FORAGING BEHAVIOUR OFTH E CARABID BEETLE PTEROSTICHUS COERULESCENS L. (= Poecilus versicolorSturm ) AT DIFFERENT DENSITIES AND DISTRIBUTIONS OFTH EPREY .
(PARTII )
P.J.M.Mols .
Departmentof Entomology, Agricultural University Wageningem Binnenhaven7, P.O.B8031,6700 EH Wageningen, theNetherlands.
(Comm.N o 501 ofBiologica lStatio n Wijster) (Theoreticalproductio necology ) CONTENTS
ABSTRACT 107
1.0 Introduction. 109 1.1 Components ofbehaviour . 110 1.2 Approach. 112
2.0 Quantification ofth ecomponent so fbehaviou ri nrelatio nt ohunger . 113 2.1 Locomotory activity. 2.1.1 Methods. l\3 2.1.2 Results. „ 118 2.1.3 Discussion.
2.2 Analysiso fwalkin gpatterns . 120 120 •2.2.1 Methods. 123 2.2.2 Results. 132 2.2.3 Discussion. 134 2.3 Reaction distancet oprey . 134 2.3.1 Methods. 135 2.3.2 Results. 135 2.3.3 Discussion.
1A O 136 tA auccesratio . 136 2.4.1 Method. 136 2.4.2 Results. ]37 2.4.3 Discussion. 137 2-5 Validation ofprédatio ni na narena . 13g 2.5.1 Methods. 138 2.5.2 Results. 138 2.5.3 Discussion. 141 3.j-u0 simulationSimulation. _ 141 3-l Development ofsimulatio nmodels . ,._„,„ 141 3.1.1 Simulation ofwalkin gbehaviou ran dpre ydiscovery ^ 3.1.^•22 CouplinCouplingmotivat^^^gmotivationa l statean ^d ^^ ^ jJJ 3.• 1. 3 Simulation ofsearching ,prédatio nan aeg gp 105 WageningenAgric. Univ. Papers93-5 (1993) 3.2 Simulation experiments. 148 3.3 Results ofsimulations . 150 3.3.1 Searchingwithou t motivation. 150 3.3.2 Searching and prédation coupled to motivation. 154 3.3.3 Searching,prédatio n and eggproduction . 157 3.3.4 Dispersal of beetlesa sa result ofwalkin g behaviour. 167 3.3.5 Comparison ofvalidatio n experiment with simulation. 172
4.0 General discussion. 173 4.1 Predatory behaviour and prey distributions. 173 4.1.1 The advantage of specific walking behaviour. 174 4.1.2 Theeffec t oflocomotor y activity. 176 4.1.3 Theeffec t of successratio . 179 4.1.4 Theeffec t ofreactio n distance. 1^9
4.2 Prédation and eggproduction . 179 4.3 Dispersal. 180 4.4 Coupling ofprédatio n to population models. 181 4.4.1 Functional responsemodels . 182 4.4.2 From behavioural components to functional response. 184 4.4.3 From individual predator models to population models. 185
4.5 Methodology ofevaluatio n ofpotentia l predators for biological control. 187
Acknowledgements. 189
References. 191
Appendix I The searching and prédation model *95 Appendix II Functional responsemodel s 200
WageningenAgric. Univ. Papers93-5 (19 ABSTRACT
By means of systems analysis and simulation, prédation and eggproductio n ofth ecarabi d beetle Pterostichus coerulescens L( = Poecilus versicolor Sturm) isstudie di nrelationshi p topre ydensit yan dpre ydistribution . Foragingbehav iour is divided into its most dominant components: searching, acceptance of preyan d feeding which are in turn related to the most important internal and external factors. Hunger or its opposite, the relative satiation level (RSATL), is the internal factor that determines the 'motivation' for a large part of the behaviour and it results from the physiological state of the beetle. RSATL is estimated by means of a simulation model (Mols, 1988)an d correlated to the behaviouralcomponent stha tpla ya rol ei nsearchin gan dprédation .Th ehunge r levelha sa stron ginfluenc e onth elocomotor yactivity ,walkin gspeed ,duratio n ofarea-restricte d search and prey acceptance.Thre e types of searchingbehav iourwer e distinguished: 1.Straigh t high-speed walkingwhe n RSATL isbelo w 5%,2 .Intermediat ewalkin gwhe nRSAT Lexceed s5 %an d3 .Intensiv etortuou s walkingbehaviou r (area-restricted search)afte r consumption ofa prey . The searching model developed shows the advantage of the tortuous walk (TW)whe n prey is aggregated and its disadvantage in random prey distribu tions.Whe n thesearchin gmode li scouple d toth emotivatio nmode lth eadvan tage of TW is restricted to aggregated prey at overall low prey densities (<1 prey/m2generally) . Walking speed, time spent walking and successrati o (prey captured/prey discovered), which in turn all depend on the idaüve satoüon level,i ncombinatio n withpre ydensit yan dpre yaggregatio ndetermin eth epre - dationrat ean d theeg gproduction .
107 WageningenAgric. Univ. Papers93-5 (1993) 1.0 INTRODUCTION
Obtainingfoo d isa basi crequiremen t for everyorganism .Animal stha tacti velysearc hfo r food, for themselveso rfo r theiroffsprin g makedifferen t choices concerning the locality to search for, the period during which to search, the kindo ffoo d to search for and ultimately thequantit y offoo d toingest .I n that searching behaviour a number of factors play an important rolewhic h can be dividedin :a )specie sspecifi c properties,lik eth ewa yo flocomotion ,th epercep tion of habitat and prey and the internal motivation to come into action and b)environmenta l properties which determine the availability and attainability ofth epre ylik evegetationa lcompositio nan dhabita tstructure ,an dth eprevail ingmicroclimatologica l conditions that affect the rates at which several vital processeso fbot h preyan dpredator tak eplace . The ultimate aim of this study is to gain insight into the impact of spatial distribution and density of prey on predatory behaviour and on the resulting eggproductio n of the carabid beetle Pterostichus coerulescens. Thismay^lea d tobette rinsigh tan dunderstandin go fth esurviva lstrateg yo fthi scarabi dbeetle , reflected in its ability to copewit h specific preydistribution svaryin gfro m ran-
'ThSbifbetle, P*rastlcte caerulea is apredato r of small arthropods sucha saphids ,spider s caterpillars andma g got.(Hengeveld , 1980),an d livesi nheathlan d ^f^^^ Inmos t cases prey distribution is aggregated, which is* gener a v (Southwood, 1966). Flight has only rarely been ob^^^«™ Therefore, ail vita/behavioural functions such as searchm g ^fo°d f ding amate ,escapin g from prédation bybirds , ^t^^^^Z a,b) occur by walking. The pattern of ™*£ZL and as Consequence the distribution of the prey affects the rate of feeding ^?j**.f;je popula te ofreproductio n and thusth espatia lan dtempora ldynamic so t popu tioni nth e field. ft^nrocesses governingsearchin gan dpreda - Tounderstan d thedynamic so f^^^oi i drivesforpredator y torybehaviour ,informatio n isrequire do nth emotiv a ^^ ^otivatio. behaviour. In many speciesbehaviou r isgovern* ^y ^ ^ equivalent naldrive' .Fo r severalpredator sthi smotivatio na onv ^^ ^ toth esatiatio n level of the gut (Holling, 1966;Nakanu i , ^ ^oeTukscens the Rabbinge, 1976; Sabelis, 1981;^areiva et^al ^ ^ ^ divided byth eappar - satiationleve lo fth egut ,define d asth eactua lgu t :o ^ ^ ^^ ^ ^^ me ent gut capacity (which is the weight ol a * he WageningenAgric. Univ. Papers93-5 (1993) (the maximal gut size) and it depends on the size of other organs and tissues neededfo r eggformatio n and storageo freserve sa swell .Th eactua lgu tconten t changesb yingestion ,excretio nan dresorption .Th erate so fchange sar epredom inantly affected by ambient temperature and daylength, the latter determining the onset of vitellogenesis. Thus the physiological drive for behaviour, i.e. the satiation level or its complement hunger, results from a complex of internally related stateswhic hi nthei rtur n areaffecte d byth erat e ofpre yingestio n under variousclimati cconditions . The internal factors which determine the 'motivational state' of the beetle (here used as an equivalent for the term relative satiation level: RSATL) were integrated in a simulation model (Mols, 1988).Th e output of that model was compared with the results of experiments and showed that it was possible to estimate continuously the 'motivational state' of the beetle.Thi s 'motivational state' of the beetle is used as the most important state variable that dictates walkingan dpredator y behaviour. 1.1 COMPONENTS OF BEHAVIOUR In general the prédation rate is determined both by the encounter rate (Er) with prey, and by the fraction of encountered prey killed by the predator :the succesrati o( Sr )(Fransz , 1974;Sabelis ,1981) . Theencounte rrat ei sa functio n ofth efollowin g variables- (A) Locomotoryactivity :Th efractio n ofth etim etha tbot hpredator s andpre y arelocomotor yactive .I fth epre yi smainl ysessil ean dth epredator y beetle hides away in the soil or litter when resting, only the locomotory activity otth epredator ha st ob econsidered . (V) Velocity: The walking speed of the beetle (cm/sec) of both predator and P1"t^ \ coerulescens the majority of prey items are small caterpillars, apnids and maggots (Hengeveld, 1980), which show a very low walking speedi ncompariso n toth ebeetle .I nthos ecase sth espee d and the turning rateo fth epre yca nb eneglected . Ifmobil espider s and ants are important preyitems ,the nwalkin gspee d hast ob einclude d inth eresultin g velocity, buti fonl yimmobil eo rslowl ywalkin gspeciment sar eimportan tpre yitem s theirvelocit yma yb eneglecte dals o (EW Effectiveness of searching per unit of walking distance depends on the wndmgnes s of the walking pattern. The latter can be expressed by the unhofVf <**%?****degrees/tim e unit) or by the turning angle per ITn/r w ^en the Pattern is Ver^wind ythe effectiveness ofsearch - S I °f,rlkmS distance ^creases because recrossing of previous visitedspot swil loccu rmor e often (R) d'eTerm^tfnœ": ? ****** * Which a Predator «acts to a prey. It anfrört ' ^ 7 ?ë Path Width 0f the Predator and therefore itplay s (0\ S ^ m thC arCa °f disCOVery of the beetle. V) Densityo fth eprey .I ncas eo fpre y aggregation itsdensit y willdiffe r from 110 WageningenAgric. Univ. Papers93-5 (1993) placet oplace .T o avoid confusion interminolog yth efollowin g termswil l beused : 1. 'Overalldensity 'i sth etota lnumbe ro fpre yitem s(pre ytota li na narea ) divided byth esurfac e ofth etota larea . 2. 'Within cluster density' isth enumbe r ofpre yitem si na cluste r divided byth esurfac e ofa pre ycluster . From this follows that the area of discovery will bedependen t both on the walking speed, the effectiveness of searching (determine d by the windingness ofth ewalkin g track) and on the reaction distance.Fo r clumped preydistribu tionsincrease d winding may result in a longer stay ofth epredato r in thepre y clusteran di na mor eintensiv esearc hove rth earea ,whic hultimatel yma yresul t ina highe rencounter ratewit hprey . If it is assumed that the predator searches at random and that the walking directions of both predator and prey aremutuall y independent, theprédatio n rateca n be calculated from the encounter rate multiplied withth e succesrati o (Sabelis, 1981;Mol s 1986) P =Er.Sr fi? Er = 2.R.V.D.A.Eff *• ' However, searching isno t at random whena predator isabl et o orientitsel f towards prey individuals or to prey cues,o r when both thewalkin g speed and direction of walking are changed after contact with prey. In such cases these formulaecanno t beused , orhav et ob erestricte d tothos epart so f tmin^hich searchingi sstil la t random. Then iti snecessar y to r^^SÄ iouritsel f and to relate its features (speed and turning rate)t o ^*™J"f externalstimulUnthatcasethedistr^^ andthu swit h theefficienc y ofsearching .Th esearchin gemue -, y F onth etyp eo fwalkin gbehaviou r (speedan dturnin grate )an dha st ob einclude d asa separat efunctio n inth eprédatio nfunction . fniinwed bv an In the prédation process not every encounter ™* *^ j^ *£ attack and not every attack is successful. ^J^^^V motivationalstat eo fth epredator (Fransz, 1974, Rabbinge, is-/o, ^ Mols, 1987).A hungry predator will be -re eager to at^ ck P^ continue an attack longer resulting in a higher success «üo-M adefensiv e reaction, for example some<*«g^* £ refaüve satiation toescape .Thi simplicate s that thesucce srati odepend so n levelo fth ebeetle .Thu sth eprédatio nrat ei sa functio n ot. (3) P = f(R,V,Eff,D,A,Sr) The behavioural components ^tion^bo^y^^^^ therelativ e satiation levelo fth ebeetl ean db yexterna l stimuli P WageningenAgric. Univ. Papers 93-5 (1993) prey density FIG. 1.1 Relational diagram of the relationship between behavioural components involved in sear ching and predation.( Rectangles are state variables, valves arerat e variables, circles are auxiliarly variables, underlined statements are parameters. Solid lines represent streams of matter, broken linesrepresen t streamso f information). ture;an d diurnal rhythmicity (fig. 1.1). These factors change both throughout heday ,an d after consumption ofpre ya sha sbee nobserve d inman y predators (e.g. Coccmelhds,Dixo n 1958; Anthocorids,Evans ,1976) . 1.2 APPROACH Therefore, the relationships between the relative satiation level and locomo- Zll2V yHW fmg ?haVi0Ur 3nd SUCCes ratio had t0 be Quantified experi mentally and integrated mto amode l that simulates prédation and that iscou - simullt17 ft?™1 m0dd (Mols' 1988>" With this model it is possible to ^Zlrnë "'T1"and6g g Producti°n under different setso fenviron mentalconditions ,pre ydensitie san dpre ydistributions . canZl^LtHT1!0 beh,arural componentsi n the total prédation process beLviourS f°n f' dlfferent C°nditions thus §iving^ t when specific bSTCkîT8H f ntagefo rth epredator -Theresult sobtaine d ™yoffer r^lucÎrZni rTTf ** ^ interPr^tion of thefunctiona lan d featuresnfS ??* ^ '°differen tW densitie s which are important leatureso fth epopulatio n dynamicso fthi sspecie si ntim ean d space. 112 WageningenAgric. Univ. Papers93-5 (1993) 2.0 QUANTIFICATION OFTH E COMPONENTS OF BEHAVIOUR IN RELATION TO HUNGER These tu po fth eexperiment si ngenera li ssuc htha tthe yar edon ei nrelativel y simpleenvironment s (Petri-dishes,arena' swit hligh tvegetatio netc. )unde rrela tivelyconstan t conditions oftemperature ,humidy ,ligh tintensit yan dpre ytyp e toquantif y therelationship s between the components ofsearchin g behaviour andth emotivationa l state.Th efield situatio nma yb emuc hmor ecomplex ,bu t the basic processes are assumed to beth esam e andtherefor e this appraoch maylea dt oth eunravelin g ofthi scomple xsystem . 2.1 LOCOMOTORY ACTIVITY 2.1.1. Methods Measurements oflocomotor y activity inrelatio n toth esatiatio n levelwer e restricted toth ereproductiv e period, because the beetles aremos t active then. Beforeth eexperiment sth ebeetle swer eweighe dan dthei rapparen tgu tcapacit y wasestimated . Tenpair s ofmal e andfemal e beetles wereeac h placed inlarg e Petri-dishes (20c mdiam.) . The substrate onth e bottom ofth e dishconsiste d ofloam ysan d andsom e peat-mull. On the substrate smallpiece so fbar kwer e Placedunde r which thebeetl ecoul d hide.Th efemale s weremarke d bya smal l doto fyello w paint on one ofth e elytra sotha t during observation theycoul d beeasil y distinguished from themales . The observations were carried outa t 20±1°C anda ï 12+1°C during a period of 16hour s ( from 5a m to9pm , thiswa s also theduratio n of the photoperiod). Two days before thestart o theobservation sth ebeetle swer eplace di nth edishe swithou tfoo d to^standard izethe man d to accustom themt oth esituation .Th efirst da y ^otoznton fortw ohour sfro m 6-8a mth ebeetle swer egive nabundan tfoo d £^e^ Thefoo d consisted ofdea d blowfly maggots.Afte r thisfeedingp enoth e prey -mains were removed. Next the ^ ™£^T^£^ sequenceo ffeedin g and starvationwa srepeate dthre etimes ^ in Period took five days. Thefifth da yo f the last star!a^Ctm4pm wereoffere d food at 11 am..Tha tda yth eactivit ywas ;fcflowc d un'» 4 Pm" Everyhou r the beetleswer eobserve dfo ra perio d '^^ with Period)an dthei r activity was recorded. Thesatiatio n thehel po fth emotivationa l model(Mols , 1988). game petri After theperio d ofhourl yobservation sth ebeetle swer en e ^ ^ ^ ^ ^ dishes andfe d abundant maggots every third aay. ^ production ua r 2 Pmth eactivit y was recorded fora 4 f °'*"]lowing the methodo fMol s wasmeasure db ywashin gth esubstrat eeac hwee kfollowin g ^ Wageningen Agric. Univ.Papers 93-5 (1993) Locomotoryactivit y Pterostlchuscoerulescen s L. 100 90 80 70 60 50 day 1 40 30 20 10 0 IlMlMMlbLa^ 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202 1 50 day 2 40 30 20 10 JUL 6 7 8 9 10 11•ilLy 12 13 14 15 16 17 18 19 20 21 A : " 50 : day 3 • r 40 30 20 10 Il I 1111\ .6 7II 8 I9 11 0 11 12 13 14 15 16 17 18 19 202 1 70 \: 60 50 day4 40 30 20 10 i 6 7 8 9 10 11 12 13 14 15 16 1MA7 18 19 202 1 «u 50 : day 5 40 30 20 10 0 LIL 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Timei nhour s I I male Mü female FIG. 2.1 Hourly distribution of locomotory activity of P.coerulescens at 20° Cfo r starved beetles on5 successiv edays .Th e5 thda yfoo dwa soffere d at 12.00.Ligh tperio dfro m 5.00t o21.00 . 114 WageningenAgric. Univ. Papers 93-5 (1993) etal . (1981). The observationswer efinishe d atth een do fth ereproductio nperi od ofeac h beetle. From these observations arelationshi p between locomotory activityan d eggproductio n couldb eestablishe d andinformatio n onth epersis tenceo f the individual locomotory activity in the course of time both during theintensiv ean d theextensiv eobservatio nperio dcoul db ecollected . 2.7.2Results Frequencydistribution ofthe locomotory activity during daytime. Thedistributio n of the percentages of hourly locomotory activities over the dayfo reac h of thefive day si n sequencei sshow ni nfig 2.1 .I ngenera llocomo toryactivit yincrease sunti lnoon ,nex ti tdecreases .Th eleve lo factivit yincrease s upt oth e third day. At the fourth and fifth day activity isalread y high at the starto fth ephotoperiod . At theen d ofth eda yals oa wea kincreas ei nlocomo tory activity can be observed. When food is offered at the noon of the filth dayth e activity drops drastically especially in the females. Thisclearl yshow s the influence of satiation on the level of locomotory activity. Theeffec t o the satiation level on the daily distribution pattern of locomotory activity is elmu- natedb ydividin gth eduratio n ofactivit ycalculate d foreac hhou rb yth ecorres pondingdail y duration of activity.Thi sgive sa naverag epatter n ofl^m^f activity over the day that is independent of the relative satiation lev1. Thus adistinc t diurnal rhythm of locomotory activity was found (fig. 2.2 ),wit h maximuma tnoo n and ammimu mdurin gthe =nigh t ^.^ Inth eexperimen t carried out at 12 Cth e oeeue^ MIU J duringth e observational period. Only veryshor t ^^^^ recorded.Th eactivit ya tthi stemperatur ewa sabou t 10/ „o fth eactivit y Durationof daily locomotory activity. sufficient information is It is assumed that during a quarter of an hour surent obtained to be able to estimate the hourly ^^^^ItX^- Therefore,th eduratio n oflocomotor yactivit y ^^iZTZ^mrtcT Plyingb y four the duration of locomotory f^J^Ä^on ofanhour.Bysummingupthehourlyestim^ wa Periodth e duration of daily locomotory activity ^™ng feeding is shown da oflocomotor y activities during the successive ^fthedayof satiation infig 2.3 .Th eduratio n oflocomotor yactivit yincreasesr r ^ ^ untila leve l(MAXACT ) of 5.3 hours/day »<^*^o significant differ- remainsapproximatel y constant atleas tunti lme n -j- bserved between encei n the duration of daily locomotory activity couia thesexes . the elatlve Thelocomotory activity in relation to [ (^T \°988)wn ile inth eexperi - At20° Ci t takes two days to empty thegu t MO , locomQtoTy activity. To ments it took 2 days to reach the maximum ie ^ ^.^ satiation «press the relationship between locomotory activity ^ ^ Wageningen Agric. Univ. Papers 93-5 (1993) circadian rhithmicity Pterostichus coerulescens L. 0.20 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 time in hours male female FIG.2. 2Averag efrequenc y distribution oflocomotor y activitydurin gth elightperio d at2 0"C . Sum of the mean daily activity in hours 5.0 H 4.0 H 3.0 2.0 H KM 12 3 4 5 Days after feeding Ro-Wlncreaseoftouü dailylocomotor yactivit yafte r completesatiatio n onth efirst day . 116 WageningenAgric. Univ. Papers93-5 (1993) level,th eeffec t ofth etim eo fth eda yo nlocomotor yactivit y(diurna lrhythmicit y oflocomotor yactivity )ha st ob ecorrecte dfor .Therefore ,th elocomotor yactivi tiesdurin gth ehourl yobservatio nperiod so nth efirst an dsecon dda ywer ecalcu lateda sa fractio n ofth eaverag emaximu mactivit yfoun d forth ecorrespondin g houro fth ethird , fourth andfifth day . Therelativ e satiation levelo fth ebeetl e ineac hobservatio nperio dwa scompute db yth emotivatio nmode l(Mols ,1988) . In this way it was possible to obtain an estimate for the relative locomotory activitya ta rang eo fsatiatio nlevels .Th erelatio ni sshow ni nfig.2.4 .Th erelativ e locomotoryactivity ,her ecalle dth erelativ eactivit ycoefficien t (AC),ha sa corre lationwit h the relative satiation level(RSATL) .Thi srelationshi p can be fitted byth ehyperboli cequatio n: 2 AC= 1/(5.7*RSATL+1) r = 0.80 Thelocomotor y activities ofth emale san dth efemale swer ecombine di nthi s figure, becausebetwee nth esexe sn osignifican t difference inlocomotor yactivit y couldb eobserve d Locomotoryactivity and reproduction. j„„t;^B Theaverag elocomotor y activitymeasure d at9 aman d2 p mdurin gdaytim e ü < o '5 fe ll o o > ü SI o > S œ CC 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 RSATL coefficient (see text) and relative F>°- 2.4 Relationship between the relative locomotory activity satiationlevel . 117 WaSeningenAgric. Univ. Papers93-5 (1993) was used as an index for the overall locomotory activity of each beetle. These data are given in table 2.1togethe r with the individual total reproduction and the average of the locomotory activity at the same hours during the intensive observationperiods . To compare activity levels of the beetles in the pre-reproductive period and in the reproductive period the activities are expressed as a percentage of the totalactivit yo fal lbeetle si nth eexperiment . TABLE 2.1 The relationship between the locomotory activity (LA) in the pre-oviposition and in the oviposition period and the eggproductio n of a beetle. (Spearmans r :ab r= .87, P= 0.009 ;b e r= .81, P= 0.015;ac r =.56, P= 0.093 ) beetle no 1 2 3 4 5 6 7 8 9 10 egg production 376 73 320 32 113 134 141 211 198 465 a) eggs% of total 21.0 4.8 17.9 1.8 6.3 7.5 7.9 11.8 11.1 26.0 b) LA in repro% 25.4 4.7 9.8 1.4 5.4 2.6 11.1 7.4 24.4 32.9 c) LA.in pre-repro% 27.1 9.0 11.8 10.5 16.7 10.1 23.1 7.9 23.9 42.2 The table shows that if the activity and the egg production are ranked in increasingorde rbeetle swit ha hig hleve lo factivit yhav eals oa hig heg gproduc tion. The ranks of locomotory activities in the pre-reproductive period and in the reproductive period resemble each other quite well, though not yet signifi cantlyso .Th etabl eals oshow sth egrea tdifference s inth egenera lleve lo factivit y between the beetles, for instance beetles 2 and 4 are 'low activity' beetles and 1 and 10ar e'hig hactivity 'beetles . 2.1.3 Discussion Underth ehighl ysimplifie d experimentalcondition sth ecours eo flocomotor y activitythroug h theda ya tconstan t temperature apparently follows a rhythmic periodicity with a peak at daytime and a dip at night, although the latter was not measured in the experiments. This rhythmicity is similar to observations in other carabids (Greenslade, 1963;Luff , 1978). For example the nocturnal groundbeetle Pterostichus oblongopunctatus L. at constant temperatures shows aclea rpea k during thenigh t and non ora lo wactivit y during daytime (Brunst- mg 1983) Buti n thisspecie sth eactivit y increaseswit h increasing temperature and extendspartl y to thedaytime . InP. coerulescens atfield temperature snoc turnalactivit yamount st oapproximatl y 10%o ftota lactivit y(Greenslade ,1963 ) and the levelo fthi snocturna l activity probably depends on night temperature. Although itwa sno t measured in the experiments the high activity, at the start ofth ephotopeno d after twoday s ofstarvation , may bea n indication that noc turnal activity was raised also. In thefield th e difference between diurnal and nocturnalactivit ywil lb emor eextreme ,becaus e ofth edifferenc e between day timetemperature san dthos eoccurrin gdurin gth enigh t Satiation levelinfluence s the levelo f daily locomotory activity. The increase 118 WageningenAgric. Univ. Papers93-5 (1993) from alo w activity level after satiation till the maximum level after two days corresponds closely to the time needed for a beetle to digest the food at 20° C (Mols,1988) .Th e effect of satiation, orth einverse ,hunge ro nth eleve lo floco - motoryactivit yo finsect swa sfirst foun d byEdne y(1937 )wh oprovide dquanti tativedat atha t starvation for afe whour scause da marke dincreas ei nth e'spon taneous activity' of the locust Locusta migratoria migratorioides. Further evidence is given in later papers by Ellis(1951) and Chapman(1954). Barton- Brownean dEvan s(1960 )studie dth eeffec t offeedin gan dstarvatio no nlocomo - toryactivit y in thefly Phormia regina (Meigen).I twa sfoun d that flies fed glu cose,fructos e or mannose were much lessactiv etha n wereflies tha t had been starved for 24 hours. Immediately after feedingflies wer e less active than any othertime , but activity increased progressively thereafter. Evidence wasgive n thatlocomotor y activity issom efunctio n ofcro pvolum eand ,henc eo lth erat e ofcro pemptying .Thi slas thypothesi scorrespond sclosel ywit hth eobservation s inP. coerulescens. Also Sirota (1978) found that the larvae ofCulexpipwns molestusmove dmor eintensivel ya tlo wfoo dlevel stha na thighe rones .William s (1959)wa sabl et oincreas eth eactivit ydurin gda yo fth enocturna lcarabi dPter- ostichusmadidus b yfeedin g thebeetle sdurin gdaytim eonly .Gru m(196 6 l*r ) found that starving beetles showed a higher overall locomotory activity and moreactivityb ydaytim e extremd low. Thelocomotor y activity at 12 C (1U/< > oi mai «u z.w , „<•*;,„relativ e Onemaywonde rwhethe rthi si scause d»old y* the»to wd« ^ of to ^ satiation level after satiation or by a combination of temperatu ean d relaùv satiation level. The relative satiation level can be f^™*^££ emptyingrat e at 12°C(Mols , 1988). The ^^^S.S5Ä ate 54-68hour sRSAT Ldi ddecreas et o ab^ cienta t 20° Cfo r this hunger leveli sabou t 0.45(se etig .^ h total maximumdail yactivit y (= 5. 3hours )i sth esam efo reac h mperatuxe th to daily activity at the third day should be ^roximf ^dinXauency distri- observationperio d of aquarte r ofa nhou r »^^JÄ/^^inutes butiono ftota l activityi nfig 2.2 )th ebeetle s^ ^ observed. active(o r32.5 % ofth eobservatio nperiod) ,bu tonl> - w/o ' ture_depen- Thisi s anindicatio n that totaldail yactivit yi sals of^^ dsaeues with dent and not only governed via the ^*™ ^^^^(LofT, 1978, Iie decreasingtemperature .Thi si sals oknow nIro m f } • • positively Kegel,1990 )Th elatte r statestha ti ndiurna lspecie sdaytim eactivit y correlatedwit hsoi ltemperature . t^nk adirec tstimulu sfo rloco - Itma yb ehypothesize d thatfo rinsect sstaryatio n s ^ ^ metaboIic motion but that its level also depends directly^>n. y ^ This was ••ate ofPoikilothermi e animalsincrease 19b8jswith^^ ^ the need for food. also found in P.coerulescens (Mols, :"d/orthe speedo fwalkin ghav e Therefore theduratio noflocomotor y activitya n / ^ t0 cover a iarger area tob e extended with increasing temperature to d (Mossak. insearc h for food. In P.coerulescens wekno w now that °wsky,1985 )an d locomotory activityar eincreased . ^ ^ WageningenAgric. Univ. Papers93-5 (1993) In the experiments theindividua l difference in locomotory activity wasver y high. Thisindividua l variation in locomotory activity was strongly correlated witheg gproduction .A sth elatte rresult sfro m ahig hintak e offoo d and arapi d and efficient food conversion it may be hypothesized that the relative rate of fïL?P y!ng ( RGE) and the efficiency of food conversion (EFF) (SeeMol s 1988) areth emos timportan tvariable sa tthi sleve l 8 DeS der et L( 1984) and Ke el inÄS -'» t? / r ë (»»O)di dno t found differences study and females'which is confirmed bythe Present 2.2 ANALYSIS OF WALKING PATTERNS 2.2.1 Method Setup for observationsin thelaboratory conste^onLrVT^11 ^ f*** ^ °f 85"100 cm" ™esubstrat e consisted ofloam ysan dwit hsom elitte r and afe wheathe rplant s Video-eauio- mentwa suse dt ore glstrateth ewalkin gpatter n ofth ebeetl e(fi g 2.5^ TVcamer a WageningenAgric. Univ. Papers93-5 (1993) 1 sr^-^a« IIS ,, , : r - ',~. •**^7' - 1...' ". •*••:.* r>ï FIG.2. 6Experimenta l set-upfo r observingo fwalkin gpattern si nth efield . Topreven t possible orientation ofth ebeetl et oa n ^f^^^ ort oa horizo n silhouet, theexperimenta laren awa senclose db yfour opaLFer s pexplates , which spread the light of the light tubes;behin d hem. A_ro w of 6 fluorescent light-tubeshun gabov eth earena .Th eligh tintensit ywa sabou t180 0 lux.Th etemperatur e duringth eobservation swa s2 0± 1C . Setup for field observations. constructed of To registrate the walking patterns in thefield a n arena j 1 100*200cm . The temperature in the arena was »fff^J^ *™°viour(fig Here also video-equipment was used to »l^.^J^^^pa^ 2.6).Th eintentio n herewa st ose eho wfa r the ^ZtZZZiïJowd Wewit htha t found in thelaboratory . Theote«ratio n quipment^ y ^ observations during dry weather. The vegetation inth e arenaw thani nth elaborator y setup . ofvello wpain to nth eelytra . Beetleswer emarke dindividuall ywit hsmal ldot so tyello wp Experiments. motivational states were The walking patterns of beetles with different^ rn ^^ ^ ^ observed. The beetles used in the observations ^^J^ from: starved aknow n quantity of food in their gut. Thehunge r (RSATL= 1).Th e forthre eday s at 20°C (RSATL= 0 )tc»^^Ä£iesu p to satiation different relativesatiatio nlevel swer eobtaineao y recording the walking and then starve them for different time periods betore ^ WageningenAgric. Univ. Papers93-5 (1993) behaviour.Befor eth e observationsth e beetleswer ebrough tint oth earen awher e theywer eallowe dt oadap tt oth esituatio nfo r approximately halfa n hour. Theobservation smad ewere : a) the walking pattern of the beetle without extra feeding. This pattern repre sents the behaviour belonging to a specific relative satiation level. As time passed ondurin gthes eobservation sth eappropriat e RSATL wascalculate d foreac hwalkin gpatter n recorded. b) the walking pattern after consumption of a small prey. A weighed maggot of 1-2 mgwa scarefull y offered at thepoin t of a long pincetjus t before the mandibles of the beetle. In most cases the beetle accepted the maggot and startedfeedin gimmediately . The appropriateRSAT Lo fth ebeetl ewa s calcu lated. c) Thewalkin gpatter n in an arena withpre y clusters. Small prey clusterscon sisted of 7 maggots of 2 mg. at 10c m from each other: One in the centre and the others at the corners of a hexagon at a distance of 10c m from the centralone . Analysis. Therecorde dwalkin gpattern swer etrace do na plasti cshee ttape d ona moni tor. Ih e walking pattern was recorded in units of two-second steps. Theposi - H°MSt T, tW h k) C be re resente fxVf S"vT u T P d by a sequence of points (X0,Y0), for My IN vector PLVXYVV \ ''( TEGER,1 0 th h an8e f direCtion between vectors p algtóallt hv tr t ° *'an d P,+l ismeasure d ^Sis^^J^ ' «*'*"-»• The distribution of changes tion^^S^ÏÏ^1 / "mCa n VeCt0r M (Batschelet, 1981).It s orienta- ^tö^Ti °S^ defmeS the an§ular mean of the distribution.T o tribute ofchanIS ' r°7ard tCndenCy of'amotion ofmos t animals,th edis - mTu-ojZZ '"'TiS taken t0 be ^metrical and havea n angular around Man dS ™ CXpreSSeS the eventration ofth e distribution cessivestep s When Z "'T"6 °f correlations between thedirection s ofsue - whenth ecorrelaten ; C°rreIatl0n 1Szer o °ne obtains therando m walkmodel , correlation ,s onea straigh tlin emovemen t is obtained. 122 WageningenAgric. Univ. Papers93-5 (1993) Thust o characterize the tracks the following variableswer eestimate d from theexperiments : 1. Theturnin g rate in degrees per time unit and turning angle per length unit respectively. 2. Themean , standard deviation and kurtosis of thefrequenc y distribution of theturnin grate s according toth eTUKE Ydistributio n (Montford &Otten , 1976).Thi si sa theoretica ldistributio nwhic hca nb efitte dt oa rang eo fexper imentally observed frequency distributions, from uniform to contagious. It isa symmetrica ldistributio n andi ti scharacterize d bythre eparameters : The mean(M) ,th e standard deviation (a),an da kurtosi srelate d parameter(K) . Init scummulativ efor m thedistributio nca nb edescribe dby : Xp = M+ «7*Yp 3. Thevelocity ,expresse di ncm/sec . Toobtai n ^f^^ZXrZ ofth e tracks were divided in 10secon d parts and analysed byhan d for walkingvelocit y only. tu„fVprtnrr 4. Theconcentratio n around Maccordin gt oth elengt h ofVectoi£ Allthes e variables were analysed for thewhol erang eo fRSAT L Possiblerelationships . 2-2.2 Results. Generalobservations. f, ü in different motivational Visualobservation s onth ewalkin gtracKs : oiv waiking. Hungrybeet - dis c statessoo nreveale dtha tther ewer ethre e ™ "^' with some food in their leswalke d more straight and at ahighe rspeed ,o ^.^ beetleg ^ stomachu pt o satiated walkedmor ewindin ga ™ * 'ma t a speed that hadconsume d a prey showed a very winding ws ^^ walking patterns gradually increased. When no other prey were called high speed have been given the indications of straight (also som ^ WageningenAgric. Univ.Papers 93-5 (1993) FIG.2. 7Type so fwalkin gpattern sobserve di nP. coerulescens. Z^nTtelT^itOTtUOm (TW) Walk' respectively. These patterns %£2^Z^?™^ °f *~ Patterns Jturning ratean d tortuouswal k !1 ,^ ° m°re prey items are found in a prey cluster tortuouswal kcontinue san dremain sver ywindin ga ta lo wwalkin g speed. Turningrates. Pre de rees üiSr^ Speed Turningrat e Turningangl e Concentration cm/sec SE degr/sec SE degr/cm SE mean SD 0.1 Straight( RSAT L< 5% ) 20 4.66 0.71 16.00 4.7 3.51 0.97 0.76 Intermediate 1.32 0.68 0.07 (RSATL>5%) 20 2.2 0.33 19.64 2.91 9.34 2.65 0.59 0.08 Tortuouswal k 23 1.04 0.22 23.5 2.77 23.33 3.08 0.43 0.08 TWi npre ycluste r 4 1.03 0.34 30.2 3.16 30.1 thetortuou spatter n startsove ragain ,thi sresult si na neve nlarge raverag eturn ingrat ean d turning angle. ... Theturnin grate spe r2 second so fal lth etrack sgroupe dfo r thethre ewal kn g typeswer esummarize di nfrequenc y distributions,whic happea rt ob esymmetri calaroun d zero and extend from -180 degreest o +180 degrees (fig. 2.8) . 1h e Turning rate/2 sec intermediate straight tortuous 180 -150 -120 -90 -80 "30 Angle classes (10 degr.) periods)fo rth ethre ewalkin gtypes .Al lresult s FIG.2. 8Fequenc y distribution ofturnin grat e( 2se c ofobservation s combined. 125 WageningenAgric. Univ. Papers93-5 (1993) ü15 - H O ~T~ nr~ T-1 "T" T" 510 20 30 40 50 60 70 80 9010 0 Relative satiation level % FIG.2. 9Walkin gvelocit ya tdifferen t relativesatiatio nlevel sa t2 0° C morewindin gth ewalkin gtyp eth elarge r thestandar d deviation ofth edistribu tion. Velocity The relationship between walking speed and relative satiation level, with exclusion oftortuou s walk, isshow n infig. 2.9 .I n this figure both theresult s ol completely analysed tracks and those of tracks which were only analysed for speedar ecombined .Th efigure show sa breakpoin t around asatiatio nleve l Ziel\t S,atlfti0n the aVeraSe velocityis almost constant havinga ten - is ann olnCre tT \ f" "the higher satiation ,evels- B* ingenera l thevelocit y ÎJîrr f^ 2-5,Cm/fc' whichi sa littl ebi thighe r than the speedfoun d velocitvZ y " y,?d trackS" Bd0W a relative »tiation levelo f5 %walkin g tóSumTT886" Td y t0 aPProximately 5cm/sec . Thus using velocity as a ^ZÎhïTt? ng PatternS COuld be distinguished. After prey con- ncTea eduntiH t TT* WaUdng at &^ low ***»• Gradually thespee d SfvAT**1 ' Vel0dty of proximately 2-3 cm/sec. The average ^ÄS^feJTTnption °f a Prey was approximately 1 cm/sec. patternswer e 1 „ *^ «***° fa "the trac*s °f thesedifferen t walking T^^SV Trding t0 the three walki«g types this givesfig. 2.10 . frequency of these distributions of velocities per 2 sec. time steps shows 126 WageningenAgric. Univ. Papers93-5 (1993) Intermediate straight tortuous 30 0 5 10 I«» velocity classes (cm/2 sec) FIG.2.1 0Frequenc ydistributio n ofwalkin gvelocit yfo r threewalkin gtypes . that tortuous walk appears to have the narrowest ^^o^St walkshowin gmor etim estep swit ha hig hspee dtha nintermediat ewaik . Relationshipbetween velocityand windingness. qnnears thatth emea n Whenth evelocit yi scorrelate dwit hthe '^ »^ JX^rtasing speed, turning rate decreases significanly (r- 0.w , onship between velocityan d lut However,th evariatio n ishig h(iig/.iU- . . The relationship would be average turning angle per cm shows less variatie, . ^ ^^ In fig- a perfect hyperbole, if the turning rate was cons ^ aU the 2.12a hyperbole (Yl) with ^ »J*^^k a« positioned left of the Points. Most of the turning angles ol tortuous ^ ^^ walking typg curve. This may be an indication that tortuou This curye has Apowe r curve (Y2) offers the best fit through^ai n ^p^ ^ ^ ^ The a limit at x= 0 which indicates that the Deei zero degrees turningangl echange sgraduall y and continuesfro m36 0 withincreasin g speed...... _ of the turningrat epe r2 sec .tim e Fromeac h track thefrequenc y distnbutioriu ^ ^ frequency distnbu- stepwa smade .A Tuke y distributionwa slir e deviation andth ekurtosi s «onan dthu sfo r eachtrac kth eappropri a esu * ^ ^ analysed tracks,rela - y81 5 werecalculate d (according toSabeh s J ^. 2 seconds(V )o fth ebeetl e tionshipswer eestimate dbetwee nwalkin gveio u yv ^ WageningenAgric. Univ. Papers 93-5 (1993) tu - 35 J- 4» Y = 26.11 - 2.166*X ; • • u 30 • r - 0.65 o GO • • • • o» 25 o • • • • g, r • • • 1 • CD 20 • *•» • to • • • —"—-SJÜ • 15 • • • c 3 10 - • * * ' 5 _i—i i j • • 0 • _J i i i i i—i—i—•— Velocity (cm/sec) FIG. 2.11 Relationship between walking velocity and turning rate. Velocity (cm/sec) F.G.2.1 2Relationshi p between turning angle (degrees/cm) and walking velocity. 128 Wageningen Agric. Univ. Papers 93-5 (1993) CO c .2 •s (S (O E O) w FIG.2.13 aRelationshi pbetwee nth eS Do fth efrequenc y distributiono fth eturnin grat eo fa walkin g track(fitte d withth eTuke ydistribution )an daverag ewalkin gvelocity . k=-0.06612*V+0.2 12 14 16 Velocity cm/2sec. .«• krn fth efrequenc y distribution ofth e Re- 2.13b Relationship between kurtosis related Pf*™^™ '^ turningrat e(fitte d withth eTuke ydistribution )an dwalkin gvelocity . • cm of the turning rates frequency andit s standard deviation (a)an d kurtosis uv 2 13a+b) . The faster distribution. A significant relationship was touna ( g ' he standard the beetle moves the narrower the distribution and the sma deviationo fit ,an d themor enegativ ekurtosis . ^ WageningenAgric. Univ. Papers93-5 (1993) ü a> «o "E o •o tt U wa > a 1234>»1 2 3 4 5 6 7 8> » 1 23456789 minutes after start of tortuous walk FIG.2.1 4Exampl eo fincreas eo fwalkin gspee di ntortuou swal kafte r preyconsumption . Thisgive sth efollowin g expressions: a = exp(-0.173*V+0.208) r2= .7 (p<0.01) (5) K =-0.0661*V+0.2 r2= .49 (p<0.01) Durationof tortuous walk. After prey consumption the velocity of the beetle gradually increases and whenn oothe rpre yi sfoun d rapidlyth etrac kstraighten sou tan deithe rbecome s intermediate walk or thebeetl e stops walking or reaches the edge of thearena . Anexampl eo fsuc ha nincreas eo fspee d during thecours e ofa typicaltortuou s walk track is given in fig. 2.14. The time span of tortuous walk appeared to De a function of the relative satiation level (fig. 2.15). When the gut isalmos t emptythi sbehaviou rma ylas tfo r about 11 minutes,bu twhe n therelativ esatia tionleve lexceed s80 % itdoe sno t occuranymore . Concentration rfiTho7^nwutrati0n Parameter r decreases with the tortuousity of the track tng.2.16) .Whe nal lth ewalkin gtrack sar etake nfo restimatio n ofth ecorrelatio n betweenw akin gvelocit yan dconcentratio n thisrelationshi p showst ob esignifi - Snl r -61 f°r n =6 7 > P< <0.01) .Th ecombine d walkingpattern s (table2.2 ) shown osignifican t difference betweenth emea nvalue so f straight andinterme - 130 WageningenAgric. Univ. Papers93-5 (1993) •g 1000-1 c o u Si 800 c Q) .i 6004 400- 200- .2 .3 À .5 .6 .7 .8 .9 1.0 Relative satiation level FIG.2.1 5Relationshi pbetwee nduratio n oftortuou swal kan drelativ esatiatio nlevel . 1.00 0.80 C O +3 cd 0.60 c CD Ü C 0.40 O Ü Y=0.538+0.048*X 0.20 r=0.61 0.00 Velocity (cm/sec) PIo.2,6Re1atlonsh,pbetweenconcentrat1onP—ter ofwalk,ng patternsan daverag eve.oc.t , diatean d between intermediatean d tortuous walk buti tdoe sbetwee n straight andtortuou s walk. Fieldobservations. observed rather easily byeye .O n the Beetles walking in the arena could be observe ^^^ WageningenAgric. Univ. Papers93-5 (1993) video they were more difficult to follow, especially when they walked in the vegetation.Thi shampere d theregistratio n ofth etrack san d limited thenumbe r of tracks which could befollowed . At least one track per beetle was analysed. Theresult s aregive n intabl e 2.3. The speed ofwalkin g in the field wasusuall y lower than found inth elaboratory , both for hungry beetles and for thosewit h some gutfilling. Afte r prey consumption in the field, tortuous walk occurred alsobu ta ta lowe rvelocity . When a beetle was placed in the arena together with prey clusters of ± 10 maggots, it could be observed also that during sunny weather the beetles took themaggot sfro m thecluste ran d dragged them to ashade d placei n thevegeta tion.Afte r preyconsumptio n theyreturne d ina rather straight way to thepre y clustert ocaptur eanothe rprey .Thi sproces swa srepeate du ntil lsatiation .Whe n itwa scloud yth ebeetle sstaye di nth ecluste r until satiation. When morebeetle s were placed in the arena in the prey clusters often fights between beetlescoul d beobserved . Then dragging away ofpre yfro m thepre y clusters occurred more often. TABLE2.3 .Observation s onvelocit y (cm/sec),turnin g rate (degr.sec), turning angle (degr/cm)an d concentration ofbeetle swalkin gi nth efield. Th etemperatur evarie d between 17-23°C .Th eresult s aregroupe d for twosatiatio nlevels :hungr ybeetle s(RSAT L< 5%,straigh t walk) and beetleswit h somegu tfilling (RSATL > 5%, intermediatewalk) ,an d for tortuouswalk . (n= numbe r ofbeetles , SD= standarddeviatio nbetwee nth etracks ,S E= standar d error ofth emea n ofth etracks) . Speed Turning rate Turning angle Concentration n cm/sec SE degr/sec SE degr/cm SE mean SD RSATL< 5 %(straight ) 9 4.3 0.4 16.2 5.1 4.8 1.2 0.74 0.15 RSATL>5% (intermediate) 8 1.6 0.25 22.2 7.0 13.8 4.2 0.63 0.10 Tortuouswal k 6 0.9 0.15 28.5 10.0 32.4 11.2 0.55 0.12 2.2.3 Discussion Observation ofwalkin gtrack swit h thehel p ofvide o equipment isa nic ebu t also aver ylaboriou s technique. In the laboratory the tracks could be followed ra hereasily . Thefield observation sgav emor eproblems .I twa sespeciall y diffi cult to indicate the timesteps correctly. The time lag between the moment of hearingth etim esigna lan ddrawin gth etim emar k onth eplasti cshee t attatched er TfTT" 7aS " S°UrCe °f err0rs- This time la§ is in the order of 0.3-0.5 variai t I"1' g W?UM be COnstant there is no Problem, but because ofit s velôdttf™ T m M err0r °f about 10-20% °f «Peedestimates .A tlo w sas;mtrks rlT fs 81Veetogethe ° ther Problemsrby whic h' becausth eveiocitie e distances«*>»** s are smalha -l antobde thcone - andTfactToH' *"* 2f ^ haW been omitted- They occurred irregularly and in fact do decrease the calculated average velocity of the track. Brunsting 132 WageningenAgric. Univ. Papers93-5 (1993) (1983)go t the same problems duringhi sobservation s ofdisplacemen t ofP.ob- longopunctatus in thelaboratory , but heeve ninclude d pausesu pt o 30second s intoth eactivit y pattern. When we correct his measurements adequately the speed of active,wel l fed beetlesappeare d to be:a t 7°C 0.85cm/sec , 10°C 1.1 cm/sec, 16°C, 1.9cm/sec , 20°C2. 2 cm/sec. and at 25°C 3.4 cm/sec.Thes e velocities are about the same for fed beetles of P.coerulescens. As beetles of both species are of about the samesiz e this could be expected (Evans, 1977).Jus t as in P.oblongopunctatus alsoi nP. coerulescens arais e oftemperatur eincrease sth espee do flocomotio n aswa sobserve d by Mossakowski and Stier (1983).The ydi d experimentswit h hungry beetles and forced them through a tunnel and found at.10 C l±u.z cm/sec, at 15°C 3±0. 5 cm/sec, at 20°C 5.8+ 1 cm/sec, at25 C 8.5± 1 cm/sec anda t30° C9 ± 1.5cm/sec .Th evelocit ya t ±20°Ci sabou tsimila rt otha t found inm yobservation sfo r hungrybeetles . f In this analysis of the walking pattern spatial and temporal componentso f thewalkin g pattern are blended. To get insight in the effect of ve£*o n tte structure of the path both its relationship with the turning rate (*«*«/"4 andthetUrningangle(degrees/cm)havebeenconsidered.Fromtheto it is quite clear that the turning angle depends on the speed of walking The turning rate on the other hand is for most of the tracks almost constant.B u atextrem e low and high velocities therat ei srespectivel y higherorTowe .Tins results in a significant negative correlation between «^^^7!^ (fig.2.11) .whe nal lth etrack sar einvolved .Therefore , heturnin gangl e0 -t u n ingrate/speed ) becomes relatively smaller asth espee d ^^^1, producto fturnin g anglean dvelocit ywoul dresul ti na «"»^^3 sec).Thi s is mainly due to the relative high g^^^^Sg and the low turning rate at high speed At low^speedtn ed aS windingsearchin g pattern. Thisi swha ti susu a ly f- ° j rf ^ h e search'. This offers an argument for the hypothesis fj" j ' als0 trackma y be determined bymor e factors than> by^J^Ä «ter- betha ta tlo wvelocities ,afte r preyconsumptio n boi*a nex t ^ nal[stimulusmake s that the the distributionof ^h eturnin g ^ ^ ^ and the average rate becomes higher. This extra g ^ ^^ ^ initiated by the remains of the prey (external sumuy wane thecro p expansion. When no other-prqrj*™^iL feeding. sotha tth ebeetl ereturn st oth espee di tha d Deiore y Pxoeruiescens espe- obseT Differences betweenfield an dlaborator y ™™hl caused by the vege- ciallyhol dfo r thewalkin gvelocit y Thiswa sm o p ^ ^ laboratory experi- tationdensit ywhic hwa smuc hhighe ri ntn e ^ ^ r()Ughness of the ments. Structure and density of ^S6^" "important factors that influence soilsurfac e (Mossakowski and Stier, lWi>* .^ Although velocity in the thespee d and thus the walking pattern ot tn ^ walking patterns could field was lower than in the laboratory tnesam ^^ indication that in this beobserve d both in laboratory and field, i walking speed ismainl ygov - beetlethes ewalkin gpattern s aregeneral ,an dtha twalkin g ^ WageningenAgric. Univ. Papers93-5 (1993) erned by the hunger level in combination with temperature, soil surface and vegetation structure. 2.3 REACTION DISTANCE 2.3.1Method Reactions ofbeetle stoward spre ywer eobserve d in anarena .Thes ereaction s could be: a sudden stop with distinct waving of the antennae, a sharp change indirectio n towards theprey ,bitin gth epre y orjus t investigating thepre ywit h antennae and maxillae. When a beetle showed a reaction towards a prey this wascalle da discovery . 2.3.2Results In an arena most hungry beetles observed showed reactions when they touched a prey item (maggots of 2 mg ). The percentage of beetles being in theimmediat e vicinity of apre y and reactingwit h a sharp turn or with distinct antenna wavingdecrease d with increasing distance. Between a distance greater than zero but smaller than 1 cm, 75%showe d reactions. Between 1an d 2 cm, 40% reacted, and this decreased to 30% when the distance between prey and predatorwa sbetwee n2 an d4 cm . Whenth edistanc eexceede d 4c mn oreactio n ofth ebeetle swa sobserve d (fig2.17) . s? c _o Ü CS o cc 0-1 cm 1-2 cm 2-4 cm »4 cm Distance to prey Fta.2.1 7Distributio n of% o fbeetle sreactin gt opre ydependin g ondistanc e to theprey . 134 WageningenAgric. Univ. Papers93-5 (I99i) 2.3.3 Discussion P.coerulescens is a diurnal beetle with reasonably developed eyeswhic h are ablet oobserv emovement so fobject si nit sneighbourhoo d (Pers. observations). Thissuggest s that hunting by eye may be a means of tracing prey. Antenna wavingi softe n observed in the immediate vicinity of theprey , which suggests thatodour sma yals ob einvolve di npre ysearching .However ,preliminar yexper imentso nth ewalkin gspher ea tth eDepartmen to fEntomolog y(fo r description ofapparatu s seeThier y &Visser , 1986)wit hP.coerulescens, didno tsho wreac tionst oodour s ofmaggots ,contrar y toth ecarabi dP. madidustha tinmediatel y reactedb ychangin g its walking direction.Th eobservatio no fsmal lpre yseem s to be restricted to distances up to 4 cm, but from 0 to 4 cm the proportion ofbeetle sreactin g decreased sharply. Although thebeetl e oftenchanged^direc tion in the immediate vicinity of a prey it is difficult to d^ghmsh thisfrom anaccidenta lturn ,whic hi sals opossible ,o fcourse .Th enumbe ro f observons is nothig h enough to give a clear picture.Th e chancet o make sue!iamrby accidentmus t beknown . Thisca nb ecompute d ^^ob^™ ^ frequency distribution. The observed angle directed to the prey must beco m paredwit hth echanc et omak eth esam etur nb yaccident . Reaction distance may beinfluence d bysiz ean dmoven t of^^ thelatte r factor has not been investigated. The beete, surdy * no pecü eyehunte r such as the carabid Notiophilusbiguttatus (Bauer «TC5, ™f™T etal.,1977,Ernstin g, 1977,1978)™^ is important, and running into a preyjus tg™™T£ verv. contactwithmouthpartsandantenna emayb e anobviouswa^ of y' Jdisc0 Nevertheless,i tmus t bestresse d thateac h enlarge^^Xbservation will have a positive effect on the discovery rate ^^^^^ the of prey by e'ye at a greater distance: than J^S^L*»'^ efficiency of searching. In thecas eof P. «f^S^Bu t this also depends tance should theoretically double the rate of dicovery ^ ^^ ^ onth e satiation level, because this-determines thesp determines ^ degree beetlewil lwal k more ore less*^™ ^ effectiveness ofth esearchin g ofrecrossin go fth ewalkin gpat han dtheretor em e expresseda sth eencounte r rate. fth e beetle t0 theoutsid e Thereactio n distancewa smeasure d from me* » ^ &s ^fic diame. oftheprey. Whenpredatoran dpreyareconsiderea o j^.^ ^ ^ ^ radius terth erea l reaction distance of apredato r toa t p y also skellam, Plusth e predator radius plus the above! mentionedd«^ ^ ^ ^ ^ & 2 1958). The predator has a lenght of about ' 25 cm wide. As anaverag e mgmaggo tmeasure s about 0.5c mi nlengt na n "^ another cm can be f or the distance of discovery between prey ;a p^ ^ think about taking added. Instead of the beetle diameter (1cm j averagereactio n dis- themaximu m distance between theantenna e tipsbu t tancethe nwil lals ob ebetwee n 1 and2 cm . ^ the reaction distance. Iti sno tknow nwhethe ro rno thunge relicu s ^^^ evidence that hunger Theresult s of thefe w experimentsd ono tg ^ ^ WageningenAgric. Univ. Papers93-5 (1993) is involved. It seems a matter of chance whether or not within a distance of 0-4 cm a beetle discovers a prey. 2.4 SUCCESS RATIO Experiments were executed in the laboratory with P. coerulescens to assess the relationship of RSATL of the beetle with a few prey types it may encounter in the field. 2.4.1 Method The observations wereexecute d in large Petri dishes (diam 20cm ) with loamy sand on the bottom. A beetle of known weight and satiation level was placed in the dish with a specific prey item. The following prey types were tested: mag gots of the blow fly (Calliphorasp. ) (2-4mg) ,larva e of the Heather beetle Loch- mea suturalis, earthworms (2 cm long) and Leatherjacket s (larva of Tipula sp., 1 cm long).Whe n the beetle didn't react to the prey after 40 contacts with prey the observations were stopped. Then the discovery rate was considered to be close to zero (smaller than 1/40).Afte r consumption of the prey the beetles were weighed. Later on they were used again. Maggots and Heather beetle larvae were tested overmor e levelso f satiation than earthworms and Leatherjackets . To get an impression of the eagerness of a beetle trying to kill a prey also the attack ratio was measured. The attack ratio differs from the success ratio by that only those discoveries are involved in which the beetle tries to kill the prey by biting. Some observations were also executed with wolfspiders (Lycosi- dae) and ants (Myrmica sp.) as prey because they were often found in the gut ofP.coerulescens (Hengeveld , 1980). 2.4.2 Results The succes ratio of the beetle with the maggots is found to be clearly related to the relative satiation level.Maggot s appear to bever y attractive to the beetles even at a high relative satiation level. The attack and the succes ratio are high and run similar even at high satiation levels (fig 2.18a). An attacked maggot is always succesfully attacked. The Heather beetle larvae are also attractive at high satiation levels but an attack is not always followed by subsequent killing ofth e prey(fi g 2.18b). } When earthworms and Leather jackets are encountered a different result is round i(tig.2.18 can d d). Earthwormsar eattacke d heavely,the y seemt o berathe r attractive but in most cases the earthworms escape from the attack by giving a strong lash with their body, while also the slime gives problems to the beetle. JttrWÏTZ T * in a l0W SUCCes rati0- Leatl*r jackets are also easily ?h^n,i-w P uu °f the krVa is so tou8h that only with the highest effort, mosHv1 1 tï beetle Can Penetrate"After a few Witless attacks the beetle WnlfcH Prey alm°St unham*d, thus resulting in a low succes ratio. Woltspiders are too rapid for the beetle, they always escape and cannot be 1 ^fi WageningenAgric. Univ. Papers93-5 (1993) (a) D 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 1 I SRTIpulal« 3 ARTIpulalai (b) (d) % O.B0 A 0 0.1 O.Z 0.3 0.4 0.5 0.< 0.7 0.« 0.» 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 RSATL kscenswhe nA )maggots ,B )Heathe r beetle(L.suturalis), C)earthworms ,D )leatherjacket s(lipula sp.)wer eoffere d asprey . captured. The same holds for the ants. The latter attack the beetle furiously, whichtrie st oge tri d ofthe ma ssoo na spossible . 'wZÏÏ is a generalpredato ro fal l kind «^^£& Aphtds,lepidopterou s ^^f^^gX^*»** alsoremain s of Lycosidae and antswer e»3° ^ defend themselves, andaphid s are prey types with a soft body that had yca n ^ ^ ^ whichwil lresul t inhig h successsratio' swhe n^f^J * ^ beetle larvae. Portedb y the experiments with themaggot s andwit n i ^ egp in earth. Theexperiment s show that defense reactionso tP«*- * jherapi dwolfspider s wormsan dtha tcounterattac k ofant si seve nmor eeHec t . ^ ^ scapedb ythei r higherspeed . Theobservatio no lrem a ^ ^ specimens. lr0 >« the gut of P.coerulescens must therefore be ™" to get by thebeetle . Otherles srapidl ymovin gspide rspecie sma yb ea neasie rpre y g 2.5 VALIDATION OF PRBDATION IN ANAKBN A fthi scarabi dunde rfield condi - Validation ofprédatio nan deg gproductio no for instance t0 «ons is hardly possible, because of experimental difhcui ^ WageningenAgric. Univ. Papers93-5 (1993) get a reliable average of prédation a great number of repetitions is necessary and sincefield condition s changecontinuousl y thiscanno t bereache d bydirec t observations. Egg production can be measured directly by sieving of the soil, but therefore the beetle has to be disturbed by placing it in another arena and this may influence the predatory behaviour negatively. Nevertheless, to geta t leastsom eobservation so fprédatio ni naggregate dpre ydistribution s thesewer e madeunde rconstan tenvironmenta lcondition si na nartificia l arenai nth elabo ratory. 2.5.1Methods Observations werecarrie d out in an arena of 100*150cm . The soil consisted of loamy sand with light vegetation and some leaves and small pieces of bark under which the beetles could hide. The temperature was about 22°C and the observations were recorded with video (seechapte r 2).Onl y laboratory-reared female beetles,whic h hatched in late summer and were kept cool at 12°Can d which were not fed before in their adult stage were used in the experiment.A single beetle wasuse d per observation. Before each observation the beetlewa s set at 20° C for one day and weighed just before it was placed in the arena. The observational period lasted V/2 hour. The observations occurred between 10:00 and 14:00o'clock , because of diurnal rhythm in locomotory activityo f the beetle (chapter 2).Eac h day one beetlewa s observed. The prey was Droso- philamaggot s of 2m geach , which were arranged in two clusters of 7pre yi n a hexagonalwa ywit h onepre yi n thecentr e and placed 10 cm apart. Theplac e of the clusters was randomly chosen but more then 50c m apart. The maggots werekep t at their placei n thecluste r by amicroneedl e through the outer parts ofthei rskin . 2.5.2Results In the beginning it usually took half an hour before the beetles found the firstprey . They walked rather straight and spent a lot of time running around the edge.Captur e of thefirst pre y took 36.7 ± 32.5minute s (X ± SD). After capture and consumption of the first prey others followed rapidly. The beetle changed its walking behaviour into an intensive search by walking tortuously and 'border running' did hardly occur anymore. The time between captures withoutth etim eneede dfo rconsumptio n (thehandlin g time)i nth esam ecluste r was about 4.3 ± 4.6 minutes (X±SD n= 42) . The interval time between prey capture inanothe r cluster was7. 5 ± 5.7 minutes (X± SDn = 7). The handling timetoo k 171 ±3 8 secpe rpre y( n= 57) .N o relationship between handlingtim e and hunger level could be found. The average prey capture per beetle for the observation periodwa s5. 7 ± 3.7( X+ SD) . 2.5.3 Discussion 0 h l he Üme needed t0 ca ture ml ' "'T! tT rM P the first prey is extremely long comparedt oth efollowin g periodsneede d for thesuccessiv ecaptures .Thi swa s mostly due to running behaviour along the borders of the arena and to the 138 WageningenAgric. Univ. Papers93-5 (1993) straightwalkin gbehaviou r intha tperiod .Thi sborde rbehaviou rma yb ea con sequence of straight walking on such a small surface. It is striking to see that theborde r behaviour disappears after capture of the first prey. The increase ofwindingnes s appeared to be very effective in capturing successivepre yeve n in another prey cluster. Another point is the individual difference in cap ure succes between the beetles, it varied from zero to 11pre y captured. Whether thisoccur s by accident or depends on individual differences in behaviour can besolve d by simulation of predatory behaviour in an arena as has been done inth enex t chapter. 139 WageningenAgric. Univ. Papers 93-5 (1993) 3.0 SIMULATION 3.1 DEVELOPMENT OF SIMULATION MODELS Tosimulat eprédatio nrat ean dth eresultin geg gproductio n atdifferen t densi ties and distributions of the prey a model was constructed that integrates the most important components ofprédatio n and eggproductio n ofth ebeetle .T o analyseth eeffec t ofth evariou scomponent so fbehaviou rthi swa sdon ei nthre e steps. 1. Amode l ofwalkin gbehaviou r andpre yencounte r wasdevelope d that simu latesth ewalkin gpattern s and prey discovery at different prey densitiesan d distributions. With this model the importance for the searching efficiency ofvariou scomponent s ofwalkin gbehaviour , resultingi nth ethre e observed walking patterns, can bestudied . This also offered thepossibilit y toinvesti gate at which prey distribution the various types of walking behaviour are mostprofitabl e for thebeetle . 2. Integration of the relationship between relative satiation level (without the influence ofovar y size)an d locomotory activity, succesratio ,walkin gspee d and duration of tortuous walk into the previous model, to study the effect ofsatiatio n onpredator y behaviour. 3. Integration of ovary growth and egg production into the relative satiation model, resultingi na complet emode l that, for onebeetl ea t severaldistribu tions and densitieso fth eprey , simulatesprédatio n and eggproductio n over a season. 3.1.1 Simulationof walking behaviour and prey discovery Agenera ldescriptio n ofth esimulatio nmode lo fwalkin gbehaviou r andpre y discovery is given below. An annotated computer program listing is given in appendixI . Thefollowin g aspectsar eincorporate d inth emodel : a) Walkingvelocity . b) Standard deviation andkurtosi so fth efrequenc y distribution ofth eturnin g ratean d theirrelationshi pwit hwalkin gvelocity . c) Duration oftortuou swalk . d) Preycluste rscannin gan dindividua lpre yscanning . e) Reactiondistanc et oprey . f) Preydensit yan dpre ydistribution . Theaspect sfro m (a)t o(d )ar epropertie so fth ebeetle ,( 0concern spre ypro - WageningenAgric. Univ. Papers93-5 (1993) 141 perties and (e) concerns properties of both. In this model satiation effects are notye t incorporated. Velocityand turning rate. Theaverag espee do fth ebeetl ei sintroduce d asa forcin gvariabl ea tth ebegin ning of the simulation. Beetles do not walk with a constant speed but show variationsi nvelocity .Therefor e eachtim este pa valu ei stake n at random from a uniform distribution around this average value (the speed in a track varied randomly around the average speed with a standard deviation of 50% of the meana sthi swa sobserve d tooccu ri nth eindividua l tracks ofth ebeetle s(chap . 2)).Th edirectio no fwalkin gi scalculate db ydrawin grandoml ya directio n from theexperimentall yestablishe ddistributio no fth eturnin grate .Thi si sdon eagai n ateac htimestep ,an d thenex tangl ei sadde d toth eforme r direction which then givesth ene wdirectio n (fig.3.1). Asth espee d (V)o fth ebeetl ei sknow n (fo r each timeste pthi si sth edistanc e between twoset so fcoordinate s XP,,YP, and XP2,YP2i ti spossibl e to calculate thene wcoordinate so fth ebeetl ewit hth ecosin erule . XP =XP + COS(DIR)*V YP =YP + SIN(DIR)*V Thewalkin g direction (DIR) of thebeetl edepend s both on the former direc tionan d onth eturnin grat e(A )draw n randomlyfro m theTuke y distribution. DIR= DI R + A A= AV + SIGMA * (PKURT-(1-P)KURT)/KURT FIG.3. 1 Turningrat e(A,,A I+1,AI+2)a tconsequetiv etimestep s 142 WageningenAgric. Univ. Papers93-5 (1993) Thisformul a calculatesth eturnin grate/ 2se ca sa functio n ofth eaverag e(AV) , thestandar ddeviatio n(SIGMA )an dkurtosi s(KURT )o fth eturnin grat edistri bution (seeChapte r2.) . Themode l simulates thewalkin g ofbeetle si n an arena ofa specifi c size.Th e moment thebeetl ereache sth eborde r ofth earen ai twil lreboun dint oth e field. Duration oftortuous walk. Just after consumption of a prey, the beetle resumes searching at a verylo w speed. When no new prey is encountered the speed increases gradually to the speed before consumption or to a level that corresponds with a specific level of satiation. In the discovery model the duration of tortuous walk iskep t con stant at 300 seconds being the average duration of tortuous walk. During this period thespee dgraduall yincrease st oth espee da twhic hth ebeetl ewa swalkin g before prey consumption. Parallel with the increase of speed the distribution of the turning rate changes from wide to narrow because the speed determines theSIGM A and Kurtosisparamete r ofth eTUKE Y distribution. Preydistribution and prey encounter. In theprogra m the distribution of the prey can bearrange d suchtha t itma y varyfro m randomt over yaggregated .Thi si sdon eb yputtin gth epre yi ndiscret e prey clusters ofa specific size.Th enumber s ofpre y ineac hcluster , thenumbe r of clusters and the size of the clusters can be varied. The prey is considered to be immobile. In the clusters they are randomly distributed, and the clusters themselves are also randomly distributed in the arena. The arena is a square whichca nb evarie di nsize .Th ecluster sar ecircular . Thearea of discovery. Inth emodel ,th ebeetl ei srepresente da sa circula robjec twit ha specifi cradius . Thepre yi sconsidere d inth e sameway .Togethe rwit h thedistanc e ofpre ydis covery they constitute the reaction distance (radius predator + radius prey + discoverydistance )whic hvarie sbetwee n 1 and2 cm .Whe nth ebeetl ei swalkin g it covers a path with a width of 2 times the reaction distance in which it can discover apre y (the area of discovery).I n the model prey discovery in the area ofdiscover y iscalculate d bygivin geac h prey in thecluste r coordinates relative toa ne wcoordinat e frame. Thisfram e isperpendicula r onth emovin gdirectio n ofth ebeetl edurin gth etim este p(fi g3.2) . Whena beetl emove sfro m onepositio n toth enex ta nare ai scovere dconsist ing of a strip of 2 times the reaction distance in width but also consisting of the half of a circle at the start and end of the step. When the beetle moves to the next position with a change in direction a portion of the area is covered twice(fig 3.3) .Doubl ecountin go fpre ypresen ti ntha tare aha st ob eavoided . Twosituation sca nb edistinguishe d (fig3.4, 1an d II) I)Th edistanc e abeetl ecover sdurin g onetim este p( V= th espee d pertimestep ) islarge rtha n itsreactio n distance. Inthi scas ethre earea' sca nb edistinguishe d (fig3.4,1) . WageningenAgric. Univ. Papers93-5 (1993) '43 -axis x-axis • newx-axi s \ newy -axi s FIG. 3.2A ne wcoordinat e frame isconstructed , to determine whether a prey isi n the beetles area of discovery. For a number of points the coordinates are given in this new frame. xv,yv= (0,0) . xp,yp= (V,0) .A = ( V+ radius,0) .B = (0,radius) .C = (0,-radius) . A)X-coordinat ei ssmalle r than reaction distance B)X-coordinat ei slarge rtha n reaction distancebu t smaller thanV C)X-coordinat e largertha nV The preyitem s located in each part of theare a ofdiscover y must be scanned separately to see which one has already been discovered in the previous time step(fo r detailso fth eprogra m seeappendi xI) . II) The distance a beetle covers during one time step is less than its reaction distance (fig. 3.4.II). In this case only those prey items further away than the reaction distance from XV,YVan d closer toXP,Y P than the reaction distance (thewhit eare ai nth efigure) ar econsidere dt ob ediscovered . In this model the discovered prey are put back into the cluster with a new 144 WageningenAgric. Univ. Papers93-5 (1993) 'E F.G.3 3 A,locatio n ofth ebeetl ea t threeconsecutiv e timestepsI II III.B areasearche d from.times It oI Ia „d IIt oIII .C ,are asearche d from timeI t oIII .Th edoubl ehatche darea. ,covere dtwice . 145 WageningenAgric. Univ. Papers93-5 (1993) B I xv,yvf RADIUS'I (o,-rad) (rad.-rad) (v,-rad)(v+rad,-rad) n xv,yv (o,-rad)(v,-rad)(v+rad,-rad) FIG. 3.4Pre ylocate d in non-hatched areasi sencountere d byth ebeetle .Tw o situations are shown: I) The speed > RADIUS, II) The speed < RADIUS, xv.yv is the former position of the beetle and xp,yp ist e newpositio n of the beetle. Coordinates given in the figure are the new coordinate frame (see text). seto fcoordinate si fth e preydensit yha s toremai nconstant ,o rthe yar eremove d from the cluster when this isno t necessary. For the calculation of a functional response of a predator to prey density the average density in the field has to remainconstant .I fth e preyremain sa tth esam espo tth e chanceo fencounterin g the same prey twice or more is very high especially when the speed is low and thepre ydensit yi nth ecluste rhigh .Thi sma ygiv eerroneou shig hrate so fdiscov ery. Clusterscanning. It isles slaboriou s to first determine which cluster iswithi n thereactio n dis tance of the beetle and subsequently to scan only the prey of that cluster than tosca nal lpre yi nth efiel d eachtim estep .T odetermin ewhethe r orno t acluste r is within the reaction distance of the beetle the coordinates of the centrally located prey of a cluster are used. If the distance measured between the center ofth ebeetl ean d thecente r ofth ecluste ri ssmalle rtha n thesu mo fth e reaction distance ofth e beetlean d thecluste r radius,onl ythe n thedistanc e to eachindi vidual prey in that nearest cluster willb emeasured . If thisconditio n isno t ful filledth e next walking step will be taken and cluster scanning will start over again. 3.1.2 Couplingmotivational state and searching behaviour To analyse the searching behaviour in relationship to themotivationa l state of the beetle the following relationships were integrated into the searching model: a)Locomotor yactivit y(TWALK) ,b )Succe srati o (SR)an d c)Walkin gvelocit y 14" WageningenAgric. Univ. Papers 93-5 (1993) (V) all with respect to the relative satiation level (for the appropriate values seechapte r2) . In this simplified model afixed maximu m gut capacity isuse d and RSATL is only determined by ingestion and by gut-emptying. Prey size is given as a fraction of the maximum gut capacity. Thus each time a prey is consumed RSATLi sincrease d withtha tfraction . Gutemptyin gi ssimulate dwit hth erela tivegu temptyin grat efoun d at20° C(Mols ,1988) . a) Calculation ofth eleve lo flocomotor yactivity .• The time a beetle spentswalkin g during a specific timestepca n becalculate d from therelation sfoun d inth eexperiment sconcernin gth erelationshi pbetwee n the relative activity coefficient (AC= (actua l activity)/(maximum activity of hungrybeetle spe rtim eperiod) )an dRSAT L(chapte r2) .Pe rtimeste pth eactivi typerio d canb ecalculate dwith : WALK = AC*FREQ*MAXACT WALK = Thetota ltim ea beetl ei slocomotor yactiv edurin ga timestep . AC = The relative activity coefficient related to the relative satiation FREQ = Thefractio n ofth etota ldail ylocomotor yactivit yrealize ddurin g MAXACT = TS Son oflocomotor yactivit yo fa hungr ybeetl eexpresse d inhour spe rda ya t2 0° C In the motivational model the timestep of integration V^*^ ofa n hour, which issufficien t tocalculat eth edecrease ,o RSATLb ycbgMttm . The walking part of the program is running during that quarter for TWALK seconds. b) Successrati o and RSATL ,,_„:„« tue chance The relationship between the success ratio and RSATLdetrmme s the hance ofa discovere d preyt ob ecaptured .Th erelationshi p found for maggots inth emode l(se echa p2. ) »£Ä% -he av«,age »^—™£^ 5 cm/sec to an average of 2.5 cm per sec (fig 2.12). This is inciu model. d) Duration oftortuou swalk . „it twine that period the Each prey consumption is followed by tortuous waIk.P™*™ ^ The velocity is adapted to the value that correspond^^^^ beetle duration depends on RSATL ^^^ ^ walk ™* ^ is still very hungry after consumption ot a sman prey WageningenAgric. Univ. Papers93-5 (1993) 11minute s during which the speed increases slowly to the level of 5 cm/sec. When RSATL is about 50% tortuous walk is shorter (about 4 minutes) and thanspee dreturn ssoone rt oth eleve lo f2. 5cm/sec .Whe nRSAT Lexceed s80 % tortuouswal kdoe sno t occur any longer. 3.1.3 Simulation ofsearching, prédation and egg production In this extended model the relationship of locomotory activity with RSATL and with the diurnal rhythmicity is combined with the complete motivational part including egg production and with the searching and prédation part. RSATL is governed by ingestion and egestion and by the egg load. One run ofth emode lconcern sth esimulatio no fsearching ,prédatio nan deg gproductio n duringa whol eseason ,whic htake sabou t 35 daysa t2 0°C . 3.2 SIMULATION EXPERIMENTS I) Simulationo fsearchin gindependen to fmotivation . Simulations weredon e with the searching model (appendix 1)i n which only walking behaviour was incorporated. The goal was to investigate the range of prey distributions and densities at which thewalkin g behaviour of P. coerules- censi s most profitable. The distributions varied from random to extremely aggregated. The overal prey density per arena was varied over a wide range dependingo nth esimulatio nexperiment .Pre ycluste rsiz ewa sinvestigate d from 5, 10, 20, 30, 40, 80, 160 to 320 cm diameter. Prey number in the cluster was varied from 5, 10,20 ,4 0 to 80.Al l different combinations of cluster diameter andprey/cluste rwer etested . Theeffec t ofth efollowin g characteristicso fwalkin gbehaviou rwer eanalyse d inth esimulations : 1) Speed ina rang evaryin gfro m 1 to 5 cmpe r seci nth erando m prey distribu tions, and average speeds of2. 5an d 5 cmpe r seci nth e aggregated distribu tions.Th elatte rwer echose nbecaus ethe yresembl eth eaverag espeed s found inbeetle swit hfoo d inth egu tan d inhungr ybeetle srespectively . 2) Theeffec t ofhavin gtortuou swal kafte r consumption ofa pre yitem . The beetle's discovery rate with prey per hour was used as output variable ofth esimulations . The number of repetitions of the simulations was dependent on the aggre gation ofprey .Th estronge r theaggregatio n themor e simulationswer eneede d to obtain reliable values of the discovery For 5-20 prey/cluster 50 runs were necessary and for more than 20prey/cluste r 100runs ,becaus ei n the latter case onlyfe w clusterswer epresen t inth e arena when the overall prey densitieswer e keptlow . II) Simulationo fsearchin gan dprédatio ncouple dt omotivation . Simulation runswer emad efo r periodso fon ehour . For eachru ni nsequenc e prey was replaced in the arena with the same density and distribution, but not WageningenAgric. Univ. Papers93-5 (1993) at the same place. In the simulations the beetles were considered to be active duringth ewhol eperiod .Wit hth eresult so fth esimulation sfunctiona l response curves could be constructed. This isdon e for different prey densities and prey distributions,varyin gfro m randomt ostrongl yaggregate dwit hth esam ecluste r diametersan dpre ynumbe rpe rcluste ra smentione d before. Inaggregate d preydistribution s simulationswer edon ewith : a) Constant prey density. A captured prey was randomly replaced at another placei nth ecluster . , b) Decreasingpre ydensit yb yremova lo fcapture dprey .B ythi sprocedur eloca l depletion of prey occurs, which is a natural phenomenon m predators. As a consequence prey density in the arena doesno t remain constant. Thusn o normal functional response curves can be constructed in this way. It is to be expected that at locally high prey densities the average density/m will not changemuc hafte r acaptur ebu ta tlocall ylo wpre ydensitie sloca lremo val of prey may exert a negative influence both on the discovery rate and onth eprédatio nrate . III) Simulationo fsearching ,prédatio nan deg gproduction . Simulationswer edon ea t constant temperatures withrando ma swe l a with aggregated prey distributions. Thepre y isreplace d everyday .Th eoveral lpre y dSsity varied from 0.125t o 16prey/m 2fo r randompre y<^£ ™ ^f™ 0.125 to 8fo r aggregated prey distributions.Th e aggregated dstributions^wer e done with 20 p'ey/cluster, and the cluster diameters used were 5 10 20 0 40, 80, 160, 320 cm. The prey density in the clusters with 20 prey P cluster depends on cluster surface and isrespectivel y: 1 088 2546, ^f^f^ 99 4 and 24 8 nrev/m2 Reaction distances of 1an d 2cm . were tested in tne J^iï^SSdtoL ofT Wan d ofpre y depletion^was«rfm« ^ W distributionsan di naggregate ddistribution sa tpre ydensitie srangin gfro m0.25 , 0.5an d 1 prey/m2. IV) Simulation ofdispersal . „i «:t exclusively The beetle P.coerulescens only rarelyflies, thu s dispersalla lmos mrt ^^ occurs by walking. Therefore, dispersal of ^/^Z^ToZo^ speed,o nwindingnes s ofth ewalkin gtrack , and on^J^^S S 2 activi y. These are determined again by themotivation of the ^™ turn depends on prey density and distnbution. With the^elp «f ^ searC ^ model it is possible for each walking speed to simula edispera l of the from a fixed'point in the ^^^^£^^S1^ for displacement from the ^^f^^^J^Z time periods 1,2 ,4 , the walking velocit.es ranging from 1 to 6cm/sect o J^ ^ 8, 16,3 2an d 64minute s and for 5.4 hours a the*" combination is of activity per day for a hungry beetle. Each velocity time repeated 100times . 149 WageningenAgric. Univ. Papers93-5 (1993) V) Simulationo fth evalidatio nexperiment . Simulation was done ina nare a with thesam e surface asi n theexperimen t (seechapte r 2.5).Tw o clusters with 7prey , each wereplace d at random in the arena. The complete model was runfo r theappropriat e part ofth e day: Start at 11 pmfo r9 0minutes .A sa compariso n themode l wasals oru nwit h 14 prey placed atrando m inth earena . Thecapture d preyitem swer eno treplaced . The simulation modelwa s adapted for this small arena byincludin g walking along the border of the arena into it. Themomen t the beetle reaches the border of thefield i twa sno trebounde d intoth efield bu ti tfollowe d theborde r depending on the choice of the subsequent angle. When an angle is chosen that should lead the beetle outside thefield th e border will be followed, other angles will bring thebeetl e back into thefield again . This approach isa nassumption ,bu t as noquantitativ e information wasavailabl e about behaviour of the beetlei n thefiel d toborder sthi swa schosen .I tresult si npattern stha tresembl eth ewalk ingbehaviou r observedi nth eneighbourhoo d ofborder san d obstacles. 3.3 SIMULATION RESULTS The simulated walking pattern was analysed inth esam e manner asth erea l walkingpatterns . The turning rate at different walking speeds obtained inthi s way were thesam e as those found for therea l tracks. This wasals o thecas e with theconcentratio n parameter. In wasconclude d that themode l simulated thewalkin gpattern s correctly. Therefore, the simulation experimentswer ecar riedou ta splanned . 3.3.1 Searchingwithout motivation. a) Randompre ydistributions . The discovery rate perhou r ofth e beetle with randomly distributed prey with and without performance oftortuou s walk after each discovery isshow ni n fig 3.5( aan db) .I nbot hcase sth ediscover yrat eincrease ssteadil ybot hwit hincreas ingvelocit y andwit hincreasin g density ofth e prey.Whe n thevelocit y exceeds 2.5cm/se cth ediscover yrat eincrease sstrongl ybecaus e ofth edecreas e ofwind - ingness. When prey is randomly distributed tortuous walk has an inhibiting effect onth ediscover yrate .Thi seffec t becomesstronge rbot hwhe npre ydensit y andwalkin gvelocit yincreases .A tlo wvelocitie s( < 1 cm/sec)th epat hi ss owind ingtha t afurthe r decreaseo fspee d caused bytortuou s walk,an dconsequentl y followed bya nincreas ei nwindingnes sha shardl yan yinfluenc e onth ediscover y rateanymor esinc eth elinea rdisplacemen t isver ylow .Th edifferenc e indiscov eryrat ebetwee nwalk swit han dwithou t tortuouswal kincrease swit hpre yden sity anddepend s onwalkin g velocity. Ata speed of 5cm/se cth edifferenc e at a prey densityo f 1 prey/m2i sabou t 11% andincrease su pt o45 %a t 5prey/m 2 and becomes greater athighe r prey densities.I ntabl e 3.4.1 thesimulation sar e given for V= 5an d 2.5cm/se c at an increasing range of prey densities.Th e *•*" WageningenAgric. Univ.Papers 93-5 (1993) Walking speed -TW (a) ' -o- 1 s " / -o- 2.5 / ••»•• 3 20 .X -o- 4 ^' . / y'..... —'— 5 cm/sec / „o ; / x ,.A'"' 10 h -° "•""„_..+ •iy •••' -0*** „ - - -+-"• •* y'P -A ~0" r ^r -s-"^ -9—9 . 2 3 4 2 3 4 s 2 prey density /m prey density/m FIG. 3.5 Discovery rate (discoveries/hour) with randomly distributed prey simulated for different walkingvelocitie s(cm/sec )o fth ebeetle ,a )withou tan db )wit htortuou swal kafte r preyencounter . coefficient of variation (SD/mean) isabou t similar for trackswit h and without The efficiency of the walking track can beexpresse d as the distance covered per discovered prey (= path length/discoveries). When a comparison ismad e between tracks with and without tortuous walk than it appears that up till a prey density of 8 prey/m* the efficiency is approximately the_same foi'both m nefficien b tracks.Abov ethi spre ydensit yT Wbecome smor ean d ^/ ^ h™ by the high discovery rate the amount of time spent mT W increases thus he averagewalkin g speed decreasesmor ean dmor eresultin gi na walkin g patteren that becomes more and more winding. Recrossing occurs more often and this decreasesth eefficienc y ofth etrack . b)I?SZÄEÄi™ » weever, is ». followed by tortuous P y wl L S dto ve, , rate isth esam ea Si nrando m **£*%££* density per cluster (for an example seefig.3 6) .Th e smaller inec i higherpre ydensit yi nth ecluste rth ehighe rth e «^^"^J^ erv rate At a high prey density in the cluster the number of clus ers per area dietse because fheoverall prey densitype rm > inthese ; simulation s re= constant),thu sth edistanc ebetwee nth ecluster screase s andtherefor e a l«Ue needsmor e timet ocove rthi sdistance .Therefore , ^^^ZTZ eries will be followed by series of short periods w^J^^^fS cluster.Tortuou s walk after preydiscover yincrease sth ediscover yrate , 151 WageningenAgric. Univ. Papers93-5 (1993) TABLE3.4.1 .Th eeffec t oftortuou s walk on thediscoverie s per hour at two walking velocities (V= 5 and 2.5cm/sec) . Simulations without motivation and and success ratio. Prey israndoml y distri buted and thedensit yi skep t constant. Adiscovere d prey isplace d elsewhere inth earena . Reaction distance = 2 cm. Averages are based on 50 runs; path+/pat h is the ratio of the pathlength with andwithou t TW;disc+/disc - isth erati o ofdiscoverie swit han d without TW. coefficient Disc variation pathlength ratio overies path/ prey density/m average SD sd/disc average path SD discoveries disc+/disc- V = 5cm/se c - -TW 0.05 0.30 0.51 1.70 18000 100 60000 1 0.1 0.74 0.72 0.97 18000 100 24324 0.97 0.25 1.60 1.25 0.78 18000 100 11250 0.97 0.5 3.36 2.00 0.60 18000 100 5357 0.93 1 6.60 3.12 0.47 18000 100 2727 0.89 2 13.39 3.16 0.24 18000 100 1344 0.61 4 25.74 4.72 0.18 18000 100 699 0.50 8 49.00 6.97 0.14 18000 100 367 0.38 16 98.00 13.6 0.14 18000 100 184 0.26 32 191.70 12.9 0.07 18000 100 94 0.18 V = 5 cm/sec +TW path+/path- 0.05 0.30 0.58 1.93 17779 459 59263 0.99 0.1 0.72 1 1.39 17505 706 24313 0.99 0.25 1.56 1.1 0.71 16891 756 10828 0.96 0.5 3.12 1.42 0.46 15795 1002 5063 0.94 1 5.86 1.73 0.30 13940 1124 2379 0.87 2 8.16 1.43 0.18 12501 917 1532 1.14 4 12.82 2.51 0.20 9974 1208 778 1.11 8 18.72 2.55 0.14 7881 919 421 1.15 16 25.24 2.76 0.11 5798 600 230 1.25 32 33.70 3.21 0.12 4347 353 129 1.37 V = 2.5 cm/sec -TW disc+/disc- 0.05 0.15 0.27 1.80 9000 60 60000 1 0.1 0.26 0.56 2.15 9000 80 34615 0.85 0.25 0.76 0.89 1.17 9000 80 11842 0.87 0.5 1.48 1.13 0.76 9000 80 6081 0.80 1 2.62 1.66 0.63 9000 80 3435 0.85 2 5.32 2.65 0.50 9000 80 1692 0.76 4 10.28 3.30 0.32 9000 80 875 0.70 8 20.50 5.14 0.25 9000 80 439 0.53 16 43.78 8.19 0.19 9000 80 206 0.37 32 85.78 11.11 0.13 9000 80 105 0.25 V = 2.5 cm/sec +TW pathd+/path- 0.05 0.15 0.44 2.93 8933 194 59553 0.99 0.1 0.22 0.42 1.91 8905 159 40477 1.17 0.25 0.66 0.74 1.12 8756 261 13267 1.12 0.5 1.18 1.06 0.90 8548 399 7244 1.19 1 2.22 1.33 0.60 8233 444 3709 1.08 2 4.06 1.52 0.37 7547 532 1859 1.10 4 7.20 1.94 0.27 6591 585 915 1.05 8 10.96 2.50 0.23 5647 577 515 1.17 16 16.22 2.16 0.13 4335 395 267 1.30 32 21.38 2.86 0.13 3410 346 159 1.52 152 WageningenAgric. Univ. Papers93-5 (1993) coefficient of variation (SD/mean) v=2.5 cm/sec, No tortuous walk FIG. 3.6Coefficien t ofvariatio n (SD/mean),withou t tortuous walk ofpre y discoverieswhe npre y isdistribute d aggregated.I ntha tcas eth emea ndiscover yrat eequal stha twit hrando mpre ydistribu tions.Overal lpre ydensit yi s1 prey/m . 153 WageningenAgric. Univ.Papers 93-5 (1993) sizeo fth eeffec t depends both on walkingvelocity , on cluster size,an d on prey densityi nth ecluster .T o showth epositiv eeffec t oftortuou swal ki n aggregated preydistributions ,th eratio so fdiscover yrate spe rhou rbetwee nwalkin g tracks with (+TW) and without tortuous walk (-TW) are given in figures (3.7 a to d)fo r4 differen t preydensities . The figures show an optimum for the positive effect of tortuous walk that depends on the walking velocity as well as on the cluster size and prey density in the clusters. In general, increase of the average prey density decreases the positiveeffec t oftortuou s walk, becauseafte r each discovery thewalkin g speed decreases thus decreasing the average walking speed over the whole searching period.Whe nV = 2. 5cm/se ctortuou swal kshow sit shighes tprofi t atintermedi atecluste rdiameter sfro m 10t o4 0cm . The efficiency of the walking pattern (path length/discovery rate) is demon strated in fig 3.8.a,b for V= 5an d 2.5 cm/sec. These figures show that at the average prey density of 0.5 prey/m2 the effort for the beetle to discover a prey is minimal between small clusters crowded with prey and large clusters that almost appraoch arando m preydistribution . In smallcrowde d clustersi t takes a longer walk to reach a cluster, because the distance between the clusters is long. In large clusters the prey density in the clusters is so low that tortuous walk becomes lessprofitabl e also. Both for walking speeds of 5an d 2.5cm/se c it shows that prey in clusters of an intermediate size are discovered with the lowest cost in terms of walking distance. Simulations done at higher average preydensit y show that the lowest effort shifts more to the smaller clusters and toth ehighe rnumbe ro fcluster spe rarena . 3.3.2 Searchingand prédation coupled to motivation 1) Randompre ydistributions . The effect of the successrati o on prédation isclearl y shown in fig (3.9 a and b). At increasing prey density the discovery rate steadily increases, while the prédationrat ei slevellin gof f toapproximatel y 12capture spe r hour atth ehigh estpre ydensity .Thi seffec t ismainl ycause d bya decreasin g successrati o when satiation level increases, although at low prey densities the walking speed also influences thefor m ofth ecurve .A t the start ofth e simulation walking velocity is5 cm/se cbu t after captureo fth efirst pre yth evelocit ydecrease st o2. 5cm/sec . Therefore the first prey will be captured at a rate which is twice that of the second prey. At prey densities below 1 prey/m2 no difference can be found be tween the discovery rate and the capture rate as almost each discovered prey will be captured. At prey density 4/m2 the discovery rate curve seems to bend upwards when TW isinvolved . This is caused by the decrease of the duration of tortuous walk when the beetle becomes more and more satiated, and which is absent above 80% of RSATL. Above this satiation level the walking speed remainsconstan tthu sfro m thatpre ydensit yth ediscover yrat eincrease slinearl y withpre ydensity . When prey density is not kept constant after capture of a prey it decreases 5 WageningenAgric. Univ. Papers93-5 (1993) pothlength/discoveries prey density 0.5 prey/m, v=5 cm/sec a,o oo 7.000 6 . O O O 5.O O O 4,000 3.0 0 0 2,0OO l.OOO ao J / 20 prey/cluster pothlength/discoveries Prey density O.S/m, v=2.5 om/i FIG. 3.8Distanc e walked byth e beetle perpre y discovered in aggregated prey distributionsfo r twowalkin gvelocities : a)5 cm/sec ,b )2. 5cm/sec .Overal lpre ydensit yi s0. 5prey/ m . WageningenAgric. Univ. Papers93-5 (1993) slowly after each capture, which leads to a slightly lower discovery rate, but ithardl yinfluence sth ecaptur erat e(fig .3. 9a an db) ,becaus eth epre yi sreplace d everyhour . Whenth ereactio ndistanc ei shalve dfro m 2t oon ethi sdecrease sth ediscover y rate also with 50%, but as the capture rate levels off at increasing prey density theeffec t ofdecreasin greativ edistanc ebecome ssmalle ra tincreasin gpre yden sity. 2) Aggregatedpre ydistributions . Figures 3.10 (a to d) and 3.11( a to d) show the effect of walking behaviour in situations of constant and decreasing prey densities respectively caused by prédation in relation to cluster diameter, and prey number per cluster, at two averagepre ydensitie sviz .0. 5an d 1 prey/m2.T oillustrat eth edifferenc e between random prey distributions and aggregated distributions the discovery and the capturerat e ofrando m preydistribution s for these twopre ydensitie sar egive n by the horizontal lines. It shows clearly that both discovery rate and capture rate at these twopre y densities are significantly higher when thepre y isaggre gated. It also showstha t this strongly depends on thecluste r diameter assmall , but larger than 5 cm diameter, clusters, result in higher discovery rates than largecluster san dextremel ysmal lclusters .Pre ydepletio ndoe saffec t thediscov ery rate at cluster diameter up to 80c m and when thepre y density per cluster ishigh .Thi sca nb eexplaine db yth eincreas eo fth edistanc ebetwee nth eclusters . Thecaptur e rate ismuc h lower than thediscover y rate and seemsonl y affected by local prey depletion when prey number per cluster is low. This is because thediscover yrat eremain s sufficiently high.Thi si sonl yth ecas ewhe n thearen a issufficientl y largei nrelatio n topre ydensit y( > 100m 2)t o overcomea serious decrease in overall prey density. When the clusters have a high prey number (thus only a few clusters per arena) the capture rate decreases to the average Discoverlas of randomly distributed prey Captures of randomly distributed prey effect of TW and prey depletion effect of TW and prey depletion 10 15 10 15 (initial) prey densfty/m* (initial) prey density/m2 FIG. 3.9 Discoveries (a) and captures (b) when prey is randomly distributed. Effect of tortuous walk (+ or-TW) , and effect ofpre ydepletio n (densityconstan t =dc, density not constant= dnc) areshown . 156 WageningenAgric. Univ. Papers93-5 (1993) Motivation Included 60 120 160 200 240 280 320 cluster diameter (cm) prey per cluster FIG. 3.10 Effect of cluster diameter (a,c) and prey/cluster (b,d) on ^TdSoofX distance walked per prey in aggregated prey distributions at an ^f^l^^l^Z /m2 at constant prey density (dc) and with depletion of prey (dnc) by the beetle. The therando mpre ydistributio n aregive nfo rcomparison . value of the random prey distribution, because of the station of th beetle and of the long distance between the clusters. <^*WJ^"™£ the beetle cannot eat more then up to sattation the ^^>££%£ strongly and although more prey arediscovere d theywtl lnotJ *"* ^ ™ sameca n be said for thepathlengt h walked per prey ^^eZtZ^Zc ture (fig 3.10 and 3.11 can d d).Th e searching is ^^^^ZtTd clustersize s(10-8 0c mdiameter) .Whe ncluster sar e ^^^^Zd long distances have to be walked per p«y discovery ^P^^n^ above 80c m the distance increases to the distance walked as for random p y distributions 3.3.3 Searching, prédation andegg production Randompre ydistributions . WageningenAgric. Univ. Papers 93-5 (1993) Motivation included /\ prey density 1/m' -o- dlsdc - •- capdc A (a) —o— disc.random ]' fc. •••*•• • cap.ra n —'— dfsdnc 1 —'— capdnc i 40 80 120 160 200 240 260 320 cluster diameter(cm ) 0 10 20 30 40 50 60 70 60 prey per cluster FIG. 3.11 Same as Fig 3.10 but with overall prey density of 1 prey /m2. 60 -o- -TWdc.rd-2 -•- -TWdnc,rd-2 -A— +TWdc,rd-2 >. 40 a f •••*•• +TWdnc,rd-2 •o CO -o- -TWdnc,rd-1 a> fc 30 > -•- +TWdnc,rd-1 o o ca (initial) prey density/m2 FIG. 3.12 Effect of tortuous walk r+r.r TUA J , • ( r W) prey letlon = 1 or2cm)onnumberoa) onnumbe r ofdisc fH,^loveri ii° D e:Tp |; ^ & ™ «M and reaction distance(r d lespe r daylo r random prey distributions of increasing density. 158 Wageningen Agric. Univ. Papers 93-5 (1993) 300 -o- -TWdo.rd-2 - •- -TWdnc,rd-2 -A- +TWdc,rd-2 A +TWdno,rd-2 -a- -TWdnc.rd-1 -•- +TWdnc,rd-1 6 8 10 12 14 16 (initial) preydensity/m 2 Fïo. 3.13 Effect of tortuous walk (+ or -TW), prey depletion (de or dM> ^ «^£^ (rd = 1 or2 cm )o nlocomotor yactivity ,expresse di nminute spe rday ,fo rrando mpre ydistribution s ofincreasin gdensity . hardly to affect the discovery rate when prey is replaced daily. Even on tins time scaleloca lpre y depletion doesno t seemt o play an m»por^A^w prey densities (smaller than 4prey/m » the curves *^.^%™£?^ Abovethi sdensit yth edicoverie sincreas ealmos tlinearl ywit hp eyden«rty.Jh * can beexplaine d by the switch ofth ewalkin g speedfrom 5 to 25 cm/se;whe n RSATL exceeds 5%.after thefirst pre y capture. At low densites mor^. spentb ywalkin g at high speed.A spre y density increases ^^f^ laced byintermediat e speed and in themea n timeth etota l ^J"*^* is decreasing. Above 4 prev/m>, almost all the walking is^done^tanav«ge speed of 2.5cm / sec.an d locomotory activity doesno t decreasemuc h anymore ^Capture and consumption rate per day follow >fo ^ 2cur^. M J and b)an d the sameca nb eobserve d for theeg gP rof^^»üo n rate c). No strong effect of prey ^^^^^^^ST^lo as on eggproductio n can be observed. The interval ot prey rep shortfo r that. ratewhe npre ydensit yi sbelo w 1 prey/m . nw WageningenAgric. Univ. Papers 93-5 (1993) Random prey distribution, captures/day effect TW, reactive dlst.,prey density- (initial) preydensity/m 2 FIG. 3.14 Effect of tortuous walk (+ or -TW) nrev HenW,™ (A A ^ J • ,• - P y de Jetlon d frd = 1o r 2 cm »r m ^ant„™ j ,1 '' P ( c or dnc) and reaction distance 160 Wageningen Agric. Univ. Papers 93-5 (1993) of tortuous walk is increasing up to 20%. With tortuous walk the pathlength per day is shorter and locomotory activity isapproximatel y 5% higher than in behaviour whithout tortuous walk. Thus locomotor activity is only partially compensatingth eeffec t oflowe rpre ycaptur ewhe ntortuou swal ki sperformed . Concerningprédation ,consumptio n andeg gproductio n thedifferenc e result ing from behaviour with and without TW is small. Generally having TW in random prey distributions results in a lower prédation rate. Per prey density the effect is not significant. The negative effect óf TW on egg production is greatestbetwee n 1 and 8prey/m 2 Reactiondistance. Up to prey density 4prey/m 2 halving the reaction distance from 1 to 2c m has only a smalleffec t on thediscover y rate.U p tillthi sdensit y locomotory activityi salmos tcomplet ecompensatin gth eeffec t ofth edecrease d reaction distance. Above this density the effect of reaction distance becomes more and more important up till about 50% at 16prey/m 2. This effect can be explained by the form of the locomotory activity curve in relationship to prey density (fig. 3.13). Compensatory effects are strong up to 4 prey/m2 , above thispre ydensit ylocomotor y activityremain salmos t constant. Above prey density of 1prey/m 2 the effect of halving the reaction distance on the capture rate is about 15%. Below this density no difference can be observed. For consumption and egg production (fig.3.14 b and c) the same effects canb eobserve d becausethe yar ea direc tresul t ofpre ycapture . Aggregatedpre ydistributions . Since prédation rate is hardly affected by local prey depletion when prey is replaced once per day this schedule is used further on for the simulations of searchingan dprédatio ni naggregate d preydistributions . Clusterdiameter: Infig 3.1 5 theinfluenc e ofcluste rdiamete ri sgive no ndiscov eryrate ,captur erat ean dconsumptio npe rda yfo r2 0prey/cluste ran da reactio n distanceo f2 cm . Prey discovery is clearly influenced by the cluster diameter. The discovery rate isalway s higher in clustered then in random prey distributions. Thelowe r prey densities show the highest discovery rate in clusters with 30c m diameter, butwhe nth epre ydensit yincrease sthi sshift s tocluster swit ha smalle rdiamete r Generally it can be stated that at low overall prey densities (< 1 prey/m ) preyclusterin gresult si nhighe rcaptur erate scompare dt orando mpre ydistribu tions. At higher prey densities only the very small clusters result in a higher capture rate than the others and random prey distribution. At higher overall prey densities the intercluster distance is shorter which makes the small (high density) clusters becoming better attainable. The larger clusters give capture rates that are similar to those found at a random prey distribution. Up till an overall prey density of 1prey/m 2 prey clusters of 20, 30 and 40 cm diameter preyar eutilize d betterresultin gi nhighe rconsumptio n rates.Abov ethi soveral l density the capture, consumption (fig 3.15) and eggproductio n rates (fig 3.16) WageningenAgric. Univ. Papers 93-5 (1993) prey density (20 prey per cluster) 40 0.125 0.25 0.5 1 8 ca T3 a- 5 cm b- 10 cm —•— discoveries Ë. 30 - c- 20 cm E d- 30 cm e- 40 cm —A— captures ca c f- 80 cm o o- consumption ü g- 160 cm co h- 320 cm o 20 r- random a. co o co •o2 10 >es o ^V^-A-A^A-A o co I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I abcdefghr*abcdefghr*abcdefghr*abcdefghr*abcdefghr*abcdefghr*abcdefghr cluster diam (cm) FIG. 3.15 Effect of prey cluster diameter on discoveries, captures and prey consumption (mg)pe r day for different overall prey densities. The number of prey/cluster is 20. The captured prey was removedfro m the field. prey density 20 prey per cluster 300 0.125 0.25 0.5 1 2 4 8 250 -a- 5 cm c " b- 10 cm o '. c- 20 cm .• CO ## CO - d- 30c m ## A .• ••*•' •* CO 200 r e- 40 cm •' * * ak>. ! f- 80 cm • • • ** a. g-160 cm . /•/\ / c 1 h- 320 cm A V * •• 150 . r- random ?\ I • a •ua f • « o • \/* a. 100 a • • • a> < 50 : \ • • n 11111111111111111111 111111111 m abcdefghr*abcdefghr*abcdefghr*abedafghr*abcdefghr*abcdefghr'abcdefghr cluster diameter (cm) FIG. 3.16 Effect of prey cluster diameter on total egg production per season for different overall preydensities .Th enumbe ro fprey/cluste r is 20. Thecapture dpre ywa s removed from the field. 1" 2 WageningenAgric. Univ. Papers 93-5 (1993) are not different from those in random prey distributions. The high capture rate in the very small clusters at high prey densities do not result in high con sumption rate because of rapid satiation in those clusters. Thus profitability, expressed in capture rate, consumption and egg production, of the beetle's be haviour occurs onlyi n aggregated preydistribution s atlo woveral lpre y densities (smaller than 1 prey/m2). Walking behaviour. When walking behaviour is considered (spending of time and walking types fig 3.17), it is found that in aggregated prey distributions at low overall densities high activity and much high speed walking is alternated with days with low activity spent in a prey cluster. High speed walking occurs especially at low overall densities and when clusters with small diameters are available. The time spent in high speed walking not only decreases with overall prey density, because the chance to discover and capture a prey increases, but also with increasing cluster diameter, because the distance between prey clusters is shorter. The fraction of time spent in tortuous walk is very short when the prey density in the cluster ishigh , because once in a prey cluster captures follow each other rapidly, thus leaving less time to complete the whole duration of TW. When prey clusters with the same amount of prey items become larger the distance between the prey in thecluste r increases thus giving the beetle more space and time to complete itstortuou s walk. Therefore more timewil l be spent walking tortously when the clusters are larger. When the prey distribution ^rey_dMMty__-20_Hey-EejLÇluster 300 0.125 0.25 0.5 1 250 MM high speed I"""""-—J Intermediate >» at 200 •o j^l tortuous (O m C 'Ë 150 Ç o E 100 50 - lb8-.,Bhr..6.-.f.hr-.b.d...h,..b.d...h,-.».*..Bhr-.bed..«hr..b.d...hr cluster diam (cm) FIG 3 17Tim e (in minutes) per day spent on the three walking types depending on prey duster diameter( wit h2 0prey/cluster )an doveral lpre ydensity . WageningenAgric. Univ. Papers93-5 (1993) 163 Distance walked / discovery or capture various cluster sizes and prey densities prey density (20 prey per cluster) 350 0.125 0.25 0.5 1 8 300 a= 5 cm b= 10c m c= 20 cm •o 250 d- 30 cm e- 40 cm •o f= 80 cm 160 cm Q) 200 SJ- h- 320 cm CO r- random a> o 150 100 0 t>- ,•••%? o- " o-oo. •O — meter/captur - - • - - meter/discov FIG. 3.18 Distance walked (m.) per discovery or per capture depending on prey cluster diameter (20prey/cluster )an do noveral lpre ydensity . approaches randomness thefractio n oftim espen t in tortuous walk isgenerall y longercompare d toaggregate d preydistributions . Simulations with the complete model have also been done without perfor mance oftortuou s walk to seet o what extent havingthi s behaviour is advanta geous with respect to prey discovery and prey capture and to egg production in aggregated prey distributions. The results are that the positive effect of TW is only present at very low overall prey densities (< 1prey/m 2 ) and that it is inversely related to prey density. For prey densities 0.25, 0.5 and 1prey/m 2 performance of TW compared to non-performance gives resp 38%,23 % and 2% higher number of discoveries per day, this resulted in resp 32%, 18% and 0% increase incaptures/da y and a 120%, 16% and 3%highe r eggproduction . Thestron geffec t oneg gproductio n atth elowes tpre ydensit yi sbecaus e perfor mance of tortuous walk in such poor food situations leads to such an increase of the capture rate that the metabolic threshold (a consumption of 2mg/day ) leading to eggproductio n isexceeded . Therefore, in such poor food situations walkingtortuousl yafte r preycaptur ei sextremel y important. The averagedistanc e which has to becovere d by the beetlebetwee n twodis coverieso rtw ocapture sdepend sbot h onth ecluste rdiamete ran d onth eoveral l preydensit y(fi g 3.18) .Th efigure show stha t onlya tlo wdensitie st o 1 prey/m2 164 WageningenAgric. Univ. Papers93-5 (1993) discovery rate in relation to various clustersizes and prey densities 40 >» a •a "w .5 <>D O O co prey density (pc=20) —D — 5 cm --0-- 10 cm - O- 20 cm 30 cm — V— 40 cm —• — 80 cm — T — random F,o. 3.19Discoverie s perda yi nrelatio n tooveral lpre ydensit yan d ^^[^ZSIKZ cluster). The largest,cluster s (160 and 320 cm diameter) are omitted because their results samea sfo r randompre ydistribution . and with small cluster diameters between 10an d 40c m the behaviour is^most profitable because than the shortest distance has to becovered .A t higher prey densitiessuc ha minimu mi sno tobserve d anymore. Prevdensity To showth epositiv eeffect s ofth ecombine d behaviouralcompo - nZtT^Z and predion in ^^^^^T^ ZeSS to random prey distributions the functional (fig 3.19 and 3.20) anc > ™™"c respons curvesfig 3.2 1ar egiven .Thes esho wtha te spe c^ " °^ *^ ingoffer s stillan yadvantag efo r thebeetle . Reactiondistance: Decreasing the reaction distance from 2t o 1 cm when prey 165 WageningenAgric. Univ.Papers 93-5 (1993) capture rate in relation to various clustersizes and prey densities "(0 Q) D. aCO prey density (pc=20) " G — 5 em --O-- 10 cm O - 20 cm 30 cm - V — 40 cm — • — 80 cm " T — random FIG. 3.20 Captures per day in relation to overall prey density/m2 (functional response) and prey cluster diameter (20prey/cluster) .Th elarges tcluster s (160an d 320c mdiameter>ar e omitted because their results areth e same asfo r random prey distribution. is aggregated highly decreases discovery rate (30%) but less so prédation rate (15%) and egg production (13%). The greatest effect is found at low overall preydensitie si nsmal lclusters .Thi si si ncontras twit hrando mpre ydistribution s where no effects of changing reaction distance could be observed at suchlo w overallpre ydensities .I naggregate dpre ydistribution san d lowoveral lpre yden sitiesmor etim ei sspen ti nstraigh twalk ,whic hi seffectiv e becauseo fth esmalle r amount of recrossings as compared to intermediate walk. But it also results trom the fact thati nclustere d situations themos t important capture isth e first one. Then the chance to find the first prey is the chance to find a cluster and because behaviour changes and the prey density in a cluster is higher than the overallpre ydensit yth enex tpre ywil lb ediscovere d sooner. Therefore, because ot thisphenomenon ,reactio n distancemus tb econsidere d relativet oth ecluste r esrTt nfT a /e ?freactio n distan<* from 2t o 1 is relatively smallwit h 2 f 'he Slz^ ofa cluster .A constrain t in thispredator y behaviour isthat , once acluste r isdiscovered , satiation isreache d soon, because of the highpre y Wageningen Agric. Univ. Papers 93-5 (1993) Egg production per season in relation to various cluster sizes and prey densities 250 225 t c 200 o CO CD 175 CO CD 150 Q. C O 125 *-Ü» 3 100 •Oo I- a. 75 o> ra CD 50 25 prey density (pc=20) 20 cm 30 cm — D — 5 cm --0-- 10 cm - O- ... A.. — V — 40 cm —• — B0 cm — T — random FIG. 3.21 Eggproductio n per seasoni n relation overallpre y density (numericalresponse )an dpre y clusterdiamete r(2 0prey/cluster) .Th elarges tcluster s(16 0an d320c mdiameter )ar eomitte dbecaus e theirresult sar eth esam ea sfo rrando mpre ydistribution . densityi na cluster ,leadin gt oa relativ esmal leffec t oncaptur erate ,whe nreac tiondistanc ei shalved .Whe npre ycluster sar ever ylarge ,residenc etim ei nsuc h clusters becomes longer. In such casesreactio n distance becomesmor e impor tant because the longer the beetle has to deal with the prey density and prey distribution in that cluster, the more the daily capture rate will be determined byth eloca lsituatio ninstea do fb yth eoveral lpre ydensity . 3.3.4 Dispersalof beetles as a result of walking behaviour ,.,,.••„ The relationship between velocity and linear displacement (Ld) Ug>«na fig.32 2 This figure shows that linear displacement strongly depends on the 8 Sp eedan d therefore on thewindingnes s of thetrack . TortuouswaIk£* » h beetlealmos t on the spot, whileintermediat ewal kgive sa linea rJ» P J^ ofapproximatel y 2-3meters/hour , and high speedwalkin glead st oa displac e ÄÄ2 meters/hou, According to the **™*™££^ is dependent on the velocity and is proportional with the square root of the 167 WageningenAgric. Univ. Papers93-5 (1993) linear displacement intim e for different velocities 1300 _,,' 1200 -""'" 1100 .-'v^ „_< E 1000 900 c 800 .--*'' --o""'" E time inminute s velocity —D — ï 1 •+ -•2 2 —O-O— - 3 3 •• • .--A" A •• • 4- 4—O —O— -5 —V FiG.3.2 2Linea rdisplacemen t ofth ebeetl ei ntim efo r different walkingspeeds ,(cm/sec ) walking time according to: Ld = &y/t (1) For each velocity the constant (a)i s calculated with linear regression. The tnT^P , the Walking Vd0city (V in cm/se^) and the constant (a) tollows closely apowe r curve according to: 1.82 V1-385 2 r = .99 (2) C^rrtimng equations (1) and (2) results in a general equation with which 1 385 Ld= 1.82V - *yt (cm) ofS^tTetrT^ ÏJS P0SSible t0 Calculate the daily tar displacement olttSS^Ä :r " ' asthis ;esultsin a sp-fic durar ypcno a t^see tig.2.4) and in aspecifi c walking speed (fig 3.23) 168 WageningenAgric. Univ. Papers93-5 (1993) linear displacement per day (m) depending on satiation level at 20C c 0 E o o « o. co « c • A- _ _ . -T ' - A- T- _1_ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 relative satiationleve l —• — meanmi n A- meanma x FIG. 3.23 Rangeo flinea rdisplacemen tpe rda y(mi nan dmax )dependin go nRSAT La t2 0°C . Calculatedwit hformul a usingv + 0. 5(resultin gi nmin .an dma xId ) Inthi sfigure i ti sshow ntha thungr ybeetle shav ea naverag edail ylinea rdisplace ment that varies between 17 and 23.5 meter. From 0.K RSATL <0.6 this distance varies between 4-9.5 meter and well fed beetles show a displacement of2- 4meter . Discussion. T The dispersal of the beetle is determined by its walking behaviour In areas with a lowpre y density more time willb e spent in high speed walkingthu sthi s will lead to leaving an area which isunsuitabl e and reaching another one that is more profitable in the fastest way. The moment a more profitable areaii s reached both locomotory activity and speed decrease because the RSA1Lde creases,resultin gi na longe r stayi n theprofitabl e area•Jh « »PPOrts to J~A of Baars(1979) who measured daily distances covered by radioactivellabeled P.coerulescensm twodifferen t habitats:a poo r Molimafield an da m o a,c^type ofheathland .H efoun d twodistinc tpattern s ofmovemen t in ^^^ There were periods, sometimes very prolonged, during which the beetles ony incic were pciiuuo, = • „f rom n.13me ter) mcontinuall y covered smalldistance s (average2. 5m rangin g iromu 13 mcic > 169 WageningenAgric. Univ. Papers93-5 (1993) changingdirection swhic hh ecalle d 'random walk' that alternated with periods in which long distances were covered (average 22 m ranging from 2-87 m)in a more or less constant direction, which he called 'directed movement'. In the Molinia field the beetles performed shorter periods of 'random walk' than in the mosaic field. The duration of 'directed movement' was about equal, but the distances covered during 'directed movement' were larger in the Molinia fieldnl . 28m compared to 17m in the mosaic field. These distances measured at warm days (maximum temp. 24-28°C ) come closely to those calculated for hungrybeetle swit ha naverag etemperatur e of2 0°C .Th ealternatio n ofperiod s with short distances to periodswit h longdistance s supports theide a of thebee tlesreactin g to clustered prey in thefield. I n this view the Molinia field should havepre ycluster stha tar esmalle ro roccupie db ylowe rpre ydensitie stha nthos e in the mosaicfield. Althoug h alternating periods of low and high temperature may give the same results, the observation that at the same day beetles could beobserve dtha tonl ycovere dshor tdistance swhil eother swalke dlarg edistance s isno ti nagreemen twit hthat .Simulation s ofsearchin gbehaviou rwit h clustered prey at constant temperatures show the same alternation oflon g and shortdis tancesa tlo woveral lpre ydensities .Thi sals osupport sth ehypothesi s that daily lineardisplacemen t to animportan t leveli sdetermine d byth epre y distribution andpre ydensit yi nth e field. ByOkub o (1980)muc h attention isgive n to therelationshi p between thedis persal oforganism s and diffusion processes.Diffusio n isdefine d as a' basically irreversible phenomenon by which matter, particle groups, population, etc spread out within agive n space according to individual random motion. When thistheor yi sapplie d toth ebeetle si tca nge tth efollowin g meaning: 1. Thenetflu x ofbeetle sove ra lin eo fon emete ran dpe rtim euni t (for example the border between an unprofitable and a profitable area) equals the diffu- sionconstant multiplied with the difference in beetle density over that dis tance. 2. The difference in density is determined by the immi- and emigration of the beetles. 3. Ifth ediffusio n constant isdifferen t for the2 area sthi swil llea dt o aconcen tration ofbeetle si ntha t areawit hth elowes t diffusionconstant. With the information above and assuming that walking is at random it is possible to calculate the diffusion constant D from the walking behaviour in thefollowin g indirectway : 2 D= linv >00 (Ldis) /(2t)Thi s holds when a track issimulate d long enough such that the D is constant in the end. This leads to the following equation for the diffusion constant inrelatio n toth ewalkin gvelocity : D = 5840*V2-738 (cm2/hour) With the diffusion constant the general spread of a population beetles over an areaca n becalculated .Thi soffer s atoo lt oestimat e theexchang e ofindivid ualso fdifferen t localpopulation si ndependenc eo fwalkin gcharacteristics , food 170 1 ' " Wageningen Agric. Univ. Papers 93-5 (1993) TABLE3.2 . Calculationo fdiffusio n constantD wit hhel po fth e walkingprogra ma tdifferen t walking speeds. vcm/se c D (nr/hour) SD 0.6 .025 3.7 .15 10.6 .43 26.6 .97 51.7 1.9 level and temperature as these determine mainly thewalkin g behaviour. It can alsob euse dth eothe rwa y around toestimat eth egenera lfoo d levelo fa locatio n onceth eindividua lwalkin gcharacteristic so fa specie sar eknow n in relationship tosurfac e structure and temperatureb ymeasurin gth eimmi -an d emigration. Simulation of validation experiment^.5) number of captures In 90 minutes 95% confidence interval A1 a aT 10 of experiment ^-^~ Reactive distance (cm) FK, 3.24Result so fth evaHdado n expérimenta;£*"£^^^£|li2 cm.(chapter2.5)compare dt o resultsofsmulatonora^^ prey (R) related to reaction distance.Pre y content is 5A (A1.K1) I respectively. 171 Wageningen Agric. Univ. Papers 93-5 (1993) 3.3.5 Comparisonof validation experiment and its simulation Themea nresul t ofth eobservations , 5.7 ± 3.7pre ycaptured/perio d (10bee tles) (see chapter 2.5) and its 95% confidence interval of the mean are give in fig.3.2 4togethe rwit hth eresult so fth esimulatio n(averag eo f 100runs) .Becaus e only 10beetle swer eobserve dth econfidenc e intervali squit elarge .Nevertheless , theresult s of simulations with clusterd prey agreerathe r wellwit h the observa tions.Simulation swit h randomlyplace d preysho wa significantl y lowerpréda tionrate .Sinc eth emaggot soffere d inth eexperimen t differed slightlyi nweight , effects ofvariation si npre yweigh to nth ecaptur erat ewer esimulate db y offering prey with a weight of 5% or 10% of the maximum gut capacity of the beetle. Byfeedin g on heavier prey satiation occurs sooner resulting in alowe r capture rate,bu teve nthi sremaine dwithi nth e95 %confidenc einterva lo fth eexperimen talresults . Reaction distance of the beetle is not exactly known therefore simulations have been carried out on a range of reaction distances (ranging from 1t o 4 cm) to test the effect of it on prédation rate. Changing reaction distance has onlya mino reffec t onprédatio nrate .Probabl y thisi smainl ydu et opre ydeple tion in such a small arena, because after each prey capture it is more difficult to get the next one. The type of prey distribution has a much stronger effect on prédation rate than the reaction distance. Concerning prey depletion, the difference withth eresult so fpreviou ssimulations ,wher eeffect s oncaptur e rate by prey depletion hardly occurred, is due to the size of the arena. In a large arena local lower densities of prey are easily compensated for by the beetle as itwalk srelativel y largedistances .I n a smallaren a thebeetl ei skep t at the same locationwer epre ydensit ydecrease srapidl y byprédation . * '2 Wageningen Agric. Univ.Papers93-5 (1993) 4.0 GENERAL DISCUSSION Theultimat eai mo fthi sstud ywa st oinvestigat eth eimpac to fspatia ldistribu tionan ddensit yo fpre yo nth epredator ybehaviou ran dresultin geg gproductio n of the carabid beetle Pterostichus coerulescens L. Firstly the driving force ('the motivation') behind foraging behaviour was studied, secondly themos t impor tantcomponent s offoragin g behaviourwer eidentified , andthirdl yth erelation ships between the behavioural components and motivation were quantified. Mols (1988) showed that in addition to the emptiness ofth e gut the sizeo f the ovaries and of the ripening eggs had to be taken into account, because they limits gut expansion and thusdetermin e therelativ esatiatio n levelo f thebeetl e and also the rate of change of the satiation level. The latter depends both on the gut-emptying rate and on the egg deposition rate, because egg laying has an effect on the extent of expansion of the gut. Because of the clear influence of the size of ovaries and eggs in P. coerulescens the definition of motivation differs fromthatfoundforpredatory mites(Fransz ,1974,Rabbing e 1976,Sabe- lis, 1981),wher egu tsiz ewa sconsidere d tob econstant . Next,th erelativ esatia tion level was related to the components of predatory behaviour The most important components are: locomotory activity, walking velocityan[turn ng rate, reaction distance to the prey, and success ratio. 7^™?^*™^ relationshipsfoun d for prédation and eggproductio n in relation to the spatial distribution ofth eprey ,ar ediscusse dbelow . 4.1 PREDATORY BEHAVIOUR AND PREY DISTRIBUTIONS An important factor determining theprédatio n rate of apredato r is thewa y it searches for its prey. Firstly, the prey habitat has to, belocatod^and then the prey itself has to be found. In P.coerulescens^ takes place bv ^ k>"g as the beetle rarely flies. Lastly the suitability of the ^^l^^Î- SÄÄSÄ» S«* sorts wi.- ,w -r;:;nr„r WagenmgenAgric. Univ. Papers93-5 (1993) Thus, the beetle has to deal with prey with all kinds of spatial distributions. Prey density in the beetle's habitat, may be temporarily very low, as in poor heathland andmoorland , orsometime sexcessivel yhig ha sdurin gheathe rbeetl e outbreaks. In previously cultivated land prey density may bemoderat e to high depending on the nitrogen content of the soil. From experiments and simula tions,i tappeare dtha tth ebeetl e was adapted tosuc hvaryin gpre ydistributions , and canrespon d tothe m by changing its behaviour. 4.1.1 The advantageof specific walking behaviour In theexperiment s weobserve d that thebeetl e may show three distinct types ofwalking . A) Walkinga thig hspee dwhe ni ti s hungry, B) walkinga ta ninterme diate speed when it has something in its stomach and C)a slo w very winding walk after eating of a prey. High-speed walking is very useful when largedis tances have to becovered . It only occurs when the beetle ishungry , disturbed, orwhe n trying to escapefro m enemies.I ti sprofitabl e when prey isaggregate d or when largepre y israndoml y distributed at a low density. In these situations high-speedwalkin gbetwee nth e clustersresult si n asubstantia lincreas e in préda tion becauseth edistanc ebetwee nthe mi scovere di nth eshortes t time.Th etim e between encounters with clusters ismor e than halved, because at higher speed thebeetl ewalk sstraighter . Intermediate speedi sadvantageou s inpre yclusters , because it results in a longer stay in the clusters where there is a good chance of meeting the next prey. Tortuous walk (TW) is only profitable if prey are aggregated(Chapte r3.3.1) ;wit hrandoml ydistribute dpre yi ti s disadvantageous as it decreases the discovery rate because the high degree of recrossing results in a low linear displacement. If the duration of TW could remain constant it would have more effect as the prey density increased. However,the duration of TW isno t constant, rather it depends on RSATL and decreases as thesatia tion levelincreases .Thi smean stha t atincreasin gpre y densities itwil lhav eles s andles seffec t untilli tdisappear sabov ea RSAT Lo f 80%. Considering the rate of discovery that results from the walking behaviour without the feedback of the motivational part, sizes of clusters can be found in which TW behaviour ismor e useful. Tortuous walk was of most use within clusterssmalle rtha n 30 cmdiameter .Th ehig h degreeo frecrossin g atvelocitie s of below 3cm/se c decreases the effectiveness of the search (area searched/dis tancewalked) .O nth eothe r hand, because ofthi sintensiv e search, a smallare a will be inspected very thoroughly. Of course, this is only profitable when prey isaggreggated . J H dislowrvïf 'f?? °u th,iS Walking Pattern can be estima*d by simulating the b tedJZ ru bCetle at different walkinS sPeed*a« dwit hrandoml ydistri - Z ZZl A °UlCOmeS °f theSe simulations can be compared with estima- urnnr^f ™* ** Skelkm formula (ChaP*r 1-D, where the effect of So smS-m"7? ^i Sn0 t included The differences betweenth e heeffect nfr, ancLf calcula^n with this formula gives an estimate for thCPath thC m re reCr0SSingS £lowe lAttïïA*- icmveness. ine effectivenes« s isestimate ' d by° dividing thesimu ^- 174 WageningenAgric. Univ. Papers 93-5 (1993) Efficiency of walking depending on walking velocity 1.00 0.90 0.80 s 0.70 © E id 0.60 ^CS Q. 0.50 >O . 0.40 'o H— eg 0.30 0.20 0.10 0.00 walking velocity (cm/sec) FIG.4. 1 Searchingefficienc y parameter(E ff)calculate dfro mresult so fth estochasti csearchin gmode l andth eSkella mmode l(se etext )offer s acorrectio nfacto r for thewindingnes so fth ewalkin gtrack . lated results by those calculated with the Skellam formula. This is illustrated in fig 4.1,whic h shows that the effectiveness of the walking pattern depends on the speed of walking.Therefore , the efficiency of tortuous walk isver ylow . That, nevertheless, it isprofitabl e in clustered prey distributions must beattri buted wholly to the compensation by the increased time spent mpre yclusters , onlythe ndoe si tresul ti na highe rprédatio nrat ean di na highe reg gproduction . Whenn omotivatio n isinclude d Skellam'sformul a providesa neas ywa yo t esti matingdiscover y rates,bu tfo r thebeetl ei thighl yoverestimate sth ediscover yrat e below a speed of 3cm/sec .Thi s effect shows that Skellam's formula can onlyb e used for rather straightwalkin gpatterns ,unles sa necessar ycorrectio n lor«cross ing,dependin go nturnin grat ean dthu so nspeed ,i sincluded .Th esecon drestnctio n istha ti tonl yca nb euse dfo r theestimatio no fprédatio nfo r periodswit hconstan t behaviour,becaus echange si nbehaviou rar eno tinclude di ni t When walking behaviour iscouple d to motivation itma y beconclude d that the searching behaviour of P.coerulescens is adapted to various type«of prey distribution, buttha t itshow sit sgreates t profitability atoveral llo wpre ydensi ties with aggregated prey. Especially when the prey is small, i.e. 5-10/ . oi the maximumgu tsize ,tortuou swal ki sver y profitable. 175 WageningenAgric. Univ. Papers93-5 (1993) But how will the situation be in the field with varying temperatures, rain, and varying structures of both soil surface and vegetation? Walking velocity ispositivel yrelate dt otemperatur e (Mossakowski &Stier , 1983). Ifth erelation ship between velocity and turning rate remains the same at different tempera tures, the model takes care of the effect of fluctuating temperatures. But if the relationship changes this has to be carefully studied before reliable statements about theth efiel d situation canb egiven . The influence of soil surface structure and vegetation was only incorporated to a small extent into the experiments. Dense vegetation and a rough surface hamper walking speed and increase the turning rate so that these may deviate alo tfro m therelationshi pestablishe dexperimentall ybetwee nvelocit yan d turn ing rate. On the other hand, the agreement between the dispersal found in the field (Baars, 1979)an d that found by simulation indicates that thiseffec t could beles simportan t thantha t ofth etemperature . Bysampling ,w eca n estimate prey density and prey distribution in the field, but what we assess, may differ completely from what the beetle experiences. Alsobetwee nvariou spre yspecie sdifference s inavailabilit ywil lb ever y difficult to assess,i fno t impossible. Thismake si t difficult tomak e adirec t comparison between the results obtained by simulation and those estimated from the field, andals ot opredic tprédatio nrate si nrelatio nt o'real 'pre ydensitie san ddistribu tions. However, a rough estimate of the total prey situation may be obtained using the state variables of the beetle, such as weight of the adult beetle and number of eggsi n the ovaries, to calculate at which overall prey consumption the values of these state variables can be reached. The mean and variance of theseindividua l statevariable so fth ebeetle si nrelationshi pt oth elocalit ywher e theywer ecaugh trepresent s thefoo d availablea ttha tparticula r timean dplace . The variation in beetle weight in thefield ma y thus give an indication of prey consumption and consequently of prey availability and prey clustering. Prey quality is an essential element in food availability as it is difficult to consider apart. Buti t may obscure theinterpretation s ofth ebeetl eweight , because prey quality influences the motivation and eggproduction . Nevertheless, the model may beuse d as atoo l toillustrat e howth edifferen t prey densities and distribu tionsle dt oth edistributio n ofth einterna lstate so fth ebeetle si nth e field. 4.1.2 Theeffect oflocomotory activity Two factors significantly influence the locomotory activity, namely tempera ture(Thiele , 1977),an d thehunge rleve lo fth ebeetle .A sth elocomotor y activity of the beetle decreases like a hyperbole with the increase of the satiation level, thus decreasing strongest at low satiation levels, this points to an adaptation to clustered prey. Bydecreasin git slocomotor y activity after consuming a prey (even a small one), the beetle stays longer in a location profitable for feeding. While resting it digests the prey and produces eggs of it. In combination with the slow and tortuous walk this is highly profitable. In contrast, long periods of locomotory activity together with high speed walking during periods of hungerincreas eth echanc eo ffinding place swher efoo d ismor e abundant. *' " WageningenAgric. Univ. Papers93-5 (1993) In the experiments, locomotory activity differed highly between individuals. This variation was strongly correlated with eggproduction . Because high egg production resultsfro m ahig hintak eo ffoo d andit srapi d andefficien t conver sion, it may be hypothesized that the relative rate of gut emptying (RRGE) andth eefficienc y offoo d conversion(EFF )(Se eMols ,1988 )ar eth emos timpor tant variables on an individual level.Th eenerg y used by thebeetl e for wakin g depends on its locomotory activity and walking speed (Alexander et al 1977, Delcomyn, 1981, 1984, 1985, Heath et al.1982, Herreid et al., 1981) thus an increase ofactivit y and speed isonl yadvantageous ,i fi tenhance sth ediscover y rate of prey We have no information about the difference in energy usagebe tween high-speed walkers and intermediate-speed walkers. Respiration experi ments showed no difference in relative weight loss between starved and non- starvedbeetles ,s otha tthes edifference s mayb esmall .Eg gproductio n asa resul t of ingestion, digestion and respiration is a good measure of energy surplus Therefore it can be used to show the differences between the beetle ssearchin g effort inrandoml y and aggregated preydistributions . Because of differences in individual locomotory activity, we may also talk about 'active' and 'lazy' beetles as high and low eggproducer s ™^™£A 'lazy' beetlema y remain longer under thecove r oflitte r etcan d thu.my^have a lower chance of being victim to a predator. Different str^«f survival may be represented: a) Being active and thus ^^^^^^ extra prey and increasing eggproductio n but with a higher risk o bem*«o_ vexed by an enemy and being eaten itself, or b) being ^™^2^Ze- eggproduction ,bu thavin gth echanc eo fsurvivin glonger .Whic h °™^££ gS is most successful will depend on the prédation pressur e It ould also be hypothesized that 'lazy' beetles, because * a ^.^^^^^ surviveperiod swit h anextremel y lowpre yavailabilit y (duringa dr yspell )tha n 'active'beetles . Locomotory activity and temperature. rplatinnshio with To simule locomotory activ*^^Ä^intlsTcEir SCÄ (BaZ SStSSSZ reasoningca nb euse dt oge t anestimatio n ofthi srelationship . acüvity A1_ eetl a,y In the observations done at 12 Cth e b ™ , production still though locomotory activity was very low, Ceding and egg, prxd occured at alo wleve l(Mols , 1988). Therefore, not 12 but 10 Cwa s tob eth etherma lthreshol d for locomotory activity. temoeratures, the To estimate the maximum *«%W£™ fXX^ factor maximum locomotory ^^p^'^lîoty activity relative toth e ACTEMP wasintroduced .ACTEM P ^Jocom £e valueo fACTEM P= maximum locomotoryactivit ya t2 0 C,wlncbMg^ ^^ observationswer elacking .Theretor e tog s ^ ^ ^^ ty at other temperatures, weuse d the catcnes 01 p F WageningenAgric. Univ.Papers 93-5 (1993) whenn oyoun gbeetle semerge ,an d corrrelated them to air temperature (Baars, 1979).Th e catches at different temperatures were scaled to those of 20°C , and thusth eestimate so fACTEM Pwer eobtaine d(tabl e4.1) .A ttemperature sabov e 22° C pitfall catches decreased and above 30° C became zero. This is a rough estimateo fcourse ,becaus ew eonl yrelate d trapcatche st otemperature ,assum ingtha tothe rfactor s haveth esam eeffec t on activity. TABLE4. 1Relativ elocomotor y activity(ACTEMP )estimate d asa functio n oftemperatur e(degree s Celcius). Temperature ACTEMP Temperature ACTEMP 10 0 22 1.2 12 0.1 25 0.75 15 0.5 30 0.15 20 1.0 35 0 Observations showed that locomotory activity ofth ebeetle si n thearen a in the field almostdecrease d tozer owhe ntemperatur ewa snea rt oo rabov e3 0°C . Locomotory activity and pitfall trapping Another field of interest is the estimation of population density by means ofpitfal l trapping,wher eth elocomotor y activity ofa beetleplay sa n especially importantrole ;th enumbe ro fbeetle scapture dreflect s theirlocomotor yactivity . Asstate d earlier welearne d that the change oflocomotor y activity isgoverne d by temperature and by satiation level. Beetleswit h a high locomotory activity are caught sooner than beetles with a low one. Hungry beetles have therefore a higher chance of being caught by a pitfall trap than those who are full. In good feeding areas,pitfal l captures willunderestimat e therea lpopulatio n den sity, while in poor feeding areas they will overestimate it. This hypothesis is supported byChiverto n (1984),wh ofoun d thatsignificantl y morefemal eP.me- lanariuswer ecaugh t inplot streate d withinsecticide stha n inth euntreate d con trol plots. The females from the treated plots had a lower gut content than females from untreated plots. Estimations of state variables based on dissection of beetlescaugh t in pitfall traps, sucha sgu tconten t and thenumbe r ofegg si n theovaries ,bot h ofwhic h are highly related to how much food they can get, will severely underestimate thebeetle' sweight ,averag egu tconten tan d theaverag enumbe r ofegg snumbe r in the females of thepopulation . Estimations of the quantity of food available inth efield, base do nth econditio no fth ebeetle scaugh ti npitfal l trapsunderesti mate the real food situation. To get an impression of the real distribution of the different feeding conditions of beetles in a field population, the frequency distribution of the numbers caught over specific feeding conditions, needs to be corrected for their chance of being captured, which for hungry beetles is 5 timeshighe rtha nfo r satiatedbeetles . ' '° WageningenAgric, Univ. Papers93-5 (1993) 4.1.3 Theeffect ofsuccess ratio The success ratio for different kinds of prey, depends on the satiation level of the beetle As this ratio decreaseswit h increasing level of satiation it largely determinesth eshap ean dleve lo fth efunctiona l responsecurv e(especiall ywhe n prey handling time is relatively short with respect to the total searching time). Thisi sals ofoun d with otherpredator s (Fransz , 1974;Rabbinge , 1976; Sabelis 1981) The relationship between success ratio and RSATL is specific for each kind ofprey .Preference s for different kindso fpre yma yb efoun d bycomparin g the success ratio - RSATL curves, as these are hunger dependent. Thus, tor polyphagous predators the difference in the succes ratio -RSATL relationship between different kind of prey may explain the preference for particular kind ofpre ya t aspecifi c satiationlevel . 4.1.4 Theeffect of reaction distance . In the simulations, reaction distances are 1an d 2 cm The simulations show that in random prey distributions reaction distance plays a "bsümtrt, role because discovery rate is linearly related to it. When the prey distnbution is aggregated differences in reaction distance do not result in the same change fnS c8over;Îate. Simulations showed that doubling ^^J^*™ 1t o 2c m results neither in a doubling ofdiscover y rate (42 W'™"^^ of captures/day (17%).Whe n the prey isclustered , it »^^^^ beetle to increase its reaction distance to about the radius o the pr c\v«bn P.coerulescens is diurnal and hunts by eyean d it does M^ to °™^™ from a distance by olfactory queues. In preliminary expenments on a walking sphere it showed no reactions to a stream of air with JJffi^^. wMea nocturnal hunting species(Pterostichus madidus ) reacted ™™^h?™^ may have an effect on reaction distance in P.coerulescens, however, the ofa fe wexperiments ,giv en oreliabl eevidenc eo ft His . 4.2PREDATIO NAN DEG GPRODUCTIO N vioural components were i« prédationrat ei stake nint oaccount . .g ,ow Prédation and egg production are only hf^^J^ ^ £ found and preyi saggregated .Wit hmor ethan 1 P^ n0 " hypothesized that betweenaggregate d andrando mpre ydistributions , may ^ ^ WagemngenAgric. Univ. Papers93-5 (1993) predatory behaviour ofth e beetlei sadapte d to clustered prey occurring at low densities. (3) Belowoveral lpre ydensitie so f 1 prey/m2'th ebeetl ei smos tadapte d tosmal l prey clusters (up to 40 cm), resulting in higher prey capture, consumption and eggproduction . However, within this range of small cluster diameters the beetle can reach a similar rate of prédation and eggproduction . In the simulations the distance between the clusters decreases with the decrease of the prey density in the clusters, so that over this range of cluster sizes, differences in prey density and distance are more or less compensated for byth echang eo fth ebeetle' ssearchin g behaviour. (4) Although prey capture is always higher when the clusters are very small (< 10cm) ( fig. 3.15), this does not result in a higher prey consumtion and eggproduction .I nsmal lpre yclusters ,pre yi sencountere drapidl yafte r each other, therefore satiation isreache d very soon, and as a result only a small part of each captured prey is consumed. This decrease in prey utilisation hasa negativ efeedbac k oneg gproduction . Byit swid erang e ofbehavioura l reactionsi nrelatio n to therelativ e satiation level, the beetle is able to adapt to the prey distribution encountered. At low prey densities and small cluster sizes (smaller than 40 cm) a high locomotory activity, straight walk alternating with tortuous walk, are responsible for an optimal result. When prey density aswel l as cluster sizeincrease , intermediate walkreplace s straight walk more and more, locomotory activity decreases and tortuouswal kbecome sles simportant . It is of interest to compare this simulated behaviour with that found in the field byBaar s(1979 )fo r the same species.H eobserve d periodsi n whichbeetle s day after day covered long distances (straight walk) alternating with periods in which only short distances were covered. To a great extent this behaviour can now be explained by the relationships between behavioural components ofth ebeetl ean dit smotivation ;becaus ei nsimulation sth esam epatter ni sfoun d for lowoveral lpre ydensitie san daggregate dpre ydistributions . 4.3 DISPERSAL Inpoo r habitats,suc h asthos eo fP.coerulescens dispersa li simportant , lead ing to the exchange of individuals between subpopulations. From experiments and bysimulatio n welearne d howP.coerulescens ca ncop ewit h alo wpre yden sityi na mozai clandscap ewit halternatin gric h andpoo r preypatches . Bothfro m Baars'( 1979 )field experiment san dth eresult so fcalculation susin g walking behaviour components, such as velocity, turning rate and locomotory activity,w eca npredic t thedispersa l power ofthi s species. Linear displacement calculations agree rather well with Baars' field observations (Chapter 3.3.4). Dispersal isgoverne d bytemperatur e and food; temperature has a direct influ ence (Massakowski et al., 1983) on walking speed and locomotory activity (Chapter2.2) ,bu tals oa nindirec tinfluenc e viath erat eo fchang eo fth emotiva - 180 WageningenAgric. Univ. Papers93-5 (1993) tionalstate .Th erelativ eamoun t offoo d inth egu tha sa direc teffec t onwalkin g speed and locomotory activity. When the beetle isi n a prey cluster linear dis placement of the beetle isJo w(2- 4meter) ,outsid epre y clusters itincrease s and when nopre y isfound , daily distancesca nvar ybetwee n 17 and 24metres .Thi s high-speed walking behaviour may last only for a few days e.g. depending on temperaturefo r abouta wee ki nJune ,becaus eafte r thatperio degg sar eresorte d and the beetles become 'spent' (van Dijk, 1979) producing no more eggs for theres to fth eseason .Roughly ,thi simplie stha tdistance sbetwee ncluster smus t not be more than about 45metres . If there is food available between clusters, thedistance sma yb emuc hlarger . ., ,. c <. „<.*„,* Fieldwork and simulationsma yhel pt oderiv eguideline sfo r natureconserva tion topredic t for thisan d other speciesho wfa r theyca nwal kbetwee nsuitabl e pieces of landscape or habitats, and whether it is necessary to help»themL by constructing corridors or steppingstone sbetwee nsuc hareas .Suc h^ormatoo n can thus help to increase the attainability of suitable sites for certain species andincreas eexchang ebetwee n subpopulations. 4.4 COUPLING PRÉDATION TO POPULATION MODELS In predator-prey population models, the interaction between the growth of the prey population and the predator population isobtained Ib y the funcUond and numerical response of the predator to its prey Aceo^ ^ t° S° ™ (1949),functiona l responsei sdefine d asth enumbe ro fho» asuxesfJ £ atüutod per natural enemy (a predator or a parasitoid) as a function of hos^srty. Thus it describes the way a predator or parasitoid *g"^^Seï abundance ofit spre yb ykillin go rparasitizin gmor eo rfewe rpre ya si tbecome s respectively easiero rmor edifficul t to find predator/parasitoid The numerical response is defined as the reactio n °'* P ';ff ing tothechangingabundanceofthepreyby:(l)P^ whenth epre yi srespectivel yeasie ro rharde rt ofind an dt oconsume .W M g ingt oo r aggregatingi narea swit h^V^^ ^ if the eggs are laid in The functional response is also a numerical response it W gg or near ahost , asoccur swit h mostparasitoids , theadult so tw n a B sume the prey. In predator models, /^^ ^^^^<ïtural sys- of prey consumed into the number of offspring p^^dLtaa^ ^ terns,th e functional responsei sa commonl y^^^SoLit y below enemieso fcro ppests .Th efailur e ofnatura l^"^^t o pestdensit y theeconomi cthreshol d hasbee nassociate d ^^^^^^^àoeh et e which overwelms the enemies functiona and n« ^ ^ limitations al., 1985).Thi s may be due to the ^^^^^Z caseo fpreda - controlb yth ebeneficia lenem y(O'Neil , 1990). ^ WageningenAgric. Univ. Papers93-5 (1993) 4.4.1 Functionalresponse models Inpredator-pre ypopulatio n models,simpl edescriptiv emodel so fth e functio nal response are preferable as they are easy to understand and, unlike the sto chastic models, do not need much computer time. One may ask, what models are available to describe the functional response of a general predator like P.coerulescensappropriately , andi si tpossibl et oappl ythem ? Holling (1966) describes 3type s of functional response models for random preydistribution s(se eappendi xII) . Type 1response : When a predator kills a constant proportion of the prey the relationship between prey density and number of prey killed is linear until a plateau is reached were the number of successful attacks remains constant. The plateau represents the maximum prédation rate. That rate is physically determined. Type2 response :Jus t as in the type 1 response a saturation level is reached, but in a gradual way. This is probably the most widespread type of response. If we realise that a predator or parasitoid only has a limited amount of time, thistyp ei seas yt ounderstand .Som eo fthi stota ltim e(T )i sneede dfo r searching for prey while another part, collectively referred to as 'handling time', is used for the pursuit, attack and consumption of prey. At increasing prey densities (N0) the time available for searching (Ts) decreases as more time is used for thehandlin g ofpre y(TJ .Thi slead st oHolling' s 'dis cequation 'fo r thecalcula tiono fth enumbe r ofpre ykille d(N e) Ne = a'*T*N0/(l+a'*Th*N0) a'= thesearchin gefficienc y orrelativ erat eo fsuccessfu l attack. Hollingassumpe s thatwhe na predato r orparasitoi d searchesfo r preyi tdoe s not change its behaviour during the whole searching period. The number of prey encountered is an instantaneous rate which only holds for short periods when the prey density remains constant. In case of predators, this is not true becausewhe npre yi skille di ti sremove d from thepopulation . Incas eo fparasi - toids, it is assumed the parasitoid searches in such a way that a host is only encountered once, thus the number of prey encountered equals the number of prey parasitized. This only holds for a short observation period. It can also besai d that theparasitoi d searches systematically. What wese ei nmos texperi mentsi stha t parasitoids do not avoid previous parasitized hosts thus that they encounter a host more than once. To account for this effect, the approach of Nicholsonan d Bailey(1935 )ca nb euse d(se eRogers , 1972).The yassum e that: - Searchingi srando m anddoe sno tchang edurin gth eobservatio n period, thus eachpre yha sa nequa lchanc eo fgettin gparasitize d ina certai n period. - Parasitoidsd ono tdiscriminat ebetwee nparasitize d and unparasitized hosts. - Parasitoidst ono tinterfer e witheac h other. - Theparasitizatio n timei szer o( i.e .n ohandlin gtime ) then the chance of a host being encountered is a Poisson process. The chance I°^ WageningenAgric. Univ. Papers93-5 (1993) of having no encounters ( and thus no parasitization) equals the zero term of the Poisson distribution. Including the 'Disc equation' in the Nicholsons competition equation leadst oth e'rando mparasite ' ort oth e'rando m preda torequation' .(Se eappendi xII) . Type3 response :I f apredato r reactst o anincreas ei npre ydensit yb yincreas ing the proportion of prey it kills over a specific range of prey densities, this resultsi na sigmoi d curve.Thi styp eo frespons ei scause db ya numbe ro fpreda torycharacteristics ,an di tma yb efoun d inpredator swhic har ecapabl eo flearn ing. pyreyTfS an aggregated distribution, resulting in ^Äg for them in an adapted way. In functional response m<^J^*™ thezer o term ofth ePoisso n distribution thezer oterrr, io fth eneg a rvebmonad distribution is used for expressing theproportio n of prey that escapes from prédation(Crawley , 1992): P0=(l +/^ ) . mnatm„ narameter thus 1-Poi sth eproportio n thatwil lb epredated ,k i s ^^J^^SS Ask gets large (> 10 )th e negative binomial ?PP™^^°™E f^Ily tion. For small values of k « 1)th e distribution 0^f^^ZfZ PrT^ty^ sible to use these models to describe the same ^^^SdU time in thiswa ydifferen t estimates ofth e«^^^^ ^ hat the predator will be obtained. This is because ^ .^^^Ä reiarching searches systematically for itspre y and doesno t ^f ^^^tthepredator partofthelrena, whilst^ searches at random. The values of fhe parameters a ^ ^ ^ ^ regression of the experimental results. AKüougn i imentany. Itma y getint o troublewhe nth erea lhandlin gtim e^^^Xc h shows that appear to deviate substantially from ^ calcula ed value wh ^ searching efficiency (a') ^^XoItX^ does not searches meant to. This may imply that the predato ^ iyit changes wlth randomly, that Th is not constant, that the Jj^J density etc. m prey density, or that the searching veorange s w P y functional such cases it isbette r not to estimate a ^J^^^fo experimental response experiments, because they apply ^£eto^*P™* chan8eS- K conditions. When co^^^^^J. of the predator isbette r to estimate their value from behaviour parasitization. orparasitoi d duringth eproces s°'*^^^^ ^ JL^, especially Lmthestochasticsimu ations^^^orvc. can be constructed at low prey densities, different Holling P ^ WageningenAgric. Univ. Papers93-5 (1993) for eachpre ydistribution .Usin gth enegativ ebinomia lzer oter mfo r aggregated prey in the Random predator equation model seems not to be appropriate, becausei t results in a lower prédation when prey isaggregate d than when prey israndoml yd itrib uted .Thi sresul ti si ncomplet econtradictio nwit hth estochas tic simulation experiments of P. coerulescens (Chapter 3),wher e it was found that the functional response of the beetle, which, both for random and aggre gated prey distributions looks like a Holling II response curve,i ssteepe r when preywa saggregated,an d thusprédatio nhigher , than wheni twa srandoml ydis tributed. Therefore, using the (1-P0) term of the negative binomial, seems not to be appropriate for estimation ofprédatio n in aggregated prey distributions, becausechange si n behaviour areno t accounted for. Thisagree swit h Murdoch etal .(1989,1990 )wh osay ,tha trearrangemen t ofpredator st opre yaggregation s during the season makes the functional response curve steeper. That result is good for biologicalcontro l but notfo r thestabilit y ofth epredator-pre y system. Foraggregate ddistribution sa solutio nca nb efoun d bydividin gth esearchin g time into periods when the predator is either present inside or outside a prey cluster, becauseo fpossibl e changesi n behaviour ofa predator/parasitoid . This mostly resultsi n complexmodel sinvolvin g thebehaviou r ofbot h predator and prey. 4.4.2 Frombehavioural components to functional response To include real behavioural components in the functional response models, Skellam'sextente dformul a for calculationo fth eprédatio nrat eoffer s asolutio n (Chapter 1.1;Sabelis , 1981).Thi s model uses behavioural components for the calculationo fprédation ,whic hca nb emeasure d separately,suc has :th ewalkin g velocity, the effectiveness of walking depending on windingness, locomotory activity,reactio ndistanc ean d successratio ;al li nrelatio nt oexterna lan d inter nal conditions. If the handing time (Th) is included in the searching time (Ts) theequatio nca nb eextende dto : Npred= T s/{l/(a'*N0)-Th} a'=V*D**En*Sr Ifth ehandlin gtim ei sinlude di nth erestin gtim e Npred= a'*N 0*Ts= a'*N 0*A*T Theassumption sare : - Thepredato rwalk srandoml ywit hrespec tt oth epre y - Thevelocitie so fpre yan dpredato rar emutuall yindependen tan dth eresultan t velocity isV = y(V 2pred+ V 2prey).I f thisi sno t the case (for example when thepredato r follows thetrai lo fa prey )th eformul a isno t applicable. - Thebehaviou r doesno tchange . If the handling time is difficult to measure and relatively short with respect to the exposure time (T), it iseasie r to measure the active searching period Ts ' °4 WageningenAgric. Univ. Papers93-5 (1993) directly and ignore Th.I f Thi srelativel y long(an d therefore strongly influences Ts)i ti sbette r tomeasur eboth .I npredator shandlin gtim ema yb ever yvariabl e as it may depends on satiation level and prey size (Mols, 1988) and sometimes also ona digestiv epaus e (Holling,1966) . For inclusion of specific searching behaviour, like tortuous walk, searching timeshoul d bedivide dint o periodswit han dwithou t tortuouswalk . As these are instantanious rates they can be substituted in The Nicholson &Baile yequatio n toge ta Rando m predator orRando m Parasite equation. Then weobtai n equations in which behavioural characteristics are included, thus the vague variable 'a" isno w replaced bybiologicall y clear variables. The problemremain stha tpredato rbehaviou r(especiall ywalkin gspeed ,locomotor y activity andpre yacceptance )change saccordin gt oloca ldifference s inpre yden sity. Therefore this approach is only be applied to short periods when it can be assumed that behaviour isconstant . A disadvantage isals o that population models including these functional response models with changing behaviour cannot besolve danalyticall ybu t onlynumerically . 4.4.3 From individualpredatormodels topopulation models The stochastic searching model (Chapter 3)ma y be useful for analysing the effect of walking behaviour at different prey densities and prey distributions at theindividua l predator level.Th emode lca nb eextende d topopulatio n level bybringin g inmor e beetlesan d bymakin g thestationar y preydistributio n and prey density dynamic. This willlea d to a complete stochastic model which can be used to estimate the effect of the beetle as acontro l agent of a specific pest, for example, aphids in cereals. However, many simulation runs and a large amount of computer time areneeded ,du et oth estochasti cnatur e ofth emode l for walking behaviour and the small time step (2 sec). ^f^*«^^ theaverag eprédatio nvalue sfo rindividua lbeetles ,calculate dwit hthestochatfr c model as input for the predator-pest model; assuming that the oucomefrom average input values is identical to the average outcome ™*™£^^ values This is generally only true when the variation m mput .P«;ersJ smallo rwhe nth emode lha slinea rrelationship sbetwee nit sva™^ . H^. therei sa larg evariatio nbetwee nindividua lbeetle s «P^^»»^ ties, while several relationships (e.g. the functional response) n lJe m°del are non-linear and depend on prey distribution. Thus average cannot be^used as inputs in the simulation. A solution for this problem is °^*^™ simulation (Fransz,1974;Rabbingeetal,1989).The^^^ is divided into three classes according to the types ofwalkin g ^™°uM class is split into two subclasses, for beetles ins.de and ^^V^^S 185 WageningenAgric. Univ. Papers93-5 (1993) residence timeo f predator inpre y cluster Inrelatio n towalkin gspee d 120 I I cluster radius n —+— 10 cm 100 - A- 20 cm —o— 40 cm 80 •• • • • 80 cm a> —A- 160 cm E 60 \ \ —•— 320 cm ü C \ velocitycm/se c FIG. 4.2 Residencetim eo f thebeetl ei na pre ycluste r dependingo nwalkin gspee d and preycluste r size. Each timestep ,th epopulatio n model isru n for eachclas so fbeetle s separately andbeetl enumber si neac hclas sar eadjuste d accordingt omotivatio n dependent behaviour and the residence time in the cluster. When beetles (or fractions of the beetle population) shift from one class to another also all contents of the statevariable s ofth emotivationa l part also shift toth enex tclass ,an d are aver aged with those that are still there (fig 4.3). In this way, a stochastic model of anindividua l beetlei sreplace d bya deterministi cmode li nwhic hth emotivatio nal state of all beetles in a classchange s by the average state in that class.Pre y numbers may be distributed randomly or clustered and can be calculated with a population growth model. For example an aphid growth model in cereals (Rabbinge et al., 1979, Rabbinge & Carter, 1984, Carter, 1985). Preliminary simulationswit h thismode l showtha t Pterostichuscupreus, thedominan t cara- bid species in cereals on clay soil, which is very closely related, and similar in size to P.coerulescens, may have a considerable impact on aphid population growth. The relationships found for P.coerulescens were used in the model, therefore theconclusion swer ebase d onth eassumptio n that P.cupreus behaves similart oP. coerulescens. 186 WageningenAgric. Univ. Papers93-5 (1993) outside outside outside prey cluster CIDJ «*•»•"— prey cluster .\/ - /\ intermediate walk tortuous walk fast walk / >> ST/ > 2S± < \Lv * > inside inside inside 1 prey cluster prey cluster < V' K- - /\ tortuous walk inermediate walk fast walk K7 A / \ / \ \z/^ state variable v v, rate variable Ä ^ ,. ,, ,,,„„ „f waikine behaviour and being F.o. 4.3 Division of the states of the beetle ^^S^o'lüon. insideo routsid ea pre ycluste ruse di nth ecompoun dmode l 4.5 MBTHOOOLOCV O, -VALUATIOH OFPOTENTIA L PRBOATORS FOR BIOLOGICAL CONTROL The relationships found i*/-^ and behaviour andth e prey density ^^Ä^«»» Aould becar - obsQ a list ofrecommendation s onho w ™T*ff^Ze in biological control redat f logicalpropertie so fa P ° n , size and roomi nth eabdomen , tiveo rnot) , c) Gutemptyin grate - ductive and non-reproductivestate . d) Metabolicneeds ,bot hi nrepro u ^ WageningenAgric. Univ. Papers93-5 (1993) e) Uptake and conversion efficiency inrelatio nt opre ytype . f) Eggweigh t 2. Forth eestimatio n ofsearchin gan dprédatio nrat eth efollowin g behavioural components arenecessary . a) Walkingbehaviou r (walkingspee d andturnin grate )an dduratio n ofspe cificwalkin gbehaviou r (e.g.intensiv e search) b) Relationships of behavioural components, like locomotory activity, succesrati oan dreactio n distancewit hinterna lvariable slik eth e satiation level. 3. Validation experimentsconcernin g themotivationa l part and the functional response. a) Independent egg production experiments under controlled food condi tions. b) For functional response experiments, the area of observation must be related to theradiu s ofactio n (walking distancepe r day)o f the predator. If thisi s not the case, border effects will strongly influence the outcome ofth eexperiments . c) The experiment must be long enough for the predators to adapt to the preydensit y and prey distribution such that feed back mechanisms show their effect. Historical effects like gut content, fat quantity, ovary size andnumbe ro fegg si nth eoviduc tstrongl ydetermin eth epredator ycapac ity (e.g. effect of egg load on the expansion of the gut). Not doing this overestimates the advantage of the predator. As the predator becomes older, the responses to internal and environmental stimuli may change, resultingi na differenc e inprédation . d) Experiments to find out thefunctiona l response ofa predator, especially atlo wpre ydensitie san dals owhe nth epre yi sclustere dnee dman yrepeti tions. To obtain confident averages the number of repetitions required is often so high that this is not practical, because of the time and space needed and above all the stochastic nature of thematerial . Nevertheless, ifthe yar ecarrie d out, resultswil lb ever y arguable.Functiona l response curves carried out with standardized predators only hold for that type of standardization, meaning that different standardizations result in dif ferent functional responses. The results of an experimentally established specificfunctiona l responseo fa predato r areonl yindicativ efo r itspreda tory capacity. Therefore simulation modelsincorporatin g the behaviour of the natural enemy may be a better tool for estimating its functional responses. 188 WageningenAgric. Univ. Papers93-5 (1993) ACKNOWLEDGEMENTS Thanks are due to R. Stouthamer, who as a student programmed the core of the searching part of the simulation model, to Prof. Dr. ir. R. Rabbinge for his stimulating discussions and encouragement during the long course oi the study to Dr. P.J. den Boer for his enthusiastic and critical comments on the manuscript, to Dr Th van Dijk for his energetic and useful discussions during the experiments and to Mr. P. Kostense for drawing some of the illustrations^ I am very grateful to Mrs Claire Hengeveld who improved the English text of thegenera ldiscussion . 189 WageningenAgric. Univ. Papers93-5 (1993) REFERENCES ALEXANDER, R.MCN., G.GOLDSPINK, eds., 1977. Mechanics and energetics of animal locomotion. Chapman and Hall, London, 247pp . . ARDITI, R., 1983.A unified model of the functional response of predators and parasitoids. J. Amm. Ecol. 52,293-303. , ..„..,.. BAARS, M.A., 1979. Patterns ofmovemen t ofradioactiv e carabid beetles. Oecologia (Berlin), 44, BAARS, M.A. AND TH.S. VAN DIJK, 1984. Population dynamics of two carabid beetles in a Dutch heathland. II. Egg production and survival in relation to density.J . Anim. Ecol.,53, 389-400. BAARS M A & TH.S. VAN DIJK, 1984.Populatio n dynamics of twocarabi d beetlesi n a Dutch heath- land. I. Sub-population fluctuations in relation to weather and dispersal. J. Anim. Ecol.,53, -37*: TOO BARTON-BROWN L. &D . R. EVANS, 1960.Locomoto r activity of the blowfly asa functio n of feeding and starvation. J. Insect Physiol.,4,27-37 . .„..../• BAUER, T., 1975.Zu r biologie und autökologie von Notiophilus biguttatus F. und Bembidionforami- nosum Strm. (Coleopt. Carabidae) alsbewonde r ökologisch extremer Standorte. Zool. Anz. Jena, BAS,3T!,"31981. Prey capture and structure ofth e visual space ofa n insect that *™*JW»&t on the litter layer (Notiophilus biguttatus F., Carabidae, Coleoptera). Behav. Ecol. Soc.ob.ol.,8, 91-97 BAUER, T., U. BRAUNER, E. FISCHERLEITNER, 1977. The relevance ^^^.^^21 prédation and activity ofvisuall y hunting ground beetles (Coleoptera, Carabidae). Oecologia Bns°s,6cï!'l971. The aggregation of species within spatial units. In '^^fg' ^ ^ eds. O.P. Patil, B.C.Pielou ,W.E . Waters), 311-335.Pennsylvani a State Statistical Series. BATCHELET, E., 1981. Circular statistics in biology. Ac.Pres sInc . London Ltd,372!p p BRUNSTING, A.M.H., 1983. Population ecology of Pterosnchusoblongopmctatus F life cycle, loco motion and density regulation. PHd Thesis,Vrij e Universiteit te^^^. ^ heter. BRYAN KM &SD WRATTEN 1984.Th eresponse sofpolyphagou s predators topre yspatia l neter ÄÄ«w «ast ^Iinidbeetle st 0thei rcerea laph 'dPrey -E ÄS Simulation modelling of the population dynamics of cerea!aphid , Biosystems CHAPMAN'RF., 1954. Responses of Locusta migratoria migratorioides (R. and F.) to light inth e 6 3 CSRÏ i £ C0CKRELL, 1978.Predato r ingestion rate and its bearing on feeding time and the theory of optimal diets.J.Anim . Ecol 47(2),™;™ . . thdr p In 'Natural Ene- and Pharmacology', (ed. G.A.Kerkut, L,I. uiiu« ;, 191 Wageningen Agric. Univ.Papers 93-5 (1993) DELCOMYN, F., 1985. Factors regulatinginsec t walking.Ann . Rev. Entomol.,30,239-56. DESENDER, K., J.MERTENS, M.D'HULSTER & P. BERBIERS, 1984. Diel activity patterns of Carabidae (Coleoptera) and Collembola in a heavily grazed pasture. Revue d'écologie et biologie du sol, 21,247-361 DIXON, A.F.G., 1958.A study ofsearchin g behaviour of certain insects feeding onaphids . D.Phil . Thesis, Oxford ENDNEY,E.P. , 1937. Astud yo fspontaneou s locomotoractivit yi n Locustamigratoriamigratorioides (R. andF. )b y the actograph method. Bull.Ent . Res.,28,243-278. ELLIS, P.E., 1951.Th emarchin g behaviour of hoppers of the African migratory locust {Locusta migratoria migratorioides R.e nF. )i nth e laboratory. Anti-Locust Bull.7 ERNSTING,G. , 1977.Effect s offoo d deprivation and typeo fpre yo nprédatio nb y Notiophilusbigutta- tus F. (Carabidae )o nspringtail s (Collembola). Oecologia 31,13-20. ERNSTING, G., 1978. Prédation of springtails. Phd Thesis VU Amsterdam, Drukkerij Ernsting, Wageningen, 88pp. ERNSTING, G.& J.A . Isaaks, 1986.Foo d intake andphysologica l time ina carabid beetle. In 'Proc. 3rd European Congress of Entomology part 2', (ed. H.H.W. Velthuis),255-257 . EVANS, H.F. , 1976.Th e seurching behaviour of Anthocoris confuses (Reuter) inrelatio n to plant density and plant surface topography. Eeol. Ent. 1,163-169. EVANS, M.E.G., 1977. Locomotion in the Coleoptera Adephaga, especially Carabidae. J. Zool., Lond., 181,189-226. FRANSZ, H.G., 1974.Th efunctiona l responset opre ydensit yi na n acarinesystem .PUDOC , Wagen ingen, 149p . GREENSLADE, P.J.M., 1963.Dail y rhythms of locomotory actvity in some Carabidae (Coleoptera). Ent. Exp. Appl.,6,171-180. GRIFFITHS, E.,S.D . WRATTEN &G.P . VICKERMAN, 1985.Foragin g byth e carabid Agonum dorsale in the field. Ecol. Entomol.,10,181-189. GRÜM, L., 1966.Diurna l activity rhythm of starved Carabidae. Bull.Acad. Pol.Sci. 14,405-411. GRÜM, L., 1971.Spatia l differentiation ofth e Carabus L. (Carabidae, Coleoptera) mobility. Ekol. Pol., 19,1-34. HASSELL, M.P., 1978. Thedynamic s ofarthropo d predator-prey systems.Princeto n University Press, Princeton, New Jersey, 237pp. HASSELL, M.P., 1982.Wha t issearchin g efficiency?. Ann. Appl. Biol.,101,143-203. HASSELL, M.P., J.H.Lawton, &J.R . Beddington, 1977. Sigmoid functional response by invertebrate predators and parasitoids.J .Anim . Ecol., 46,249-262. HEATH, J.E& M.S . HEATH, 1982.Energetic s oflocomotio n inendodermi c insects.Ann . Rev. Physi- ol.,44,133-143. HENGEVELD, R., 1980.Polyphagi , oligophagi and food specialisation in ground beetles (Coleoptera, Carabidae). Neth.J .Zool. , 30(4) , 564-584. HERREID, CF., D.A. PRAWEL &R.J .FULL , 1981.Energetic s ofrunnin g cockroaches. Science 212: 331-33. HEYDEMANN, B., 1955.Zu r Systematic und Öcologievo n Pterostichus cupreusun d coerulescens (Col. Carabidae). Bonn. Zool. Beitr., 6,235-239. HOLLING, C.S., 1966.Th e functional response ofinvertebrat e predators topre y density. Mem.Ent . Soc. Can., 48,86pp. KAREIVA, P. & G. ODELL, 1987. Swarms of predators exhibit 'preytaxis' if individual predators use area restricted search. Amer. Nat. 130,233-270. KEGEL, B., 1990. Diurnal activity of Carabid beetles living on arable land. In The role of ground beetles in ecological and environmental studies' (ed. N.E. Stork), 65-75. Intercept, Andover, Hampshire. LAROCHELLE,A. , 1974a. Carabid beetles (Coleoptera, Carabidae) aspre y ofNort h American frogs. Gt. Lakes Entomol.7,147-148. LAROCHELLE, A., 1974b. The American toad aschampio n carabid beetle collector. Pan-Pacif.Ento- mol. 50,203-204 LENTEREN, J.C., VAN& K. BAKKER, 1976. Functional responses in invertebrates. Neth. J. Zool., 26(4), 567-572. *° 2 Wageningen Agric. Univ.Papers 93-5 (1993) LUFF ML , 1978.Die l activity patterns of some field Carabidae. Ecol.Entomol., 3,53-62 . MILL'S, N., 1982. Satiation and the functional respons: a test ofa new model. Ecol. Entomol.,7 , 305-315. , . , , MOLS PJ M 1979 Motivation and walking behaviour of the carabid beetle Pterostichus coerules cens L. at different densities and distributions ofth e prey. Misc. papers LH Wageningen,18 , 185-198. , . MOLS, P.J.M., TH.S. VAN DIJK & Y. JONGEMA, 1981.Tw o laboratory techniques toseparat e eggs ofcarabids from a substrate.Pedobiologia , 21,500-501. MOLS, P.J.M., 1983.Simulatio n of themotivatio n and eggproductio n of thecarabi d beetle Pterosti- chuscoerulescens(L). Report 4th symposium on carabids 1981,35-43. MOLS, P.J.M., 1986.Prédatio n in the carabid beetle Pterostichus coerulescensL . Report 5th sympo sium on carabids 1982.Warsa w Agricultural University Press,49-58 . MOLS, P.J.M., 1987. Hunger inrelatio n tosearchin g behaviour, prédation and egg production of the carabid beetle Pterostichus coerulescens L, Results of simulation. Acta Phytopathology et Entomologica Hungarica, 22,187-196. WJI^I,»,™,/,' MOLS.P.J.M, 1988. Simulation conger feeding and eggproductio ni n the car^ chus coerulescens L. (= Poecilus versicolor Sturm). Agricultural University Wagen.ngen Papers MONTFÔÏ MA'.J. VAN & A. OTTEN, 1976. Quantal response analysis enlargement of the logistic model witha kurtosi s parameter. Biomedische Zeitschrift, 18(5),37 -38U. MossAKOWSKi,D .& J.Stier , 1983. Vergleichende Untersuchungen zurlaufgeschw.nd.gke. t der Cara biden. Report 4th Symp.Carab. 1981,19-33. JW«;,™« in hinlnmcal MURDOCH, W.W., 1990. Ecological theory and biological control. In'New directions in biolog.cal control', (eds R.R. Baker and P.E.Dunn), 49-55. Alan R. L.ss, Inc. New Yorfc MURDOCH, W.W., J. Chesson & P.L.Chesson, 1985.Biologica l control m theory and practice. Am. 4 36 MuRtSw:W & A.Steward-Oaten, 1989. Aggregation by parasitoids and predators: effects on equilibrium and stability. Am. Nat 134 2 288-310 sion of degree ofhunge r and NAKAMURA, K.,1972 . The ingestion in Wolf spiders II. The express on oi aeg amount of ingestion in relation to spiders hunger. Res. Popul. Eco ™W*>- bioloEical control 0'NFIL,R.J., 1990.Functiona l response of arthropod predatorsan d i^ of insect pests in agricultural systems. In < New directions in biological control, (eds K.K. «a and P.E.Dunn), 83-96.Ala n R. Liss,Inc .Ne w York. „nnnlations Part I Proc. Zool. NICHOLSON, A.J. &V.A . BAILEY, 1935. The balance ofanima l populations. Part.1 . Soc. London., 1935,551-598. „MA herrie(Pterostichus melanarius)to\low- PLOTKIN, H.C., 1981. Changes in the behaviour ofa carabid beetle (Pterostwn ing exposure to food and water. Ann. Behav 29, 24>tz:>i. Syst, 15,523-575. P™JG!H.. 1984.Optima l foraging;theory: a^^^^fÄievie w of theo* PYKE G.H., H.R.PULLIHAM & E.L.CHARNOV, 1977. Optimal toraging, a and tests.Quart . Rev. Biol. 52,137-154. -j„m:.. PI IDOC Wageningen, 228p. some postage», predator*i n relation to aphid denoty ,n cool »Ids. «PP a A subsystem ofEPIPRE ,p p 242-253.I n Pestan d ™ °& . : h wiley & Sons. mode.J(ed. ^«^""SÄi ^ «ment '" RABBINGE R., S.A. WARD & H.H VAN LAAR teas;, i™ crop protection. PUDOC, Wageningen. Ecol.,41,368-383 . ROGERS D.J., 1972.Rando m search and insect VW**«£™ ^fusing phytoseiid predators. SABELis, M.W., 1981. Biological control «J y°^%^™ " ' Part 1.Agricultura l Research Report, 910,PUDO C wag * Naturaiist 116,281-290. S.H,A. , 1980.Optima l foraging: partial consumption of prey. American ^ Wageningen Agric. Univ.Papers 93-5 (1993) SIROTA, Y., 1978.A preliminary simulation model of movement of larvae of Culex pipiens molestus (Diptera:Culicidae) (experimental studies on the dispersal of insects,II). Res.Popul.Ecol., 19,170-180. SKELLAM,J.G. , 1958. Random dispersal in theoretical populations. Biometrica 38,196-218. SKELLAM, J.G., 1958. The mathematical foundations underlying line transects inanima l ecology. Biometrics,14 , 385-400. SOLOMON, M.E., 1949.Th e natural control of animal populations. J.Anim. Ecol. 18,1-35. SOUTHWOOD, T.R.E., 1966.Ecologica l methods. Methuen, London,391 p. THIELE, H.U., 1977.Carabi d beetles in their environments. Springer Verlag, Heidelberg, 369pp . THIERY, D. & J.H. VISSER, 1986. Masking of host plant odour in the olfactory orientation of the Colorado potato beetle. Entomol. Exp. Appl. 41,165-172. WERF, W.VAN DER,W.A.H . ROSSING, R.RABBINGE, M.D. DEJON G& P.J.M . MOLS, 1989. Approaches to modelling the spatial dynamics ofpest s and diseases.I n 'Parasitis 88, Proceedings ofa scientific congress, Barcelona, 25-28 October 1988',(R . Cavalloro and V. Delucchi (eds)), Boletin de Sani- dad Vegetal, Fuera de Serie,n o 17,549 pp. WILLIAMS, G., 1959.Seasona l and diurnal activity of carabidae, with particular reference to Nebria, Notiophilus and Feronia. J. Anim. Ecol.,28 ,309-330 . 194 Wageningen Agric. Univ. Papers 93-5 (1993) APPENDIX ITH E SEARCH MODEL APPENDIX I Simulation ofwalkin gbehaviou r anddiscovery . The direction of walking is calculated by drawing randomly adirectio n out of the turning rate distribution. Each timestep this isdon e again and the next angle isadde d to the former direction which then gives the new direction. This is accomplished by drawinga rando m number out of a uniform distribution between 0 and 1. P = RAN(IS) ISi s asee dnumbe rneede dfo r therando mgenerator .P i suse di nth efollowin g equation: A= AV+ SIGMA *(P**KURT - (1 . -P) **KURT)/KURT Whichi s theTuke ydistributio n (Montfort etal . 1976) giveni n chapter2 Theangl ei s nowadde d toth eforme r directiongivin gth e new directiono tth ebeetle . DIR = DIR + A Asth espee do fth ebeetl ei s knowni ti s possiblet ocalculat e thene wcoordinate so fth ebeetl e(XP,YP ) XP=XP + COS (DIR) *V YP=YP + SIN (DIR) *V The moment the beetlereache s theborde r of the field itwil lfollo w itwheo,anglesar echose n that shouldlea dth ebeetl eoutsid eth efield, othe rangle slea dth ebeetl ebac kint oth efield agam . Durationo ftortuou swalk . . „,„„„„ in«, sneed If none w a Just after consumption of a prey, the beetle resumes searching ^^J^^simullilion. prey is discovered the speed increases gradually to ^ ^ *™\f "^^ of tortuous In Llity this will be the speed belonging toa specifi c ^[f^^Su^TspL equals walk isthu s the time from theen d ofconsumptio n whensearchin gi^^ ^ ^"ing ratedistribu - thevalu ebefor eth epre ywa s discovered. Paia^ tion changes from wide to narrow, as the speed determines the SIGMA and Kurtos ofth eTUKE Y distribution. Preydistributio nan dpre ydiscovery . , , .• . v varv from random In theprogra m thedistributio n of the preyca n bearrange d su h hat ^mayv ^ ^ to very aggregated. This done \^XKO^^T^TZ clusters can begive n numbers of prey inth e cluster, the number f duste^ and ^ ^^ ^^ a specific value. The immobile preys are located in Nt aus• • ^ Therefore> NC*IC preys through themode lfield. Withi n acluste r ICprey sareran a , . (expressed incm.) , are present in thefield. Th e modelfield i sa squar ewit h sides of UNO leng Thecluster sar ecircu lwit ha diamete r ofCLUN11 . 195 WageningenAgric. Univ. Papers93-5 (1993) Thedistributio n ofpre ythroug h thefield ca nb earrange d asfollows : Random distribution: 1)Pu t onecluste r in thefield wit h the same diameter asth efield lengt h and place allth epre y randomly intha t cluster or 2)tak e asman ycluster s aspre y areneede d and place onepre yi neac hcluster . Aggregateddistributions :Aggregatio no fpre yincrease sb ybot hdecreas eo fth enumbe ro fcluster s per field and by decrease of the cluster size and consequently increase of the number of prey per cluster. Procedureo fpre ylocation . First the centers of the clusters are randomly placed in thefield, an d stored in two arrays. The X(L) and Y(L) memories,wit h the Lbein g a multiple of IC, and in the CCX(I) and CCY(I),wit h Irunnin gfro m 1 toNC .Th ecoordinate sstore di nth elatte rarray sar euse dt odetermin eth edistanc e from the beetle to the cluster centre. This procedure is needed for cluster scanning. Obviously it isles slaboriou s iffirstly th eneares t cluster isdetermine d and subsequently thepre y of that cluster have to bescanne d than to scann allth eprey si nth etota lfield eac h timestep .T odetermin ewhic h cluster is nearest, it is necessary to identify that cluster. The centrally located prey of a cluster is used asidentificatio n mark. Subsequently theprey s arerandoml y located around thecente r ofth e cluster in a square with dimensions CLUNPCLUNIT. To acquire a circular cluster, the preys located in this square are shecked to see if they are within a distance of 0.5*CLUNIT from the center.Thi si steste db ycalculatin gth edistanc efro m thepre yt oth ecenter .I fthi sdistanc ei sgreate r than0.5*CLUNI Tth epre yi sdisgarde d and ane wpre yi sselected .Th epre ydistributio n isaccom plishedi nth efollowin gprogra msection : Doll =1,N C L =IC*I X(L) =RAN(IS)*UNIT Y(L) =RAN(IS)*UNIT CCX(I)=X(L ) CCY(I)=Y(L ) D01J =1,(IC-1 ) M =IC*(I-1)+J 11XM =RAN(IS ) YM =RAN(IS ) X(M) =X(L )+ (XM-0.5)*CLUNI T Y(M) =Y(L)+ (YM-0 .5)*CLUNI T DIST =SQRT(X(M)-X(L))*(X(M)-X(L) )+ (Y(M)-Y(L))*(Y(M)-Y(L) ) HCLUNI =0.5*CLUNI T IF(DIST .GT .HCLUN I) G OT O1 1 1CONTINU E Clusterscanning . Firstth eprogra m determineswhic hpre ycluste ri sneares tt oth ebeetle . DO 4L =1,NC DIST1 =SQRT((CCX(L)-XP)*(CCX(L)-XP) + (CCY(L)-YP)* (CCY(L)-YP)) DIST =AMIN1(DIST1,DIST) IF(DIST.EQ.DIST1) L1=L*IC T4 CONTINUE Preyi sonl ylocate d inth eclusters ,thu sth ebeetl eca nonl ydiscover ya pre ywithi na certai ndistanc e from thecluste r center. The sum of the reaction distance of the beetle and the cluster radius form thisdistanc e(CLDIST) .A sstandar dreactio n distance2 c mi staken . RADIUS =2. 0 CLDIST =0.5*CLUNI T+RADIU S IP(DIST.GT.CLDIST )G OT O6 196 WageningenAgric. Univ. Papers93-5 (1993) If the distance is greater than CLDIST, for allclustres ,th e beetle did not find anycluster . Hence, ILprogra^ ^ mÄbeetle is represented as a round objet with a radius of 2-Whe n ab « moves from one position to the next an area is covered consisting; of a strip of 4 cm widthtart also consisting of a halve circular start and end area.Whe nth e beetle™ « * ^^J^ with a change in direction a part of the area iscovere d twice( fig ^^^^^ awindi„gwalkingtrackneverreacheslOO% searchingefficienc y even ^^^L^ Prey dlscovery in the area of discovery-j ^^^^^^^SL^ cluster coordinates relative to a newcoordinat e trame, lm siram e P y direction ofth ebeetl edurin gth etim estep . Thecoordinate so fth eprey sca nb edetermin dwit hth eformul a s. Xnew=(Xold-XV)*COS(alpa) + (Yold-yV)*SIN(alpha) ynew=(yold-yV)COS(alpha) + (Xold-XV)*SIN(alptia) Thesene wcoordinate s givent oth eprey si na specifi cpre ycluste ran dth escannin go fprey slocate d inth eare ai sprogramme das : DO5J =1,IC I =L1-IC+J DX =X(I)-XV DY =Y(I)-YV CX(J) =DX*CSDR+DY*SND R CYfJ) =DY*CSDR-DX*SVDR ,„„^15 IÎ(CX(J).LE.( V+RADIUS).AND.CX(J).GB.0.)G0T 01 5 GOT O5 15 IF(ABS(CY(J)).LE.RADIUS)G0T01 6 GOT O5 16 NL =NL+1 B(NL) =J 5 CONTINUE Twosituation sca nb edistinguished . ici,rn„ thanit sreactio ndistance , a)Th edistanc ea beetl ecover sdurin gon etim este pi slarge rtha n Inthi scas ethre earea' sca nb edistinguished . A) X-coordinatei ssmalle rtha nreactio ndistanc e y B) X-coordinatei slarge rtha n reactiondistanc ebu tsmalle rtha nV C) X-coordinatelarge rtha nV h aiready been discovered The prey located in area A must be scanned to see^°™™ ne selection takes place by in the previous time step; viz. all the prey l^m Stance issmalle rtha nreactio ndistanc e determiningth edistanc efro mth epre yt pth eXV ,Y v .11 1 ance reaction distance thepre yi sdiscarded .Fro mth epre ylocate di nare aC onythosew i from XV,YVar eretained ,wherea sal lpre yi nare aB ar esaved . 197 WageningenAgric. Univ. Papers93-5 (1993) Determination whether a prey is located in area A,B or C DO 71 =1,NL AM =B(J) IF(CX(AM).LE.RADIUS)G OT O1 7 GOT O1 8 17 D =AM GOT O7 1 18 IF(CX(AM).GT.V)G OT O1 9 GO TO2 0 19 E =AM GOT O7 1 20 NF =NF+ 1 F(NF) =AM 71 CONTINUE The chance that a prey will be located in Bi s much greater than the chance to locate a preyi n sector A or C. The preys located in Bar e stored in the F(NF) memory. A and Cca n maximally contain 1 prey each. In the next section of the program iti s prevented that in two consequetive time steps the same prey is scored in part A and C. This part of the program may be omitted ifth e prey is removed after an discovery or when it is not sessile. IF(D.EQ.O)G OT O2 1 DIST1 =SQRT(CX(D)*CX(D)+CY(D)*CY(D)) IF(DIST1.LT .RADIUS )G OT O2 1 G =D 21 CONTINUE IF(E.EQ.O)G OT O2 2 DIST2 =SQRT((CX(E)-V )*(CX(E)-V )+CY(E)*CY(E )) IF(DIST2.GT.RADIUS )G OT O2 2 H =E The selected prey from sectors A, Ban d C arepotentia l prey, and they arepu t in memory POT(CNT). In fact these are all the prey discoveryed by the beetle in one time step. 22 CONTINUE IF(G.EQ.O )G OT O2 3 I =L1-IC+ G CNT =CNT+ 1 P0T(CNT)=I 23 CONTINUE IF(NF.EQ.0)G OT O2 4 DO2 4J =1,NF I =L1-IC+F(J ) CNT =CNT+1 POT(CNT)= 1 24 CONTINUE IF(H. EQ.O) GOT O2 5 I=L1-IC+H CNT=CNT+ 1 POT(CNT)= 1 25 CONTINUE 198 WageningenAgric. Univ. Papers93-5 (1993) b)Th edistanc ea beetl ecover sdurin gon etim este pi sles stha nit sreactio ndistance . In thiscas eonl y thosepre y at larger distance than thereactio n distancefro m XV,Y Van dclose r to XP,YP than reaction distance are also put in memory POT(CNT) and can also be considered asdiscoveryed . DO8I =1,N L AM =B(I) DIST3 =SQRT(CX(AM)*CX(AM)+CY(AM)*CY(AM ) DIST4 =SQRT((CX(AM)-V)*(CX(AM)-V)+CY(AM)*CY(AM)) IP(DIST3.GT.RADIUS .AND .DIST4 .LE .RADIUS )G OT O4 1 GOT O8 41 NF =NE+1 F(N:F) =AM 8 CONTINUE IF(NP.EQ.O)GOTO4 3 DO4 3J =1,NP I =L1-IC+E(J ) CNT =CNT+1 POT(CNT) =1 43 CONTINUE In the discovery model the discovered prey are given new coordinates in the cluster The^average density in the fields remains constant. If thisi sno t done the chance ofd.scov e n! thesa m prey in sector Bi s very high when the speed is low and the prey density in the cluster high.Thi sma y giveerroneou shig hrate so fdiscovery . 199 WageningenAgric. Univ. Papers93-5 (1993) APPENDIX II Functionalrespons emodels . Holling (1959,1966)describe s3 typeso ffunctiona l responsemodel sderive dfro m different types ofpredators. Type 1 response: When a predator killsa constan t proportion of thepre y therelationshi p between preydensit yan dnumbe ro fpre ykille di slinea runti la platea ui sreache dwer eth enumbe ro fsuccess ful attacksremain sconstant . Thenumbe r ofpre yencountere d (Ne)i slinearl yrelate d topre ydensit y(N 0)an d toth esearchin g time(T s): Ne = a'*N0*Ts (1) a'= relativerat eo fsuccesfu l attack,als ocalle dth esearchin g efficiency. Whenth eplatea ui sreache d Ne= constan t Type 2response :Jus t as in the type 1respons e a saturation level is reached but now in a gradual way.I fa par to fth etota ltim eavailabl e(T )i suse dfo r preyhandlin g(Tj J thesearchin gtim eequals : Ts = T-Th*Ne Formula ofHollin gfo r type2 respons ecurve : Ne = a'*Ts*N0 where Ts= T-T h*Nethus: Ne = a'(T-Th*Ne)N0 IfN ei sbroug tt oth elef t hand sideth eformul a becomes: Ne = a'*T*N0/(l+ a'*T h*N0)th e'dis cequation * (2) This only holds for a short observation period. It can also be said that the parasitoid searches systematicly.Wha tw ese ei nmos texperiment si stha t parasitoids donot avoidpreviou s parasitized hosts thus that they encounter a host more than once. To account for this effect the approach ofNicholson & Bailey(1935) is used (see Rogers,1972). The chance of a host being encountered isa Poisso nprocess .Th echanc ehavin gn oencounter s (thusn oparasitization )equal sth ezer oter m ofth ePoisso n distribution: P0= exp(-N e/N0) Thefractio n that ahos ti sencountere d onceor emor ei sthu s(1-Po ) Thenumbe ro fpre yattacke d byon epredato ro rparasitoi dis : Ne= N0(l-exp(-Ne/N0)) (3) substitution ofequatio n (1)fo r Negive sth eNicholson' s'competitio ncurve 'fo r asingl eenem y Ne=N0(l-exp(-a'*Ts)) (4) Therelativ erat eo fsuccesfu l attack a'= (ln(N 0/(N0-Ne))/Ts Thusw eca ncalculat ea 'fro m theresult so fa parasitizatio nexperiment ,becaus ew ekno wth edensit y N0 andcoun t Npar= N e asth enumbe r ofhost sparasitize d intim eT s. If it is assumed that the parasitoid searches at random, equation (2)ca n be built into equation (3),the nw ege tth es ocalle d 'RandomParasite Equation': Npar= N 0{l-exp(-a'*T*/(l +a'Th*N0))} (5) Equation (5)ca n not beapplie d for most predators because they remove their prey asthe yfind one, at the first encounter. No time is wasted in repeated encounter (re-handling) with prey, and moretim ei savailabl efo r searching.Thu sfo r apredato r Ts = T-Npred*Th For theequatio n ofHollin gthi slead st oth esam e'dis cequation ' ifi ti sassume d that~Npred=~Ne which also holds for a short period. The parameter Ne in equation (3) describes the number of 200 WageningenAgric. Univ. Papers93-5 (1993) encounters that the predator would have with the prey if the predator did not consume its prey or if the prey density remained constant. Had these encounters been distributed at random, the number ofpre y that would havebee nencountere d onceor emor e times(an d therefore the number ofpre y eaten)wa s the samea s in equation (4).Substitutin g for Ts .equation (4)give sth e 'Random PredatorEquation' Npred= N 0{l-exp(-a'(T-N pred*Th)} W TheRando mParasit eEquatio nca nb eadapte dfo rparasite stha td odiscriminat ebetwee nparasit ized and non-parisitized hosts by taking different handling times for both types of hosts (Ardm, 1983). Type 3 response:I f a predator reacts to an increase of prey density by increasing its proportion ofpre ykille dove ra specifi c rangeo fpre ydensit ythi swil lresul tm a sigmoi dcurve . If is found that the relative rate of encounter a' or the searching time Ts increases with (N0) or that Th decreases with N0> then a sigmoid relationship between prédation or parasitation and prey density may be found. For example, the parameter a' can be assumed to increase with N0 inth efollowin gwa y(Hassel!, Lawton& Beddington, 1977). a'= b* N /n+c*N„) (ban dc ar econstants ) , • / i a' rises from 0whe n no hosts are present to a maximum b/c.Thi s relationship can be substituted in(5 )o r(6 )an dgive sa sigmoi dfunctiona l responsefo r apredato ro ra parasitoid . 201 WageningenAgric. Univ. Papers93-5 (1993)