (protonymphs) Developmental time (days) number larva protonymph deutonymph eggt o 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 (adult ?) 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 t any food andwithou t anyretardatio n of development, but moulting from the first to the second nymphal stage does require food consumption.Whe npre y eggs are in abundance Phytoseiulus per similis and Metaseiulus occidentalis consume 15 and 8eggs , 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 replacemento fth epre y consumed;T =23°C .Source :va nd eVri e (1973).

Prey (larvae) Developmental period Preovipositionperio d 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 ldevelopmen t (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 on66 %o f the food quantity described previously (own observation). Although their bodies were flattened undercondition s oflo w food supply,the ywer e still able to moult into the next stage despite their obviously hungry state. Apparently development allows forsom e flexibilitywit hrespec tt oth e food requirements inth enympha lstages .

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,a s 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 db y thelos s and/or heterochromatization of half of the chromosomes. Thus parahaploidy, not arrhenotoky, as found inth espide rmites ,i sth egeneti c system (Hoy, 1979). The probability that aneg gbecome s amal e or afemal eca nb e estimated from the sex ratio (9/(9 + a) in a large sample taken from eggs lainb y randomly selected phytoseiid parents.Se xdistinctio n ismos t conveniently made in the adult phase: female s are largertha nmales .Th eproportio n of femalesca nthu sb e assessed inth egrou p ofadult semergin g from alabora tory ab ovo cultivation.Thi sproportio n equals the sexrati o ifth erela tive rate of juvenile mortality of both sexes areth esame .I nTabl e 20a data survey is givenfo r 'laboratory'se xratio 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 four phytoseiid species according to references in the literature.

Predator Temperature Sex ratio Number Number of Reference species (°C) 9/(9 + <*)o f eggs parental females

PhJjtoseiulus 23 0 89 954 Amano & Chant, 1978 persimilis 25 0 86 816 11 Schulten et al., 1978 25 0 84 930 13 Hamamura et al., 1976a 25 0 82 400 100 Takafuji & Chant, 1976 15-28 0 804 245 20 Laing, 1968 22-27 0 79 247 20 Kennett et al., 1968

Metaseiulus 18 0.66 50 Tanigoshi et al., occidentalis 1977 21 0.70 50 Tanigoshi et al., 1977 24 0.64 50 Tanigoshi et al., 1977 27 0.68 50 Tanigoshi et al., 1977 29 0.68 50 Tanigoshi et al., 1977 32 0.62 50 Tanigoshi et al., 1977 35 0.60 50 Tanigoshi et al., 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 54 Blommers, 1976 bibens

Amblgseius 15-30 0 69 238 85 Rabbinge, 1976 potentillae

a. Ph.D. thesis, referred to in Croft & McMurtry (1972).

52 seems justified toconclud e that foral l four species these xrati ogeneral lyexceed s 50%an dtha tther e are interspecific differences.Th e sexratio s of Amblyseius potentillae and Metaseiulus occidentalis arearoun d 66%,whil e those of Phutoseiulus persimilis and Ambluseius bibens areclos et o83% . Based onbot h laboratory sexratio s and sexratio s observed inth e field, the sex ratio may be considered constant, although a few exceptions are noteworthy: - Tanigoshi et al. (1977)establishe d a slightdecreas eo fth e sexrati o of Metaseiulus occidentalis attemperature s exceeding 30°C. - Dyer & Swift (1979) found that short-term variations inse xrati ower e related to meteorological changes,particularl y humidity, temperature and wind speed.Th ereaso n isno tye tclear . - Amano & Chant (1978)observe d thatth e sex ratio of Phutoseiulus persi milis was constantwit h age,excep t fora highe rproportio n ofmal eprogen y atth eonse to freproduction . Amano & Chant (1978) found that the sex ratio was independent of the feeding history of the female as ajuvenile ,bu ti ncompariso nwit hwell - fed females temporary food deprivation in the adult stage gave riset oa decrease ofth e sexrati o inth e subseguent offspring. The causes of the deviating 'laboratory' sexratio sma yb e duet obot h differences inmortalit y amongth e sexesan d the sexdeterminatio nprocess . The 'field' sex ratios areals o influenced by the shorter life spano fth e males, differential susceptibility todetrimenta l factors,etc . There seems to be no reason why adult females shouldno tmat e shortly afteremergence : The eggs are deposited inpre y aggregations,s otha temergin gmale s and females are inclos evicinity . The tendency to disperse is low in all stages relative totha t inth e fertilized females (Section3.4) .Th e foodrequirement s fordevelopmen tar e very low and even flexible to acertai n extent (seeSubsectio n 2.2.1), so that the aggregation of the juvenile, male and virgin femalephytoseiid s hasn o severe effecto npre y availability andwhe npre ybecome s scarce,th e strongest individuals can survive and develop bywa yo fcannibalis m (Sub section 2.2.6). The sex-attractingcue s areprobabl y onlyeffectiv e over shortdistance s (Rock et al., 1976;Ho y & Smilanick, 1979)an d theproportio n ofmale s in theoffsprin g isalway s less than50% . Severe starvation is notdetrimenta l toth ewillingnes s tomat e (Ragusa & Swirski,1977 ;Blommer se t al., 1979). A single mating is sufficient to achievemaxima l fecundity inth ecas e of Phutoseiulus persimilis (Schulten et al., 1978;Aman o & Chant, 1978). HoweverHamamur ae t al. (1976a)found ,tha tthos e females thatha d deposited lesstha n4 3 eggs,restarte d tooviposi t after thereintroductio no fa mal e onda y 33 since firstoviposition . Surprisingly these x ratio ofth e 'second'

53 Table 21. Survey of the literature on fecundity (number of eggs) and on life-span of some phytoseiid predators.

Temperature Potential Net Reference (°C) fecundity fecundity

Phytoseiulus 81.2 - Begljarow & Hlopceva, 1965 (A) persimilis 75.0 - 51.8 - - 63 15-28 53.5 - 14-101 Laing, 1968 (B) 20 43.8 23 3 McClanahan, 1968 (C) 53.5 20 7 62.0 - Kamath, 1968 (D) 25-26 59.0 - Böhm, 1966 (E) 22-27 56.1 - Kennett & Caltagirone, 1968 (F) 22-27 64.7 - 74.5 - Plotnikov & Sadkowskij, 1972 (G)' 71.9 15 3 Amano & Chant, 1977 (H) 79.5 25 2 Takafuji & Chant, 1976 (I) 25 71.5 20 4 13 23-93 Hamamura et al., 1976a (J) 17 12 51-79 Pruszynski, 1977 (K) 21 12 60-85 74.1 12 66-87 78.0 18 52-93 70.9 19 42-91 (eggs as food) 57.9 12 36-89 (larvae as food) 74.2 11 59-98 Schulten et al., 1978 (L) 78.8 16 12-95 Fernando, 1977 (M) 0 Pralavorio, 1979 (N) 16.8 31.0 80.2 16.4

Amblyseius 10 9.0 Babbinge, 1976 (O) potentillae 15 20.0 20 25

Blommers, 1976 (P) Amblyseius 65.0 63.2 bibens 64.1 60.1

Schulten et al. , 1978 (Q)

Metaseiulus 24 33.7 21-56 Lee & Davis, 1968 (R) occidentales 15-2 34.0 14-53 Laing, 1969 (S) 22.5 Croft & McMurtry, 1972 (T) Croft, 1972 (U) 33.8 13-55 Pruszynski & Cone, 1973 (V) 35.2 21-54 28.2 17-48 21.9 Tanigoshi et al., 1976 (w) 28.1 29.6 33.1 28.2 33.4 27.8 Küchlein (to be published) (X)

a. Females had mated only once.

54 Table 21. Continued.

Ref .Preovipositio n Oviposition Postoviposition Female period period period longevity

\i a n

22 21

6-39 -3 1 - 17

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 IS.S - 12 16-23 - - - 38.2 - 12 15-5 8 33.8 - 18 25-48 - - - 77.9 - 18 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 - 9 - 25 -

7.4 1.1 4.0 1.0 22.2 11.8 4-41 8.0 9.1 0-28 34.2 1.9 0.9 15.1 8.5 6-28 7.6 8.4 0-28 24.6 2.9 0.8 13.4 7.8 2-44 10.8 11.0 0-45 27.1

-4 6 _ . -2 8 - - -2 3 - -

1.3 51 1-2 38.7 51 21-56 3.2 18 2.5-4.0 7-25 20.2 18 10-30 1.5 27-41 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 50 - 17.6 - 50 50 - 16.0 - 50 50 - 13.9 - 50 50 - 13.4 - 50 50 - 11.5 - 50 50 - 11.4 - 50 1.5 50 - 9.5 - 50 1-2 27.1 13.8 67

55 brood had decreased to 76%. Amblyseius bibens (Schulten et al., 1978), Meta- seiulus occidentalis (Küchlein,persona lcommunication )an d Amblyseius potentillae deposit only about2/ 3 ofthei r total eggpotentia l foronl yon e mating.Henc emor e thanon ematin g isrequire d tomaximiz e reproduction.

2.2.3 Adult life span and fecundity

From the literature data inTabl e2 1o nphytoseii d longevity andfecun dity atvariou s temperatures andhig hpre y density, it followsthat : Interspecific differences in female longevity areabsent ,bu tth especies - specific fecundities decrease in the following order: Phutoseiulus persimilis (approx.70) ,Amblyseius bibens (approx.60) , Metaseiulus occidentalis (approx.35) , Amblyseius potentillae (approx.30) . Strain specific fecundities may be present, as indicated by thediffe rences between the Dutch strain of Phytoseiulus persimilis (Pruszynski, 1977; Schulten et al., 1978) and the others. A similar indication canb e found by comparison of thedat a ofKüchlei nan d theNort hAmerica n reports for Metaseiulus occidentalis. - Net fecundity is 70-97%o fth epotentia l fecundity (femalemortalit y ex cluded). The oviposition period is shortened by increasing temperatures.Femal e longevity is less affected as the postoviposition period israthe rvaria ble. Fecundity is probably maximal inth e temperature rangeo f17-28°C .Onl y a few data are available attemperature s below 17°C,bu t adecreas e isex pected. At temperatures above 28°C such a decrease will eventually occur also,bu t the critical temperature isno tknown . To complete these results interspecific comparisons atlo w (12an d 15°C) andhig h (30an d 33°C)temperature s arenecessary . These reproductionexpe riments were carried out in Munger cages with ample supply ofpre y (eggs and larvae) and high relative humidity (relative humidity = 85%).A tth e start a young fertilized female and twomale swer epu t into eachcag e and subsequently the number of eggs deposited was recorded daily. The results (Table 22) indicate that except for Amblyseius potentillae the critical upper limit is above 33°C. In the latter case the limit issomewher ebe tween 25 and 30°C. On the other hand, when considered relative to their maximal fecundity the decrease in fecundity below 17°C was almost equal among thespecies . Several authors have established adecreas e inth erat e of reproduction athumiditie s below 65%(Ustcheko w et al., 1968;Begljarow , 1968;Pruszynski , 1977; Pralavorio, 1979). However these data were notderive d fromexperi ments onintac tplants, s otha tth eeffec to fth ehumidit ybufferin gcapac ityo f theplan twa sno t included inth e assessment of thecritica l humidity level. Relative humidity iscritica lbelo w 50%,a sexperiment s onth esensi -

56 Table 22. Net fecundity (numbero feggs )o ffou r phytoseiid speciesa t someextrem etemperatures .

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

Phytoseiulus 20.2 7.2 15 40.9 15.22 5 62.8 19.22 5 60.814. 32 5 persimilis Amblyseius 13.45. 2 20 48.2 16.42 0 60.8 16.32 0 58.8 14.21 0 bibens Metaseiulus 9.4 2.8 20 30.1 12.41 8 41.3 11.02 0 44.012. 27 0 occidentalis Amblyseius 10.23. 3 15 22.59. 81 5 21.413. 22 5 16.57. 72 5 potentillae

tivityo fhatchin g successt ohumidit y indicate. Thereforei ti sassume d thatn odetrimenta l effectso fhumidit y aret ob eexpecte d underth e cli matic regime occurring forth egreenhous e culture ofornamenta l roses. The rateo ffoo d conversion into eggbiomas s isver y high.Ovipositin g phytoseiid females havea dail y eggbiomas sproductio n equal tohal fthei r maximum body weight, whichi stake n tob e theirmea nweigh tjus tprio tr o egg laying.Moreover , although the fecundityo fphytoseiid si s2- 4 times lower than thato fth e spider mites, the biomass ofegg sproduce dma yb e equal {Amblyseius bibens) or eventw o times larger (Phytoseiulus persimilis) Becauseo fth e high productiono feg g biomass the supply ofpre ywil bl e very importantt othes epredator s inrealizin g theirreproductiv epotential . The effecto fpre yeg gdensit y onth e life spanan dne t fecundity of Meta seiulus occidentalis isgive ni nTabl e2 3an d Fig.14 .Th emea nlif e span is doublea tapre y densityo f1- 2 eggspe r5 cm 2 leafdisc ,replacin g the prey eatenb yth e predatoro rdie d from other causes atdail yintervals . Thecumulativ e numbero fegg sproduce d per living female isplotte d against time elapsed since the last moult ofth e female forvariou s levelso f the prey density. The ultimatenumbe ro fegg sproduce d (=potentia l fecundity) decreased from74 %a t4 pre y eggspe r5 cm 2 to44 %a t2 pre yegg spe r5 cm 2 andnex tt o 10%a t1 pre y eggpe r5 cm 2. The rateo freproductio n does not depend onth e ageo fth e female, but rathero nth enumbe r ofegg s already deposited: Virgin females retain theabilit y toproduc eegg s allthei rlife .Thei r agea tfertilizatio n doesno tinfluenc e the subsequent rateo freproductio n nor the sexrati o (Schultene t al., 1978). - Adult female Phytoseiidae retain their ability toproduc ea norma l egg number after any periodo ffoo d deprivation,unles sprevente d bydeat oh r old age( >5 0days) . See Table2 4 andBlommer se tal . (1979). Ashiharae t

57 Table 23. The influence ofpre y density on female longevity of Metaseiulus occidentalis. T = 27°C;relativ ehumidit y =60-80% ; dailyreplenishmen t of thepre y consumed. Source:Küchlei n (tob epublished) .

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

(number/5 cm2)

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 E66SPRODUCE D PERAREN A( 5CM 2)

0 90 100 TIME(DAYS ) Fig. 14. Influence of prey egg density on the potential fecundity of Metaseiulus occidentalis. (Data fromKüchlein ,t ob e published) al. (1978) similarly found, that the reproductive potential of females of Phytoseiulus persimilis had beenmaintaine d afterbein g reared for3 5day s on adie t ofhoney . Reproduction stops after deposition of a specified number of eggs; if unfavourable conditions delay the achievement ofthi s deposit itcontinue s on theresultin g sub-optimal levelunti l the fecundity isrealize d orunti l the critical ageo f 50day s is attained. Situations therefore occur inwhic h therat e of reproduction atth e older (but< 5 0days )age s ofth epredator y female is largerunde r sub-optimal conditions thanunde r optimal conditions

58 Table 24. The influenceo fth e starvationhistor y onsubsequen t fecundity offou rphytoseii d species.

Species Starvationhistor y Net fecundity

temper food presence M â n ature deprivation3 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 Metaseiulus 20 40.8 11.4 18 occidentalis

Fooddeprivatio nwa sbegu n after deposition of1- 3 eggspe rfemale .

at the same age. Examples of thisphenomeno n areth erat eo freproductio n of Amblyseius bibens at low temperatures (Fig. 15),tha t of Metaseiulus occidentalis at low prey densities (Fig. 14)an dtha to fth esam e species atunfavourabl epredato r densities (Küchlein, 1966). Just before reaching the specified level ofeg gproductio n adeclin e in the rate of oviposition takesplace .Consequentl y therat eo f reproduction is not related toth e femaleag e ina fixe dway ,bu tdepend so nth eovipo sition history, which becomes relevant after amajo rpar to fth eegg sha s been deposited. For this reason itmake smor e senset ostud yth einterre lations between the availability ofprey ,o nth eon ehand , andth esearch ingbehaviou r andconversio nphysiolog y onth eothe rhan d (Chapter 3),tha n toestablis h age-relatedreproductio n curves under allkind s ofconditions . The reproduction curves presented here only serve tovalidat e concepts of theunderlyin gprocesse s (Section3. 1 andSubsectio n 3.3.5), rather thant o be used directly inth epopulatio nmodels .However ,th edat ao fth epoten tial fecundity areactuall y 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 EGGSPE RFEMAL E

Fig. 15. Cumulative number of eggs produced per living female of Ambly- seius bibens at different temperature levels and for ample food supply. Data atT =29 ,2 5 and 22°C areobtaine d fromBlommer s (1976).

used instead ofth emea n life span.Thi s time span isobtaine dvi a aleast - squares estimate ofth e 97-99%poin t of acumulativ e frequency distribution of life spans plotted on probability paper of the Gaussian distribution. From this linear equation the relative rate ofmortalit y canb e estimated for ten age classes.Simila r tomortalit y ofth e adult spidermite s itap peared from simulations ofth epopulatio n growth (Part 2), thatth enumer ical effects of thetemperatur e dependency couldb eneglecte d aswell . For this reason the relative rateswer e smoothedb y repeated simulation ofth e available survival and reproduction experiments until anacceptabl e overall fit was found. The fitted values aregive n inTabl e25 .The y show aclea r dependency on the relative age (i.e.th e agerelativ e toth emaximu m life span).

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 class

123456789 10

Phutoseiulus 0.004 0.009 0.017 0.042 0.053 0.108 0.170 0.220 0.220 0.320 persimilis Ambluseius 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. Theeffec to fpre y supply onth erelativ e rateo f femalemortalit y (day" )o f Metaseiulus occidentalis.T =27°C ;relativ e humidity= 60-80%. Source:Küchlei n (tob epublished) .

Prey density Female age classa (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 0.026 0.030 4- 10 0 0.004 0.004 0.014 0.014 0.016 0.040 0.050 0.149 0.209 25-150 0.004 0.013 0.017 0.026 0.042 0.043 0.088 0.098 0.101 0.153 a. See Table 27.

Table 27. Smoothed estimates of the duration ofa nag eclas s inrelatio n totemperature .

Temperature Duration (°C) ofa nag eclas s (days)

15 9.0 20 7.0 25 6.0 30 4.5 35 3.3

61 The effecto fth epre y supply on survival isincorporate d inth epopula tion model by appropriate modification of the relative rate ofmortality , for which the residence time per ageclas s ishel d constant.B ymodellin g in this way a low prey supply only causes additional mortality,whil e the survivors are not affected inan ywa yb y their feedinghistory .Th eobser vations on the recovery of starvation (Table 24 and Section 3.1) support this approach. Data on the relative rate of mortality aregive ni nTabl e 26, but only forth ecas e of Metaseiulus occidentalis at27°C . Inth e sim ulations ofpopulatio n growth these datawer e extrapolated toothe rtemper ature levels anduse d forth e fourphytoseii dspecies .

2.2.4 Prédation capacitif

The reproducing female determines the prédation capacity of the four Phytoseiidae in this study: developmental time is short compared to the oviposition period, the sex ratio favours females,an d their food intakei s considerable because themea neg gbiomas sproduce dpe r day ishig h compared to the body weight of amatur e female. Therefore, the young ovipositing female was chosen forth edetaile d study ofth epredator ybehaviou r ofth e four Phytoseiidae. To support this choice with quantitative arguments the prédation capacity of an individual predator over its whole life spani s estimated and the contribution of the reproducing female tothi s capacity is assessed. Such anestimat e canb e obtained by taking 'snapshots'o fth e rate ofprédatio nwhil e development and ageingproceeds ,an db y integrating the rate of prédationmultiplie d by the fraction of surviving predators over thephytoseii d lifespan . The measurements of stage-specific prédation are presented inFig .16 . Except forthos e of Metaseiulus occidentalis the larvaewer eno tpredaciou s as confirmed by direct observation of the larval behaviour. The nymphs, males and postoviposition females were much lessvoraciou s thanth eyoun g oviposition females.Simultaneou s measurements of thereproductio n ratein dicated that approximately 70%o f the biomass of prey killed isutilize d forphytoseii d eggproduction ; forexample , afemal eo f Phutoseiulus persimilis consumed 6.6 eggspe r eggdeposited ,whic h corresponds toth e results of Ashihara et al. (1978)measure d atdifferen t temperatures inth erang e of 10-35°C. Because the food content of apre y eggweigh s approximately 1 ug and the eggo f Phytoseiulus weighs4. 7 ug,th eutilizatio n ratio equals to 71%.Thu s aroug h estimate of the amounto fpre y eggs killed during the whole oviposition period can be obtained from the net fecundity and the utilization ratio. Furthermore, the amounto fpre y killed during theothe r stages can be computed from the product of the stage-specific prédation rates and the appropriate mean duration ofthes e stages (Subsection 2.2.1). Taking into account the probability that an individual develops into a female or amal e (Subsection 2.2.2)an d that itma y die from some abiotic

62 RATEO FPREDATIO N (PREYEGG SDAY -1) 25-

22-

19-

16-

13-

10-

1- 0 —i o* 1 1 1 1 r 1 1 1 Ç d1 ç d1 E L PN DN AM PF AF1 AF2 PREDATORSTAG E Fig. 16. Stagespecifi c rateso fprédatio no fthre ephytoseii d speciesfo r T =20° Can dR H= 75% .o , Phytoseiulus persimilis; •, Amblyseius bibens; A, Metaseiulus occidentalis. Preyeg gdensit y= 30-6 0eggs/cm 2;webbe d area 4-11 cm2;numbe r ofreplicate s = 20-30.E ,egg ;L ,larva ;PN ,protonymph ; DN, deutonymph;AM ,adul tmale ;PF ,preovipositio n female;AFI , oviposition female;AF2 ,postovipositio n female. cause (Subsections 2.2.1an d 2.2.3), acrud e estimate ofth eprédatio n capacityo fa nindividua lpredato rca nb emad efo reac hphytoseii d species. The following overallprédatio ncapacitie s (onegg san dlarvae )wer e found: - Phytoseiulus persimilis about55 0pre yitem seac ho f1 p g Amblyseius bibens about20 0pre yitem seac ho f1 p g - Amblyseius potentillae about15 0pre yitem seac ho f1 |j g - Metaseiulus occidentalis about10 0pre y itemseac ho f1 M9 - The prédation capacity dependso nth esiz eo fth ephytoseii d species:a larger species produces larger eggs and,thus ,require smor e foodfo reg g growthetc .Thi si sonl ymodifie db yinterspecifi c differencesi nfecundit y

63 WEIGHT [jjg] 28 n T

25-1 -EGG DEPOSITION IS CEASED

22-

19-

16-

13-

\l * i U-

~r 3 L, 5 6 7 8 TIMEO FFOO DDEPRIVATIO N(DAY S

Fig. 17. Weightdecreas e during the starvationo ffou rphytoseii dspecies , startingwit hyoun gwell-fe d femalesi nth e initialphas eo fthei roviposi - tionperiod .T = 20° C andR H= 60-80% .o ,Phytoseiulus persimilis; •, Ambly- seius bibens; +Amblyseius potenti11ae;A ,Metaseiulus occidentalis; , dry-weight levels;±, standar d deviation( n= 20). andse xratio ,a si sdemonstrate db yth eprédatio ncapacit yo f Amblyseius bibens, being superiort otha to f Amblyseius potentillae. The contribution ofth e ovipositing femalest othes eprédatio ncapacitie s amountst o84 , 80, 66an d60 %respectively . Becauseo fthi s important roleo fth e ovipositing females these were chosent ostud y interspecific differences inpre ysear chingbehaviou r (Chapter3) .

64 2. 2. 5 Starvation and survival

After depletion of their food source Phytoseiidae are able to survive for some time.Whe n well-fed young females were placed in aMunge r 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 ndeposited . Because the weight of an egg corresponds to 20%o f thematur e femaleweight ,th e initialweigh tdeclin ewa sver y steep,a sillustrate d by the electrobalance measurements of the femaleweigh tdurin g 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 severedehydration , jj Theirbod yweigh tapproache d dryweight ,bu tthe ydi dno tdie .A s discussed in Subsection 2.2.3, these starving females are able torecove r andsubse quently oviposit as well as they didbefor e starvation.Th erate so fsur vivaldurin g thesean dothe r starvationexperiment s aresummarize d inTabl e 28 as the 90, 50 and 5%point s ofth e survival curve.Larva edevelo p into1 , protonymphswithou t any food,bu tafte rthi smoul tthe yrequir e foodt ode - L- velop intoth enex tnympha lstage . Two factors are very important with respect to the rate of survival. First, dehydration is enhancedb y anincreas e oftemperature .Second ,hig h humidity and drinking water enables prolonged survival. The role ofbot h factors is demonstrated inTabl e2 8usin g additional data fromth elitera ture.Becaus e inros ecultur e themea n temperature isabou t20° C andbecaus e water spraying takesplac e frequently, itma yb eexpecte d thatPhytoseiida e are able tosurviv e for2- 3 weeks afterth eexterminatio n ofthei rpre y and inth e absence ofalternative ,non-tetranychi d food supply. Whether non-tetranychid food sourcesprovid e amean s tosurviv e duringa longerperio d inth egreenhous e cultureo fornamenta l roses,wil lb e treated inth e remaining subsections ofthi schapter .

2.2.6 Cannibalism

Whenothe r foodresource s arelacking ,th e adult female andoccasionall y; Î the nymphal stages of the Phytoseiidae are reported to feedo nthei row n j young, mainly eggs and larvae.Th etendenc y towards cannibalism maydiffe rl from species to species and even from population to population. Croft & McMurtry (1972)observe d cannibalism among four strainso f Metaseiulus occidentalis originating fromdifferen tpart s ofth eU.S.A . They foundsignifi cantdifference s inth eexten to fth ecannibalisti c behaviour.Lain g (1969) reported thatwhe n several ofeac h stageo f Metaseiulus wereplace d together ina cell , the adults fedo nimmatur e stages,bu tno to neac hother .H e also observed thatnymph s of Metaseiulus couldb ereare d tomaturit y onegg s and larvae ofth e same species.Howeve r theresultan t adults laidonl y fewegg s

65 ^f r- oo co en r> r> M Ol CJ1

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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 yBravenboe r (1959). Amblyseius bibens mayb ecompare dwit h Metaseiulus occidentalis inthi sre spect. According to our own observations Amblyseius potentillae becomes cannibalistic to someexten tafte r 1-2 dayso f fooddeprivatio n atT =20°C . Itma y then feedprimaril y onegg s andlarvae . Dosse (1958)wa s firstt orepor tcannibalis m in Phytoseiulus persimilis. The extent of cannibalism is relatively high inthi sspecies :1 2hour s of f food deprivation at T = 20°C induced cannibalism of eggs; longerperiod s j led to feedingo nth e larval andnympha l stages.I na starvatio nexperimen t! with only an initial supply of 30 fresh predator eggs, the longevity of female Phytoseiulus persimilis did not exceed the mean value measured in presence of free water inan yo fth e2 0replicates .A s expected,th ewell - fed females deposited oneo rtw 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 J food content of the larvae and nymphs decreased exponentially with time, | until death, as shown for example in Fig. 17.Therefor e the food supply decreased drastically duringth eexperiment . 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 ytherefor eb econclude d thati nth e longru n theeffec to fcannibalis m on female longevity doesno texcee d theeffec to f water supply. Under the present glasshouse conditions iti sreasonabl et o assume thecontinuou s availability of freewater ,whic hthu s determines the predator capacity to survive irrespective of cannibalism. However, under drycondition s cannibalism mayprovid e amean s forth e strongest individuals to survive forsom etime ,whe nn oothe r food items areavailable . Cannibalistic behaviourma yb e favouredb ynatura l selection,whe ndiffe rentgeneration s ofth epredato r areconfronte d attime swit htemporar y food scarcity. Sucha situatio nca nb e inducedb y ahig hpredator y andreproduc tivecapacit y ofth ephytoseii d itself. Itwil lb e shown inPar t2 tha tth e capacity of Phytoseiidae indeed leads toloca l exterminationo fpre y clus ters. Ifneithe r alternative foodno rwate r sources are available,canniba lism can be expected. It is not surprising, therefore, that especially Phytoseiulus persimilis is the most cannibalistic of the species studied here, for the individual weight and thevoracit y ofthi s species arerela tively high and, as will be discussed in Subsection 2.2.7,thi spredato r feeds itselfexclusivel y withTetranychidae .

67 2. 2. 7 Alternative food supply

ThePhytoseiida econtai nman y diverse formswit h respectt othei r feeding habits (McMurtry et al., 1970). Some species seem tob e specializedpreda tors of Tetranychidae and show no tendency toreproduc e onothe r types of food. Phytoseiulus persimilis issuc ha species .Althoug h the other species studied could certainlyb e ranked asspecialize d predators ofTetranychidae , their dietary range is not restricted to this kind ofprey ,bu t includes otherplant-inhabitin g mites,youn g stages ofvariou s insects and somenon - animal foods, like pollens and fungi.A brie f reviewo fth e literatureil lustrates the interspecific differences of anumbe r ofPhytoseiidae : - Phytoseiulus persimilis is very dependent onth e availability ofTetra nychidae (Dosse, 1958; Chant, 1961;Ashihar a et al., 1978). According to Mori & Chant (1966) the addition ofnutritiv e substances such assucrose , glucose,pollen ,hone y and fishmeal s ofvariou s kinds toth edrinkin gwate r did not significantly increase longevity compared to the effect ofwate r drinking alone.Ashihar a et al. (1978)als o demonstrated, that Phytoseiulus persimilis did not reproduce on honey or pollen (strawberry, castor,re d pine), butmea n adultlongevit ywa s increased to4 5 daysb y nutritional sub stances such as fresh honey or a 10%sucros e solution, ascompare d to1 2 dayswit h onlywate r available.Lain g (1968)report s thatstrawberr y pollen did not promote longevity ordevelopmen t of Phytoseiulus, compared tospe cimens kept without food. Similarly, McMurtry (1977)foun d thatpolle n of Hymenocyclus croceus was not an acceptable food forthi s species,i ncon trastt o some otherPhytoseiidae . Metaseiulus occidentalis has been observed to feed, develop andrepro duce on tarsonemids (Huffaker & Kennett, 1956; Flaherty, 1967), tydeiids (Flaherty &Hoy , 1971), Brevipalpus phoenicis, thrips and some crawler spe cies (Swirski &Dorzia , 1969). According toFlahert y &Ho y (1971), Metasei ulus occidentalis could not reach adulthood onCa ttai lpolle n (Typha lati- folia), which is animportan t food for Amblyseius hibisci (Kennette t al., 1979). Lee & Davis (1968) reported feeding on this pollenb y theadults , butonl ywhe nTetranychida e wereabsent . Amblyseius bibens is able torel y oncertai npollen s inabsenc e ofTetra nychidae (Blommers, 1976). Among several pollens tested as food forthi s predator,polle n of some Papilionaceae and Carpobrotus spp.,appl e and rose (!) enabled the predator tomor e or lessmaintai n reproduction. Pollenwa s thebes t food substitute.Mas s rearing of thispredato r exclusively onpol lencoul db e continued byBlommer s (1976)fo rmor e than ayear . Amblyseius potentillae fed and reproduced readily on apple pollen and Aculus spp. in the experiments of Kropczynska (1971). Especiallyinteres ting areth e experiments ofMcMurtr y (1977), which indicated thatpolle no f Malephora was utilized evenwhe n anabundanc e ofspide rmite swa spresent . For a diet of only pollen, he found a lower rate of reproduction (about

68 two-thirds thenorma l rate)an d alonge rpreovipositio nperio d than foronl y Tetranychidae. Notal lpollen 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 eo f itssiz e (75-100pm ) (Kennette t al., 1979). Inman y othercase s iti spresume d that the negative responses to certain pollens are related to thechemica l or physical nature ofthei rwax yo r resinousexin e (Kennette t al., 1979). Several authors statetha thoneyde w canmerel y servet opromot esurvival , but allows littlereproductio n (Huffaker& Kennett ,1956 ;Chan t& Fleschner , 32 1960; McMurtry& Scriven,1964 ,1965) . Ina nexperimen t inwhic h a Psolu tionwa smixe dwit hbe ehone y andoffere d asdroplet s tohungr yyoun g females 32 of the phytoseiid species inhunge r cages,th edegre e of P ingestionwa s measured with the aid of-th e Cherenkov-method.Th eresult s indicated that Amblyseius potentillae was farmor e ablet oinges tth ehone y (500-2000count s per minute)tha n the other species, evenwhe nthes ewer e starved forlon g periods (Amblyseius bibens 100-200count spe rminute ; Metaseiulus occiden talis 50-100 counts per minute; Phytoseiulus persimilis 0-50 counts per minute). From therevie wo fth e literature thedegre e ofspecialis m on tetranychid prey canb e derived usingth epreferenc e forth edifferen tpollen s relative totetranychi dpre y 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 thelatte r species isabl et orel yo nnon-anima l foodwhe ntetranychid s are absent. Amblyseius \ potentillae, however,seem s toaccep tbot hpolle n and tetranychidswhe nof - ( fered simultaneously. The original criterion thus leadst oa sequenc e that 32 correspondswit htha tobtaine d fromth e P ingestionexperiments . The short survey above indicates differences inth edietar y rangetha t may be important forthei r survival andreproductio n ina natura lhabitat . Itma y be importantto o inth egreenhous e cultureo fornamenta l roses,bu t| thehairles s rose-leaves are less suitable aspolle ngatherin g centres and, | besides, other plant feeding arthropod orhoneyde w areabsen tand/o runde - j sirable. Itwa s thereforepresumed , thatunde r thegreenhous e conditions to' be investigated, the effects ofa nalternativ e food supplywil lno texcee d that of simple water supply to an important extent. Thispresumptio nwa s Ij confirmed by release experiments with the four phytoseiid 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.Th e roses were sprayed daily with water. Therat eo fsurviva lwa smeasure d in twoways :b y direct inspectiono fth e leaves;and ,i fthi smetho d indicated lownumber s ofpredators ,b y inspectingmit e infestedbea n leaflets 10hour s after being pinned on to the rose leaves (10 leafletspe rbush) . Ifbot h checks rendered negative results,th epredator swer e assumed tob eabsent .

69 Table 29. Survival of young phytoseiid females of four species on rose bushes scatteredwit hpollen .T = 17-22°C ;relativ e humidity = 60-80%.

Species Number ofpredator s found Number ofpredator s found by directinspectio n of bytrappin g inmit e colonies leaves onbea nleave spinne d ontoth e rose leaves

Number ofday s after release Number of days after release

10 15 21 29 29

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

Survival appeared to beno tsignificantl y promotedb y thepolle n treatment (Table 29);i t did not exceed the survival expected under conditions of water supply and the actual climate (T= 17-22°C ;relativ e humidity = 60-80%). However, Blommers (1977) foundpositiv e effects ofth epolle n treatment on the survival of Amblyseius bibens, even ata hig h temperature (T= 28°C). Heuse dpeanu tplant s amplypopulate d withpredator s shortly after theyex terminated the spider mite population on theseplants .Consequentl y these plants were covered by some (sticky)webbing ,whic hma y serve as abette r pollen gathering centre than the bare rose leaves. This reportdoe snot , however,trea tthi saspect . Although it seems difficult to maintain thepredato rpopulatio nperma nently by the addition ofnutritiona l substances,th e survival ofeve nth e most specialized phytoseiid, Phytoseiulus persimilis, may be promoted by spraying 10%sucros e solutions (Ashihara et al., 1978). This possibility should beevaluate d under greenhouseconditions .

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

As argued inChapte r 2th eprédatio ncapacit y ofphytoseii dpredator s is largely determined by thehig h rateo f food conversiondurin gth eoviposi - tionperiod ;unde r favourable conditions phytoseiid females areabl et opro ' duce an egg biomass per day equal tothei row nweight .Th erat eo frepro duction will therefore depend on the searching efficiency ofth epredato r and the availability ofth eprey . Itwa soutlined ,moreover ,tha tpreviou s reproductive success (i.e.th e number of eggs already deposited) ismor e important in determining future reproductive food demands than ageing. Apparently, among Phytoseiidae there is a tendency todeposi ta 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 fromcolon y tocolon y insearc h ofa satisfactor y supplyo fpre yan d aminimize d level ofinterferenc ewit hothe r conspecific females. The availability of the two-spotted spider mite is restricted to the plant areacovere db ywebbing .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 nth eundersid e ofth e leaf iscompletel ywebbed . During the residence ofth epredato r ina certai ncolony ,pre yconsump tion will lessen the local supply of prey until thepredato r 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 linter ference among the predators,whic h enhances the tendency todispers e from thecolony , independent ofth e localpre y supply.Moreover ,mutua linterfe rence can lead to a decreased rate of reproduction, asshow nb yKüchlei n (1966). In this chapter the relation between onth e onehan dpre y andpredato r density inth ecolon y and,o nth eother ,th erat e ofprédation , reproduction and departure is analysed.Thi s analysis isconfine d toth e level ofa fe malepredato r foraging ina colon y ofspide rmites .Thos e aspectso fforag ing behaviour that takeplac e after departure from acolon y aretreate d in Part 2o fthi sAgricultura l ResearchReport ,a swel l asth easpect sconcern ingpopulatio ngrowth . Theanalysi s iscarrie dou tb yvalidatio n ofconceptua lmodel so fpreda tory behaviour. A prédation model is constructed that is based onrando m searching periods between successive encounters with prey items and ona

71 relation between the motivational stateo fth epredator s (Section 3.1) and the prey density related rate of successful capture (Section3.2) .Th ein dicator of the motivational state ofth epredato r ischose n tob e the food content of its gut.Accordin g toAkimo v& Starovir (1978)th egu twall s of phytoseiids are markedly extensible, compared toothe r gamasids.Neverthe less there has to be amaximu m load, whether this iscause db y alimite d extensibility of the body orgu twalls ,o rb y anegativ e feedback to feed ing via gut or body wall stretch receptors,a s found in Phormia regina by Gelperin (1971) and Beizer (1979). Because ingestion,maxima l gutconten t and gut emptying may be quantified byus e ofth eelectrobalance , the food content of the gutca nb e related tobehavioura l components by observation of the predatory behaviour and simultaneous calculation of the amounto f foodpresen t inth egut . The behavioural components needed tocalculat e therat e ofencounte r at any level ofth emotivationa l state andpre y density area sfollows : width ofth e searchingpat h (cm) distance ofpre y detection (cm) walking speed (cm/s) walking pattern walking activity (%) coincidencebetwee npre y andpredato r inth ewebbe d space success ratio (%) handling and feeding time(s) . The relations between the motivational state ofth epredato r and these behavioural components are used ina simulatio nmode l ofth equeuein g type (Taylor, 1976; Curry & DeMichele, 1977), where thepredato r is considered to be the service facility, i.e. 'thedentist' , and thepre y 'theclient' , who may enter (at a certain rate)th e 'waiting room' (i.e.gut )i nexpec tance ofth e service (i.e. 'digestion, absorption and egestion'). In another model the walking behaviour is simulated to calculate the rate of encounter between predator and prey orth e rate ofdepartur e from the prey colony (Sections 3.2 and 3.4) onth ebasi s ofmeasurement s ofth e above components of walking behaviour. Video equipment enabled theregis tration ofth ewalkin gpattern ,whic hwa s used tomeasur e thewalkin gveloc ity and the frequency distribution ofchange s inwalkin g direction aftera fixed step size. Themode l simulates thewalkin gbehaviou r onbasi s ofth e assumption that the direction of each stepdeviate s from the direction of the previous step with an angle chosen at random from the experimentally defined frequency distribution, autocorrelations being accounted for.Th e calculation of the rate of predator-prey encounter serves toestimat e the effect of recrossing the areas already searchedb y thepredator .Th e cal culation of the rate of departure from thecolon y serves toelucidat e the role of patch specific cues in the intracolony residence time ofth epre dator.

72 Apart from fundamental ecological interesti nanalyzin g the foragingbe haviour, there aremor ereason st oundertak e adetaile dcomponen t analysis instead of direct measuremento fth eresultin grat eo fprédation .Extrapo lation of the measured prey consumption to the population level is only allowed ifth emotivatio no fth epredato r isi na stead y statedurin gthes e measurements of the rateo fprédation ,a swel l asdurin gpopulatio n growth of predator and prey.Rabbing e (1976)solve d the firstproble mb y allowing thepredato rt oadap tit smotivationa l statet oa constan tpre ydensit ybe fore measurement of the rate of prédation.Pre y densitywa skep tconstan t by replacement of the prey captured (ordie d fromothe rcauses )a t1 5mi n intervals.Howeve rpre yreplacemen ti sessentiall y impossible inth ewebbe d colony, because mite transfer with the aid of abrus hca ndamag eth ewe b structure and can disturb thepredato rbein g sensitive tomovement s ofth e web. Numerical simulationo fth eprédatio no nth ebasi so fa componen tana lysis may provide a means to keep tracko fa changin gpre y density andt o estimateprédatio na tconstan tpre y density.Wit hrespec tt oth eextrapola tion of prédation measurements to the level ofpopulatio n growth- th e secondproble m -Rabbing e (1976)assume d instantaneous equilibrationo fth e phytoseiid motivation to any change inpre y density. This assumption is tested inPar t2 o fthi sAgricultura l ResearchRepor tb yusin ga simulatio n' model of population growth anddispersa l ofpre y andpredato rtha tca nac count fornon-stead y states ofth emotivation . Finally, thecomponen t analysiswa s undertakent ostud yth erol eo fweb bing in the acarinepredator-pre y interaction. Inmos to fth ereporte dex periments webbingwa s eitherno tinclude d or itwa 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 bdifferen t fromtha to f the adult female.Althoug h female-produced webbing has aver ychaoti cstruc ture, it can be considered as acoheren tuni t (Figure 8),whic h shouldb e distinguished from the uncolonized parts of the leafi nacarin epredator - prey studies. Actually some unexpected types of functional response of phytoseiid predators to thedensit y ofthei rpre ywer e attributed"t oclumpe ddistribu \ tions ofwebbin g inspac e (Mori,1969 ;Fransz , 1974). Other deviating forms ofth e functional responsewer e attributed todisturbanc e offeedin gpreda tors by active prey, resulting in anattac k onth e interferingprey ,tha t bumped into it (Sandness& McMurtry , 1972), orattribute d tocontac tdistur bance, decreasing the number of successful captures (Mori& Chant , 1966). Küchlein (tob e published) found a second rise ofth e functional response of Metaseiulus occidentalis athig hpre y eggdensities .Probabl y thispheno menonwa sno trelate d toth e food satiation level ofth epredator ,bu trath er to a contact stimulus.Howeve r itma y be questionedwhethe r theabov e behavioural factors operate in the webbed area. Preliminary observations indicated thatbot hpredato r andpre ywer e lessactiv e inth epre y colonies

73 ;an d disturbance of the predator was rarely observed. Furthermore,webbin g may change prédation simplyb y surface enlargement orb y inducing specific changes inth epredator ybehaviour , asdiscusse d inSubsectio n 2.1.6.There foredetaile d observation ofprédatio nwa spreferred .

3.1 DYNAMICS OFTH EMOTIVATIONA L STATE

\ By assuming the foodconten to fth egu tt ob e themai n indicator ofth e Imotivationa l stateo fth epredator ,th e dynamics of thepredator y motivation !ca nb e simulated by integration ofth erat eo fingestio n (Subsection3.3.1 ) |an d the rate ofgu temptyin g (Subsection 3.1.2). This simple concept allows Ith e calculation of themotivationa l state during observation ofth epreda torybehaviour , sotha tpredator ymotivatio n andbehavioura l components can be related toeac hothe r (Section 3.2). These relations areuse d intur ni n the prédation models to calculate the rate of prédation (Section3.3) . Validation of this type of prédationmodel s did notresul t ina rejectio n of the concept (Holling, 1966;Nakamura , 1974;Fransz , 1974). However the postulation of one intervening variable, indicating thehunge r drive,ma y beto o simple ahypothesi s toaccoun t for allhunge r relatedbehaviour .Fo r example itma y be questioned, whether themotivationa l state adapts itself instantaneously to a change inth e food content ofth egut . Inothe rword s does a certain level of gut filling induce the same searchingbehaviour , whether it is achieved via ingestion orgu temptyin g starting from lowo r \larg e amounts of food in the gutrespectively ? Thisproble m is considered at some occasions in this chapter (forexampl e Subsection 3.2.7). Another problem concerns the quality ofth e food.Th e existence of specific hungers forproteins ,sugar s orwate r hasbee n shown inth eblo w fly (Dethier, 1976). Because phytoseiids are known torel y onpollens ,honeyde w andwate r apart from tetranychids and because the developmental stages ofth e spidermit e Ima yno thav e the same food quality toth epredator , dietcompositio nma yb e relevant in defining themotivationa l state ofth epredator .Howeve r ade tailed quantitative understanding of the metabolic consequences of diet composition for absorption, synthesis and allocation of food elements does not yet exist, even for insect physiologists pets. For thetim ebein g the food contento fth e gutwil l beexpresse d interm s ofweigh t (|jg),assumin g the quality of the ingested food tob e constant. InSubsectio n 3.1.3 this assumption iscriticize d onth ebasi s of available references pertaining to dietcompositio n andphytoseii d reproduction. The phytoseiid females used forth eexperiment s were all treated inth e same way. They developed on bean leaves with an abundance of Tetranx/chus urticae at all developmental stages (T = 25°C, relative humidity =abou t 75%). Female deutonymphs were collected from this stock and transferred to other leaveswit h abundant food (T= 20°C) , where theymoulte d and copulated after supply of males.Whe n the femalepredator s had deposited their first

74 eggs, they were ready forexperimentation . Subsequently, whenever these predatorswer e deprivedo ffood ,car ewa stake nt ous eonl y satiatedpreda torsb ysamplin g them immediately aftera nactua l feedingperiod .Nex tthe y werepu tindividuall y inMunge r cages (Figure10 )fo rdifferen ttim einter vals anda tdifferen ttemperatures ,dependin go nth eparticula rpurpos eo f theexperiment .Unles s stated otherwise,th efemal epredator sneve rexceede d theag eo f1 0day sa sa nadult .

3.1. 1 Ingestion

Aftera successfu l captureth epredato r starts ingestingth epre ycontent , the movements ofth eingeste d fluid beingvisibl e throughit stransparan t bodywall .Presumabl y praedigestive fluidsar einjecte d forextra-intestina l digestion (Akimov& Starovir , 1975).Th eamoun to ffoo dingeste ddepend so n the followingfactors : (X, - theamoun t offoo d thatca nb eingeste db yon eo rmor epredator s froma singlepre y stage (theingestabl e food contento fth eprey ) the suction forcei nrelatio nt oth ephytoseii d species involvedan dth e fluidityo fth efoo d (theingestio n constant) c thedifferenc ebetwee nth emaximu m foodconten tan dth eactua l foodcon tento fth egu to fth epredato r (thesatiatio n deficito fth egut ) ci the sumo fth eperiod si nwhic hth emout hpart so fth epredato rar ein trudingth ebod yo fth epre y (thefeedin g time,Subsectio n 3.2.8). (y^ Asa first approximationo fth eingestabl e foodconten to fth epre yon e

Table 30. The ingestable food content ofth e developmental stageso f Tetranychus urticae.

Prey stage Weightincreas e (pg)afte r feeding Freshweigh tminu s dryweight 3 Metaseiulus Amblyseius Phyt oseiulus occidentalis potentill ae persimilis +h*hll M ô n M â n Û ô n JÀ-U* egg 1.0 0.2 30 - - - - - 0.8 larva 1.1 0.2 24 1.1 0.2 12 - - 1.3 protonymph - - 2.3 0.3 14 - - 2.7 deutonymph9 2.9 0.2 16 5.1 0.3 30 7.3 0.5 21 8.6 male - - 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

a. Accordingt oth edat ao fMitchel l (1973).

75 could measure the difference between the fresh and thedr yweight s ofth e different prey stages. These estimations can be obtained from thewor k of Mitchell (1973).A mor eprecis emetho d ist ocompar e theweight so fa nini tially hungry predator (2 days starvation at T = 20°C)befor e and after feeding on a certainpre y stage.Th e results ofbot h types ofmeasurement s are given in Table 30,whic h showscorrespondenc e onlywit h respectt oth e smallpre y stages.Becaus e the amounto f food ingested from the adult female prey increased with thebod y size ofth ephytoseii d species,on ema y suppose the ingestable food contento fthi s stage tob emuc hhigher . Ina nexperi ment with females of Phytoseiulus persimilis and Tetranychus urticae the total weight of food consumed by three hungry predators from one single prey amounted to 16.6 pg, which result closely approximates the estimate based on the differencebetwee n the freshan d dryweigh to fth eprey .Appa rently the amount of food inth e femalepre y exceeds themaxima l foodcon tento f thephytoseii d gut. Itca ntherefor eb e concluded, thatth eingest able prey content per singlepredato r is limitedb ybot hpre y size andgu t size. '/") In another series of experiments ingestion wasmeasure d inrelatio nt o feeding time. By interruption of feeding after fixed time intervals the amount of food ingested by ahungr y predator canb emonitore d with theai d of the following methods.Th e firstmetho d ist omeasur e theweigh to fth e predator before and after a predetermined feeding period. However this method is not reliable, when the weight differences are below 0.5 ug,a s 32 e.g. in the egg stage. In thatcas e anothermetho d was applied using P- labelledprey .Th e spidermite swer e labelledb y feedingdurin g 12hour s on a bean leaf, previously put with its stem ina P solution3 2(1 mC i) fo r1 day. Radioactive eggs were obtained from radioactive females.Th e labelled prey was offered to an unlabelled femalepredator ,bein g deprived offoo d for 2 days at T = 20°C since satiation. Fransz (1974) assumed, thatth e amount of radioactivity in the prey wasproportiona l to its foodcontent . However the author's experiments indicated such a high variability among prey individuals ofexactl y the same age and labelled onth e samebea n leaf thatthi s assumption is invalid.Thi svariabilit y mayb e due toth eunhomo - geneous distribution of P 3i2n the leaf or to individual differences in sucking activity ofth emites . Therefore the ingestion experiments with P 32 labelled prey can only be interpreted, when theradioactivit y ingestedb y thepredato r isexpresse d as afractio n ofth e total radioactivity initially present inth e individual prey.Fo r this reason theexploite r and itsvicti m werebrough t into separate glassvial s after apredetermine d feedingperiod . Subsequently theywer e crashedb ymean s of aglas s stick and their contents were dissolved in1 0m lwater .Thes evial swer ebrough t into a radioactivity counter,whic h directly registers theß-radiatio nemittanc e of Pb ymean 3s2 of the Cherenkov method. The neutrons emanated by the Pmolecule 32s were

counted during 10 minutes andnex tcorrecte d forth emea nnumbe r ofcount s

76 registrated invial s containing only water.Th eproportio n ofth etota l radioactivity ingested byth epredato r canb ecompute d from thesecount s and this indicates the level ofingestion .Th eshape s ofth eingestio n curves obtainedb yth eabov emethod swer e invariablyo fth esaturatio ntype . Thereforeth efollowin g formulawa sadequat efo rdescriptio no fth e fraction ingested relativet omaxima l (i.e.uninterrupted )ingestion :

T, 4., , -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(o r ingestion constant)o fth epredato ran dth eviscosit yo fth epre ycontent . Thevalu eo fthi s ingestionconstan tca nb eestimate d fromth eslop eo fth e linear regression ofln(l-FI )o ntime .Thes e estimatesar egive ni nTabl e 31. Apparently theingestio nconstant sd ono tdiffe rver ymuc hbetwee nth e species studied.However ,on eexceptio nmus tb enote di ncas eo f Amblyseius potentillae attempting toinges t theconten t ofth etetranychi d egg. For some reason this predator hasdifficultie s inpuncturin gth eeg gchorion , i as suggested by direct observation ofth epredator y behaviour. Küchlein (personal communication)measure da muc hlowe rrat eo freproductio no fthi s predator: ifegg s of Tetranychus urticae instea d oflarva ewer e offered as prey. This result corresponds with themeasurement s ofingestio n that indicatedn oabsolut ebarrie rt oingestion ,bu tsom ehindranc ewhe ncompar -

Table 31. Theingestio nconstant s RRFI (min~) o ffou rphytoseii d species inrelatio nt oth estag eo fth eprey .

Predator Egg Larva Proto- Deuto- Male Female species nymph nymph9

MnpnunpniJnpn

Metaseiulus 1.9 27 1.1 10 - - 0.111 0 0.7 12 0.071 8 occidentalis Amblyseius 1.8 12------bibens Amblyseius 0.2 52 0.8 9 0.6 26 0.3 14 0.4 21 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 ozero .

77 edwit h the otherphytoseii d species.Anothe r conclusionca nb edraw n from the measurements in Table 31 with respectt oth e effecto fth epre y stage on the ability to ingest its content; the more developmentproceeds ,th e more difficult iti s forth epredato r to suck thepre y content.Thi sma yb e caused by the internal structure ofth ebod ybein gver ycompartimentalize d in the adult femalephase .Anothe r explanation mayb e found inrelatio nt o the time required for extra-intestinal digestion of solid structures.De spite thesedifference s inth emeasure d ingestion constants itca nb e stated, that 90%o f the overall ingestion perpre y takesplac e during the initial 20% ofth epre y stage specific feeding times ofth edifferen tpredato r spe cies (Subsection 3.2.8). Because the feeding times are rather shortand , therefore, also the period needed for 90%foo d intake,i ti sno t far from reality toconside r the ingestionproces s asa nimmediat e swallowing ofth e food content of the prey. This concept is aprerequisit e forth e queueing approach ofth eprédatio nprocess ,t ob e discussed inSubsectio n3.3.1 . Several times observations indicated, that even small prey were not consumed completely, as also reportedb y Lee& Davi s (1968), Fransz (1974) andRabbing e (1976). Rabbingepresente d indirectevidenc e for thisphenome non. By assuming that ingestionb y thepredato r equals its gutemptyin g on the average at a constant prey density,h e estimated the prey-utilization from this equation aftermeasuremen t ofth e rate ofprédatio nan d gutempty ing.Thes e indirect estimations pointed toth e importance ofpartia linges tion of the prey content. Direct proofwa s givenb yth e followingexperi ments, using the electrobalance. Females of Phytoseiulus persimilis were deprived of food for different periods starting from full satiation and subsequently a female of Tetranychus urticae was offered asprey .Th edif ference inth eweigh to f thepredato rbefor e and after feedingwer emeasure d with the electrobalance and the results areplotte d inFig .18 .A similar

INGESTION(ju g 9

T r ~1 12 16 20 2U 28 32 36 iO 48 TIMEO FFOO DDEPRIVATIO N [HOURS) Fig. 18. Weighto f the food ingested by young females of Phytoseiulus per similis from females of Tetranychus urticae after differentperiod s of food deprivation (T= 20°C)._ L= standar d deviation.

78 FRACTION OF32 P-LABELED EGG INGESTED i.u- m mtt •• •• i • t • 0.5- i • • • • • t i i 0 1i 2 4 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 occidentalis afterdifferen tperiod s of fooddeprivatio n (T= 20°C).

32 experimentwa s donewit h females of Metaseiulus occidentalis and P-label ledegg so f Tetranychus urticae (Fig.19) .Bot h experiments demonstrate the \\ occurrence of partial ingestion.Moreove r the shapeo fth e ingestioncurv el ' is of the saturationtyp e instead ofsigmoid ,whic h suggeststha tth epre --7 datortend s toempt y itspre y as fara sallowe db y the satiationdefici to f itsgu to r the food contento fit sprey . As discussed before, theamoun to f food inth e adult female spidermit e largely exceeds the phytoseiid gutvolume . Inthi swa y anestimat e ofth e gutvolum ewa salread y available.Howeve r asecon destimat ewa sneeded , be-| cause the apparent gut volume may depend onth epre y stageinvolved .Thi si was accomplished by allowing hungryphytoseii d females (2day s fooddepriva tion at T = 20°C)t o feed on eggs and larvae instead of feedingo nadul t female prey until they were satiated. Satiationwa s definedb y theoccur renceo fa tleas t1 0successiv e contactso fth epredato rwit h itspre ywith out subsequent attack. The weight difference between the predator before and after feeding until satiationwa smeasure d usingth eelectrobalanc e to estimate the apparent gut volume in case of small prey stages.Predator s unable to achieve satiationwithi n twohour swer e discarded topreven tover - estimation ofth evolum e duet ogu temptyin gb y absorption oregestion .Th e results indicated only asligh tinfluenc e ofth epre y stage onth e estimated gutvolume , as shown in Table 32.Therefor e this aspectwa sneglecte d in further analyses for the sakeo fsimplicity .Moreove r theresult s indicate that the interspecific differences ingu tvolum e areproportiona l tothei r size, asexpected . Insummary , the ingestionproces s canb econsidere d asa n immediate swal-

79 Table 32. Theapparen tgu tvolum eo f fourphytoseii d species, estimated from theweigh t increase ofhungr y femalepredator s after feeding onegg s and larvae of Tetranychus urticae until satiation.

Phytoseiid species Weight increase ((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

lowing ofth eprey .Th e amounto f food consumed isdetermine d by theavail able space in the gut or the food contento fth eprey ,dependin g onwhic h ofbot h factors isth e smaller one.T o inlcude this aspect thepreviou sin gestion formula canb e extended asfollows :

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

FT = feeding time I =ingeste d food IF =ingestabl e food contento fth epre ype rpredato r SDG =satiatio n deficito fth egu t FCP =ingestabl e foodconten to fth epre y

3.1.2 Gut emptying

The rate of gutemptyin g canb emeasure d byweighin g the amounto ffoo d required to satiate the predator after differentperiod s of fooddepriva tion.Afte r acertai nhunge rperio d thepredator s were 'drugged'b y asligh t amounto fCO « toreduc e theirmobilit y andweighe d using anelectrobalance . Next they were brought toa feeding area,consistin g ofa pre y colonywit h abundant numbers of eggs and some females,wher e theywer e allowed to feed until satiation.Afte r acertai nnumbe r of successful attacks predators tend to leavepre yunharmed , despite contactwit h thepredators ' front legs.Whe n 10 successive failures ofthi s kindwer e recorded, thepredato rwa sconsi dered to be satiated. To prevent overestimationo fth e food consumed, due togu temptying , this series ofevent s had totak eplac ewithi n ashor ttim e interval. Predators requiring more than two hours (T = 20°C) to achieve

80 satiation were therefore not considered. After an anaesthetic, the final weighto fth epredato rwa smeasure d andth eweigh t increase afterth ehunge r period inquestio ncoul db e calculated. Theresult s ofthes eexperiment s are shown inFigur e 20 foryoun g females of Phytoseiulus persimilis, at three different temperatures. Inagreemen t withHollin g (1966)an dGree n (1965), theresult s showtha tth egu ti semp tied ina nexponentia l fashion:

™ _ i -RRGE-time FE =1 - e FE =fractio nemptie d RRGE= relativ e rateo fgu temptyin g (time- ) Moreover, temperature is an important factor influencing the rate ofgu t emptying. The RRGE values estimated fromth emeasurement s werealmos ti na straight line when plotted against temperature (RRGE in day" = 0.21 x (temperature -11°C) .Moreove r 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 perday . Although this experimental procedure did produce some useful results, there were some problems in applying it for all the species inquestion . Weighing of the individualsbefor e 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,th e time period allowed for the achievement of satiationmad e itnecessar y todis card almost 60%o f the replicates from the final results.Therefor e some alternatives were applied.Th e firstmetho dwa s toomi tth eweighin gproce -

WEIGHTO FFOO D CONSUMED(ju g) 9-

i i i 1 1 1- 1 1 1 1 1 1 0 U 8 12 16 20 2U 28 32 36 iO U 48 TIMEO FFOO DDEPRIVATIO N(HOURS ) Fig. 20. Weight of the food consumedunti l satiationb yyoun g femaleso f Phzftoseiulus persimilis after differentperiod s of fooddeprivatio n and at three temperature levels,o ,T = 25°C ;A ,T =20°C ;D , T =15°C ; .- L= standard deviation.

81 durean dt o feedth epredato rmerel ywit h eggs.A simpleenumeratio n ofth e number ofegg sconsume d and thedat ao n the ingestable food contentprovide d awa y toestimat e the ingestionunti l satiation, thereby neglecting partial ingestion. Although the procedure was much more simple,th ecriterio n for full satiation remained a central problem toobtainin g replicates easily. Therefore another method was developed, based onth eenerg y expenditure in thephytoseii d physiology. As discussed in Subsection 2.2.3, the phytoseiid female is capable of producing a daily eggmas s equal tohe r ownweight .Obviousl y the levelo f energy conversion is quitehig h inth e ovipositionphase .Therefor e itma y be expected thatth e rateo fabsorptio n ofdigeste d food into thehaemolymp h isclosel y linked to therat eo freproduction .Accordin g toTrehern e (1967) andHous e (1974)th e absorption of amino acids and sugars from the gutdif fers from that ofth evertebrat e intestine intha tthes e substances dono t appear to be absorbedb y specific activetranspor tmechanism s againstcon centration gradients.Wit h respect to lipids, there are also no valid a priori reasons for active transport across the gut wall, as argued by Treherne (1967). Thene t absorption appears tob e linked towate r movements and toresul t from the concentration gradients developed across thegu twal l due to the uptake of water into thehaemolymph .Thes ewate rmovement s can be the result of osmosis and arthropods arecapabl e ofperformin g osmotic work (Berridge, 1970), so that absorption of gut stores may even occur against concentration gradients between the gut fluid andth ehaemolymph . However thesemechanism s couldb e overruledb y diffusive absorption induced by thewithdrawa l ofbloo d stores.A rapid conversion of amino acidst opro teins and monosaccharides to disaccharides will tend to maintain astee p concentration gradient across thegu twall . Thus,becaus e the absorbed food elements are utilized ineg g formation and fuel supply therat e ofabsorp tion will be related to these processes too incas e of ahig h turnover of energy. Hudson (1958), for example, has shown that the delivery of gut stores is greatly speeded by increased energy expenditure, as for example flight. Similarly, thewithdrawa l ofwate r molecules from the (hind)gut into the blood will influence theconcentratio n gradient andwil lb e related to water loss from thebod y due totranspiratio n andoviposition .Therefor e it isver yprobabl e thatth e absorption rate inphytoseii d females,whic hhav e a high rate of reproduction, will be closely related toeg g formation and transpiration, and,o fcourse , vice versa. The rate of absorptionwil lprobabl y dominate the rate ofgu temptying , forth epresenc e of acolo n andMalphigia ntubule s (Akimov& Starovir, 1975) indicate some degree ofrecyclin g ofth ewater , asoppose d to thegu tstruc ture ofth e two-spotted spidermit e (Subsection 2.1.4). A rough estimate of theegestio n rate onbasi s ofth e size of fresh faeces droplets and the fre quency ofdefaecation s ofa satiate d female Phytoseiulus resulted ina valu e ofth eegestio n constanttha t is 5%o fth e relative rate ofgu temptying .

82 Based onth e above,tentativ e reasoning,th erelativ e rateo f absorption (RRA)ca n be estimated from thebalanc ebetwee ningestio n andweigh t loss. Under conditions of abundant foodth egu twil l approach satiation,an dbe cause thegu tvolum e ismeasure d (Subsection 3.1.1), RRAca nb e fitted such that the rate of absorption compensates the weight loss occurring under these circumstances.Th eweigh tlos sdu et oeg gproductio n canb e estimated from thespecifi cweigh to fth ephytoseii d eggan dth emeasure d rateo fovi - position. As well, an approximation of theweigh tlos sdu et o respiration and-transpiratio nca nb eobtaine d fromth eweigh tdecrease smeasure d inth e starvationexperiment spresente d inSubsectio n 2.2.6.Th eestimatio no fth e relative rateo f absorption iscarrie d outwit h asimulatio nmode li nwhic h RRA isth eonl yunknow nparameter ,whil eth eoutpu tconsist s ofth erat eo f oviposition. The structure of the model is based on the principle that arthropods avoid gluttony, sotha tther ema yb e anoptima lbod yweigh tabov e

w ^s' IF ^-s. TERMINAL E s^ WEIGHT >/ OPTIMUM^^ OOCYTE I

Fig. 21. Flowdiagra m ofphytoseii d energyexpenditure ,relatin g ingestion tooviposition .

83 whichth e absorbed food isspen to neg g formation andbelo wwhic h iti s spent oncompensatio n ofweigh t loss due torespiratio n and transpiration. Because the terminal oocyte absorbs the major parto fth e lipoproteins andwater , egg production can be simulated by extrusion of the egg,i fth e specific weight of the phytoseiid egg is achieved. A flow diagram of this simple concept of the relationbetwee n ingestion andreproductio n ispresente d in Fig. 21;th eprogra m isliste d inAppendi xA .Wit h thismodel ,th erelativ e rate of absorptionca nb e fitted suchtha tth erat e ofovipositio n calculat ed by the model corresponds with thatmeasure d experimentally. Theexperi I mentalvalue s ofth e oviposition (Fig.22 )wer emeasure d atsevera ltemper atures ina colon ywit h abundantnumber s ofpre y eggs foryoun g femalepre datorso f Phytoseiulus persimilis and Metaseiulus occidentalis. Theoviposi tion data concerning Amblz/seius bibens and Amblx/seius potentillae wereob tained from Blommers (1976)an dRabbing e (1976). Theresult s arepresente d inTabl e 33.Thes e show that Metaseiulus occidentalis and Ambluseius bibens resemble Phutoseiulus persimilis greatlywit h respectt oth eestimate d val 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 Phutoseiulus persimilis itca nb econclude d thatth eRR A estimates obtained by the present curve fitting procedure correspond very closely with the estimates of RRGE (= RRA) obtained by adequate useo fth eelectrobalance . This correspondence may justify further use ofth eRR Avalue s obtained for theothe rphytoseii d speciesb y thecurv e fittingprocedure . Because these model estimations of RRA were obtained from reproduction

OVIPOSITIONRAT E (EGGS-DAY-1)

0 10 15 20 25 30 TEMPERATURE(° C) Fig. 22. Rate of oviposition of young females of fourphytoseii d species in relation to temperature (abundant food), o, Phutoseiulus persimilis (n= 32);• , Ambluseius bibens (Blommers, 1976); A, Metaseiulus occidenta lis (n= 25) ;+ , Ambluseius potentillae (Rabbinge, 1976).

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

Predator speciesTemperatur e (°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 Amblyseius 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 Amblyseius - 0.76 - 1.26 - 2.10 - - 1.52- potent illae Relative rateo f- 0.45 0.68 0.78 - 1.01 - - 1.46- colour decrease A. potentillae (Rabbinge,1976 ) Relative rateof ------10.44 - gutemptyin go f M. 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 luse sth eRR Avalu eesti mated atabundan t food supply andth erat e ofprédatio nmeasure da tsub - optimal levels offoo d supply,bu tth erat e ofovipositio ni scalculate d for lower food supply levelsfo rcompariso nwit hth emeasure d reproduction. Twocomparison sconcernin g Metaseiulus occidentalis and Amblyseius poten tillae arepresente d inTable s 34an d35 .Th eresult ssho wa 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 tmeasuremen t for Phytoseiulus persimilis. Inth esimulatio nmodel ,th etim erequire dfo r transport,synthesis ,utilizatio nan dallocatio no fth eabsorbe d gut-stores inth eacarin e body isno tconsidered , because itwa sassume d that each molecule absorbed wasmatche db ysimultaneou s utilizationo fanothe rmole cule.Thi s assumptionwa steste di ntw oexperiment s concerningth ereactio n of thereproductio n onsudde nchange si nfoo d supply.Th efirs texperimen t consistedo fth emeasuremen to fth enumerica l responseo f Metaseiulus occi dentalis tosudde n changes inpre y eggdensity , using twolevel so ffoo d supply, both giving rise tosom e level ofreproduction .Th emeasurement s carried outb yKüchlei n were compared with matching simulations basedo n

85 Table 34. Simulated and measured rates of oviposition for different food regimes for young females of Ambluseius potentillae. The relative rate of gut emptying is estimated by fitting its value in the model such to obtain an oviposition rate of 0.85 (or 2.26) eggs per day at an average level of 95% gut filling.

Temperature Coloration of the Measured rate of Simulated rate of (°C) the gut (expressed oviposition oviposition in colour units (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. Data from Rabbinge (1976). the functional response at the given prey densities (Table 36).Bot h model and experiment indicate the adjustment of the rate of oviposition to the new food level within one day. The initially larger reproduction rate after the change from high to low egg density will therefore be caused by the presence of the gut stores and by the eggs already developed near to ovipo sition. Similar but opposite reasons apply to the oviposition response after a change from low to high egg density. In another series of experi ments the above assumption was tested by measurement and simulation of the time required to resume egg production after different periods of food de privation. The results, presented in Table 37, demonstrate that the female predator has to recover from the deleterious effects of severe starvation (3 days food deprivation at T = 25°C) before egg production was restarted. A similar conclusion was drawn by Blommers (1977) for Amblyseius bibens. Therefore simulation on basis of the assumptions discussed above is only valid for shorter periods of starvation.

86 Table 35. Simulated andmeasure d rateso fovipositio n at differentpre y eggdensitie s foryoun g femaleso f Metaseiulus occidentalis.

Prey dens ity Measured rate of Simulated rateo f (eggs/cm2 )a 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.Dat a fromKüchlei n (personalcommunication) ;T = 25-27°C ; leafare a= 5 cm 2; dailyreplacemen to fegg sconsumed .Th e rateo fprédatio nwa sno tmeasure d inth e sameexperimen tbu t ina simila r experimentb yKüchlein ,presente d inTabl e57 .

Table 36. The oviposition response of Metaseiulus occidentalis to sudden changes inpre y eggdensity .

Female age (in days) Prey egg Measured rateo f Simulated rateo f starting 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 8 0.4 0.5 0.5 9 0.4 0.55 0.4 10 0.4 0.3 0.4 11 0.4 0.4 0.4 12 0.4 0.3 0.4 13 10.0 1.3 1.5 14 10.0 3.2 3.3 15 10.0 3.2 3.3 16 10.0 3.1 3.3 a.Unpublishe d data fromKüchlein ;T = 25-27°C ;lea fare a= 5 cm 2; dailyreplacemen to fth epre yegg s consumed. 87 Table 37. The time required for the production of the first egg after differentperiod s of fooddeprivation .T = 25°C ;hig h density ofpre y eggs.

Predator species Period of food Timerequire d forth eproductio n deprivation (days) ofth e firsteg g (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 6.0 occidentalis 1 15 9.4 7.9 3 30 18.6 10.9 6 15 27.2 11.7

Ambli/seius 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).

Comparison ofth edat a obtained onRRG E (orRRA )value swit h those given irSTliteratur e reveals many discrepancies. A closerexaminatio n isneeded , therefore, of the methods adopted by thedifferen t authors (Fransz,1974 ; Rabbinge, 1976). Fransz estimated RRGE by a fitting procedure related to the observed predatory behaviour, instead oft oth e conversion physiology. He simulated thepredator y activities ina par to fhi sbehavioura l observa tions using the relationsbetwee n the food contento fth egu t andth ebeha vioural components estimated from theothe rpar to fth eobservations ,select ing some starting value for the gutemptyin g constant.Thi sprocedur e was repeated until a value ofRRG Ewa s obtained thatenable dpredictio n ofth e behaviour inon epar to fth eobservation s onth ebasi s ofth ebehaviou rob served in the other part. Such aprocedur e doesnot ,however , guaranteea correctestimatio n ofRRGE ,becaus e therema yb emor e thanon esolution . Rabbinge applied amor e directmetho dbase d onth eprey-induce d gutcolo ration of Amblyseius potentillae, the colorationbein gvisibl e through its transparantbod ywall .Th e coloration isbrough t aboutb y carotenoids pres enti nth ehaemolymp ho fth e spidermite ;i ti scorrelate d with the rateo f prédation. Although Rabbinge introduced coloration merely as apredation -

88 correlated state variable, itma ygiv ea nestimat eo fth erelativ e rateo f gutemptyin g (RRGE).However ,i ti squestionabl ewhethe rth erat eo fabsorp tion ofothe r metabolically more important food elements, likeproteins , lipids and sugars,equa l to that ofth ecarotenoids .Anyway ,th eresult s obtainedb yRabbing e andFrans z (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 onth edevelopmenta l stageo fth epre y consumed.Becaus e 60-70%o fth eingeste d foodi sutilize d in theproductio n ofeg gmass , effects of food qualityma yb edetermine d from the rate of reproduction of aparticula r prey stage,i.e .i na pre y monoculture. However these kind ofexperiment s aredifficul tt ointerpre t when thepre y stages have no equal capture probability, which isdu et o prey-stage preference ofth epredato r orth eescapin g capacities ofth e prey stages. Inothe rwords ,eg gproductio nma yb elowere dmerel yb ya de crease inth e foodweigh tconsumed , insteado fprey-stag e foodquality .A s will be shown inSubsectio n 3.2.7, adult femalepre yru nmuc hles sris ka t being captured than anyothe rstage .Especiall y thispre y stagegive sris e to a lower rate of reproduction when offered abundantly inmonocultur e (Metaseiulus occidentalism. Croft &McMurtry ,1972 ;Croft ,1972 ;Pruszynsk i & Cone,1973 )( Phytoseiulus persimilis: Shehata,1973 ;Begljaro w& Hlopceva , 1965). Therefore,t oanalys ewhethe rth elo wrat eo freproductio ni sdu et o a lowrat e ofprédatio no rt onutritiv e quality,measurement so fprédatio n in monocultures ofpre y stages canb e supplied toth emode lpresente di n Appendix A and subsequently the reproduction ofth epredato rca nb esimu lated assuming that 1|j go ffoo d ingested froman ypre y stageha sth esam e nutritive quality as1 p geg gmass . Inthi swa yindication swer e found that spidermit e femalesa spre y giveris et oa lowe rrat eo freproductio nmainl y becausethe yar ecapture d lesseasil y andhenc econsume d less frequently. Another approach ist ocompar e reproduction ratesi nhig hdensit ymono cultures of different prey stages thathav ebee nmeasure d atsimila r rates ofprédation .Fo rexample . Croft& McMurtr y (1972)use d Metaseiulus occiden tales andmeasure d a rate ofprédatio n of about 10pre ype rda yfo rbot h egg monocultures andnymph-mal e cultures,whil e the appropriate rateso f reproductionha da rati oo f3:2 .Similarly ,Blommer s (1976)use d Amblyseius bibens andmeasure d corresponding rates ofprédatio n foregg s andmales , whileth ematchin g reproductionha da rati oo f4:3 .Pruszynsk i& Con e (1973) used Metaseiulus occidentalis andmeasure d a higher rate ofprédatio no n eggs then onnymphs .Howeve r the rateso freproductio nwer e equalo reve n higher incas eo fnymph s asfood . Of course, under more natural conditions ofpopulatio n growth theag e distribution ofth epre y mites will neverresembl eth eextrem eo fa mono -

89 culture of a specific agegrou p ofth emites .Althoug hth eproportion so f the different age groups inth epopulatio n arerathe r variable,ther ei s alwaysa mixtur eo fyoun g andol dstage sdu et oth econtinuou s reproductive effort ofth e adult females.Th e author's experiments indicate thateve n slight supplies ofegg st omonoculture s ofpreovipositiona l females resulted ina maxima l rateo freproduction ; additiono f1 0egg st o3 0postovipositio n femaleso na lea fdis co f5 cm 2 raised thereproductio n of Metaseiulus occidentalis from 2.7 eggs perda yt o3. 6 eggs perda y (n= 18, T = 27°C). Shehata (1973)foun d similar results for Phytoseiulus persimilis. Therefore food quality isno tconsidere d inth emodel s presented.

3.2 RATEO FSUCCESSFU L ENCOUNTER

In thepreviou s section (3.1), methods toquantif yth edynamic so fth e food contento fth egu twer ediscussed . Inthi s sectionth ebehavioura l com ponents, such aswalking , resting, attacking andfeeding ,ar edescribe di n relation to the food content ofth egut .Thes e components aremeasure d during continuous observations ofth epredator ybehaviou r andsubsequentl y related toth efoo d contento 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 h respectt oag e(3-1 0days) , feedinghistor y andadaptatio nt oth e experimental arena (6hours) . The computation ofth estat e dependentrat e ofsuccessfu l encounter isgive nb yth efollowin g formula forth etota l time spentpe rsuccessfu l encounter insearching ,handlin g andfeeding :

1 =F T X RSE + (RE-COIN-SR)

RSE =rat eo fsuccessfu l encounter (time ) FT =feedin g andhandlin g time (time) RE =rat eo fencounte r (time ) COIN= coincidenc e inth ewebbe d space (%) SR =succes s ratio (%) The rate ofencounte r of apredato r withit spre y isdetermine db yth e prey detection distance (Subsections 3.2.1an d3.2.3 )an dth ewalkin g speed ofbot hpredato r andpre y (Subsection 3.2.2). Assuming thatth ewalkin gdi rections ofth emite s aremutuall y independent, Skellam (1958)derive dth e following formula:

RE= 2- d •v •D prey where: D isth e symbol fordensit y (number/cm2)an dd fo rth edistanc eo f prey detection (cm);v (cm/time unit)i sth eresultan tvelocit y ofth espee d vectors ofpredato r andpre y andi ti sgive nby : 2 2 2 v=v +v .. -2-v -v ^, _ -cos6 prey predator prey predator

90 e representsth eangl ebetwee nth emomentar y directionso fpredato ran dprey . Takingexpectation sw eget :

^2 =^prey * ^predator' sinc{e cos 6 = ° Mori& Chan t (1966)sugges tth 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 attention ofth epredato r toactiv e prey. These hypotheses areteste di n Subsections3.2. 1an d3.2. 3b ycomparin gth eresult so fa nactua l experiment concerningth erat eo fencounte ran da 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 io fth ecircumference so fpre yan dpredator . Within apre y colony thephytoseii d predators display aver y tortuous walking pattern. Thisma yhav etw oconsequences .Th erat eo fencounte rma y be depressed byrevisitin g 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 will occur, provided thepredato r does nottur nwhe n arrivinga tth eedg e ofth ecolony .Th eanalysi so fbot hth e'recrossing 'phenomeno nan dth efac tors involved inth eresidenc e timei scarrie dou tb yobservatio nan dsimu lationo fth ewalkin gbehaviou r (Subsection3.2. 4an dSectio n3.4) . The rate ofencounte ri sals o determinedb yth ewalkin g activityo fth e mites (Subsection 3.2.5). Iti sdefine da sth epercentag eo fth eobservatio n time thatth emit e spendswalking .Assumin g thatth eactivit yo fbot hpreda toran dpre yi sindependen to fth emomentar y activityo fthei r neighbouring mites, therat e ofencounte r canb ecompute d byaddin git ssub-estimate s that pertain tothre e combinations ofpredato ran dpre y activity (walk- walk,wal k- rest ,res t- walk) :

2 (r + r 2 2 ^WW = - prey pred> 'V v preyvv+ vpre d ••act - prey •act pred

RREWR =2 -(rprey+ rpred} ' vpred '^'^prey * "aCt pred

RRERW =2-(r prey + rpred)• vprey •act prey •U-act pred)

RE = (RRE^+ RREwR + RRERW) •D prey

RRE =relativ e rateo fencounte r (RE/D ) prey r =radiu so fth ecircumferenc eo fa mit e(cm ) act =activit y (%) The formula ofSkella m presented here isrestricte d toth ecas e ofa homogeneous andtwo-dimensiona l surface. Itca nb eeasil y extended toa three-dimensional space, asi nth eweb . However thedistributio n ofth e mites andthei r walking behaviour inth eheterogeneou s webstructur ei s

91 such that theprobabilit y ofa visi ti sno tth esam e forever y locationi n the vertical plane ofth ewebbe d space.Therefor e thecoincidenc e inspac e (Subsection 3.2.6)i sintroduce d asa factor ,whic h accounts forth epheno menon that predator andpre y maypas s over andunde r eachother . Inthi s wayth epotentia l numbero fencounter s ona two-dimensiona l leaf surfacei s corrected toobtai nth enumbe ro frea l contacts inth ewebbing . Notal lencounter s resulti nprédation .Th egreate r andstronge r thepre y stage,th emor e difficult iti sfo rth epredato r tocaptur e theprey .More over, the motivational state ofth epredator , as indicated by the food contento fit sgut ,ma ydetermin e itschance s ofseizin gprey .Therefor eth e rate of encounter hast ob e multiplied by the success ratio (Subsection 3.2.7)t o obtain an estimate ofth erat eo fsuccessfu l encounter.Finall y the time spent handling andfeedin gth epre y after successful attack (Sub section 3.2.8)ha st ob esupplemente d toth 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 of apredator ymit e isno tfull y determinedb ytakin g the distance between the tips ofth elatera l forean dhin dprojection so f the mite. Iti s also related tobehaviou r that enlarges theare a covered (Fig.23) .I nthi s respecttw obehavioura l components canb edistinguished :

WIDTHO F WIDTH OF THEBOD Y THE SEARCHING PATH

• 1 t mm -i i \ Yf

Jk- — 1 -- - 1 —1—1—1—1—I—I—r-

Fig. 23. Width ofth e searching path determined by body and frontleg - movements of aphytoseii d predator.A ,tars i ofleg s2 ,3 an d4 ;A ,tarsu s of leg1 ; arrows indicate leg-movement; straight line represents position ofbody-axis .Eigh t successivephase so fforwar d locomotion aregiven .

92 first,th efrequen tturnin go fth ebod y fromon esid et oth eother ;second , a superimposed fast ambushing with the front legs, resembling theus eo f antennae inhyménopterou sparasiti cwasps .T omeasur ethes e actionssepara tely avide o equipment (camera,recorde r andmonitor) , connectedt oa bino cular microscope,wa sused , thus offering the facility to fixth emovin g image. Theobservation s indicated thata nincreas eo fth ewalkin g speed results ina decreas eo fth elatera l reacho fth epredator y female.Whe nth epreda tori sdisturbe db ysomethin gth ewalkin g speedi srelativel yhig h (Subsec tion 3.2.2)an dth e lateral reach almost equals thebreadt ho fa restin g mite. Ina stateo fcomplet eres tth efron tleg sar edraw nu pclos et oit s mouthparts, which causes thelengt ht ob eequa lt oth elengt ho fth esoma . Spidermites ,wit hthei rrigi d shufflingwa yo fwalking ,d ono tsho wan yo f thesecharacteristics . The measurements ofth e lateral anddista l reacho fundisturbe d female predators indifferen t stateso factivit y arepresente d inTabl e38 .Thos e of the spider mites are given inTabl e 39,relate d to the developmental stage. Itma yb econclude d thatexcep t forth erestin g stateo fth epreda tors, thebreadt h ofth emite s isver ynea rt othei r length,s otha ti ti s notunrealisti c forsimulatio npurpose st oconceiv emite sa scircula runit s witha diamete requa lt ohal fth esu mo fth erea l lengthan dbreadth .Thes e measurements will beuse d incalculation s with Skellam's formula forth e rate of encounter, forwhic h the distanceo fpre ydetectio ni sassume dt o be equalt oth esu mo fth eradi io fpredato r andpre y (Subsection 3.2.3).

Table 38. The lateral reach andth edista l lengtho fth efemale so ffou r phytoseiid species (n= 20).

Predator State Length (mm) Breadth (mm) Diameter (mm) species M â M ô (length+ breadth)/ 2

Phytoseiulus walking 0.98 0.147 0.84 0.068 0.91 persimilis resting 0.71 0.040 0.42 0.020 0.565

Amblyseius walking 0.81 0.038 0.71 0.040 0.76 potentillae resting 0.69 0.034 0.43 0.027 0.56

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

Metaseiulus walking 0.62 0.033 0.52 0.018 0.57 occidentalis resting 0.62 0.031 0.27 0.028 0.445

93 Table 39. Length andbreadt h ofth e developmental stages of 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 deutonymph9 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 d asth e displacement along thetrac k peruni to ftime .Thes ewalkin g trackswer e registered withth evide oequip ment shown inFig .24 .Thi s experimental setu pprovide d analmos tperpen dicular projection ofth epath s witha magnificatio n ofabou t8 times .Al thoughth eexperimenta l leaveswer e selected onthei r flatness,th ewalkin g tracks near toth eedg eo fth elea fwer e incorrectly projected onth escree n due t<->th e curvation ofth e leaf and therefore discarded.T opreven tan y possible orientation by themite so na surroundin g unequal lightdistribu tion, the experimental leaf was enclosed in an 'opal' Perspex cylinder, which diffused the lateral incoming light.Th eligh tdistributio nwa smea suredwit h aseleniu m unitconnecte d toa nampère-meter .Th eradiatio n flux variedbetwee n2 an d2. 3Wat tpe rm 2 nearth eleaf . The walking time wasmeasure d simultaneously bymean s ofa sto pwatch ; each 10 second periodwa smarke do nth edrawing s ofth ewalkin gpaths .Th e walking activity ofth emite s was frequently interruptedb yshor to rlon g stops. Those stops that lasted less than1 secon d couldno tb eseparate db y observers from thewalking-tim eregistratio n duet olag s inreactio ntime . From these measurements ofwalkin g timean ddisplacement ,th emea nwalkin g speed was computed. Anattemp twa sals omad et ocharacteriz e thevariatio n in walking speed by computing thevarianc e ofth evelocitie s inth earbi trary 10-secondperiods . Thewalkin gvelocit ywa sstudie d inrelatio n toth eperio d offoo ddepri vation, temperature,webbin g andth esid eo fth eleaf .T ostud y theserela tions itwa sver y importantt odistinguis hbetwee n edge-oriented walksan d walking paths on thelea fsurface .Th eedge-oriente d walkingbecome s appa rentb yintensiv e inspectiono fleaf-edge-relate d structures andth eregula r

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97 return of the mite towards the leafedg e after loosing contactwit h it.A fewtime s themite s lostcontac twit h the edge and didno treturn .O n those occasions they were swaying to and fro;t oth e author they appeared tob e disoriented. Only the walking paths on the leaf surface, i.e. notedge - oriented, are used inth etreatmen t ofwalkin gvelocity .Th e edge-oriented walkwil lb e discussed inrelatio n toth e time spent outside thepre yaggre gations (Part2) . Thewalkin gbehaviou r canb e strongly influenced by experimentalmanipu lation.Fo r example,disturbance s canb e observed after thepredator y might aredisplace d by abrush .T o illustrate theeffec t onth ewalkin g speed some measurements were made of the walking behaviour of disturbed predators; these aregive n inTabl e40 .Disturbanc e diminishes within twohours .There foreth ebehavioura l observations ofpredator s wereuse d only after arest ing period of some length (> 5min.) , sotha tth epredato r started walking spontaneously. The effecto fth e starvationperio d onth ewalkin g speed ofth epredator s isprobabl y rather complicated (Table 40). When starved fortw o consecutive periods of awhol e day, the walking speed of all fourphytoseii d species studied increased by less than 30%.However , when Amblyseius bibens was starved for periods of less than 1 day, the walking speed initially in creased, subsequently followed by a decrease. The latter effect was also measured by Sandness &McMurtr y (1972)fo r Amblyseius largoensis. Küchlein (tob epublished )foun d indirectevidenc e fora nincreas e inwalkin gveloc ity/activity for the case of Metaseiulus occidentalis atlo wdensitie s of thepre y (from3 egg spe r 5cm 2 to 1eg gpe r 10 cm2). The effect of temperature on the displacement of femalephytoseiid s (= observation time x walking speed x fraction of theobservatio n time spent walking)wa s studied byEverso n (1979)an dPenma n &Chapma n (1980). Everson concluded, that the displacement of Phytoseiulus persimilis was notinflu enced by temperature on both a glass substrate and abea n leaf.Penma n & Chapman obtained similar evidence for Metaseiulus occidentalis inth e range of 15-30°C (relative humidity = 75%), butbelo w 15°Cdisplacemen twa sclear ly decreased. This result was also obtainedb y these authors for thecas e of Tetranychus urticae. The results ofth epresen t study (Table40 )indicat e a small orn o increase ofth ewalkin g speed ofth epredator s at temperatures increasing from 15°C to30°C .Accordin g toPenma n& Chapman (1980)th ehumi dity level is ofmino r importance forth edisplacemen t of females of Meta seiulus occidentalis and Tetranychus urticae. Although temperature did exert some influence onth ewalkin gvelocit y of the predators, its effect was minor compared totha to fth e structure and position ofth e substrate.Th ewalkin g speed ofth e fourphytoseii d species studied was reduced to 15-30% as a consequence of their position on the downward-facing side ofth e leaf.Turnin g experiments with the experimental leaf showed that this resultwa s notcause d by the texture differencesbe -

98 Fig. 25. A.Bac kvie wo fa femal epredato r (Amblyseius potentillae) resting nextt oa lea fmid-ri b (magnification:9 0 x). B.Detai lo fth etarsu so f thehmdle g (magnification:600 0x )snow n inA .Notic eth epositio no fth e claws andth eswab-lik eempodiu man dcompar ewit hth epositio no fth ecla w remnantsan dth eempodia lhair so fth espide rmites ,show ni nFigur e2 6

99 tweenth euppe r and lower cuticle,bu tprobabl yb y gravitational force.Thi s phenomenonma yb e related toth e adhesive properties 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 of thedownward-facin g side ofth eros e leaf.Th ewalkin g speed ofth e spidermite swa sno tinflu encedb y thepositio n ofth e leaf,possibl ybecaus e they arealway s attached toth e leaf,a swe b threads arecontinuousl y produced duringwalkin g (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 afterthi smanipulation . Both spidermite s andpredator ymite swalke dmor e slowly ina webbe den vironment (Tables4 0 and41 )i fcompare dwit h theirwalkin gvelocit y onth e upward-facing side ofth e rose leaf.Eve n aver y lowwebbin g density caused the predatory mites to slowdown .Th ewe b structureswer e inspected inten sively with their front legs. Once apassag e through these structures was detected a forward movement was made. Presumably the long dorsal setae pointing backwards on the pear shaped phytoseiid body serve as awedg e in the sticky web during forward locomotion. Sandness & McMurtry (1972)re ported that the stickiness and thephysica l presence of several strands of webbing impeded theprogres s of Amblyseius largoensis. Inth epresen t study itwa s observed afe wtime s that females of Amblyseius potentillae stuckt o thewe bwit h their dorsal plate.A n explanation forthi s factcoul db e found in the absence of long setae onth e dorsum of Amblyseius potentillae, the longer setae being positioned near the edge ofth edorsa lplate . Itma yb e worthwhile toreconside r acarinepredator-pre y relations from thispoin to f view. When mites are in the webbing the influence of gravity can bene glected. Likewise,th e effecto ftemperatur e onth ewalkin gvelocit ywa s not significant formite s moving inth ewebbing . Surprisingly the same ruleap plies toth e interspecific differences.Thi s implies thatth ewalkin gveloc ity isno tresponsibl e for any interspecific difference inth e intra-colony rate ofprédation ,bu t itma yb e relevant inth e specific capacity ofinter - colony dispersal (Part2) .

3. 2. 3 Distance of prey detection

As stated byMor i &Chan t (1966), initial contacto f Phytoseiulus persimilis with its prey appears tob ematte r ofchance .Th epre ymite s areap parently first detected by contact with the anterior tarsi of the front legs, which are extended in front ofth ebody .Afte r contactth epredato r usually moves closer toth epre y andpalpate s itwit h itspedipalp s before penetrating the mite's soma. On the basis ofbehavioura l observations and scanning electronmicrograph s ofth e setaeo nth epedipalp s andth e anterior tarsi of legs IJackso n (1973,1974 )suggest s thatmechanoreceptio nan dcon -

100 Fig. 26. Tarsuso fa mal eo f Tetranychus urticae (magnification:600 0 x). Noticeth epositio no fth eempodia lhair s on thewebbin g strandan dth e positiono fth efou rcla wremnant s (tetpaovuxoi ,fou rfingers ) aside of thisstrand .

101 M O

Si T3 4-> IT) 01 O o > u tu o 0> Is MH M 3 10 •H 0) U Si U o 3 0) IS) Oi •q •o O o fi c 3i 3 •H « 11 P £1 is .fi •p Ü1 o D \ rd Es 11

MH 0) O •a Oi en -H W U! IV fi fi 0> Si 0) (0 Si ft 4-> 0) ft 01 s 3

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102 tact chemoreception isinvolve da tbot htarsa lan dpalpa l contactwit hth e prey. However webma yinterfer e with searchingb yprovidin ga warnin g signal to thepre y orb ydrawin g theattentio n ofth epredato r toactiv eprey . Thereforea distinc tvalidatio no fSkellam' smode li sneeded .T oaccomplis h this, estimates ofth erat eo fencounte rwer e comparedwit hth eresult so f anexperimen twher eth eencounter sbetwee npredato ran dpre ywer e scoredo n a time scale.Hungr y predators (0.5day s food deprivation,T = 20°C )wer e used toensur e reaction toth epresenc e ofprey , ifany .Th eexperiment s weremad ei nth epresenc ean dabsenc eo fweb .Th eeffec to fth emobilit yo f thepre ywa sals o investigated, usingegg san dfemale so f Tetranychus urti-

Table 42. Measured andsimulate d rateso fencounte rbetwee n female phytoseiid predatorsan da mobil e (female)o rimmobil e (egg)stag eo f Tetranychus urticae in absenceo rpresenc eo fwebbing .

Predator Prey stage Webbing Rateo fencounte r (number/min) Total and density observation species simulated measured time (min)

Phytoseiulus 4 eggs absent 3.26 3.35 32 persimilis per cm2 Amblyseius 36egg s absent 16.3 18.9 21 potentillae per cm2 2 eggs absent 0.91 1.08 96 percm 2 0.25 eggs absent 0.12 0.14 160 percm 2 Netaseiulus 4 egss absent 1.13 1.10 86 occidentalis per cm2

Phytoseiulus 4 egss present 0.47 0.57 222 persimilis percm 2 Amblyseius 4 eggs present 0.32 0.36 245 potentillae percm 2 Metaseiulus 4 eggs present 0.30 0.34 250 occidentalis percm 2

Phytoseiulus 109 a present 1.76 1.73 92 persimilis percm 2 Amblyseius 109 a present 1.37 1.24 110 potentillae percm 2 Metaseiulus 109 a present 1.34 1.25 82 occidentalis percm 2

a.Th ewalkin g activityo fth efemal e spidermit e= 4% .

103 cae as prey. The activity of the female spidermit ewa s registered andac counted for in the calculation ofth erat e ofencounter .Th e femalepreda tors, however, were only observed when they were active. Care was taken that the mites were accustomed to theexperimenta l leaf,whic hwa splace d onwe tcotto nwoo l tokee p the leaf fresh andpreven tth emite s from leaving the leaf surface.Th e arenawa smarke d by asquar e onth eocula ro f abino cularmicroscope . Itwa s smaller thanth e rose leaft o avoid anyedg eeffect . Therein the eggs (immobile category)wer e spread equidistantly. Inthi swa y unnecessary variation in theresult s asa consequenc e ofth e casualoccur rence of clusters of eggs were prevented. For themobil e femalepre y this was obviously notpossible .Th eprojectio n ofth e ocular squareo n the leaf surface resulted in animaginar y arena of4 cm 2. A femalepredato rwa sal lowed to traverse this arena and the number of contacts during the time spent in the arenawer e scored.O n awebbe d substrate encounters were also scored when the projections of prey and predator on the horizontal leaf plane overlapped. The mean rate of encounter was calculated asth etota l number ofencounter s scored dividedb yth e cumulative time spentwalkin g in thearena . In Table 42 themeasure d rates ofencounte r aregive ntogethe rwit hth e estimates according toSkellam' s formula.Fro m theseresult s itca nb econ cluded that the contribution ofolfactio n orwe b (=th edifferenc e between the measured and the calculated rate)wa s always less than 20%o fth e cal culated rate.Fo regg s asprey , alldifference s between simulation andmea surement disappear when thediamete r ofth e simulated egg isdoubled . This suggests that the eggs arescente d fromnea rby . Incas eth epre y isa mo bile female, the measured rate turns out to be consistently smaller than the calculated rate. An explanation for this small but consistentdiffe rence may be found in the warning action of web vibrations causedb yth e predator. The overall conclusion istha t the influence ofolfactor y orothe rstimu liemergin g from thewe b is low, sotha t iti s allowed tous e the formula of Skellam for the calculation ofth erat eo fencounter .Thi smean s thatpre datorypreferenc e for apre y stage orth eescapin g capacity ofth epre yma y forcomputationa l purposesb e considered to arise atth emomen t ofcontact .

3.2.4 Walking pattern

The walking pattern of the predator affects the rate ofencounte rwit h prey intw oways . Inth e firstplac e itdetermine s the time spent ina pre y colony.Whe nth eedg e ofth ecolon y doesno t influence thewalkin g behaviour of the predator, a straight path causes the residence time tob eminima l and thedistanc ebetwee n starting andmomentar ypositio n (=linea rdisplace ment) to be maximal. The more tortuous thewalkin gbehaviour ,th e smaller the linear displacement and thus the longer theresidenc e time ofth epre -

104 dator ina pre y colony.O fcourse ,th etransitio no fcolonize d leafsurfac e to uncolonized parts ofth eplan tma yinduc e theretur no fa predato r when itarrive s atthi sedge .However , such amechanis m hasno tbee nreporte d so farwit h respectt oPhytoseiidae . Inth e secondplace ,a ver y tortuouswalkin gpatter nma ycaus e adepres siono fth erat eo fencounte r ifth epredato r devours thepre y itemsencoun tered; the predator may stay too longo na spo tpreviousl y occupiedb yde voured prey. Predatory mites walk tortuously when searching in webbing (Fig. 27).Therefore , the walking paths being available fromth emeasure ments ofth ewalkin gvelocit y (Subsection 3.2.2), itwa sworthwhil e toana lyse the effect ofth ewalkin gpatter n onth e residencetim eo fa predato r in a prey colony and on the rate of encounterbetwee npredato r andprey . For thispurpos e asimulatio nmode l ofth ewalkin gbehaviou rwa s constructed. Thewalkin gbehaviou r ofa nindividua l animal canb e simulated asfollows . Each time interval,whic h isequa l toth equotien to fste p sizean dwalkin g velocity, the animal makes a forward movement with a change indirectio n over a fixed distance. This angular deviation is chosen atrando m froma distribution of changes in walking direction (-n,+71 )obtaine d from the walking paths registered on video equipment. These angular deviations 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 the frequency distribution strongly depends on themagnitud eo fth estep . 'Advancing with seven-league boots' thedistributio n tends toth eGaussia n

FINISH

•-£*-,

Fig. 27. Walking patho fa femal epredato r (Phytoseiulus persimilis) ona webbed leafarea .

105 Fig 28. Determination of three consecutive angular deviations (A s-2' A ,,A )afte rpacin g linear distances of fixed length. or uniform-type, while for asmal l step the tendency istoward s aStudent - type distribution.T o justify comparison ofdifferen t distributions measured and to fulfill the requirements of anaccurat e description ofth ewalkin g paths, a step size is selected ofhal fth e average length ofth emite s (= 0.04 cm), which corresponds to about2 time s the step length of adultmites . Correlationbetwee n successive changes inwalkin g direction canb e accounted forb y anaut o regressionmodel :

al-As-l + a2'As-2 + + a -A + X m s-m s A =directiona l change atste pnumbe rs X =rando m process toobtai n angular deviations from a frequency distribution, corrected for autocorrelations a....a = autoregressioncoefficients m =orde r ofth eproces s The first-order auto regressive process isthen :

A s= a -s-,- A1 s-.,+ X1 s

Theprocedure s toobtai n andt o interpret thevalue s ofth e auto correlation coefficients, to calculate the auto regression coefficients from theaut o correlation coefficients, and finally todetermin e the order ofth eproces s areexplaine d inAppendi xB . For comprehensive representation of theresult s iti susefu l to describe the frequency distributions by their moments. However, the Gaussian and Student-type distributions proved to be inadequate due toth eprobabilit y 'mass' located inth etail s ofth emeasure d distributions.Th eTuke ydistri -

106 bution was chosen duet oit s flexibility inthi srespect .Th emathematica l formo fthi s inverse,symmetric ,continuou s andcumulativ e distributionis :

Xsc = M + CT-Y^ p (pA - (l-p)X)A A* 0 YP = ln(p/(l-p)) A =0 (j =mea n angular deviation a =scal eparamete r A. =kurtosis-relate dparamete r p =cumulativ e frequency ofangula r deviations The flexibility ofthi s three-parameter distribution findsexpressio ni n the fact that the kurtosis related value of A causesth edistributio nt o approximate the shape of somewel l knowndistributions : A = 1 uniform A = 0.14 normal A= 0 logistic A =-0.8 5 Student's t.o rCauch y The maximum likelihood procedure for the estimationo f \i, a andA ,plu sa testo ngoodnes s of fit,ar e giveni nAppendi x C. The simulation process isa s follows.A change inwalkin g direction (in radians), X ,i scompute d fora rando mp valu e (0< p 4 1)draw n from auni form distribution. This change in direction is subsequently added toth e actual direction, and from the cosine and the sine ofthi sne wdirectio n the new x andy position s areobtained ,takin gth este p size asth e length ofth ehypotenuse . InFig .2 9th erelatio nbetwee nth e shapeo fth edistri bution and its matchingwalkin gpat h arevisualized . These simulationsde monstrate the influence ofth e scale andtai l lengtho fth e frequency dis tribution onth e simulated walkingpath . Comparable simulation approaches canb e found inSinif f& Jesse n (1969), Kitching (1971), Cody (1971, 1974), Jones (1977, 1978), Pyke (1978),Yan o (1978), Sirota (1978), Inoue (1978), Waddington (1979) and Baars (1979). Some of these authors have based their frequency distributions on angular deviations aftervariabl e timeperiods ,whic hmake s comparisono fdifferen t distributions essentially impossible.Othe r authorsuse d angular deviations after fixed timeperiods ,s otha tthei rconclusion spertai n tobot hwalkin g velocity and pattern. Pyke (1978) and Jones (1978)note d thepossibilit y that an arthropod has some limited memory concerning thedirectio no fth e immediately previous movement.The y didno tpresen ta mode l ofthi spartic ularaspect . Thewalkin g tracks registeredb ymean s ofth e setu pdiscusse d inSubsec tion3.2.2 ,wer euse d forth emeasuremen t ofth e frequency distributions of angular deviations. In principle this was done by proceeding along the

107 P(%) 50 < 60 - -\2^v A="Ö"Ï4 ' 70 - o^në '

LX <^>^ iv -<£>

98 - 99 - .. 99.5 - — 1

99.9 - — 99.95 - — ._.. - i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 : ANGLE DEVIATION (RA D

X = 0.U a=0.8 X=0.U CT=0. 2

UNIT=DISPLACEMEN TAFTE R 25STEP S

Fig. 29. Relation between the shape of the frequency distribution of angular deviations and the actual walking path. Two differently scaled Gaussian distributions and another distribution with a longer tail are plotted on probability paper of the Gaussian distribution. The matching simulations of walking paths are shown below and the computerprogra m is listed inAppendi x D.

108 trackwit h fixed linear stepsan db y subsequentdeterminatio no fth e angular deviation between successive directions (Fig.28) .A tth een do feac hpat h the collected angles were ordered into afrequenc y distribution(-n , +n). This procedure and the subsequentestimatio no fth eTuke yparameters ,aut o regression and correlation coefficients,plu s afina ltes to nth e goodness of fit,wer e executed with the aid of a computerprogra m constructed for this purpose (Ruardij, 1981). The paths canb e supplied toth eprogra m in the form of aserie s ofx, y coordinatesvi a anx- y tabletconnecte d toth e computer.Th edistance s between thosecoordinate s are inevitably subjectt o irregularities due to human inaccuracy. Therefore aninterpolatio nmetho d (Spline or Aitken-Lagrange)operate s inth eprogra m toobtai na continuou s walking path along which the fixed step sizeca nb epaced .Overshoo tprob lems with the interpolation atshar p turns inth ewalkin gpath s are solved initially by interpolation over smaller parts of the walking track and ultimately by simple linear interpolation. The program was tested in a serieso fexperiment s with straightan d circularwalkin gpaths . The walking tracks analyzed in this paragraph originate from solitary mites, walking on explicitly defined substrates. Ifth eeffec to fcontac t betweenpredato r andpre ywa s studied, thiswa s accomplishedb yputtin g the prey close to apredato r and subsequently removing itafte rth e occurrence ofth edesire d action.T oobtai n awebbe d areawithou t anyprey ,bot hmale s andpreovipositiona l femaleswer epu to na fres hleaf , fromwhic h theywer e discarded after about 2day st opreven teg gdeposition .Th eresult s ofth e analysis ofthes ewalkin gpath s arepresente d inTable s4 3 and44 .T oge ta better estimationo fth ecorrelatio nbetwee n successive angulardeviations , only the longest walking paths were used. Inmos tcase s the autocorrela tions showed a low level of correlation, if any. Whensignifican tvalue s occurred( \a^\ > 2/VN; N =tota lnumbe r of steps), thesenormall y indicated a first-order auto regressive process.Th e irregular pattern of positive and negative values also supports the conclusion, that the mites do not show an autocorrelated walk.Th eevaluatio no fth edifferen ttreatment s is facilitated by tabulating the lineardisplacemen t after20 0ste punit snex t toth evalue s ofth eTuke yparameter s and the autocorrelations .Fro m these displacements it can be concluded thatth eeffec to fth estarvatio nperio d is rather small, eveni ncombinatio nwit hpreviou s contactwit hprey .How ever, the substrate appeared tob ever y important,a swa s alsoth ecas e for thewalkin gvelocity .Th etortuosit y ofth ewalkin gpath s inth ewebbin gi s expressed by an increase in the value of the scaleparamete ra ,whic hi n turncause s thedecreas e inth eestimate d lineardisplacement .Th epositio n of the predator on the upper orundersid e ofth e leafdoe sno taffec tth e walking pattern, althoughth ewalkin g speedwa s severely reduced onth e side facingdownward . Consequently three regionsca nb e distinguished onth e leaf withrespec tt oth ewalkin g speed andth ewalkin gpattern : - the upperside of theleaf ,th emid-ri b onth eundersid e ofth e leafan d [

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MEANLINEA RDISPLACEMEN T

»=0 H

X= -0. 1

X=-0.85

1000 NUMBERO FSTEP S Fig. 30. Mean linear displacement, expressed in step units, inrelatio n toth enumbe r of stepsmove d atdifferen t levels ofA .( a= 0.2) .

112 MEAN LINEAR DISPLACEMENT 200- 180- 160- K0 120

100

80-

60-

i.0

—I 1 1 1 1 1 1 1 0 0.1 0.2 0.3 QÂ 0.5 0.6 0.7 0.8 0"(RAD ) Fig. 31. Mean linear displacement after 200 steps, expressed in step units, inrelatio nt oth escal eparamete ra atdifferen t levels ofth eshap e parameter A.

cients, threegraph s aregive nbase do nth emea nvalue s ofa serie s of100 0 Monte Carlo simulations. Ineac h graphth emea nchang e inwalkin g direction is chosen to bezer o and thevalue s ofA ar ethos eo fth e approximate uni form (A = 1),norma l (A= 0.14 ) and Student (A.= -0.85)distribution ,sup plied with one realistic intermediate (A = 0.1).I nth e firstgrap h (Fig. 30) the number ofstep s takenb y theanima l arevarie d ata constan tleve l of the scale parameter. The relation between the linear displacementan d the distance walked appears to be non-linear.Thi s resulti sexplaine d on basis ofth eprobabilit y toretur nt oth eorigina lposition .Afte r oneste p this probability is ofcours eequa l tozero .Eac h successive stepwil lin crease theprobabilit y ofreturn ,dependin g onth etortuosit y ofth ewalkin g pattern. However, by moving away from the original starting position the possible returningpath sbecom emor e andmor e complex andthu s lessprobable . Inothe rwords ,th eprobabilit y of leaving acircula r environment decreases with enlargement of the circle. With respectt oth eothe rgraph s onlyth e linear displacement after 200 steps is given. The second graph (Fig.31 ) shows an exponential increase of the linear displacement with decreasing values ofth escal eparameter . Seemingly smallvariation s inth e scalepara meter canthu shav ever y importantconsequence s forth e lineardisplacement . The third graph (Fig.32 )show s theeffec to fpositiv e andnegativ evalue s ofth e first-order autoregressio n coefficient.Negativ e correlations cause subsequent correction of sharp turns in the walking pattern by amor eo r lessopposit e turn.A s canb e seen fromth egraph s thiseffec t substantially

113 MEANLINEA RDISPLACEMEN T 200-1

-075

Fig. 32. Mean linear displacement, expressed inste punits ,i nrelatio nt o the firfirst-orde: r auto regression coefficient a. atdifferen t levels ofA (a =0.2) .

promotes the linear displacement.Positiv e correlations,however , intensify the turnings instead of correcting them, thus causing a decrease of the linear displacement.Fro m these simulations itca nb e concluded, thatwithi n the range of measured parameter values (-0.4 < A < 0.14; 0.1 < a <0.6 ; -0.2 < a < 0.2) the value ofth e scaleparamete r ismos tdecisiv e forth e linear displacement, subsequently followed by the shape parameter, while the autoregression coefficients areo fmino r importance. The abovemetho d to simulate thewalkin gbehaviou r ofa nindividua l ani mal can be extended for the case oftw o ormor e animals encountering each other. Then the animals are represented by circles and each time stepi s considered to be equal to the quotient of the step size and thewalkin g velocity of the fastest animal. For each time step the positions of the circles are traced and new encounters registered if the distance between thecentre s ofth e circles issmalle r thanhal fth e sum ofthei rdiameters . Such amode l is listed in AppendixD forth e simple case of immobilepre y and equidistant distributions ofth epre y items.Thi smode l isuse d toexa mine theeffec to ta tortuou s path onth e rate ofencounter . Imagine anare a so large that even a straight path ofth epredato r starting atth ecentr e does not result ina confrontatio nwit h theedge .Th epre y eggs are spread equidistantly and every eggcrosse d by thewalkin gpat ho fth epredato r is removed. Because of the large area thenumbe r ofeg g removalswil lhardl y affectth evalu e ofth eoveral l prey density.A tortuouspat hb y thepreda -

114 torma ygiv erise ,however ,t oa frequentrecrossin g ofa sub-are aprevious ly freed of prey, so that apredictio n of therat eo fencounte rwit hth e aido fSkellam' s formularesult s ina noverestimatio n duet o its dependency on the overall prey density.O n awebbe d substratepredator ymite s exhibit a tortuous walk, independent of the presence of prey (Subsection 3.4.1). Therefore a simulation experimentwa s donea ta pre ydensit y of4 eggs/cm2 over a 1000 stepwalkin g track.Th e simulatedmea nrat eo fencounte r after 100 replicates appeared to be equal to 81%o f theSkellam' sestimate .O f course,apar to fth eegg s and themoultin g stages,th emobilit y ofth eothe r prey stages lower the probability on local depressions in theirdensity . Simulations for the caseo fmobil e larvae resulted ina nestimat e equalt o 94%o fth eSkellam' s estimate,s otha tth eeffec to f atortuou swal ko nth e rateo fencounte r ina pre y colonyma yb econsidere d tob ever ysmall .

3.2.5 Walking activity

Thewalkin g activity ofth epredato r refers toth e fractiono fth eobser vation timeth e animal spendswalking .Th ewalkin g andrestin gperiod swer e measuredpartl ywit hth e aido fth evideo-equipmen t described in Subsection 3.2.2, andpartl ywit h theai d ofa binocula rmicroscope .Durin g theconti nuous observations the start and end ofth ewalkin gperiod swer e recorded on a time scale.Th e activity isno tcompute d asth e quotiento fth e total walking period and the observation time sinceonc e amit e startswalking , walking during the next time unit is very probable. Therefore to reduce these correlations, the activity is conceived asa Bernouill ivariabl e (0 or 1) the value ofwhic h isdetermine d atrando mmoment s duringth eobser vations within the desired limits ofth erelativ e foodconten to fth egut . The number of determinations ofth eBernouill ivariabl eneede d to attaina specified accuracy at the 5%level ,wer ecalculate d withth ebinomia l sam pling formula (a =0.05 ;d = 0.0 4 x \/min(p,q)';Pr(|p-P| > d)= a ) . There sults arepresente d inTabl e45 . The existence of interspecific differences inth e level ofactivit ybe come clear by comparison of the activity levelsunde rwebbe d andunwebbe d circumstances.Th e activity of Phytoseiulus persimilis decreases duet oth e factor web, almost irrespective of the presence ofprey . Incontrast ,th e activity of Metaseiulus occidentalis seems to beunaffecte d byth e factor web andth e same applies to Amblyseius bibens, butthi s species issignifi cantly less active forabundan tpre y supply inth ewebbin g (Blommers, 1977). According toth eobservation s ofth ewalkin gbehaviou r of Amblyseius potentillae itpreferre d thethickes tpart s ofth erib so r similarplace s onth e stems as arestin gplace .Eve nwhe nthe ywer epresen t ina webbe d area,thi s typeo fpreferenc ewa s observed. Itsactivit y inth ewe b seemst ob e rather low, butthi s iscause db y the facttha tonl ywalkin g activities leadingt o displacementwer e scored. Itwa s frequently observed thatalthoug hthi sspe -

115 Table 45. Theactivit y levels of Tetranychus urticae andfemale so ffou r phytoseiid speciesi nrelatio nt oth esubstrat ean dth etim eperio do ffoo d deprivation.Ow nobservation s madea tT = 20° Can dR H= 60-80%.

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

leafwit h lleae fwithou t artificial webbing we tig substrates

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

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

Metaseiulus 0 (+ prey) 36 39 52 occidentalis 48 43 - 120 41 -

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

Tetranychus urticae females 4 - 72 males 5 - 65-80h juveni les 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.Küchlei n (tob epublished) ; T= 27° Can dR H= 70%. d. Fransz (1974);T = 27° Can dR H= 70%. e. Blommers (1977);T = 28° Can dR H= 70%.

116 cies moved actively inth ewebbing ,n oeffectiv edisplacemen twa smade .O n rareoccasion s thepredato r evenbecam e stuck inth ewebbin gwit h itsdorsum , presumably due to a lack of longdorsa l setae inth ecentr eo fit sdorsa l plate. Under circumstances ofabundan t foodth espide rmite s aremuc h less active in the webbing than any predator species studied.Thi s isprobabl y due to their predominant feeding activities. When the food sourcebecam e exhausted, theactivit yo fal lstage sincreased , leadingt oa stee p increase ofth ewebbin gdensit y asmeasure d inSubsectio n2.1.6 . The walking activity of the predators was unaffected after starvation periods of more 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. Hungry females of all phytoseiid species were very sensitive to contact.Whe na female spider mite was used to bump against the back of the predatorsa drastic increase of the activity occurred duringth e subsequenttw ohours . Satiated femaleswer e almostunaffecte db y theseactions .Fro m theseobser vations itca nb e concluded thatth erelationshi p between thehunge r status[ j andth eactivit y isindirectl y expressed bywa yo fdisturbance . t| As found forth ewalkin g speed (Subsection 2.2.2), theeffec to fth etem perature onth ewalkin g activity ofth epredator s iso flittl e orn oimpor tance, especially when the predators are studied in the webbed areao fa prey colony (Table 46).Spide r mites,however , are probably activatedb y increasing temperatures.Thi s canb e derived fromth e facttha tth erat eo f web production (Subsection 2.1.6)i s increased by increasingtemperature , incontras tt oth ewalkin g speed,whic h isonl y little affected inth erang e of15-30° C (Penman& Chapman ,1980 ;ow nobservation) . Mori & Chant (1966)studie d the effect of humidity onth e activity of femaleso f Phytoseiulus persimilis ando f Tetranychus urticae. Theactivit y of both prey and predator was reducedb y increasinghumidit y levels.How ever, although thequalitativ e effects ofhumidit y wereclearl y demonstrated, the extrapolation of their results to the plant substrate isno t allowed duet oth eus eo fa nartificia l substrate.Moreove r thereaction s ofpreda tor andpre yma yb edifferen ti nth ewebbin g of apre ycolony . Apart from itseffec to nth emea n activity, the substrate alsoexert sa n influence on the activity rhythm. In the webbed area therestin gperiod s

Table 46. The activity (%) offemal ephytoseiid s residing ina pre y colony, inrelatio nt oth etemperatur elevel .

Predator species 15°C20° C29° C

Metaseiulus occidentalis 38 36 41 Phytoseiulus persimilis 10 8 12

117 are frequently alternated with walking periods,whil e on anunwebbe d sub strate these activities weremuc h less fragmented; inth e lattercas ewal king periods and resting periods were longer than those for webbed sub strates.Thi s factan d the findings discussed inSubsectio n 3.2.3 justifya modelling approach based onrando m inter-arrival times ofth epredato rbe tween itsencounter s withpre y items. Iti so fimportanc e tostres s thatth e factors discussed inthi ssubsec i\ tion do not determine the activity ina fixe dway .Fo rexample ,th eleve l of starvation does notdetermin e the activity level,bu trathe r determines the level ofreceptivit y tostimuli .Also ,th e substrate doesno t determine the level of activity nor the walking speed;hungr yphytoseii dpredators , t when disturbed artificially, can walk very fasti nth ewebbin g structure. Disturbance by artificial means orb ybumpin g against anothermit e areno t the only stimuli evoking bursts ofwalkin g activity. For example,whe na predatory female leaves a prey colony onhe row n accord (Section 3.4) and thus leaves thewebbin g and enters theunwebbe d parto fth e leaf,th ewalk ing activity and thewalkin g speed ishig hdurin g the firsthou r andtend s to stabilize towards the activity levels giveni nTabl e45 .

3.2. 6 Coincidence in the webbed space

The three-dimensional structure of the webbing may cause the predator and itspre y topas s above andbelo w eachother .Assumin g theoccurrenc e of the mites to be equally probable ateac hpositio n inth ewebbing , thefor mula of Skellam can be easily extended to the three-dimensional case by taking the mites as spherical units andb ymeasurin g the deptho fth eweb bing. However, a vertical section through thewebbin gwil l certainly show that the spider mites are clustered near toth e leaf surface duet othei r predominant feeding activities. Moreover, theegg s ofth e spidermite s are for the major part located in the lower layer ofth ewebbin gnea r toth e leaf surface. Due to this heterogeneity anextensio n ofSkellam' s formula toward the three-dimensional casewoul d bemuc h too complicated, yetleav ing the peculiarities in the walking behaviour of both predator andpre y unconsidered. This problem can be solved more easily by multiplying the two-dimensional formula of Skellam with the fraction ofrea l contactsbe tween predator and prey outo f all coinciding perpendicular projections on the leaf surface. Themeasuremen t ofthi s fractionwa s doneb y observation with abinocula r microscope maintained continuously ina perpendicula r posi tionabov e afemal epredator .Th enumbe r ofobservation s needed to attaina specified accuracy atth e 5%leve lwa s computedwit h the aido f thebinomia l / sampling formula (a = 0.05; d =0.0 8 x v n>ïn(p7q7;Pr(|p-P |J -d )= a). In this way a roughestimat ewa s obtained of thereductio n ofth erat eo fen counter due towebbin g forthre e differentphase s incolon ygrowth :

118 - Phase 1 The webbing intensitybrough t aboutb yfemal espide rmite sin creases rapidly inth einitia l colonizationperiod ,bu ti tlevel sof fafte r lesstha na da y aslatera l expansiono fth ewe bbecome spredominant . - Phase 2 After hatchingo fth e eggs, the juveniles contributet oth e production ofweb . - Phase 3 When the newbor n juvenileshav ematured ,th e fooddemand sin crease exponentially,s otha t ultimately the food source will becomeex hausted, causinga nincreas eo fth e walking activityo fal l stages and, thus,a nincreas ei nth ewebbin g intensity. The measurementso fth ecoincidenc ei n thesethre ephase s arepresente d inTabl e47 .Thes e results showtha tth erat eo fencounte r isbein g reduced bya facto ro f45-55 %a sa consequenc eo fth eheterogeneit y ofth ewebbing , and,tha tthi s resultis ,surprisingly , independento fth epredato r species and thepre y stage involved.A mor e expected resultwa s thedecreas eo f the coincidencea tth e increasedwebbin g intensityo n thehighl y infested rose leaf. Duringa par to fthes e experiments the activity statuso fpredato r and prey was taken into account (walk-walk,walk-rest ,rest-walk) .Th ere -

Table 47. Coincidencei nth e webbed spacebetwee n femalephytoseiid s and different stages ofthei r prey atthre e phases ofcolon y growth, n= 350-600 ;pre y density= 20-6 0mites/cm 2; adaptationperio d= 1 2hours ; T= 20°C .

Predator Prey stage Coincidence(% ) species colony growth colony growth colony growth phase1 phase2 phase3

Phytoseiulus eggs 47.3 43.4 33.0 persimilis ., 48.3 28.2 r juveniles - females 56.2 49.0

Amblyseius eggs 50.1 potentillae ., r juveniles females 43.2

Amblyseius eggs 47.8 bibens juveniles 46.3 females 55.0

Metaseiulus eggs 49.1 52.2 occidentalis .. 46.1 24.3 juveniles females 43.8 55.8

119 Table 48. Coincidence in the webbed spacebetwee n femalephytoseiid san d mobile stages ofthei rpre y atthre e different combinations ofth e activity ofth epredato r and thato fth eprey .Pre y density =20-4 0mites/cm 2; adaptationperio d =1 2hours ;T = 20°C .

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

walk-wa lka walk-res tb rest-walk

Phytoseiulus 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 r ofreplicate s per ratio =100-150 . b. Number ofreplicate s perrati o =200-400 . c.Numbe r ofreplicate s per ratio =150-300 .

suits, presented in Table 48, do not show effects ofquantitativ e impor tance. A similar conclusionwa s drawn frommeasurement s ofth e coincidence usinghungr ypredator s (Table 49). Itma y thereforeb e stated, that -excep t for exhaustion of the food source ofth e spidermite s -webbin g acts asa constant 'labyrinth' inth epredator-pre y interaction atth ecolon ylevel . It may be worthwhile to point out the difference between the present definition of the coincidence in space and that of Fransz (1974). Fransz measured the same catalogue ofbehavioura l components of Metaseiulus occi dentalis oncircula r leafdisc s ofth e Limabean . Inadditio n he recognized theproble m of spatial heterogeneity incomputin g therat e ofencounte rbe tweenpredato r andpre y onthes e discs.Th e spatial heterogeneity iscause d here by the ribs and the edge ofth e leafdisc .Sinc epredator s prefert o walknea r tothes e structures inabsenc e ofwebbing , asmalle r leafare ai s scanned by the predator.Moreover , according toth eexperimenta l designo f the functional response (Küchlein,t ob epublished ; Fransz,1974) , theegg s were placed outside the ribbed area and atsom e distance of the leafedge . Forthes ereason s theedg eoriente dwal kcause s aspatia lheterogeneit yre sulting in a reduction ofth e rate ofencounte rbetwee npredato r andprey . By conceiving the problem in this way, the coincidence onth e leafdisc s canb e determined directly aswa s doneb y the author, instead of indirectly as was done by Fransz (1974). Thiswa s accomplished bymeasurin g thetim e spentwalkin g on therib s andnea r toth eedge s ofth e leaf disc,bein gap parently wasted time with respect to thetim e available forsearchin g the

120 Table 49. Coincidence inth ewebbe d spacebetwee n hungry femalephytoseiid s andegg so f Tetranychus urticae. n= 150-250 ;pre y density= 20-6 0mites/cm 2; adaptationperio d= 0. 1 hour;tim eo ffoo ddepriv ation= 2 days ;observatio nperio d= 1- 2 hourspe r predator;T = 20°C .

Predator species Coincidence(% )

Phytoseiulus persimilis 46.6 Metaseiulus occidentales 44.0

prey eggs. Inthi swa y itwa s found that58 %o fth e searching time (133min utes)i sbein g spent inefficiently. This resultca nb e comparedwit hFransz' s indirectmethod ,usin gKüchlein' sbehavioura l observations onth elea fdiscs . He measureda walkin g speedo f0.4 7 mm/s anda walkin g activity of39 %i n presenceo fpre y eggs.H eals omeasure d the numbero fencounter s during 6-hourtim eperiod s atsevera l densities ofth epre yegg so nth elea fdisc s and founda linea rrelatio nbetwee nth enumbe r ofencounter s andth enumbe r of prey eggso nth e5 cm 2 leafdiscs ,th etangen tbein g equalt o 2.236.I f the spatialheterogeneit ywer e tob ediscarded , thetangen tcompute daccor dingt oth eSkella m formulao nth ebasi so fKüchlein' sbehavioura lobserva tions wouldb eequa lt o5.5 4 (encounters per 5 cm2 per6 hou rpe regg) . Dividing both the directly measured tangentb yth e estimated tangent, an estimateo fth e coincidencei sobtained , which amountst o40.2% .Th erat e ofencounte r isthu sreduce db y 60%,whic h approximates theorigina l direct estimate closely.

3. 2.7 Success ratio

After detectiono fa pre y with itstarsa l sensillae (trichobothria)o f the front legs thepredato rma ymov e closet oit scaptiv e and subsequently its maxillary mouth parts are pushed through the integument ofth eprey , meanwhile inspecting thepre ywit h itspedipalps .Whe nthi s serieso fhand lings was noticed duringth ebehavioura l observations,a successfu l attack li- was scored, while tarsal contact ledt oth eregistratio n ofa nencounter . The fractiono fsuccessfu l attacks outo fth etota lnumbe ro fencounter si s furtherreferre d toa sth e successratio .Thi sdefinitio n fitsprecisel yt o thato fth e coincidencei nth e webbed space,whic h reduces theSkellam' s estimateo fth e rateo fencounte r betweencircula r items intoa nestimat e ofth erat eo f tarsal contact.Howeve ro na nunwebbe d leaf,larg e andfast - walkingpredator s inspectth e areacovere d lessintensivel ywit h theirtip -

121 ping front legs, which may laed to afailur e todetec t asmal lpre y stage located inthei rwalkin gpath . Intha tcas e another factor shouldb edefined , one thatexpresse s the tipping intensitywithi n the areacovere db y thepre dator's circumference.Anothe r complication ariseswhe nth epre y encounters ___ -,a resting predator atth eback . Inth ewebbing , this type ofprey-predato r _\M- 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 apparentenlargemen to fth e width ofperceptio nb y thehungr y females canb e accounted forb ymultiply ingth e rateo fencounte rbetwee n activepre y and therestin gpredato rwit h a factor,rangin g from 0.5 (noturn )t o 1. (turn). At the start ofth e continuous observations ofth epredator ybehaviour , femalepredator s wereuse d thatha dbee ndeprive d of food fordifferen tpe riods since satiation. By transferring thepredator s from theMunge rcage s to the experimental arena with abrus h severedisturbanc e would havebee n brought about very frequently. To prevent this artefact the predatory females were transferred on a leaflet, whichwa splace d previously inth e hunger cage as a refuge for thepredators . Inthi swa y thepredator swer e allowed toente r the experimental arena onthei r ownaccord . The experimental arena consisted of apre y colony founded after aprece ding infection of female spidermite s on aros e leafo fa nintac tplan t in the greenhouse. These leaves were cut off and placed upside down on wet cotton wool in a petri dish. In another series of experiments unwebbed leaves were used still connected toa par to fthei r shoot.Th e shootswer e put in a test-tube filled with wet cotton wool and closed byplasticine . This leaf system formed aneasil y turnableunit .Th epre y itemswer e offered one by one toth epredator ,excep t forth epre y eggs,whic hwer e 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 afterwardsb ycom puting the food contento fth ephytoseii d guti na paralle l time serieso n basis of the observed ingestion history of the individual phytoseiid females and the physiological variables measured inSectio n 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 of the phytoseiid gut. The number of encounters needed to determine the class specific success ratio with apredefine d accuracy atth e 5%leve lwa scom puted using the binomial sampling formula (a= 0.05 ; d= 0. 1 xvmin(p,q) ; Pr(|p-P | S-d )= a) . Thenumbe r ofobservation spe r food contentclas swer e regulated to achieve the desired accuracy bymanipulatin g the deprivation history ofth e startingpredato r and the subsequent observation time.More over, the 'normal'pre y densities in thepre y colonies happen tob e quite

122 high,e.g . theeg gdensit y ranged from 20-60egg spe rcm 2 webbed leafarea . Thereforeman y observations canb e obtained ina reasonabl y shorttim espan . Most of the observations were made at T = 20°C with colonies containing onlypre y eggs oronl y larvae andnumph so ronl y females oronl ymales .Som e observations were donea tT = 15° C andT = 29° Ci ncolonie s containing only eggs. The results are presented in Table 50Awit h respectt oth ewebbe dsub strate and in Table 50B with respect to the unwebbed substrate. Smoothed curves are drawn in Fig. 33 to accentuate themai ncharacteristics .Thes e reveal conspicuous interspecific differences among the phytoseiid species studied, when comparing the success ratios on webbed and weblessleaves . The factor webbing induces alowe r level ofsucces s forth ecas eo f Ambly- seius potentillae, favours Phytoseiulus persimilis andhardl y affects Ambly- seius bibens and Metaseiulus occidental is. With respectt oth eprey-stag e i)- preference, the success ratio curves resemble eachothe r ina qualitativ e sense.Becaus eth eabilit y ofth epre yt oescap e from anattac ko fth epre dator increaseswit h itsmobilit y and itsstrength ,egg s areeasie r tocap turetha nlarvae ,etc. ;femal e spidermite s areth emos tdifficul t staget o capture. In a quantitative respect, the prey-stage related successratio - curves differ among the phytoseiid species studied. For each predator species on its most favourable substrate,th einterspecifi c differences in successrati o levels suggesta relatio nbetwee nth ebod y sizeo fth epreda tor and its predatory success.However , ifth e foodconten to fth e guti s expressed in weight units instead of fractions ofth emaximu m level ofgu t filling, the relation of the success ratio with the satiationdefici to f thegu tdoe s reveal the samebu tles sconspicuou s interspecific differences. Some notes on the predatory behaviour underlying the measured success ratios should be made. The adverse effects of webbing on the success of Amblyseius potentillae may notb e surprising duet oth e foregoingnote s on the restricted mobility ofthi s species inth ewebbin g (Subsection 3.2.2). The effect of webbing on the success of Phytoseiulus persimilis, however, needs further explanation. On an unwebbed substrate thispredato r species walks fast and spendsmor e time inwalking .Whe na femal epredato r ofthi s species bumps into a female spider mite,i tturn sbac k andrun s awaywit h anincrease dwalkin g speed,whic h indicates disturbance.Mor i& Chant (1966) reported the very same effect. They foundonl y 5successfu l attacks among 480 contacts between Phytoseiulus females and Tetranychus females.A tth e side ofth e leaf facingdownward ,wher e thewalkin g speed islowe rbu twher e walking activity is still high compared totha t inwebbing ,thes e effects were observed to the sameextent .Apparentl y thewebbe d environment,wher e both predator and preywal k slowly,offer s amor e favourable substrate for predatory activity of this species, disturbance being a rare phenomenon (Subsection 3.2.9). With respectt oth esucces s ratio againstegg sdistur \ & bance was never observed, so that other factors operate causing the

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125 SUCCESS RATIO (%)

100 METASEIULUS OCCIDENTALIS AMBLYSEIUS BIBENS 90H /^

T r 0 102 0 30 i.0 506 0 708 0 9010 0 0 102 03 0 iO 50 60 708 0 9010 0 RELATIVEFOO DCONTEN TO FTH EGU T (%)

Fig. 33. Smoothed curveso fth e success ratio inrelatio nt oth e relative food content of the gut for four phytoseiid species onsmal lpre y stages (E, eggs; L, larvae)an d adult females (AF); ,predator ybehaviou r on anunwebbe d leaf; ,predator ybehaviou r on awebbe d leaf.

|decrease d success of Phytoseiulus persimilis againstthi s stage atunwebbe d substrates.Althoug h tarsal contactoccurred , the females leftth eegg sfre - ;'quentl y unharmed without showing a rejective reaction, like running away, [f For some reason their sensitivity indetectin g thepresenc e ofth epre y is decreased in absence ofwebbing .Possibl y the inspection ofth esubstrate , being intensified inth e diversely structured webbing, ensures the detection of a prey by several consecutive contacts. Anyhow it can be stated that Phytoseiulus persimilis is very much web oriented, being less adapted to

126 capturea pre ywhe ndispersin g fromwebbe d areat owebbe d area,withi nwhic h success is ensured. Thedisturbanc e described abovewa sals oobserve dwhe n fj7 a femaleo f Amblyseius potentillae bumped againsta nactivel ywalkin g female j of Tetranychus urticae atth esid eo fth elea ffacin gupward .Th ebehavioura l reactions were very similart o Phytoseiulus persimilis exceptfo rth efac t that hungry females wereusuall yno tdisturbe dbu treacte dmor e frequently 4f by attack upon contact. Incontras t to Phytoseiulus persimilis, thedis turbed reactions were almost absent when the female-female contacts were observed atth e side ofth e leaf facing downward, wherewalkin g speedi s low. Itma yb e stated that thesucces srati o dependso nth ewalkin g speed ofbot hpredato r andpre yan dbecaus e thewalkin g speedvarie swit hth etyp e and thepositio n ofth esubstrat e (Subsection 3.2.2), thesucces s ratioi s relatedt othes e aspectstoo .Fro m thispoin to fvie wi ti sconceivabl e that thesmall-size dphytoseii d species,lik e Metaseiulus occidentalis and Ambly seius bibens, are less affectedwit hrespec tt othei r success ratio,bein g ! relatively sluggishan dles ssensitiv et odisturbanc e (Subsection 3.2.2). | t Apart fromth einfluenc eo fth ewalkin g speed, alsoth elocomotor y acti vity ofbot h predator andpre yma yaffec tth esucces s ratio.Th eintensit y of attack stimuli emanated by thepre yma yvar ywit hth epre y activity.A walkingpre ymit ema yevok epursui tb yth epredator .Thi s effectma ya swel l ft be counteracted by agreate rchanc eo fescape .Furthermor e thereactio no f an active predator toactiv epre yma ydiffe r fromtha to fa ninactiv epre dator. Forthes e reasons itma yb eworthwhil e todifferentiat e thesucces s ratiowit hrespec tt oth estat eo factivit yo fth eattacke r andth eattacked . Theelaboratio no fthi sbehavioura l aspecti sdon efo rth ecas eo fpre ymale s and females (preoviposition).Th eresults ,presente d inTabl e51 ,sho wtha t thedifference s aresmal l andfa rfro m systematic.Frans z (1974), measuring the success ratioo f Metaseiulus occidentalis againstpre ymales ,similarl y found small differences between the success ratios of active predators againstactive/inactiv e preymale s (SRWW= 0.03 8an dSRW R= 0.034) ,bu tth e resting predator seemed to react less aggressive (SRRW= 0.026) .Bu tthi s difference isth econsequenc e ofhi sdefinitio no fth esucces sratio ,whic h focusseso nth esuccessfulnes s ofmutua l contacts,whethe r thepredato rwa s encountered frontally, laterally orposteriorly . Inth epresen t studyth e] | successfulness wasmeasure d inrelatio nt otarsa lcontact .Thi s definition| j ismor e logic froma behavioura lpoin to fview ,becaus eth epredator y female first detects thepre y with thetarsa e ofhe r frontlegs.A prey bumping against thebac k ofa femal epredato r usually evoked locomotory activation JE of thepredator , rathertha nattac k stimuli.Fo rthi s reasonposterio ren counterswit ha restin gpredato rar erelate d toth eactivit y level (Subsec tion3.2.5 )an dth efrequenc yo ftarsa l contactafte rnon-tarsa lcontac ti s measured separately. The latter variable, adequately called therat eo f 'turning',wil lb ediscusse dbelo wi nthi ssubsection . To elucidate whether thetemperatur e affectsth esucces s ratio,simila r

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128 experiments were carried out at T = 15 and 29°Cusin gpre y colonieswit h eggs only.Th eresult s arepresente d inTabl e 52.The y indicate theabsenc e of any temperature effect. On the basis ofthi spreliminar y result itwa s supposed that the food content of the gut determines the probability of success, while the temperature related rateo fgu temptyin g determinesth e dynamics of the success ratio. This simple hypothesis is tested in some prédationan d simulation experiments presented inSubsectio n3.3.4 . The success-ratio curvespresente d inthi s reportresembl e thoseobtaine d by Fransz (1974: Metaseiulus occidentalis vs eggso fmale so f Tetranychus urticae atT =25°C )an db yRabbing e (1976: Amblyseius potentillae andlar vae of Panonychus ulmi atT = 18°C). Thepresen t results invariably showed a success ratio of about 90%a ta lo w levelo fgu t filling;thi swa sals o foundb yRabbing e (1976)an d corresponds with the indirectly estimatedsuc cess ratios of Küchlein (tob epublished) .Howeve rth e success ratiosmea suredb yFrans z differed largely,bein g always less than 50%.Crof t (1972), studying thepredator ybehaviou r of Metaseiulus occidentalis inrelatio nt o Tetranychus pacif.icus, measured the success ratio in a different way.H e measured the percentage of successful capture bypredator s after twocon tacts with aparticula r prey. In thepresen twor ka nencounte rwa sscore d

Table 52. Success ratios (%) ofyoun g females oftw o phytoseiid species inrelatio n toth etemperature . Eggs asprey ;webbe d leafsubstrate .

Relative food content 15°C 29°C ofth e gut MO PP MO PP

0- 5 77.5 - 70.4 - 5-1 0 91.4 - 82.3 - 10- 20 86.2 - 80.1 - 20- 30 30.1 - 30.8 - 30- 40 19.4 - 23.0 - 40- 50 13.8 - 14.7 - 50- 60 9.8 - 9.0 - 60- 70 70- 80 - 71. .4 - 76.5 80- 90 - 47. .3 - 50.1 90- 95 - 31, .1 - 28.0 95-100 - 6. .2 - 6.7

MO= Metaseiulus occidentalis. PP= Phytoseiulus persimilis.

129 once tarsal contactwa s noticed,whethe r itwa s succeededb ymor e palpations ontha tparticula rpre y itemo rnot .Th enex tencounte rwa sno tscore dunti l after the predator had leftth eprey .Anothe r difference withCroft' swor k istha th ewithdre w thepre y after apredato rha d captured aparticula rpre y stage and had assumed the feeding position. Inthi swa y thepredator sob tained little,i fany , food, sotha tthe y couldb euse d again after further starvation. A final difference istha tencounter s resulting iandisturbanc e were excluded from the computation of the success ratio. Croft observed that direct frontal approaches of the predator to the adult female prey l' nearly always resulted in an avoidance response by the predators at all starvation times, and these were not counted,whil e theywer e included in the present experiments. For these reasons the results ofbot h studies are not comparable, except forth e facttha th e found 90%succes s ratios after 1 day starvation,whic h correspondswit h the author'sresults . The effecto f ales s intensive inspection ofth e areacovere db y thepre dator was studied simultaneously during the behavioural observations. As discussed before this aspecto f searching shouldb e investigated separately at the unwebbed substrate but not at the webbed substrate,becaus e iti s implicit to the definition ofth e coincidence inth ewebbe d space.Th eob servations indicate that smallprey ,e.g . eggs and larvae,wer e onlyover looked by the predatory females of the large species whenwalkin g atth e sideo fth e leaf facing upward. Itwa s estimated that Phytoseiulus persimilis missed about 30%o f the eggs in their walkingpath ,whil e Amblyseius potentillae missed less than 10%.O nth eundersid e ofth e leaf these large predators walk more slowly andhenc e inspectthei rwalkin gpath smuc hmor e thoroughly. The other twophytoseii d species (Metaseiulus occidentalis and Amblyseius bibens) walk relatively slower andar e small sized, sotha tan y prey stage located inthei rwalkin gpat h isdetected . An encounter of a mobile prey with thebac ko fth epredato r resulteda few times in a turn of thepredato r towards theencounterin g prey sotha t tarsal contact occurred afternon-tarsa lcontact .Thi sphenomeno nwa sver y rarely observed in thewebbing ,probabl y due toth erestricte d mobility on this substrate. Amblyseius potentillae, inparticular , showed aturnin gre sponse on unwebbed substrates. InTabl e 53th e relative frequency ofturn s towards prey females encountering the back of Amblyseius potentillae (9) are given. It isclearl y demonstrated, thatth ewidt h oftarsa l perception is enlarged by prolonged starvation. Apart from the turning reactions the predator also reacted by forward locomotion as a consequence of the en counter. The relative frequency ofthi sbehavioura l reaction isals o given in Table 53.Thi svariable ,too ,appear s todepen d on thetim eo f foodde privation.Afte r thepre y ispuncture d by thepredato r asucces s isrecorded ; feeding starts soon after.However , itma yb e questioned whether feedingb y thepredator s results inth e death ofth eprey .Hoy t (1970)studie d themor tality of differentpre y stages ofth eMcDanie l spidermit e after shortpe -

130 Table 53. The relative frequency ofturnin go fa femal epredato r (Ajnblyseius potentillae) towards afemal epre y encountering thebac k of the predator. T = 20°C; each value is based on a minimum of 170 encounters.

Relative foodconten t Relative frequency of Relative frequency of ofth egut ,ordere d turning activations inclasse s

0-2 0 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 feedingb y females of Metaseiulus occidentalis. These investigations revealed that a high percentage of eggs and larvaeo fth epre y arekille d afterbein g fedo n for 5-30 seconds.Feedin gperiod so f30-12 0 secondscause d a high percentage of mortality among the nymphs and 5minut e feedings on adult female spidermite s resulted inonl y40 %mortality ,bu t substantially reduced oviposition by thesurvivin g females.Va nd eVri e (1973)similarl y found 50%mortalit y among adult femaleso f Panonychus ulmi aftershor thand lingperiod s of Amblyseius potentillae. He reportedtha tthi smortalit y was established withinon eda y anddi dno tincreas e afterwards.A compariso no f the lengtho fth eabov e feedingperiod swit h thosemeasure d duringth epre sentbehavioura l observations (Subsection3.2.8 )show stha tthes e constitute a very small part of the total feedingperio d except forth erar ecas eo f anattac ko fa satiate d femalepredato ro na female spidermite . Apparently theprobabilit y ofa successfu l capture isrelate d to the food content of the gut.However , there are two exceptions to be considered, which set limits to the applicability of this relation. First, severely starved predators can respond differently tothos euse d inth epresen tex & periments, which are starved forn o longertha n2 day s atT = 20°C . Inth e dehydrated state, Amblyseius potentillae is very aggressive,a s indicated & by the increase of the success ratio against female spidermite s forlo w foodcontent s init sgut .On emea l ona femal e spidermit ewoul denabl eth e gut to be filled completely, so thatth esubsequen tprobabilit y ofa suc cessful capture is expected tob ever y low,accordin g toth emeasurements . However,severel y starved females (6day sa tT = 20°C )appeare d tomaintai n a high success ratio after their firstmeal , and evenafte rthei r second # meal the success ratio was higher thanexpecte d (Table 54). Theamoun to f food ingested after the first meal wasver y low according tomeasurement s

131 Table 54. The success ratio (%) ofyoun g and hungry females of Amblyseius potentillae against adult females of Tetranychus urticae. T= 20°C ; observation timemaximu m 6hour spe rindividual ; eachvalu e isbase d on aminimu m of20 0encounters .

Prédationhistor y Starvationperiod s

2 days 6day s

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

/ of the female weight,s otha t thispredator ybehaviou r isinduce db y other V': motivational variables than the acquired amounto f food.Presumabl y theper sistence of aggressiveness iscause db y the relaxation time ofth ephysio logical processes, leading torecover y ofth emetaboli c imbalance. Incon - >. trast to Amblyseius potentillae, severe starvation of Metaseiulus occidentalis led to alowe r success ratio than found after 2day s food deprivation. :Thi s effect was clearly related tothei r losso f strength, as indicated by Ï Ith edecreas e inwalkin g velocity and their sluggish reactions.Bot h thein - V''- \>-' creased and decreased aggressiveness after severe starvation areno tuniqu e ; for the species mentioned, butwer e observed more frequently inthes epar - • !ticula r cases.Apar t from this lower limitt o theapplicabilit y ofth e food concept there is also anuppe r limitcause db yhig h rateso fencounte r with e liprey. Küchlein (to be published) found a second rise of the rate ofeg g y 2 ._r--~" prédationb y Metaseiulus occidentalis above the density of3 0egg spe r cm . u/,„ ;Becaus e the femalepredator s arecertainl y well fed atthes e densities,thi s phenomenon canno tb e related toth e food contento fthei r gutbu tpossibl y tosom e stimulus resulting from frequentcontac twit hprey . These examples clearly demonstrate the limitations of food consumption asa nindicato r ofth ehunge r level.Nevertheless ,wit h respectt o therang e ofcondition s relevant inth egreenhous e theus e of food consumption isac ceptable; for,th e lower limitwil lb e only relevantafte r extermination of thepre ypopulatio n and theuppe r limit atfrequen tpre y contact isprobabl y not met within the rangeo fprevailin gpre y densities.Althoug h the effect of frequentcontac twa s assessed ata seemingl y realistic eggdensit y of4 0 eggspe rcm? ,i tshoul db e stressed that therat e ofeg g encounter israthe r high inthes e experiments due toth e absence ofwebbing . Inth e caseo f Meta seiulus occidentalis thedifferenc e inrat e ofencounte rbetwee nwebbe d and 132 unwebbed substrates isapproximatel y proportional toth edifferenc e inwalk ing velocity so that the critical egg density in awe b amounts to 40x 0.47/0.18 = approximately 100 eggs per cm?.Suc hhig hpre y densitieswer e never measured in natural colonies grown on greenhouse roses, even with respect to all stages.Thes e densities rangedbetwee n20-6 0pre y itemspe r cm? and occasionally densities up to 80 mites per cm?wer e observed. For these reasons it isallowe d toappl y the simple concepto f food consumption forth epurpos e intended.

3.2.8 Handling time

The time spent handling a captured prey was also measured during the continuous observations of thepredator ybehaviou r and subsequently itwa s related to the foodconten to fth egu taccordin g toth emetho d described in the previous subsection. Thehandlin g timeconsist s ofsevera lactivities , like palpating, piercing, feeding, 'guarding' and return feeding. Hungry predators feed almost immediately after contact withthei rprey ,bu twel l fedpredator s spendmor e time ininitia lpalpatin g andpiercing . Feedingi s frequently interrupted for a short period and subsequently continued on other parts of the prey, especially when the prey is a deutonymph ora n adult. A few times the predatory female seemingly left its captive, but subsequently returned towards thepre y and started to feed again.A tothe r occasions the predator was observed to sit and wait next to its captive during a handling period, cleaning its extremities in the meantime .Th e actual feedingperio d duringhandlin g amounts to 90%i nth eyoun g stageso f thepre y and 60-70%whe n feedingo nmatur eprey . Themea nhandlin g times atdifferen tlevel s ofgu t filling are tabulated in Table 55 in relation to thedevelopmenta l stageo fth eprey . Itca nb e concluded that the handling time increases withdevelopmenta l progression of the prey andwit h theperio d of fooddeprivation .Th e lattereffec twa s also foundb yPutma n (1962), Sandness& McMurtr y (1972)an dFrans z (1974). Somepeculiaritie s concerning the species studiedma yb enoticed . Ambly- seiulus potentillae spends littletim e inth ehandlin g of spidermit e eggs. As discussed before, this is due to this species having someproblem s in piercing the egg chorion (Subsection 3.1.1). The majority of the feeding attempts fail, but successful feedingswer eobserve d too andthes e feeding periodswer eequa l tothos eobserve d inth eothe r species.Becaus e theegg s were harmed by the piercing attempts, thetim espen tpe reg gwa s recorded as a handling period despite the absence of ingestion. Theothe r species studied ingest the contento fth eegg swithou t anyproble m inpiercin gth e eggchorion . Phytoseiulus persimilis requires lesstim e inemptyin g theeg g than Metaseiulus occidentalis and Amblyseius bibens. However these three species spend equal amounts of time in handling the other stages of the prey.

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134 3. 2. 9 Disturbance

Inth eacarin epredator-pre y system,disturbanc e shows itselfi nsevera l ways: as adecreas e inth eprobabilit y ona successfu l capture,e.g .i ncas e of frontal encounters between a female predator and a female prey, both walkingo na nunwebbed ,upward-facin g substrate (Subsection3.2.7 ) as an increase inwalkin g speed,e.g .afte r frontal contactbetwee nac tive adults asa nincreas e inwalkin g activity,e.g .afte rcontac tbetwee na restin g predator and anactiv e stage ofth epre y resulting inreactivatio no fth e former (Subsection3.2.5 ) - as adecreas e inth ewidt ho fperception ,e.g .afte rcontac tavoidance , lateral inspection by the antennae-like frontlegs (Subsection 3.2.1)de creases, resulting ina decrease dwidt ho f 'antennal'perceptio n as adecreas e inth ehandlin g time,e.g .feedin gpredator sbein ginter ruptedb ypre ybumpin g intoth epredato r (Mori,1969 ) asa nincreas e inth esucces s ratioo ffeedin gpredators ,e.g .th eprey , bumping into the predator, is immediately attacked (Haynes& Sisojevic,. 1966; Sandness& McMurtry ,1972 ;Hoyt , 1970). Theeffect so fth eabov etype so fdisturbanc e onth efunctiona l response ofphytoseii d predators topre y density areconsidere d tob ever y important by various authors.Mor i & Chant (1966) attributed thedom eshap eo fth e functional response of Phx/toseiulus persimilis to contact disturbance of feeding predators by thenumerou s female prey.Sandnes s& McMurtr y (1972) founda secon d riseo fth erat eo fprédatio na tpre ydensitie so f1 0female s per cm2.Thi s effect was attributed to successful attacks ofth efeedin g predatorso nth epre y occasionally bumping intothem .Hoy t (1970)suggests , that this "two flies inon eblow " principle will increase thepredator y efficiency inreducin g preypopulation s athig hdensities .Lain g& Osborn e (1974), offeringpre ymale s insteado ffemales ,di dno tfin dan ydeclin eo r riseo fth efunctiona l response athig hpre ydensities . Itshoul db estresse d thatdisturbanc e isa consequenc eo fth evigou ro f the interference.Activatio n anddisturbanc e arebrough t aboutb yhig hwal king speed andhig h walking activity. Consequently, the size ofth epre y andth esubstrat e arever y important.Becaus eth eabov e studieso fth efunc tional responsewer ecarrie dou to nartificia l substrates (paper,perspex) , itma yb equestione d whether disturbance isimportan to nnatura l substrates. Everson (1979)showe d thatth erat eo fencounte rwit h femalepre yo na lea f substratewa sonl ya fractio no ftha to nth eartificia l substrates,becaus e ofthei rprevailin g feeding activities.O na webbe d leafthi sreductio nwil l be evenmor e conspicuousdu et olo wcoincidenc e inth ewebbing ,lo wwalkin g speedan dlo wwalkin g activity.Henc e itma yb equestioned ,whethe rth ein terferences in thewebbin g arevigorou s enough to cause disturbance and

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136 whether these disturbances occur frequently atth epre y densities prevailing in the greenhouse crop.Thi s questionwa s studiedb y recording thewalkin g behaviour and the encounters in prey colonies, grown on greenhouse roses and containing alo to fmobil e stages.Tw otype s ofcolonie swer e selected: - colonieswit h20-4 0nympha l andmal e stagespe r cm2,plu s afe w females colonieswit hegg s and 10-15 femalespe r cm2. Onepredator y femaleo f Metaseiulus occidentalis or Phytoseiulus persimilis was released on each leaf and the observations started half a day later. The results arepresente d inTabl e 56.I tca nb econclude d thatfo r bothphytoseii d species andbot h typeso fpre y colonies,disturbanc e during feeding is a rarephenomeno n and thewalkin g speed andwalkin g activityo f both predator and prey areunaltere dwhe ncompare d toth edat aobtaine d in colonies containing few, or even no, mobilemites .Whe n afemal epre yen countered a feeding predator,th epredato rmostl y continued feeding andi n the rare case of feeding interruption thepre y captivewa s already sucked dry,whil e attacko nth edisturbe rwa s observed onlyonce .Disturbanc e phe nomenama yoccu rupo nexhaustio n ofth eplan t food source,causin g the spi der mites to increase their locomotory activity in search offres hfood . However this situationwa sno tstudie dbecaus e itimplie s aninfestatio nb y spidermite s thatsurpasse s aneconomicall y acceptable damagelevel .

3.3i PREDATIO N

Theprédatio nwil lb emodelle d forth ecas eo fa predato rwhos egu t fil lingdetermine s therelativ e rateo fsuccessfu l attack (=RS E forD =1). prey The dynamics of the food contento fth egu ti ssimulate db y integrationo f therat eo f food intake and therat eo fgu temptyin g over shorttim einter vals. B y assuming thateac hpredato r ina serie s ofsimultaneou sprédatio n experiments consumes uninterrupted by searchingperiod s and atth esam e time acquires the sameportio no f food, foragingwoul db econceive d asa determin isticprocess .Howeve r therando m distribution ofth epre y and theundirec ted searching behaviour of the predator giveris et osequence so f feeding and searching periods that are subject to stochastic variation. Forthi s reason each predator goes through a unique timeserie s of feedingevents , so that at onemomen tdurin gth eprédatio nproces seac hpredato rwil lhav e a different amount of food in itsgut .Therefor e stochasticmodel s ofth e prédationproces s arediscusse d andsubsequentl y comparedwit h deterministic analogues toelucidat e theeffec to fth eunderlyin gconcepts . After selection of themos tadequat emode l fromth eabov epoin to fvie w a series of prédation experiments on both webbed and unwebbed substrates are discussed and compared with appropriate simulations to validate the measured inputs and the concepts underlying thatmodel .Subsequentl y iti s recalled that the majority ofth ebehavioura l inputswer emeasure d athig h orzer opre y density, ata standar d temperature and ina standar d ageperiod , 137 studying solitary predators only.Thi s raisesth eproble m ofho wt oextra polate thosemeasurement s to intermediate prey densities,othe rtemperatures , ageperiod s andpredato r densities?Henc e aconcep to fth e relationbetwee n reproduction and prédation is proposed on thebasi s ofexperiment sprevi ously discussed inSubsection s 2.2.3 and 3.1.2,whic h enables extrapolation in asimpl eway . Somevalidation s ofthi s conceptar epresented . Finally, there is the similar problem ofextrapolatin g measurements of 'monoculture' success ratios to 'mixed cultures' of prey stages. This is discussed on the basis of the behaviourmeasurement s described in Section 3.2 and of the available references pertaining toprey-stag e preference of phytoseiidpredators .

3. 3. 1 Models of prédation

Ensuing from thebehavioura l component analysis (Section 3.2),prédatio n is determined by the food content ofth ephytoseii d gut,whic h intur nde pends on food intake andgu temptyin g (Section3.1) .I nCSM Pnotation ,th e dynamics ofsuc h asyste m canb e simulatedb y the followingnumerica linte gration: FCG = INTGRL (IFCG,RF I -RGE ) RGE =RRG E *FC G (I)FCG = (initial)foo d contento fth e gut (pg) RGE =rat eo fgu temptyin g (|jg-day~) RRGE= relativ e rate ofgu temptyin g (day ) RFI =rat e of food intake ((jg-day- ) Because ofth e small time constanto fth e ingestionproces s and the short duration ofth ehandlin gperio d needed for 90%o fth eultimat e foodintake , ingestionma yb econceive d asa n immediate swallow ofth epre y content,th e size ofth eportio nbein g limitedb y the satiation deficito fth e gut (Sub section 3.1.1): RFI =AMINKSDG/DELT , RSE *FC P) SDG =GUT C -FC G SDG =satiatio n deficito fth egu t(|jg ) GUTC =gu tconten t(|jg ) FCP = food contento fth epre y(^g ) RSE =rat e ofsuccessfu l encounter (preyday " ) The rate of successful encounter can becompute d fromth emeasure dbe havioural components andpre y density: RSE =l./TS C TSC =F T+ 1./(RR E* COI N *S R *DPREY ) TSC =tim e spentpe r successful capture (day) FT = feeding time (day) RRE =relativ e rate ofencounte r =RE/DPRE Y (day )

138 SR =succes s ratio (%) COIN= coincidenc e inspac e (%) Severalo fthes ebehavioura l componentspositivel y influenceth erat eo f successful encounter atlo wlevel so fgu tfilling .Fo rexample ,th esucces s ratio increases ifth e food content ofth egu tdecrease s (Fig.34) .A ta constant density ofth eprey , soonero rlate rth erat eo ffoo d intakewil l become equalt oth erat eo fgu temptying .The nth efoo dconten to fth egut , andconsequentl y therat eo fprédation , attaina constan tleve lan dth epré dationproces s entersa stead ystate . However,a sa consequenc eo fprédatio npre y density decreases unless each prey killedb yth epredato r (orb yothe rcauses )i sreplace d immediatelyb y a fresh one.Becaus e immediatereplacemen ti sgenerall y impracticable,th e rate ofprédatio n intha tcas ei sno tassesse d ata stead y state,du et oa changingpre ydensity . Incas eo ffixe dtim edelay so fpre y replacementth e fluctuation ofth epre y density canb emonitore d duringth esimulatio ni n the followingway :

DPREY= INTGRL (IDPREY, (-RSE/AREA)+ (REPL* (IDPREY-DPREY)/DELT) ) REPL = IMPULS (0.,REPDEL ) (I)DPREY = (initial)densit yo fth epre y (prey/cm2) AREA =experimenta l leafare a (cm2) REPL =replacemen t action (0o r1 ) REPDEL= tim edela yo fpre y replacement(day ) The fluctuation inpre y densityca nb edampe db yenlargemen to fth eex perimental leafare aan db yshortenin go fth etim edela yo fpre yreplacement .

RELATIVEFOO DCONTEN T SUCCESSRATI O OFTH EGU T(% ) (% ) 100-1 -100

80- 80

60- -6 0

40- -4 0

20- -2 0

-dît i—'—r 1 12 18 24 30 36 42 48 TIME(HOUR )

Fig. 34. Graphic display ofth emai n counteracting processes underlying prédationfo ryoun g female Metaseiulus occidentalis andegg so f Tetranychus urticae. Gutemptyin g givenb ydotte d line,an dsucces srati ogive nb yhis togram.

139 Adequate manipulation of these measures can approximate astead y state of theprédatio nproces swithi n the limits ofpracticability . The above type of simulation (Appendix E)i scalle d deterministic,becaus e each moment in theprédatio nproces s allows foronl y onepossibl e state of the system.Th epredator s areconsidere d tob e identical foragers,eac hcon suming the same portion of 'crumbs'o fth epre 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 ofth e satiation level of the predator. It goes without saying that the actualprédatio nproces s is quite different from thispicture .Th e random distribution ofth epre y and 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 stochastic models thattak e into account the instantaneous variationo fth e motivational state. Monte Carlo simulation of the predatory behaviourma y serve as afirs t illustration of astochasti c model. Ina mit e colony the searching behaviour of the predator and the spatial distribution ofth epre y are approximately random, sotha tth e inter-encounter periodswil l be random too. Inthi s case the inter-encounter periods, as well as the inter-attack periods (Fransz, 1974), meet thecondition s of aPoisso nprocess .Th eprobabilit y ofn osuc cessful attacks isthe n equal toEX P (-RSE *TIME) , sotha t ina sufficient ly short interval (=DELT ) at moston 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 on acaptur 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 o 1: RDRAW =RNDGEN(U ) INCONU =3 CATCH = INSW(PRC -RDRAW , 0. ,1 . ) U =startin gvalu e ofth erando m number generator (RNDGEN) RDRAW =rando m drawing from aunifor m distribution ranging from 0t o1 CATCH =indicato r of acatc h event (0o r 1) When CATCH equals zero, the predator is searching; CATCH= 1denote sa catch event. Inthi swa y sequential time intervals of searching aresimula ted. Interruptions for ingestion are simulated asdiscret emoments ,s otha t the ingestion statement ofth e deterministic model canb emodifie d as fol lows: RFI =CATC H *AMIN1(SDG , FCP)/DELT

140 Thus food intake takesplac e asa n immediate swallowing ofth e foodcon tent of the preydurin g atim e interval inwhic hCATC Hhappen s toequa l 1. An example of such a simulation is presented in Fig.35 ,whic h showsth e course ofth e food contento fth egu tdurin g aforagin gperiod . From random draws fora serie s ofDELTs , the feedinghistor y ofa nindi vidualpredato r canb e simulated.T oobtai n anaccurat e estimateo fth emea n numbero fpre y attacked, alarg enumbe r ofrerun s arerequired ,e.g . atleas t 100,whic hmake sMont e Carlo simulation acomputer-tim econsumin gprocedure . Theprogra m is listed inAppendi x F. The above formulation ofa stochasti cprédatio nproces s canb e extended in several ways. Thecaptur e eventan dsimultaneou s swallowing ofth epre y content can be replacedb y anexplici t feedingperio d and adynami cinges tionproces s (e.g.Fransz ,1974 ;i ncontras tt oFransz' smodel ,th e feeding

RELATIVEFOO D CUMULATIVE CONTENTO FTH E NUMBER OF GUT (%) CAPTURES 100 10 \ i\ i t 9 i \ i \ i \ i \ i v 8

M 1 h 7

50- 5

- A

- 3

i 2U 48 TIME (HOURS) Fig. 35. Graphic representation of the prédationproces s simulated by MonteCarl omethod s (Appendix F). Thedynamic so fth erelativ e food content of the gut is given by thedotte d line.Th ecumulativ e number ofcapture s during the period ofprédatio ni sgive nb y the straightline .Th epredato r (Metaseiulus occidental is) starts at full satiation and ingestspre y eggs afterrando m searchingperiods .

141 time in the model discussed above was only considered aswast e timewit h respect to the time available for searching).Anothe r 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 sreplace db y simulation ofth ewalk ing behaviour of the predator (and prey)a ta certai n distribution ofth e prey.A t themomen to f asimulate d encounter theoccurrenc e of asuccessfu l attack canthe nb e determined by the same type ofMont e Carloprocedur e but where theprobabilit y of acaptur e (=PRC )equal s theproduc t ofth ecoinci dence in space and the success ratio (=COI N *SR) .However ,becaus eimme diate swallow of the prey content isno t far from reality, and theintra - colony distribution of the prey is close tobein g random,bot h extensions were considered tob e irrelevant toth epresen tproblem . Besides,th emino r effect of 're-crossing areas already visited by the predator' 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 onqueuein 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 treatedb y theden tist and the 'queue'o f ingestedpre y 'waiting'i nth e gutt ob e digested, resorbed and egested by the predator. The treatment time isequa l toth e time needed for digestion, resorption and egestion ofth emas s equivalent toon eprey , referred to as 'gut-emptying time'.Th e gutconten t isdivide d in classes, also equivalent to the mass ofon eprey .A t full satiation (= N class) no 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 the searchingperiod s and anexponentia l distribu tion of the 'gut-emptying time', a seto fN+ l difference equations canb e derived by computing the short interval changes inth e relative frequencies (= p (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 (t+DELT) can be computed fromP_(t )b y summation ofth e following transitionproba bilities: theprobabilit y tocaptur e and ingeston epre ymas s without simultaneous resorption of amas s equivalent toon eprey , causing anincreas e ofth e food contento fth egu t from classn- 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 content of the gut (=n ) theprobabilit y ofn o capture and no resorption,resultin g ina constan t level inth e food contento fth e gut (=n ) the probability of no capture and onepre ymas s resorbed, causing ade crease ofth e food contento f thegu t from classn+ l ton .

142 Theprobabilit y ofa captur e ofon epre ymas sca nb e found fromth e fol lowing formula (CSMPnotatio n isno tuse d inal lsubsequen t formulas): 2 RSE DELT PRC= 1- exp(-RS E *DELT )= 1 - (1- RS E *DEL T+ ( * 2 ) ) 2 Neglecting the terms involving DELT , this formula can be simplified: PRC= RS E *DEL T Because RSE depends on the amount of food inth egut ,thi s formulaca nb e rewrittenb y adding the suffixn ,whic h indicates thesatiatio nclass :

PRC n= RSE „ n*DEL T and PRC..= RSE. .= 0 N N The probability of theresorptio no fon epre ymas s ingested canb ecom puted in the same way after calculation of the timeneede d toresor b the mass equivalent to onepre y atdifferen t levelso fth e foodconten to fth e gut (0< n < N):

PRE„ =RGE 1 *DEL T and PREQ =0

RGE1 =1/TGE 1 and RGE1Q =0 n ' n TGEln = ln(n/(n-ONE))/RRGE for (1< n < N ) ONE =0.99

PRE =probabilit y toempt yth egu twit h amas s equivalentt o one prey TGE1 =tim e required toempt y thegu twit h amas s equivalentt o one prey Now iti spossibl e togiv eth e formulas ofth eabov e fourtransitio npro babilities, which form theelement s ofa summatio no fal lpossibl eway st o arrive atsatiatio n level nafte r asmal l time incrementDELT :

- Pn_i(t)* (1- PRE n)* PRC n

- Pn(t) * PREn *PRC n

- Pn(t) * (1- PRE n)* (1- PRC n)

- Pn+1(t)* PREn * (1- PRC n) 2 Again, theterm s involvingDEL T drop outi ncas eo fsmal lDELT ,s otha t the distribution of the predators over the satiationclasse s canb esimu lated by recursive useo fth e following seto fdifferenc e equations,star ting from any initial distribution ofp (t=0):

Pn(t+DELT)= P n(t)* (1- (RSEn+RGEln)* DELT )+ ...

Pn+1(t)* RGEl n+1 *DEL T+ P n-1(t)* RSE n_x *DEL T The expected number of prey killed pertim e interval (=PRED )i sequa lt o the amount of foodconsume d inDELT ,whic h canb ecompute d from thediffe rence between the successive distributions of the satiation levels, plus the amounto f food resorbed fromth egu tdurin g time intervalDELT : N N PRED= I (pn(t+DELT)- P n(t))+ I pn(t+DELT)* RGEl n *DEL T

Thecumulativ enumbe r ofpre y killed (=CUMPRD )i sthe n foundb y addingth e instantaneousvalue s ofPRED .

143 When prey density iskep tconstan tb y immediate replacement ofth epre y killed by the predator, the rate of food intake willbecom eequa l toth e rate of gut emptying sooner or later,s otha tth eprédatio nproces s enters into astead y state.Th e relative frequencies ofpredator s atth e different satiation levels can then be solved directlyb y equating the differential quotients to zero:

dPn pft+DELT)- p (t) W -*? • g^SSS »-- •

Theequation s obtained canb e rearranged asfollows :

RGE1 RSE RGE1 RSE n+l *Pn +1 - n *P n= n *? n " n-l *"n- 1 Because PO

144 may exceed the amounto f foodequivalen t toon eclas s and canb e expressed interm so fclas sunits : ENLARG= NCLASS/GUT C f =min(FC P *ENLARG ,N -n ) (SDG =N -n ) ENLARG= factor accounting forth eenlargemen to fth egu t size (andpre y size)du et o subdivision insatiatio nclasse s (Nclass) f = food intake ofa successfu lpredato r atsatiatio n leveln , expressed inclas s units (= INTEGERS) In this way ingestioni srepresente d asa discret e jumpove r fclasses , sotha tth eter m inth equeuein g equations thatrepresent s the ingestiono f

onepre y itemu p tostat en isequa l toRS E _* P n_f (f 4 n 4 N-l), instead ofRS E ,* p ,.Th emaximu m satiation level canthu sb e attainedvi acom - n-1 n-l plete and partial ingestion of the prey content, i.e. starting fromeac h class inth erang eo fN- f toN-l .I ntha tcas eth eingestio nter m ofth e N-l RSE As a queueing formula isequa l to2 n *P n- consequenceo fpartia l n=N-f ingestion the expected number of prey killed during DELT isno tequa l to the amount of food consumed. It can therefore only be computed from the term inth edifferenc e equations thataccount s forth esuccessfu lcaptures : N PRED= 1 p (t)* RS E *DEL T n=0 n n Thecomputatio n ofth e steady-state distribution,p ,i ssimila r totha t of the complete ingestion of the prey content.Startin g from anarbitrar y

value ofp. , thevalu e ofp 1 canb e solved fromp ' =0 :

- RSE0 *P 0 +RGE ^ *P l =0

Forn = 1,2,3 , ....N- l thevalu e ofP_ +1 canb e solved consecutively from d*n dtr = 0: - (RSEn +RGEl n)* P n +RGEl n+1 *p n+1 =0 (0« n« f)

- (RSEn+ RGEln)* p n + RGEln+1 *P n+1 + RSEn_f *P n_f= 0 (f< n « N-l) Subsequent rescaling ofth ecompute dp values suchtha tthei r sumequal s 1 results inth esteady-stat e distribution ofth epredator s overth e satiation classes (= P_). Again,whe nRS Eo rRGE 1var y during theprocess ,numerica l solutiono fth edifferenc e equations isth eonl ymetho d thatca nb eused . Whenonl y discrete changes inth e foodconten to fth egu tar e considered, whether these are due to food intake orgu temptying , iti sinevitabl et o expressthes echange s interm s ofprobabilities , sotha tbot hth e searching time andth egu temptyin g time are subjectt ostochasti cvaraiation .Becaus e of the random distribution of the prey within the colony and the random searching behaviour of the predator this seemst ob e obviouswit h respect

145 to the searching times between captures. Thenth ecatc h 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 fromwhic h 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 gutemptyin g time stochastic variation seems much less obvious.Eac h gutconten tclas s isemptie dwit h aprobabilit y ofRGE 1 *DEL Tdurin g asmal l timeincrement :

p(t+ DELT )= (1- RGE 1 *DELT )* p(t ) Hence

dpjtl= L.m PÖBELT) -p (t)= .RGE 1 * dt DELT+O DELT

This differential equationha s the solution p(t)= c *exp(-RGE l *t ) Sinceeac h gutconten tclas swil l be emptied sooner or later it follows that

05 ƒ c *exp(-RGE l *t )d t= 1 0 Hence c= RGE1 .Thu s the gutemptyin g time isdescribe d by thenegativ eex ponential distribution with density RGE1 * exp(-RGEl * t).Th e mean gut emptying time therefore equals 1/RGE1, and the variance is 1/RGE1 .Fro m 2 this it can be seen that because RGE1 depends onth enumbe r of satiation classes distinguished (= n),th e stochastic variation ingu temptyin g time canb e reduced by dividing thegu tconten t intomor e (butsmaller )satiatio n classes. In case of aninfinit e number ofsatiatio n classes theproces s of gut emptying is completely deterministic (variance =0).I f onewant s to reduce the variance, the effecto fenlargin g thenumbe r of satiation clas ses isgoverne db y the lawo fdiminishin g returns.Simulation s indicate that the introduction of stochastic variation of the gut emptying timehardl y affected the end results. Even the modification of the distribution from negative exponential to constant, uniform or normalprove d 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 enumbe r ofsatiatio n classes)mainl y depends onth e accuracy one iswillin g to sacrifice indescribin g therela tionbetwee nRS E andn .Te nt o twenty satiation classesprove d tob esuffi cientwit h respect toth edescriptiv epower . The reclassing principle shown in the queueing equations was used by Fransz (1974)i na mor e extended form.H e alsodistinguishe d satiation clas ses (= n) and appropriate relative frequencies ofpredator s (=p (t)),bu t he additionally recorded themea n satiation levelwithi n eachclass .Accor ding to thequeuein g approach the satiation level isonl yexpresse d indis -

146 creteclas sunit s and food intake and gutemptyin g areaccounte d forb y the probability ofdiscret e jumps fromon eclas s (n-fo rn+ 1resp. )t oth eothe r (= n).Th e reclassingmetho d appliedb yFrans z ismor e complicated. Within eachsatiatio n class themea n foodconten to fth egu ti smonitore d byinte grating the food intake andgu temptying .Whe nthi s integrationresult s in a satiation leveloutsid e theclas sboundaries ,bot hrelativ e frequencyan d themea n food contento fth egu tar etransferre d toth e appropriate satiat ionclass .Afte r allreclassings ,whic h areneede d aftera tim este po fin tegration, a weighted mean of the class-specific food content ofth egu t and of the matching relative frequencies ofpredator s iscomputed .Du et o this reclassingprinciple ,calle d Compound simulationb y Fransz,th eproces s of gut emptying can be simulated in a deterministic way,whil e searching conserves its stochastic character.However , asstate dbefore ,Mont eCarl o simulations have showntha tth eestimate dprédatio ni salmos tunaffecte db y thestochasticit y ofth egut-emptyin g time,whethe r uniform, exponential or Gaussian distributions were used.Therefor e forreason so feconom y there classing principle of thequeuein g approach ist ob epreferre d since iti s based onon e instead oftw ovariable s perclass . A realistic aspect ofth eCompoun dmode l (Fransz,1974 )i stha tth ein gestion can be integrated over small time increments instead ofbein gre presented by discrete jumps inth e satiation level.Frans z accomplished this by splitting each satiation class into 2 subclasses: one with predators handling apre y andon ewit hpredator s searching forprey .Eac h subclass is again split into a fraction of predators continuing the same occupation (handlingo r searching)an d acomplementar y fraction shifting fromhandlin g tosearchin g (=abandonin g thecaptive )o rvic evers a (=catchin g the prey). Within the handling subclasses ingestionca nb emonitore db ynumerica lin tegration. However one may askwhethe r thisrealisti c detail isnecessary : the short period needed to achieve 90%o fth eultimat e food intakedurin g the total handling period and thehig h suction forceo fth eingestin gpre datorma y justify aconcep to f 'immediateswallow' .T oestablis h anypossi ble effect of the underlying concepts of food acquisition, the following models are compared for the case of a young femalepredato r (Metaseiulus occidentalis) hunting for eggs ofth etwo-spotte d spidermit e (Tetrant/chus urticae): Deterministic model (Appendix E) - Monte Carlomode l (Appendix F) - Queueingmode l (Appendix H) - Compoundmode l (Fransz,1974 ;inpu tadapte d toresult s ofthi s study). Both the Monte Carlo model and theCompoun dmode l are ablet omak eus eo f separate recordingo fth e ingestionproces s duringth ehandlin gperiod .Th e numerical integration procedures required toaccomplis h this arediscusse d by Fransz (1974). Asdiscusse dbefore, th edeterministi cmode l isbase do n the concept of continuous feedingb y identicalpredators ,an dth eQueuein g

147 RATE OF EGG CONSUMPTION ( DAY"') 16

PREYEG GDENSIT Y( CM "

Fig. 36. Comparisonbetwee n four differentmodel s ofth eprédatio nproces s foryoun g females of Metaseiulus occidentalis and eggs of Tetranychus urticae (T = 27°C). (Coincidence in space isno tconsidered) . ,Compoun d simulation; ,Queuein g approach; ,Deterministi c simulation;i . themea n and standard deviation of10 0Mont e Carlosimulations .

model is based onth e concepto f immediate swallowing ofth epre ycontent . The results ofth e simulations with these fourmodel s aregive n inFig .36 . Both the Compound model and the Queueing model give prédationrate s that fall within the confidence limits of those obtained from theMont e Carlo simulations. Itma y therefore be concluded that in the presentmodel s of the acarine predator-prey system detailed representation ofth e ingestion process is superfluous and can be replacedb y immediate swallowing ofth e prey.Th e deterministic modelproduce s consistently lowervalue s ofth epré dation than allothe rmodel s presented. As discussed by Fransz (1974), this difference iscause db y the curvilinearity ofth erelatio nbetwee n the sati ation level and several components of the searching behaviour (e.g.succes s ratio). For the remainder of the simulations the Queueing model ispreferred , because of itstractabl emathematica l properties,parsimon y with respectt o the number of variables and relatively economic demands on computertime . Moreover, theQueuein g model canb eprogramme d as acomprehensiv e subroutine, which can be coupled toth emode l of thepredator-pre y interactions onth e population level (Part2) .

148 3.3.2 Prey density

Itshoul d be stressed thatth emajorit y ofdat aconcernin g thepredator y behaviour (Section 3.2) were obtained at highpre y density or incomplet e absence ofth eprey .Fo r thisreaso n iti snecessar y tovalidat e simulations of the rate of prédation at intermediatepre y densities.Th erelatio nbe tween the rate ofprédatio nan dpre y density shouldb e determined atstan dardized initial conditions (standard age,sex ,feedin ghistory ,temperature , relativehumidit y andpre y distribution), aswel l asa tsteady-stat econdi tions during theexperimenta l period.Thes econdition s implythat : - the motivational state of the predator is independent of its initial level and oscillates around astabl e level the prey density remains constant, despite prédation,b y immediatere placemento fth epre y killed andb y rulingou tth epossibilit y ofreproduc ingo rdevelopin g into anex tstage . However immediate replacement ofth epre y killed (ormoulted )i s frequently impractical,i ncontras t toschedule d replacement. Inth e lattercase ,pre y density fluctuations depend onth etim e interval ofpre y replacement.Con sequently the mean motivational state is destabilized. The fluctuationo f the prey density can be damped by shortening thereplacemen t interval and enlarging the experimental area,provide d the initialpre ydensit y iskep t at the same level by adequate increases inth enumbe r ofprey .Du et oth e fluctuatingpre y density therat eo fprédatio nwil lb eunderestimate d rela tivet otha tobtaine d ata constan tdensity . Thedegre eo funderestimatio n atsevera lvalue so fth ereplacemen tinter val and of theexperimenta l area aregive ni nFigure s 37an d 38 fora spe cial case studied by Küchlein (young femalepredato r of Metaseiulus occidentalis, eggs of Tetranychus urticae asprey , unwebbed substrate, T = 25-27°C). As the density initially established declines,th eunderestima - tions become more and more severe at all schedules of prey replacement. This is a consequence of the curvilinear shapeo fth e functional response curve: the effect of auni tchang e ofth epre y densityo nth erat eo fpré dationbecome smor e andmor e severe asth einitia lpre y densitydeclines . The functional response, measured by Küchlein (tob epublished) ,meet s mostrequirements :th eexperimenta l leafare awa s large (5 cm2), theinter val ofpre y replacementwa s short (0.5hour )an d thepredator swer estandar dized before use and adapted tothei rexperimenta l environment for several hours. The leaf discs were put on water-soaked cotton in a petri dish, which largelyprevente d dispersal ofth epredato r fromth e leafdis cwithi n the experimental time alloted (6 hours). Thewel l replicated measurements and the appropriate simulationsar epresente d inTabl e 57.Thes e correspond with each other inth erang e 5-30 prey eggspe r cm2.Howeve r atlowe rpre y density the simulatedprédatio nexceed s themeasure d valueb y afacto r 1.5. This deviationma yb e explained by alowe rcoincidenc e betweenpredato ran d

149 RELATIVE UNDERESTIMATION( % 1.0

PREYEG GDENSIT Y(CM "

Fig. 37. Influence of the prey replacement interval on prey consumption relative toth e rate of steady stateprédation .Experimenta l conditions are takensimila r tothos e inKüchlei n (tob epublished )excep t forth eexperi mental area (=1 cm 2; comparewit h Fig.38) .

RELATIVE UNDERESTIMATION (%) 1£h

0.6-

0.4-

0.2-

0 1 5 10 PREYEG GDENSIT Y(CM" 2)

Fig. 38. Influence ofth e sizeo fth e experimental area atconstan t initial prey density onth erat e ofprédatio nsimulate d under conditions ofa 12-hou r prey-replacementschedule .Th eunderestimatio n ofth epre y consumptionrela tive toth e simulated rate of steady stateprédatio ni splotte d againstth e initial prey-egg density. Experimental conditions are similar tothos e in Küchlein (tob epublished) . 150 10 IV rH •p 0 rd 10 C •a m 41 0fi 4c) •0 U> tai •H Oi •Q Xl P •P •H rfiO ->^1 10 (0 •cH: -Q P fi T3 CO •0 •H •H ai 3 w 4) •rai M 3 4) •>H fi 0, CO ft •P >1 Ol ca U •P a-H 01 m rfl pQ •fiH 4a) rH U3 5 •fiH T) •sH 3 r^ *rH 10 in CM O CO CN m r> o CN r> Oi •H ai i ai 4) •p M rfl 0fi 0. u •H •p •P 0 10 (0 •P Xl 73 ai CD 3(0 M •H 0. 10 rH •0 M ID ai •a 3 •P X) ai 0 XI •P X! 4fi1 ai •o S r«H •H 3 * r> in M in O CN rH in m O Oi CN CO m 0 3c E M rH Cl t~ 01 rH CN in r•*- o o o o rH rH H rH rH Cl CO 10 O in 01 rH CN CN ai r« ta •0 t> r> r- r> CO CO C^O o rH t- rH a» >o f •rl 10 in (0 u in l1 IH •H II U (0 O • O • rH M m 1" lO co 41 ai H co in r> o CM o -fiH O a* •P 2 0,u r-l rH rH CN 41 •sH ft rH 3fi U afii XI a> -i-i u 'M a> u tv •fiH 0 Cd IH «1 X) 10 XI ai M u 41 •P ai ai M ai 3 •H ••H Q 0 •O « -c» s a. g3 XI 3 O O O O co o m in in o o o O O co a m vi IH 1 P •* r> o O o o r> t> r> in 10 lO lO 10 o t« 0 0 23 «3 0a CN CN rH rH CM rH CM 01•

151 prey, causedb y an increased tendency towards anedg e orientedwal k (=dis persal). Possibly the ribs and edge of the leaf are frequented more often in this range of low prey densities than indicatedb y themeasurement s at high prey densities (Subsection 3.2.6). Atver y lowpre y densities thesi mulatedprédatio nbecome s equal and subsequently lowertha n the actualmea surements. As discussed by Küchlein (to be published), themeasure dprédatio nre veals two particular phenomena at the extremes of the prey density range under investigation. Firstly the eggconsumptio n does notdecreas eprogres sively below a food supply of8 egg spe r disc,bu trathe r ittend st osta bilize despite the decreasing prey supply. Küchlein argues that probably the searching behaviour is stimulated by increasedwalkin g 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 iti sinteres ting to include thesebehavioura l measurement inth e input for anothersimu lation experiment. The agreement between simulated andmeasure d prédation is somewhat improved,bu t a full explanation ofth e sigmoid prédationcurv e is stillno t achieved. The second peculiarity ofth e functional response curve showsu p athig h prey-egg density. Comparison between simulation and measurement reveals a second riseo fth emeasure d prédation.Thi s differencema y indicate another motivational component, which is not related toth e amounto f food inth e gut; the piercing ofth eeg gchorio nma yb e stimulated by frequent contact withpre y eggs.Th e question ariseswhethe r this level ofcontac t frequency operates under more realistic circumstances. The prey density of 40egg s per cm2 is certainly relevant under field conditions.Howeve r the rateo f contact atthi sdensit ywil lb eprobabl y toohig hdu et oth e absence ofweb bing in these experiments. The difference between simulation andmeasure ments athig hprey-eg g densityma yb e caused aswel lb ychange s inth e wal king pattern related to the eggs which were distributed ingroup s ofte n eggs to easify counting;th epredato rma yb e arrested by thehig h eggden sity inth e egggroups .

3.3. 3 Webbing

The webbing produced by the spidermit e causes therelativ e rate ofen counterbetwee npredato r andpre y (=RE/DPREY )t ob e reduced by a factor1 0 to 100.Thi s reduction isdu e toth edecreas e ofth ewalkin g speed, thewalk ing activity and thecoincidenc ebetwee npredato r andpre y inth ewebbing . Moreover, webbing can induce drastic changes inth e success ratio (Subsec tion 3.2.7). Therefore distinctvalidatio n ofth emode l and itsbehavioura l inputdat a isneede d forth e caseo f asubstrat e covered withwebbing . Including thewebbin g factor causes several experimental problems.First ,

152 prey replenishment turns outt ob e animpracticabl eprocedure .Contac tbe tweenth ebrus h andth ewe bthread s frequently results inactivatio no fth e predator,whic h issensitiv e tomovement s ofth ewe b threads.Th ewe bstruc ture may be harmed, too, by thesemanipulations .Besides ,positionin g and settlement ofth eegg sb y abrus hma y differ fromth enatura leg g deposition ofth e female spidermite .Fo rthes ereason s themeasuremen to f steady-state prédation is hardly possible. Simulation accounting for non-steady state conditions isth eonl ywa you tthen .T oenabl e these simulations theexperi mentswer e startedwit h fully satiated femalepredator s and aspecifie d ini tial density ofpre y eggs inth ecolony .Accordin g toFig .3 9th eunderesti mation ofth erat eo fprédatio nca nb e keptwithi ncertai n limitsb yenlarg ingth ewebbe d area,shortenin g ofth eexperimenta lperio d andomittin gth e study of prédation atlo wpre y densities.Anothe rproble m israise db yth e dispersal tendency ofth epredators .Lea fdisc s surrounded by awate rbarrie r proved tob e asatisfactor y substrate for Metaseiulus occidental is. However the leaf disc-water barrier system proved tob e insufficient forth ecas e of Phytoseiulus persimilis-, whenth epre ydensit y islow ,thi spredato r is frequently observed to disperse from the discs andt odrow ni nth ewater . The best solution istherefor e tous enatura lcolonie s formed onth eplan t and toomi tth e studyo fprédatio na tth erang eo flo wpre y densities,whic h

RELATIVE UNDERESTIMATION (%) 1.0

0 5 10 15 20 PREYEG GDENSIT Y(CM -2) Fig. 39. Influence ofth e sizeo fth ewebbe d area atconstan t initialpre y density on the rate of prédation simulated under conditions ofa 12-hou r prey-replacement schedule.Th eunderestimatio n ofth epre y consumptionrela tivet oth e simulated rateo fstead y stateprédatio ni splotte d againstth e initialprey-eg gdensity .N oprey-replacement ;experimenta l period =1 0hours ; T =20°C ;R H= 70% .

153 give rise tohig h dispersal tendency ofth epredator s (seeSubsectio n 3.4.2). At the start ofth e experiments rose leaves connected to a5-1 0 cmpar t ofthei r shootwer e cutoff .Subsequentl y the leaf systemswer eplace d ina water filled test tube. Young female spidermite swer e allowed toproduc e egg colonies on these leaves during 2day s atT = 25°C .Nex tth e leaf sys tems were transferred to aroo m kept ata lowe rtemperatur e (T= 20°C), to postpone hatching. After removal ofth ecolonyfounder s thewebbe d areawa s measured andth e appropriate number ofegg swer e counted ateac hreplicate . The size ofth ewebbe d area should exceed 4cm 2, sotha t anextrem e rate of prédationo f2 0egg spe r 10hour swoul d cause adecreas e ofonl y 5unit s of thepre y density. The eggdensit y should match some specified levels (14-15, 30-40o r 50-60), otherwise thesehav et ob e adjustedb y crushing the surplus eggs with a thinneedle .On eyoun g and satiated femalepredato rwa strans ported to the upperside ofeac h leaf system on anexcise dpar to f itsori ginal leaf. This procedure disturbs the predator less.Th epredator s left the excised leaf parts and entered the egg colonieswithi n anhour .Thei r position in the colonywa splotte d foreac h leaf system.Durin g 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), butthes ewer e notuse d infurthe r calculations ofth e rateo fpré dation. The results are presented in Table 58,togethe r with simulations formatchin g conditions.A t allpre y densities tested, the simulationscor respond with themeasurement s forbot hphytoseii d species studied. Because most studies ofphytoseii d prédationi nth epas thav e neglected the factor webbing, it may be worthwhile to comment onthei r reliability

Table 58. Prédation inpre y colonieswit h spidermit e eggs.Webbe d area= 4-11 cm2; nopre y replacement; experimental period =1 0hours ;temperatur e 20°C;R H= 70% .

Predator species Number of Range ofpre y Measuredprédatio n Simulated replicates eggdensitie s 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 2.42

154 for the purpose ofextrapolatio n toth epopulatio n level.Accordin g toth e data presented in Tables 57 and 58 the rate of prédation of Metaseiulus occidentalis islowe ro na webbe d substrate (0.36egg spe rhou rv s 0.55 eggs per hour). Behaviouralmeasurement s and simulations indicate thatthi sdif ference isexplaine d largelyb y thedifferenc e inwalkin g speed, associated withthes e substrates.Beside s itshoul db e recognized thatth ecoincidenc e between predator and prey eggso nth ebea nlea fdisc suse db yKüchlei n(t o be published) accidentally correspondswit h thati nth ewebbe d space.Thu s it may be stated thatth e artificial edgeo fth e leafdisc scontribute s to theconcealmen t ofth erea l differencesbetwee nth esubstrates . Another example of theimportanc e ofth e substrate is found inth ecas e of Phytoseiulus persimilis, which showsdrasti cbehavioura l changes inre sponse towebbing .Th erelativ e rateo fencounte rdecrease sb y afacto r 100 asa consequenc e ofth ewebbing ,bu tth esucces s ratio isincreased .Simula tions based on these behavioural data show that the rateo fprédatio no n the webbed substrate exceedstha to nth ebar e leafdis cb y afacto r 1.5-2. Apparently the effect on the success ratiooverrule s thato nth e relative rateo fencounter .Schmid t (1976), whomeasure d theprédatio no fthi sphyto - seiid onbar e andwebbe d leaves,foun da ver y similar difference.Th edat a ofTakafuj i & Chant (1976)an dLain g (1968), obtained onunwebbe dsubstrates , are therefore likely to be underestimations of the prédation rate.Lain g found aprédatio nrat eo f1 4egg spe rda ya tT =20°C ,whic h is substantially lowertha ntha t 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 rda y atT =25°C ,whic hcontrast swit hth emeasure ments and simulations atthi stemperatur epresente 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 so r inan ycavit y thatca nb edistin guishedo nth estem .Muc hles s frequently thanth eothe rphytoseii d species studied, theyentere d 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 ngrowt ho f Tetranychus urticae, as found ina populatio nexperimen tdescribe d inPar t2 . These examplesundoubtedl y prove the importance ofth e factorwebbin g inth e quantitative assessment ofth eprédatio ncapacit y ofphytoseii dpredators .

3. 3.4 Temperature

Mosto fth ebehavioura l observations (Section3.2 )wer e carried out atT = 20?C,s otha tthes emeasurement s shouldb e repeated forothe rtemperatures . However the few additional experiments carried outa tothe rtemperatures ,

155 indicated ratherunimportan t effects onth e searchingbehaviour . Temperature 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 foodconten to fth egu ti na wa y independent of temperature, while the temperature-related dynamics ofth e food conversion determine the rateo fprédation . Inothe rwords ,th erela tion between the relative rateo fgu temptyin g andtemperatur e may explain the effect of the temperature onth erat e ofprédation .Thi s assumption is evaluated in anumbe r of simulations andexperiment s concerning the rateo f ! i 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 fromth esimulation sbase d onth eabov e assumption, may indicatebehavioura l changes,associate d with the temperature.Fo rexam ple thewalkin g speed, thewalkin g activity orth e ability tocaptur e apre y may be decreased by temperatures lowertha n20°C . Intheor y iti spossibl e thatcounteractin g effects ofth e temperature neutralize eachother ,s otha t the resulting rate ofprédatio ndoe sno tdeviat e from thesimulation .Howeve r iti sno t likely thatth etemperatur e has apositiv e effecto n one behavioural component and anegativ e effecto n another. Iti smor e likely, thatth eef fecto ftemperatur e onth e searchingbehaviou r showson econsisten ttendency , if any. In that case an evaluation, as outlined above,ma yb e apowerfu l tool inlocalizin g relevant areas of further research onth e searchingbeha viourunderlyin g the functional response atdifferen t levels oftemperature . In Table 59 the simulated and measured egg consumption of Metaseiulus

Table 59. The rate ofprédatio no ftw ophytoseii d species (young females) atthre e levels ofth etemperatur e andhig h density ofth epre y inth e webbed area.Pre yeg gdensit y =40-6 0eggs/cm 2;webbe d area =4-1 1 cm2;n o prey replacement; experimental period =1 0hours ;young , satiated female predators.

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

Phytoseiulus 31 15 5.16 1.44 4.71 persimilis 22 20 9.59 3.10 8.92 35 25 2.16 2.72 12.58

Metaseiulus 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. Therat eo fprédatio no f Metaseiulus occidentalis atdifferen t levels oftemperatur e andhig hdensit yo fth eprey .Numbe r ofpre y eggspe r leafdis c= 100;lea fare a= 5 cm 2; unwebbed substrate;th epre yegg skille d were replaced afteron eda y= adaptatio nperio d ofth epredator ; subsequent periodo f 1da y= experimenta l period.

Numbero f Temperature Egg consumption Simulated replicates (°C) per daya 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. Therat eo fprédatio no f Amblyseius bibens atdifferen t levels ofth etemperatur e andhig hpre y density.Pre yeg gnumbe r =40 ;lea fare a= 4.5 cm2,-unwebbe d substrate;th epre y eggskille dwer ereplace d afteron e day =adaptatio nperio d ofth epredator ;subsequen tperio d of1 da y= expe rimentalperiod ;egg so f Tetramjchus neocaledonicus.

Number of Temperature Egg consumption Simulated replicates (°C) per daya egg consumption

32 18 4.4 1.8 7.5 21 22 9.7 1.8 10.3 30 25 13.4 2.2 13.5 25 28 17.2 1.7 16.6 37 31 21.2 2.3 18.9 a.Dat a fromBlommer s (1976).

occidentalis and Phytoseiulus persimilis isgive nfo rthre edifferen tlevel s oftemperatur e andhig hpre ydensity .Thes eexperiment swer e carried outo n webbed leaves according toth eprocedur e discussed (Subsection 3.3.3). There is a striking correspondencebetwee nth e simulated andmeasure dprédation , which indicates the absence ofrelevan teffect s ofth etemperature .Th esam e

157 Table 62. The rate of prédation of Amblyseius potentillae at different levels oftemperatur e and atdifferen tdensitie s ofth e larvae of Panonychus ulmi. Leaf area = 3.8 cm2 (or7. 6 cm2); unwebbed apple leafo f 'GoldenDelicious' ;interva l ofpre y replacement =1 5minute s (T= 25°C )o r 1 hour (T = 15°C); experimental period = 1 day;predator s areadapte d to theenvironmenta l circumstances forsevera lhours .

Number of Temperature Number ofpre yPre y consumption Simulated prey replicates (°C) per leafdis c perda y 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 a.Dat a fromRabbing e (1976).

conclusion can be drawn from a similar analysis of the experiments of Küchlein with Netaseiulus occidentalis over abroa d range of temperatures (Table 60).O n the contrary the analysis of Blommers's experiments with Amblyseius bibens reveal aneffec to fth etemperatur e (Table 61);th esimu lations at low temperature result ina noverestimatio n ofprédation , those athig htemperatur e result ina nunderestimatio n ofth eprédation .Apparent lyth e searching behaviour of Amblyseius bibens isstimulate db yhig htemper 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 a concerning 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 ,th e functionalre sponse of Amblyseius potentillae to the density of the larvae and adult females of the spider mite are simulated. Comparisonbetwee n the dataan d the simulations again shows atendenc y tooverestimat e theprédatio na tlo w

158 Table 63. The rateo fprédatio no f Amblyseius potentillae atdifferen t levels oftemperatur e and atdifferen tdensitie s ofth e adult femaleso f Panonychus ulmi (eggso f Panonychus ulmi wereno tconsumed) . Leafare a= 3.8 cm2 (or7. 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 =1 day ;predator s are adapted toth eenvironmenta l circumstances forsevera l hours.

Number of Temperature Number ofpre yPre yconsumptio n Simulatedpre y replicates (°C) per leafdis c perda y a 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 fromRabbing e (1976).

temperature (15°C) and to underestimate at high temperature (25°C),whil e there iscorrespondenc e atintermediat e temperature (18°C). Indeed there aresom edirec tmeasurement s ofth esearchin gbehaviou r that indicate thati ti saffecte db y temperature, though only slightly.Fo rexam ple, the walking speed increases somewhat for an increase intemperatur e (Subsection 3.2.2). It isquit epossibl 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•{ ( I- webbed substrates,whic h areth eusua l substrate foran ypredato r foraging on the two-spotted spider mite, similar analyses showed that temperature hadn oeffec to npredator y searchingbehaviour .Thi s resultcorrespond s with the assessment of onlymino reffect so fth e temperature 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,whic h does not produce web aggregates, it is more careful to study the effect oftemperatur e onth e searchingbehaviou r atth e sideo fth e leaf facingdownwards ,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 may consequently besmall .

159 3. 3.5 Age and oviposition history

So far only young females, aged 3-8day s after their finalmoult ,hav e beenconsidere d inthi schapter .Becaus e thepopulatio nmode l ofth epreda tor-prey interaction includes prédationa tal lphase s ofageing ,th ebeha vioural study ofth ephytoseiid s should beextende d accordingly.However , before doing so,th enee d forfurthe r experimentation isconsidered . Itma y be assumed tentatively that the ability tocaptur e apre y successfullyi s constantwit hag ei ncontras tt oth econversio no ffoo d (digestion,resorp tion, synthesis and allocation). Inothe rwords ,th erelativ e rateo fsuc cessful encounter (=RS E ,i fDPRE Y=1 ,0 < n< N)ar econstan tdurin gth e whole period of female adulthood,bu tth erelativ e rateo fgu temptyin g (= RRGE) isvariabl e in this respect. Inthi s case anychang ei nth erat eo f prédation during the adult period is thought tob e causedb ya chang ei n the intrinsic food utilization ofth epredato r apart from changes inth e prey density. Ifthi s conception is true,i ti ssufficien tt omeasur eth e behavioural components aton e specific ageperiod , while theag erelate d changes inth e relative rateo fgu temptyin g canb eestimate d fromth ere 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 againstexperimenta l obser vation. The assumption thatRS E isconstan twit h ageca nb eevaluate db ycompa risono fth eobserve d prédationrat eo ffemale so fdifferen t ages thathav e the same levelo ffoo d conversion.Thi si sachieve db ycomparin g thepréda tiono fnon-ovipositin g femaleso fdifferen t ages: unmated young females (2-4day s after finalmoult ) 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 eth esam 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 (=RSE n, ifDPRE Y=1 ,0 < n« N) areobtaine d fromth e3- 8da yfemale s (Section3.2 )an dusin gth emode l ofphytoseii d mass expenditure (Subsection 3.3.1)unde r conditions ofsatia tion,a valu e ofRRG Eca nb efitte d such thatth eweigh tlos sb ytranspira tion and respiration (=fres hweigh tminu s food contento fth egut ,multi pliedb yth erelativ e rate ofweigh t loss; seeSubsectio n 2.2.5an dSectio n 3.1)ar e compensated byresorptio no ffoo d fromth egu tstore .Th esimula tionso fth erat eo fprédatio no nbasi so fthes 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 M Il 4)

id •g ai 3 M a -0 (0 0) 0fi 4J •H •o m +J 41 £(0 i-i id a •0 3 •O XI E 0) co O 4) rH •ri M w O, Ol in m > II u •0 c o 0 0 O •H •H X>I . m M M •P in 01 •d 0fi i II a •0 -^>»i •H m Ol 01 id •P *e EH r-t M T3 •H o Id 0. ta S M Ol 0 (0 •H 3 to 0> rH M m 0i •p id to •P 01 id 0i to E o co 00 c P. 01 01 0 O) >id ! 01 X S N^> H p.. . 0 N -H c •ri X) in n 01 P c CO g id »—•* 0 i M-l 01 "0 >i •ri in o o 0) •d •p CS M •0 -ri »1 .«H a. ta <<-i 01 M o p rH &o> •0 0) •O 18 M 01 •ftH to i-t S M ft Ol 0 01 0i 3 to 0> l-i >H 0i 10 Ol +J id to 01 id Oi to S >1 00 "* 0> 01 Ol 0 Ol id c >i S •w 1 o 0 0 •H XI •p to a c "•«• •H 1 r-i 0> l\l 01 id id 1 6 M •0 •o a 0 a Oal rH 0 M 1 XI 3 (0 •p rd tfl ta Oi id •0 c Oi id Oi g CO cs m o 0i 0) Ol o •ri 01 S 1 0 1 0 tO o •ri XI •P (0 ofi * id "—V Ol u II •0 >i rH 01 •d id -0. Di >1 M •O E r^ Oi •p Ol O 01 -ri ft M 1 0 01 IT) u Ol id •o rH 3 to •p TJ 01 1 to Ol id rH 01 r» •p 01 O id Ol s (S 0i rH Ol Ol ^1 O * * M 01 S s 3fi CS rH II -' 01 >i xi 01 to n V to w p 3 w -H 111 >-H W w 3 -H u 3'H 3 "1 ld 1* i\i •H M •f» "H 'H 3 HJ S H 0 to 41 -N 4) •M C3 <& 0 a •P Ol to S VI (* pQ J5 •u o m 4-< i-i Q. •Q 01 S •M 0) tj | 0 »4 Ss <* to Û. ö. •^ •4 * 0

161 females is somewhat lower than theothers ,whic h indicates asligh teffec t due to ageing. However this effect can alsob e leftou ti nsimulation s of the interactionbetwee npredato r andpre ypopulations ,becaus e the fraction ofth e females reaching thisphas e ofadulthoo d (50days )i s small,anyway . For this reason the simulations onth epopulatio n levelhav ebee nbase d on the assumption of searching ability,whic h isconstan twit hage . The second assertion ofa variabl e relative rate ofgu temptyin g (RRGE) with age is therefore probably true,becaus e thereproductio n has acurvi linear relation with age (Subsection 2.2.3). The relation of RRGE toag e appears to have a flexible character duet o the strongtendenc y amongth e Phytoseiidae to achieve the deposition of aspecifie d number ofeggs ,for , as argued in Subsection 2.2.3, therat eo freproductio n doesno tdepen d on age, but rather onth enumbe r ofegg s already deposited.Becaus e reproduc tiondepend s onth edeliver y ofgu t 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 thatdirec tmeasuremen t ofth eRRG Ecorrespond s with its indirectestimatio nb y amode l ofth ephy - toseiidmas s expenditure.Therefor e thismode lha sbee nuse d forth eappro priate rates ofreproductio n toestimat eRRG E for several 'history'classes . These estimates weremad e forth ecas e ofampl e food supply, sotha ta swel l asth e rate ofreproduction , the food contento fth egu t isknown .Thu s the relative rate of gutemptyin g canb e fitted inth emas s expendituremodel . For sufficientdescriptio n ofth echange s inth e food conversion, theovipo sitionhistor y shouldb edivide d into atleas tfou repisode s (classes)wit h respectt oth erealize d parto fth epotentia l fecundity: lesstha n 60%o fth e eggs deposited 60-85%o fth eegg s deposited - 85-100%o fth e eggs deposited allegg s deposited (=post-ovipositio n period). The appropriate values ofth erelativ e rateo fgu temptyin g aregive ni n Table 65.Thes e estimates were obtained from thereproductio n curves pre sented orreferre d to inSubsectio n 2.2.3,whic hwer e obtained atcondition s ofabundan t food supply.Th e estimates wereevaluate d atlo wprey-eg gdensi ties for the case of Metaseiulus occidentalis, using data of itsreproduc tionhistor y (Küchlein,t ob 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 densitieswer e available and theRRG Evalue s ofeac hhistor y classwer e estimated from the reproduction curve ata hig hpre y density (150egg spe r 5 cm2), therat eo f reproduction at lower prey-egg densities were simulatedwit h themode l of 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 50days ,

162 Ol Di I C M « 0> M 9< g to co io co o •o 0) 0) co co oo •H CM P M I I I •o « 5 co CO co a > n) a o •H •P •H 01 O Oi 13 >1 -rt •ri M >i > O •P •P O o o o o +J Og)* •^ . to ra H O -H •P H 04 43 g. 1« H ta o « i to Sft o I« 4) ai 0 H •P •p Ü (0 H • M •^ 1 >i X >1 M H a< *w to •P o •H 10 j u 43 iH w h 00 (U O M o o o M u J 0 o w 4-1 C u a) Ü ai O S a«s CS •P ai >—• H >—• (0 43 N 1 (0 n U a) G o 0 H 0 P 0 •H to H • •P •H 1 >1 43 >1 M i«H 11) 0 ai C •0 •P M O «V (0 •H •r-l ai •P w 43 •O •H Ol Ol •a. a> (0 o M •a• 01 to 5 0 J O o 01 10 •H m UI IH (O •H •H 0 •ftH -H l-l (8 > i-H 18 01 ai 0 U 0. r-l ai u o ai M >i i-i 43 H -~- 10 >l •P to •p 1 to >t •p •H u IS •p •H •a ai C 0 i-H •H •O a 43 -H ü •o 13 3 •p H • c 3 0 ta 1 3 0 0> >H ai >i >M , O ai M-l o (0 1« 0 01 —' ta i-l 10 c Oi •H i-H 10 •r-l 0 W 43 in II) •H •P •H U CM H in o Ol •H •P C •P 3 O M M CS r-l •P f3 01 It) o J O rt C 01 •p E (3 W 't) 1 o m| "-H Oi •o u •u m •-I 0) I-I 01 m -M •Q B ai ai Sn Is •O *J rQ 45 •w O m ai M a <: ai s •M O) U h +J tt. 0. 3I oö. •3! •Q S: o 18 45 O

163 HISTORYCUMULATIV E NUMBERO F CLA5- NUMBERO F PREYEGG S SES EGGSPRODUCE D PERAREN A(5CM 2)

4- 3

v 90 100 TIME(DAYS )

Fig. 40. Cumulative reproduction inrelatio n toag e andovipositio n history of Metaseiulus occidentales atdifferen t levels ofprey-eg g density.Measure d data of Küchlein (to be published) ( )an d simulated values ( ). Unwebbed leaf disc; area = 5 cm2; daily replacement of eggs consumed; T =25-27°C ;R H= 70% . reproduction stopped, irrespective ofth eovipositio n history. Becauserela tively few females reach thisperio d ofadulthood , this aspectma yb e ignored in simulations of the interaction between predator and prey populations. Unfortunately, such evaluations of the estimated values ofRRG E could not be carried out for theothe rpredato r speciesbecaus e oflac k ofreproduc tion-history data at low prey densities and for the whole life-span of phytoseiid females.

3. 3. 6 Predator density

When predators aggregate in colonies with a high prey density, it is likely that they will encounter each otherwhil e searching forprey .Thi s contactma y intur n lead to anincrease d tendency toward dispersal (Subsec tion 3.4.3)or , ifth epredator s areconfine d toth epre y colony, to ade creased prey consumption.Th e latter casewil lb e considered below. Küchlein (1966)observe d adecreas e inth e rateo freproductio n of Meta seiulus occidentalis at predator densities exceeding one female per leaf disc. Fernando (1977) found adecreas e ofth erat eo fprédatio nb y females of Phytoseiulus persimilis. Because the ingested food is utilized to a great extent in egg production, reproduction decreases whenpre y consump tiondecreases . A decline in the rate of prey consumption can be caused by adecreas e

164 therat eo fcontac twit hpre y items (i.e.RRE ) thereceptivit y tocontac twit hpre y (i.e.Succes s ratio) therat eo f foodconversio n (i.e.RRGE) . Because thetim epredator s spend incontac twit heac hothe ri sneglegible , and the walking speed and activity remain unchanged after mutual contact (ownobservation ;Küchlein ,persona l communication),th etim eavailabl e for prey searching remains nearly unchanged, at realistic predator densities and therefore the firstpossibilit y canb e cancelled.Th e lattertw oexpla nations are difficult to illustrate by experiment. Itma yb e hypothesized thatth ereproductio n site inth e acarine functions as a 'sink'wit h respect toth enee d for food andtha tthi s 'sink'i scontrolle d by theneurophysio - logicalstat eo fth epredator .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 taffecte db ypreviou s contact,th edecrease d rate ofpre yconsumptio n 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 ofgu t 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,measure d byKüchlei n (1966)fo rth ecas eo f Metaseiulus occidentalis. This estimation is again made with the model of the mass expenditure (Subsection 3.1.2), assuming that the success ratio isunaffecte d bymutua l interference.Eve n ifthi s tentativeconceptio n turnsou tt ob ebiologicall y invalidafterwards , it is still a very easy wayo fimitatin g theobserve d effects ofpredato r densityo nth e rateo fprédation .Th eestimate d values ofRRG E aregive ni n Table 66 for different phases in theovipositio nhistor y ofth epredator y mites.

3. 3. 7 Prey stage preference

Ifpre y stage preference is not expressed until the momento fcontac t with apre y stage,i tca nb edefine d quantitativelyb y thedifference sbe tween the success ratios related to thedifferen tpre 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 aggressiveness and attackingmeasure s takenb y thepredator .Th e successratio shav ebee nmea sured in 'monocultures' of each prey stage (Subsection 3.2.7). Thesedat a are suitable for extrapolation to 'mixed cultures' of prey stages ifth e actual success ratio isno taltere db y experiences at 'past'contact swit h prey stages,an d ifthi s ratio isdetermine d merelyb y theactua l amounto f food inth egut ,whic h isth eresul to f 'past'ingestio n and 'past'conver -

165 aIl p T3 a H >i >i SH u >1 o o m •p •p •a w m «w •H •H 43 Ä w o M iß lu lO lu G 05 O O >H O O O O -H « •P •H U &O •H > O 1) Si •p

>1 Ol a-? c o o •H f- p >i m +j M •H o, J3 W œ ID a) 2 u >-i O o 4-1 - « 'M 3 u öi o "H • •H (0 P "M >1 td f-s M rH OJ O m P >-i 10 •H

U m m es

•0 ai •a ai m m 0] •ri i ^iO >i p u o lu >i p •H 01 p •H T3 O H •H •O G .G P T3 C 3 •p *^ C 3 U C 3 O ai 1 0e 0c) p 0 •rH •H p M p 0 a, P P «H 0 0. •H 0. H O C) 4H o a •a 73 m 0 5* •H O, m •>H o io M U is-n« o >o O O V *o« 00 rH p P p T3 lO i 1

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

Hence the probability toreac h staten vi apre y capture and subsequentin gestionconsist s ofth esu mo fth eprobabilitie s oneac h- pre y stagespeci fic -ingestio n (= FCPS), which arrives atstat en :

S I = X RSE -f *p n-f *DEL T (f = FCpS *ENLARG ' N"n > FCPS) n s=l n

At full satiation itincludes ,furthermore ,th e sumo fth eprobabilité so n eachpossibl epartia l ingestion,whic h arrives atN :

S N-l S S IN = Z 2 RSE *p *DEL T (f= FCP *ENLARG ;N- n« FCP ) ™ s=ln=N- f n n

Thecomplet e seto fdifferenc e equations isthen :

S pn(t+DELT)=pn(t)* (I RSE^+ RGEl n)* DEL T+ P n+1(t)* RGEl n+1 *DEL T+ I f s=l

PN(t+DELT)=pn(t)* RGE1 N *DEL T+ IN

Theexpecte d amounto f foodconsume dpe rtim e intervalDEL T (=CONS )ca nb e computed from the difference between the successive distributions of the satiation levels, plus the amounto f food resorbedo r egested fromth egu t duringDELT :

N N CONS= 2 (pn(t+DELT)- P n(t))+ I pn(t+DELT)* RGEl n *DEL T

The expected number of each prey stagekille d duringDEL Tca nb e computed from the product ofth erelativ e frequencies ofpredator s atth edifferen t satiation levels andth e appropriatepre y stagespecifi c rateo fsuccessfu l capture:

167 PRED = I P (t) RSEn *DEL T n=0

The steady state distribution of the predators over the satiation classes (= p )ca n be computed in awa y analogous totha tdiscusse d in Subsection 3.3.1. Incas eRGE 1 andRS E arevaryin g duringth eprocess ,numerica l solu tiono fth e seto fdifferenc e equations isth eonl ywa yout . With the aid of this model extension iti spossibl e toextrapolat e the inputdat ameasure d in 'moncultures'o fth epre y stages toth e case ofmixe d populations ofpre y stages.Thi s approach canb evalidate d using experimental data of Rabbinge (1976). He offered 10 spider mites oftw odistinc tpre y stages (larva and adult female) to ayoun g female Amblyseius potentillae. The prey stages were offered in different proportions (8:2,5:5 ,2:8) , which were maintained by replacing the prey killed (ormoulted )afte rin -

PRED FEMALE PRED LARVA 10

AREA= 50 0CM ^

AREA=5 CM' AREA= 50CM 2

0.5 -\

0.1 - 0.05-

—I— 0.01 0.05 0.1 0.5 10 D FEMALE D LARVA Fig. 41. Measurements (Rabbinge,1976 ;Experimenta l area= 5 cm 2; interval of prey replacement = 1 hour; T = 25°C) and simulations (thisreport )o f prey-stage specificprédatio ni nmixe dpopulation s oftw opre y stages (lar vae and adult female of Panonychus ulmi). The quotient of thepre y stage specific prédation rates isplotte d againstth equotien to fth e respective densities of the prey stages,bot ho n alogarithmi c scale.Measure d values (•)a t 3 prey stage combinations: 2 ?+ 8 larvae; 5 9+ 5 larvae; 8 V+ 2 larvae .Simulation s ( )a t3 overal lpre ydensities : Dprey = Dfemale+ Dlarvae= 10/AREA< where AREA equals 5,5 0o r 500 cm?.

168 RELATIVE FOOD CONTENT OF THE GUT 1.0T .

1 l l 1 FEMALE C ) 2 5 8 10 LARVA 1 0 8 5 2 0 PREY STAGE COMBINATION

Fig. 42. Simulatedmea n levelo fth egu tfillin ga tthre eoveral lpre y densities, consisting of different combinations of larvae andfemales . Thisplo tfit st oth esimulatio nexperiment spresente di nFig .41 .

spections at short time intervals (1hour) .B yassuming ,tha tth epre y stagesi nquestio nresembl eth etwo-spotte dspide rmit ei nthei rrol ea s prey,thes eexperiment s canb esimulate do nbasi so fth ebehavioura ldat a ofthi sAgricultura lResearc hReport .Th eresult sar epresente di nFigure s 41an d4 2a sa plo to fth equotien to fth epre ystag especifi cprédatio n ratesagains tth equotien to fth erespectiv edensitie so fthes epre ystage s (2:8, 5:5,8:2) .Th esimulation s agreewit hth eexperimenta ldat ai fth e larvaeconstitut ehal fo rmor eo fth epre ypopulation .Whe nth eadul tfemal e preys formth emajority ,however ,th eprédatio no fthi sparticula rstag e seemst ob e favoured incompariso nt oit ssimulate dprédation .Presumabl y thiseffec ti scause db ya disturbin geffec to fsom econtact sbetwee nadul t femalepredator san dth elarge-size d femaleprey .Th econtac tcause dth e predatort ob eles sattentiv ei nlocalizin gth esmal lsize dlarva lprey . Thesucces srati ocurve spresente d inSubsectio n3.2. 7 showtha tpre y stage preference is strongly relatedt oth esiz eo fth eprey .Moreove r thesedat asuggest ,tha tth epreference sten dt ovanis ha sth esatiatio n levelo fth epredato rdecreases .Thi seffec ti sdemonstrate di nFig .4 2wit h theai do fsimulation sa tlowe rlevel so fth epre ydensit y (=enlargin gth e experimental area).A ta pre ydensit yo f0. 2 (=10/5 0cm 2)th elarva ear e capturedmor esuccessfull ytha na tth edensit yo f2 ( =10/ 5cm 2).A furthe r decreaset oth ever ylo wdensit yo f0.0 2 (=10/50 0cm 2)tend st orende rth e predatorles sfuss ywit hrespec tt obot hpre ystages .Henc ei ti sshow ntha t

169 preference could be far from a stablephenomenon . Forthi s reason theus e of descriptive formulas of the functional response curve -lik e the Disc equation (Cock, 1977)o r other equations (Rabbinge, 1976)- i n analyzing preference isdiscouraged : fussinesso fth epredato r islikel y todepen d on the foodconten to fth e gut (orth e availability ofth e prey).

3.4 RATEO F DEPARTURE

So farth epredator ybehaviou r hasbee nconsidere d isolated from anyten dency to leaveth epre y colony.B y staying ina colony ,prédatio ndecrease d the food supply of the predatory female and, also,it sprogeny . Therefore departure to other colonies is likely tooccu r soonero r later.Moreover , aspredator s aggregate incolonie swit hhig hpre y density, iti sincreasing ly likely that theywil l detecteac h otherwhil e searching forprey ,whic h may lead to anincrease d tendency toward dispersal.Thi s sectiondeal swit h the quantitative assessment of the rate of departure in relation topre y supply and interference between phytoseiid females,bu tbefor e discussing these measurements the walking behaviour of the predator and the sizeo f the colonized area on residence time in a colony isinvestigated .Du et o its apparent avoidance of the webbed area Ambluseius potentillae hasbee n excluded fromth emeasurements .

3. 4.1 Walking behaviour

As discussed inSubsectio n 3.2.4, iti spossibl e tosimulat e thewalkin g behaviour andth e lineardisplacement ,base d on analysis ofmeasure d walking tracks.Thi s simulation technique couldb euse d toestimat e therat eo fde parture, assuming theedg eo fth ecolonize d areaexert sn o influence onth e walking pattern. Before turning to such simulations itshoul db e recalled thatth ewalkin gpath s of Subsection 3.2.4 weremeasure d inabsenc e ofpre y orothe rpredators .Therefor e iti snecessar y toascertai nwhethe r thewal kingpatter n ismodifie d by theirpresence .Th e observations weremad ewit h thevide o equipment,describe d inSubsectio n 3.2.4, tocop y thewalkin gpaths . Thepath swer e registered for 1o r4 predator y femaleswalkin g inside afres h prey colony (eggs and females). Theparameter s ofth e experimentally defined frequency distributions of angular deviations were used toestimat e thelin ear displacement after 200 steps.Thes e estimates,togethe rwit h thewalkin g speed and activity, are given in Table 67.The y canb e comparedwit h the results of Subsections 3.2.2 and 3.2.5.Thi s clearly demonstrates thatth e walkingpatter n isno t affected bypre y orpredato r density,no r thewalkin g speed and activity. Thus the rate of departure is independent ofpre yo r predator density, if iti stru e thatwhe nth epredator s arrive atth eedg e ofa colon y theymak en odistinc t decision toleav e orstay . Totes tthi shypothesis ,simulation s ofth erat e ofdepartur ewer e compared

170 Table 67. Walkingbehaviou r of females oftw ophytoseii d species in presence and absence ofpre y andpredator s inth ewebbe darea .

Predator Prey Number of Walking Walking Simulated linear species density predators speed activity displacement after (number/ (mm/s) (%) 200 steps (number cm2) of steps)

Phxftoseiulus 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 s ofth e actual rateo fdepartur e from acolony .Thre e kinds ofcolonie swer eused : small webbed areas without prey, founded by males and preoviposition females large webbed areas without prey, founded by males and preoviposition females large webbed areas withpre yegg s only,founde db yovipositin gfemales , whichwer e removedbefor e theexperiment . Such a colony was located onon e leafleto fa compose d leafan d topro vide an alternative residence for the predator, one or moreo fth eothe r leaflets were also colonized withTyp e3 colonies .On e femalepredato rwa s released onth euppersid e ofa leafle tcontainin g the adequatekin do fcol onyAfte r thepredato r invaded thecolony ,th eresidenc e timewa s registered by continuous observation (i.e.1 4hour spe rday )ove r aperio d of3 days . The departures were scored after detection of the predator inth e acto r after discovery ofth epredato r inon e ofth e alternative colonies.Th emea n distance walked to reach the edge of a circular colonywa s computed from 100 Monte Carlo simulations of the walkingpattern ,an dthi sestimat ewa s converted into theresidenc e timeusin gth ewalkin g speed, thewalkin g acti vity and, if preywa spresent ,th e feeding time.Th eresidenc e times esti mated from the experimentally definedwalkin gbehaviou r correspond withth e directly measured residence times, as long as the prey was absent (Table 68). Therefore it can be concluded thatth eresidenc e time inth ewebbin g isdetermine d by the lowwalkin gvelocity ,th e lowwalkin g activity andth e tortuouswalk .Probabl y surface enlargement,walkin g impedement andth ein creased frequency oftactil eprobin gbefor e advancement inth e heterogeneous web structure are the factorsdeterminin g the.residencetim e inth ewebbe d

171 Table 69. Rate of departure by young femalephytoseiid s from acolon yi n relationt opre y density.T = 20°C ;R H= 70% ;webbe d area= 4-1 1 cm2.

Predator Prey Simulated Number ofpredator s in Relative species density relative the colony rateo f (number/cm2)gu tfillin g departure (%) atth estar t after 10hour s (hour ) N.t= 0 N t=10

Phgtoseiulus 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 < 81 32 0 0.868

Metaseiulus 40-60 92 45 44 0.002 occidentalis 25-35 90 32 29 0.010 10-15 87 36 16 0.081 0- 5 < 80 19 0 0.977

Amblyseius 30-40 91 30 30 0 bibens 10-15 88 30 14 0.076 0- 5 < 81 29 0 0.792

are given inTabl e 69 inrelatio n toth edensit y ofth eprey .Becaus eth e fractiono fresidin gpredator s decreased ina nexponentia l fashion,th edis persal tendency canb echaracterize db yth erelativ e rateo fdepartur eac cording toth efollowin g formula:

-ln(Nt/N0] RRD=

RRD relative rateo fdepartur e (hour ) N, =numbe r ofpredator s residing inth ecolon y attim et (hours). Ifpossible , theRR Dvalue s were computed fromth etim e elapsed until50 % ofth epredator s hadlef tth ecolonies .T oprovid e some insight inth emea n level ofgu t filling atth edifferen t density classes,simulate d valueso f the relative food contento fth egu tar egiven . The results demonstrate thedependenc y ofth erat eo fdepartur e onprey - egg density while interspecific differences seem tob e absent.A s prey densitydecreases ,th erat eo fdepartur e increases.Thi s effectcanno tpos sibly be explained by a decreased time expenditure infeedin gactivities . Even forth e extreme caseo f1 6eg gcapture s inth e1 0hou rperio d (Phyto ne seiulus persimilis), the total feeding time would amount to 1hour .Th e residence times aretherefor epredominantl y determinedb yth ewalkin gbeha viour at the edge ofth ecolony , as argued inth epreviou s subsection. Finally iti s a glaring fact, that atth edensit y of 10-15egg spe rcm 2 half theinitia l numbero fpredator sha dlef tthei rcolon y after1 0hours , although their gut fillingwa sstil l ratherhig h accordingt oth ecomputa tions. » This high rate of departure mayb edu et oth eabsenc eo ffemal e spider mites inth eexperiments .Henc e the experiment hasbee n repeated forth e prey density of 10-14egg s and 0.5 femalepe rcm 2.Despit e theinevitabl e ovipositionb yth efemal e spidermite sprey-eg g density remainedwithi nth e limits indicated. Theresult s (Table70 )sho w thatth eadditiona l presence of the female spider mites didno t alter the rateo fdeparture .Henc ei t may be supposed, thatpra ydensit yi sth egovernin g factori nth erealiza tiono fth eresidenc e timeo fth efemal epredators . Evidently therei sa stron gtendenc yt oforag ea tdensitie s above2 0egg s per cm2.Natura l selectionma yhav e favoured thisdispersa l behaviour asa consequence ofth eachievemen to fa large rprogeny ,bu tthi s simplifiedex planationi sno tclear ,a slon ga sth eenerg y expenditure involved inreach ingothe rmor e favourable food areasi sno tknown .I tma ya swel l havebee n evolved asa n anticipation onth e survival chances ofthei rprogeny .Th e experiments, discussed in Subsection 2.2.1, demonstrate, thatdevelopmen t was retarded andmortalit y was increased below a food supplyo f1- 2 eggs perday .Howeve rth eassessmen to fjuvenil e dispersal yielded only someac cidental departures atthi s critical rateo ffoo d supplyan deve nunferti lized femalesha da lo wtendenc yt odispers e (Table 71). Becauseth edensit y ofphytoseii d eggsca nris eabov eth eleve lo f1 eg gpe rcm 2colonize d area

Table 70. Rateo fdepartur eb yyoun g femalephytoseiid s froma pre y colony containing eggs and females.T = 20°C;R H= 70%;webbe d area= 6-1 0cm 2; 10-14eggs/cm 2 and0. 5 female spidermite/cm 2.

Predator Numbero fpredator s inth epre y colony Relative rateo f species departure (hour- ) atth estar t after1 0hour s Nt=0 Nt=10

Phytoseiulus 30 16 0.063 persimilis Metaseiulus 42 23 0.060 occidentalis Amblyseius 28 17 0.050 bibens

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

Predator Predator stage Number of pre dators inth e colony of development at the start after 10hour s Nt= 0 Nt=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 effecto fth e dis persalbehaviou r ofth e adult femalepredator s onth edevelopmenta l prospects ofthei r lessmigrator y juvenileprogeny .Thi s questionwil l be investigated furtherb y sensitivity analysis ofth epopulatio nmode lwit h respectt oth e relative rate ofdepartur e (Part2) .

3.4.3 Predator density

Küchlein (1966)measure d anincrease d tendency ofyoun g females of Meta seiulus occidentalis todispers e fromth eexperimenta l leafdisc swhe nmor e than one predator waspresen tpe r area;predator s leaving the disc drowned in the water-soaked cotton surrounding the disc.Küchlei nstate d thatth e data on migration tendency thus obtained areo f arbitraryvalu e aslon g as a similar study ofth edispersa l on anactua lplan ti s lacking.A nexperi mentt oprovid e this informationwil l nowb e described. The experimental procedure differs from that discussed inth epreviou s subsection inth e following respects.One ,tw oo r four females of Metaseiulus occidentalis were released onth e 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 on the leaf.Onl y colonies thatcontaine d adequate (1,2 ,4 )number s ofpredator s were selected. The departures were assessed atconsecutiv e time intervals of 4 hours by detection ofth epredato r inon e ofth e alternate colonies on the other leaflets of theros e leaf.Whe n apredato r leftth e

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

Initialnumbe r The range Relative rateo fdepartur e (hour ) ofpredator s ofpre y egg invaded inth e densities first after one 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 itwa s removed to prevent re-invasions;th eobservation swer econ tinued forth e remainingpredator s until allwer e goneo runti l theexperi mental period, of 24 hours,ha d elapsed. This experimental procedurewa s carried outa ttw olevel s ofpre y density: 10-20egg spe r cm2 and20-4 0egg s per cm2. The predator densitieswer ebiase ddu et ovariatio ni nth ewebbe d areas per colony (p= 6. 2 cm2, â= 3.1 ;range :3-1 4 cm2), butthi svariat ionwa spresen t foreac h levelo fpredato r release.Th evalue s ofth erela tive rate of departure, each computed from an initial amounto fa tleas t 100 predators, are given inTabl e 72.A spredato rdensit y decreases during theexperimen t asa consequenc e ofth edeparture s fromth epre ycolony ,th e relative rate of departure was computed for each 4-hourperiod , thereby classifying the replicates with respect to the predator density at the start of these periods. In this way itwa spossibl e tocalculat e theRRD - values after one, twoo rthre edeparture s incas e fourpredator swer e ini tially present in the prey colony and, similarly, after onedepartur e in casetw opredator swer e initially inth ecolony . Evidently there isa tendenc y to avoidpredato r aggregation even forhig h prey densities. This can be recognized from the data intw oways . First; the relative rate of departure increases fora nincreas e inth enumbe r of predators initiallypresen t inth ecolony . Second,eac hdepartur e is followed by aperio dwit h alowe rvalu e ofth e relative rateo fdeparture .Thes eten dencies are very similar atbot h levels ofpre y density.Also ,th ehighe r dispersal atth e lowerdensit y rangeconfirm s the findings discussed inth e previous subsection.Fo rsom ereaso n (e.g.difference s intemperature , dis tributiono fpre y densitieswithi n theclas s range)th eRR Dvalue s obtained afterth eon epredato r release arehighe r thanthos e stated inth eprecedin g subsection.

177 4 The use of experimental and theoretical results in dynamic population models

Theprecedin g chapters ofthi sAgricultura l ResearchRepor tdescrib e the modelling of an acarine predator-prey interaction atth e individual level andth emeasurement s ofth e inputdat aneede d fortha tmodelling ; 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 aret ob euse d forth emo 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 ewhic h assumptions underlying theprédatio nmodel s are stillunvalidated , andwhic h inputdat a arestil lmissing . Inaddition ,som e important questions arise thatar ebase 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 t2 (tob e published) of this report, which dealswit h themodellin g ofth epredator-pre y inter action atth epopulatio nlevel .

4.1 UNVALIDATED ASSUMPTIONS

InChapte r 3,model s havebee ndevelope d for the simulation ofth ewalk ing behaviour and the rate of prédationo fphytoseiids .Thes emodel swer e used for the analysis ofth epredator-pre y system atth e individual level. The results are to be used in the population modelspresente d inPar t2 . Someo fth e assumptions underlying thesemodel s arebase d onmeagr eexperi mental evidence;other s haven oempirica lbasi s atall . Though the Queueing model ofth eprédatio nproces sprove d 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), itshoul db e remembered that itrest s on fourbasi c assumptions,eac ho fwhic h needssepa ratevalidation .First ,a Poisso ndistributio n isassume d forth enumbe r of prey capturespe runi ttim e ata certai n level ofth emotivationa l stateo f the predators. Second, the food content ofth egu t is assumed to determine the state dependent rate of successful encounter, whether this state is achieved by previous gutemptyin g orb ypreviou s ingestion of food.Third , iti sassume d thatth e food quality ofpre y isth e same foral lpre ystages . This assumption is implicitly made since the flowo f ingested food ismerel y

178 treated in terms of weight. Some attempts have been made tovalidat e the assumption by considering the available datao fprédatio nan dreproductio n rates in monocultures ofdivers epre y stages,bu tthe ydi dno tprovid e any decisive evidence (Subsection 3.1.3). Fourth, the model of the prédation process is based onth e assumption thatth estat edependen tsucces s ratios measured in 'monocultures'o feac hpre y stage areals oapplicabl e in 'mixed cultures' of several prey stages (Subsection 3.3.7); theprobabilit y ofa prey capture afterpre y detectionmerel y depends onth e levelo fgu t filling and past experience in capturing other prey stages isonl yregistere d via changes in the level ofgu t filling.Thi s assumption isno trefute db yth e available experimental evidence, butmor evalidatio n experiments arestil l needed. Another point for comment is the concept of food conversion,whic hi s basic toth epopulatio nmode l ofth epredator-pre y interaction.Th epresen t status ofth e systems analysispoint st oth eimportan trol eo fth e relative rateo f foodconversio n indeterminin g therat e ofprédatio na tvariou s tem peratures, different oviposition histories,an dpre y andpredato r densities (Section 3.3).Th e increase inth erat eo fprédatio nwit h increasingtemper ature isdetermine d notb y temperature-related changes inth esearchin gbe haviour, but by theeffec to fth e temperature onth erelativ e rate offoo d conversion into egg biomass.Th erelativ e rateo ffoo d conversion isshow n to depend on the number of eggs already depositedb y the femalepredator , i.e. its oviposition history. However, only circumstantial evidence was given for the assumption thatth edecreas e ofth erat eo fprédatio na tin creasing predator density is caused by adecreas ei nth erelativ erat eo f food conversion, andno tb ybehavioura l changeso fth epredator s aftermutua l contact, nor by thetim ewaste d forpre y searchingupo nmutua l contactbe tweenth epredators .Furthermor e itshoul db e recalled thatth e food content of the gut isno ta goo d indicator ofth emotivationa l statewhe nth epre dator isseverel y starved (Subsection 3.1.2 and3.2.7 ) Simulations ofexperimentall y definedwalkin gbehaviou rwer e carried out todetermin e theeffec to frecrossin g areas already searchedb y thepredato r on searching efficiency, and to estimate theresidenc e time ina circula r webbed areaunde r the assumption thatth eedg eo fth ewebbe d areaexert sn o effecto nwalkin gbehaviour .Thes e simulationexperiment s show thatth etor tuous walk of the predatory mites inth epre ycolon y leadst oa napproxi mately 20%decreas e inth erat eo fencounte rwit h immobilepre y (Subsection 3.2.4), and thatth epredato r cannot stay ina profitabl epre ypatc hbu tb y turning at the edge of the webbed leaf area (Subsection 3.4.1).However , thewalkin gpath s simulated onth ebasi s ofexperimentall y determinedpara meters (M, O, A.an d a ) were not explicitly tested for goodness offit , though with the naked eye the simulatedpath swer e indistinguishable from the paths originally measured. The auto regression model of the walking processwa s thebes t availablemode l tocomprehensivel y describe thecharac -

179 teristic properties of thewalkin gpatter n (Subsection 3.2.4). Anyway,th e simulated level of recrossing is low and is hardly affected by even20 % changes inth eparamete rvalues .Moreover , longresidenc e times ina profi table prey patch are best explained by the edge-turning strategy; without theedg e effect simulated residence times equal tothos e determinedexperi mentally could onlyb eobtaine d forextrem e typeso fwalkin 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 generatedb y themode l atth e populationlevel .

4.2 MISSING INPUTS

InChapter s 2an d 3experiment s with individualmite shav ebee n described that serve tomeasur e ratevariable s forus e inpopulatio nmodels .Fo r some cases the seto finput s isincomplete ,o rth eresult s cannotb euse d inth e population models without making new assumptions,whic h intur nnee dsepa ratevalidation .T ogai n insight into these limitations iti sworthwhil e to looka tthes e aspects inmor edetail . The possibility of maintaining apredato rpopulatio n inperiod s ofpre y scarcity inth e greenhouse iso fconsiderabl epractica l importance;i twoul d be convenient if thepredator s residing inth e crop areabl e todetec tne w spider mite infestations indu e time forcontro l ofth emit epest .Litera ture data and some additional experiments haveprovide d some insightint o the survival chances ofth epredator ymite s inth egreenhouse .Whe npre y is scarce in the greenhouse rose crop, the availability ofwate r seems tob e most important for the survival ofth ephytoseiid s (Subsection 2.2.5). Can nibalism provides only a limited means for survival,a s itdepend s onth e survival ofothe rpredators , and asth e food andmois tconten to fthes epre dators decreases exponentially with the length of food deprivation (Subsec tion 2.2.6). The supply ofpolle n onth e roseplant 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 supplywa s tried,n o 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 fromth e flowering roses inth e greenhouse isinsufficien t inthi s respect.A thighe r levels of pollen supply, especially Amblyseius bibens mayperfor mbetter , asshow nb yBlommer s (1976)i nsmal l scaleexperiments . By extrapolating data on individual lifehistorie s measured atconstan t temperatures to the greenhouse situation, an important assumption ismad e that has been only partially validated. The rate ofdevelopment , the rate ofreproduction , the rate ofmortality , the rateo fwebbin g and therat eo f prédationwer emeasure d atconstan ttemperatur e levels inth erang e 10-35°C. Ofcourse ,temperatur e will fluctuate inth egreenhous e albeitwithi n limits

180 (10-35°C). The effect of variable temperature regimes on these rateswa s investigated for the two-spotted spider mite,bu t hardly at all for the phytoseiids considered inthi s report.Bu tbecaus e thepopulatio nmode l pre sented inPar t2 isbase d onth e assumptiontha tbirth ,deat han dprédatio n processes react instantaneously to changes in temperature, validation of this assumption isstil lneede d 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), the level of food supplyt oth e spidermite sha sno tbee n considered. Some argumentshav ebee ngive nt oconside r thenutritiona l value ofth ehos tplan ta sa constan t forspide rmite s infestinggreenhous e roses (Section 2.1). However, incontras tt oth e food quality ofth eros eleaves , food quantity canb e affected by feeding of the spidermite sthemselves . The available leafparenchy mdecrease s duringpopulatio n growtho fth e spider mitesunti l thehos tplan ti sexhauste d as afoo d source,o rth egrowe rap plies pesticides. Also, the juvenile spidermite s arelef tstrande d inal ready exploited areas,becaus e they areles sabl et odisperse .A s thelif e 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 dt ob e studied inmor edetail ,a greenhouse experiment on population growth of the spider mites shouldb e carried out and the numerical results shouldb e comparedwit h simulations thatneglec tth eeffect s ofcompetitio n forfoo d among the individual spider mites. Thispopulatio n experiment and theadheren t simulationswil lb e dis cussed inPar t2 . Another subject that is important in the interpretation ofth eresult s of population 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 ageo fth e spider-mite 'mother' (Subsection 2.1.3), iti sassume dt o be afixe drati o thatdoe sno talte r inrespons e toenvironmenta l conditions. Butthi s isa nassumptio nmad ebecaus e oflac ko fexperimenta l data,rathe r than awell-establishe d foundation forpopulatio nmodelling .Contro l ofth e fertilization process and hence these xrati o inrespons e to environmental conditions may play a role in arthropods reproducingb y arrhenotoky.Thi s 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 l ofth epredator-pre y interaction isth epre y density. Inthi srepor tth epre y density isdefine d as the number of prey per square centimetre of webbed leafarea ,becaus e two-spotted spider mites only inhabitthos epart s ofth e leafare acovere d bywebbing .Durin gpopulatio n growthno tonl yd opre ynumber s increase,bu t alsoth eexten to fth ewebbe d area.Therefore , forcalculatio n ofpre yden sity for simulations at the population level,lif ehistor ycomponents ,a s well asth erat e ofincreas e ofwebbe d leafarea ,hav ebee nmeasure d atth e

181 individual level (Section 2.1).Th e rate of increase of webbed leafare a can depend on the host plant species thati scolonize db y the two-spotted spidermite .Fo rexample ,th ewebbin g cover onLim abea ni s less aggregated thano nrose ,an d thewebbin g iseve nmor e spread outo n leaves ofGerbera . Presumably the hairiness ofth e leaves isa nimportan t factor inthi s res pect. The rate of colonization estimated inthi s studyo nros e 'Sonia'i s therefore by no means generally applicable and should be determined for otherplants . By distinguishing webbed leaf areas fromunwebbe d leaf areas iti sneces sary to assess which factors determine the residence time ofth epredator s inside andoutsid e thewebbe d area.Th e residence timeo findividua lpreda tors in the webbed area of apre y colony hasbee n studied inthi sreport , but their residence time outside thewebbe d area isa naspec t thatha sno t yet been considered fully at the individual level.Som edetail s havebee n discussed inSubsectio n 3.2.4 and3.4 . 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. Amblyseius potentillae behaved differently. Thisphytoseii d predator tends to avoid the webbed leaf area andprefer s tosta ynex tt oth ethic kpart s of the main rib of a rose leaf or atothe rprotecte d spots onth eplant . More knowledge isrequire d on thequestio n ofho w apredator ymit e searches forne wpre ypatches ,especiall y how the searching is influenced by themod e ofplan to rcro p colonization by thetwo-spotte d spidermites .Thes e aspects will be discussed inPar t2 o fth eAgricultura l ResearchReport .

4.3 IMPACTO F INDIVIDUAL CHARACTERISTICSA TTH EPOPULATIO N LEVEL

Themeasuremen t ofmit epropertie s atth e individual levelca n 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 t affected inthi s range.Henc e egg mortality isprobabl y ake y factor inth e failure ofphytoseiid s to control thepopulatio n growth ofth e two-spotted spidermite s atlo whumidities .I n other cases, the measurement ofmit epropertie s atth e individual level is not sufficient forth e evaluation ofthei r relative importance atth epopu lation level.Fo r example,wha t isth e importance of a10 %shorte rdevelop mental time relative toa 10 %ris e ofth e rate ofreproduction ? Bothdevel opmental time and reproduction affectth e rate ofpopulatio n increase,bu t their relative effect cannotb e determined without thehel p of aquantita tive tool, such asa mathematica l model ofth epopulatio n growth.Th eeval uation of such effects iseve nmor e difficultwhe nthei rrelativ e importance has to be assessed forinteractin g populations ofpredato r andprey .Henc e theevaluatio n ofth e interspecific differences in lifehistorie s isdeferre d toPar t2 ,wher e thepredator-pre y interaction ismodelle d atth epopulatio n

182 level. Because severalprocesse s inth epredator-pre y system interactwit heac h other, and several ratevariable s depend ina non-linea rwa yo nstat evaria bles, it is often not possible event odescrib e theconsequence s ofinpu t datameasure d atth e individual level forth e interaction atth epopulatio n level, let alone to indicate their relative importance. The role dynamic simulationma ypla y inthi srespec t isfurthe r illustrated inthre eexamples . Example 1 - the role of webbing in prédation The searchingbehaviou ro f individual female predators has been studied in the webbed leafarea ,a s well aso nunwebbe d leaves (Section 3.2). Webbing interferes generally with searching by decreasing the rate of encounter per unit prey density (the relative rateo fencounter) , as aconsequenc e of areductio n inth ewalkin g speed, the walking activity and the coincidencebetwee npredato r andpre y inth ewebbe d space.Th erelativ e rateo fsuccessfu l encounterwa s affected by thewebbin g indifferen tways , however,dependin g onth ephytoseii d spe cies involved: the success ratio of Phytoseiulus persimilis increases in the presence of webbing;th e success ratios of Amblyseius bibens and Meta- seiulus occidentalis are unaffected by the webbing;bu tth esucces s 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 etha ncompensate s forth ereduc tion of the relative rate ofencounte r inth ewebbing , resulting ina nin crease in the rate of prédation in a prey colony (Subsection 3.3.3). The factor webbing may thereforeb e important forfutur e studies ofth einter action between phytoseiid predators and the two-spotted spider mite, but the relative importance of the substrate-related differences inprédatio n rateha sye tt ob edemonstrate d atth epopulatio n level (Part2) . Example 2 - prey-stage preference of the phytoseiid predators Thepro bability of capturing a prey depends verymuc h onth 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 difficultt ocapture .Thes eprey-stag e specific differencesi nsucces srati o may mean that the diet of thepredato r largely consists ofth eyoun gpre y stages and that the reproductive spider mite females are allowed to continueth ereproductio nproces s forsom e time.Henc e theexterminatio n of the prey population may be postponed due to the initial concentration of thepredator s onth eyoun gpre y stages.O nth eothe rhand , the adult female spidermite s dono tliv e foreve r andeac hconsumptio n ofa femal e juvenile prevents thedevelopmen t ofa reproductiv e female.Therefor e thehypothesi s thatpredator s keep 'layinghens ' shouldb e evaluatedb y dynamic simulation ofth epredator-pre y interaction atth epopulatio n level (Part2) . Example 3 - dispersal of the predator from colony to colony When female predators tend to stay incolonie swit hhig hpre y densities,thi s tendency

183 can lead to predator aggregation in theprofitabl e preypatches ,whic h in turn leads to adecrease d rate ofprédatio n (andthu s reproduction), or to predator dispersal from thepre ypatc h (Section3.4) .Wha teffec tthi smod e ofpre ypatc hexploitatio n has onth epopulatio n level isa n important ques tiontha tma yb e solved by dynamic simulation ofpopulatio n growth and dis persal. For these simulations,wher epredator sma ymov e from onepre y colony to the other, possibly differing in prey density, and wherepre y density continually changes in time,i ti snecessar y to account forth enon-stead y state of the prédation process. The Queueingmode l developed inChapte r3 offers that facility and, moreover, it canb e easily coupled toa popula tionmode l inth e formo fa subroutine .

184 Summary

The two-spotted spidermite , Tetranychus urticae (Acarina:Tetranychidae) , is amajo r pest ofman y foodan dornamenta l crops.I nth egreenhous e cul tureo fornamenta l roses,a nacaricide ,calle d dienochlor [perchlorobi(cyclopenta-2,4-dienyl)] is used to control it. Forenvironmenta l reasons iti s desirable to replace chemical spraying with abette r alternative. This Agricultural Research Report describes investigations intoth epossibilit y of biological control oftwo-spotte d spidermite s ingreenhous e roseswit h predatory mites (Acarina: Phytoseiidae). Biological control hasbee nsuc cessful in the greenhouse culture ofcucumbers ,fo rexample . Ingreenhous e roses, however, much less damage can be tolerated because the ornamental value ofthei r flowers and leaves determines theeconomi cvalu e ofth ecrop . This quality demand applies especially to the rose shoots thatgro w above the rose hedge, which are cut offa ta beginnin g stageo fflowering ;mor e damage can be tolerated in the rose hedge itself. Spidermite s shouldb e controlled insuc ha wa y thatdamag e toth eyoun gros eshoot s isminimized . Two-spotted spider mites are able to double their number inth e short period of2- 4 days.Eve nafte rth ereleas eo fth epredator ymite sth epopu lation of spider mites will increase initially.Onl yafte rsom etim ewil l itdecrease .Henc e iti simportan t toestimat e theminimu m numbero fpreda tors tob e released foracceptabl emit econtrol .Th econtro l ofnewl ydevel oped infestations will depend onth e ability ofth ephytoseiid s to survive periods of prey scarcity. Because phytoseiid species can differ inthei r ability to survive orreproduc e on alternative food,an d inthei rprédatio n capacity, four species arecompare dwit h eachother ,i.e . Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens, Metaseiulus occidentalis. The potential role ofthes epredator ymite s forth econtro l ofth etwo - spotted spidermite s hasbee n investigated by 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 (tob e published) the results ofthes eexperiment s andmodel swil l be used in a new model to simulatepopulatio n growtho fbot hpredato r and prey; simulations with thispopulatio nmode lwil lb ecompare dwit hpopula tion experiments in thegreenhouse .Afte rvalidatio n themode l canb euse d forcalculatio n ofth eminimu m release ofpredator ymite s ata certai n stage of pest development. These estimates may then be transformed into simple rules ofthumb . For a systems approach it is necessary toquantif y thepre y supply (in

185 particular, two-spotted spider mites)t oth epredator ymite s inth egreen house. Because the spider mite numbers increasewit h time,th epropertie s oftetranychid swer e investigated thatdetermin e therat eo fpopulatio 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. It was showntha t therelatio nbetwee n temperature and theserate s is linear inth e range 12-35°C;unde rgreenhous e conditions rel ativehumidit y isno t important.Furthermore , itwa s showntha tth e rateo f reproduction and the proportion ofth eprogen y thatar e females depends on the age of the reproductive female. With respectt oth e quantification of the prey supply to the predators, iti sals o importantt odistinguis h the stages ofdevelopment ,becaus e each stage runs different risks ofbein gcap tured by the predatory mites.Henc e therat e ofmortalit y and development were measured for each developmental stage, sotha t inpopulatio n simula tions thepre y supply canb e subdivided perpre ystage . The prey supply toth epredato r isals o determined by themea n distance between prey items, i.e. thepre y density. Two-spotted spidermite s havea strong tendency to aggregate.The yconstruc t labyrinths ofsil k strands on the lower side of the leaf, starting from the leaf edgeo r ari b and dis persing over the leaf surface. Inth ewebs , theegg s aredeposite d andde velop into adults. The preoviposition females are inseminated immediately after the lastmoul t and subsequently disperse, frequently toothe rleaves , where they form newcolonies .Henc e colonization isa nessentia l aspecto f the prey supply to thepredator .Th epredator ymit e has to invade theweb bingt ocaptur e itsprey .Therefor e thepre y supply isdefine d asth enumbe r 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). Onth ebasi s ofth emeasure d rate ofwebbin g and themeasure dlife - history components, apopulatio n model can be constructed that simulates preynumber s and prey density inth ecours e ofth epredator-pre y interaction (Part2) . Inth egreenhous e culture ofornamenta l roses, food substances othertha n spider mites are rare.Henc e the survival of the predators inperiod s of prey scarcity will depend on cannibalism and abiotic factors,suc h asth e availability of water, temperature and relative humidity. In contrast to theothe rphytoseii d species studied, Amblyseius potentillae and Amblyseius bibens can reproduce when feeding onpollen , sotha tth eadditio n ofthes e plant substances may lead toth emaintenanc e of thepredato rpopulatio n in thegreenhous e crop.Experiment s indicate thatth e amounts ofpolle n required areprobabl y high (Subsection 2.2.7). Honey and sucrose solutions can improve the rate ofpredato r survival toa significan t extent.T o date thepossibil ityo fmaintainin g apredato rpopulatio n in aros e cropwithou t spidermite s has stillno tbee n demonstrated.

186 Population growth of the predatory mites will depend on thenumbe r of spidermite s inth ewebbe d leafare a andth etemperatur e andrelativ e humi dity there (Subsections 2.2.1-2.2.3).A s forth e spidermites ,th e rateo f development and therat eo freproductio n arelinearl y related totemperature . However,whe ntemperatur e rises above30° C andrelativ ehumidit y dropsbelo w 70%, juvenilemortalit y becomeshigh .A s thespide rmite s aremuc h lessvul nerable to temperatures in the range 30-35°C and humidities inth erang e 40-70%, thesecondition s arecritica l forthei rcontro lb ypredator ymites . The four phytoseiid species studied differedwit hrespec tt o developmental time, size of progeny and proportion of females in theprogeny .However , all phytoseiid species matured ina shorte r time-span,bu t laid feweregg s than the two-spotted spidermites .Th erelativ e importanceo fthes ediffe rences can not bedetermine d withoutth ehel p ofa quantitativ e tool, such as a population simulationmodel .Th eevaluatio n ofthes edifference swil l thereforeb e treated inPar t2 o fthi sAgricutlura l ReseachReport . Whenpre y supply is sufficient,youn gphytoseii d femalesutiliz eapproxi mately 70%o f the ingested food foreg gproduction . Inaddition ,th erat e ofovipositio n iss ohig h thatth ereproducin g females determine thepréda tion capacity of the phytoseiids. The rate atwhic h the ingested foodi s utilized foreg gproductio n ofne wprotoplas m was foundt ob emainl ydepen dento nth e individual ovipositionhistory , thati st o sayo nth enumbe ro f eggs already deposited by the female predator; female predators tend to achievepotentia l fecundity almost irrespective ofthei r age.Henc e there productive females represent themos tvoraciou s stageo fth epredator ymites , and they decide where andwhe nth eegg s aredeposited . Forthi sreaso nth 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 e rate of food conversion is high, it makes senset ous eth e foodconten to fth egu ta sa n indicator of the motivational stateo fth epredator .Th edynamic s ofth egu t filling can be computed when ingestion, resorption andegestio nar equantifie db y experiment. By weighing hungry predators before and after food intaketh e foodconten to fth edifferen tpre y stages,th egu tconten t andth e foodde ficit of the gutwer emeasure d (Section 3.1). Likewise,i twa spossibl e to quantify the rate of ingestion and the rate of gut emptying. These data were used ina mode l of food conversiontha ti sbase d onth eassumptio n that the surplus of the resorbed food substances is used for egg production (Fig. 21).Thi s modelwa stested , forexampl eb ycomputin g thetim eneede d for a hungry female to produce anegg .Th ecalculation swer ecorrec t ina broad rangeo f fooddeprivatio nperiods ,bu t after acertai nperio d offoo d deprivation aperio d ofrecover ywa snecessar ybefor e the female restarted eggproduction .

187 The food conversion model (AppendixA )wa s used forth e analysis ofth e observations of the predatory behaviour. Young femalepredator s belonging to four different species of Phytoseiidae were deprived of food forsom e specified period, starting from astat eo fsatiation , andthe nplace d ina prey colony. Their behaviourwa s recorded and thedynamic s ofth e gut fil ling computed. Thus iti spossibl e torelat ewalkin gvelocity ,walkin gac tivity, walking pattern, success ratio and feeding time to the estimated level of food inth e guto fth e femalepredato r (Section3.2) . This experiment was carried out on two substrates:webbe d leaf andun - webbed leaf. Itwa s thereforepossibl e to assess therol e ofwebbin g inth e searching behaviour of thepredator y mites. Inth ewebbin g the rateo fen counter peruni tpre y density was found tob e lower,becaus e predatorymites , as well as spidermites ,mov e slowly onthi s substrate and spend less time inwalking . The slow advancement ofth emite sprevent sbumpin g ofon emit e into another, so that disturbance ofth epredato r is arar ephenomenon .O n an unwebbed substrate disturbance is important, as isreporte d by several authors. The coincidence betweenpredato r andpre y andhenc e also the rate of encounter are lowered as a consequence of the labyrinth formedb y the webbing: predator and prey may move over andunde r eachothe rwithou ten countering one another. The predatory mites probably search atrando m and locate theirpre y after contactwit h thetars i ofthei r front legs (Subsec tion 3.2.3). However, notever y encounter leads to asuccessfu l attack. It was showntha tth e success ratio depends onth egu t filling ofth epredator , thepre y stage and, intw o specific cases,o nth e substrate: inth ewebbin g the success ratio of Phytoseiulus persimilis increases and thato f Amblyseius potentillae decreases (Subsection 3.2.7,Fig .33) . Theresult s ofthi sbehavioura l component analysiswer euse d ina préda tionmode l derived from queueing theory (Section 3.3).Thi s theoryha sbee n used in problems concerning waiting-lines ofcustomer s and service facili ties. Consider, forexample , aqueu e ofpatient s in adentist' s waiting-room. The patients represent the prey, the dentist represents the predator and the waiting-room represents the gut of the predator. The rateo fpatien t arrival inth ewaiting-roo m isequivalen t toth e rate ofprédation ; thetim e needed to help the patient is equivalent to the timeneede d toempt y the gut of the predator by the amounto fon eprey .A smor epatient s enter the waiting-room, the dentist will shorten theconsultin g timepe rpatien t and itbecome s increasingly probable thatnewl y arrived patientswil l refuset o wait and decide to return at another time.Analogou s tothi s example,th e rate ofgu temptyin g increases with an increasing level ofgu t filling,and , simultaneously, themotivatio n ofth epredato r to attack itspre ydecreases , while the probability ofpre y escaping increases.Bot h tendencies werede monstrated byexperiment . A stochastic queueingmode l canb e derived ifon e assumes thatth enumbe r ofsuccessfu l attacks by apredato r with acertai n level ofgu t filling fits

188 a Poisson distribution and thatth egu temptyin g timepe r ingestedpre yi s distributed according to thenegativ e exponential distribution.Thi smode l was compared with adeterministi c model,a Compoun d simulationmode l anda MonteCarl o simulationmode l ofth eprédatio nproces s (Appendices E-H). The Queueing model is preferred because of its economic use ofcompute r time and because it uses aminimu m number ofvariable swithou t losingprecisio n (Subsection 3.3.1). The Queueing model was validated in a series of prédationexperiment s carried out on webbed and unwebbed leaves (Subsections 3.3.2 and 3.3.3). The rate of encounter per unit prey density is loweredb y thepresenc e of webbing, which results in a decreased rate of prédation for Amblyseius bibens and Metaseiulus occidentalis. Opposed tothi sdecreas e in searching ability, thepre y density inth ewebbe d area ishig h (20-60mite spe r square centimeter of webbed leaf area). Soth erat eo fencounte rbetwee npredato r andpre y turns outt ob ehigh , anyway.Accordin g toth esimulations , Phyto- seiulus persimilis and Amblyseius potentillae are affectedb yth ewebbin g in a similar way, but the probability ofthes epredator s capturing apre y after tarsal contact (success ratio) is strongly influenced. Amblyseius potentillae has alowe r success ratio inth ewebbin g thano nunwebbe dleaves , and this results ina nextr adecreas e ofth erat eo fsuccessfu l attack.I n contrast, Phytoseiulus persimilis has ahighe r success ratio inth ewebbing , which more than compensates for the decrease of the searching ability (= the rate of encounterpe runi tpre y density): therat eo fprédatio ni nth e prey colony is higher thano nunwebbe d leaveswit h the samenumbe r ofpre y per leafarea . Systems analysis of the prédation process at different levels of the temperature shows that the effect of temperature onth erat eo f foodcon version determines the rate of prédation (Subsection 3.3.4). Behavioural changes related totemperatur e areprobabl y ofmino r importance forth ein crease of the rateo fprédatio nwit h temperature.Presumabl y the decreased rate of reproduction at increased predator densities is also causedb ya decrease inth erat eo f foodconversion ,an dno tb ychange s inth e searching behaviour orb y an increase ofth etim ewaste d duringmutua l contactbetwee n predators (Subsection 3.3.6). Because female phytoseiids tend to achieve their potential fecundity, iti s supposed thatth erat eo f food conversion aswel l asth erat eo freproductio n isno tdependen to n agebu to nth enum ber of eggs deposited by the female (Subsection 3.3.5). Inconclusion ,th e rate of food utilization foreg gproductio n isprobabl y themos t important factor indeterminin g the rateo fprédation , and the ability tocaptur epre y canprobabl yb e considered asa constan trelate d toa specifie dsubstrate . Finally the Queueing modelwa s extended toth ecas eo f 'mixedcultures ' of prey stages (Subsection 3.3.7 and Appendix I).Th epreferenc e foreac h specificpre y stagei sdetermine d inth emode lb y successratios ,whic hwer e measured in 'monocultures' of these prey stages.Thes e measurements show

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 showtha t thedifference sbe tween success ratios ofth e differentpre y stagesbecom e smaller asth egu t filling ofth epredato r decreases:th epredato r is less fussy asit shunge r increases. Simulation and measurement of prédation in mixed cultures of larvae and adult females ofth epre 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 ina pre y colony ismainl y determined by thepre y density (Subsections 3.4.1 and 3.4.2). This iseviden t fromth e comparison of the residence time of predators in webbed areas with and withoutprey .Analysi s ofth ewalkin gpatter n ofth epredator y mites inth e webbing and, based upon this analysis,simulatio n ofth eresidenc e timei n the webbed area shows that the tortuouswalkin gpat h ofth epredato r does notexplai n the lengtho fth eresidenc e time inth epre y colony.Th eexperi mentally measured residence times inpre y colonies canonl yb e achieved by the predator when it turns back atth eedg e ofth ecolony .Th e simulation ofth ewalkin gbehaviou r ofth epredato r showstha t itcome s incontac twit h theedg e frequently enough toreac t adequately to adecreasin gpre y supply. When female predators stay incolonie s ofhig hpre y density,predato rden sityma y increase there. Itwa s shownb y experiment that an increase ofth e predator density leads to ashorte r residence time despite the ample supply of prey (Subsection 3.4.3). Hence predator andpre y density areth emajo r factors determining the residence time of the predatory mites in apre y colony. In distinguishing webbed leaf areas onth eplan 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 mineho wmuc h time isspen toutsid e thepre y colonies:ho w does apredator y mite search forne wpre y colonies?O fcourse ,thi s is also anaspec to fth 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 ndiscusse d inSubsectio n 3.2.4 and Section 3.4. Itwa s found that the predatory mites walk along the leafedg e ora rib and that they invade the prey colony aftermakin g tarsal contactwit h the silk strands attached toth e leafedg e or therib . Amblyseius potentillae behaves very different inthi s respect.Thi sphytoseii d predator tends to avoid the webbed leaf area andprefer s to staynea r toth e thickpart s 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 questionswhic h canb e solved onlyb y simulation and experimentation atth epopulatio n level (Chapter 4).A n example isth emeasuremen t ofth e rate ofdepartur e ofth e

190 predator from a prey colony atdifferen tpre y andpredato r densities.Wha t is the role ofthi sdispersa lmechanis m inth epopulatio ndynamic so fpre dator andprey ?A sth enumbe r ofmite s andth ecolonizatio npatter n arecon tinuously subjectt ochange ,dynami c simulation incombinatio nwit hpopula tionexperiment s inth egreenhous e mayprovid e theanswer .Thi s systemsap proach may also beusefu l indetectin gmissin g knowledge onth e individual level ofth epredator-pre y interaction.Fo rexample ,th erat eo f development and reproduction ofth e spidermite swer emeasure d forampl esuppl yo f food. Because the spider mites feed on thecontent s ofth e leafparenchym ,foo d quality may decrease andpossibl y the life-historyvariable s areaffected . Ifthi s isso ,simulate dpopulatio ngrowt hwil lexcee dth emeasure dpopula tiongrowt h inth egreenhouse .Populatio nmodel s canthu sb euse d toeluci date the role of certain measured properties of predator andpre y andt o determine which experiments atth e individual levelma y stillb enecessar y to improve theexistin gpopulatio nmodels .

191 Samenvatting

De kasspintmijt, Tetrangchus urticae (Acarina:Tetranychidae) ,vorm tee n belangrijke plaag inee ngroo t aantal voedings-e n siergewassen. Ind esier teelt onder glas wordt het kasspint chemischbestrede nme tbehul 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 vankasrozen . Deze methode wordt reeds met succes toegepast in de komkommerteelt en andere teelten van kasgroenten.He tproblee mva nd etoepassin g ind eteel t van kasrozen is echter, dat hier veel minder zuigschade vanhe t kasspint kanworde n getolereerd, omdathe tbla d sierwaardeheeft .Dez e hogekwaliteits eis geldt voor derozenscheute n diebove n derozenhe g uitgroeien en inee n vroeg stadiumva n debloe iworde n afgesneden enverhandeld . Veelmee r schade kan worden getolereerd ind e rozenheg;he tkasspin tza l daar zodanig onder controle gehoudenmoete nworden ,da td e jonge scheuten zomi nmogelij k schade ondervinden. Depopulati e vanhe tkasspin tka nzic hi nd ekort eperiod eva n2- 4 dagen verdubbelen. Ook na het loslaten van de roofmijten zal depopulatiegroe i van het kasspint nogwe l even doorgaan alvorens het aantal spintmijte nza l dalen. Daarom is hetva nbelan g om tewete nhoevee l roofmijtenbi j eenbe paalde spintaantasting minimaal moeten worden uitgezet om een gewenstbe strijdingsresultaa tt everkrijgen .O fd epredatorpopulati e na onderdrukking van de plaagontwikkeling ook op eigen krachtnieu w opkomende spinthaarden de baas zal kunnen zijn,hang t afva nhaa rvermoge n omperiode nva nprooi - schaarste te overleven. De bepaling van ditvermoge n isdaaro m vanbelan g voor het inzicht inintroductiestrategieë n vanroofmijten .Omda tverschil lende roofmijtspeciesverschillend e combinaties vanpredatie -e noverlevings - capaciteit bezitten, zijn eenvierta l soorten roofmijtenme telkaa rverge leken, nl. Phytoseiulus persimilis, Amblyseius potentillae, Amblyseius bibens en Metaseiulus occidentalis. Voor de oplossing van bovenstaande problematiek werd een systeemanalytische aanpakgekozen , 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 deresultate nva n deze indi vidu-experimenten end egevalideerd e individu-modellen wordenbetrokke nbi j deconstructi e van eennieu w simulatiemodel,da td epopulatiegroe i vanpre -

192 datore nproo i intij de nruimt eberekent .D eberekeninge nme tdi tpopulatie model zullenvergeleke nworde nme tpopulatie-experimente n ind ekas .Pa sn a gebleken bruikbaarheid zal ditmode l kunnen dienenvoo rberekenin gva nhe t minimale aantal lost elate npredatore nbi jee nbepaald e spintaantasting en een bepaald wensenpakket van de tuinder. Wellicht kunnendez e schattingen danvoo r depraktij kvertaal d worden invuistregels . Voor de systeemanalytische benadering ishe tvereis t omhe tvoedselaan bodvoo r deroofmijte n tequantificeren ,t ebeginne nbi jd ekasspintmijten . Omdat het aantal spintmijtenverander t ind e tijd,werde n eerstdi eeigen schappenva nd eparenchymzuigend e spintmijten onderzocht,di ebepalen d zijn voor desnelhei dva npopulatiegroei ,t eweten :d eontwikkelingsduur , deleef - tijdsafhankelijke reproductie en degeslachtsverhoudin g inhe tnakomeling schap (paragraaf 2.1.1-2.1.3).D e omgevingstemperatuiM?-speel tee nbelangrij - ke rol bij de ontwikkelings- en reproductiesnelheid vandez e koudbloedige arthropoden. De relatie tussen de temperatuur endez evariabele nblee k in grote trekken lineair tezij ntusse n 12°Ce n35°C .Onde r kasomstandigheden speelded eluchtvochtighei d geenbelangrijk e rol.D ereproductiesnelhei d en de geslachtsverhouding van het nakomelingschap bleken sterk af te hangen vand e leeftijdva nhe treproductiev evrouwtje .D e leeftijdva nd e juveniele spintmijt is ook van belang voor de kwantificering van hetvoedselaanbo d voor derovers ,omda td edivers e ontwikkelingsstadia eenster k verschillende kans lopeno mdoo ree nroofmij t teworde n gevangen.Daaro mwer d deontwikke lingsduur en de mortaliteitva n elkontwikkelingsstadiu m experimenteelbe paald,zoda the tvoedselaanbo d ind e simulatieva nd epredator-proo i inter actie op populatie-niveau kanworde n gedifferentieerd naarontwikkelings stadium. Het voedselaanbod voor depredato rword too kbepaal d doord e gemiddelde onderlinge afstand tussen de prooi-individuen, m.a.w. de prooidichtheid. Spintmijten vertonen een sterke neiging tot aggregatie.Zi jhuize n inee n labyrinth van spinseldraden dat zij construeren aan de onderkant vanhe t blad,beginnen d langsd ebladran d ofd ehoofdner fe nva ndaarui t expanderend over het hele blad. Indez espinsel sworde nd eeiere ngeleg d engroeie nd e juvenielen op.D e preovipositievrouwtjesworde nonmiddellij kn ad elaatst e vervelling bevrucht door de mannetjes en verhuizenda nveela l naar andere bladeren, waar een nieuwe spintkolonie wordt gesticht. Kolonievorming is dusee nessentiee l aspectva nhe tvoedselaanbo d vand epredator .Al s deroof mijtspintmijte nwi lbemachtigen , zaldez ed e spinselsmoete nbinnendringen . Daarom werd het prooiaanbod voor de predator gedefinieerd als hetaanta l spintmijten per cm2 bespinseld bladoppervlak en werd tevens de snelheid, waarmee individuele spintmijtenbijdrage n aand ebespinselin g vanhe tblad oppervlak, experimenteel bepaald (paragraaf 2.1.6). Met behulp van deze resultaten en de bepalingva nd eeigenschappe n died epopulatiegroe ibepa len, zal een modelworde ngeconstrueer d datd eprooiaantalle n énd eprooi dichtheid ind e tijd simuleert (Deel2) .

193 Naast spintmijten komen er in de teelt van kasrozen nauwelijks andere prooien of andersoortig voedsel voor. De overlevingva n depredatore nbi j afwezigheid van spintmijtenza l dus afhangenva n demogelijkhei d totkanni balisme en abiotische factoren,zoal s debeschikbaarhei d vanwater ,tempe ratuur en luchtvochtigheid (paragraaf2.2. 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.D ebenodigd e hoe veelheden zullen waarschijnlijk groot zijn (paragraaf 2.2.7). Honing of sucrose-oplossingen kunnen deoverlevingskanse n vanroofmijte n 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 lijktprak tisch realiseerbaar. De populatiegroei van de roofmijten zal afhangenva nhe t aantalspint - mijten dat zich op het bespinselde bladoppervlak bevindt,maa r tevens van 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°C en vochtighedenbenede n 70%veroorzake n eenhog emortalitei tonde rd e juveniele roofmijten. Omdat spintmijten veel minder kwetsbaar zijnbi j temperaturen tussen3 0e n35° Ce nbi j lageluchtvochtighede n (40-70%), zijndez eomstan digheden inhe tkasklimaa tkritie k voor debeheersin gva nspintmijtenplage n m.b.v. roofmijten.D evie r onderzochte soorten roofmijtenvertoonde nonder ling verschillen in ontwikkelingsduur, grootte van hetnakomelingscha p en de geslachtsverouding hiervan. Zij ontwikkelden zichechte r allemaal snel lerda nd espintmijten ,maa r legdenminde r eieren.D e consequentiesva ndez e verschillen zijnmoeilij k teoverzie n zonder gebruik temake nva ncomputer modellenva n depredator-proo i interactie oppopulatie-niveau . De evaluatie vandez everschille n zal daarom inDee l 2va n ditrappor tworde nbehandeld . Als het prooiaanbod voldoende groot is, kunnen jongeroofmijtvrouwtje s ongeveer 70%va n hetopgenome nvoedse lbestede n aand e aanmaakva neieren . De eiproduktie is zohoog ,da the tvoornamelij k dereproduktiev e vrouwtjes zijndi e depredatiecapacitei t vand eroofmijte nbepale n (paragraaf 2.2.4). De snelheid waarmee het voedsel wordt gebruikt voor de aanmaakva nnieu w protoplasma bleek in hoofdzaak af te hangen van de ovipositiehistorie, d.w.z. het aantal reeds gelegde eitjes;roofmijtvrouwtje slijke nt e 'stre ven' naar volledige realisatieva n depotentiël e eiproduktie.D e reproduk tieve roofmijtvrouwtjes zijn dus het meest vraatzuchtig enzi jbepale n in welke kolonies deeiere nworde n gedeponeerd. Daaromwer d hetzoekgedra g van deze roofmijtvrouwtjes bestudeerd inee npogin g omhe tprooiaanbo d terela teren aand epredati e end edaarui tresulterend e reproduktie (Hoofdstuk3) . Bij debestuderin g vanhe t zoekgedrag ishe tva nbelan g om demotivatie toestand van de predator te karakteriseren.Gezie n dehog e snelheidva nd e

194 voedselconversie ligt het voor dehan do m devoedselinhou d vand edar m als indicator voor demotivatietoestan d tekiezen .D edynamie kva nd edarmvul ling kan worden berekend als de ingestie,resorpti e enegesti eexperimen teel kunnen worden gekwantificeerd. Dit bleek mogelijkme tbehul pva nee n elektrobalans,waarme ehe tgewich tva n individuelemijte n kanworde nbepaal d Doormetin gva nhe tgewich tva nee ngehongerd e roofmijtvoo r enn avoedsel - opname kon de voedselinhoud van de verschillendeprooistadia ,d emaximal e darmvulling en het verzadigingsdeficitworde nbepaal d (paragraaf 3.1). Ook was hetmogelij k omd e ingestiesnelheid end esnelhei dwaarme ehe tvoedse l uit de darm verdwijnt, te bepalen. Deze kwantitatieve gegevenswerde nge bruikt inee nmode lva nd evoedselconversie ,da ti sgebaseer d opd e aanname dathe tsurplu sva nd egeresorbeerd evoedingsstoffe n wordtgebruik tvoo rd e aanmaakva neiere n (Figuur 21). Ditmode lwer d opbruikbaarhei d getestdoo r bijvoorbeeld uit te rekenen hoeveel tijd een gehongerd roofmijtvrouwtje nodigheef to mwee r eene i teproduceren ,e ndi tt evergelijke nme texperi menteel bepaalde tijdsperioden.D eberekeninge nbleke n juistt ezij ni nee n breed trajectva nhongerperioden ,maa rn aee nbepaald ehongerperiod everoor zaaktevoedseldeprivati e effectendi eo m eenherstelperiod e vroegen alvorens hetvrouwtj ewee r toteiprodukti e konovergaan . Hetmode lva nd evoedselconversi e (AppendixA )wer d gebruiktbi jd eana lyseva nd egedragswaarnemingen . Jongevrouwelijk epredatore n dievana fver zadigde toestand waren gehongerdvoo r eenbepaald eperiode ,werde nbi jee n prooikolonie geplaatst. Het gedragva nd epredato rwer d geobserveerd end e dynamiek van de darmvulling werd berekend. Op dezewijz eko nd eloopsnel heid, deloopactiviteit ,he tlooppatroon ,d ekan so pprooivangs te nd eduu r van de voedingsperiode worden gerelateerd aan hetgeschatt evoedselnivea u 1 ind edar mva nd epredato r (paragraaf3.2) . Dit experiment over het gedrag van devie rpredatorspecie swer duitge voerd op twee substraten: bespinseld blad en onbespinseld blad. Op deze wijze kon de rol van het spinsel bij het fourageergedragva nd e roofmijt wordenvastgesteld . Inhe tspinse lblee k deontmoetingssnelhei d per eenheid prooidichtheid lager te zijn, omdat zowel roof- als spintmijten zich er langzaamvoortbewege n enoo kminde r tijd aan lopenbesteden .Dez etrag ever plaatsingvoorkom theftig ebotsinge n tussenroof -e nspintmijte n zodatver storing van de roofmijt,zoal sveelvuldi gwaargenome n ophe tonbespinseld e substraat, nauwelijks meer optreedt. De coïncidentie tussen predator en prooi en dus ookd eontmoetingssnelhei d wordenverlaag d doord elabyrinth - structuur van het spinsel. Immers predator en prooi kunnen overe nonde r elkaar doorlopen zonder dat onderling contact plaatsvindt. De predatoren zoeken waarschijnlijk op de tast (paragraaf 3.2.3). Nadat zij een prooi met de zintuigen op de tarsi vanhe teerst epotenpaa rhebbe nontdekt ,ka n een aanvalworde n ingezet.Echte rnie tel k contactleid tto tee n succesvolle prooivangst. De succes ratio bleek af tehange nva nd edarmvullin gva nd e predator,he tontwikkelingsstadiu m enhe tgeslach tva nd eproo i en,i ntwe e

195 bijzondere gevallen,va nhe t substraat;i nhe tspinse l neemtd e succes ratio van Phytoseiulus persimilis sterk toe,terwij l dieva n Amblyseius potentillae dan juistster k afneemt (paragraaf 3.2.7, Figuur33) . Op basis van deze gedragscomponentenanalyse werd eenpredatiemode l ont worpenme tgebruikmakin g vanwachttijdtheori e (paragraaf 3.3). Deze theorie wordt veel gebruikt bijd e analyseva n dienstverleningsprocessen, bijvoor beeld debehandelin g vanpatiënte n ophe t spreekuur vanee n arts.D epatiën tenzij nn ud eprooien ,d e arts isd epredator , end ewachtkame r isd edar m van de predator. De snelheidwaarme e 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 tverteerd e voedsel in de haemolymphe op te nemen. Naarmate er meer patiënten in de wachtkamer zitten, zal deart s depatiënte n snellerbehandele n ennaarmat e dewachtkame r voller is,za l eree ngroter e kans zijn datd enieuw-aankomen depatiënte nva nee nbehandelin g afzien.Analoo g aandi tvoorbeel 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 nd edarmvullin g enda td eresorp - tietijd per prooi een negatief exponentiële verdeling heeft,ka nee n sto chastischwachttijdmode lworde n afgeleid.Di tmode lwer dvergeleke nme tee n deterministisch model,ee nCompound-simulatiemode l enee nMont e Carlo-simulatiemodel van het predatieproces (Appendix E-H).Dez e vergelijking viel uit inhe tvoordee l vanhe twachttijdmodel ,omda tdez eminde r rekentijdver bruikt en spaarzaam is in het gebruik vanvariabele n zonderda td eessen tiesverlore n gaan (paragraaf 3.3.1). Het wachttijdmodel werd opbruikbaarhei d getest inee n serievalidatie - experimenten, uitgevoerd op bespinselde enonbespinseld e 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 enda tdi t effect resulteert in een verlaagde predatiesnelheid bij Amblyseius bibens en Metaseiulus occidentales. Tegenover deze daling inhe tzoekvermoge nstaa t 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 substraatteven sbeinvloe d voorwa tbetref td e kans om een prooi te vangen na tarsaal contact (succes ratio). Amblyseius potentillae heeft een lagere succes ratio ophe tbespinseld e blad, hetgeen deverlagin g vanhe tzoekvermoge n meerda n alleen compenseert: depredatie snelheid in de prooikolonie ishoge r dano p onbespinselde bladerenme tde zelfde hoeveelheidprooi .

196 Systeemanalyse vand epredati ebi jverschillend e temperaturen leerde dat het effect van de temperatuur op de voedselconversiesnelheid bepalend is voor de vraatsnelheid (paragraaf 3.3.4). Gedragsveranderingen tengevolg e van de temperatuur bleken dus van veel minder belang. Vermoedelijk wordt óókd everlaagd e reproduktie bijhoger epredatordichthede n veroorzaaktdoo r eenverlagin gva n devoedselconversiesnelhei d ennie tdoo rveranderinge n in het zoekgedrag of door tijdverspilling bij onderling contacttusse nroof - mijten (paragraaf 3.3.6). Omdatroofmijtvrouwtje sstreve nnaa rd erealisa tieva nd epotentiël 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). Hetgebrui k vanvoedse l \ voor de eiproduktie bleek bij deze predatoren centraal testaa ni nd ebe paling van de predatiesnelheid, terwijlhe tvermoge no mprooie nt ebemach tigenal see nsubstraa tgebonde n constanteblee k tekunne nworde nbeschouwd . Hetwachttijdmode lwer d tenslotte uitgebreid voorhe tgeva l datmeerder e prooistadiame tel kee nverschillend evoedselinhou d aanwezigzij n (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 n eenmakkelijke r prooi vormen dan larven, larven eenmakkelijke rproo ivorme nda nnymphen ,e nda t de adulte spintvrouwtjesverrewe ghe tmoeilijks t tebemachtige n zijn.Boven dienblee k datd everschille n inprooivangkanse n voord everschillend e sta diakleine rworde nnaarmat e dedarmvullin gva n depredato r lager is:d epre datorword tminde r kieskeurignaarmat e zijmee rhonge rheeft .Simulati e van de predatie in een 'mengcultuur' suggereerde dat de 'monocultuur' succes ratios ook onderdez eomstandighede n deprooivangkan s kunnenweergeven .Ech ter, ermoete nno gvee lmee rvalidatie-experimente nworde nuitgevoerd . De duur van hetverblij f in eenprooikoloni eword tvoora lbepaal d door deprooidichthei d (paragraaf 3.4.1 en 3.4.2). Ditblee kui td evergelijkin gj vand everblijfsduu rva npredatore n inspinsel sme te nzonde rprooien .Ana lyse van het looppatroon endaaro p gebaseerde simulatiesva n deverblijfs duur leerde,da the tkronkelig e looppadva nd epredato r geenverklarin g kan geven voor de duur van het verblijf in de prooikolonie.D e experimenteel vastgestelde verblijfsduur in een prooikolonie kan alleen worden bereikt indiend epredato rbi jd eran dva nd ekoloni e omkeert.Volgen s de simulaties van het loopgedrag komtd epredato rvaa kgenoe gbi jd ekolonieran d omsne l te kunnenreagere no pverlagin gva nhe tprooiaanbod .Doorda troofmijtvrouw tjesblijve n zitten ind ekolonie sme thog eprooidichthei d zald epredator dichtheid ter plekke toenemen.Experimentee l werd aangetoond datverhogin g van de predatordichtheid leidt tot een kortere verblijfsduur ondanks een ruim aanbodva nprooie n (paragraaf 3.4.3). Predator-e nprooidichthei d blij ken dus de belangrijkste factoren te zijndi ehe tvertre kva nd epredato r bepalen. Doordat eronderschei d werd gemaakttusse ngekoloniseer d blad enongeko -

197 loniseerd blad is het niet alleen nodig om de factoren tebepale n died e verblijfsduur in de kolonie regelen,maa r ook de factoren diebepale nhoe veel tijd een predatorbuite n dekolonie s 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 ndi trappor t wordenbehandel d in samenhangme td ekolonisati e vand eplan tdoo r 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 lopene nee nkoloni e binnendringen na tarsaal contactme td e spinseldraden. Amblyseius potentillae vormthier opee nuitzondering .Dez e roofmijtheef td eneigin g om debespinseld eblad delen te mijden en zit bij voorkeur naastd edikk e delenva n dehoofdner f ofi nander ebeschermd e hoekjes opd eplant . De metingen op het individu-niveau kunnen aanleiding geven tot vragen die slechts door simulatie en experimenten oppopulatie-nivea u kunnenwor denopgelost .Den kbijvoorbeel d aand emetinge nva nhe tvertre k vand epre dator uit een prooikolonie bijverschillend e prooi-e npredatordichtheden . Welke rol speelt ditdispersie-proce s ind epopulatiedynamie k vanpredato r enprooi ?Doorda t deveranderinge n ind e aantallen enhe t kolonisatiepatroon continuplaatsvinden , zoudynamisch e simulatie incombinati eme tpopulatie experimenten een oplossing kunnen leveren. Ook hetbelan gva n ontbrekende experimentele gegevens ophe t individu-niveau kunnenworde n opgespoord.Den k bijvoorbeeld aan het feit dat de ontwikkelingsduur end ereprodukti e zijn gemeten aan individuele spintmijte n bij een overmaat aanvoedsel .Doorda t de spintmijten het bladparenchym leegzuigen zal dekwalitei tva nhe tbla d achteruitgaan en mogelijk zullen degroei-variabele ndaardoo r wordenbein - vloed. Wanneer dit eenro l speelt,da nzoude n simulatiesva nd epopulatie - groeiva n despintmijte nee ngroter e aantalstoenamet ezie ngeve nda npopu latie-experimenten in de kas.Dez e voorbeelden laten zien hoepopulatie - modellen kunnen worden gebruikto mhe tbelan gva nbepaald e karakteristieke eigenschappenva nproo i ofpredato rvoo r depopulatiedynamie k tedemonstre rene no mnieuw emetinge n ophe t individu-niveau terechtvaardigen .O p deze wijze zijnee n aantalvrage n geformuleerd inHoofdstu k 4,di eopgelos tzou den kunnenworde n doorcombinati e van simulatie enexperimen t oppopulatie niveau.D ebeantwoordin g van dezevrage n zal inDee l 2plaatsvinden .

198 Acknowledgements

Thanks aredu et o allthos ewh ohelpe dm ewit hm y research andthi sbook . Ofsome ,I shoul d liket omak e specialmention : my promotor, CT. deWit , for his inspiration during the research and forth ecritica l readingo fth edraft so fth emanuscript . - myco-promotor ,J . deWilde ,fo rconstructiv e comments onth ephysiolog ical and acarologicalpart s ofth emanuscript . M.va nd eVri e for suggesting the project, for introducing me to the practice ofgreenhous e culture and forreadin g themanuscript . R.Rabbing e for initiating the project and for his comments on the manuscript. J.H. Küchleinfo rreadin gth ethir d chapter and forgenerousl y providing mewit h someo fhi s datao nprédatio nan d reproduction of Metaseiulus occi dental's (Table 19,23 ,26 ,35 ,36 ,5 7an d 60;Fig .14) . the students that participated inth eproject :P .Ruardi j forconstruc ting acompute rprogra m forth eanalysi so fwalkin gpattern s andT .Rennen , T.D. Keja, D.Adhidarma , Q.d eRanit z and R.J. Klei for theirpar t inth e observations ofth epredator ybehaviour . M.A.J,va nMontfor tan dA .Otte n forsuggestin g theus eo fth eTuke y dis tribution and forothe radvice . - W.J.Tigge s andH . Snellen forth econtinuou s supplyo f Metaseiulus occi dentales andA.Q .va nZo n fora startin g culture of Ambluseius bibens. J.P.W.Noordin k forhi shel pwit hradioactiv etechniques . F.Thie l forassistanc ewit h ScanningElectro nMicroscopy . S.G. Wever andW.C.Th .Middelplaat s fordrawin gth efigures . - Mrs.W.M . Laoh-Gieskes fortypin g themanuscript .

199 APPENDIX A MODEL OFREPRODUCTIO N INRELATIO N TO FOOD INTAKE

TITLE REPRODUCTION INRELATIO N TO POOD INTAKE TITLE DETERMINISTIC SIMULATION OP THEPOO D CONVERSION TITLE DISCRETE FEEDING SCHEDULE INITIAL DELX=1./DELT ******•»*******»**»*******»»**»****»»*»**»*»***»****»•****•***•»•******* *** INPUT DATA ***METASEIULU S OCCIDENTALS *** PARAM GUTC=3.3,0PIFW=2.2,DRYW=2.7,EGG=1 . 9 ***•»»****»****»*••«**•*»***#*********»*»*•*»*****••************»******* ***RELATIV E RATES *** RRRES =(TEMP-11.)*0.195 RREG =(TEMP-11.)*0.01 RRWL03=(TEMP-11 .)*0.0 4 PARAM TEMP =26. **»*•*************»#»**********»****«•••*•••*•»***»•******»»•»*•*»*»»**• *** INITIAL CONDITIONS *«* PARAM PDEPRT=0. IFRW =OPTFW *EXP(-RRWL03*PDEPRT) IPCG =GUTC *EXP(-RRRES »FDEPRT) IREP =0. DYNAMIC **•******•***•*»»*»•*#•**•»*****•**•»»*•»-•»•**••**-«••****•»****»*•»*****••• *** STATE VARIABLES *»* WEIGtlT=PRESHW +DRYW +PCGUT FRE3riW=INTGRL(IFRW,RRE3W-RWL03S) FCGUT =INTGRL(IFCG,RFI-RRE3-REG) REPR0D=INTGRL(IREP,RRE3R-PU3H*EGG*DELX) NEGG =INTGRL(0.,PU3H*D£LX) PUSH =INSW(REPROD-EGG,0.,1.) POOD =INTGRL(IFCG,RFI ) FAECE3=INTGRL(0. ,REG ) MTBOL =INTGRL(0. ,RRE3tf) ***RAT E VARIABLES **+ RFI =AMIN1(GUTC-FCGUT,PREY)*PUL3«DELX RRES =RRRE3 *PCGUT RRESR =INSW(FRE3liW-0PTFW,0 . ,RR£3) RRESW =IN3W(FRES;iW-0PTFW,RRE3,0. ) REG =RREG *FCGUT RWL0S3=RRWL03*FRE3riW ************************************************************************ *** FEEDING SCHEDULE *** PARAM PERI0D=1. PULS =IMPULS(0..PERIOD) PARAM PREY =1.

200 ***OUTPU T STATEMENTS *** PRINT POOD,FAECES,MTBOL,FCGUT,FRESHW,WEIGHT,REPROD,NEGG TIMER FINTIM=50.,OUTDEL=2.,PRDEL=2.,DELT=0.05 METHODREC T END STOP ENDJOB

201 APPENDIX B TIME SERIES ANALYSIS

Sequential changes of walking directions mayb ecorrelated . This canb e analysed intw oway s: Markov chain analysis with regard toth e signo fth echange s inwalkin g direction; Auto correlation analysis with regard to the sign andth emagnitud e of changes inwalkin g direction.

Markov chain analysis

Ifa sig no f anelemen t ina tim e series depends onth e signs ofpreced ingelements ,a Marko vmode lma yb e adequate.Th ecas emos t commonly treated is the first orderMarko vmodel ,fo rwhic h only the lastelemen t ina tim e series influences thechoic e of ane welement :

Prob(A k, )= Prob( A ]i s-1 s-2 s-1 J) forpositiv e ornegativ e j, i,k This iscalle d atransitio nprobabilit y from jt oi .Fou r transitionproba bilities arepossible :p ,p ,p andp Supposew ewan tt otes tth enul lhypothesi s that adirectio n choicepro cess has order zero (no feedback atall )agains tth ealternativ e thatth e order is one (aninfluenc e ofonl y the lastelement) . Then iti susefu l to order the sequences inth e following contingencytables : For N , the point indi ^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. Under thenul l hypothesis,p equalsN_,/ N (i= + o r -). According toAnder son& Goodma n (1957)th e following Chi-square statistic applies:

(N-p-N J' 2 -V +i i (Ni_-(l-p)-Ni.r X, = ^ (l-p)-N. !=-,+ FN"

202 If this zero-order testreveal sdependency , itma yb e asked ifth epro cess is of order one or higher. The null hypothesis of order =1 ca nb e tested against the alternative of order =2 wit hth e aido fth e following contingency tables:

^o + - vtO + - from\ from\

-+ N N ~ N N -++ -+- -+

++ N N +- N N +++ ++- +-+ +~ According toAnderso n& Goodman , thesetable sma yb etreate d ascontingenc y 2 2 tables again.Th e sum ofth ex ,statistic s hasth ex _ distributionunde rth e nullhypothesis .

Auto correlation analysis

Correlation between successive observations in a series iscalle d auto correlation (see e.g. Chattfield, 1975). The autocorrelatio n coefficient is calculated with the aid ofth ecovarianc e coefficientc. ,whic hb yana logywit h theususa l covariance formula isdefine das :

ck = n"", '< As - Ä>- s-l +k This is called the auto covariance at lag k, inwhic h si sth enumbe ro f theelemen t inth eseries .Th e autocorrelatio n coefficientp . isestimate d 2 asth equotien to fc . andth evarianc ea (=c.__): K A K—U

r. =— ,fo rk=l , 2, ,m andm <

Supposetha tA 1# A-, A are independent and identically distributed random variables with an arbitrary mean, then it can be shown (Kendall & Stuart, 1966,chapte r 48)that :

£'(rk)s -1/n and var(r.) = 1/n , and that r. is asymptotically normally distributed.Afte rplottin go fth e rfcvalue s againstk , approximate 95%confidenc e limits canb edraw na t

-1/n ± 1/Vn •t n, _ 0 = -l/n ±2/Vn .Value so fr k that fall outside these limits are significantly different fromzer o atth e 5%level . For thepurpos e ofsimulatio na multipl e regressionmode l isadequat et o account for correlation between successive ranges in walking direction

Ag (1< s« n).Thi sproces sca nb e described by the autoregressio nequation :

As = °VAs-l + =^ As> =° '

203 A isno tregresse d on independentvariable s buto npas tvalue s ofA Hence the term auto regression; m is theso-calle d ordero fth e auto regressive process. Thecoefficient s a areth e auto regression orpar tial auto correlation coefficients andX isdetermine d by apurel y random process. To obtain a series X ,whic h is freed of correlation, the auto regression equation isrewritte na s

X" s ""s >-'l(« ! s-1 T u2 "s-2 T T m "s-mr Theparameter s u, a, andA o f theTuke y distributionma yb e estimated again onthi s corrected seriesX . s Now tworelate d questions remain tob e answered: How todetermin e theorde rm ofth eprocess ? 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 .o r a,, which are significantly different from zero (i.e.outsid e the range ± 2/4u). The relation between a and r can be obtained by multiplying the auto regression equationwit hA , andb y calculating expectations: . n-k n-k a n-k I (A -A .) A -±r-n-k .,x s s-k' n-k 2 (A s-1i s- ki ) —rn-k* 2 .(,Av s- m- A s-k.) ' s=l s=l s=l for E(Xv s ) = £( A )= s0 . Forn > > k, thisequatio nma yb e simplified with the aido fth e formula for the auto covariance coefficient

Vck-i + + a m•c ,k- m -2 Ifth e auto covariance coefficientc , isdivide d by thevarianc e a (=c) , weobtai n theYule-Walke requations :

rk =a l-rk-l + + a •rm , k-m Because r, is equal tor them unknown auto regression coefficients can be solved outo f ase to fm Yule-Walke r equations. Inmatrix-notatio n these equationsare : Lm-1

m-2 m-3

204 Note, that for a firstorde r auto regressiveprocess ,th e auto correlation coefficients decrease exponentially withk : rk =

205 APPENDIXC MAXIMUM LIKELIHOOD ESTIMATIONO FTH EPARAMETER SO FTH ETUKE Y DISTRIBUTION

Theprocedur et oestimat eth e parameters |j,a an dAo fth eTuke ydistri bution consistso fa roug hestimatio no fthes eparameter st oobtai n starting values,an da subsequen tmaximizatio no fth elikelihoo d functiont ooptimiz e theparamete r estimates (vanMontfor t& Otten , 1976).

Starting values

Estimate approximate valueso fX forth e10% , 30%,70% ,90 %point so f themeasure d cumulative frequency distribution.Wit h these estimations,A „ canb esolve d fromth efollowin g equationb yNewton-Raphso n iteration:

X0 7" X 03 (O-7*0 -0.3 A°)- (0.3 A°- 0.7 A°) 0.7A°- 0.3 A° X09 " X 01 (°-9A° -0.1 A°)- (0.1 A°- 0.9 A°) 0.9A°- 0.1 A°

The50 %poin to fth ecumulativ e frequency distribution,X n -,serve sa sa startingvalu efo ru 0.Th estartin gvalu eo fa 0ca nno wb eobtaine d from equation:

X = M + a A 0.9 ° °-<-°-^° -0.1 °)/Ao

Iterative optimization procedure

Thisprocedur ei sbase do nNewton-Raphso n iterationwit hth eLog-Likeli hood function:

'jj) = Q + (-L-r^L. K+l K K =iterativ e step number L =ln(L* ) (theLog-Likelihoo d function) c L* =n p .i (theLikelihoo d function) i=l1 i =1,2, c c =numbe ro ffrequenc y classes n. =frequenc yi nclas si p. =probabilit yi nclas si In. =N

206 When g.i sdefine d asth eclas s boundary, theLog-Likelihoo d functionca n be computed as follows:

c 2 n.• I n ;1(^). ?(%*)| i=l

and p YP • 'x<»> To maximize theLog-Likelihoo dh function< v , L,th efirs t andsecon d deriva tives L'an dL "ar eneeded . Because ofth ediscret e character ofth eL function, these derivatives aredetermine d numerically, accordingt o Abramowitz & Stegun (1975,p . 883-884).

/6L» I 6L' ÔL^ ÔA. ÔKÔK 6A.ÔM ÔA.ÔCT

ÔL 6L2 6L2 6L2 L" 6M ÔMÔA. ô|j6|j ô|jôa 2 ÔL 6L2 ÔL2 6L^ ôa ôaôA. ôafip ôaôa

It ispossibl e that -L"ha sa negativ e eigenvalue inth ebeginnin g ofth e iterative procedure. Therefore vanMontfor t& Otten (1977) propose a repara- meterization toreduc e this inconvenience. This isdon e by replacement of a e fa s a Y for K=1 0.731 y = ' P(K=i) e< > = rr-e"

The iterationproces s canb e stopped whenL LK-1 °r L' -( M K+l issufficientl y small.A Xc_-._3tes t (c= numbe ro f frequency classes)i s used totes tth e fito fth eTuke ymode l toth emeasure d frequency data.A confidence interval forth eparameter s canb e constructed onth ebasi s of thecovarianc e matrix

= | •("L")" 1.

207 APPENDIX D MODEL OF WALKING BEHAVIOUR

TITLE TORTUOUS '«ALK + PREDATION / DIMENSION C(100,100) FIXED U,I,J,K,X,Ï INITIAL DELX =1./DELT INCÛN U =1 PAHAh UNIT =.b

*** PROPERTIES OF PREY AND PREDATOR **# SPEED =0.010*60. DIAK1 =0.091 UIAK2 =0.013 RADIUS=0.D*(DIAH1+DIAH2)/UNIT PARAK LABDA=-0.8ü,aiGKA=ü.2,KU=0. NÛSORT ***

*** REGULAR DISTRIBUTION OF THE PREY *** DO 1 1=1 99 DO 1 J=1 99 C(I ,J)"1 1 CON TINUE DYNAMO

*** NÜN-AUTÜCURRELATED WALK

P =RIiDGEN(U ) A =MU+SIGMA*(P**LABDA-(1 -P)**LA3DA)/LABDA DIR =INTGRL(0.,A*DELX) CSD R =COS(DIR) SNDR =SIN(DIH) X1 =INTGRL(W ..CSDR/UNIT ) Y1 =INTGRL(50..SNDR/UNIT) NOSORT ***

*** REGISTRATION OF PREDATOR-PREY ENCOUNTERS DO 5 1=1 , 7 DO 3 J=1, 7 X =X1-4+I Y =Y1-4+J IF (C(X,Yj.EQ.O.)G O TO 3 DIST =3QRT((X-X1)**2+(Y-Y1 *2) in' (DIST.GT.RADIUS)G O TO 3 WRITE(6,100) X,Y 100 F0RKAT(1X,2(F3.0,1X)) C(X,Y)=0. SU..I =SUM+1. 3 CONTINUE SORT CLOCK =TIKE/SPEED

208 ««ft***************************************************** *** OUTPUT STATEMENTS *#* PRINT SUM,CLOCK TIKES FINTIM=100.,PRDEL=1.,OUTDEL=0.04,DELT=O.04 METHOD RECT FINISH X1=0.5,X1=99.5,Y1=0.5,Y1=99.5 INTERACTIVE OUTPUT X1(3Ü.,70.).Ï1(3Ü.,70.) LABEL PHYTOSEIULUS PEKSIMILIS PAGE XYPLOT END STOP ENDJOB

209 APPENDIX E DETERMINISTIC MODEL OFTH EPREDATIO N PROCESS

TITLE FUNCTIONAL RESPONSE OP A PREDATOR TO THEDENSIT Y OP ITS PREY TITLE DETERMINISTIC APPROACH TITLE YOUNG-FEMAL E PREDATOR OFMETASEIULU S OCCIDENTALIS VERSUS TITLEEGG S 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=AFGEN(VLPT,PCG/GUTCON) ACPRED=AFGEN(A CPT,PCG/GUTCON ) SR =AFGEN(SRT ,FCG/GUTCON) FT =APGEN(PTT .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 . »** ************************************************************************ *** COMPUTATION OF THERAT E OP SUCCESSFUL ENCOUNTER *** RREWW =DM*SQRT(VLPREY** 2+ VLPRED**2)*ACPREY*ACPRE D RREWR =DM* VLPRE D •ACPRE D * (1.- A CPREY ) RRERW =DM* VLPRE Y *ACPRE Y * (1.- ACPRED ) RSA =(RREWW +RREW R +RRERW )* DPRE Y *COI N *S R *86400 . TSC =FT+ (1./AMAX1(RSA.1.E-5)) RSE =1./TSC CUMPRD=INTGRL(0.,RSE) *** ********************************************************************* ***DYNAMIC S OF THE FOOD CONTENT OP THEGU T *** FCG =INTGRL(IFCG,RF I -RG E ) RGE =RRGE *PC G RFI =AMIN1(SDG/DELT.RSE *FCPREY) SDG =AMAX1(0.,GUTCON -FCG ) *** ************************************************************************ *** FLUCTUATION OF THE PREY DENSITY INRELATIO N TO *** THE TIME INTERVAL OF PREY REPLACEMENT

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

211 APPENDIX F MONTE CARLO SIMULATION OFTH EPREDATIO N PROCESS

TITLE FUNCTIONAL RESPONSE OPA PREDATO R TO THE DENSITY OF ITS PREY TITLE MONTE CARLO APPROACH TITLE YOUNG FEMALE PREDATOR OFMETASEIULU S OCCIDENTALS VERSUS TITLE EGGS OF TETRANYCHUS URTICAE ***** ***************************************************************** *** PHYSIOLOGICAL AND BEHAVIOURAL INPUT VARIA3LES *** PARAM GUTCON 3.3 PARAM IFCP 1. INCO N IFCG 2.95 PARAM TEMP 26. RRFI 1.8*60.*24- RRG E (TEMP - 11.) * 0.195 PARAM DMPREY='0.01 3 PARAM DMPRED='0.05 7 DM DMPREY + DMPRED PARAM VLPREY 0. PARAM ACPREY='0 . PARAM COIN =' 0.42 VLPRED= AFGEN(VLPT,FCG/GUTCON) ACPRED= AFGEN(ACPT,FCG/GUTCON ) SR AFGEN(SRT ,FCG/GUTCON) FT AFGEN(FTT ,FCG/GUTCON) FUNCT VLPT =0.,0.047,1.,0.047 FUNCTnon ION ACP T =0.,0.39,1.,0.39 FUNCT ION 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, .1 52 , .5,-083,.6,.103,.7,.0469,.8,.0217,.9,.007,.98,O.,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 =PT*CATCH/DEL T -INSW(DELT-IITÏM,1.,HTIM/DELT ) ABAND =INSW(-HTIM,C.,1.)* HANDL E *** ***** ******************************************************************* *** COMPUTATION OF THERAT E OF SUCCESSFUL ENCOUNTER *** RREWW =DM*SQRT(VLPREY** 2+ VLPRED**2)*ACPREY*A CPRE D RREWR =DM* VLPRE D *ACPRE D * (1.- A CPREY ) RRERW =DM* VLPRE Y *ACPRE Y * (1.- ACPRED ) RSE =(RREWW +RREW R +RRERW )* DPRE Y *COI N * SR *86400 . PRC =1. -EXP(-R3E*DELT ) RDRAW =RNDGEN(TELLER*200.) CATCH =IN3W(PRC -RDRA W ,0. ,1. )* SEARC H CUMPRD =INTGRL(0.,CATCH*INTERV/DELT) INTERV =INSW(TIME-ADAPT,0.,1.) PARAM ADAPT =0.1 ***

212 ******#**•»*•»***#*»#****»*»»*#**»**»#•#*****#***•»***••#*«»***»*»******* *** DYNAMICS OP THE POOD CONTENT OP THE GUT **» PCG =INTGRL(IFCG, RPI - RGE ) RGE =RRGE * PCG RPI =AMIN1(SDG,FCPREY)*HANDLE*RRFI 3DG =AMAX1(0.,GUTCON - PCG) PCPREY=INTGRL(0.,CATCH*(IPCP-PCPREY)/DELT -RPI ) APCG =INTGRL(0.,FCG/DELT/NUM*IMPULS(ADAPT,PERIOD) ) NUM =(PINTIM-ADAPT)/PERIOD PARAM PERIOD=0.05 *•* «»»»A***********»*»»****»»****»»»»*****»******»*************»***«******» *** 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. *** *********»**•*******»•»*»***»••***»******»*#*****»»**#*#**»»»#*•***»••*» ***OUTPU T STATEMENTS *** TIMER PINTIM=0.25,PRDEL=0.01,DELT=0.001 METHOD RECT TERMINAL PARAM NREP =100. INCONMPRED=0.,MPCG=0 . INCONSPRED=0.,SPCG=0 . INCONVPRED=0.,VPCG=0 . INCONTELLER=0 . MPRED =MPRED+CUMPRD/NREP MPCG =MPCG +AFC G /NREP SPRED =SPRED+CUMPRD*CUMPRD SPCG =SPCG +APC G *AFC G TELLER=TELLER+1. IP (TELLER.GE.NREP)G O TO1 CALLRERU N GO TO2 1 VPRED =(SPRED-NREP*MPRED*MPRED)/(NREP-1. ) VPCG =(SFCG -NREP*MFCG*MFCG)/(NREP-1. ) WRITE(6,100)IDPRE Y 100 P0RMAT(11H DENSITY = ,F8.0) WRITE(6,101)REPDE L 101 F0RMAT(23H REPLACEMENT IN DAYS = ,P8.4) WRITE(6,102) 102 P0RKAT(25HMPRED ,VPRED ,MPCG ,VPCG ) WRITE(6,103)MPRED,VPRED,MPCG,VPC G 103 P0RMAT(2(4X,2(P8.4,4X))) 2 CONTINUE *** ************************************************************************ END STOP ENDJOB

213 APPENDIX G MATRIX ALGEBRAIC SOLUTION OF THE QUEUEING EQUATIONS

Under conditions of constant RSE and RGE1 the gueueing eguations can be solved as follows: Let A be the matrix of the coefficients in the gueueing eguations

fl-RSEQ RGE1 0 0 .. .

RSE0 1-RSE^RGE^ RGE12 0 .. .

RSE., 1-RSE2-RGE12 RGE1, A = RSE„

RGE1N-1 1-RSE„ .,-RGE. RSEN-1 'N-l—N- l RGE1N .0 RSE 1-RGE1 'N-l Nd

Let p be a vector of the state probabilities, p , in the gueueing eguations

;p0(t) , p1(t)

P2(t> p(t) =i

ipN(t)/

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

/*0

Q = R """-A-R

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

p(t)= e A'fc-p(0)= R-(e R 'A'R)-R"1-p(0)= R-e Q't-R-1-p(0)

/eV*.

.Q't

BV*/ The solutiono fthi s seto fequation s isrepresente db yß nn + ••«j-* Pn«^ = Ko '*=1 ßnj n =1 ,2 ,3 , N q isnegativ e

ß0 =equilibriu m coefficients

Thenumbe r ofpre y killed during atim espa nt (=CUMPRD t)ca nb e foundb y integration ofth eprédatio nequatio n

PRED =Li mPRE D =afK£, "t =2 n-p (t)+ 2 RGE1 -p (t) DELT+O dt n=0 n n=0 n n N N t CUMPRD^.= 2 n-p (t)+ 2 (RGE1 -J"p (u)du) n=0 n n=0 n 0 n

q t q t ƒ pn(u)du =ß -t+ i •ßT,1-(l-e" K l* )+ i •ßT,.-(l-e" 2' )+ nO qx nl q2 "n2

215 APPENDIXH QUEUEINGMODE L OFTH EPREDATIO N PROCESS

TITLE FUNCTIONALRESPONS E OF A PREDATOR TO THE DENSITY OF ITS PREY TITLE QUEUEING APPROACH TITLE YOUNG FEMALE PREDATOR OFMETASEIULU S OCCIDENTALIS VERSUS TITLE EGGS OF TETRANYCHU3 URTICAE STORAGE PST(22),PTD(22) FIXED NCL INITIAL »it********************************************************************* *** ENUMERATION OF THEFOO D CONTENT CLASSES OF THEGU T *** 1 2 3 4 5 I 192 02 1 22 =N C *** 1 2 3 4 N 181 92 0 =NC L *** 0 1 2 3 17 18 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 TERP =26. RRGE =(TEMP-11.)*0.195 MDPREY=0. MFCG=0 . CUMPRD=0. DYNAMIC REPL =IMPULS(0..REPDEL) NOSOHT CALL FREDA(RRGE,DPREY,PREÜ,FOOD,FCG) DPREY =DPREY -(PRED /AREA)+REPL*(IDPREY-DPRS Y ) IF (TIME.LT.DELT)G O TO5 CUMPRD=CUMPRD+ PRED MDPREY=MDPREY+(DPREY*DELT/FINTIM) MFCG =MFCG +(FCG *DELT/FINTIM) *•» ************•**•**#*•#«*******#»*•*****•*******•**»****•*****»********** *** OUTPUT STATEMENTS *+* IF (TIME.LT.FINT1M)G O TO5 WRITS(6,111)CUMPR D ,KDPREY ,MFCG 111 F0RMAT(2X,3(2X,F6.3,2X)) * DO 5IG=1,NC L * GUTCON =IG * WRITE(6,112)GUTC0N,P3T(IG+1),PTD(IG+1 ) * 112 F0RMAT(2X,3(2X,F8.4,2X)) 5 CONTINUE

216 SORT TIMER FINTIM=.25,PRDEL=.25,DELT=.00 1 *** ************************************************************************ END STOP SUBROUTINE PREDA(RRGEMP,DS, $ PN.PI.GT) COMMON C** PHYSIOLOGICAL AND BEHAVIOURAL INPUT DATA C** DIMENSION RSE(22),RS1(22) DIMENSION SR(20) ,FT(20) DIMENSION PT(22) ,RGE1(22) DIMENSION VL(20) ,AC(20) DATAVL/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 FT/2*.009,2*.007,2*.006,4*.005,10*.004/ FCP =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 E OP SUCCESSFUL ENCOUNTER AND C*** THE INVERSE OP THETIM ENEEDE D TORESOR B AND EGEST C*** THEMAS S EQUIVALENT TOTH E CLASS-SPECIFIC PART OP THE PREY C*** DO 51 N=1,NCL I=N+1 RGE1(I)=-RRGEMP/ALOG((N-.99)/N) RREWW =DM*SQRT(VL(N)*VL(N)+VLPREY*VLPREY)*AC(N)*ACPRE Y RREWR =DM*VL(N)*AC(N)*(1.-ACPREY ) RRERW =DM*VLPREY*ACPREY*(1.-AC(N))*0. 5 RSA =(RREWW+RREWR+RRERW)*DS*SR(N)*C0IN*86400. TSC =(PT(N))+(1./(AMAX1(RSA,1.E-5))) RSE(I)=1./TS C PST(I)=0 . 51 CONTINUE * RGE1(1 )=0. RGE1(NC)=1. RGE1(2 )=0. RSE(1)=0 . RSE(NL)=0. RSE(NC)=0. C*** C*#**»**»*»**•****•»**»»***»*******»»#*»*»*********•*»#**»»#•** C*** COMPUTATION OP THESTEAD Y STATE DISTRIBUTION OF C*** THEFOO D CONTENT OF THEGU T C*** PST(1)=0 . PST(NC)=0. PST(2)=1 . SUMST =0. DO 52N=1,NC L I=N+1 FCPREY =AMIN1(NL-2.,PCP*ENLARG)

217 11 =MAX1(I-FCPREY. 1. ) PST(1+1)=(-PST(I 1)*RSE(I1)+PST(I)*(RSE(l)+RGE1(I)))/RGE 1( 1+1 ) SUMST =SUMST+PST(I) 52 CONTINUE DO 53N=1,NC L I=N+1 PST(I)=PST(I)/SUMS T 53 CONTINUE C*** C*»*»-»»»«***»«****»*»**»**»**»***»****'****»****»***********»***»«******* C*** INITIALIZATION OP THEFREQUENC Y DISTRIBUTION OF C*** FOOD CONTENT OF THEGU T

PT(1 )=0 . PT(NC)=0 . DO 54N=1,NC L I=N+1 PT(I) =PTD(I) IF (TIME.LE.DELT)PT(I )= P3T(I ) RS1(I)=0 . 54 CONTINUE C*** Q*********************************************************************** C*** COMPUTATION OF THERAT E OF PREDATION AND TUEFOO D INTAKE C*** ACCOUNTING FOR PARTIAL INGESTION Q*** PN=0 . FI=0 . IP =FCP*ENLARG 11 =MAX0(NCL-IP+1,2) DO 55N=I1,NC L I=N+1 PART =RSE(I)*PT(I)«-DELT RS1(NL)=RS1(NL)+PART/DELT PN =PN+PART FI =FI+PART*(NL-I) 55 CONTINUE 12 =MINO(NCL,IP) DO 56 N=I2,NCL I=N+1 WHOLE =RSE(I-IP)*PT(I-IP)*DELT RS1 (I)=RS1 (D+WHOLE/DELT PN =PN+WHOLE FI =FI+WHOLE*IP 56 CONTINUE C*** C***^*************»*»»»************************************************ C*** COMPUTATION OF THEFREQUENC Y DISTRIBUTION OF FCGUT C*** AT TIME+ DEL T SUM =0. DO 57N=1,NC L I=N+1 RS1(I)=(RS1(I )+RGE1(1+1)*PT(I+1))*DEL T PTD(I)= PT(I)*(1.-(RSE(I)+RGE1(I))*DELT)+RS1(I ) SUM =SUM + PTD(I) 57 CONTINUE GT =0. GUT =0. DO 58N=1,NC L I=N+1 PTD(I)=PTD(I )/SU M G =N-.5 GUT =GUT+PTD(I)*G/ENLAR G GT =GT +PST(I)*G/ENLAR G

218 58 CONTINUE

Q**»*«»ft******************************************************#***#***** RETURN END ENDJOB

219 APPENDIX I QUEUEINGMODE LO FPREDATIO N INA MIXTUR EO FPRE Y STAGES

TITLE FUNCTIONAL RESPONSE OFA PREDATO RT O TITLE THEDENSIT YO FA MIXTUR EO FPRE Y STAGES TITLE QUEUEING APPROACH TITLE YOUNG FEMALE PREDATOR OFMETASEIULU S OCCIDENTALIS VERSUS TITLEAL LPRE Y STAGESO FTETRANYCHU S URTICAE TITLE EGG,LARVA,PROTO-AN DDEUTONYMPI iC.Q .CHRYSALES.MAL EAN DFEMAL E STORAGE DSI(10),DS(10),PST(22),PTD(22),PN(10) FIXEDNCL.NS T INITIAL NCL=20 NST=9 •» * ************************************************************************ *** COMPUTATION OFTH EFLUCTUATIO N OFTH EDENSITIE SO FSEVERA L *** PREY STAGES INRELATIO N TOTH ETIM E INTERVALO FPRE Y 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-,S ,10.) DSI(2)=NPREY/ARE A DSI(9) =(10.-NPREY)/AREA DO2 IG=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) DO4 IS=2,9, 7 DS(IS) =DS(IS)-(PN(IS)/AREA)+REPL*(D3I(IS)-D3(IS)) PN(IS) =PN(IS)*DELX *** •••••fr****************************************************************** ***OUTPU T STATEMENTS IF (TIME.LT.DELT)G OT O4 WRITE(6,111) PN(IS),DS(IS),FC G 111 FORMAT(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=I G

220 * IF (TIME.LT.DELT)G O TO5 * WRITE(6,112)GUTC0N,PST(IG+1),PTD(IG+ 1) * 112 FORMAT(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(RRGEriP, S REPR,WEIGHT,GUT) COMMON Q***»*****#***#***»»***********»*»**»*************»»***»*****• ******* * C*** PHYSIOLOGICAL AND BEHAVIOURAL INPUT DATA DIMENSION PT(22),RGE1(22) DIMENSION RS(22,10),RS1(22) DIMENSION PY(9),SR(20,9),?T(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*0.085,5*0.08,5*0.075,5*0.068/ DATA AC/O...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., S .325,.325,.302,. 115,-115,- 08,.08,.07,.07,.06, $ .0 6 , . 06, . 06, . 06,. 06, . 05,. 05, .04 , .02,0 . / DATA PT/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,.01 O,.01 O,.009,.008,.008,.008, $ .01 5, . 01 3, •0 11 , .01 1 , . 01 O, .01 O, .009, .008, .008 , .008, $ .01 5,.013,.011,.011,.01 O,.01 O,.009,.008,.008,.008, S .024,.021,.020,.020,.019,.014,.010,.009,-009,-009, $ .027,.023,.023,.023,-023,.022,.020,.020,.018,.015, $ .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 .)/GUTC 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 Q*********************************************************************** C*** COMPUTATION OF THE RATE OP SUCCESSFUL ENCOUNTER AND C*** THE INVERSE OF THE TIME NEEDED TO RESORB AND EG-EST C*** THE MASS EQUIVALENT TO THE CLASS-SPECIFIC PART OF THE PREY

DO 52 N=1 ,NC L I=N+1 RGE1(I)=-RRGEMP/ALOG((N-.99)/N) DO 52 M=1,NS T AC2 =0.01?*(T3MP-11.9)*AC(M)/0.1094 AC1 =AC(MP) ENCA A =(DM(KP)+DM(M))*SQRT(VP(N)*VP(N)+VL(M)*VL(M))*AC1*AC2 ENCAR =(DI1(KP)+DM(H))*V P( N)*A C1 * (1.-AC2 ) 3NCHA =(DM(KP)+DM(M))*VL(M)*AC2* (1 .-AC 1)*0.3 3 RSE =(ENCAA+ENCAR+ENCRA)*DS(M)*SR(N,M)*86400. TSC =(PT(I/2,M)/86400.)+(1./(AMAX1(R3E.1.E-5))) R3(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*****»*****************************»*«#*************#****************** C*** COMPUTATION OF THE STEADY STATE DISTRIBUTION OF C*** THE POOD CONTENTS OF THE GUT C*** 3UMST =0. PST(1) =0. PST(2) =1. DO 54 N=1,NC L I=N+1 RS1(I) =0. DO 53 M=1,NST PREY =AMIN1(GUTM-2.,PY(M)*ENLARG ) 11 = MAX1(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)))/RGE 1(1+ 1) SUMST =SUMST+PST(I) 54 CONTINUE DO 55 N=1,NCL I=N + 1 PST(I) =PST(I)/SUM3T 55 CONTINUE C*** C*******•**•**•*»***•**•»****•***••******••*• •it-*»**»»»*»»*»**»*»»*»***» » C*** INITIALIZATION OP THE FREQUENCY DISTRIBUTION OF C*** POOD CONTENTS OF THE GUT C*** PT(1 )=0 . PT(NC) =0. DO 56 N=1,NCL I=N+1 PT(I) =PTD(I) IF (TIME.LE.DLT) PT(I) = PST(I) RS1(I) =0. 56 CONTINUE C*** C******* **************************************************************** C*** COMPUTATION OF THE RATE OF PREDATION

?22 DO 58tf= 1,NC L I=N+1 DO 58 M=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 RS1(NL)=RS1(NL)+PART /DLT PN(M) =PN(K) +PART+WHOLE 58 CONTINUE c*********************************************************************** c*** COMPUTATION OP THE FREQUENCY DISTRIBUTION OPPCGU T c*** AT TIME+ DEL T c*** RGE =0. SUM =0. DO 59 N=1,NCL I=N+1 DIG =RGE1(I+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)*DIT SUM =SUM +PTD(I) 59 CONTINUE GT =0. GUT =0. DO 60N=1 , NCI I=N+1 PTD(I)/SUM PTD(I) N-.5 G GUT+PTD(I)*G/EIJLARG GUT GT+PST(I)*G/ENLAR G 60 CONTINUGT E C*** C************************************************************#********** C***REPRODUCTIO N INRELATIO N TOPOO D INTAKE C*** IP (TIME.EQ.DLT)PRESHW=OPT W WEIGHT =AMIN1(0PTW,FRESHW) PRESHW =PRESHW+(RGE-(TEMP-11.)*(GUT*0.01+WEIGHT*0.04))*DLT PROD =AMAX1(0.,PRESHW-OPTW) PRESHW =PRESHW-PROD REPR =REPR+(PROD/EGG) C*** (J*********************************************************************** RETURN END ENDJOB

223 APPENDIX J LISTO FABBREVIATION S USED INCOMPUTE R PROGRAMS

A = angular deviation ABAND =abandonin g thecapture d prey AC- = activity ADAPT = adaptationperio d allotted toth epredato r CATCH =catchin g apre y item COIN =coincidenc e inspac e D- = density DIST =distanc ebetwee npredato r andpre y DM- = diameter ENLARG = factor accounting forth eenlargemen t ofth e gutsiz e FC- = food content FDEPRT =tim eperio d of food deprivation -FI = food intake FINTIM = finishing time ofth e simulation FT = feeding time -G =gu t -GE =gu temptyin g GUTC(ON) =gu tconten t H- =handlin g HANDLE =handlin g acapture dpre y I- = initial M- =mea n N- =numbe r OPT- =optimu m PART =partia l ingestion (vs.WHOLE ) PN =prédatio nrat e PRC =probabilit y ofa pre y capture PST =stead y state probability PT =p(t ) PTD =p( t+ DELT ) PY = food contento fth epre y R- =rat e RDRAW =rando m drawingusin g the random number generator -REP = replicates REPDEL =tim e delay ofpre y replacement REPR = reproduction -RES = resorption

224 RR- =relativ e rate RSA =rat eo fsuccessfu l attack (excluding feeding time) RSE =rat eo fsuccessfu l encounter (including feeding time) -RW =predato r isrestin g andpre y iswalkin g S- =su m SD =satiatio n deficit SEARCH =searchin g forpre y SR- =succes s ratio TEMP = temperature TSC =tim e spentpe r successful capture V- =varianc e VL- =velocit y VP =velocit y ofth epredato r -W =weigh t WHOLE =complet e ingestiono fth epre y content -WR =predato r iswalkin g andpre y isrestin g -WW =predato r andpre y arewalkin g

225 References

Abramowitz, M. & I.A. Stegun, 1972.Handboo k of mathematical functions. Dover Publications, Inc.,Ne wYork . Akimov, I.A. & V.V.Barabanova , 1977.Morphologica l and functional charac teristics of the digestive system in tetranychid mites (Trombidifor mes, Tetranychoidea).Revu e d'Entomologie de l'URSS 56(4):912-922 . Akimov, I.A. & I.S.Starovir , 1978.Morpho-functiona l adaptation ofth edi gestive system of three species of Phytoseiidae to predatoriness. Dopovidi AkademiaNau kUkrai n SSR 7:635-638 . Alberti, G. &V . Storch, 1974.Übe rBa u und Funktion derProsoma-Drüse n von Spinnmilben (Tetranychidae,Trombidiformes) . Zeitschrift fürMorpholo gieun dÖkologi e derTier e 79:133-153 . Amano, H. & D.A. Chant, 1977.Lif ehistor y and reproduction oftw o species ofpredaciou s mites, Phytoseiulus persimilis Athias-Henriot and Ambly- seius andersoni Chant (Acarina: Phytoseiidae). Canadian Journal of Zoology 55:1978-1983 . Amano, H. & D.A. Chant, 1978. Some factors affecting reproduction andse x ratios in two species of predacious mites, Phytoseiulus persimilis Athias-Henriot and Amblyseius andersoni Chant (Acarina:Phytoseiidae) . CanadianJourna l ofZoolog y 56:1593-1607 . Anderson, T.W. & L.A. Goodman, 1957. Statistical inference about Markov chains.Annal s ofMathematica l Statistics,28 :89-110 . Ashihara, W., N . Shinkaji &T .Hamamura , 1976.Experimenta l studies onth e prey consumption and ovipositional rate of Phytoseiulus persimilis Athias-Herriot asa predato r of Tetranychus kanzawai Kishida (Acarina: Phytoseiidae).Bulleti n ofth e FruitTre eResearc h Station Series E1 : 135-144. (InJapanese ,Englis h Summary). Ashihara, W., T . Hamamura & N. Shinkaji, 1978. Feeding, reproduction and development of Phytoseiulus persimilis A.-H. (Acarina: Phytoseiidae) onvariou s food substances.Bulleti n ofth eFrui tTre eResearc h Station JapanE 2:91-98 . Baker, J.E. & W.A. Connell, 1963.Th emorpholog y ofth emouthpart so f Te tranychus atlanticus and observations on feedingb y thismit eo nsoy bean.Annal s ofth eEntomologica l Society ofAmeric a 56:733-736 . Begljarow, G.A., 1967.Ergebniss e derUntersuchunge n und derAnwendun g von Phytoseiulus persimilis Athias-Henriot (1957)al sbiologisch eBekämp fungsmittel gegen Spinnmilben inde r Sowjetunion.Nachrichtenblat t des Pflanzenschutzdienstes 21(47):197-200 .

226 Begljarow, G.A. & R.I.Hlopceva , 1965.Entwicklun g derRaubmilb e Phytosei- ulus persimilis A.-H.be i Ernährungmi tverschiedene nArte nvo nSpinn milben. W "Issledovaniap o Biologiceskomu Metodu Borbys Vreditelam i Selskogo iLesnog o Chozajstva".Novosibirs k 2:104-106 . (InRussian ) Bekker, E.G., 1956.Th e food and the alimentary canal of Tetranychus urticae Koch, when the mite is in an active state.Vestni k Moskovskogo Universiteta, Seryya Fiziko-Matematiceskich iYestetvennyc h Nauk 2: 103-111. Beizer, W.R., 1979.Abdomina l stretch in theregulatio no fprotei ninges tionb y the blackblowfl y Phormia regina. Physiological Entomology4 :7-13 . Bengston, M., 1970.Effec to fdifferen tvarietie s ofth e applehos to nth e development of T. urticae Koch. Division of Plant Industry Bulletin 530: 95-113. Berridge, M.J., 1970. In: Insect ultrastructure (A.C. Neville,ed.) . Blackwell,Oxford ,p .135-153 . Blauvelt,W.E. ,1945 .Th e internalmorpholog y ofth ecommo nre dspide rmit e (Tetranychus telarius L.). CornellUniversit yAgricultura l Experimen tal StationMemoi rnumbe r270 . Blommers,L. , 1973.Fiv ene w species ofphytoseii dmite s (Acarina:Mesostig - mata)fro m southwestMadagascar .Bulleti nZoologisc hMuseu m Universiteit Amsterdam 3(16):109-117 . Blommers, L., 1976.Capacitie s forincreas e andprédatio ni n Amblyseius bibens. Zeitschrift fürAngewandt e Entomologie 81:225-244 . Blommers, L. & R.C.M,va nArendonk , 1979.Th eprofi to fsenescenc e inphy toseiidmites .Oecologi a44 :87-90 . Blommers, L. & R.Blommers-Schlösser , 1975.Karyotype s ofeigh tspecie s of phytoseiid mites (Acarina:Mesostigmata )fro mMadagascar .Genetic a45 : 145-148. Blommers, L.& J.va nEtten ,1975 . Amblyseius bibens (Acarina:Phytoseiidae) , a predator of spidermite s (Tetranychidae)i nMadagascar . Entomologia Experimentalis etApplicat a 18:329-336 . Blommers,L. ,P . Lobbes,P .Vin k& F.Wegdam ,1977 .Studie so nth erespons e of Amblyseius bibens (Acarina: Phytoseiidae) to conditions of prey scarcity.Entomophag a 22(3):247-258 . Boczek, J., Z.T. Dabrowski &T .Kapaa ,1970 .Studie s onth ehibernatio n of phytoseiid mites (Acarina: Phytoseiidae)i norchards .Zeszyt yProble - mowePostepo wNau kRolniczych , 109:43-64 . (InPolish ,Englis h summary) Böhm, H., 1966.Ei nBeitra g zurbiologische n Bekämpfungvo n Spinnmilben in Gewächshäusern.Pflanzenschutzbericht e XXXIV, (5/6): 65-77. Böhm, H., 1970.Beobachtunge nübe rde nEinflus sverschiedene r Temperaturen aufdi eEntwicklungs -un dVermehrungs-Geschwindigkei t vom Phytoseiulus riegeli Dosse und Encarsia formosa. Proceedings ofth eConferenc e on Integrated Control inGlasshouses .Naaldwijk ,Netherlands ,p .37-42 . Boudreaux, H.B., 1958. The effect of relative humidity on egg-laying,

227 hatching, and survival in various spider mites. Journal of Insect Physiology 2: 65-72. Boudreaux, H.B., 1963. Biological aspects of some phytophagous mites. Annual Review ofEntomolog y 8:137-54 . Bravenboer, L., 1959.D e chemische enbiologisch e bestrijding vand espint - mijt Tetranychus urticae Koch.Pudoc ,Wageningen . Bravenboer, L., 1963.Experiment s with the predator Phytoseiulus riegeli Dosse on glasshouse-cucumbers. Mitteilungen SchweizerischenEntomolo gischenGesellschaf t 36:53 . Bravenboer, L. & G. Dosse, 1962. Phytoseiulus riegeli Dosse alsPrädato r einiger Schadmilben aus der Tetranychus urticae-Gruppe. Entomologia Experimentalis etApplicat a 5:291-304 . Bund, C.F.va nd e& W .Helle ,1960 .Investigation s onth e Tetranychus urticae complex inNort hWes tEurop e (Acari:Tetranychidae) .Entomologi aExpe rimentalis etApplicat a 3:142-156 . Chant, D.A., 1961.Th eeffec t ofpre ydensit y onpre y consumption andovi - position inadult s of Typhlodromus occidentalis Nesbitt (Acarina:Phyto - seiidae)i nth e laboratory. Canadian Journal ofZoolog y 39:311-315 . Chant, D.A. & C.A. Fleschner, 1960. Some observations on the ecology of phytoseiid mites (Acarina: Phytoseiidae) in California. Entomophaga 5(2): 131-139. Chattfield, C, 1975.Th e analysis of time series: theory and practice. Monographs on Applied Probability and Statistics. Chapman andHall , London. Cochran,W.G. , 1963.Samplin gTechniques .Secon dEdition .Joh nWile y& Sons , Inc. Cock, J.W., 1978.Th e assessment of preference.Journa l ofAnima l Ecology 47:805-816 . Cody,M.L. ,1971 .Finc h flocks inth eMohav e desert.Theoretica l Population Biology 2:142-158 . Cody,M.L. ,1974 .Optimizatio n inecology . Science,Ne wYork , 183:1156-1164 . Cone, W.W., L.M. McDonough, J.C. Maitlen& S.Burdajewicz ,1971 .Pheromon e studies ofth e two-spotted spidermite .1 .Evidenc e of ase xpheromone . Journal ofEconomi c Entomology 64(2):355-358 . Cone, W.W., S. Predki & E.C. Klostermeyer, 1971.Pheromon e studies ofth e two-spotted spidermite .2 .Behavioura l response ofmale s to quiescent deutonymphs.Journa l ofEconomi c Entomology 64(2):379-382 . Cone, W.W. & S. Pruszynski, 1972.Pheromon e studies of the two-spotted spider mite. 3. Response of males to different plant tissues,age , searching area, sexratios ,an d solvent inbioassa y trials.Journa l of Economic Entomology 65(1): 74-77. Croft,B.A. , 1971.Comparativ e studies on four strains of Typhlodromus occi dentalis (Acarina: Phytoseiidae).V . Photoperiodic induction ofdia pause.Annal s ofth eEntomologica l Society ofAmeric a 64:962-964 .

228 Croft,B.A. ,1972 .Pre ystag edistribution ,a facto raffectin gth enumerica l response of Typhlodromus occidental is to Tetranychus mcdanieli and Tetranychus pacificus. TheGrea tBasi nNaturalis t32(2) :61-75 . Croft,B.A. , 1976.Establishin ginsecticide-resistan tphytoseii dmit epre datorsi ndeciduou stre efrui torchards .Entomophag a21(4) :383-399 . Croft,B.A .& J.A .McMurtry ,1972 .Comparativ estudie so nfou rstrain so f Typhlodromus occidentalis Nesbitt (Acarina:Phytoseiidae )VI .Lif e historystudies .Acarologi atom eXIII ,fasc .3 :460-470 . Curry,G.L .& D.W .DeMichele ,1977 .Stochasti canalysi sfo rth edescriptio n and synthesis ofpredator-pre y systems.Canadia nEntomologis t109 : 1167-1174. Dabrowski,Z.T. ,1976 .Som ene waspect so fhost-plan trelatio nt obehaviou r and reproduction ofspide rmite s (Acarina:Tetranychidae) .Symposi a BiologiaHungari a16 :55-60 . Dabrowski,Z.T .& B .Bielak ,1978 .Effec to fsom eplan tchemica lcompound s onth ebehaviou r andreproductio no fspide rmite s(Acarina :Tetrany chidae).Entomologi aExperimentali se tApplicat a24 :117-126 . Dabrowski,Z.T .& Z .Marczak ,1972 .Studie so nth erelationshi po f Tetra nychus urticae Kochan dhos tplants .1 .Effec to fplan tspecies .Bul letinEntomologigu ed ePologn eXLII(4) :821-855 . Davis,D.W. ,1952 .Influenc eo fpopulatio ndensit yo n Tetranychus multisetis. Journalo fEconomi cEntomolog y45(4) :652-654 . Davis,D.W. , 1961.Biolog yo f Tetranychus "multisetis", thepolychaetou s formo f Tetranychus cinnabarinus (Acarina:Tetranychidae) .Annal so f theEntomologica lSociet yo fAmeric a54 :30-34 . Dethier,V.G. ,1976 .Th eHungr yFly .Harvar dUniversit yPress . Dosse,G. , 1956.Übe rdi eEntwicklun geinige rRaubmilbe nbe iverschiedene n Nahrungstieren (Acarina: Phytoseiidae). Pflanzenschutzberichte 16: 122-136. Dosse,G. , 1958.Übe reinig eneu eRaubmilbenarte n(Acarina :Phytoseiidae) . Pflanzenschutzberichte21 :44-61 . Dover,M.J. ,B.A .Croft ,S.M .Welc h& R.L .Tummala ,1979 .Biologica lcontro l of Panonychus ulmi (Acarina:Tetranychidae )b y Amblyseius fallacis (Acarina:Phytoseiidae )o napple :a prey-predato rmodel .Environmenta l Entomology8(2) :282-292 . Dyer,J.G .& F.C .Swift ,1979 .Se xrati oi nfiel dpopulation so fphytoseii d mites (Acarina:Phytoseiidae) .Annal so fth eEntomologica lSociet yo f America72(1) :149-154 . Everson,P. ,1979 .Th efunctiona lrespons eo f Phytoseiulus persimilis (Aca rina:Phytoseiidae )t ovariou sdensitie so f Tetranychus urticae (Acari na:Tetranychidae) .Canadia nEntomologis t111 :7-10 . Everson,P. , 1980.Th erelativ eactivit yan dfunctiona lrespons eo f Phyto seiulus persimilis (Acarina:Phytoseiidae )an d Tetranychus urticae (Acarina:Tetranychidae) :th eeffec to ftemperature .Canadia nEntomo logist112(1) :17-24 . 229 Feldmann, A.M., 1981. Life table and malematin g competitiveness ofwild - type and of a chromosome mutation straino f Tetranychus urticae Koch (Acarina: Tetranychidae) in relation to genetic control.Entomologi a Experimentalis etApplicat a 29 (inpress) . Feldmann,A.M .& M.W . Sabelis,1981 .Karyotyp e displacement ina laborator y population of the two-spotted spider mite Tetranychus urticae Koch: experiments and systems analysis.Genetic a 55 (inpress) . Fernando, M.H.J.P., 1977.Prédatio n of the glasshouse red spider miteb y Phytoseiulus persimilis A.-H.Ph.D .Thesis ,Universit y ofLondon . Ferrari, Th.J., 1978.Element s of system-dynamics simulation. A textbook withexercises .Pudoc ,Wageningen . Ferro, D.N. & R.B. Chapman, 1979.Effect s ofdifferen t constant humidities and temperatures on two-spotted spider mite egghatch . Environmental Entomology 8:701-705 . Flaherty,D. , 1967.Th e ecology and importance of spidermite s on grapevine inth e southern SanJoaqui nValley ,wit hemphasi s onth e role of Meta- seiulus occidentalis Nesbitt. Ph.D.Thesis ,Universit y ofCalifornia , Berkeley. Flaherty, D.L. & M.A. Hoy, 1971.Biologica l control of pacificmite s and Willamette mites in San Joaquin Valley vineyards: Part III.Rol e of tydeid mites.Researche s ofPopulatio n Ecology XIII: 80-96. Fleschner, CA., M.E. Badgley,D.W . Ricker &J.C . Hall, 1956.Ai r drifto f spidermites .Journa l ofEconomi c Entomology 49:624-627 . Forrester, J.W., 1961.Industria l Dynamics.MIT-Press ,Boston . Fransz, H.G., 1974.Th e functional response topre y density ina n acarine system. SimulationMonographs .Pudoc ,Wageningen . French, N. & F.A.B. Ludlam, 1973.Observation s onwinte r survival anddia - pausing behaviour of red spider mite (Tetranychus urticae) onglass house roses.Plan tPatholog y 22:16-21 . Fritzsche, R., 1959.Morphologische ,biologisch e undphysiologisch eVaria bilitätun d ihreBedeutun g fürdi eEpidemiologi e undBekämpfun g von T. urticae Koch. Habilitationsschrift der Landwirtschaftlichen Fakultät derMartin-Luther-Universitä t Halle-Wittenberg. Fritzsche,R .& H . Lehmann, 1975.Mikroklimatisch e Bedingungen fürda sVer lassen der Winterlager von Tetranychus urticae Koch alsGrundlag e für dieWah l desBekämpfungstermins .Archie v fürPhytopathologi e undPflan zenschutz,Berli n 11(1): 43-48. Gasser, R., 1951. ZurKenntni s dergemeine n Spinnmilbe Tetranychus urticae Koch. 1. Mitteilung: Morphologie, Anatomie, Biologie und Oekologie. Mitteilungen der Schweizerischen Entomologischen Gesellschaft, XXIV(3): 217-262. Geispits, K.F., F.D. Sapozhnikova & M.M. Taranets,1971 .Seasona l changes in photoperiodic reactions and physiological conditions of the red spidermit e Tetranychus urticae. Entomological Review 50:156-162 .

230 Gelperin, A., 1971.Regulatio n of feeding.Annua lRevie wo fEntomolog y16 : 365-378. Gerson, U., 1979. Silk production. Recent Advances in Acarology (J.G. Rodriguez, ed.)Vol . I:177-189 . Gerson,U. ,R .Kennet h& T.I .Muttath , 1979. Hirsutella thompsonii, afunga l pathogen of mites. II.Host-pathoge n interactions. Annals ofApplie d Biology 91(1): 29-40. Gibbs, K.W. & F.O. Morrison, 1959. The cuticle of the two-spotted mite, Tetranychus telarius L. (Acarina:Tetranychidae) .Canadia nJourna l of Zoology 37:633-639 . Goudriaan, J., 1973.Dispersio n in simulation models ofpopulatio n growth and salt movement in the soil.Netherland s Journal of Agricultural Science 21:269-281 . Goudriaan, J., 1977.Cro pMicrometeorology : asimulatio n study. Simulation Monographs.Pudoc ,Wageningen . Hall, C.A.S. & J.W.Day ,1977 .Ecosyste mmodellin g intheor y andpractice . Wiley-IntersciencePublication ,Ne wYork . Hamamura, T., N. Shinkaji & W. Ashihara, 1976a. The relationship between temperature and developmental period and oviposition of Phytoseiulus persimilis A.-H. (Acarina: Phytoseiidae).Bulleti n of theFrui tTre e Research Station JapanE 1:117-125 . Hamamura, T., N. Shinkaji &W .Ashihara , 1976b.Studie s onth ehibernatio n of Phytoseiulus persimilis A.-H. (Acarina:Phytoseiidae) .Bulleti no f the Fruit Tree Research Station Japan E 1: 127-133. (InJapanese ; English summary). Hamamura,T. ,N . Shinkaji &W .Ashihara ,1978 .Studie s onth e low temperature storageo f Phytoseiulus persimilis A.-H. (Acarina:Phytoseiidae) .Bulle tino fth eFrui tTre eResearc h StationE 2 :83-90 . (InJapanese ;Englis h summary). Harrison,R.A . &A.G . Smith, 1961.Th e influence oftemperatur e and relative humidity onth edevelopmen to fegg s ando nth eeffectivenes s ofovicide s against Tetranychus telarius L. (Acarina:Tetranychidae) .Ne w Zealand Journalo f Science,4 :540-549 . Hasseil, M.P., 1978. The dynamics of arthropod predator-prey systems. PrincetonUniversit yPress . Haynes,D.L . &P . Sisojevic,1966 .Predator ybehaviou r of Philodromus rufus Walckenauer (Aranea:Thomisidae) .Canadia nEntomologis t98 :113-133 . Hazan, A., U. Gerson & A.S.Tahori ,1973 .Lif ehistor y and lifetable so f thecarmin e spidermite .Acarologia , tomeXV , fasc.3 :414-440 . Hazan,A. ,U .Gerso n& A.S .Tahori ,1974 .Spide rmit ewebbin g I.Th eproduc tion of webbing under various environmental conditions.Acarologia , tomeXVI ,fasc .1 : 68-84. Hazan, A., U. Gerson & A.S.Tahori ,1975a .Quantitativ e evaluation ofth e feeding of the carmine spider mite Tetranychus cinnabarinus Boisd.

231 (Acarina: Tetranychidae). Bulletin of Entomological Research 65: 515-521. Hazan,A. ,U .Gerso n& A.S .Tahori ,1975b .Spide rmit ewebbin g II.Th e effect ofwebbin g oneg ghatchability . Acarologia, tomeXVII , fasc. I:270-273 . Helle, W., 1967 . Fertilization inth etwo-spotte d spidermite , Tetranychus urticae (Acarina:Tetranychidae) .Entomologi aExperimentali s etApplicat a 10:103-110 . Helle, W., H.R. Bolland, R. van Arendonk, R. de Boer, G.G.M. Schulten & V.M. Russell, 1978.Geneti c evidence for biparental males in haplo- diploidpredato r mites (Acarina:Phytoseiidae ). Genetic a 49:165-171 . Helle, W., & H.R. Bolland, 1979. Genetic evidence forbiparenta l males in haplo-diploidpredator ymite s (Acarina:Phytoseiidae) .Recen tAdvance s inAcarolog y Vol. II:399-405 . Helle,W .& W.P.J . Overmeer, 1973.Variabilit y intetranychi d mites.Annua l Review ofEntomolog y 18:97-120 . Helle, W. & M. van de Vrie, 1974.Problem s with spidermites .Outloo k on Agriculture,8 :119-125 . Hislop, R.G., N. Alves& R.J . Prokopy, 1978.Spide rmit e substances influ encing searchingbehaviou r ofth emit epredato r Amblyseius fallacis on apple. FruitNote s 43(6): 8-11. House, H.L., 1974.Nutrition . In:Th ephysiolog y of Insecta (M.Rockstein , ed.), Vol.V , Chapter I. Hoy, M.A., 1979. Parahaploidy ofth e "arrhenotokous"predator , Metaseiulus occidentalis (Acarina: Phytoseiidae) demonstrated byX-irradiatio n of males. Entomologia Experimentalis etApplicat a 26:97-104 . Hoy, M.A. & D.L. Flaherty, 1970.Photoperiodi c induction ofdiapaus e ina predacious mite, Metaseiulus occidentalis. Annals ofth e Entomological Society ofAmeric a 63:960-963 . Hoy, M.A. & J.M. Smilanick, 1979.A sexpheronom eproduce d by immature and adult females ofth epredator ymite , Metaseiulus occidentalis (Nesbitt). Entomologia Experimentalis etApplicat a 26:291-300 . Hoy,M.A . &J.M . Smilanick, 1981.Non-rando m prey locationb y thephytoseii d predator Metaseiulus occidentalis: Differential responses to several spidermit e species.Entomologi a Experimentalis etApplicat a (inpress) . Holling, C.S., 1966. The functional response of invertebrate predators to prey density.Memoir s ofth eEntomologica l Society ofCanad a48 :1-86 . Hoying, S.A. &B.A . Croft,1977 .Comparison s betweenpopulation s of Typhlo- dromus longipilus Nesbitt and T. occidentalis Nesbitt:Taxonomy , Dis tribution and Hybridization. Annals of the Entomological Society of America 70(1): 150-159. Hoyt, S.C., 1970.Effec t ofshor t feedingperiod sb y Metaseiulus occidenta lis on fecundity andmortalit y of Tetranychus mcdanieli. Annals ofth e Entomological Society ofAmeric a 63(5):1382-1384 . Hoyt, S.C. & L.E.Caltagirone , 1971.Th edevelopin gprogram s of integrated

232 control of pests of apples in Washington and peaches inCalifornia . In: Biological control (C.B.Huffaker , ed.),Chapte r 18,p .395-421 , PlenumNe wYork . Hudson, A., 1958.Th eeffec to f flighto nth etast ethreshol d andcarbohy drateutilizatio no f Phormia regina Meig. Journal of InsectPhysiolog y 1:293-304 . Huffaker,C.B. , 1958.Experimenta l studies onprédation :dispersio n factors andpredator-pre y oscillations.Hilgardi a 27(14):343-383 . Huffaker, C.B. & C.E. Kennett, 1956. Experimental studies on prédation: Prédationan d cyclamenmit epopulation s onstrawberrie s inCalifornia . Hilgardia 34(9):305-330 . Huffaker,C.B. ,M .va n deVri e& J.A .McMurtry , 1969.Th eecolog y oftetra - nychid mites and their natural control.Annua l Review of Entomology 14:125-174 . Huffaker,C.B. ,M .va nd eVri e& J.A .McMurtry , 1970.Ecolog y of tetranychid mites andthei rnatura l enemies:a review . II.Tetranychi d populations and theirpossibl e controlb ypredators :a nevaluation .Hilgardi a 40(11): 331-458. Hussey,N.W. , 1972.Diapaus e in Tetranychus urticae Koch and its implications inglasshous e culture.Acarologi a 13(2):344-350 . Hussey, N.W., W.J. Parr& CD. Crocker,1957 .Effec to ftemperatur e onth e developmento f Tetranychus telarius L.Nature ,Londo n 179:739-740 . Hussey,N.W .& N.E.A . Scopes,1977 .Th e introduction ofnatura l enemies for pestcontro l inglasshouses :ecologica l considerations. In:Biologica l controlb y augmentation ofnatura l enemies (R.L.Ridgwa y& S.B.Vinson , eds), PlenumPress ,Ne wYor k andLondon ,p .349-377 . Iglinsky,W .& CF . Rainwater,1954 .Lif ehistor y andhabit so f Tetranychus desertorum and T. bimaculatus oncotton .Journa l ofEconomi c Entomology 47: 1084-1086. Inoue,T. , 1978.A ne wregressio nmetho d foranalyzin g animalmovemen tpat terns.Researche s ofPopulatio n Ecology 20:141-163 . Jackson, G.J., 1974.Chaetotax y and setal morfology of the palps andth e first tarsi of Phytoseiulus persimilis A.-H. (Acarina:Phytoseiidae) . Acarologia, tomeXV I fasc.4:583-594 . Jackson,G.J . &J.B . Ford, 1973.Th e feedingbehaviou r of Phytoseiulus per similis (Acarina: Phytoseiidae), particularly as affected by certain pesticides.Annal so fApplie dBiolog y 75:165-171 . Jesiotr, L.J., 1979. The influence of the hostplants on the reproduction potential of the two-spotted spider mite, Tetranychus urticae Koch (Acarina:Tetranychidae) . II.Response s ofth e fieldpopulatio n feeding onrose s andbeans .Ekologi aPolsk a 27(2):351-355 . Jesiotr,L.J . &Z.W . Suski,1974 .Th e influenceo fth ehos tplan tnutritiona l conditiono nth epopulatio n ofth etwo-spotte d spidermit e Tetranychus telarius L. (Acarina: Tetranychidae).Proceeding s ofth eXlXt h Inter-

233 national Horticultural Congress IA:212 . Jesiotr, L.J. & Z.W. Suski, 1976. The influence of thehos tplan t onth e reproduction potential of the two-spotted spider mite, Tetranychus urticae Koch (Acarina:Tetranychidae) .Ekologi aPolsk a 24(3):407-411 . Jones, R.E.,1977 .Movemen tpattern s and eggdistributio n incabbag ebutter flies. Journal ofAnima l Ecology 46:195-212 . Jones, R.E., 1978. Searchbehaviour : astud yo f three caterpillar species. Behaviour 60(3-4):237-258 . Kamath, S.M., 1968. Studies on the feeding habits,developmen t andrepro duction ofth epredaciou s mite, Phytoseiulus persimilis A.-H. (Acarina: Phytoseiidae)o n somephytophagou s mites in India.Commonwealt h Insti tuteo fBiologica l Control Technical Bulletin 10:49-56 . Kennett, C.E.& L.E.Caltagirone , 1968.Biosystematic s of Phytoseiulus per similis Athias-Henriot (Acarina: Phytoseiidae).Acarologia , tome X, fasc.4 :563-577 . Kennett, C.E., D.L. Flaherty & R.W. Hoffmann, 1979. Effect ofwind-born e pollens on the population dynamics of Amblyseius hibisci (Acarina: Phytoseiidae). Entomophaga 24(19): 83-98. Kendall,M.G .& A . Stuart,1966 .Th e advanced theory of statistics,Volum e3 . Griffin,London . Keulen,H .van ,1975 .Evaluatio n ofmodels . In:Critica l evaluation ofsyste m analysis in ecosystems research andmanagemen t (G.W.Arnol d & CT. de Wit, eds), SimulationMonographs .Pudoc ,Wageningen . Kitching,R. , 1971.A simple simulationmode l ofdispersa l ofanimal s among units ofdiscret e habitats.Oecologi a 7:95-116 . Knisley, C.B. &F.C . Swift,1971 .Biologica l studies of Amblyseius umbraticus (Acarina:Phytoseiidae) .Annal s ofth eEntomologica l Society ofAmeric a 64(4):813-822 . Kolodochka, L.A., & E.A. Lysaya,1976 .Surviva l ofhungr y predatoryphyto - seiidmite s Phytoseiulus persimilis, Amblyseius andersoni and Ambly seius reductus (Parasitiformes, Phytoseiidae).Vestni k Zoologii 3: 88-90. Kozai,T. , J. Goudriaan& M . Kimura, 1978.Ligh t transmission andphotosyn thesis ingreenhouses . SimulationMonographs .Pudoc ,Wageningen . Kropczynska-Linkiewicz,D. , 1971.Studie s onth e feeding of four specieso f phytoseiid mites (Acarina:Phytoseiidae) .Proceeding s ofth eThir d In ternational Congress ofAcarology ,Prague ,p .225-227 . Küchlein,J.H. , 1966.Mutua l interference among thepredaciou s mite Typhlo- dromus longipilis Nesbitt (Acarina:Phytoseiidae) .I .Effect s ofpre dator density onovipositio n rate andmigratio n tendency. Mededelingen RijksfaculteitLandbouwwetenschappe n GentXXXI(3) :740-745 . Laing, J.E., 1968. Life history and lifetabl e of Phytoseiulus persimilis Athias-Henriot.Acarologia , tome X, fasc.4 :578-588 . Laing, J.E., 1969a.Lif ehistor y and life table of Metaseiulus occidentalis.

234 Annals ofth eEntomologica l Society ofAmeric a 62(5):978-982 . Laing,J.E. , 1969b.Lif ehistor y and lifetabl eo f Tetranychus urticae Koch. Acarologia, tomeXI ,fasc .1 :32-42 . Laing,J.E .& J.A.L . Osborn,1974 .Th eeffec to fpre y density onth efunct ional andnumerica l response ofthre especie s ofpredator ymites .Ento - mophaga 19(3):267-277 . Lee, M.S.& D.W. Davis, 1968. Lifehistor y andbehaviou r ofth epredator y mite Typhlodromus occidentalis in Utah. Annals of the Entomological Society ofAmeric a 61(2):251-255 . Lehr, R. & F.F. Smith, 1957.Th ereproductiv e capacity ofthre estrain so f the two-spotted spider mite complex. Journal of Economic Entomology 50(5):634-636 . Leigh, T.F., 1963a. Considerations ofdistribution ,abundance ,an d control of acarine pests ofcotton . In:Advance s inAcarolog yvol .I .Ithaca , N.Y., CornellUniversit y Press,p . 14-20. Leigh,T.F. , 1963b.Th e influence oftw o systemic organophosphates ongrowth , fruiting,an dyiel d ofcotto n inCalifornia .Journa l ofEconomi cEnto mology 56:517-522 . Liesering, R., 1960. Beitrag zum phytopathologischen Wirkungsmechanismen von Tetranychus urticae Koch (Acarina:Tetranychidae) .Zeitschrif t für Pflanzenkrankheiten undPflanzenschut z 67:524-543 . McClanahan,R.J. , 1968.Influenc eo ftemperatur e onth ereproductiv epoten tial of two mite predators of the two-spotted spider mite.Canadia n Entomologist 100:549-556 . McEnroe, W.D., 1961a. The control of water lossb yth e two-spotted spider mite Tetranychus telarius. Annals ofth eEntomologica l Society ofAme rica 54:883-887 . McEnroe,W.D. ,1961b .Guanin e excretionb y thetwo-spotte d spidermit e Tetra nychus telarius L.Annal s ofth eEntomologica l Society ofAmeric a 54(6): 925-926. McEnroe, W.D., 1963.Th erol eo fth edigestiv e system inth ewate rbalanc e of the two-spotted spider mite. In:Advance s in Acarology Vol. I. Ithaca,N.Y. ,Cornel lUniversit y Press,p .225-231 . McEnroe,W.D .& A .Lakocy , 1969.Th edevelopmen to fPenta c resistance ina n outcrossing swarm of thetwo-spotte d spidermite .Journa lo fEconomi c Entomology 62(2):283-286 . McMurtry,J.A. ,1977 .Som epredaciou s mites (Phytoseiidae)o ncitru s inth e mediterranean region.Entomophag a 22(1): 19-30. McMurtry,J.A. ,C.B .Huffake r& M .va n deVrie ,1970 .Ecolog yo ftetranychi d mites and their natural enemies: a review. I. Tetranychid enemies: their biological characters and the impact of spray practices. Hilgardia 40(11): 331-390. McMurtry,J.A .& H.G . Johnson, 1966.A necologica l studyo fth espide rmit e Oligonychus punicae Hirst and its natural enemies.Hilgardi a 37(11): 363-402. 235 McMurtry,J.A. ,D.L . Mahr& H.G .Johnson , 1976.Geographi erace s inth epre daciousmite , Amblyseius potentillae (Acarina:Phytoseiidae) .Interna tional Journal ofAcarolog y 2(1):23-29 . McMurtry, J.A. &G.T . Scriven, 1964.Biolog y ofth epredaciou s mite Typhlo- dromus rickeri (Acarina: Phytoseiidae).Annal s of the Entomological Society ofAmeric a 57:362-367 . McMurtry, J.A. & G.T. Scriven, 1965.Lif e history studies of Amblyseius limonicus, with comparative studies on Amblyseius hibisci (Acarina: Phytoseiidae).Annal s ofth eEntomologica l Society ofAmeric a 58:106 - 111. McMurtry, J.A. & M.va n deVrie ,1973 .Prédatio nb y Amblyseius potentillae Garman on Panonychus ulmi Koch in simple ecosystems (Acarina:Phyto seiidae,Tetranychidae) .Hilgardi a 42(2): 17-34. Marié,G. , 1951.Observation s onth edispersa l ofth e fruittre e red spider mite, Metatetranychus ulmi Koch. Report of theEas tMailin g Research Station for 1950:155-159 . Mills, L.R., 1973.Morpholog y ofgland s and ducts inth e two-spotted spider mite, Tetranychus urticae Koch.Acarologia , tomeXV , fasc. 2:218-236 . Mitchell, R., 1972.Th e sex ratio ofth e spidermit e Tetranychus urticae. EntomologiaExperimentali s etApplicat a 15:299-304 . Mitchell, R., 1973 . Growth andpopulatio n dynamics of aspide rmit e Tetra nychus urticae K. (Acarina:Tetranychidae) .Ecolog y 54(6): 1349-1355. Montfort, M.A.J, van &A .Otten , 1976.Quanta l response analysis,enlarge ment of the logistic model with a kurtosis parameter. Biomedisches Zeitschrift 18(5):371-380 . Mori, H., 1961. Comparative studies oftherma l reaction in four specieso f spidermite s (Acarina:Tetranychidae) .Journa l ofth eFacult y ofAgri culture,Hokkaid o University, Sapporo, 51:574-591 . Mori,H ., 1969 .Th e influence ofpre y density onth eprédatio no f Amblyseius longispinosus (Evans) (Acarina: Phytoseiidae).Proceeding s ofth e2n d International Congress onAcarology , Sutton-Bonnington, England (1967). AkademiaKiadó ,Budapest ,p .149-153 . Mori,H .& D.A . Chant,1966a .Th e influence ofpre y density, relativehumi dity, and starvation onth epredaciou s behaviour of Phytoseiulus persimilis Athias-Henriot (Acarina:Phytoseiidae) .Canadia n Journal ofZoo logy 44:483-491 . Mori, H. & D.A. Chant,1966b .Th e influence ofhumidit y onth e activity of Phytoseiulus persimilis Athias-Henriot and itsprey , Tetranychus urti cae Koch (Acarina: Phytoseiidae, Tetranychidae).Canadia n Journal of Zoology 44:863-871 . Nakamura,K. , 1974.A mode l ofth e functional response ofa predato r topre y density involving thehunge r effect.Oecologi a 16:265-278 . Nelson, R.D., 1968.Effect s ofgamm a radiation onth ebiolog y and population suppression of the two-spotted spider mite Tetranychus urticae Koch.

236 Ph.D. Thesis,Universit yo fCalifornia ,Davis . Nelson,R.D .& E.M .Stafford ,1972 .Effect so fgamm aradiatio no nth ebio logyan dpopulatio no fth etwo-spotte d spidermite , T. urticae Koch. Hilgardia41(12) :299-342 . Nickel,J.L. , 1960.Temperatur e andhumidit yrelationship so f Tetranychus desertorum Bankswit hspecia lreferenc et odistribution .Hilgardi a30(2) : 41-99. Oliver,J.H. ,1977 .Cytogenetic so fmite san dticks .Annua lRevie wo fEnto mology22 :407-429 . Overmeer,W.P.J. , 1967.Genetic so fresistanc et oTedio ni n Tetranychus urticae Koch.Archive sNéerlandai sd uZoologi e17(3) :295-394 . Overmeer,W.P.J. ,1972 .Note so nmatin gbehaviou ran dse xrati ocontro lo f Tetranychus urticae Koch (Acarina:Tetranychidae) .Entomologisch eBe richten,dee l32 ,l.XII :240-244 . Overmeer,W.P.J .& R.A .Harrison ,1969 .Note so nth econtro lo fth ese x ratioi npopulation so fth etwo-spotte dspide rmite , Tetranychus urti cae Koch (Acarina:Tetranychidae) .Ne wZealan dJourna lo fScienc e12 : 920-928. Overmeer,W.P.J . & A.Q. van Zon,1973 .Studie so nhybri d sterilityo f single,doubl ean dtripl echromosom emutatio nheterozygote so f Tetra nychus urticae withrespec tt ogeneti ccontro lo fspide rmites .Entomo - logiaExperimentali se tApplicat a16 :389-394 . Overmeer,W.P.J. ,A.Q .va nZo n& W .Helle ,1975 .Th estabilit yo facaricid e resistancei n T. urticae populationsfro mros ehouses .Entomologi aEx perimentalise tApplicat a18(1) :68-74 . Penman,D.R . &R.B .Chapman ,1980 .Effec to ftemperatur e andhumidit yo n thelocomotor yactivit yo f Tetranychus urticae (Acarina: Tetranychidae), Typhlodromus occidentalis and Amblyseius fallacis (Acarina:Phytoseiidae ) ActaOecologica ,Seri e2 Oecologi aApplicat a1(3) :259-264 . Penman,D.R . &W.W .Cone ,1972 .Behaviou ro fmal etwo-spotte dspide rmite s inrespons et oquiescen tfemal edeutonymph san dt oweb .Annal so fth e EntomologicalSociet yo fAmeric a65(6) :1288-1293 . Penman,D.R . &W.W .Cone ,1974 .Rol eo fweb ,tactil estimuli ,an dfemal e sexpheromon ei nattractio no fmal etwo-spotte dspide rmite st oquies centfemal edeutonymphs .Annal so fth eEntomologica lSociet yo fAmeric a 67(2):179-182 . Plotnikov,W.F .& W.P .Sadkowskij ,1972 .Applicatio no f Phytoseiulus persimilis inbiologica lcontro lo fth etwo-spotte dspide rmit ei nhydropon e glasshouses. In:"Biolog .Meto dBorb ys vred .owoscn .Kultur" .Moskv a "Kolos":18-25 .(I nRussian ) Ponti,O.M.B .de ,1977a .Resistanc e in Cucumis sativus L.t o Tetranychus urticae Koch. 1.Th erol eo fplan tbreedin gi nintegrate dcontrol . Euphytica26 :633-640 . Ponti,O.M.B .de ,1977b .Resistanc e in Cucumis sativus L.t o Tetranychus

237 urticae Koch. 2. Designing a reliable laboratory test for resistance based on aspects of the host-parasite relationship. Euphytica 26: 641-654. Ponti, O.M.B. de, 1978. Resistance in Cucumis sativus L. to Tetranychus urticae Koch. 4. The genuineness of the resistance. Euphytica 27: 435-439. Potter,D.A. , 1978.Functiona l sex ratio inth ecarmin e spidermite .Annal s ofth eEntomologica l Society ofAmeric a 71(2):218-222 . Potter,D.A . &D.L . Wrensch, 1978.Interrupte d matings and the effectiveness of second inseminations inth e two-spotted spidermite .Annal s ofth e Entomological Society ofAmeric a 71(6):882-885 . Potter, D.A., D.L. Wrensch& D.E . Johnston, 1976.Guarding , aggressivebe haviour, and mating success in male two-spotted spidermites .Annal s ofth eEntomologica l Society ofAmeric a 69(4):707-711 . Pralavorio,M . &L .Almaguel-Rojas , 1979. Influence de latemperatur e etd e l'humidité relative sur ledéveloppemen t etl areproductio n de Phyto- seiulus persimilis. Fourth Meeting ofth eWorkin g Group on Integrated Control in Glasshouses, Helsinki, June 1979. 0.I-L.B./S.R.O.P., I.O.B.C./W.P.R.S . Pruszynski,S. , 1977.Fro m the researches onth epredator ymit e Phytoseiulus persimilis Athias-Henriot. 1.Observation s onth edevelopmen t andfecun dity of P. persimilis females.Prac eNaukow e IOR 19(2): 145-166. Pruszynski, S. & W.W. Cone, 1973.Biologica l observations of Typhlodromus occidentalis (Acarina: Phytoseiidae) onHops .Annal s ofth eEntomolo gical Society ofAmeric a 66(1): 47-51. Putman,W.L. ,1962 .Lif ehistor y andbehaviou r ofth epredaciou s mite Typhlo dromus caudiglans Schuster (Acarina: Phytoseiidae) in Ontario, with notes on the prey of related species. Canadian Entomologist 94(2): 163-177. Putman, W.L. & D.C. Herne, 1966. The role of predators and other biotic factors in regulating thepopulatio n density ofphytophagou s mites in Ontariopeac h orchards.Canadia n Entomologist 98:808-820 . Pyke, G.H., 1978.Ar e animals efficient harvesters? Animal Behaviour 26: 241-250. Rabbinge, R., 1976. Biological control of the fruittre e red spidermite . SimulationMonographs .Pudoc ,Wageningen . Ragusa, S., 1977.Note s onphytoseii d mites inSicil ywit h adescriptio n of a new species of Typhlodromus (Acarina: Mesostigmata). Acarologia, tomeXVIII , fasc. 3:379-392 . Ragusa, S.& E .Swirski ,1977 .Feedin g habits,post-embryoni c and adultsur vival,mating ,virilit y and fecundity ofth epredaciou s mite Amblyseius swirskii (Acarina: Phytoseiidae) on some coccids and mealybugs. Entomophaga 22(4):383-392 . Rasmy, A.H., 1972.Effec t ofcrowdin g onovipositio n of Tetranychus cinna-

238 barinus (Acarina:Tetranychidae) .Applie dEntomolog y andZoolog y7(4) : 238. Regev, S. & W.W.Cone ,1975 .Evidenc e ofFarneso l asa mal e sex attractant of the two-spotted spider mite, Tetranychus urticae Koch (Acarina: Tetranychidae).Environmenta l Entomology 4(2):307-311 . Regev, S.& W.W .Cone ,1976a .Analyse s ofpharat e femaletwo-spotte d spider mites for Nerolidol and Geraniol:Evaluatio n for sex attraction of males.Environmenta l Entomology 5(1):133-138 . Regev, S. & W.W. Cone, 1976b. Evidenceo fgonadotropi c effecto f farnesol in the two-spotted spider mite, Tetranychus urticae. Environmental Entomology 5(3): 517-519. Rock,G.C. ,R.J .Monro e &D.R . Yeargan,1976 .Demonstratio n ofa se xphero - mone inth epredaciou s mite Neoseiulus fallacis. Environmental Entomo logy 5(2):264-266 . Rock,G.C. ,D.R . Yeargan& R.L .Rabb ,1971 .Diapaus e inth ephytoseii dmite , Neoseiulus (T.) fallacis. Journal of InsectPhysiolog y 17:1651-1659 . Rodriguez, J.G., 1953. Detached leaf culture in mite nutrition studies. Journal ofEconomi c Entomology 46:713 . Rodriguez, J.G., 1964. Nutritional studies in the Acarina.Acarologia , tome 6:324-337 . Ruardij, P., 1981. Internal Report.Departmen t of Theoretical Production Ecology,Wageningen ,Th eNetherlands . (Available on request). Saaty,T.L. , 1961.Element s ofqueuein gtheory .McGraw-Hill ,Ne wYork . Saito, Y., 1977a. Studyo nth e spinningbehaviou r ofth e spidermit e (Aca rina:Tetranychidae) .I .Metho d forth equantitativ e evaluationo fth e mitewebbin g andth erelationshi p betweenwebbin g andwalking . Japanese Journal of Applied Entomology and Zoology 21: 27-34. (In Japanese; English summary) Saito, Y., 1977b. Studyo nth e spinningbehaviou r ofth e spidermit e (Aca rina:Tetranychidae) .II .Th eproces s ofsil k secretion andth ewebbin g onth evariou s stages of Tetranychus urticae Kochunde r different envi ronmental conditions. Japanese Journal ofApplie dEntomolog y andZoo logy 21:150-157 . (InJapanese ;Englis h summary) Saito,Y. , 1979a.Stud y onspinnin gbehaviou r of spidermites .III .Respons e ofmite s towebbin g residues and theirpreferenc e forparticula rphysi calcondition s oflea fsurfaces .Japanes e Journal ofApplie d Entomology andZoolog y 23:82-91 . (InJapanese ;Englis h summary) Saito,Y. , 1979b.Comparativ e studies onlif ehistorie s ofthre especie s of spider mites (Acarina: Tetranychidae).Applie d Entomology and Zoology 14(1): 83-94. Sandness, J.N. & J.A.McMurtry , 1970.Functiona l response ofthre e species of Phytoseiidae (Acarina) to prey density. Canadian Entomology 102: 692-704. Sandness, J.N. & J.A.McMurtry , 1972.Pre yconsumptio nbehaviou r of Ambly-

239 seius largoensis in relation to hunger. Canadian Entomologist 104: 461-470. Sapozhnikova, F.D., 1964.Photoperiodi c response of themit e Typhlodromus (Amblyseius) similis Koch (Acarina: Phytoseiidae). Zoologie Zhurnal 43: 1140-1144. (InRussian ;Englis h summary) Schmidt,G. , 1976.De rEinflus s dervo n denBeutetiere n hinterlassenen Spu ren auf Suchverhalten und Sucherfolg von Phytoseiulus persimilis A.-H. (Acarina: Phytoseiidae). Zeitschrift für Angewandte Entomologie 82: 216-218. Schulten, G.G.M., R.C.M, van Arendonk, V.M. Russell & F.A. Roorda,1978 . Copulation, egg production and sex ratio in Phytoseiulus persimilis and Amblyseius bibens (Acarina:Phytoseiidae) .Entomologi aExperimen talis etApplicat a 24:145-153 . Schuster, R.O. & A. Pritchard, 1963.Phytoseii d mites ofCalifornia .Hil - gardia 34(7): 191-285. Shagunina, V. (ed.), 1977.Entomopathogeni c microorganisms and their use in the control of plant pests. Entomopatogennyemikroorganizy m iik h ispol'zovanie v bor'be s vreditelyami rastenii. Riga,USSR ;Zinatne , (InRussian ) Shehata,K.K. , 1973.Pre y type and density andthei reffec to nth eprédatio n potential of Phytoseiulus persimilis A.-H. (Acarina: Phytoseiidae). Biologia 28(8): 619-626. Shih, C.T.,S.L .Po e& H.L . Cromroy, 1976.Biology , lifetabl e and intrinsic rate of increase of Tetranychus urticae K.Annal s ofth e Entomological Society ofAmeric a 69(2):362-364 . Simova, S., 1976.Hibernatio n places of mites on plum trees.Rastiteln a Zashchita 24(3): 28-30. Siniff, D.B. &CR . Jessen, 1969.A simulation model of animal movement patterns.Advance s inEcologica l Research 9:185-219 . Sirota, Y., 1978.A preliminary simulation model ofmovemen t of larvae of Culex pipiens molestus (Diptera:Culicidae) .Researche s inPopulatio n Ecology 19:170-180 . Skellam,J.G. , 1958.Th emathematica l foundations underlying line transects inanima l ecology.Biometric s 14:385-400 . Stenseth, Chr., 1965. Coldhardines s inth e two-spotted spidermit e Tetra nychus urticae Koch.Entomologi a Experimentalis etApplicat a 8: 33-38. Stenseth,Chr. ,1979 .Effec to ftemperatur e andhumidit y onth e development of Phytoseiulus persimilis and its ability toregulat epopulation s of Tetranychus urticae (Acarina:Phytoseiidae ,Tetranychidae) .Entomophag a 24(3):311-317 . Storms, J.J.H., 1969.Observation s on therelationshi p betweenminera lnu trition of apple root stocks in gravel culture and the reproduction rate of Tetranychus urticae (Acarina:Tetranychidae) .Entomologi aExpe rimentalis etApplicat a 12:297-311 .

240 Suski,Z.W . &T .Badowska ,1975 .Effec to fth ehos tplan tnutritio no nth e population ofth etwo-spotte d spidermite , Tetranychus urticae Koch (Acarina:Tetranychidae) .Ekologi aPolsk a23(1) :185-209 . Suski,Z.W. , T.Badowsk a& M .Olszak ,1975 .Th einfluenc eo ffertilizer s andsoi lmanagemen tsystem so nth epopulatio no ftetranychi dmite si n theappl eorchard .Frui tScienc eReport s 11(1):85-93 . Swirski,E .& N .Dorzia ,1969 .Laborator ystudie so nth efeeding ,develop ment and fecundityo fth epredaciou smit e Typhlodromus occidentalis Nesbitt (Acarina:Phytoseiidae )o nvariou skind so ffoo dsubstances . IsraelianJourna lo fAgricultura lResearc h19(3) :143-145 . Takafuji,A .& D.A .Chant ,1976 .Comparativ estudie so ftw ospecie so fpre daciousphytoseii dmite s (Acarina:Phytoseiidae) ,wit hspecia lrefe rencet othei rresponse st oth edensit yo fthei rprey .Researche si n PopulationEcolog y17 :255-310 . Tanigoshi,L.K. , S.C.Hoyt ,R.W .Brown e& J.A .Logan ,1975 .Influenc eo f temperatureo npopulatio nincreas eo f Metaseiulus occidentalis (Acarina: Phytoseiidae).Annal so fth eEntomologica l Societyo fAmeric a68(6) : 979-986. Tanigoshi,L.K. ,R.W .Browne ,S.C .Hoy t& R.F .Lagier ,1976 .Empirica lana lysiso fvariabl etemperatur e regimeso nlif estag edevelopmen tan d populationgrowt ho f Tetranychus mcdanieli (Acarina:Tetranychidae) . Annalso fth eEntomologica lSociet yo fAmeric a69(4) :712-716 . Thurling,D.J. ,1980 .Metaboli crat ean dlif estag eo fth emite s Tetranychus cinnabarinus Boisd. (Prostigmata)an d Phytoseiulus persimilis A.-H. (Mesostigmata).Oecologi a46(3) :391-397 . Taylor,R.J. ,1976 .Valu eo fclumpin gt opre yan dth eevolutionar yrespons e ofambus hpredators .America nNaturalis t110(971) :13-29 . Treherne,J.E. ,1967 .Gu tabsorption .Annua lRevie wo fEntomolog y12 :43-58 . Tulisalo,U. ,1969 .Fecundity ,developmen tan dlongevit yo fth etwo-spotte d spidermit e Tetranychus urticae Koch(Acarina :Tetranychidae )o ncucum bervarieties .Annale sEntomologic iFennic i35(4) :224-228 . Tulisalo,U. ,1970 .Th etwo-spotte dspide rmit e Tetranychus urticae Kocho n greenhousecucumber .Annale sEntomologic iFennic i36(2) :110-114 . Tulisalo,U. ,1971 .Fre ean dboun damin oacid so fthre ehos tplan tspecie s andvariou s fertilizertreatment saffectin gth efecundit yo fth etwo - spottedspide rmite , Tetranychus urticae Koch(Acarina : Tetranychidae). AnnalesEntomologic iFennic i37 ;155-163 . Ustchekow,A.T .& G.A .Begljarow ,1968 .Effec to fth etemperatur ean dhumi dityo nth edevelopmen to fpredator ymit e Phytoseiulus persimilis A.-H. Proceedingso fth eXlllt hInternationa lCongres so fEntomology ,Moskva , p.198-199 . Veerman,A. ,1977a .Aspect so fth einductio no fdiapaus e ina laborator y straino fth emot e Tetranychus urticae. Journalo fInsec tPhysiolog y 23:703-711 .

241 Veerman, A., 1977b. Photoperiodic termination ofdiapaus e inspide rmites . Nature, London 266(5602):526-527 . Vrie, M. van de, 1972.Potential s of Typhlodromus (A.) potentillae Garman toreduc e Panonychus ulmi Kocho nappl ewit hvariou s nitrogenfertili zations. Entomophaga 15(3):291-304 . Vrie, M. van de,1973 .Studie s onprey-predato r interactions between Pano nychus ulmi and Typhlodromus potentillae (Acarina: Tetranychidae, Phytoseiidae)o nappl e inth eNetherlands .Proceeding s ofth eFAO-Con - ference ofEcolog y inRelatio n toPlan tPes tControl ,Rome ,p .145-160 . Vrie,M .va nde ,J.A .McMurtr y &C.B .Huffaker , 1972.Ecolog y of tetranychid mites and their natural enemies: a review. III.Biology , ecology and pest status andhost-plan t relations of tetranychids.Hilgardi a 41(13): 343-432. Waddington, K.D., 1979. Quantification ofth emovemen tpattern s ofbees :A novelmethod .America nMidlan dNaturalis t 101(2):278-285 . Watson,Th.F. ,1964 .Influenc e ofhos tplan tconditio n onpopulatio n increase of Tetranychus telarius (Acarina: Tetranychidae).Hilgardi a 35(11): 273-322. Wiesmann, R., 1968.Untersuchunge nübe r dieVerdauungsvorgäng e bei derge meinen Spinnmilbe, Tetranychus urticae Koch.Zeitschrif t fürAngewandt e Entomologie 61:457-465 . Wit, CT. de & J. Goudriaan, 1978. Simulation of ecological processes. SimulationMonographs .Pudoc ,Wageningen . Woets, J., 1976. Progress report of the integrated pestcontro l inglass houses inHolland .Bulleti n OILB-SROP4 :34-38 . Wollkind,D.J . &J.A .Logan ,1978 .Temperature-dependen t predator-prey mite ecosystem on apple tree foliage. Journal of Mathematical Biology 6: 265-283. Wrensch,D.L . & S.S.Y. Young, 1975.Effect s ofqualit y ofresourc e and fer tilization status on some fitness traits in the two-spotted spider mite, Tetranychus urticae Koch.Oecologia ,Berli n 18:259-267 . Wrensch, D.L. & S.S.Y. Young, 1978.Effect s ofdensit y andhos tqualit y on rate ofdevelopment ,survivorship , and sex ratio inth ecarmin e spider mite. Environmental Entomology 7(4):499-501 .• ' Wysoki,M .& E .Swirski ,1968 .Karyotype s and sexdeterminatio n ofte n species ofphytoseii d mites (Acarina:Mesostigmata) .Genetic a 39:220-228 . Wysoki,M .& E .Swirski ,1971 .Studie s onoverwinterin g ofpredaciou s mites of the genera Amblyseius Berlese, Typhlodromus Scheuten and Iphiseius Berlese (Acarina:Phytoseiidae )i n Israel.Entomologica l Essays toCom memorate theRetiremen t ofProf .K .Yasumatsu .p .265-292 . Yano, E., 1978.A simulation model of searching behaviour of aparasite . Researches ofPopulatio n Ecology 20:105-122 . Zon, A.Q. van &W.P.J . Overmeer, 1972.Inductio n ofchromosom e mutationb y X-irradiation in Tetranychus urticae with respectt o apossibl e method ofgeneti c control.Entomologi aExperimentali s etApplicat a 15:195-202 . 242