OPTIMUM PREY CAPTURE TECHNIQUES IN FISH
CENTRALE LANDBOUWCATALOGUS
0000 0002 3321 Promotor:dr .J .W .M .Osse ,hoogleraa r ind ealgemen edierkund e JOHAN L. VAN LEEUWEN
OPTIMUM PREY CAPTURE TECHNIQUES IN FISH
Proefschrift terverkrijgin gva nd egraa dva n doctori n de landbouwwetenschappen, opgeza gva nd erecto r magnificus, dr.C.C .Oosterlee , hoogleraar ind eveeteeltwetenschap , inhe topenbaa r teverdedige n opwoensda g2 9jun i 1983 desnamiddag st evie ruu ri nd eaul a vand eLandbouwhogeschoo l teWageningen .
H.VEENMA N &ZONE N B.V.-WAGENINGEN- 1983 BIBLIOTHEEK DEK LANDBOUWHOGESCHOOL WAGKNINGEN
M* l^;l\ -0$ Inhoud/Contents
Voorwoord 5
Inleiding 7
Generalsummar y 17
Hoofdstuk 1/Chapter 1 19 A quantitative study of flow in prey capture by rainbow trout, withgenera lconsideratio n ofth eactinopterygia nmechanism . J. L.va nLeeuwen ,submitte d inrevise dfor m toTrans .Zool .Soc .Lond .
Hoofdstuk 2/Chapter2 79 Optimum suckingtechnique sfo r predatory fish J.L .va nLeeuwe n& M .Muller ,Trans .Zool .Soc .Lond. ,i npress .
Hoofdstuk 3/Chapte r3 Ill Therecordin gan dinterpretatio n ofpressure si nprey-suckin g fish J.L .va nLeeuwe n& M .Muller , submitted inrevise dfor m to Neth.J .Zool .
Curriculumvita e 163
Coverdesign: Wim Valen Coverphotograph: Johan van Leeuwen WtâZoîjlYé,
STELLINGEN
!. Maximization of the initial prey distance by an exact adjustment ofmout h ex pansioni suseles sfo ra fish, contrar yt oa nadjustmen t thatmaximize sth eveloci tyo fth epre ywhil ei tenter sth emouth . Thisthesis .
2. Jawprotrusio ni sth emos tefficien t way,achieve di nfish, t oincreas eth erelativ e preyvelocit ytoward sth efish's mouth . Thisthesis .
3. The opercular and branchiostegal valvesar eimportan t control devicest o opti mizeth eflow rat ethroug h themout h aperturedurin gsuctio n feeding in fish. This thesis.
4. Conclusionst ounfunctiona l morphologyb yLaude ran dLie m(1981 )ar ecause d bya lac ko fphysica l insight.Ther ei sn oevidenc efo r anunfunctiona l construc tioni nLuciocephalus pulcher. Thisthesi scontr a Lauder, G.V .& Liem , K.F .(1981) .Pre y capture byLuciocephalus pulcher. implications for models ofja w protrusion inteleos tfishes. Env. Biol. Fish. 6,257-268.
Functional morphology can support phylogenetic studies infish, a sargue d by Liem and Greenwood (1981). In their examples, however, the authors merely addmovement -an dEMG-pattern st oth elis to fmorphologica l features already usedb ytaxonomists .The yd ono tsho wth erelation sbetwee nfor man d function. Contra Liem, K. F. &Greenwood , P. H. (1981). A functional ap proach to thephylogen y ofpharyngognat h teleosts.Amer. Zool. 21, 83-101.
BIBLIOTHEEK
LANDBOUWHot *EiJGHOO L WAG£NINGEH 6. The available data strongly suggest that theimportanc e of tendon elasticity to reduce theenergeti ccos t of terrestrial locomotion decreaseswit h a smaller size ofth eanimal . Biewener,A . A.,Alexander ,R .McN .& Heglund ,N .C .(1981) . Elas tic storage in the hopping kangaroo rats (Dipodomis spectabilis). J.Zool., Lond., 195, 369-383. Heglund, N. C, Fedak, M. A., Taylor, C. R. &Cavagna , G. A. (1982). Energeticsan dmechanic so fterrestria llocomotion .IV .Tota l mechanical energy changes as a function of speed and body sizei n birdsan dmammals .J. exp. Biol. 97,57-66 .
7. Voor het interpreteren van ethologische gegevens is kennis van de functionele morfologie vanbelang .
Bij het toetsen van de rijvaardigheid van automobilisten dient het vermogen tot stereoscopisch zieni nd ebeoordelin gt eworde n betrokken.
9. Het betoogva nPvdA-leide r Den Uyl tegen dedoo r hem aangeduide 'oneissu e partijen' wijstallee nmaa ro phe tbelan gva nhe tbestaa nva nbedoeld egroeperin gen. Het isi ndi t verband interessant om na tegaa n wanneer, na de anti-kern energie gedachte,oo k degedacht eva n deeconomisch e nulgroei zal postvatten ind ePvdA . ContraDrs .J .de nUyl ,Volkskran t 14me i 1983,pag .13 .
10. Metd etoenemend ewerkelooshei dmoete nvele nsteed sharde r gaanwerke no m betaaldwer kt ekunne nblijve n uitvoeren.
11. In het kader van debezuiniginge n en geleto p de toenemende papierwinkel ten behoeve van planning en coördinatie van het universitair onderwijs en onder zoekverdien the taanbevelin go mall ewetenschappelijk e medewerkerst ebenoe mento twetenschappelij k ambtenaar.
12. Bijd ebeoordelin g vanee nproefschrif t dient deaa n het werk bestede tijdsduur in de beschouwing te worden betrokken. Een politiek waarbij de beschikbare (betaalde)tijdsduu rword tverkor te nd eeise nunveränder tblijve ni sonmenselij k en verwerpelijk.
Behorendebi jhe tproefschrif t vanJoha n L. vanLeeuwen : 'Optimumpre ycaptur etechnique si n fish' Wageningen, 29jun i 1983 Voorwoord
Dit proefschrift werd bewerkt bij de sectie Functionele morfologie van de vakgroep Experimentele diermorfologie en celbiologie van de Landbouwho geschool teWageningen . Dit onderzoek werd mogelijk gemaakt door mijn aan stelling bij BION/ZWO (14.90.18)voo r een periode van (effectief) driejaar. Het onderzoek werd gestart op 1 december 1979, aanvankelijk voor halve dagen als student assistent, na mijn afstuderen op 23januar i 1980o p "full time" basis. Een aantal personen wil ik bedanken die een belangrijke rol hebben gespeeld in mijn opleiding tot bioloog en/of het tot stand komen van dit proefschrift. Mijn promotor Jan Osse dank ik voor zijn stimulerende onderwijs in de dier kunde, zijn vele goede ideeën en adviezen, het op zich nemen van organisatori sche taken, waardoor het onderzoek kon starten en voortgang vinden, en het kritisch doornemen en bespreken van de manuscripten, waardoor deze veel aan duidelijkheid wonnen. Mijn vriend en begeleider Mees Muller heeft mij in belangrijke mate in gevoerd in de regeltechniek, hydrodynamica en kennis van vissen. Met plezier denk ik terug aan onze talloze discussies, die zeer veel hebben bijgedragen tot dit proefschrift. ArieTerlou w dank ikvoo r zijn deskundige technische assistentie. Met genoe gen herinner ikm e onze vele,altij d in prima sfeer verlopen experimenten. Jan Verhagen dank ik voor zijn deskundige hydrodynamische adviezen. NeillAlexande r enAla n Jayeshebbe n mij begeleid gedurende mijn doctoraal stage in Leeds, die tesamen met de vele geschriften van Neill van veel betekenis wasvoo r mijn wetenschappelijke vorming. Thank you very much! Johan van der Veere n Ton de Lange dank ikvoo r hun adviezen op fotogram- metrisch gebied, en de constructeurs van de TFDL voor het vervaardigen van de nodige hulpmiddelen. Gert van Eek verrichtte wonderen bij het opstarten van onze onmisbare MINC-11 computer. De bijdragen die Jan Kremers, Ineke Oomen, Maarten Drost en Ben Cattel alsdoctoraa l student aan dit werk hebben geleverd stel ik zeer op prijs. De vriendschap en belangstelling van de collega's van de sectie Functionele morfologie, RieAkste r enNan d Sibbing,e nva n demense n van de sectiesHisto logiee n Celbiologie hebi k altijd bijzonder gewaardeerd. Wim Valendan k ikvoo r zijn goede tekenwerk en fotografische hulp en Sietse Leenstra,Pie tva n Kleefe nSyts eva nd eBer gvoo rd everzorgin gva nd e proefdie ren en de technische hulp. Chris Secombes, Nicolas Cohen en Seamus Ward dank ik voor hun adviezen wat betreft het Engels. Annet Kroon dank ik voor het kritisch doorlezen en corrigeren van de manuscripten. Tenslotte wil ik al diegenen bedanken die nog niet genoemd zijn maar toch hebben bijgedragen tot dit proefschrift. Inleiding
Indi t proefschrift wordt getracht omvi a het hanteren van fysische principes (deductieve methode) te komen tot een verklaring van een aantal aspecten van debou we nwerkin gva nhe tvoedselopname-mechanism e vanvissen . Hetgepre senteerde werk sluit in sterke mate aan op het proefschrift van Muller (1983), waarin een uitgebreide inleiding, inclusief literatuuroverzicht, te vinden isom trent hetprooiopname-mechanism e vanvissen .Teven sword tdaari n degevolg demethodologi e aan deord e gesteld. Ik zalda n ook relatief kort zijn overdez e aspectene nd enadru k leggeno pd eresultate n vanhe t onderzoek.
Hetproces van prooiopname Van de meer dan 20,000 recente soorten vissen zuigt ruim de helft de prooi aandoo ree nexpansi ee nkompressi eva nd ebuccal ee noperculair eholte s(tesa - men aangeduid als mondholte in het vervolg van deze inleiding). Niet alleen deproo i met hetomringend e waterword t verplaatst, maard evi szuig tzichzel f hierbij ook vooruit. Bij veel vissoorten wordt de zuigbeweging aangevuld met zwemmen en een vooruitschuiven (protrusie) van de kaken. Vissen hebben de mogelijkheid ommee rwate r door demondopenin g opt eneme n dan demond holtemaximaa l kan bevatten, doordat opee nzeke r ogenblik in het zuigproces de operculaire en branchiostegaal kleppen (hieronder kortweg aangeduid als "kleppen") geopend worden. Het vooraan opgenomen water stroomt daarna wegvi ad ekieuwspleten .D ezuigbewegin gword tmeesta lbinne n 50to t 100mse c uitgevoerd, waarbij versnellingen vanhe twate r ofdele nva nd evi sva n 10maa l dezwaartekrachtversnellin g ofzelf shoge roptreden .He t voedselopname-proces isdu s hoogst instationair en de watersnelheid kan niet uit de druk worden af geleid(zi eoo kMulle re tal. , 1982).Al sgevol gva nd ebekexpansi ekunne nonder drukkento t0. 4to t0. 6atmosfee r (40to t6 0kPa )worde ngegenereerd .Ee nbestu dering van het proces van prooiopname is nuttig, niet alleen omdat hiermee inzicht wordt verworven omtrent bouwprincipes van vissen, maar ook omdat habitat-preferenties, ethologie envoedselzoekstrategieë n van vissen beter kun nenworde nbegrepen .
Modelvorming Hetprooiopname-mechanism e vanvisse ni sdoo rvel eauteur sbestudeer d(zi e vooroverzichte nOsse ,196 9e nMuller , 1983). Veelalbetreffe n dit morfologische studies,som si ncombinati e metexperimentel e waarnemingen (zie bijvoorbeeld Osse, 1969). Deze soms gedetailleerde werken geven een indruk van de bouw en verrichtingen van een gering aantal soorten, maar resulteerden nog niet in eengeneral ebeschrijvin g vanhe tzuigproces ,omda td edeductiev emethod enie t 7 of nauwelijks is toegepast of de modelvorming van de stromingsverschijnselen foutief is(zi eMuller , 1983,voo r een gedetaileerde bespreking van dezematerie) . Recent hebben Muller etal .(1982 )e nMulle r &Oss e(i npress )ee n hydrodyna misch model van de zuigende voedselopname van vissen gepresenteerd, dat een belangrijke stap vormt in de richting van een meer generale beschouwing van dit proces. De dichtheid van water ligt in dezelfde orde van grootte als die van de prooi. Dit maakt het mogelijk om de prooi met de waterstroom mee naar binnen te zuigen. De door de vis opgewekte waterstroom bepaalt dan ook in sterke mate ofd e prooi al dan niet gevangen wordt. Door hetbestudere n van de hydrodyna- mica van het zuigproces kunnen morfologische en kinematische kriteria worden opgesteld waaraan de vis zou moeten voldoen als deze de waterstroom zodanig manipuleert dat de prooivangkans wordt geoptimaliseerd. Via deze weg blijkt het mogelijk om een uitspraak te doen over de mate van aangepastheid van structuren aan bepaalde functies. Tevens kan de samenhang tussen de bouw van verschillende structuren binnen het expansie-apparaat aangetoond worden en kunnen wijzigingen in het prooiopname-proces als aanpassing aan verschil lende uitwendige omstandigheden logisch worden verklaard. Een aantal voor beelden zullen hieronder worden vermeld. Muller et al. (1982) hebben de waterstroom voor de bek van de vis gemodel leerd als een combinatie van een circulair wervelfilament en een parallelstroom. De wervelsingulariteiten (hier is de snelheid oneindig) liggen op de lippen van de vis en de wervelsterkte wordt bepaald door de volume vergroting of verklei ning van de mondholte door expansie of compressie en door de voortbeweging van de vis. Een snellere voortbeweging reduceert de bijdrage van de wervel aan de waterstroom door de mondopening. De voorwaartse beweging van de vis wordt evenalsee n eventuele protrusie van de kaken verdisconteerd in de sterkte van deparallelstroom . Demondholt e wordt inbovenbedoel d model voorgesteld als een rotatie-symmetrisch profiel. Bij het simuleren van bekbewegingen van de visword t vrijwel altijd uitgegaan van een aan de voorzijde afgeknott e kegel. Een belangrijk aspectva nd emodelvormin g washe tonderscheide n vanee n aard- vast en een bewegend assenstelsel. In het aardvaste assenstelsel (gefixeerd t.o.v. het aquarium) dienen krachten, drukken en impulsen berekend te worden. Het bewegende assenstelsel (gefixeerd t.o.v. de bek van de vis) wordt gebruikt voor de bestudering van de prooivangkans.
Experimentele toetsing van modeluitspraken Het model is op diverse wijzen door Muller & Osse (in press) getoetst. Van een achttal vissoorten zijn snelle films gemaakt van de voedselopname (tot 400 beelden/sec). Vanaf deze films konden de bewegingen van de vis en de prooi worden opgemeten. Daarnaast isdoo r het aanbrengen van polystyreen bolletjes van 0.5 of 1 mm doorsnede de stroming rond de vis en de prooi gevisualiseerd. Deze bolletjes zijn klein ten opzichte van de diameter van de bek en hebben vrijwel dezelfde dichtheid als water, waardoor zed e waterstroom zeer goed vol gen. Voor het meten van watersnelheden in de bek zijn zogenaamde "hot-film anemometers"gebruikt ,me tee ngrot ebandbreedt ezoda tsne lwisselend ewater - snelheden goed geregistreerd kunnen worden. Voor het meten van drukken in demondholt ezij nmetinge nverrich tme tee naanta lverschillend etype ntransdu cers. Behalve de "hot-film anemometry" heb ik al deze technieken ten nutte ge maaktvoo rmij n onderzoek.Ee naanta ltechnieke n hebi kverde r verfijnd. Inhoofdstu k 1 wordtonde rmee ree nstereoscopisch efilmtechniek behandel d waarmee het mogelijk is om vorm- en positie-veranderingen van de predator enva nd eproo i ind eruimt e teregistreren . Een stereoscopische opname vand e opstelling in een vroeg stadium van ontwikkeling is gegeven in Fig. 1.Teven s kan viad epolystyree n bollen dei nd etij d variërendewaterstroo m ind eruimt e worden bestudeerd. De nauwkeurigheid van de gebruikte methode wordt be perktdoo rhe tklein eoppervla k vand ebeelde nva nee n 16m mfilm. Ee ngroter e nauwkeurigheid werd bereikt m.b.v. multi-flash fotografie, waarvan een voor beeld staat afgedrukt op pag. 11. Andere voorbeelden zijn te vinden in hoofdstuk 1. Door een afnemende intensiteit van de opeenvolgende flitsen is debewegingsrichtin gva nd eobjecte n aangegeven.Me tbehul pva ndez etechnie ken werd aangetoond dat de forel na klepopening ongeveer vijf maal zoveel water door de mond opneemt als voor klepopening. Tevens werd een goede indicatie verkregen over de initiële vorm van het opgezogen volume water. In
Fig. 1.D e stereoscopische fïlmopstelling in een vroeg stadium van ontwikkeling. Een belichtingstijd van 1/4000to t 1/2000second e is nodig om bewegingsonscherpte te vermijden. De batterij filmlam- pen maakt het mogelijk om toch met een diafragma van 8 of 11 te werken. Verder zijn te zien dehigh-spee dcamer ae nhe t stereo-voorzetstuk. Dit stereopaar kan bekeken worden metee n pocket- stereoscoop,waardoo r eenruimtelij k beeld ontstaat. Diei sm.b.v . tweelenze nme tee n brandpuntsaf stand van + 120m m gemakkelijk te vervaardigen. hoofdstuk 1 wordt ook beschreven hoe door het aanbrengen van draden bij de operculaire spleten variaties in de bewegingsrichting van het water op deze plaats kunnen worden afgeleid. In hoofdstuk 3 worden voor- en nadelen van een aantal technieken voor het meten van de drukken in de vissebek behandeld. Met behulp van Fourier analyse zijn de dynamische responsies van een aantal drukopnemers en defrequentie-inhou d van een aantal drukregistraties bepaald.
De balanstussen zuigen en zwemmen De viska n op eenaanta l manieren deproo i naar zijn mond toedoe n bewegen. Hetnaa r deproo i toezwemme n isee neffectiev e methode alsd eproo i nog relatief ver weg is.Dich t bij de mondopening dreigt de prooi echter met het hem omrin gendewate r vooruit geduwd teworden . Ditlaatst eka nworde n voorkomen door de expansie van de mondholte van de vis, waardoor water aangezogen wordt. Als deze expansie snel genoeg verloopt zal het water in de mondopening van devi snaa r achteren bewegen, terwijl tegelijkertijd bij gesloten kleppen het water achterin de mondholte naar voren toe geduwd wordt; dit alles in een aardvast assenstelsel. Ergens in de mondholte zal dan het water stilstaan. De positie van dit stilstandspunt, is een functie van de tijd en kan als de kleppen gesloten zijn exact berekend worden. Bij geopende kleppen kan tot nu toe slechtsee n benade ring gegeven worden van deze positie (ziehoofdstu k 1).D e benodigde expansie snelheid om het stilstandspunt halverwege ind emondholt e tehoude n met geslo tenkleppen ,d ekritisch eexpansie-snelheid , neemt toeme td ezwemsnelhei d end e straal van de mondopening. Het wordt dus voor de vis steeds moeilijker om met het wijder openen van de mond deze expansie-snelheid nog te halen en het stilstandspunt zou uit de mondopening verdwijnen (met als direkt gevolg stu wing van de prooi), als niet de kleppen zouden openen. Klepopening heeft tot gevolg dat: 1) water door de operculaire spleten kan uitstromen. 2) het stilstandspunt in de mondholte gehouden wordt, of mogelijk zelfs de mondholte aan de achterzijde verlaat. 3) hetdebie t door demondopenin g gemaximaliseerd kan worden. De regenboogforel (Salmo gairdneri, zie Fig. 2) is in de eerste fase van het proces,waarbi j dekleppe n gesloten zijn, zeergoe di n staat om het stilstandspunt achterin de mondholte te houden (zie hoofdstuk 1,Fig . 18).Ditzelfd e is gevon den voor een zestal andere vissoorten (nog niet gepubliceerd werk van Oomen, Van Leeuwen, Muller en Kremers). Daarna zou het punt echter zeer snel naar demondopenin g bewegen (binnen 10msec ) alsd ekleppe n continu gesloten zou den blijven. Voor het creëren van een efficiënte waterstroom is het van groot belang dat de kleppen snel geopend kunnen worden. Een te vroeg openen heeft een caudale instroming door de operculaire spleten tot gevolge n dientengevolge een gevaar van beschadiging van de fragiele kieuwfilamenten. Een te late ope ning veroorzaakt stuwing van de prooi,juis t op het moment van prooiopname. De forel heeft een relatief langzaam klepopeningsmechanisme (ongeveer 10 msec, afhankelijk van de grootte van de vis), waardoor het begin van klepope ning noodzakelijk voor het "ideale tijdstip" van klepopenen ligt. De verwachte, 10 Fig.2 .A .Stereopaa rva nee n"mishap" va nee nregenboogforel . Devi srichtte o pd emoe rwaarme e de voedselbrok werd neergelaten. Let op de vrijwel rotatie-symmetrische bek en de van elkaar af staandekieuwbogen ,waarlang she twate rnaa rachtere nka nwegstromen . B.Stereopaa rva nd estromin gvoo rd ebe kva nee nregenboogfore ltijden sd evoedselopname ,verkre gend.m.v . "multi-flash" fotografie. zeergering ecaudal einstromin gi sinderdaa d experimenteel aangetoond metbe hulpva nd ebovengenoemd edrade n (hoofdstuk 1). Deontwikkelin gva nee nvee lsnelle rklepopeningsmechanism e binnend ePa - racanthopterygii en de Acanthopterygii kan worden beschouwd als een es sentiëlesta pi nhe tcreëre nva nee nmee reffectiev e waterstroom doord emond . De korte mondbuis van uitgestorven Palaeoniscoidea alsPteronisculus heeft naar allewaarschijnlijkhei d eenvroe gopeningstijdsti p van dekleppe n noodza kelijk gemaakt. De zeer korte branchiostegaal stralen bij deze vis kunnen ook geengeslote n kleppen bij eengrot e operculumabductie hebben toegestaan. Dit staat inschri l contrast metd elang emondbui se nlang eaciniform e branchioste gaal stralen in deParacanthopterygi i (bijvoorbeeld de kabeljauw) en deAcan thopterygii (bijvoorbeeld de baars), die het voedselopname-proces minder af hankelijk hebbengemaak tva nzwemmen . 11 Speciale aandacht verdient de protrusie van de kaken. Hierdoor wordt de mondholte verlengd enderhalv ed ekritisch e expansie-snelheid verlaagd. Protru sie treedt bijvoorbeeld in extreme mate op bij Luciocephalus pulcher, een vis diebi j oppervlakkige beschouwing veel op de snoek (Esox lucius)lijkt . De snoek heeft echter geen protrusie enLuciocephalus protrudeert dekake n over ongeveer 30 procent van de (rust)koplengte. Door de als gevolg van protrusie verlengde kop kan de vis het stilstandspunt langer achterin de bek houden dan de snoek, waardoor bijgevolg de kleppen later moeten openen. De hiervoor benodigde lange branchiostegaalstralen zijn inderdaad bij Luciocephalus aanwezig. Ik wil hier benadrukken dat deuitle gva n Lauder &Lie m(1981 )va n het prooiopname- proces vanLuciocephalus foutief isomda t zeonde r andere heteffec t van stuwing over het hoofd hebben gezien (zie hoofdstuk 1).
Optimalisatie vande vangkans van deprooi In hoofdstuk 2 worden de effecten van zuigen, voortwaartse beweging van de vis en protrusie van de kaken op de snelheid van de prooi in het bewegende assenstelsel eerst afzonderlijk en later ook gezamenlijk gekwantificeerd. Het blijkt dat de effecten van zuigen en zwemmen sterk afhangen van de afstand van de prooi tot de mondopening. Op een grote afstand heeft het geen effect voor de vis om te zuigen (afgezien van de bijdrage aan de eigen snelheid). Als de prooi zich dicht bij de mondopening bevindt zou stuwing van de prooi op kunnen treden;he t relatievezwemeffec t (hoofdstuk 2)nader t hierto t nul. Zuigen heeft nujuis t welee nster k effect. Protrusie heeft een tweeledigeffec t op deprooi snelheid in het bewegende assenstelsel. In de eerste plaats is er het translatie effect op de prooisnelheid. Dit is onafhankelijk van de prooiafstand, hetgeen een groot voordeel inhoudt t.o.v. zuigen en zwemmen. Bovendien vereist het protruderen van de kaken slechts weinig energie, in tegenstelling tot activiteiten als zuigen en zwemmen waar relatief grote massa's moeten worden versneld. Zoals boven vermeld wordt door protrusie de mondholte verlengd, waardoor de watersnelheid in de mondopening t.g.v. zuigen wordt vergroot. De invloed van dit effect van de protrusie op de prooisnelheid blijkt bij de koraalduivel (Pterois russelli)e n de bot (Platichthys flesus) een ondergeschikte rol te spelen. De op de bodem levende zeeduivel (Lophius piscatorius) beschikt over een uiterst effectief prooiopname-mechanisme. Deze vis (Fig. 3) zet zich af van het substraat waardoor het geleverde vermogen (bij een stevige ondergrond) vrijwel geheel aan de eigen voortbeweging ten goede komt. Ook is deze predator in staat tot een geweldige bekexpansie. Bovendien kan de zeeduivel de kaken over een aanzienlijke afstand protruderen. Alle mogelijke manieren om de snelheid van de prooi ten opzichte van de mondopening zo hoog mogelijk te maken zijn dus benut (zieformul e 8ui t hoofdstuk 2). De richting en de snelheid van een eventuele vluchtreactie van de prooi is moeilijk voorspelbaar, zowel voor ons als waarschijnlijk ook voor de vis. Prooi en die snel kunnen vluchten, zoals vissen, wekken een snellere zuigbeweging op vand esnoekbaar s (Stizostedion luciopercd)da n wormen (zieElshoud-Olden - have, 1979). Ook voor andere vissen is een dergelijke respons waargenomen. 12 Fig.3 .D ezeeduive l(Lophius piscatorius, standaardlengte21 5mm )i see nuitsteken d gecamoufleerde bodemvis (zie A), die m.b.v. het zogenaamde "ilicium" prooien naar zich toe lokt. Als de prooi dicht genoeggenader d isword tdez erazendsne l opgeslokt. (B)e n(C )zij n respectievelijk 30.7 msec en 61.4mse c na (A) opgenomen. Let op deenorm e levatie van de schedel en de protrusie van de kaken.D emaatverdelin gi n(A )duid tee nafstan d aanva n5 0mm .
13 Vrijwel altijd oriënteert een viszic h zodanig dat de prooi zich op de lengte-as vand eko pbevindt . Menka nzic hafvrage n vanwelk eafstan d eenvi sz' nproo izo umoete naanzui gen,zoda t dezeo pee n gedefinieerd tijdstip door demondopenin gnaa r binnen stroomt. Dit tijdstip kan zijn het moment waarop de mondopening maximaal is(al sd eproo i groot is), of eerder, alsd evi sd e snelheid van deproo i zogroo t mogelijk wilmake n(zi ehoofdstu k 2).Indie nhe tgewenst etijdsti p vanprooiop name bekend iska n door een terugberekening de initiële prooiafstand worden bepaald.Ui tmodelsimulatie sblijk tda tee nmaximalisati eva nd einitiël eprooiaf stand door een precies afstemmen van de expansie van het rostrale deel van demondholt e op deabducti e van deopercul a weinig nut heeft voor devis .D e dimensiesva nd eko pbepale nnamelij k insterk emat ehe taandee lva nhe tzuige n ind einitiël eafstand . Zwemmene nprotrusi eva n dekake n zijn veel effectievere middelenvoo rhe tvergrote nva nd einitiël eafstand . Heti svoo rd evi svee lgunsti ger om met zijn zuigapparaat de uiteindelijke prooisnelheid te maximaliseren, dat is de snelheid van de prooi als deze de mondopening passeert. Om dit te bereiken dient de visd e kieuwdeksels met de maximale snelheid te abduceren alsd eproo inaa rbinne n spoelt. Eenverhogin gva nd ezwemsnelhei dvergroo the tgevaa rda td eproo ivoortge stuwdword ti nhe taardvast eassenstelse l(zi eboven) .Stagnatie-effecte n kunnen (deels)worde nvermede n door demaximal emondopenin g teverkleine n bijee n vergroting van de zwemsnelheid. Hiermee wordt echter tevens de maximale prooigrootte verkleind. Opening van de kleppen maakt het mogelijk dat ook bijee nhog ezwemsnelhei d groteprooie n kunnenworde n gevangen. Zowel de gemiddelde als de uiteindelijke prooisnelheid kunnen worden ver grootdoo rd eproo ivoo rhe ttijdsti pva nd emaximal emondopenin gnaa rbinne n te laten spoelen. Dit is met name van belang als de prooi dicht benaderd kan worden,zoal sbi j voedselopname vanaf een substraat. Alsoo k dekieuwdeksel s relatief vroegabducere n wordt dit effect nogversterkt . Het samengaan vanee n tijdstip van prooiopname voor het tijdstip van maximale mondopening, met eenvroe gmomen tva noperculumabducti evinde nw ebijvoorbeel d bijd ekoraal - duivel.Ee nbeschouwin gva n dekinematic a van deko p levert opda t voordez e wijze van prooivangst een relatief kort hyoid voordelig is. Met korte hyoiden kan echter relatief weinig water worden opgezogen. Aangezien het bezit van een protrusie-apparaat het mogelijk maakt dehoeveelhei d opgezogen water te reduceren,vorme nrelatie f kortehyoide nhierme eee ngoed ecombinatie .
Simulatiesvan drukfluctuaties in de mondholte De mechanische belasting tijdens de zuigende voedselopname is veel hoger dan die tijdens de meeste andere activiteiten. Het kunnen voorspellen van de drukfluctuaties ind emondholt etijden sd evoedselopnam ei sdaaro mva nbelan g voor eeninterpretati e van debou w van de vissekop. M.b.v. het hydrodynami sche model van Muller et al. (1982) zijn drukfluctuaties in de mondholte van demoddersnoe k(Amia calva), d esnoe k(Esox lucius), d eregenboo gfore l{Salmo gairdneri)e nd ekabeljau w (Gadusmorhua) gesimuleerd (ziehoofdstu k 3).Hier - 14 toe worden de bewegingen van de mondopening en de operculumabductie op gemeten vanaf de film en ingevoerd in het model, benevens een aantal andere parameters. Deversnellinge n van de bewegingen kunnen niet nauwkeurig vanaf de film worden bepaald. De gegenereerde druk isjuis t erg gevoelig voor variatie van deze versnellingen. Hierdoor kunnen in eerste instantie grote verschillen optreden tussen de gemeten en de gesimuleerde druk. Door geringe veranderin gen van de modelparameters, binnen de foutengrenzen van de bewegingsregis tratie, kan echter een zeer goede overeenstemming tussen modeluitkomst en drukregistratie worden verkregen. Dit betekent dat de modelbeschouwing een goede benadering isva n het feitelijk optredende zuigproces. In hoofdstuk 2word t beargumenteerd hoe een vis zijn mond zou moeten ex panderen om de prooivangkans zo groot mogelijk te maken en tegelijkertijd degegenereerd e onderdruk zo veelmogelij k te reduceren.
Perspectieven Devoorspellinge n indi tproefschrif t vand ebeweginge ndi eee nvi szo u moeten maken om de kans van prooivangst te optimaliseren leveren belangrijke infor matie voor gedragsstudies van vissen. Een vergelijking van de reactietijd en de vluchtsnelheid van diverse prooien met de snelheid die door de predator aan de prooi gegeven kan worden, kan laten zien welke range van prooien gevangen kan worden. Dit gegeven kan bij oecologische studies of oecologische ingrepen een belangrijke voorspellende waarde hebben. Vanaf het embryonale stadium dienen door predatoire vissen gedurende elke fase van degroe iprooie n gevangen teworden . Ook demeest elate r niet predatoi revisse n leven aanvankelijk van levend zoöplankton. De in dit proefschrift aan gegeven lijn van onderzoek maakt het mogelijk om te voorspellen hoe de groei zou moeten verlopen als het prooiopname-apparaat steeds zo goed mogelijk zou zijn aangepast aan zijn functie. Uit recente studies blijkt dat boven bepaalde afmetingen van de visee n verdere groei onmogelijk isomda t de kans van prooi vangst tevee li safgenome n (Kremers &Va n Leeuwen, in prep.). Een zeer kritische fase in het leven van de visis ,vanweg e de hoge mortaliteit, het larvale stadium. Gedetailleerde kennis van het prooiopname-mechanisme indez efas e maakt eengericht emanipulati e van milieuomstandigheden mogelijk ter verbetering van de levenskansen.
Referenties Elshoud-Oldenhave, M.J.W. (1979).Pre y capture in thepike-perch , Stizostedion lucioperca(Teleos - tei, Percidae):A structural and functional analysis.Zoomorphologie 93: 1-32. Kremers,J.J.M . &Leeuwen , J.L. van (inprep.) .Th e influence ofgrowt h on thepre ycaptur e mecha nism of the pike (Esox lucius). Lauder, G.V. & Liem, K.F. (1981). Prey capture by Luciocephaluspulcher: implications for models ofja w protrusion in teleost fishes. Env. Biol. Fish. 6,257-268. Leeuwen, J.L. van (in prep.). A quantitative study of flow in prey capture by rainbow trout, with general consideration of the actinopterygian system. Leeuwen, J. L. van &Muller , M. (in press). Optimum sucking techniques for predatory fish. Trans. Zool. Soc. Lond. Leeuwen, J.L. van & Muller, M. (in prep.). The recording and interpretation of pressures in prey sucking fish. Muller, M. (1983). Hydrodynamics of suction feeding in fish. Proefschrift, Landbouwhogeschool Wageningen. Muller, M. & Osse, J.W.M, (in press). Hydrodynamics of suction feeding in fish. Trans. Zool. Soc. Lond. Muller, M., Osse, J.W.M. & Verhagen, J.H.G. (1982). A quantitative hydrodynamical model of suction feeding in fish. J. theor. Biol. 95:49-79 . Osse, J.W.M. (1969). Functional morphology of the head of the perch (Perca fluviatilis L.): an electromyographic study. Neth. J. Zool. 19(3) :289-392 .
16 Generalsummar y
In this thesis hydrodynamic principles are used to quantify relations between form and function in the prey capture mechanism of actinopterygian fish. This work is closely related to the papers on the hydrodynamics of fish feeding by Muller et al. (1982) and Muller & Osse (in press). The effectiveness of different head forms and movements for prey uptake (in various habitats) is investigated by model simulations and verified by flow visualization and pressure measure ments. Chapter 1 presents a technique to visualize the flow in 3-D around the mouth ofth efish, suckin git sprey .A nexpandin g and compressingcylindrica l or conical model of the fish's mouth cavity is used to quantify the relation between head movements and swimming. The opercular and branchiostegal valves are shown to function ascontro l devices to obtain an optimal flow rate through the mouth aperture. The theoretical predictions were verified experimentally for the rain bowtrou t (Salmogairdneri). Likewise ,dat a from theliteratur e appeared to agree with these hypotheses. Chapter 2 quantifies the contributions of the forward movement of the fish, the expansion of the mouth cavity and a possible protrusion of thejaw s to the velocity of the prey. Optimum sucking techniques (i.e. techniques maximizing thechanc e ofpre ycapture ) in relation to swimming speed and habitat properties are derived by model simulations. Maximization of the initial prey distance by an exact adjustment of mouth expansion israthe r useless for a fish. Much more isgaine d ifth efish abduct s itsopercul a at themaxima l rate when the prey enters the mouth. Chapter 3 discusses recording techniques for pressures in prey-sucking fish. The dynamic properties of different measurement systems are investigated by Fourier analysis. Also, the frequency content of records of the fluctuating pres sure inside the fish's mouth during feeding is shown. Prey capture events of different fish species are simulated using the hydrodynamical model of Muller et al. (1982). Measured and simulated pressure curves are compared and the effects of the use of different boundary conditions in the model are discussed. The literature on pressure measurements inprey-suckin g fish is reviewed.
References Muller, M. & Osse, J.W.M, (in press). Hydrodynamics of suction feeding in fish. Trans. Zool. Soc. Lond. Muller, M., Osse, J.W.M. & Verhagen, J.H.G. (1982). A quantitative hydrodynamical model of suction feeding in fish. J. theor. Biol.95:49-79 .
17 HOOFDSTUK 1/CHAPTERl
Aquantitativ estud yo fflow i npre ycaptur eb y rainbowtrout ,wit hgenera lconsideratio no fth e actinopterygian feeding mechanism.
19 Aquantitativ estud yo fflow in pre ycaptur eb y rainbowtrout ,wit hgenera lconsideratio no fth e actinopterygianfeedin g mechanism.
JOHAN L. VAN LEEUWEN
(Department ofExperimenta l AnimalMorpholog y andCel lBiology , Agricultural University, Marijkeweg40 , 6709P GWageningen ,Th eNetherlands) .
Keywords:Actinopterygii , Flow visualization, Hydrodynamics, Photogrammetry, Salmo gairdneri, Stereoscopy, Suction feeding, Swimming.
Summary
Prey suction events of the rainbow trout (Salmo gairdneri, Richardson) were filmed stereoscopically (175 to 400 frames/sec). Polystyrene spheres (density 1033 kg/m3) were put in the water surrounding the prey, as a means for flow visualization. Individual spheres could be recognized in successive frames, and particle path lines were obtained in 3-D. Additionally, multi-flash photography was used for flow visualization. The water in front of the trout, containing the prey, appeared almost stationary in anearth-boun d frame during feeding (except veryclos et o themouth) ,althoug h separate pushing and sucking effects could be distinguished. Hence, the impulse added to this water by the swimming and suction movements of the predator was small. At distances greater than about 15% of the head length ahead of the fish's mouth aperture, the flow towards the mouth (enclosed by the dividing streamline) was close to a uniform stream of varying strength and cross-sectional area. The total volume of water entering the mouth during feeding was about 5.5 times the volume taken up till the actual moment of opercular and branchiostegal valve opening. Thus outflow through the opercular slits is highly important in the suction process. The maximal distance from which water was taken into themout h was slightly more than thefish' s head length. With a cylinder and cone model it was shown that the mouth of the forward moving fish must expand at least at a threshold rate to prevent pushing of the prey in front of its mouth before the moment of caudal valve opening. The optimal moment of valve opening,suc h that thevolum e flow through themout h aperture ismaximized , was calcu lated from the fish's head length, swimming velocity, mouth radius, mouth expansion rate, opercular abduction and opercular abduction rate. After valve opening the fish must at least reach a threshold translational velocity, to prevent an inflow through the opercular slits. A minor initial inflow through the opercular slits of the rainbow trout was detected. Good agreement was found between theory and experiment. Many mor phological and kinematic features of the feeding system of "higher teleosts" serve to generate a unidirectional flow inside the mouth. Possiblefeedin g strategies of actinopterygian fish in relation to their head construction and swimming velocity were discussed in the light of the above results. Previous papers on feeding mechanisms in fish could beproperl y explained with the current approach. 21 Contents
Summary 21 1. Introduction 22 2. Materialsan dmethod s 24 2.1. Experimentalse tu p 24 2.2. Theacquisitio no fa thre edimensiona lpictur e 25 2.3. Theacquisitio n ofparticl epath -an dstreamlines ;earth-boun d and movingfram e 26 2.4. Calculationo fposition -an dvelocit yvector si n3- D 28 3. Results 33 3.1. Experimentalobservation s 33 3.1.1. Pterois 33 3.1.2. Salmo:observation sfro m cinefilm an dmulti-flas h photog raphy 34 3.1.3. Salmo:velocity-an dvolum ecalculation s 37 3.2. Aquantificatio n ofth erelatio nbetwee nsuctio nan dswimmin g . . 45 3.2.1. Suctionwit hclose dvalves ;th eavoidanc eo fpushin geffects . 46 3.2.2. Suction with open valves; the avoidance of an inflow throughth eopercula rslit s 49 3.2.3. Maximizationo fth eflo wrat eint oth emout han dth echoic e ofth emomen to fvalv eopenin g 54 3.2.4. Themout hclosur ephas e 57 3.2.5. Streamlinesi nth emovin gfram ethroughou tth efeedin gact . 61 4. Discussion 62 4.1. Hydrodynamicmodel so fth eflo wdurin gsuctio nfeedin g 62 4.2. Thefeedin gmechanis mo fth etrout :a combinatio n ofsuctio nan d swimming 64 4.3. Acompariso nwit hothe r fish 65 4.4. Optimizationsfo ra unidirectiona lflow ;th eke yrol eo fth evalves . . 69 5. Conclusions 71 6. References 73 7. Appendix 74 7.1. Filmingrat ean daccurac yo fvelocit ycalculation s 74 7.2. Correctionfo rperspectiv edistortion s 75
1.Introductio n
Feeding by suction, accomplished by a rapid expansion and contraction of thebucca lan d opercularcavitie s(togethe r denoted asth emout hcavity) ,gener allysupporte d byswimmin gmovements ,i sth edominan t modeo fpre ycaptur e 22 in teleostfish (se eOss e and Muller, 1980).Th e mechanical events during prey capturehav ebee nampl ydicusse d (e.g.Alexander , 1967; Anker, 1974an dOsse , 1969).Littl e attention hasbee npai d to theinteractio n between the suction and swimming apparatus during prey capture. Nyberg (1971), Osse and Muller (1980),Mulle re tal .(1982 )an d Mulleran dOss e(i npress )recognize d theimpor tanceo fpushin ginduce db yswimming . Theyals ofoun d thatswimmin gcontrib utest o directing theflo w towards themouth . This last aspect wasals o put for ward byWeih s(1980) .Recently ,Mulle r and Osse(i npress )wer eabl et odeduc e theflo w infron t ofth emout h from thevelocit y ofth ewate ri n themout h aper turean dth epredator' svelocity . Thepresen t paper aimst oquantif y therelatio n between thefish' s swimming velocity and the expansion rate of the mouth. The approach to this problem wasa combinatio n ofa nexperimenta l flow analysisan dth eus ean d elaboration of the hydrodynamical model of Muller et al. (1982)an d Muller and Osse (in press).Suctio na suse di nth epresen t paperdenote sth econtributio n toth eflo w duet omout h expansion. An analysis of the flow induced by a prey sucking fish shows the amount ofenerg yan dmomentu mpu tint oth ewater ,th eforc eexerte do nth epre ydurin g itscapture , the size and shape of the sucked volume of water and permits one to estimate the chance of prey capture. Furthermore, it checks the validity of hydrodynamical models of prey suction in fish as constructed by Alexander (1967),Weih s(1980 )an d Mullere tal .(1982) . Flowvisualizatio n techniqueshav ebee nuse d to study thefligh t of birdsan d insects (ref. e.g. Kokshaysky, 1979; Spedding, Oxford S.E.B. conference 1980 andEllington , 1978)an dth eswimmin goffis h (seee.g .Hertel , 1966an d McCut- chen, 1977). Muller and Osse (1978 and in press) visualized the flow in front of and behind the mouth of a sucking fish. With their method, however, it is hard totrac eparticl epat h linesi n3-dimensiona lspace . The present paper describes a technique for visualizing the flow induced by suckingfish, usin ghigh-spee d stereoscopicfilming an dmulti-flas h stereoscopic photography.Compare d toth emetho d ofMulle ran dOss ei tprovide sth ecoor dinates of particle path lines in 3dimension s and a direct stereoscopic viewo f thefield o f flow. Some important conclusions about the feeding mechanism of the rainbow trout (Salmo gairdneri, Richardson), such as the relation between the mouth aperture and the maximal flow rate into the mouth and the adjust ment of swimming and suction during feeding, are drawn from an analysis of theflo wpatter ni nfron t ofit smouth . The rainbow trout, a protacanthopterygian, was chosen as the main experi mental animal because of relatively primitive features in itsfeedin g mechanism (e.g. shortspatifor m branchiostegal raysan dth eabsenc eo fa protrusio nmecha nism of the upper jaws). The study of its feeding mechanism, founded upon a thorough model approach, allowsextrapolation s to extinct groups aswel la s tomor eadvance d teleosts. Using the model,constraint s were formulated for the mouth expansion rate and thetim eo fth eopenin g ofth eopercula r and branchiostegal valvesa s func- 23 tions ofth e fish's swimming velocity. They showed good agreement with experi mental data and wereparticularl y useful in a general consideration of the actin- opterygian feeding mechanism.
2.Material s andmethod s
2.1. EXPERIMENTAL SET UP
One specimen each of Pterois russelli(lionfish , s.l. 13.8 cm) and Salmogaird- neri(rainbo w trout, s.l. 34.3cm )wer euse d in theanalyse d experiments. (Feeding acts ofothe r specimens of Salmo gairdneriwer efilme d and used for a qualitative comparison with the above specimen.) The lionfish was kept in a tank of 80x40x40 cm at 25°C . It was fed with live or freshly killed fish. The trout was fed with live fish {Barbus conchonius) or chopped cow heart and kept at 15°C in a 190x60 cm tank, with water 20 cm deep. The size of the aquarium allowed swimming velocities of more than 2m/sec . The nitrite content of the water was checked weekly, and always found to be lesstha n 0.05 mg/1.Th e oxygen content was always above 80%o f the saturation. To visualize the flow unexpanded polystyrene spheres (density 1,033 kg/m3) were put in the water surrounding the prey, as was done by Muller and Osse (1978). For the lionfish, spheres of 0.5 mm diameter were used; for the trout a mixture of 0.5 mm and 1m m spheres. With the lionfish the density of the water was adjusted to match that of the spheres by slightly varying the salinity. Thiscoul d not bedon e for the trout. Hence,a differenc e of 0.034 kg/m3 between the density of the spheres and the water had to be accepted. The sinking speed of the0. 5m m and 1 mm spheres in quiet water was4. 4mm/se c and 10.2mm/se c respectively. Thepre y wasalway s sucked into themout h within 50msec . During this time the displacement due to gravity is 44% of the diameter for 0.5 mm spheres and 51% for 1 mm spheres. Feeding events of both fishes were filmed at 175 to 400 frames/sec, using a Teledyne DBM 54 16m m high-speed camera with an Angénieux 10xl2A zoom lens. Filming was done with KODAK double-X negative films (25 DIN / 250 ASA). Films were taken with continuous light (power input of 12 kW, effective ly, however, almost 24 kW due to focussing) and an exposure time of 4000"1 sec in most cases. Warming of the aquaria by the filming lights was reduced by filtering out the red part of the spectrum and cooling of the water in the aquaria. The temperature increase never exceeded 1°C . The animals were trained to feed under the high light intensities before films were taken. Training lasted about 2 weeks or longer when needed. The prey was often jerked from the water with a nylon thread to elicit forceful and rapid feeding acts. As the trout leaped out of the water to the food during training as it does in the wild, the filmed sequences are presumably close to normal feed ing behaviour. For both Pterois and Salmo more than 20 feeding acts were filmed. All films of Pterois were taken by Mr. M. Muller and will be discussed 24 elsewhere in detail (ref. Muller and Osse,i n press). Torevea l thedirectio n ofth eflo w near the opercular slitsblac kcotto n threads (approximate length 1cm ) were sewn to the specimen of Salmo gairdneri near the right slit, at the positions indicated in Fig. 10. During sewing the animal was anesthetized in a solution of MS 222 (80 mg/1). It recovered within half an hour. Next day 14 feeding acts were filmed. No abnormal behaviour was observed. Apart from the cine filming, photographs were taken during several feeding attempts using a NIKON camera with a 55 mm macro lens. Lightning was by three Braun 410 VC electronic flash units in the variopower mode. Flash dura tion ranged from 0.1 to 0.4 msec. An electronic device was built to obtain three sequential flashes (for one exposure) at intervals in the range from 0.5 to 7.5 msec, with a preset accuracy of 0.1 msec. Flashes were recorded with a photo- diode and the sequence displayed on a storage oscilloscope screen. So the inter vals could be measured. Sequential flashing was used to obtain particle path- and streamlines around the fish's head, with accuracy up to 6 times that of cine filming.
2.2. THE ACQUISITION OFA THRE EDIMENSIONA L PICTURE
Initially films were taken with a mirror placed at 45° t o the horizontal plane ventrally from the fish. This was done in all films of Pterois. Both a lateral (or
Mi 1 [h
Fig. 1.A diagrammati c representation ofth eexperimenta l setu p seen from above.Abbreviations : a, aquarium withfish; C , control plane of calibration frame;ƒ ,film camera ; F,fiducial plan e of reference frame; /,filming lights ; r\, n axes of possible rotations of the outer mirrors; s, stereo adaptorwit hsurfac emirrors ;t, directio n ofpossibl etranslatio n ofth eoute rmirrors .Furthe rexpla nationsar egive ni nth etext . 25 frontal) and a ventral view of the fish were so obtained. However, it was almost impossible to obtain the three dimensional coordinates of the polystyrene spheres as it was hard to recognize individual spheres on both views. Therefore the mean velocity between successive frames of the film could be estimated only roughly. In later experiments, all those with Salmo, a stereoscopic method was used (see Fig. 1). A set of mirrors was positioned in front of the objective of the camera to record a stereoscopic pair of pictures on each frame. Two aluminized front-surface mirrors (flatness < 1nm , quartz coated, 50x80 mm each) were positioned directly in front of the objective at a distance of about 3 cm, at 45° to the plane of the objective. At both sides slightly larger mirrors (75x100 mm each) were positioned, almost parallel to the nearest medial one, but slightly toed in so as to get two stereoscopic views of the same scene on each film frame. The distance between these mirrors could be varied. To obtain an optimal accu racy this distance was as big as could be without making the views so different that the mind could not fuse them into a three dimensional impression. An al most lateral view of the fish thus obtained was sometimes combined with a ven tral view. The film could be watched in stereo by using the mirror set up as a stereoviewer. The position of individual spheres or selected points on the fish could be seen in space and their coordinates could be calculated accurately (see paragraph 2.4.) if stationary reference markers were put in the aquarium. Two parallel black bars, set 295 mm apart in a rigid frame, were used. Each bar bore whitedot s (diam.= 0.85mm) ,wit h known Cartesian coordinates. The bars were seti n aplan e about parallel to theplan e of the objective. Account was taken of all rotations made by the fish during suction when measurements of moving head parts of the fish were made. A ventral view of thefish i sneede d to measure suspensorial and opercular abduction. Lens abera- tions weremeasure d but appeared to introduce no significant errors. The stereo adapter used for cine filming was also applied in the multi-flash photography experiments.
2.3. THE ACQUISITION OF PARTICLE PATH- AND STREAMLINES; EARTH-BOUND AND MOVING FRAME
Thecurve sdescribe db y theflui d particlesi ntim ear ecalle dpat h lines.Stream lines are everywhere tangential to the instantaneous velocity in the fluid. Path lines can be obtained by printing subsequent frames of a high-speed movie over each other and connecting the successive images of the individual spheres by solid lines.Pat h linesar e directly obtained (in an earth-bound frame) when mul ti-flash photography is applied. The recognition of particular spheres in successive frames is a prerequisite for thismethod . With the stereoscopic technique a clear three-dimensional view is obtained, and it is usually easy to follow chosen spheres. The path lines can be seen as dotted lines in three dimensional space, by printing successive frame overeac h other. Theflo w direction can bemad eunambiquou s byusin g different 26 exposuretime swhe nprintin gth esuccessiv eframe s overeac hother . Soth edot tedlin eappear sheavies tat ,fo rexample ,th eearl yend . Theflo wca nb edescribe di ndifferen t ways.On eca nconside rth eflo wrelativ e to an earth-bound frame. The frame of reference (e.g. the aquarium) is kept stationary. Thus fiducial bars are kept in the same position when successive frames of the film are printed over each other. Or one can analyse the flow relativet oa particula r part ofth emovin gfish, keepin gtha tpar t ina fixed posi tionwhe n thephotograph s areprinte d or analysed (Seeals oMulle re tal. , 1982 and Muller and Osse,i npress) .I nth epresen t paper, thecentroi d of themout h aperture, M, (the point halfway along the line between themos t rostral points on the snout and the symphysis of thelowe rjaws , see Fig. 3A)wa s the datum for the moving, "fish-bound" frame. The earth-bound frame must be used to calculateforce san dimpulses .Fo rpre ycaptur eth eflo wwit hrespec tt oth emov ingfram e ismos t useful. When velocities change relatively little between two successive frames, path linesapproximat e streamlines. However, suction feeding infish i s a highly un steady process. In the mouth aperture of a sucking trout the absolute value of the velocity might increase about 0.5 m/sec per msec in the fish-bound frame, anacceleratio n of50 g(Oss ean dMuller , 1980). Thus during the worst period, the first 15mse c of the suction process, the streamline pattern might change dramatically in and near the mouth aperture in 2.5msec ,th esmalles t timeinterva l between two successive frames, and path lines are far from being streamlines. At other times path- and streamlines will beles sdissimilar . Although accelerations of thefish ar e generally less than those of the water entering the mouth in the fish-bound frame they can approach values of lOg at some stages of the suction process. Thus an increase of about 0.25 m/sec in fish velocity might occur between successive frames, using a film speed of 400fr/sec . The accuracy of calculations of fluctuations in the velocity (and thus of the streamlines)increase swhe na highe rfilming rat ei sused .However , thedistanc e travelled by the particles from frame to frame decreases with a higher frame rate, thus increasing the error in the calculation of the mean velocity between successiveframes . Inth eappendi x(7.1. )i ti sshow ntha tfo r thepresen tvelocit y rangea filming rat eo fabou t20 0fr/se c givesmos treliabl evelocit y data. Thepat h lineso fth epolystyren e sphereswil lgenerall ydeviat efro m the fluid path lines due to the density difference between spheres and fluid. In 0.1 sec the sinking distance due to gravity is about equal to the sphere diameter for both the 0.5 mm and 1 mm spheres (seeparagrap h 2.1.). When the path lines arecurve d thesphere s willdeviat e from theflui d path lines(centrifuga l effect). This isunimportan t when the centripetal acceleration of thefluid i s no bigger thanth egravitationa lacceleration ,a conditio nfulfilled , exceptclos et oth eedge s ofth emouth ,wher ehighe racceleration swer eobserve d (upt o 10g). Particles entrained in a shearing flow will suffer lift forces in the direction of the velocity gradient (Merzkirch, 1974), and again particle path lines will 27 differ from fluid path lines. In the case of a sucking fish the largest velocity islikel y to occur at the centre of the field of flow. Hence the polystyrene spheres will tend to deviate to the centre. This effect, however, will be negligible when the dimensions of the particles are small relative to the dimensions of the fine structure of the field of flow to be studied (Merzkirch, 1974).Durin g more than 50% of the suction event the mouth diameter is an order of magnitude larger than the largest sphere diameter. During this phase passes more than 90% of the total volume to be drawn into the mouth (see Fig. 12). Only at the start and end of the suction event, when the mouth aperture is smaller, might quite large deviations of the spheres from the fluid streamlines be present. At any solid wallflui d isstationary , and large velocity gradients willb e found in the boundary. Large accelerations round the fish's lips will likewise cause large gradients. Spheres of 0.5 mm are too large for a study of the flow in this area (Merzkirch, 1974),bu t will nevertheless follow the streamlines much better than most food particles.
2.4. CALCULATION OF POSITION- AND VELOCITYVECTOR SI N 3-D
Displacements, and hence the velocities of the polystyrene spheres can becal culated using reference markers mentioned earlier. (Care must be taken that
(0,0
Fig. 2.Fram e of reference for the calculation of the coordinates of points in 3-D. Lines PLF PLC and PRFPRC aresee na son epoin t inth elef t (L)an d right (Ä)picture so fa stereograph .Abbrevia tions: C, control plane; F, fiducial plane; P, point in space; PLC and PLF, left projections of P on planes C and F; PRC and PRF, right projections of P on C and F; X,Y,Z, axes of reference frame;zo ,distanc ebetwee nplane sC an dF . 28 these markers fall within the depth of focus). A simple method of calculation was used. A list of symbols used is given in Table 1.A more advanced method, applied to X-ray photogrammetry, can be found in Selvik (1974),wher e statisti calmethod san d aspecia lcalibratio n procedurear euse dt oimprov eth e accuracy ofth e method. Suppose that a set of reference points is put in a plane F (the fiducial plane) and another set in plane C (the control plane), parallel to F (see Fig. 2). Let the distance between the planes be z0. A Cartesian coordinate system is defined with the Y- and Z-axis in F and the Z-axis perpendicular to F. The coordinates of apoin t P are denoted as (xp,yp, zp). The two pictures of a stereoscopic pair are denoted with L (left) and R (right). The projections of P on F and C in L are denoted as PLF (XLF, )>LF, ZLF) and PLC(XLC, )>LC, ZIC). Similarly for R. The coordinates of the projections ofP o nF an d Cfo r L and R can bemeasure d from astereoscopi cpai r ofpictures . P lies on the intersection of the lines PLF PLC and PRF PRC The equation of PLFPLC is: XL\ /XLF\ /XLC—XLF\ yL )= I yLFJ + -^HyLc-yLF | (1) ZLJ \ZLF \ZLC—ZLF
Table 1: Symbol s and notation All physical quantities are expressed in SI units.
a Parameter describing relation between Ufan d w'i as a result of suction. A Cross-sectional area of expanding and compressing profile. b Parameter describing relation between Ufan d u'\ as a result of suction and swimming B Range of oscillating velocity (see 7.2.) C Control plane c,d Constants used incorrectio n for perspective distortion ƒ Frequency of oscillating velocity (seeappendi x 7.1.) F Fiducial plane g Gravitational acceleration h(x',t) Profile radius h;h\,h2 Radius ofcylinder ; radius at x' = Ian d x' = 0 h;h\,fi2 Expansion rate of cylinder; anterior and posterior expansion rates of cone ht,fi\,t Threshold expansion rates for cylinder and cone model he, h\,c Critical expansion rates for cylinder and cone Ineffective Effective radius of the mouth aperture i Frame number offilm / Length ofcylinder , cone and fish's head 29 L Left picture of stereograph M Centroid ofmout h aperture P Point in space PLF, PLC Projections ofP onF and C in L PRF, PLC Idem for R Pebf Point where thewate r isa t rest in theearth-boun d frame Pmf Idem for movingfram e X',Y',Z' P\ebf, Piebf Points of zero flow in cone with open valves in earth-bound frame during mouth closure phase. P\mf, Pimf Idem for moving frame X', Y',Z' q;q Velocity vector inearth-boun d frame; idem for speed (scalar) q', q' Idem in moving frame q'prey Speed of the preyi n themovin g frame qm,q 0 Mean velocity and oscillating velocity asdefine d in 7.1. Q; Q Velocity of the origin of the moving frame, M, in the experimen tal approach; idem for speed R Right picture of a stereograph rasymptote Radius of asymptote of dividing streamline s Distance along contour S Scale factor explained in appendix 7.2. t;t t Time;Momen t at which frame iwa s taken tKhnax Moment ofmaxima l opercular abduction tprey Moment of prey passage through mouth aperture ut, vi, wi Velocity components ofq i n X-, Y- and Z-directions at frame i UuVuWi Idem for Q u', r', t' Velocity components incylindrica l coordinates in moving frame Uf Velocity of cylinder, cone or fish in model approach Ut Threshold translational velocity u'\ Velocity at x' = I, relative to moving frame u'i Idem for x' = 0 u'v(x',t) Velocity ofwate r inmovin g frame before valve opening w\ Half of the width of the mouth aperture x'ro x'ro Positions ofPebf before and after valve opening x,y,z Cartesian coordinates in earth-bound frame X,Y,Z Axes ofearth-boun d frame x'.y', z' Cartesian coordinates in moving frame X',Y',Z' Axeso fm ovin g frame XAP,yAP Actual projected coordinates ofP on distorted plane yDP Explained in 7.2. xip Coordinate ofP along Xi-axis Xx Axis defined in 7.2. Zo Distance between planes F and C <5qm,<5q 0 Error in qm and q0 dt, Ox Errors indeterminatio n of time and position ta, Ti Actual and ideal moments of valve opening 30 and for PRFP'RC: (XR\ IXRF\ IXRC—XRF\ yR1 = Iy«p J H— ^\yitc-yRF J (2) \,ZRJ \ ZRFJ \zRC —ZRF J
At the intersection of the two lines ZL = ZR = zp, hence:
Zp XRF— XLF }>RF— yLF ... zo (XLF-XLC)-(XRF-XRC) (yLF-yi,c)~ ()>RF-yRc) The mirror set up is positioned almost parallel to the X-axis. Hence the X- parallax will be much larger than the F-parallax. Thus the expression in x for zpshoul d be used in calculating P. The coordinates ofP are found by substitut ing zp for ZL in equation (1). The optical axes of the left and right views are not perpendicular to planes F and C. Hence, these planes willb e subject topers pective distortions, leading to errors in the measurements of the projections of Po nbot h planesu pt o 5%.Becaus ethi swoul dcaus e seriouserror s inth e calcula tions of the z-coordinates, the measurements from the film were corrected for perspective distortions before the above calculations were carried out (the cor rection isexplaine d in appendix 7.2.). Theposition s of P can becalculate d for a particular sequence of frames (each representing a stereoscopic pair).Th edistanc e travelled byP between successive frames can be calculated by using three-dimensional Pythagoras. The compo nents in the X, Y and Z-directions in, v, and wio f the velocity q (a vector) of Pfo r a particular frame iwer ecalculate d with the following formulas: Xi+l— Xi-l Ui = ti+1 — ti-1
yt+i-yt-i Vi = -• — (4) ti+l — ti-l Zi+ 1 — Zi- 1 Wi = ti+l — ti-l where (x,_i, j>,_i, z,_i) are the coordinates of P at the foregoing frame i-l, and d-\ the time at which frame i-l was taken. Similarly for the next frame /'+ 1. The speed q( a scalar quantity) ofP isgive n by: q = ^u2i+v2i+w^ (5) The velocity of P can also be calculated relative to a particular (moving) point M, with velocity Q = Ui + Vi + Wi. The "relative velocity components" are given by:
(ui-Ui),(Vi-Vi),(wi-Wi). (6) The directions of the above components are defined by the reference frame. However, therelativ e velocity willb emor e informative when resolved into com- 31 (B)
Fig. 3.A .Drawin g showingth eearth-boun d frame, with X-,Y- and Z-axes and themovin g frame with X'-, Y'- and Z'-axes. In this figure the centroid of the mouth aperture, M, is chosen as the origin of the moving frame. In paragraph 3.2. the mouth aperture is taken at x' = /. The A"-axis ischose nalon gQ ,th evelocit yo fth efis hi nth eearth-boun d frame. B.Th e velocity q' in the moving frame X',Y',Z' can be calculated in cylindrical coordinates with components u',r' and t', in the X'-, radial and tangential direction respectively. M represents the origino fth emovin gframe .
ponents whose directions follow the orientation of the fish (see Fig. 3), with perpendicular axes X', Y', Z'. The A"-axiswa s chosen in the direction of move ment of the fish, thus along Q and the Z'-axis parallel to the ZX-plane. The centroid of the mouth aperture M was chosen as the origin of the moving frame. Forpractica l reasons,however , inparagrap h 3.2.M willb elai dalon gth el"-axi s at x' =l, wher e / is the fish's head length. This last frame equals the moving coordinate system chosen by Muller et al. (1982) when they are concerned with theflo w insideth emouth . For thistransformation , which involvesbot h rotation and translation for each frame of the film to be analysed, standard formulas were used (See Spiegel (1968), p. 49). Cylindrical coordinates (Spiegel, 1974; ps. 137, 138 and 143) proved to be useful for the expression of the velocity in the moving frame, as the sign of the radial component shows directly whether theflo w iscontractin g ordiverging .Th ecoordinat e systemsan d velocity compo nents areillustrate d in Fig.3 . The above calculation can be carried out for each of a chosen set of polystyr ene spheres throughout the suction act of the fish. The results obtained have a maximal error of about 1 to 1.5 mm in the calculated positions of the spheres. This was determined with a calibration object bearing a set of points whose coordinates were known to the nearest 0.05 mm. The same calculations can be performed for the multi-flash experiments. The complete capture event can not then be traced, but the accuracy of measurements increased to about 0.3 mm.Th emaxima lerro r inth evelocit ycalculation s from thecin efilms wa s about 0.15m/sec. All calculations were carried out by means of FORTRAN-programs run on a MINC-11-computer (Digital) and the DEC-10 system of the Agricultural uni versity. 32 Fig.4 . Acompositio n of three successive frames of a 200fr/se c film of a feeding Pterois russelli. Thus thispictur e represents a time interval of 10mse c (at 21% to 32%o f the phase that a mouth aperture is present). The white dots represent polystyrene spheres. The mouth aperture was kept at a fixed position during successive printing. Thus the flow isvisualize d in thefish-bound frame . The estimated dividing streamline is shown by dashed curves. Upper part: lateral aspect; lower part:ventra laspect ,obtaine d viaa mirror .A 1 0m mscal ei spresen ta tth elef t sideo fth epicture .
3. Results
3.1. EXPERIMENTAL OBSERVATIONS
3.1.1. Pterois Both ventral and lateral views at a certain stage of a feeding event of Pterois russelli are shown in Fig. 4. Three successive frames of a 200 fr/sec film were printed over each other. The mouth aperture of the fish was kept at a fixed position, hence the path lines shown are relative to the sucking fish. Only when a particular sphere was unequivocally followed from exposure to exposure was a path line constructed. A striking feature of Fig. 4 is the directedness of the flow. The flow isdiscusse d in more detail in Muller and Osse (in press). 33 3.1.2. Salmo: observationsfrom cinefilm and multi-flash photography Fig.5 showsa stereograp h ofa feedin g Salmogairdneri. Thefram e wastake n justbefor e preycaptur ean dpea kmout hgape . Fig. 6 shows three stages in the course of the same feeding event. The flow was visualized relative to an earth-bound frame. Two successive frames were printed over each other for each stage. These pictures show that whereas the fish wasi nmotio n thewate ri nfron t ofit smout hwa salmos ta trest ,a si sappar ent from the positions of the spheres and prey. This observation suggests that theflo wi shighl ydirecte d relativet oth e fish. The flow relative to the centroid of the fish's mouth is shown in Fig. 7, a stereograph of another feeding act of Salmo gairdneri. As expected from Fig. 6 the flow contracted only slightly towards the mouth. The estimated height ofth edividin gstreamlin e far from themout h wasabou t thesam ea sth eheigh t of the fish, aspredicte d by Muller et al. (1982).(Th e dividing streamline isth e instantaneous boundary that envelops the water that tends to flow into the mouth). Fig.8 show sth e results of amovemen t analysis of the feeding event ofFigs . 5 and 6. The plots of mouth opening and opercular abduction show a delay
Fig. 5.A stereoscopi cpai r ofpicture so fa feedin g Salmogairdneri, printed from afram e ofa high speedmovi e(abou t 175 fr/sec). Animag ewit h depth can beobtaine d whenthes epicture sar esee n through a simple pocket stereoscope (or directly by a trained person). The points denoted with arrowsar epar to fa referenc efram euse dfo rcalculatio no fcoordinate s(distanc ebetwee nsubsequen t points is 5cm , seeparagrap h 2.4.). Other white dots represent polystyrene spheres,use d for flow visualization.Thi spictur e showsa momen tjus t before themaxima lmout h opening and preycap ture.L an dR denot elef tan drigh tpicture so fstereograph . 34 between rostral and caudal expansion. The branchiostegal and opercular valves(cauda lvalves )opene d relativelyearly ,befor e themaxima lmout h open ingha d been reached and before the operculars had reached half ofthei rmaxi mal abduction. Thisi sno t soi n several other fish species(se eMulle r andOsse , inpress) .Th epre y entered themout h at the moment it was opened widest, as was noted also by Muller and Osse (in press). The mouth closed faster than it opened. Perhaps this increases the chance of prey capture. The plot of the distance between the prey and the centroid of the mouth aperture (this point isdepicte d in Fig. 3)a sa functio n oftim edi d not deviatemuc h from a straight line,no rdi dth edisplacemen tcurv eo fth ecentroi d ofth emout hapertur ewhos e slopewa sopposit e and about equal inmagnitude . These twocurve s show that thespee d ofth epredator wasfairl y constant and that most ofth etim eth epre y wasalmos t at resti na nearth-boun d frame. Careful analysis,however ,showe d that the prey was initially slightly pushed forward, about 2 mm, by thefish. Then for a period it was stationary, so that no significant impulse was given to it. This situation altered when the prey was 20 mm away from the mouth aperture (about 25%o f thefish's hea d length). From thismomen t on thepre y moved towardsth emout h in anearth-boun d frame, but at amuc h lowerspee d thantha t ofth epredator (se eals oFig .6 ,A an dB an dchapte r2) . To investigate the flow at other places the movements of three polystyrene spheres were analysed. Their positions at the start of the suction process are shown in Fig. 13. They were all slightly pushed away by the predator (in an earth-bound frame) when they came close to the mouth. This is shown by the upward curving ofth egraph s ofth edistance sbetwee n thesphere s and thecen troid of the mouth aperture given in Fig. 8. This slope is also influenced by thevelocit yo fth epredator .A chec ko nthis ,combine d withth eactua l positions of thesphere si n anearth-boun d frame asfunction s of timerevealed , however, thatchange si nth evelocit yo fth efish wer eo fmino rimportanc ei nthi srespect . Sphere 1,originall y situated between the fish and the prey, was drawn into the mouth preceding prey capture. Sphere 2wa s originally situated above the prey, near the boundary of the volume of water eventually sucked in. Before it entered the mouth it was also pushed away, demonstrating that during this phase the speed in the moving frame increased towards the A"-axis (depicted in Fig. 3).Th e samephenomeno n was observed byNyber g (1971)fo r thelarg e mouth bass (Micropterus salmoides). The third sphere wasno t sucked into the mouth, butpushe d awayjus t before and after themout h closed. Flowpattern swer eals oexamine dusin gmulti-flas h stereoscopicphotograph y with decreasing intensity in successive flashes. Over one hundred fifty stereo graphswer etaken , eachcomprisin g 3 exposuresi n 5msec ,o fth esam enumbe r of feeding acts of Salmo gairdneri. The stage of the feeeding act at which each photograph wasmad ecoul d beidentifie d easily with theinformatio n from the high-speed film A series of stereographs at stages throughout the feeding act(obtaine d from different feeding events)i sshow ni nFig . 9. Theexperimen twit hthread sreveale da mino rinflo w throughth ecauda lpart s of the opercular slitsjus t after caudal valve opening, followed by a significant 35 (A)
(B)
(C)
•" I t t t t t Fig. 6. Flow visualization in an earth-bound frame of some stages of the same feeding event of Salmo gairdneri as presented in Fig. 5. Two successive frames, each representing a stereograph, 36 m N CD ü LU S « 2 -v 5d^ z -~ O) -- to co * b » c5 ^ 3£ *^ »- ri>co • • >^ <= S Q. LU 0. CO « E O CO co O ü CJ> £ *: O O) ~ O fc S s H O O £ £ £ U. Q. *" co £ c * oM c S :=* co co T3 O) .•e o •0 c o <^ • g 5 I E •- Id3 ° S 73 g E §• 1 N CD ci> « "- co x o 2s •B z '* .o c 8D ^ £ CD LU C 'S UJ O -J t: -1 £ rf co tr -^ !>^ 1«>• ÊCD x » LU .2 E F -O O £ z 5 • (73 51 r= co »- < co 13 O _ < c co 2 • H S wereprinte d over each other with the reference frame kept at the sameposition . Thefilm camer a hadno tye treache da constan tspeed .Hence ,th etim einterva lbetwee nsuccessiv eframe s wasshorte r towards theen d ofth efeedin g event. Successivetim einterval swer ecalculate d with theai d oftim e pulses at the edge of the film. Picture A represents a time interval of 5.6 msec (30.3% to 36.8% of the phase that a mouth aperture was present). For picture Ban d C these values are 5.3mse c (61.3% to 67.9%) and 5.3 msec (80.0% to 86.5%) respectively. Arrows denote distances of 5c m inth econtro lplane . outflow (see Fig. 10). Just before mouth closure a second minor inflow was detected. Fig.9 an d 10ar efurthe r explainedi nsectio n3.2 . 3.1.3. Salmo: velocity-and volume calculations Mouth expansion causes water to flow rearward in front of and inside the mouth in an earth-bound frame. Thismas so fwate r has rearward momentum. Mouth expansion adds also forward momentum to thefish an d an additional mass of water posteriorly inside the mouth (seeMulle r and Osse, in press and 3.2.1.). The latter effect cannot be easily demonstrated by an increase in the velocity of the centroid of the mouth aperture, because it is superimposed on presumably larger effects due to swimming. The fish's forward velocity was about 1.3 m/sec (about 3 body lengths/sec). The slight oscillations (about 40 Hz) in the curve of the speed of the centroid of the mouth aperture, given in Fig. 11, cannot result from snout motions caused by swimming, because at a speed of 3bod y lengths/sec the swimming undulations occur at about 5 Hz. The 40 Hz oscillations may be due to mouth opening and closure movements ofth ejaw so rerror si nth evelocit ycalculation . Fig. 7. Visualization of the flow induced by Salmo gairdneri, relative to thefish. Tw o successive stereographso fa high-spee dmovi e(20 0fr/sec )wer eprinte dove reac hother ,representin gth ephas e that themout h hadreache d about 90%o fit smaxima laperture .Th ecentroi d ofth emout h aperture waskep ta ta fixed position .Not eth edirectednes so fth eflow . 37 distance (mm) î 120 prey 20 40 60 -»time (msec) Fig. 8. Plots of a movement analysis of the prey capture event of Figs. 5an d 6 of Salmo gairdneri. Symbols used:•&-• & The height of the mouth aperture; * - * Distance between the caudal edges of the left and right opercula (the opercular abduction); A-A The distance travelled by the centroid of the mouth aperture (depicted in Fig. 3); jç-jç The distance between the centroid of the mouth aperture and the prey (a piece of cow heart). The distances between 3polystyren e spheres and the centroid of the mouth aperture are denoted near their respective graphs. The initial positions of thepre y and polystyrene spheres aredepicte d in Fig. 13.Th e vertical linedenote d with xa represents the moment of the actual start of the opening of the opercular and branchiostegal valves. The dashed line depicted with T/denote s the ideal moment of valve opening discussed in paragraphs 3.2.2. and 3.2.3. The vertical line denoted with tprey stands for the moment that the prey passed themout h aperture. Further explanations are given in the text. Fig. 9. A series of stereographs of Salmo gairdneri obtained by multi-flash photography (3 flashes were used). Polystyrene spheres were used for flow visualization. A decreasing light output was used from the first flash to the third one, so that structures are printed darker with increasing time. Obviously, the flow is visualized relative to the earth-bound frame. Events are described relative to thisframe . Stereographs (A)t o (D) represent different stagesi n the activity of the feeding mecha nism, however, obtained from different feeding acts.Tim e intervals between successive flashes were 2.5 msec. The speed of the fish (m/sec) is denoted near each stereograph. The pictures do not show all details given in the description as there were not enough polystyrene spheres at all places of the field of flow in one picture. Missingdetail s wereobtaine d from other feeding acts. A. Phasejus t after the moment of mouth opening. Water was sucked towards the mouth aperture and pushed by the fish's lips and other head parts. A circulation around the fish's expanding mouth was started. An anterior 'vortex' was formed due to suction and a posterior one due to forward motion of the fish (see paragraph 3.2.1.). The posterior vortex is partly replaced by the fish's body and therefore difficult to recognize. Only thedorsa l aspects of the vorticesca n besee n inth e illustra tion. 38 1.45 m/s Fig. 9. 39 B. Flow at the moment of the opening of the caudal valves. The circulation of water continued to be present. Water was sucked towards the mouth. The prey started to bemove d in the direction ofth emout h aperture.Th e speed ofth epredator , however,wa sver y much higher. Water waspushe d by the forward moving the lips, neurocranium and mouth bottom. Seemingly, quite some water is sucked into the mouth from above the neurocranium, from underneath the mouth bottom and from the cheeks. However, the considerable forward motion of the fish prevents most of this water to enter the mouth. In fact, the flow is highly directed relative to the fish's mouth (see Fig. 7 and 21).Thi sstresse s the importance to make adistinctio n between earth-bound and moving frame. C. Phase after the maximal mouth opening. Water continued to flow towards the mouth aperture due to the continuing caudal expansion. Note the pushing effects of the fish's head. Two 'vortices' were present around the fish's head (see 3.2.4.). In the moving frame the flow inside the mouth wasunidirectiona l (in a caudal direction).Wate r outside themout h flowed towards the caudal parts ofth eopercula r slits,however , a net caudal outflow stillexists .Th epre y wasalread y captured. D. Phasejus t before mouth closure. Water was very slightly pushed forward in the mouth aperture. From other multi-flash pictures and the thread experiment (Fig. 10)i t appeared that a clear outflow through the rostro-ventral parts of the opercular slits during this phase exists, whereas a slight inflow through the caudal parts of the slits is present. Presumably only one 'vortex' around the fish's head islef t at this phase. Unfortunately the complete field of flow has not yet been visualized. However, the results obtained until now corroborate with the single-vortex hypothesis (see para graph 3.2.4.). Note the direction of the polystyrene spheres near the fish's lips and compare those with the direction of the streamlines of Fig. 19D. Before valveopenin g the speed of thepredator , Q,i n theearth-boun d frame was generally higher than the speed of the prey in the moving frame, q'prey (passive prey, cow heart, was used so the prey would not swim, see Fig. 11). After valve opening the reverse was true. Thus the prey was pushed slightly before the opening of the valves, and actively sucked towards the mouth by the predator (in an earth-bound frame), once the valves had opened. The ob served pushing effect inq'prey fall s within themaxima l error ofvelocit y calcula tion. It was,however , also observed in thepositio n data for a series of feeding events. A calculation of the (rearward) velocity in the mouth aperture, using Fig. 10. Series of selected pictures of a stereoscopic high-speed film (215 fr/sec) of Salmo gairdneri feeding. Each picture shows a lateral and a ventral aspect of the fish's head. Pictures (A), (D), (E) and (H) are given asstereographs . Pictures (B),(C) ,(F ) and (G) represent only the right pictures of the stereographs. The time from the start of mouth expansion onwards is given in msec near each picture. Black threads were sewn to the flap of the gill cover (-» position 1, see C, initially crossing the thread at position 2), a position just anterior to the pectoral fin (-*+ position 2, see C, one thread lies dorsally from the pectoral fin and another ventrally) and at a position near the rostro-ventral part of the opercular slit (-»-»-• position 3, see ventral aspect of Fig. C, with two free ends). The movements of the free ends of the threads depict the flow direction in the moving frame if compared to their fixed ends on the fish. The initial, rostrally directed, movements of the threads at positions 1an d 2, depict the initial caudal inflow before the instant T;( A to D). Before the instant xa these threads already moved towards the opercular cavity (A to C). Thus a minor leak current was already present before actual valve opening.Afte r the initial inflow a clear outflow occurred demonstrated by thread 2 being swept caudally (D to F). During this caudal outflow the mouth reaches its maximal aperture, and the prey is generally captured At the end of the mouth closurephas e a minor secondary caudal inflow isindicate d by themovemen t of thread 2i n a rostral direction (G to H). The threads at position 3 were not noteworthy drawn into the direction of the slits, so, an inflow at this position was absent. The prey is not clearly visable. The nut was used to drop theprey . The prey was captured quite early (at 43msec) . 40 (A) 18.6mse c (B) 32.6mse c (C) 41.9 msec (D) 51.2mse c 41 (E) 55.8mse c (F) (G) 65.1mse c 79.1mse c t;*SSÄS^t|ä«*i»t!, (H) 88.4mse c 42 Velocity (m/sec) î 40 60 -»tim e (msec) Fig. 11. Graphs of velocity calculations of the feeding event of Salmo gairdneri of figs. 5, 6 and 8. Symbols: A-A, the speed of the centroid of the mouth aperture in an earth-bound frame, Q; •fc-'k, the speed of the prey in the fish-bound frame, q'prey', A~A, the threshold swimming speed needed for the fish to prevent a caudal inflow in case of open valves, Ut(calculatio n via formula (14), paragraph 3.2.2.). q'prey is about equal to Q, indicating that the prey is almost at rest in the earth-bound frame. The actual and ideal moments of caudal valve opening (x„ and %,) and the moment of prey capture are denoted as in Fig. 8. T, falls at the moment where the curves U, and Q intersect (at 58 msec). In the model approach (paragraph 3.2) it is assumed that the fish moves with velocity Vf along the Z-axis. Pushing occurs in the earth-bound frame when q'prey isles stha n Q.Finally , thepre y isclearl y sucked towards the mouth. the multi-flash flow visualization technique, revealed a maximal magnitude of only 25%o f the fish's forward velocity. Except just before mouth closure, a pushing effect occurred only at the edges of the flow entering the mouth. It wascause db yth eforwar d movinglips . Asth e movements of the prey and spheres in front of the mouth weresmal l compared toth emovement s ofth epredator , thevolum edraw n intoth emout h by thefish wa s calculated by assuming that all the water had zero velocity in anearth-boun d frame. In otherwords ,i nth emovin gfram e thereexiste d auni form flow into the mouth of the fish, so the volume of water sucked into the mouth in a time interval At= u+\ — ft equal s the area of the mouth aperture times the distance travelled by the mouth during the interval. The area of the mouth aperture was taken equal to nh\ w\, where h\ is half its height andw\ half its width, to account for the elliptical shape of the mouth. For the prey 43 captureeven tpresente d above w\ could not bemeasure d onal lrelevan t frames. Therefore therelatio nbetwee nh\ an dw\ wa sdetermine dfro m afrontall y filmed suctionevent .Th eflo wrat ethroug hth emout hapertur ewa sobtaine db ynumer icaldifferentiatio n ascarrie d out for thevelocitie s(formul a (4)).Th eabov ecal culation underestimatesth evolum etake ni nb ya maxima lvalu eo f25% . The graph of the intake of water (Fig. 12,calculate d for the feeding event of Figs. 5,6,8 and 11) shows that the flow rate was highest when the mouth was maximally opened and the branchiostegal and opercular valves had been opened (compare Fig.8 and 12).Sphere swer esee nt oflo w out ofth eopercula r slitsdurin g thisinstan t (movingframe) . Thiscauda l outflow supports the flow through themout h aperture. Astrikin g feature of Fig. 12 isth ehighl y variable flow rate. Fig. 13depict s the fish at the start of the mouth opening and the watertha t willb eingeste d during thesuctio n event.Thi spictur ewa smad ewit h theassumptio n ofa unifor m stream intoth emouth . Thegreates t distance from Volume drawn into the mouth (ml) Î 40 60 80 ->tim e (msec) Fig. 12.Graph s of the volume drawn into the mouth by Salmo gairdneri and the occurring flow ratethroug h themout h aperture. Calculations weredon e for thefeedin g event of Figs. 5,6 ,8 and 11. So Figs. 8, 11 and 12ca n be directly compared to each other. Symbols:•&-•& , the volume sucked into the mouth; -jç-ir, the flow rate through the mouth aperture. The flow rate ishighl y variablean dreache sit spea kvalu ewhe nth emout h apertureha salmos treache d itsmaxima lampli tude. The actual and ideal moments of caudal valve opening (xa and Zj) and the moment of prey capturear edenote da si nFig .8 .Furthe rexplanation sar egive ni nth etext . 44 which water was sucked in (indicated in Fig. 13)wa s about 1.3 times the fish's head length. This distance equals the translation of thefish durin g the period thatth emout h isopen . The maximally ingested volume was about 5.5 times the volume ingested at the moment of the opening of the opercular and branchiostegal valves. Using a cone approximation to calculate the volume of the mouth cavity (seeMulle r et al., 1982)i t wasestimate d that at the peak volume change of the mouth (at about 67 msec) maximally 30%o f the ingested volume of water had already flowed out through the opercular slits. Peak volume change was calculated as the difference between the maximal volume of the mouth cavity (with valves open!)an d thevolum e at the start ofth eexpansion . The prey wasa t thecentr e ofth emas so fth evolum eo fwate rt ob esucke din .Thi spositio n mayb eoptima l for its capture. Films offifteen feedin g events were studied carefully. Changes werefoun d in thecontribution s ofth eexpansio n ofth emout h and the forward motion of the fish. The events described above, however, were recognized in each feeding attempt, though in some cases the position of the prey deviated significantly from thecentr eo fmas so fth evolum et ob edraw nint oth emouth . 3.2. A QUANTIFICATION OF THE RELATION BETWEEN SUCTION AND SWIMMING Muller etal .(1982 )hav edevelope d ahydrodynamica l modelo fsuctio n feed ing. Many biological applications of the model are worked out by Muller and Osse (in press). The model is here used to derive quantitative conditions for relatingth efish's forwar d velocityan dit smout hexpansion .Man yo fth esimpli fying approximations that are needed tob emade ,lik eth eneglectin g ofviscou s forces,rotationa l symmetryo fth eexpandin gmout h and theneglectin go finflu ences of the prey on the flow, are extensively treated by Muller and Osse and areno trepeate dhere .Tw opoints ,however ,nee dfurthe r discussion,th epushin g Fig. 13. A reconstruction of Salmo gairdneri at the start of the feeding event of Figs. 5, 6, 8, 11 and 12an d the volume of water that will be ingested during the suction act. The black dots denoted with 1,2 and 3 depict the initial positions of polystyrene spheres 1,2 and 3 (see paragraph 3.1.2.). Theinitia lpositio n ofth epre yi sdepicte d with an asterisk. Theingeste d volume(ml )a t time intervals of 7.5mse ci sdenote d in the illustration. 45 effects byth efish' sbod yan dhea dparts ,an dth ephysica limpossibilit yo finstan taneous opening of the opercular and branchiostegal valves. Several aspects of how a fish should optimize its flow rate into the mouth will be dealt with. Symbolsar eexplaine d inTabl e1 . 3.2.1.Suction with closedvalves; theavoidance of pushing effects To investigate the conditions under which pushing occurs, imagine that the fish's head is a cylinder that moves along the X-axis with velocity Ufan d at thesam etim eexpand sradially . Letth elengt h ofth ecylinde r be/ an d itsradiu s h. Let its rear end be closed. The origin of the frame moving with the cylinder was chosen to lie at the centre of its rear end, so that its anterior opening is atx'= / . Around thecylinde rcirculatio nwil lb epresent .Thi scirculatio n wascalculat edb yMulle re tal . (1982). Fig.1 4show sstreamlin epattern sinduce db yth ecylinde ra tvariou scombina tions of expansion and translation. The expanding cylinder will not only suck water through its frontal opening, but will also tend to suck itself forward. In general, the flow patterns of Fig. 14requir e an external force on the cylinder, directed forward oraf t alongth eX-axis .I n thefish , thisforc ecoul db esupplie d byth eswimmin gapparatus .N o attempt hasbee nmad e todistinguis h between the relative contributions to forward motion by the expansion and swimming apparatus.Fig . 14Ashow sth estreamline s around thecylinde rwhe ni texpand s in a fixed position. Such a situation is physically impossible in a free moving fish(i f it is not swimming backward). Around the cylinder only one vortex is present. Amor ecomplicate d situationarise si nth eearth-boun d frame whena certai n amount of forward translation is added. Then, posteriorly a vortex is present due to translation and anteriorly a vortex occurs due to expansion (Fig. 14B). The anterior vortex was visualized during feeding in rainbow trout (see Fig. 9A,B).Th eposterio rvorte xi spartl yreplace d byth efish' s bodyan d istherefor e not as clear as in the cylinder. Note that the mentioned vortices deviate from free circular vortices, as they are more or less"bound " to theprofil e wall, and alsobecaus eth ecirculatio n( Asimpl eadditio no fth eeffect s ofexpansio nan dtranslatio nclos et oth ecylinde rwal li simpossible . Theparticula r effects in this region are not important in thisdiscussio n and therefore not treated here. 47 momentum andi nfron t ofPebf it ha srearwar d momentum. For pushing to be avoided in the mouth aperture the velocity of the water at this position u'\ (relative to the cylinder or fish) should be equal to or less than -U/.Thu s with a given U/the fish should at least reach a certain threshold expansion rate, ht,suc h that P^/lies at the mouth aperture. Muller et al. (1982) derived for the velocity of the water in a rotationally symmetrical expanding or compressing profile with closed valves, u'v(velocit y relative to themovin g frame): x' u\(x',t) = — — I ^- dx' (7) "o where A is the cross-sectional area of the profile. The integral represents the rate of change of the volume of the profile. When the point of zero flow Pebf liesa t themout h aperture [//equals-u'\. Using(7 )w eobtai n for this threshold condition thefollowin g relation: d Uf= 1h. jluh^dxl ' (8) Ai2 J dt o where h\i s the radius at x' — I. From (8) the threshold expansion rate for the cylinderca nb ederived : h< =*§ (9) Theexpansio n rate of themout h cavity and thefish' s translational velocity are thus not at all independent if pushing is to be avoided. The threshold relative expansion rate ht/hi s constant if Ufi s constant. At the same time there is a mechanical limit to how widea fish ca n expand itsmout h cavity.Toward s this valueh wil lagai ndecrease .Therefor e acritica lvalu eo fh willexist ,abov ewhic h the expansion rate of the mouth cavity cannot reach the threshold value, and considerable pushing would occur if the opercular and branchiostegal valves arekep tclosed . Thecylinde rmode lca nb egeneralize d toa con emodel ,fo r whichth eanterio r and posterior expansion can be varied separately. This permits the area of the mouth aperture to be less dependent of head volume. Let the anterior radius beh\ an dth eposterio r radiusb ehi. Fro mformul a (8)i tfollow s that: 3h?Uf _(2h2 + hl) 2 (10) "'•' l(2h{ +h 2) (2A1 + A2) where h\,ti s the new threshold expansion rate, for the anterior opening ('the fish'smout haperture') .Th eflexibilit yi sincrease db yth eadditio no fa nindepen dentparameter .Th ecauda lexpansio nca nsignificantl y reduceth erequire dante - 48 rior mouth expansion rate, especially when hi»h\. Note again the impor tance of the mouth radius in this formula. For the trout its actual mouth expansion rate /it (measured in a vertical direc tion), actual opercular expansion rate hi and the threshold expansion rate (cal culated both for the cylinder and cone model and using the experimentally ob tained hi, hi, hi and hi) were plotted in Fig. 15. The actual mouth expansion rate is well above the threshold expansion rate, so that pushing at the mouth aperture is unlikely to occur during the phase that the valves are closed. At a certain instant (at t = 62 msec for the cylinder model) pushing would have occurred if the valves were still closed. In fact the actual moment of the opening of the valves fell earlier than required for the avoidance of a pushing effect in the mouth aperture. This important aspect is further discussed in paragraph 3.2.3. Anyhow, the predator avoids pushing of prey and water at the crucial moment of capture. Note that for the cone model a secondary phase is present (from about 70 to 86 msec) where hi,t 3.2.2. Suction with open valves;the avoidance of an inflow through theopercular slits Inflow of water through the opercular slits, after valve opening, might be partly avoided by rearward inertia of water sucked in before valve opening, as has been hypothesised for the perch (Percafluviatilis) by Osse (1969). For several reasons this effect is probably for the trout of minor importance. First, not all the water inside the mouth has rearward momentum at the time of valve opening. Posteriorly to Pebfth e water has forward momentum. This effect is particularly important for a fast swimming fish like the trout (see 3.2.1.). Second, mouth expansion in the trout continues after valve opening and the mass of water sucked before valve opening is only about 1/(5.5) of the total volume of thewate r drawn into themout h (see3.1.3.) .Thu s thetim e that advan tage can be taken of an inertia effect is limited and the flow pattern after valve opening willrapidl y resemble the flow pattern with a continuous open valve. Third, the flow visualization experiments revealed a minor initial inflow through the opercular slits and two vortices around the fish's head after valve opening, which isconsisten t with myexpectations . This willb eexplaine d below. Let us consider the case for the cylinder model for which inertia is of prime importance for a caudal outflow. Imagine that first the situation of Fig. 14A is attained. Then the caudal valve opens instantaneously and radial expansion is stopped (or greatly reduced) at the same time. A flow pattern as shown in Fig. 16A would result, very differently from the flow in Salmo (see Fig. 9C). Note, that forward motion of theprofil e isabsen t and that an enormous decele ration of mouth expansion would be necessary. These features are absent in the rainbow trout and other free swimming fish. As mouth expansion should 49 Expansion rate Ta - T/J ~tprey / (m/sec) g 6 j Î \ 0.4 / Vj / 0.2 -^ 0 ^^L&z&k — 0.2 If — 0.4 #\ — 0.6 — 0.8 J — 1.0 20 40 60 80 •tim e (msec) Fig. 15. Comparison between actual and threshold expansion rates. Calculations are carried out for the feeding event of Figs. 5, 6, 8, 11, 12,and 13. All these figures can be compared to each other. Symbols: A --ft actual mouth expansion rate, h\ (measured in a vertical direction); ^r—^r actual opercular expansion rate, A2(measure d in a transverse direction); Mi-A threshold expansion rate for the cylinder model, hi; O-O threshold expansion rate for the cone model, Ai,<; A-A critical expansion rate for the cylinder model, hc, discussed in paragraph 3.2.3. The actual and ideal moments of caudal valve opening (T„ and x,) and the moment of prey capture, tprey, are denoted as in Fig. 8. T;fall s at the moment where the curves of fi\ and hc intersect. From about 71 to 86 msec it seems to be favourable for the fish to have its valves again closed (only for the cone model). This phase corresponds to the secondary caudal inflow phase discussed in paragraph 3.2.4.(se e Figs. 10an d 19). dominate forward motion at themomen t ofvalv eopenin g for rearward inertia tob eimportant , theeffec t mightonl yb eimportan t inrelativel ystationar y fish. Theforwar d velocity ofth etrou t isprobabl y mostimportan t for the outflow ofwate rthroug hth eopercula rslit salthoug hi tdiminishe sth erearwar dmomen tum of the water sucked in before valve opening. To appreciate this consider again thecylinder , but now opened at both endsan d at rest.Whe n thecylinde r expandsradiall ywate rwil lb esucke di nfro m bothend s(se eFig . 16B). Halfway insideth ecylinde rth evelocit yi nth eX-directio ni szero .Thu sher ea stagnation point is present at the X-axis. Now consider a cylinder that is not expanding butmovin galon gth eX-axis .I nthi scas ea unifor m flow willb epresen t relative toth ecylinde r(se eFig .16C) . 50 Nowconside r thecombinatio n oftranslatio n withexpansion .A sfo r thepos teriorly closed cylinder there is one point where the water is at rest relative to theexpandin gprofil e andanothe rwher eth ewate ri sa tres trelativ et oth eearth - bound frame. Thesepoint s are again denoted as Pmfan d Pebfrespectively . The combinationo ftranslatio nwit hexpansio nma ylea dt oon eo fth ethre efollowin g possibilities(descriptio ngive nrelativ et oth ecylinder) : 1. Pmflie s still in the cylinder, but is displaced to a position between the rear end and the middle of the cylinder (Fig. 16D). There still is an inflow at the rear end, corresponding to a caudal inflow into the gill cavity. Note thatP mf cannotcom et oli eanteriorl y ofx'=0.51 i fth ecylinde ri smovin g forward. 2. Pmflie sa tth erea ren do fth ecylinde rwhe nth etranslationa l velocityreache s a certain threshold value Ut (see Fig. 16E). The same of course holds when the expansion has a critical value at a particular forward velocity. There isn o net in-o r outflow at the rear end of thecylinder . Behind thecylinde r a trailing vortexwil lb epresent , again,wher ei ncas eo fth efis h thefish's bod yi spresent . Utwil lb ea functio n ofth evolum eincreas eo fth ecylinde ran dit scross-sectiona l area(t ob ecalculate dbelow) . 3. Pmfha s vanished and an outflow at the rear end of the cylinder occurs if thevelocit yo fth ecylinde r islarge r than Ut. Adivergin gflo w ispresen t directly behind the cylinder (Fig. 16F). A diverging flow behind the opercular slits of Pteroisrusselli ha sindee dbee nvisualize d byMulle re tal .(1982) . Fig. 16.Flo w around a cylinder, open at both ends, with several combinations of expansion and forward motion. Theentir eprofil e and flow are rotationally symmetrical; only a section through the central axis is given. Streamlines are given in the moving frame. In (A) and (B) the cylinder stands still, so earth-bound and moving frame overlap. Symbols: O, -Pm/point where water isa t rest in the moving frame; •, Pebfpoint where water is at rest in an earth-bound frame. External forces required tomak eal l situationspossibl ear elef t out. In thecalculation smea n velocitiesove r the cross-sectional area are used. The position where the mean velocity of the water is zero (for bothframes ) mayslightl ydiffe r from thepositio nwher eth evelocit yi szer oalon gth eX- o rA"-axis . Heavy arrows depict magnitude and direction of expansion rate and swimming velocity. Further explanationsar egive ni nth etext . 51 Similar to the posteriorly closed cylinder, an external force along the X-axis is needed to make all situations possible. In case of the fish this force could again be supplied by the swimming apparatus. The flow towards the frontal opening iscontractin g in all three cases of translation and expansion; an expan ding cylinder, open at both ends will never push water forward (except near the cylinder wallwhe n thisha s a certain thickness). Water willalway s be moved towards its frontal opening in an earth-bound frame, a flow pattern actually observed for the trout after the moment of valve opening (see Figs. 7 and 9C). Thus active suction is important after valve opening. In paragraph 3.2.1. it was explained that pushing would have occured when the valves would have been closed after their actual moment of opening. Therefore, the resistance of the gill archesand gill filament s must below after valveopening. This last conclusion issupporte d by observations from high-speed films, and photographs taken during preycapture , whereth earche swer esee n tob e separa ted and the gill filaments of individual arches adducted. These features were also demonstrated for Pterois russellib y Muller et al. (1982),fo r Perça fluviatilis by Osse (1969) and for several other species, including the rainbow trout, by Muller and Osse (in press). Fig. 17 shows an example of this situation, from whichi ti sals oclea r that most ofth ewate r may be "shunted" between the hyoid arch and the first gill arch. Inflow of water through the opercular slits should be avoided by the fish to optimize the flow rate through the mouth aperture and to avoid damage of the gills (see also Muller and Osse, in press). Thus the fish's translational velocity should at least reach the threshold velocity for a given expansion rate during the phase that the valves are opened. Thus the prerequisite for valve opening with garanteed outflow is: Uf>U, (11) where Ufi s the fish's velocity along the long-axis of its mouth. When U/ M'I = — -£- Ä (12) The mean velocity at the posterior end, w'2, will be: u'2 = — u'\ (13) and hence: Ut= [-h (14) 52 Fig. 17.Stereograp h oïSalmo gairdneriafte r the opening ofth eopercula r and branchiostegal valves. The gill filaments of each arch are adducted. A large opening is present between the hyoid arch and the first gill arch (the "hyoid shunt"). Also thegil l arches are separated after the valve opening, apart from filament adduction. This feature, however, is more clearly shown in Muller and Osse (inpress) .Par t of the filament endings are bent by the flow. The limit of Utfo r ; approximates 0 is infinity when both h and h approach zero, and zero when h(t) >0. At the first stage of the suction act both h and har e increasing, however, both with variable rates.A sa result the ratio between the two can be subject to strong fluctuations during this period. Hence the streamlines in case of an open valve in this stage would change very rapidly their direction. This phenomenon might explain the early activity of the M. ad ductor operculi during feeding, recorded for instance for theperc h (Percafluvia- tilis, Osse, 1969), the ruff (Gymnocephalus cernuus, Elshoud-Oldenhave and Osse, 1976) and others. The initial adductor activity was also made feasible by an analysis of the pressure regime near the valves by Muller and Osse (inpress) . Using the cylinder model of the mouth, Ut was calculated (see Fig. 11) for the above described feeding event of the trout (cf. 3.1.2.). For h half the height of the mouth was taken and for / the head length. As expected at first instance {/(fluctuates quite strongly (0-15msec) , but is, however, already very soon hig her than Uf.The n (15-40 msec) Utis in the order of 6.5m/sec , very much higher than Uf. As expected the valves were closed during this phase. Thereafter Ut drops fast and equals Ufa t about 58 msec, the expected ideal moment of valve opening T,-.Th e decline of Utwa s caused by a decreasing mouth expansion rate and a still increasing mouth radius. The moment the valves actually started to open, to, fell about 12 msec earlier than T,, but during the fast decline of Ut. Note that xawa sdetermine d ina high-spee d moviewhe n only thefaintes t indica tion of an open opercular slit is seen. Hence, at xa the opening is still virtually zero and the interval T<-T«i s effectively smaller than Fig. 11suggests . Neverthe less a slight inflow through the opercular slits was expected to occur between Ta and Ti. This was indeed detected experimentally (see Fig. 10). The observed difference between T 3.2.3. Maximization of the flow rate into the mouth and the choice of the moment of valveopening Generally, there may be one point, Pebf, in an expanding and translating cylinder or mouth cavity where the fluid is at rest in an earth-bound frame. The position of Pebf(whic h varies with time) was expressed relative to the mo ving frame. When the valves are closed its A"-coordinate will be denoted asx'rc and when they are open as x'r0. Asmentioned , with closed valves water ispushe d forward in the earth-bound frame posteriorly to Pebf, whereas anteriorly to T^i/water is sucked backwards. To maximize the flow rate through the mouth aperture the fish should keep Pebf as caudally as possible during the suction act. When (theoretically) x''re In calculating x'rcand x'r0, P^/was assumed to be positioned at the cross- sectional area over which the mean velocity of thewate r equals zero. In case of open valves and no rearward or forward overall inertial effect due to a previous situation with closed valves,i tca n be derived for the cylinder that: X'ro = 0.5 / (15) For the cone x'ro depends on h\, hi, h\, hi and previous events (unsteady effect) and cannot easily be derived. When the valves are closed pushing and suction effects will eliminate each other inx' rc, so that: Uf(t) +U'v(x'rc,t)=0 (16) where u\ (x'rc, t) is the velocity in the X'-direction in the moving frame at x'rc. We obtain for thecylinde r (from (7)an d (16)): 54 Andfo r thecon emode l(als ofro m (7)an d(16)) : W Vf Xrc {S) (2h1+h2)h1+(2h2+h1)h2 Asexpected ,whe nth efish expand sit smout hwit hth ethreshol d expansion rate weobtain : x'rc= I- For the cylinder model the ideal time of the opening of the valvesi sdetermine dby : x'rc = x'ro = 0.5 / and 4*j< >0 (19) When x'rc is greater than 0.5 /it would be advantageous to open the valves, becausea cauda l outflow wouldb egarantee d and through thisth evolum eflo w through themout h apertureenhanced . x'rcwa s calculated for the suction act of Salmo gairdneri discussed in para graph 3.1.2. for both the cylinder and the cone model, using formula (17) and (18), and plotted in Fig. 18.Whe n suction starts the fish pushes water so x'rc will be large, x'rc drops rapidly to about 10%o f / for the cylinder model and even lessfo r thecon emodel .Close d valvesar e undoubtedly advantageous du ring this phase. From about 40 msec onwards x'rc increases rapidly for both models. At about 58 msec x'rc= 0.5 / for both models. Thus for the cylinder model Ti is 58 msec. For the cone this moment would not differ much from thisvalu edu et oth erapi dincreas eo fx'rc Thusth eerro rmad ei nth edetermina tion of Tidue to the uncertainty about the position of Pebfafte r valve opening isver ysmall . Theactua l moment of thestar t of valveopenin g xafel l about 12 msecearlie r thanT,- . Thiswil lb epartl y duet oth ephysica limpossibilit y ofa n instantaneous complete opening of the valves (an infinite force would be required). Asmen tioned the valves are still virtually closed at the instant xa. If the fish would postpone valve opening to theidea l instant pushing would occur at the critical moment of actual prey capture. Furthermore, the cone- and cylinder models overestimate the volume sucked (> 100% for the trout). Hence, actually, Pebf ispositione dmor eanteriorl yan d T,fall searlie rtha nth ecalculation ssuggest . Summarizing,i fx a> r; a reduced flow ratethroug h themout hapertur ewoul d result,i fT fl 40 30 •• 20 ~*prey \ pectoral 1 1 1 1 —i '—1~ girdle 20 40 60 80 > time (msec) Fig. 18. Graphs of the position where the mean velocity over the cross-sectional area is zero in themout h ofSalmo gairdneri,i n an earth-bound frame. Calculations weredon e for thepre y capture event of Figs. 5, 6, 8, 11, 12, 13 and 15. All these figures can be compared to each other. Water is pushed forward caudally of x'rc, whereas anteriorly of xrésuctio n dominates.Symbols : A —A, x'rccalculate d for the cylinder model; A-A, x'rc calculated for the cone model. The horizontal line at x' = 40 mm = 0.5/ denotes the position of x'ro, with the assumption of the cylinder model and no overall inertia effect of water sucked in before valve opening. Ideally the caudal valves should open when the curves of x'rc and x'ro intersect. At the start of mouth expansion x'rc will be very large (position outside the mouth). This isno t incorporated in this figure. Ta,T;an d tpreyar e denoted as in Fig. 8.Furthe r explanations are given in the text. spheres, as no cases were found where spheres were close enough to the slits. Asimila rmino rinflow ,jus tbefor e themomen to fth emaxima lopercula rabduc tion, wasfoun d during respiration in the rainbow trout by Dr. CM. Ballintijn (personal communication). Lauder (1980) mentions that particles suspended near theopercula r slitso fLepomis werecarrie d into thegil lcavit y asth evalve s first opened. The author made no distinction between the earth-bound and themovin gframe . Inthi scase ,however ,i tseem sclea rtha tth eflo wwa sconside redrelativ et oth emovin gframe . So,th eexpecte dinitia lne tcauda linflo wpresu mablyals ooccur si nLepomis. Lauderfaile d toexplai nthi sfeatur e asth eautho r tried to derive the flow direction from the pressure regimei n an essentially un steadyproces s(se eMulle re tal. ,1982) . The initial caudal inflow is reduced if the length of the time interval xi-xa isminimize d byth efish. T oobtai n thisa rapi d openingo fth evalve si srequire d as then xa could be delayed and hence x<-xa reduced. Another possibility to 56 reduce Tr-Tfli s a decrease of the effective head length of the fish directly after ta, due to the opening of the rostro-ventral extensions of the branchiostegal valves. In the trout the valves started to open at about 0.1/. Opening proceeded rapidly in both a dorso-caudal and a ventro-rostral direction. Within 10 msec the rostral boundary of the opercular slits had reached 0.3/. This reduction of the effective head length reduces T, and thereby the interval xt-Xa.However , itdecrease s the suction capacity ofth e mouth after valve opening.* For the cone model with closed valves Pee/again enters the mouth cavity just before its rostral closure (Fig. 18). So eventually closed valves would again befavourabl e for the fish. However, thisi simpossibl e due to thelarg e abduction of the opercula and the short branchiostegal rays. When x'rc is less than about 0.5/ a secondary inflowwoul d again be expected (from about 70mse c onwards). Thiswa sactuall y shown to be thecas e by theexperimen t with the threads sewed near the opercular slit (see Fig. 10). It was demonstrated for all 14feedin g acts recorded in this experiment thus supporting the theoretical expectations. From (17)an d (19)w e obtain for the cylinder model a critical expansion rate Äcfo r the mouth cavity with closed valves: hc = h.Uf=2ht (20) To obtain of a maximal flow rate through the mouth aperture the opercular- and branchiostegal valves should be open when hx 2 , 6hj Uf _ (2h2 + /ii), . C 2 ( "'• "/(2AI + A2) (2A, + A2) ' showing that T,migh t be significantly delayed for increasing h2 and h2. From (20) and (21) it is clear that T,tend s to decrease with an increasing swimming velocity, whereas the reverse istru e for an increasing head length. 3.2.4. Themouth closurephase So far little attention has been paid to the mouth closure phase. For compari son a cylinder model can be put forward. A compressing cylinder with both ends open pushes water in both an anterior and a posterior direction (earth- bound frame). After having reached its maximal mouth diameter the mouth *Th e reader might question the necessity of a detailed discussion of minor inflow effects through the opercular slits in Salmo gairdneri. However, these effects probably were major problems during the evolution of a suction mechanism from a filter system (see also paragraph 4.4.). 57 cavity of the trout deviates significantly from a cylinder as the caudal parts of themout hcavit yar estil lexpandin gwhe nth emout h aperturedecreases . The main events, however, can be explained by a comparison with a cone, compressinga tit santerio ren dwhil eexpandin gposteriorly .Le tu sfirst conside r the flow if the cone does not translate (see Fig. 19A). Three 'vortices' might bedistinguishe daroun dth econe .I nthi scas etw opoint so fzer oflo war epresen t in the cone denoted with Plebfa.nd P2ebf. Water flows out the anterior end of the cone, whereas water is sucked in posteriorly. Halfway inside the cone water ismove d posteriorly. At onepoin t along the A"-axisth e expansion rate of the cone is zero. This point separates Piebfan d P2ebf. The middle 'vortex' x' = o (C) (D) Fig. 19.Schematize d streamlinepattern s in a cone,expandin g at itsposterio r end and contracting at the opposite end. The cone is open at both ends. Arrows at both ends denote the direction of movement ofth ewall .Not etha t theentir e flow isrotationall y symmetrical,onl y asectio n is given in each case.Pieb/and Piebfaxt denoted with black dots. Pictures (A) to (D) represent streamline patterns in the earth-bound frame. In (A) to (C) the profile is at rest, in (D) the cone translates forward (denotedwit ha heav yarrow) . A. Situation with 3distinguishabl e regions.I n the middle a region of rotation ispresent . At both endsvortex-lik eregion soccur .Th efluid is a tres ta ttw oposition salon gth eX-axis . B. Situation wheretw o such regions are present; only Piebf'is left in the cone.Tw o 'vortices'wer e indeedvisualize dfo r therainbo wtrou t(Fig . 9C). C.Theoretica l situation with only one 'vortex' and acaudall y directed flow inside the entirecone . BothiVi/an d P^i/are absent. D. Situation with only one 'vortex'. The cone moves forward. Rostrally, the forward velocity of the wall is much larger than the compression rate. Hence the streamlines are directed outwards in this area and a triple-vortex effect cannot occur. Compare this illustration with Fig. 9D, the actual situation inth e rainbow trout. Ar denotes thecross-sectiona l area whereth eexpansio n rate iszero . 58 deviates stronly from a true vortex, and may be better denoted as a region of rotation (seeals o3.2.1.) . The positions of Pubfan d /^/depend on hi, h2, hi, h2, I and previous events(unstead yflo weffect) .On eo rbot ho fthes epoint sma yeve nvanish .Whe n Piebfis absent a caudal outflow exists.Whe n /V*/is absent an anterior inflow occurs (depicted in Fig. 19B). When both points are absent the flow can be directedeithe rposteriorl yinsid eth eentir econ e(Fig . 19C)o rdirecte d anteriorly. If the cone translates fast enough along its long axis all situations described aboveca nb eforce d togiv ea posteriorl yunidirectiona lflo wi nth emovin gframe . Once a vortex (or a region of rotation) has been created it cannot beeasil y destroyed as it represents a certain amount of energy, a fact to be considered in the analysis of the suckingfish. Tw o vortices are present around a forward moving, expanding cylinder closed at itsposterio r end (paragraph 3.2.1.). The posteriorvorte xi sa resul to fforwar d motion.Th etota lcirculatio n ofth eposte riorvorte xcompare d totha to fth eanterio ron eca nb ea measur efo r therelativ e importanceo fforwar d motion and suction.Th esam ehold sfo r atotall yexpan ding cone and also for thefish (wit h itsentir e mouth expanding and itsvalve s closed, see Fig. 9A). Part of the streamlines of the posterior vortex will go through thefish's bod yi n theearth-boun d frame. After valveopenin g the two vorticesremaine d associated withth etrout' s head.So ,th eposterio r vortexwa s notlef t behind asa fre e vortex.I fthi soccurre d asingl evorte x around the fish's head could develop and hence a unidirectional flow, even in the earth-bound frame. This effect could be important for feeding at low swimming speeds. In this case the posterior vortex would already be of a small magnitude before theopenin go fth evalves . A double vortex during the mouth closure phase was demonstrated for the rainbow trout by multi-flash photography (Fig. 9C). The caudal vortex was not strong enough to cause a net inflow through the opercular slitsdurin g this phase. Water was still sucked towards the mouth (in an earth-bound frame, cfFig.9C). Just before mouth closure water was slightly pushed at themout h aperture, together with a net caudal inflow through the opercular slits (see Figs.9 D and 10). Such a situation can be understood when a third vortex is added. In the mouth aperturewate rwil lb eaccelerate d ina forwar d direction and thecircula tiono fth eanterio rregio nwil lb ediminished .It scentr ema yb emove dcaudally . Anteriorly, a new vortex is formed with an opposite direction to the previous anterior one. This situation in the earth-bound frame resembles that of Fig. 19A (note that a forward velocity of the profile is not taken into account in thisillustration) .I propos et ocal lth eadditio no fa thir d 'vortex'th etriple-vortex effect.However ,whe nth eforwar d velocityo fth efish is relativel yhig hcompare d to the rostral compression rate there cannot exist streamlines going through the mouth wall and directed inwards (earth-bound frame). Hence an anterior addition ofa thir dvorte xi simpossibl ei nthi scase . A triple-vortex effect will generally be absent in the rainbow trout due to its fast swimming. It was indeed not found by flow visualization experiments 59 during feeding in the open water. On the contrary, the observations pointed toonl yon evorte x(wit hopposit eflo wdirectio ncompare dt oFig .19C) ,althoug h thefield o fflo w isno t yet visualized in itsentiret y (Fig. 9D).Thi s flow pattern would result ifth e posterior vortex of Fig. 19B would enlarge and the anterior one diminish and eventually vanish. I propose to call this transition the single- vortex effect. The resulting flow isillustrate d in Fig. 19Dfo r aforwar d moving cone. A diagram of the flow relative to the fish's head is given in Fig. 20. There is one point of zero flow, Pimf, present inside the mouth; a net caudal inflow occurs. To protect the gills,i t would be favourable for thefish i f it could keep •P2m/caudallyfro m thegil l filaments. The single-vortex effect may also be reached via the triple-vortex effect through adiminutio n ofth emiddl eregio no frotation ,followe d bya unification ofth eanterio r andposterio rvortices .Furthe rexperimenta l dataar eneeded . Fig. 20. Schematized situation of streamline pattern around a fish's mouth in the moving frame. In the earth-bound frame the flow would resemble the situation of Fig. 19A,however , with forward movement of the profile. A similar flow pattern arises from a situation with only one 'vortex' (cf. Fig. 19D). At the anterior end a pushing effect is present and a diverging flow towards the mouth results. At the posterior end a caudal inflow occurs. Both effects were detected experimentally just before the actual moment of mouth closure (see Figs. 9D and 10). At ftm/the fluid is at rest in themovin g frame. Abbreviations: Ar. cross-sectional area where expansion rate of profile wall is zero; ds\: dividing streamline that envelops the water that tends to flow through the mouth aperture; dsl: streamline enclosing all streamlines that go through the the mouth; ds"i: streamline enclosing all streamlines that do not pass theprofil e wall;g: gil l filaments. 60 3.2.5. Streamlines inthe moving frame throughout thefeeding act This paragraph summarizes the variable streamline pattern relative to the trout during one complete feeding act. Muller et al. (1982) relate quantitatively the mouth radius to the radius of the dividing streamline for x' approaches infinity (formula 32). In their formula a parameter a, is used describing the ratio between the velocity of the water in the mouth aperture in the earth-bound frame and -Uf. The authors argue that their formula isonl yvali d for a> 1.However , iti sprobabl e that the formula alsohold sfo r 0< a< 1 asth esam ethir dpowe rroo t ispresen ti nbot h the formula for rasymptote and hleffective (formulas 29 and 30 in Muller et al., 1982). These roots cancel in their formula 32 where rasymptote is devided by hleffecuve. Rear ranged formula 32o f Muller et al. becomes: u l rasymptote= hieffective , / —— (22) •Uf where rasymptote is the radius of the dividing streamline at JC'-»OO and u\ the mean velocity of the water in the mouth aperture in the moving frame. hleffective isth eeffectiv e mouth aperture (see Muller et al., 1982). Fig. 21 shows the results obtained for the rainbow trout. Muller and Osse (in press) relate the type of flow to the ratio between the velocity of the water in the mouth aperture in an earth-bound frame and the fish's forward velocity. This ratio, denoted as b by Muller and Osse, will be given for the stages of thetrou t described below. Fig. 21A shows the flow in the initial overall pushing phase. The speed of the water relative to the fish just in front of the mouth was already larger than the velocity at a large distance. The flux through each cross sectional area of thedividin g streamline isconstant . Hence, thediamete r of the dividing streamli neincrease s with thedistanc e from themout h (parameter b< 0 ;se efo r compari son Fig. 9A, giving the flow in the earth-bound frame). The prey was still about one head length away from the mouth. Thereafter suction of the predator almost exactly eliminated the effect of its own motion on the prey, resulting in a stationary prey (omitting the prey's own movements). Again the flow contracted towards the mouth (b<0) . The opercu lar and branchiostegal valves started to open (Fig. 21B). In Fig. 21C the maximal mouth diameter is reached and the prey sucked into the mouth (b< 0).A considerable caudal outflow occurs. The chance of escape seems to be minimized by this flow pattern (see also Fig. 13). In Fig. 21D the mouth is halfway its closing phase. Water in the mouth aperture is almost at rest in the earth-bound frame (b= 0). Mouth closure isnearl y completed in Fig. 21E(Z>>0). 61 (E) (F) Ta- T/" *"*pre y 30 /ie 20 /B I 10 '^ . -*Tk EV 20 40 60 80 -> time (msec) Fig. 21. Diagrams ofstreamlin e patterns ina fish-bound fram e atvariou s moments ofa feeding act ofSalmo gairdneri, asdeduce d from movements ofpolystyren e spheres and model approach. The bolt lines represent the dividing streamline. The form ofth e fish's head istake n from a film. Thisfigure shoul d becompare d toth eevent si n the earth-bound frame, showni n Fig.9 .A .Phas e just after thestar t ofmout h opening, corresponds approximately to Fig. 9A; B. Situation at the momento factua lvalv eopening ,correspond st o Fig.9B ;C .Situatio n atpea kmout hgape .Cauda l valves are open; D.Flo w pattern during mouth closure. Note depression ofmout h bottom from A toD ; E.Flo wjus t before final mouth closure; F.Grap h ofth e height ofth e mouth aperture, withth etimin go fmoment sA t oE .Furthe rexplanation sar egive ni nth etext . 4. Discussion 4.1. HYDRODYNAMIC MODELSO F THE FLOW DURING SUCTION FEEDING The present approach, using stereoscopic flow visualization techniques, has resulted in a complete picture of the flow throughout the feeding act. These techniques do not interfere with the fish's movements (as most flow velocity 62 transducers).Therefor ethe ywer euse dt otes tth eprediction sfro m hydrodynam- icmodel soffis h suction. Several models have been put forward to describe the flow in front of the mouth ofa suckin gfish. Alexande r (1967)modelle d themout h cavity asa tube . Close to the tube aperture ("the mouth aperture") he assumed a uniform flow tob epresent .A tlarge rdistance sth etub eapertur ewa sregarde d asa sink . Alex ander calculated a maximal distance from which food can be sucked into the mouth. The obtained value of one quarter of the fish's mouth length was an underestimate as acauda l outflow through the opercular slitsan d the forward motiono fth epredato rwer eno ttake nint oaccount .Thi sfirst mode lha ssevera l disadvantages. The mouth aperture cannot bedefine d exactly and the velocity approaches infinity at thisposition . Therefore, Alexander had to assumea uni form flow atth emout h aperture.Also ,th ewate ri ssucke dint o themout h from alldirections ,s otha t muchenerg ywoul d bewaste d byth efish i nsuckin gprey - free water. It is also in contrast with the general observation that a fish aims athi spre yan dthe nproceed st ocaptur eit . Osse (1969)showe d that theperc h (Percafluviatilis) is abl e to capture preys from aninitia ldistanc eo fhal fth elengt ho fth ehead .T ohi sopinio nja wprotru sioncontribute s todirec t theflo w towardsth eprey . Besides,Oss ehypothesize d thatsuctio nmigh tb eimportan t after valveopening .However ,a ttha ttim esoli d experimentalevidenc ewa sstil llacking . Nyberg (1971) observed that the sink model of Alexander does not hold for the largemouth bass (Microptems salmoides). The flow generated by the bass appeared tob emor edirected . Weihs (1980) added a uniform flow to the sink model of Alexander to take account of the forward motion of the fish. He obtained a more directed flow than Alexander. Weihs assumed a constant rate of intake of water into the mouth,thu sneglectin gth eunstead ynatur eo fth efeedin gprocess .Fo rth emaxi mal intake of water he took the maximal mouth volume change (not defined by Weihs) as a measure. At least for the rainbow trout these two assumptions areprove nt ob eincorrec t(th epresen tpaper) .Oss e(1969 )ha dalread yhypothe sizedtha ta cauda l outflow after valveopenin gmigh tb eimportan ti nth eperch . The disadvantage of the infinite velocity at the mouth aperture still exists in the model of Weihs. Weihs did not pay attention to stagnation effects due to swimming. The necessity to distinguish between the earth-bound and thefish-bound frame was for the first time recognized by Muller and Osse (1978) and Osse andMulle r(1980) ,wh omodelle dth efield o fflo wi nfron t ofth emout h aperture asth ecombinatio n of acircula r vortex and aunifor m flow. The mathematical implications of thismode l areworke d out in Muller et al.(1982) .Th e singular points (inthes epoint s thevorticit ydoe sno t equal0 an d thevelocit yi s infinite) arepositione da tth elip so fth efish. S oa circula rmout hapertur eca nb edefined . Therat eo fintak ei scouple dwit hth eactua l volumechang eo fth emout hcavit y (modelled as an expanding cone) and is a time dependent variable. Thus the unsteady nature of the process is taken into account. At a certain moment a 63 caudal valve ("the opercular and branchiostegal valves") opens and water can flow out of the cone. Thus the model permits a larger volume of water to be sucked intha n thepea k volumechang e ofth emout h cavitydurin g feeding might suggest. In myexperiment s (see fig. 12)th e importance of this effect was shown. The field of flow can be varied by changing the relative contributions of the vortex and theunifor m flow. The share of the uniform flow isdu e to the forward movement of the mouth aperture in an earth-bound frame, accomplished by a variable combination of the suction itself, a possible protrusion of the jaws and additional swimming. During most of the time the shape of the flow in front of the mouth generated by a sucking trout resembles the shape predicted by the model, except close to the fish's lips. The model does not incorporate quantitative expressions for stagnation effects due to the translation of the fish although they were recognized by the authors. Discussions about this subject can be found in Muller and Osse (in press), in the present paper and chapter 2. Flow patterns cannot be derived from the pressure regime as the process is essentially unsteady (Muller et al., 1982). Approaches in this direction (see e.g. Lauder, 1980)wer etherefor e left out in this discussion. 4.2. THE FEEDING MECHANISM OF THE TROUT: A COMBINATION OF SUCTION AND SWIMMING Important elements in the type of feeding used by Salmo gairdnerii n the open water are: 1.Initia l approach with aclose d mouth to reduce thepressur e drag in swimming and to reduce the start volume of the mouth cavity. 2.Onl yclos et oth emout h thepre yi ssignificantl y accelerated towards the mouth in the earth-bound frame (see 3.1.). Thus, the impulse added to the prey by the combination of suction and swimming is small. This feature makes early detection of the predator by a live prey more difficult and therefore enhances the chance of prey capture (seeals o Muller and Osse, in press). 3.Th e fish's hydrodynamical constraints arechange d almost instantly by caudal valve opening. A caudal outflow through the opercular slits enhances signifi cantly the flow rate into the mouth after theearl y moment ofcauda l valve open ing (see 3.1.3.). This outflow is mainly due to the forward velocity of the fish (see 3.2.2.). 4. Mouth expansion continues to add to the flow towards the mouth after valve opening (see 3.1.2. and 3.2.2.). 5.Gill resistance islo w after caudal valve opening and water is"shunted " along the hyoids (see 3.2.2.). To investigate whether these elements are also found in other salmonids, the paper on Salvelinusfontinalis by Lauder and Liem (1980) was analysed. As the relative timing of the mouth opening and the opening of the caudal valves are not described, nor details on swimming speed the comparison is based on mea- 64 surements made from their Fig. 1, consisting of a series of frames from a high speed film. The head length of their fish was about 45 mm and its velocity during prey capture about 0.3 m/sec. Initially, the prey was very slightly pushed forward; about 1 mm in 10mse c (frame 1 to 3,earth-boun d frame). Thereafter, the prey wassucke d towards themouth ; about 3 mm in 10mse c(fram e 6t o 8), represent ing a mean velocity of 0.3 m/sec in an earth-bound frame. Thus, in this interval the mean speed of the prey in an earth-bound frame was about equal to the speed of the predator. The caudal valves were presumably already open when the prey passed the mouth aperture (concluded from the dark stripe at the rear end of the opercu lum). The maximal mouth aperture divided by the fish's head length was about 0.17. Its relative hyoid depression at the time of the maximal mouth opening (measured from the ventral side of the eye sphere to the most rostro-ventral point of the hyoid) was 0.7. For the feeding act of the rainbow trout analysed inth epresen t paper(Fig .8 )thes elas ttw ovalue sare :0.4 4an d0.46 . Unfortunate ly,opercula r abduction could not bemeasure d from thepicture sgive n by Lauder and Liem. Comparing the two feeding events we can conclude (event SG: Salmogaird- neri; event SF:Salvelinus fontinalis): 1.Th e predator's speed isver y much lower in SF than in SG (also, when scaling isdon e to correct for the difference in body length). 2.Th e relativemaxima l mouth aperture iskep t smaller in SF,wherea s the buccal expansion is increased. From considerations of continuity it follows that the relative speed in themout h aperture will increase and hence: 3. In SF the prey has a higher mean speed towards the mouth in an earth-bound frame. The speed in the moving frame, however, has decreased. The above comparison indicates that salmonids adjust their head movements to their swimming speed to optimize the velocity in the moving frame and hence thechanc e of prey capture. The different EMG-patterns found in the head mus cles of Salvelinus in mid-water and bottom feeding (Lauder and Liem, 1980) support this view. A similar strategy isuse d by other fish (see4.3.) . Muller and Osse (in press) have characterized the feeding type of the trout aslow-x-suction with swimming, beingespeciall y suitablei nrelativel y open water, where swimming isno t limited by an abundance of obstacles. During searching for food and feeding by the trout far more energy will be spent by swimming than by head expansion. Therefore, the energetics of swimming needs to be known ifon e isconcerne d with optimal foraging strategies in salmonids. 4.3. A COMPARISON WITH OTHER FISH Esox In a preliminary study Mr. Jan Kremers and I have applied the model to the pike {Esox lucius),als o a fast swimming protacanthopterygian fish. The cyl indermode lwa sinsufflen t topredic tth etim eo fth eopenin g ofth ecauda lvalves . 65 Thecon emodel ,however ,gav eaccurat epredictions .Wit ha decreasin gmaxima l swimmingspee d(rangin gfro m 2t o0. 5m/sec )th emout hexpansio nrat e tended to be more rapid and the valves opened slightly earlier, but at a larger mouth aperture and buccal expansion. Thus more water was sucked into the mouth before valve opening. Also, the maximal speed of the prey in an earth-bound frame tended to be larger at a lower swimming speed. In all cases stagnation infron t ofth emout hapertur ewa savoided .Al lpre ycaptur eevent swer ecarrie d out within the constraints (conemodel ) formulated in paragraph 3.2. In terms of the feeding types distinguished by Muller and Osse (in press) a shift from low-T-suction towards high-t-suction (with less swimming) can be achieved by the pike. The data of the chain pickerel (Esox niger) presented by Rand and Lauder (1981)ar ei n accordance with our findings for thepike . Unfortunately, thedat a wereno t suitablefo r an analysis asgive ni n paragraph 3.2.a sth e data of individual feeding acts were lumped and the moment of valve opening was notgiven . x The enlarged flexibility of the cone model as\:ompared to the cylinder can onlyb etake nful l advantageo fwhe nth estructur eo fth ebranchiostega l appara tus allows the valves to be kept closed at a broad range of abduction states of thesuspensori a and the operculars. (Sotha t the second term of formula (21) can beuse d to decrease the critical expansion rate of the mouth aperture).Th e short, spathiform branchiostegalray s(McAllister , 1968)o fth etrou tallo wonl y arelativel ysmal labductio n ofth eopercular sbefor e thevalve sopen . Therefore, the effectiveness of the trout's feeding mechanism will be significantly less(re sulting in a small capture region and a low mean flow rate through the mouth aperture) ata relativel ylo wswimmin gspee dtha n ata relativel yhig hswimmin g speed. Thepik eals oha srathe rshort ,spathifor m branchiostegalrays .However ,the y arerelativel ylonge rtha ni nth etrout ,suggestin gtha t thepik eha smor eflexibili ty in its feeding mechanism than the trout has. These differences are in accor dance with the characteristic habitats of both species. The same holds for the bowfin (Amiacalva), whichwa sobserve d tofee d ata broa d rangeo fswimmin g speeds. Osse(1976 )alread yindicate dtha tth evalve sar eimportan ti nth esuctio n mechanismo fth e bowfin. Pteronisculus Schaeffer and Rosen (1961) gave reconstructions of the head of the extinct palaeoniscoid fish Pteronisculus in an unexpanded and an expanded state (see their Figs. 1A and 2A).Th eeffectiv e head length ofthi sfish i sshor t duet o the notched mouth and the short opercular region. With a given forward velocity andmout hradiu s(an da scale dhea dlength )Pteronisculus woul drequir ea criti cal expansion rate of 1.9time s that of Salmo gairdneri to prevent stagnation (calculationwit hformul a (20)). After valveopenin g thethreshol d swimmingspee d required forPteronisculus to prevent inflow through the opercular slits was estimated to be about half ofth espee d required for Salmogairdneri (afte r scalingan d with agive n mouth 66 radius and mouth expansion rate, formula 14).Th e use of an inertial effect to obtaina noutflo w throughth eopercula rslit smus thav ebee neve nles simportan t thani nSalmo. This suggests that the valves opened much earlier in Pteronisculus than in Salmo,a s it isprobabl e that Pteronisculus (with its complete dermal skeleton) was only for a short time able to expand its mouth faster than the high critical rate. Pteronisculus had even shorter branchiostegal rays than the trout (also spathiform), whichindee d would haveallowe d onlya ver ysmal l abduction be fore themomen t ofvalv eopening .Th eflo w through themout hapertur e proba bly was largely dependent on the swimming speed. Unfortunately, no studies have been made, to my knowledge, of the possible swimming capacity of pa- laeoniscoids. However, iti slikel y that the swimmingapparatu s wasfurthe r de velopedtha nth esuctio napparatus ,du et oit searl yappearanc ei nth echordates . Suction feeding at lowswimmin gspeed s(e.g .botto m feeding and feeding from crevices) was probably very ineffective. This suggests that Pteronisculus (and other palaeoniscoids with a similar morphology) captured their prey mainly in theope nwater ,o rthei rpre yconsiste d ofsluggis hbotto m organisms. Adirecte d flow towardsth emout h could probably havebee nestablishe d by Pteronisculus, in spite of its notched mouth, due to the presumably relatively largeimportanc eo fswimmin gi nit sfeedin g mechanism. Gymnocephalus The paracanthopterygians and acanthopterygians have developed long, curved,highl yrotatabl e aciniform branchiostegal rays(McAllister , 1968).Thi s allows feeding with the advantages of the cone model, i.e. effective feeding at a broad range of swimming speeds. How this is used is demonstrated by the feeding mechanism ofth eruff e {Gymnocephalus cernuus), an acanthopterygian, studied byElshoud-Oldenhav ean dOss e(1976) . Theauthor sdistinguishe d rela tivelystationar ybotto mfeedin g (typeA )an dmid-wate rfeedin g(typ eB) ,wher e large swimming velocities can beexpected . In Amout h expansion isfaster , al though the critical relative expansion rate Fic/h is lower. The maximal mouth openingi skep trelativel ysmal li nA (se eElshoud-Oldenhav ean dOsse ,Fig .14. 1) . From thecontinuit y equation it follows that larger speedso f thewate r in front of the mouth will begenerate d in A than in B.Additionally , protrusion of the upper jaws (a means to increase the speed of the prey in the moving frame, as has been argued by Nyberg, 1971)start s earlier in type A. The valves open at themaxima l opercular abduction inA . Hence,a cauda l inflow isprevented . The valves open later, but at a smaller abduction of the opercula, in type B, due to the slower expansion rate.Now , a caudal inflow will be avoided by the highforwar d body velocity.(So ,th einstan t xai sno tcouple d to afixed volum e of the mouth). Thus, bottom feeding is shortened and intensified relative to mid-water feeding and larger velocities of the water in front of the mouth (in anearth-boun d frame) aregenerated .I nmid-wate rfeedin ga larg erelativ espee d ofth epre yi sobtaine d byth evelocit yo fth epredato ritself . 67 Luciocephalus A last example is the feeding mechanism of Luciocephalus pulcher studied by Lauder and Liem (1981). Luciocephalus is an acanthopterygian fish with a body, closely resembling the pike. It also suddenly darts at the prey and reaches a high velocity at the moment of prey capture (about 1.5 m/sec was recorded byLaude r and Liem).Ver ydifferentl y from thetrou t and thepike , Luciocephalus protrudes itspremaxillae , very early in the suction phase, to theenormou s value of about 30% of its head length. The caudal valves with long aciniform rays open when the mouth is about maximally opened. From the observation that the prey is relatively stationary in an earth-bound frame Lauder and Liem have misinterpreted the fish's feeding mechanism, because a sound physical insight in the flow was lacking. On page 261the y conclude: "Luciocephalus usessuctio n only to anegligibl edegre ean d reliesalmos t exclu sively on body velocity to overtake and surround the prey with the buccal cavi ty". Onpag e 266the ywrit eabou t theprotrusio n mechanism: "In Luciocephalus, however, the prey remains nearly stationary throughout the feeding sequence (Fig. 1,4; compare the relative positions of predator and prey against the back ground) despite the enormousja w protrusion. Thus protrusion isno t an obliga torycorrelat eo fsuctio n feeding. In thiscase ,th ebehavio r ofth epredato r (initial mouth opening followed by a rapid forward lunge) limits the potential increase in the 'suction efficiency' obtainable by protrusion". However, from previous work and the present paper it isclea r that: 1.Protrusio n contributes to the directedness of the flow in the fish-bound frame (Nyberg, 1971an d Muller and Osse,i npress ,Fig .21) .A fas t swimming predator likeLuciocephalus, however, already creates adirecte d flow byit sforwar d veloc ity (Muller et al., 1982; Muller and Osse, in press and the present paper, Fig. 21). Soprotrusio n seemst o be of no advantage for Luciocephalus in this respect. Besides,protrusio n may decrease the effectiveness of the biting mechanism. 2. However, the early achieved protrusion lengthens the mouth and hence in creases the effect of a given expansion rate. Therefore the point where the fluid is at rest in an earth-bound frame can be kept more caudally when the caudal valvesar estil lclose d (see3.2.3.) .Henc edu et oprotrusio n theeffec t ofth e suction apparatus has increased relative to that of the swimming apparatus. After pro trusion has been established the flow is less directed than it would be without protrusion. 3. The additional head lengthening will result in a decrease of the critical mouth expansion rate (see paragraph 3.2.3.) and therefore in an increase in the ideal time of the opening of the valves. This requires long branchiostegal rays that allow the valves to be closed with a relatively large abduction of the opercula. These are indeed present. This isa n example of the interdependence of separate morphological features within the sucking system. 4.MullerandOsse(inpress)distinguishedanextremefeedingtypeforfisheswithpro- trusion that do not useextensiv e swimming {low-x-suction withprotrusion). They argued that protrusion enlarges the velocities relative to the mouth aperture. Hence, the feeding act can beshortene d and the total impulse added to the fish's 68 body and the water containing the prey can be kept small. The valves open relatively early. Luciocephalus, when feeding in the open water, applies another extreme feeding type, having an opposite aim in comparison to low-i-suction with protrusion. It enlarges the impulse enormously through a combination of head lengthening (larger volume sucked), a relatively late opening of the caudal valves and extensive swimming. This impulse is mainly put into the fish's body, as the prey was found to be relatively stationary in the earth-bound frame. I propose to call the open water feeding type of Luciocephalus high-x-suction with protrusion andswimming. Allmorphologica l features,distinguishe d sofar , neces sary for low-T-suction with protrusion are present in Luciocephalus. Therefore, itma y also beabl e to suck efficiently close to solid substrates. 5. Compared to the pike Luciocephalus has increased the suction capacity. Bit ing,however , isles seffien t due toth eprotrusabl e upperjaws .Therefor e Lucioce phalus seems to bespecialize d in sucking relatively small preys in one gulp, from a largeinitia l distance. 6.Th ekinemati cbehaviou r ofLuciocephalus isperfectl y adjusted toit s morphol ogy and hydrodynamical constraints and conclusions as to afunctional mor phology made by Lauder and Liem are unjustified. 4.4. OPTIMIZATIONS FOR AUNIDIRECTIONA L FLOW; THE KEY ROLE OFTH E VALVES The key role of the gill cover in the feeding mechanism of the bony fishes isapparen t from the above examples. The valves allow the fish to change almost instantaneously its hydrodynamical conditions during feeding. In the first in stance they close the mouth cavity at its posterior end to avoid a caudal inflow and to maximize the flow rate through the mouth aperture. Later, they form no obstacle when the flow rate can be enhanced through a caudal outflow. Fur thermore the gill covers lengthen the mouth (see e.g. 4.3. for the advantages ofa longer mouth). A biphasic inflow through the opercular slits occurs during feeding in the rainbow trout (at leasti n therang e ofobserve d swimming speeds,0. 5t o 2m/sec , see Fig. 10).Now , it will be discussed that several morphological and kinematic features, developed in the actinopterygian feeding mechanism, serve to generate a caudally directed flow inside the wholemout h during theentir e feeding act. The initial inflow through the opercular slits might be reduced by a faster opening mechanism. Then a delay of xawoul d bepossibl e and hence a reduction of xi-Xawoul d occur (see 3.2.3.). Second the valves may open in a rostral direc tion, thereby diminishing the effective head length and hence xa. Again a reduc tion of xi-Xa would be the result. However, the effect of mouth expansion on the flow towards the mouth is also diminished in this case. This last effect may not beto o harmful for thefas t swimming trout whichindee d opens the opercular slitsrelativel y far rostrally. Afish feedin g at low swimming speeds,lik e the lionf- ish (Pterois russelli),a n acanthopterygian, may benefit more from a fast opening mechanism. The isthmus of the branchiostegal membranes in Pterois lies far backward (especially at the moment of valve opening) as isapparen t from high- 69 speed films made by Muller et al.(1982) .Th e lionfish, however, possesses relati vely long curved aciniform branchiostegal rays allowing a significant opercular slit to be formed within only 2.5 msec (Muller et al. 1982, Fig. 9B), a second advantage of this type of branchiostegals (seeals o 4.3.). Filmsmad e by Lauder and Liem (1981)sho w that the isthmus in Luciocepha- luslie s also far caudally and that the valves open rapidly (at frame 6 the valves are still firmly closed whereas at frame 8the y are widely open, film of 200 fr/sec; cf Fig. 2 of Lauder and Liem, 1982, unfortunately the important frame 7 is not shown by the authors). This aspect again supports the view that suction isrelativel y important inLuciocephalus compared to other fast swimming fish. I suggest that a faster opening mechanism of the valvesallow s a longer effec tive mouth length after valve opening and hence a more caudal isthmus. In this way the contribution of mouth expansion relative to swimming is increased. More research, however, isneede d to becertai n about this point. Pushing in themout h aperture combined with a(secondary ) netcauda l inflow through the opercular slits may occur if the caudal parts of the mouth are still expanding, while the rostral parts are compressing (see paragraph 3.2.4.). A reduction or even a complete avoidance of a secondary inflow can be achieved by: 1. A high swimming velocity. The effect of swimming will be smalljus t before mouth closure,whe n only amino r mouth aperture ispresent . At that time, how ever, escape of the prey isunlikel y to occur. 2. A relative delay of %a. When xa is increased the time available between xa and thimax (the moment of the maximal opercular abduction) is decreased. Hence, a secondary caudal inflow becomes more unlikely. This relative delay is e.g. found in the pike, if feeding at a low swimming speed. The lionfish (see Muller et al., 1982 and Muller and and Osse, in press) opens the valves before thimax, however, at a relatively larger opercular abduction than in the rainbow trout. Asecondar y inflow was indeed not found by flow visualization by Muller and Osse. In the bottom feeding type of the ruffe (see 4.3.) rflis even postponed till the instant thimax- This was also found in the cod (Gadus morhud), a para- canthopterygian, with long aciniform branchiostegals, when feeding at a low swimming speed (see Muller and Osse, in press, Fig. 5). Muller and Osse also found that the cone like movement of the mouth could cause a biphasic caudal inflow ifth e valveswoul d open earlier (seethei r Fig. 18). 3. An earlier achieved maximal opercular abduction. This may lead to a mouth cavity compressing over its entire length, with an open mouth and open caudal valves. This obviously prevents a caudal inflow. This possibility seems to be only useful when the mouth aperture is already quite small, so that a blowing out of the prey is avoided. From Muller and Osse (in press, Fig. 11)i t appears that thiseffec t ispresen t ine.g .Amia calva,Gadus morhua, Stizostedion lucioper- caan d Pterois russelli(i n all cases with the expected small mouth aperture). 4. A reduction of hi after valve opening. If hi is less than a particular critical value (with the other parameters constant, see paragraph 3.2.3.) inflow is avoided. 70 5. Useo funstead yeffects . Anincrease d overallcaudall ydirecte dimpuls e before valve opening may delay a possible triple- or single-vortex effect and prevent a net secondary caudal inflow (but not the initial inflow). As argued in 3.2.2. thisma yonl yb eimportan t ata ver ylo wforwar d bodyvelocity .Othe r unsteady effects, due to the cone like movement may also play a role. Note that points 1t o5 ar eintimatel yrelate d toeac h other. 6.A reduce drostra lextensio no fth eopercula rslit s(se eparagrap h 3.2.4.).Thes e extensions arever yprominen t in thepalaeoniscoi d Pteronisculus, whereas they aresmal li nth ehighl yadvance d lionfish. The development of a gill cover, allowing a large opercular abduction with closed valvesan d arapi d valve opening, in theactinopterygia n feeding mecha nismha smad epre ycaptur eles sdependen to nswimming . Therefore,th enumbe r ofoption st oobtai na pre yha sincreased ,als owithi na singl especies . Asingl egil lcove r for all gillarche s of one sidewa sprobabl y first developed within the acanthodians as pointed out by Miles (1971). If this is true, then the basis for the suction feeding mechanism of the teleostomes can probably befoun d inthi sgroup .Thi ssuggestio nfro m afunctiona l point ofvie wcorrobo rates the conclusion of Miles (1973) that the acanthodians are probably more closelyrelate d toth eosteichthyan s than toth echondrichthyans . Schaeffer and Rosen (1961) distinguished adaptive levelsi n the actinoptery gian feeding mechanism, mainly based on thebitin g function of thejaws .Oss e (1976)an d Ossean d Muller (1980)stresse d that suction isa t least asimportan t asbiting ,an dtha t therefore theevolutio n ofth egil lcove rshoul db eincorporat ed in a study of the actinopterygian feeding mechanism. The present results supportthi sview . 5. Conclusions 1. Theanalysi so fth efeedin g systemo fSalmo gairdneri showe d that: a.initiall yth epre ywa sslightl ypushe d forward inth eearth-boun d frame. b. later the prey was sucked backward, toward the mouth, in the earth-bound frame. This suction continued even after the opercular and branchiostegal valvesha d opened. c. about 90%o f the total volume drawn into themout h was originally present in a sphere, centered on the prey, with a slightly larger radius than that of the maximalmout hapertur e(se eFig .13) . d. the flow rate into the mouth is highly variable, but maximal at the instant ofpre ycapture . 2.Constraint so na noptimize dfeedin gmechanis mca nb ededuce dfro m acylin der and a cone model of the fish's mouth (based on the model approach by Muller et al., 1982an d Muller and Osse,i n press).Th e constraints relate mor phological and kinematic parameters, such as head length, mouth radius, mouth expansion rate and swimming speed. Good agreement was found be tweenmode lprediction san dexperimenta l data. 71 3. To avoid pushing effects, the fish should at least reach a threshold expansion rate of its mouth aperture when the opercular and branchiostegal valves are closed. This rate depends on the fish's swimming speed, its mouth radius, its mouth length and an expansion rate in the opercular region. The rainbow trout exceeds this rate or opens the caudal valves. 4. After the valves have opened a threshold translational velocity should be reached by the fish to avoid inflow through the opercular slits. This velocity depends on the fish's head length, mouth radius and mouth expansion rate and a possible unsteady effect. This last effect was shown to be small in the rainbow trout. 5. The opercular and branchiostegal valves from an important control device for the acquisition of an optimal flow rate through the mouth aperture, by the possibility of changing almost instantly the fish's hydrodynamical constraints. They should beope n when themout h expansion ratei sles stha n acertai n critical value (seeparagrap h 3.2.3.). 6. Head expansion and thereby suction are continued after valve opening in the rainbow trout. Head expansion contributes also after valve opening to prey capture by increasing the flow rate through the mouth aperture. Generally, this flow is enhanced by a caudal outflow through the opercular slits at the actual moment of prey capture. 7.A mino r biphasiccauda l inflow through the opercular slitsoïSalmo gairdneri, expected on theoretical grounds,wa sindee d detected experimentally. Many kin ematic and morphological features of actinopterygian fishes can be explained as adaptations to obtain (or approach) a posteriorly directed flow inside the wholemout h throughout the feeding act. 8.Th equantitativ e picture ofth e flow in suction feeding developed inth e present paper allows a better understanding of the feeding mechanism of actinoptery gian fish in general asexplaine d for Pteronisculus\, Amia, Esox, Salvelinus, Ga- dus, Pterois, Luciocephalus and Gymnocephalus. 9. The prey capture mechanism of palaeoniscoids like Pteronisculus was proba bly largely dependent on swimming. The evolution of the prey capture mecha nism shows various adaptations (e.g. an increased effective head length and a larger possible abduction of the gillcove r without opening of the caudal valves) leading to an increased independence of the feeding process from swimming. However, ifth e situation allowsi t swimming iscontinue d to betake n advantage of, asa way to increase the flow rate through themout h aperture. 10.Th e stereoscopic flow visualization technique described in the present paper is an important tool in the study of the prey capture mechanism of actinoptery gian fish, as with it the predator, prey and surrounding water can be followed through time in 3-dimensional space. With it information is gained about the volume flow of water into the mouth, the shape of the volume drawn into the mouth, the velocity of the predator and prey, particle path lines,th e momentum given to the water and the prey by the fish, the occurrence of stagnation effects, the relation between suction and swimming and the role of the opercular and branchiostegal valvesdurin g suction feeding. 72 Theinvestigation swer esupporte d byth eFoundatio n for Fundamental Biologi cal Research (BION, 14.90.18),whic hi ssubsidize d byth eNetherland s Organi zation for theAdvancemen t ofPur e Research (ZWO).I had great benefit from numerous discussions with Drs. M. Muller. Prof. J. W. M. Osse and Drs. M. Mullerrea d anddiscusse dth emanuscrip t andforce d met omak em ystatement s asclea r as possible. They gave permission for publication of Fig. 4. Ir. J.H.G. Verhagen from the Delft Hydraulic Laboratory critically read a great deal of thehydrodynamica l parts ofth epape r and gaveman y useful suggestions. Iha d valuable discussions about photogrammetry with Mr. G. R. Spedding, Ir. J. T. van der Veer and Ir. T. de Lange. Mr.J . Kremers supplied data of thepike . Mr. A. Terlouw gave skillful technical assistance, constructed the multi-flash time delay device and helped to train the fishes. Mr. W.Vale n made thedraw ings.Th econtribution smad eb yal lthes epeopl ear egratefull y acknowledged. 6.Reference s Alexander, R.McN. (1967). The function and mechanisms of the protrusible upper jaws of some acanthopterygian fish. J. Zool. Lond. 151,43-64. Anker, G.Ch. (1974) .Morpholog y and kineticso fth ehea do fth estickleback , Gasterosteus aculeatus. Trans.Zool. Soc. Lond.32 , 311-416. Ellington, C.P. (1978). The aerodynamics of normal hovering flight. In: Comparative Physiology - Water, Ions and Fluid Mechanics (ed. K. Schmidt-Nielsen, L. Bolis and S.H.P. Maddrell), pp. 327-345. Cambridge University Press. Elshoud-Oldenhave, M.J.W. &Osse , J.W.M. (1976).Functiona l morphology of the feeding system of theluff-Gymnocephalus cernua(L . 1758)-(Teleostei,Percidae) .J. Morph. 150,399-422. Hertel, H. (1966).Structure, Form andMovement. New York. Reinhold. Kokshaysky, N.V.(1979) .Tracin g thewak e of aflyin g bird. Nature 279,146-148. Lauder, G.V. (1980).Th e suction feeding mechanism in sunfishes (Lepomis): an experimental analy sis.J. exp. Biol. 88,49-72. Lauder, G.V. & Liem, K.F. (1980). The feeding mechanism and cephalic myology of Salvelinus fontinalis: form, function and evolutionary significance. In: Charrs Salmonid Fishesof theGenus Salvelinus (ed. E.K. Balon),pp . 365-390.Dr . W. Junk Publishers, The Hague. Lauder, G.V. &Liem, K.F. (1981). Prey capture by Luciocephalus pulcher. implications for models ofja w protrusion in teleost fishes. Env. Biol. Fish.6,257-268 . Leeuwen, J.L. van & Muller, M. (in prep.). The recording and interpretation of pressures in prey sucking fish. McAllister, D.E. (1968). Evolution of branchiostegals and classification of telestome fishes. Bull. Nat. Mus. Can.221 ,i-xiv : 1-239. McCutchen, C.W. (1977). Froude propulsive efficiency of a small fish, measured by wake visualiza tion. In: Scale effects in animal locomotion (ed. T.J. Pedley), pp. 339-363. London, New York and San Fransisco. Academic Press. Merzkirch, W. (1974).Flow Visualization. New York and London. Academic Press. Miles, R.S.(1971) .In : Palaeozoic fishes (i.A.. Moy-Thomas), 2nd ed. London. Chapman &Hall . Miles, R.S. (1973). Relationships of acanthodians. In: Interrelationships offishes (ed. P.H. Green wood, R.S. Miles& C . Patterson), pp.63-104 . London. Academic Press. Muller, M. &Osse ,J.W.M . (1978).Structura l adaptations to suction feeding in fish. In: Proceedings of theZODIAC symposium onadaptation, pp. 57-60.Wageningen . Pudoc. Muller. M. & Osse, J.W.M. (in press). Hydrodynamics of suction feeding in fish. Trans. Zool. Soc. Lond. Muller, M., Osse, J.W.M. & Verhagen, J.H.G. (1982). A quantitative hydrodynamical model of 73 suction feeding infish. J. theor.Biol. 95,49-79. Nyberg, D.W. (1971).Pre y capture in the largemouth bass.Am. Midi. Nat. 86,128-144. Osse, J.W.M. (1969). Functional morphology of the head of the perch (Percafluviatilis L.): an electromyographic study. Neth. J. Zool. 19(3) ,289-392 . Osse, J.W.M. (1976). Mécanismes de la respiration et la prise des proies chez Amia calva Linnaeus. Rev. Trav.Inst. Pêches Marit. 40,701-702. Osse,J.W.M . &Muller ,M .(1980) .A mode l ofsuctio n feeding inteleostea nfishes wit h some implica tions for ventilation. In: Environmental physiology of fishes (ed. M.A. Ali) NATO-ASI Series A. Life Sciences, pp. 335-352.Plenu m Publishing Corporation, New York. Rand, D.M. & Lauder, G.V. (1981). Prey capture in the chain pickerel, Esox niger: correlations between feeding and locomotor behavior. Can.J. Zool. 59(6) , 1072-1078. Schaeffer, B. & Rosen, D.E. (1961). Major adaptive levels in the evolution of the actinopterygian feeding mechanism. Amer. Zool. 1,187-204. Selvik, G. (1974). A roentgen stereophotogrammetric method for the study of the kinematics of the skeletal system. Thesis.AV-centralen , Lund. Spiegel, M.R. (1968). Mathematical handbook offormulas and tables. Schaum's outline series in mathematics. New York. McGraw-Hill. Spiegel, M.R. (1974). Theory andproblems of vector analysis and an introduction to tensor analysis. Schaum's outline seriesi nmathematics . New York. McGraw-Hill. Weihs,D . (1980).Hydrodynamic s of suction feeding offish in motion. J. FishBiol. 16,425-433. 7. Appendix 7.1. FILMING RATE AND ACCURACY OFVELOCIT Y CALCULATIONS The error made in velocity calculations by numerical means depends on the time interval used for differentiation, as shown by Muller et al (1982) for their computer model of suction feeding with the aid of the contraction formula of Banach. The same holds true for velocity calculations from position data ob tained from films. Suppose that theerro r made in the determination of the posi tion of a point P on each film frame is ôx and the error in the determination of the timei t was taken dt.The n theerro r in the calculation of themea n velocity öqmi n the timeinterva l At betwee n two frames will be: 2ôx <5qm = -77 + 777^22 • 2ôt (23) At "' (At) where d is the distance travelled by P. From (23) it is clear that <5qm decreases hyperbolically with increasing At, so that a large At seems to be favourable. However, fluctuations in therea l velocityq ar ebette r recorded with a decreasing At. To appreciate this consider a point with a sinusoidally fluctuating velocity q«: q0= -0.5 Bsin 2nft (24) where B represents the velocity range and ƒ the frequency of oscillation. The maximal error <5q0dependso n B,/and At, when no error ismad e in its position, and wasfoun d to be(afte r some algebra): <5q0 = | 0.5 B sin y A sin(-nfAi) + 1) | (25) 74 (5q0 decreases with decreasing At. The maximal possible error is reached for At is 3/72. (5q0wascalculate d for a range of different B's andfs, an example of which, together with a calculation of ôqm,i sgive n in Fig. 22.Th e choice of At, used for numerical differentiation, depends on the frequency range needed in the analysis, and should be taken in the range where öqman d ôq0ar e of about equal magnitude. In thepresen t study a frequency range of 0-50 Hz,to getherwit ha At o fabou t 10mse cwa sfoun d tob emos tsuitable . 7.2. CORRECTIONFO R PERSPECTIVE DISTORTIONS In paragraph 2.4. it was explained how the coordinates of points in space couldb ecalculate donc eth eprojection s ofthes epoint si nstereograph so nplane s Can dF ar eknown .A correctio nfo rperspectiv edistortion swa sneede dbecaus e theseplane swer eno tperpendicula rt oth eoptica laxe so fth estereoscopi c filming set up. Planes C and F were positioned perpendicular to the horizontal plane. The optical axes were orientated parallel to thehorizontal . For this particular situation the distortion of a plane isillustrate d in Fig. 23.Line s parallel to the y-axis(th evertica laxis )remai n parallel toeac h other on thefilm o r itsperpen - Errorin velocity (m/sec) 0.02 0.04 0.06 0.08 0.10 -• t (sec) Fig.22 .Exampl eo fa n analysiso fth eexpecte dmaxima lerro ri nth evelocit yobtaine dfro mpositio n data from high-speed movies.Th e mean velocitywa s chosen to be 1.2 m/sec. The error in qrawa s calculated for both a ôx of 1 and 2m m (respectivelyth edotte d and dashed curves). For thecalcula tion ofq 0i twa sassume dtha t thevelocit yvarie dsinusoidall ywit ha namplitud eo f0. 6m/se c(B = 1.2 m/sec). This calculationwa sdon e for/equals 12.5,25 , 50,an d 100H z (depicted near eachcurve) . Obviously,a large rA t shoul db etake nwhe nSx increases .Th erevers ei stru ewhe na highe rfrequenc y range is needed. 75 dicular projection. Along these lines the scale factor S is constant. This is not true for lines originally parallel to the X-axis. Just one of these lines remains perpendicular to the Y-axis, which we shall call the A±-axis. Along this axis S varies linearly: S = ext + d (26) where can d dar e constants and jcith ecoordinat e along the Zi-axis. For calculation of the actual x-coordinate, XAP, of the projection of a point P the following integral should be solved: XLP 1 XAP = dx± (27) which gives: 1 1 XAP = - In (cx\_p + d) Ind (28) The actual ^-coordinate of the projection ofP, yAP, can be obtained by: yAP = yDP IS (29) Fig. 23.Diagra m of a distorted plane (as explained in appendix 7.2.) illustrating the method of calculating thecorrectio n for perspectivedistortion . The black dot denotes theprojectio n of Po n thedistorte dplane .Furthe r notationsar eexplaine di nth etex tan d Table1 . 76 where yDP is the distance to the X-axis in a direction parallel to the F-axis inth edistorte dplane .Constant sc an dJea n becalculate dfro m reference points withknow ncoordinate s onth ecalibratio n frame. 77 HOOFDSTUK 2/CHAPTER 2 Optimumsuckin gtechnique sfo rpredator y fish 79 Trans. Zool. Soc. Lond. (in press) Optimumsuckin gtechnique sfo r predatory fish J.L. VAN LEEUWEN AND M. MULLER Department of Experimental Animal Morphology and Cell Biology, Agricultural University, Marijkeweg 40, 6709P G Wageningen, The Netherlands. Keywords: Fish, Hydrodynamics, Optimization, Prey capture, Protrusion, Suction feeding, Swim ming. Synopsis The hydrodynamical model of suction feeding in fish by Muller et al. (1982 )an d Muller & Osse (in press) was used to derive conditions for optimal prey-suction. The separate contributions ofswimming ,mout h expansion and a possibleja w protrusion to theveloci ty of the prey relative to the fish were calculated as functions of time. Account was taken of the unsteady nature of the flow. The calculations are valid if the opercular valvesar eclose d before prey uptake.Th einitia l preydistanc e isgenerall y hardly affected by quite a large change in the fish's mouth expansion. However, the influence of mouth expansion on the velocity of the prey while it enters the mouth is very strong. These results permit to derive, together with considerations of the generated pressure, the opti mal phase relationship between the expansion of the rostral end of the mouth and the abduction of theoperculars .Prediction s weremad e for therelatio n between the maximal mouth aperture and the swimming speed of the fish. Estimates were made of the effect of valve opening before prey capture. These theoretical predictions were tested using data from high-speed films of fish feeding. Sucking techniques are discussed for fish feeding indifferen t habitats. Contents 1. Introduction 82 2. Definitions and symbols 82 3. Methods 83 4. Calculations 85 5. Resultsan d discussion 89 5.1. Effects ofsuction ,swimmin gan dprotrusio n 89 81 5.2. Initialpre ydistanc ean dultimat epre yvelocit y 93 5.3. Influence ofmouth gapeo ninitiatio ndistanc ean dpre yvelocity . 98 5.4. Theinfluenc eo fth epressur eo nth emout hexpansio n 103 5.5. Preyuptak e before and after peakmout h gape 105 6. General discussion 106 7. Summary 108 8. References 109 9. Appendix:mathematica l equations 109 1. Introduction Preycaptur e mechanisms inbon yfish hav e been frequently studied. The dom inant mode of prey capture consists of a combination of suction (by a rapid expansion and compression of the buccal and opercular cavities, together den oted asth emout h cavityi n thispaper ) and forward motion (by suction forward, protrusion and swimming). The success of a feeding event depends largely on the generated flow relative to the fish's mouth. Therefore, hydrodynamic princi ples may be succesfully used to study the predator-prey interaction (see e.g. Muller et al., 1982;Mulle r &Osse ,i npres s and Van Leeuwen, in prep.). The present paper attempts to derive quantitative requirements (morphologi cally and kinematically) for optimized prey capture techniques (i.e. such tech niques that the chance of prey capture is maximized). It deals with questions like: 1)A t what moment and what distance from the prey should a fish start mouth expansion? 2) How is the velocity of the prey related to the fish's mouth cavity expansion, jaw protrusion, forward velocity and distance? 3) Does the predator optimize velocity, or distance or both? Which velocity should be preferably given to the prey when it passes the mouth aperture, in order to optimize thepreventio n ofit s escape? 4) Is there an optimal combination of the expansion of the rostral end of the mouth cavity and the abduction of the operculars, to optimize the chance of prey capture (with a given effort of the predator)? It will be shown that detailed knowledge of the escape response of the prey isno t required to explain much of thebehaviou r of the predator during capture. Therefore the present analysis deals only with prey moving with the flow. 2. Definitions andsymbol s dprey distance between prey and mouth aperture diprey distance between prey and mouth aperture at tv\: th e initial prey distance esuction relative suction effect (seepag e 86) 82 ^swimming relative swimming effect (seepag e 86) hi profile radius at 'mouth aperture' (x' =I) hi profile radius at 'opercular region' (x' = 0) hüntnax maximal value ofprofil e radius, *= 1 or 2 fî*mtl minimal value ofprofil e radius, *= 1 or 2 i length of profile (or fish's mouth cavity),/ = /0 +l prot /o length ofprofil e at t =t v\ Iprot distance of protrusion t time thalf* time at which A* = A*««/+ 0.1 Ah*max, plus 0.5/r* (see page 87), * = lor2 th*max time at h*max, *= 1 or 2 tpb time at which thepre y passes themout h aperture trut rise time (seepag e 87), * = 1 or 2 tv* delay time, *= 1 or 2 U velocityi n theX-directio ni n the earth-bound frame U' idem in the A"-direction in the fish-bound frame Um velocity in the mouth aperture inearth-boun d frame U m idem in fish-bound frame: u'mk + u'mprot— Uprot M mlc velocity inmout h aperture ifprotrusio n were absent U mprot contribution ofprotrusio n to suction velocity in mouth aperture Uprey velocity of the preyi n earth-bound frame U prey idem in fish-bound frame U prey mean speed of thepre y in fish-bound frame from tv\ till tpb U'tpb velocity of the prey at t = tpbi n fish-bound frame uf velocity ofmout h aperture: Us*> + Uprot Uprot velocity of protrusion Usw velocity of fish's body X coordinate oflon g axisi nearth-boun d frame x' idem in moving frame X,Y,Z axes ofearth-boun d frame X',Y',Z' axes offish-bound frame a* shape coefficient ofprofil e movement, *= 1 or 2 ß angle between medial plane of the fish and long axis of hyoid Ahiemax h+max—h+nui, *= 1 or 2;amplitud e of movement Ta actual moment of opening of opercular valve 3. Methods High-speed films weremad e offeedin g Amia calva,(bowfin , 1 specimen), Sal- mogairdneri (rainbo w trout, 1 specimen), Esox lucius(pike , 3specimens) ,Gadus morhua (cod, 1 specimen), Stizostedion lucioperca(pike-perch , 1 specimen), Pla- tichthys flesus (flounder, 1specimen ) and Pterois russelli (lionfish, 1 specimen) as described by Muller &Oss e (in press).Th e dimensions of the specimens used 83 Table 1.Fis h specimen used. SLi s standard length, /i s head length, Prot, isprotrusio n of upper jaws.T i stemperatur eo fwater ,LA ,W Aan dH Aar elength ,widt han dheigh to faquarium . species SL I Prot. T LA WA HA (mm) (mm) (mm) (°Q (m) (m) (m) Amia calva 365 92 0 17 .9 .5 .4 Salmo gairdneri 343 80 0 15 1.9 .5 .3 Esox lucius 485 143 0 16 2.0 .5 .3 Esox lucius 253 73 0 15 .8 .5 .3 Esox lucius 195 63 0 15 .8 .5 .3 Gadus morhua 375 100 1 13 .9 .5 .4 Stizostedion lucioperca 310 90 4.6 15 .9 .5 .5 Pterois russelli 138 40 4.6 23 .8 .4 .4 Platichthys flesuslva 315 71 4.7 15 .6 .4 .2 and thecondition s in which theywer e kept are given in Table 1.Visualizatio n of the generated flow, using polystyrene spheres (0.5 and 1 mm in diameter) was carried out for Pterois russelli (as done by Muller & Osse, in press) and Salmogairdneri (a sdon eb yVa nLeeuwen ,i nprep.) . Theexperimenta l records wereuse d to verify theoretical predictions, asder ivedfro m calculations ofth epre yvelocit y andinitia lpre ydistanc edi prey( = dis tancebetwee nth epre yan dth emout hapertur ea tth estar t ofmout h expansion) The calculations are based on the hydrodynamical model of suction feeding infish b y Muller et al. (1982). They modelled the flow towards the expanding mouth cavity asa combinatio n ofa circula r vortex and aunifor m flow (to take account of forward motion and apossibl eja w protrusion).Th e singular points ofth evorte xar epositione d atth efish's lips .Thu sth eradiu so fth emout haper turehi, correspond st oth eradiu so fth evortex .Th evorte xstrengt hi scalculate d from the rate of volume change of the mouth cavity. Thus account is taken ofth eunstead ynatur eo fth eflow .Th emout hcavit ywa smodelle da sa nexpand ingan d compressing cone, of which the anterior radius can bevarie d indepen dentlyfro m theposterio r radius.Th esimplifyin g approximations ofthi smode l areextensivel y treated inMulle re tal .(1982 )an d Muller &Oss e(i npress) .Out lineso fth emode lar egive ni nFig .1 . The authors pointed out the necessity to make a distinction between events in the earth-bound frame (which isfixed relativ e to the aquarium) and events inth emovin go rfish-bound fram e (whichi sfixed relativ et oth emout h aperture of thefish). Event s inth eearth-boun d frame should beuse d tocalculat e forces and pressures. The flow in thefish-bound fram e is very informative when the chanceo fpre ycaptur ei sstudied . Experimental data, including pressure records (e.g. Lauder, 1980;Mulle r& Osse, in press and Van Leeuwen &Muller , in prep.), velocity records (Muller & Osse, in press) and flow visualization records (Muller &Osse , in press and Van Leeuwen, in prep.) could be satisfactorily explained with the model of Mullere tal . (1982). 84 x' = O opercular region Fig. 1.Illustratio n of model approach asuse d in this paper. A. Fish moving forward in the earth-bound frame X, Y,Z. The mouth aperture has velocity Uf in this frame. £//isequa l to the forward body velocity of the fish,U sw, plus the velocity of protrusion of thejaws , Uproi. Uprotismeasure d relative to the body of the fish. The expanding and compressing mouthcavit y of the fish isschematize d as a conical profile (seeB) . B. Different stages of expansion and compression of conical profile. 1.Initial , and also final stage. 2. The buccal region has expanded widely; the opercular region starts to expand. 3. The buccal region contracts whereas the opercular region is still expanding. The cone is represented in the moving frame X'.Y'.Z', so that it stands still. X and A"-axes are taken to overlap each other. h\ and h2 are the radii at x' = /an d x' = 0 respectively. The prey islocate d at the JT-axis, at a distance dpreyfro m the mouth. 4.Calculation s We assume the prey to behave as an element of the water. So the prey does not swim and its density equals that of water. Other prey reactions are paid attention toi nth egenera ldiscussion . Furthermore weassum etha t thefish aim s at its prey before it starts sucking. This means that the prey is positioned at thelon gaxi so fth emout h (theX'-axis ,take n parallel toth eX-axi so fth eearth - boundframe )durin gth esuctio nprocess .Thi sfeatur ewa sobserve di nth emajor ityo fth emor etha n20 0recorde dfeedin gevent so feigh tdifferen t species.Mulle r et al.(1982 )calculate d thevelocit y ofth ewate ri n theearth-boun d frame along the X-axis (their formula 34). With this formula and the above assumptions weobtai n thevelocit yo fth epre yi nth eearth-boun d frame: 85 Umhy1 Uprey = — (1) y/icPprey + hSy where umi s the velocity of the water in the mouth aperture in the(earth-boun d frame, and dprey the distance between the mouth aperture and centre of mass ofth eprey . The relation between velocity wi n theearth-boun d frame and veloci ty u' in themovin g frame is: u' =u-U f (2A) u'prey = Uprey — Uf (2B) u'm = Um—Uf (2C) Where Ufi s the velocity of the mouth aperture. u'm and u'prey are velocities inth emovin gfram e ofth ewate ri nth emout h aperture and thepre y respectively. u'prey is chosen to have a negative value if the prey moves towards the fish's mouth. Using (2) we can rewrite (1) to obtain the velocity of the prey in the moving frame: U'mhf W - Jtfprey + hl*?) 2 2 3 y/(cPprey + h\ f V'(é'prey + hl ) (3)ca n be written in a simplified form: = U prey Um (^suction T~ Uf ^swimming V*) where eSUctwn is the relative suction effect and eSwimming the relative swimming effect and: ^swimming = &suction 1 ( J) Furthermore wehave : Uf=USW+Uprot (6) where £/iwisth e forward body velocity of the fish (due to swimming and suction forward) and Uprotth e protrusion velocity. Also: U m = Umk + Umprot — Uprot (') where u'mic is the velocity in the mouth aperture if protrusion is absent and u'mpwtth e contribution to u'm due to the increase of / as a result of protrusion. Using (5), (6) and (7) we can rewrite (4) to show the separate effects of suction, swimming and protrusion on u'prey. = Uprey ^ mlc ^suction i Umprot ^suction ~r Usw^swimming Uprot v°/ The first term represents the component of the relative prey velocity due to suc tion ofth eprofil e ifn o protrusion would bepresent . Thecontributio n of protru sion to the suction velocity of the prey is represented by the second term of (8). The third term gives the contribution of swimming to the relative velocity of the prey. The fourth term of (8)represent s the contribution of the translation 86 velocity of protrusion to u'prey. Note that this last effect is independent of dprey. Protrusion causes no stagnation effect in the mouth aperture, except very close to the edges.Th e prey ispushe d forward in the earth-boundTrame, with velocity Usw^suction, if the fish does not suck (u'm/c and u'mprot are zero) and — 1 < eSwimming < 0 (from equations 2, 5, 6 and 8). It will be shown in the results and discussion how a fish can avoid pushing effects. Prey do have a certain sizean d may deviate from the l"-axis. A consideration ofth ecomplet efield o fflo w (Muller& Va n Leeuwen,i nprep.) ,however , showed that thisdoe s not affect the conclusions drawn in the present paper. Once the position of the prey at a particular moment during the suction pro cess is known, the distance travelled by the prey is obtained by integration of (3). In a simulation we can prescribe this position at the start of mouth expan sion, but then we do not know beforehand when the prey will enter the mouth. It seems reasonable to assume that in the optimal case the prey should enter the mouth when it is opened widest. Then, the size range of preys that can be caught is maximized, as may be the chance of prey capture. Muller & Osse (in press) indeed found that the moment of prey entering the mouth (at / =t pb) correlates roughly with the moment of the maximal mouth aperture in eight different fish species.Late r on wewil lrela x this assumption (seepag e 105). The initial prey capture distance can be obtained by a reverse calculation. Then tpb can be prescribed, which appeared most convenient. The integral to be solved (see appendix) has an implicit form, as u'preydepend s on dprey. There fore, numerical integration was carried out. The time step for integration was chosen such that an accuracy of 0.03 mm of the initial distance was obtained, representing an error of less than 1 percent. The velocity in the mouth aperture due to suction (u'mic + u'mprot)wa s calculated using formula (18) of Muller et al. (1982). The analytical solution for the cone is given in the appendix. u'm depends on hi and hi. These variables were described by Muller et al. (1982), with functions of the following form: a* /z* (t) = h*„ui + Ah*max\- — exp 1- — — (9) \}h*max »v* \ 'h*max— 'v* JJ and: K (t) = h*nui for (t ^ rv*), (10) where Ah*max = h*max — h*nui and: t, tv* 7& 0, th*max > ^v*, "*««/ > 0 hifmax > h*nui and a* ^ 2 where h*nuii s the minimal value of the profile radius, h*maxth e maximal value of profile radius, {Ui — tv\) the delay time between the starts of expansion of h\ and hi and a* the expansion coefficient of the profile. The index * from the parameters in the equations (9) and (10) may be 1t o define the movement at the mouth aperture or designate a 2 to obtain the movement in the opercular region. The rise time tr* of the movement curve is the time required for A* to go from {h*„ui + 0.1 Ah*max) to (A*«»/+ 0.9 Ah*max). The moment thatf* lies 87 80 IX 120 160 200 •tim e (msec) Fig. 2.Profil e movements.h\ (t) representsmovemen t at mouth aperture (x' = I),hi (t) isth emove ment in the opercular region (x' = 0). All symbols are explained in the text, hi and hi represent fitted curves (see formulas 9 and 10) of a feeding attempt of a pike (Esox lucius, SL 253 mm). The values of the relevant parameters (see text) are: ai = 17.2; \,h\nui= 2.5 mm; \\,h\max = 10.3 mm; fvi=0.0 msec; toi mo* = 100.0 msec; III,t r\= 32.6 msec; IV,thaif\ = 73.2 msec; 88 5.Result san ddiscussio n 5.1. EFFECTS OFSUCTION , SWIMMING AND PROTRUSION Very often fish capture their preysb ya combinatio n ofsuctio n and swimming. It is useless for a fish to start sucking if the prey is still too far away. Also a bad strategywoul d bet o swim tooclos et o theprey .No w thepre ywil lb e pushed away, or cannot pass the only partly opened mouth aperture. Furthermore, the prey may become more easily aware of the predator. We will now investigate when a fish should preferably start sucking while it approaches the prey (ques tions 1 and 2,se epag e 82). Fig. 3 shows plots of the relative suction effect and the relative swimming effect against dPrey for various values of hi (see formulas (3), (4) and (5)). The relativesuctio n effect isgreates t closet o themouth . Therelativ e swimming effect decreases also with the distance from the mouth. The relative suction effect in creases non-linearly with the mouth radius. This can be easily observed by fol lowing this effect along the dotted vertical reference line in Fig. 3. Also, the distance from the mouth at which a particular relative suction effect is found increases proportionally to the mouth radius. (Shown by the dotted horizontal reference line in Fig. 3). Naturally, this is also true for the relative swimming effect. A larger mouth aperture does not automatically increase the distance from themout h atwhic h a particular magnitude ofth e suction velocity is found, because u'mich proportional to themout h volume change, but inversely propor tional to hi2. During prey capture hi and dpreyvary . Thus, the change in esuction for an actual feeding event intersects the contours, asillustrate d in Fig. 3fo r a feeding -1 -1" K\^<; is ,---''' 4 ,'' \\\' ^8 :|: ^- -^ ' - --.8 !-''' Gswimming 6suction " VV\v" ' ,/>< 1 32 Î e \ x v\ --.6' ,.-''16 (—) JLiLJ!VLA^ >^™^S>^.ft^«»:««.:««»:« (—) \16 \'X '\ x.' ,,'"' ^~\^^ --.4 , , - ' 32 ^~~^^ ~'' \V \\ ' ' \ -''\' \^'' l' '\ '\ -'' \8 —j \ \ ,' >v „ ' >v --.2 2 :|: ^^^-^^ — ;; A ,A4 ,> 1// ^x^^ ,^C^^ l'y'!. -_'_ -|- - 1 _ 1 i 1_ L_L~-==U h 12 16 20 24 28 + prey distance (mm) Fig. 3. Plots of relative suction effect (solid curves) and relative swimming effect (dashed curves) against prey distance. The contours show values ofh\ inmm . The heavy curvewit h asterisks denotes the actual variation of esuaiondurin g a feeding act of a rainbow trout (SL 343mm) . Mouth opening proceeds so that a rapid increase oiesuctioni sobtained . Further explanations aregive n in the text. 89 event of a rainbow trout. The trout opens its mouth so that a rapid increase in esuctioni s obtained. Having this knowledge, it will be interesting to see to what extent different fish use suction, swimming and protrusion to capture the prey. Figs. 4, 5 and 6sho w thecontribution s ofth edifferen t termso fformul a (8)t o thepre y velocity, u'prey. These curves are obtained from motion analysis of the fish's head. They are compared with the actually measured prey velocity. Fig. 4 shows the contributions of suction and swimming to the prey velocity in the moving frame, for the prey capture event of Fig. 3 of the rainbow trout. This fish has no protrusion, although its maxillae rotate forward and thereby seal the mouth corners. Therefore the second and fourth terms of formula (8) are zero. The fish already started to expand its mouth at more than one head length away from the prey. This had littleeffec t on u'prey. Remarkably, the largest negative pressures were recorded during this initial expansion (Van Leeuwen & Muller, in prep.). So, the fish seems to deliver a large effort, although this does not result directly in a contribution to u'prey. It is important for the fish to be able to expand its mouth fast when the rapid increase of esuctionbecome s within reach (within about 30 mm from the mouth, see Fig. 3). This is impossible if the mouth aperture is still very small as then a very largeforc e (pressure)woul d berequired . So,initia lmout h opening should be started before the possible rapid increase of esuction. During the initial buccal expansion a slight opercular adduction was found in several fish species (see velocity (m/s) Î (6.35) , ' (23.5)(17.8)(12.2n,2,4,5 (0) 6~ dprey (mm) Fig. 4. Calculated contributions of suction and swimming to u'prey during the feeding act of the rainbow trout of Fig. 3. Protrusion of thejaw s is absent in Salmo. The actual dprey, as measured from the film, was used in the calculations (using formula (8)). The time in msec is given between brackets at eachdat a point of dprey. Notation: 1) swimming velocity. 2) minus velocity of prey due to swimming, —Usw-emimming. 3) minus velocity of prey due to suction, —u'mk-esucUim. 4) u'prey =curv e 2 + curve 3. 5) —u'prey with the assumption ofope n valves(pag e 91). 6)— u' prey, measured from the film (dashed curve). The maximal errors made in calculating Usvan d u'prey (directly from the film) were about 0.15 m/sec.Th e calculation via the cone model of u'preyappear s to be a quite large overestimate. 90 e.g. Lauder, 1980;Mulle r &Osse ,i npres san d Van Leeuwen &Muller , inprep.) . This adduction willdecreas e the magnitude of u'mk, but decreases also the mag nitude of the acceleration pressure and hence may increase the rate at which the mouth can be opened (seeals o Van Leeuwen &Muller , in prep.). Initial opercu lar adduction may therefore enhance the chance of prey capture. Note that the flow inside the mouth due to opercular adduction is very small, but sufficient to enlarge the initial volume of the buccal cavity. We wish to emphasize here that Lauder's explanation of this phenomenon (i.e. that the gills function as a caudal valve; Lauder, 1980) is incorrect (ref. for this point Muller & Osse, in press). Apart from these effects the early expansion may prevent stagnation effects due to swimming. The initial effort could be reduced if the fish would open itsmout h initially slower and hence necessarily earlier. Too slow an expan sion, however, would increase the pressure drag in swimming and is therefore not desirable. Thecalculation s for Fig.4 wer ecarrie d outwit hth e assumption that the oper cular and branchiostegal valves are kept closed until the maximal mouth aper ture isreache d (themomen t of prey passage through the mouth aperture). This is not so in the rainbow trout (see Van Leeuwen, in prep.). After valve opening the effects of suction and swimming on the flow cannot be calculated exactly. The results of an estimate that u'prey= —Usw + 0.5u'mic esuctmn after valve opening are plotted in Fig. 4. It is assumed that eSWimming has a constant value of — 1 (similar to the translation effect ofprotrusion ; stagnation effects are neg lected) and the velocity in the mouth due to suction is only half the velocity with closed valves. The actual prey velocity deviates quite strongly (i.e.i sconsiderabl y less nega tive) from the calculated velocity (Fig. 4).Thi s mainly isdu e to an overestimate of the volume change of the mouth with the cone model (up to 100 percent was found for Esox lucius by Kremers &Va n Leeuwen, in prep, who measured the actual volume change), hi was measured as half the distance between the caudal edges of the opercula. The dorso-ventral expansion in this area is, how ever, very small, so that effectively hi will be smaller than the measured one. Likewise hi was measured as half the height of the mouth aperture, which also introduces an overestimate. Furthermore, no account was taken of the mouth corners, so that /was overestimated. If u'prey is greater than —U sw, mouth expansion does not completely com pensate the stagnation effects due to swimming and the prey will be pushed forward in an earth-bound frame. To avoid this the opercular and branchioste galvalve sope n(se eVa nLeeuwen ,i nprep ,fo r adetaile ddiscussio no fthi spoint) . The suggestion which might rise from the calculations that valve opening would not havebee n needed before preyuptak e in thetrou t (Fig.4) ,shoul d be attribut ed to the abovementione d overestimate. Platichthys (Fig. 5)use sprotrusio n duringpre ycapture . Thetranslatio n effect ofprotrusio n contributes considerably to u'prey. The suction effect of protrusion is only small. The first term of formula (8) contributes most to diprey.I n Pterois (Fig. 6)uppe rja w protrusion iseve n more important than in Platichthys. Now, 91 -1.5 i— prey- velocity (m/sec) -» dprey (mm) Fig. 5. Calculated contributions of suction, swimming and protrusion to u'prey in a prey capture event of the flounder (Platichthys flesus SL 315 mm), using formula (8). The actual position of the prey, measured from the film was used in the calculation. Notation (different from the notation of Fig. 4): 1. Contribution of forward body motion to u'prey. USw •eswimming. 2. curve 1plu s the contribution of protrusion: USw'e swimming— Uprot- 3. curve 2 plus the contribution of suction, with the assump tion of a constant mouth length: u'mlc-eSUction+ Usweswimming—Uprot. 4. curve 3 plus the suc tion velocity of u'prey due to protrusion. All terms of formula (8) are taken into account. 5. u'prey as measured from the film. This curve should be compared with curve 4. The time in msec is given between brackets near each datum of dprey. The maximal error made in the calculation of curve 5 is about 0.15 m/sec. The errors made in the calculation of curves 1 and 2 are about 20%. The errors made in calculating curves 3 and 4 are difficult to give, as the exact deviation of the mouth cavity from acon e is unknown. thetranslatio neffec t ofprotrusio n contributesmos tt odi prey. Thecalculation s ofth epre yvelocit yi nth efeedin g act ofth eflounde r deviate less from the actual prey velocity than in the rainbow trout, suggesting that the cone model resembles the flounder's mouth closer than the trout's mouth. Forth elionfis h theactua l preyvelocit ywa sapproximate d best. In prey capture protrusion has two important advantages compared to for wardbod ymotio nan dsuction .First ,th erelativ etranslatio neffec t ofprotrusio n has a constant value of — 1, and is independent of dprey, whereas eSUciwn and eswimming are not. Second, it costs less energy to accelerate the jaws than to accelerate the whole body or the water and the prey, if a particular effect on u'preyi s to be achieved. The acceleration of the prey in the moving frame can therefore beincrease d and thetim erequire dfo r preycaptur edecreased . Protru sionals o increases thelengt h of themout h cavity and hence the velocity of the wateri nth emout hapertur e(bein gth eresul to fth eexpansio no fa longe rcone ,se e appendix). Figs 5 and 6sho w this,mor ecostly , effect to beles simportan t than thetranslatio n effect ofprotrusion . Theabov eeffect s werealread y qualitatively described byMulle r& Oss e(i npress )an dca nye tb egive n quantitatively. Summarizing, it can be concluded that Pterois has a highly efficient feeding mechanism, due to theinitia l protrusion followed by a short powerful suction. In theflounde r suction isrelativel y moreimportan t than protrusion and swim ming. In the trout protrusion is absent and swimming dominates, illustrated 92 (25) (A) —3 (20) (22.5L^-X 4 prey- velocity 3 (m/sec) —2 _ î 5 /- '^ \. (12.5) / - Jv (0) —1 / \ (10) (2.5) 2s s^' \ (5) 1, I I ^ I 10 20 30 ,(mm) — 3 J12.5) - (15) 5 (B) \ \ (10) 4 —S—- prey- _2 - velocity ~~Z~~ V (m/sec) " Ovj_(7.5) î - 2s \(5) 1 I i Nt (0) i 10 20 30 ,(mm) Fig. 6. Contributions of suction, swimming and protrusion to u'preyi n the lionfish (Plerois russelli, SL 138mm) . The actual position of the prey is used in the calculations. (A) and (B) represent two different feeding acts. Notation is equal to that of Fig. 5. The errors made in the calculations are almost equal to those given in Fig. 5. Note the much larger contribution of protrusion to u'prey compared to that in Platichthys. by the early moment of caudal valve opening. This feeding type can only be effective in relatively open water. 5.2. INITIAL PREY DISTANCE AND ULTIMATE PREY VELOCITY Now we will investigate our third and fourth question (page 82). Does the fishmaximiz eth einitia lpre ydistance ,o ri sth epre yvelocit ya t seizure optimized, or isther e a balance between possibly conflicting aims? Isther e an optimal com bination of mouth gape and caudal expansion to optimize prey capture? 5.2.1. Initialprey distance Fig. 7A shows graphs of the initial prey capture distance against Ui, based on a feeding attempt of a pike (Esox lucius), of which the movement curves h\ and hi are shown in Fig. 2. The mouth radius was measured from a film 93 32 tr2(msec) diprey 78 15 30 45 60 75 9010 512 013 515 0 90 10512 013 515 016 518 0 -»tv 2(msec ) -»tha n2(msec ) (C) 23.2 r j\ oi2 tr2(msec) D 2 43.25 (mm) 22.4 L £^\ A 6 35.00 Î jÊ>!È. 21.6 MTT^m x 1° 27.75 /fill \ O1 5 25.75 20.8 25 21.25 20.0 "/fffit \ • 19.2 18.4 17.6 16.8 TM 16.0 45 60 75 90 105 120 135 150 165 180 -» thaif2 (msec ) Fig. 7. A. The initial prey capture distance against t-a, using data of the pike (Esox lucius) shown in Fig. 2. The contours show values for equal 1x2 or tri. The contour without symbols represents the experimentally determined xi = 3.5, with tri = 40.0 msec. Note that each point on a contour represents a simulation of a single feeding event. For each simulation it isassume d that tpb = thimax. Note scale of initial prey distance. Usw = 0.61 m/sec. B. As (A), but tn is replaced by thaiß.Usw = 0.61m/sec .C . As(B) , but Usw = 0.0m/sec . The heavy curves crossing the contours in (A), (B) and (C) show positions of least pressure for a given initial prey distance. The asterisk in (A) and (B) denotes the actual position of the prey capture event of the pike. Further explanations are given inth e text. 94 and fitted asdescribe d in the calculations (formulas (9)an d (10)).Th e measured hinui and himax were used in the simulation, but the shape of the curve was varied to study its influence on the initial prey capture distance. The contours in Fig. 7A show the influence of different values of a2 and trZo n diprey Note that eachpoint on a contour represents a simulation of a single feeding event. The swimming speed of the fish was variable (from 0.30 m/sec to 0.78 m/sec), but its mean speed (0.61 m/sec) was used in this calculation. The prey was as sumed to enter the mouth at t = thimax, which deviated only 10 msec from the actual situation. Protrusion is absent in the pike, so that terms 2 and 4 of formula (8) are zero. Fig. 7A shows that the maximum in the prey distance shifts to a larger hi with a lower an.Althoug h the rise time shifts from a value of 43.25 msec (for ai = 2.0) to a value of 21.25 msec (for 1x2 = 25.0), this has littleinfluenc e on themaximu m in the initial prey distance. The value of tV2 indicates when the opercular region starts to expand, but givesn o information about the time of thepea k rate of this expansion. A higher 0.1 decreases tri (for the allowable range of ai ^ 2) and increases thaifi, so effec tively the expansion is delayed and shortened. Hence, hi is not a good measure for studying the delay time between h\ and hi. The moment thaifi. closely ap proximates the time at which the caudal expansion rate ismaxima l and isthere fore veryusefu l to compare the relative timing ofh\ and hi. In Fig. 7B the initial prey capture distance is plotted against thaifi. Now, the maxima of all contours fall at about the same thaifi. Thus to maximize the initialprey distance and hence the mean speed of theprey the fish should useone thaifi (with given Usw and hi), irrespective how it exactly expands caudally. The actual thaifi used by the fish was 110.5 msec, while the thaifi for which the initial prey distance is maximal is about 90 msec. However, this difference in thaifiaffect s theinitia l prey distance by only4 percent. The initial prey distance is influenced by USw. Fig. 7C shows similar plots as those of Fig. 7B,bu t now with Usw = 0 m/sec. A slight shift of the maximum in diprey towards a higher thaifi is found with an increasing hi. The thaifi at which diprey is maximal would have been 76 msec for the hi used actually by the pike, representing a larger deviation from the actual thaifi than found with Usw = 0.61. The difference in diprey would have been 18 percent. Thus dipreyi saffecte d more by thechoic e of thaifii f Uswi s decreased. The simulations of diprey show that the initial distance is largely influenced by Usw.Uprot may also have a considerable influence. At a high Usw diprey is hardly influenced by a change in the caudal expansion. At a very low Usw diprey is more affected, but still less than 20 percent in quite a big range of hi and thaifi- Thus maximizing the initial distance by an adjustment of the caudal expansion is rather uselessfor a fish. The experimental data support this view (seebelow) . 5.2.2. Theultimate prey velocity We will now investigate a quantity more susceptable to optimization, i.e. the velocity of the prey in themout h aperture, u'tpb. 95 15 30 45 60 75 90 105 120 135 150 ->tv 2(msec ) —6 3!2 t 2 (msec prey- r velocity —5 D 2 43.25 (m/sec) A 6 35.00 î X 10 27.75 O 15 25.75 • 25 21.25 45 60 75 90 105 120 135 150 165 180 —>• than2 (msec ) Fig. 8. Plot of u'prey and u'tpb against Ui (A) and thatfi (B), using data of the pike as done in Fig. 7. It is assumed that tpb = th\max. Contours connect points of equal n (and equal tr2). Each point on a contour represents a simulation of a single feeding event. The contour without symbols denotes the actual 012 = 3.5 (with ta = 40.0 msec). Heavy curves connect prey capture events of least pressure, for each u'tpb. u'prey is only slightly affected by the choice of ai. This is illustrated by the bunch of curves plotted over each other. The asterisk denotes the position of the actual prey capture event of the pike. Um = 0.61 m/sec. For small values of ui and thai/i positive values of u'tpbdooccur . Here the caudal region is already compressing at thimax. The point of intersection of all contours, describing u'tpb against Ui, in (A) shows the situation of thimax = thimax. No expansion occurs and hence u'tpb = 0m/sec . 96 Thechanc e ofpre ycaptur e willincreas e with therearwar d speed of thepre y while it enters the mouth. It would be unfavourable for the fish to maximize theinitia lpre ydistance ,i fthi sseriousl yaffect s u'tpb(th eultimat epre yvelocity) . A final escape could be easy for the prey if the speed given to it by thefish in the mouth aperture is close to zero. Fig. 8show s graphs of the mean speed of the prey from tvi till tPb,u'prey and of u'tpb against Uian d thaifi, again for arang eo f thalf 2 100 r (msec) • Amia calva Î * Gadus morhua * Stizostedion lucioperoa 80 o Platichthys flesus » * Pterois russelli o * 60 ./ 40 / ! 20 X 20 40 60 80 ' thlmax (msec) Fig. 9. The moment thaifi against thlmax for prey capture events of 5 different fish species. On the dashed line the moment of the maximal opercular abduction rate equals that of peak mouth gape, thaifi was determined as the moment at which hi = hinul+ 0.5 Ahunax- This closely resem bles themomen t ofpea k opercular expansion rate. Further explanations aregive n in the text. *The peak negative values of the velocities shown by the contours of Figs. 8,12 and 17ar e denoted as maxima in this paper. Similarly, the action of making u'prey more negative will be denoted as a maximization ofu'prey. 97 thaifitha t should be used if the speed in the mouth aperture is to be maximized (about 100msec) . The above analysis strongly suggests that aprey sucking fish shouldexpand caudally at themaximal rate at themoment of themaximal mouth aperture, if thismoment coincideswith themoment ofprey capture. We checked this hypothesis for a range of fish species (Fig. 9). Generally, the fishes behave according to the expectations. Pterois however, tends to oper ate at a slightly lower thaifi- It also tends to capture the prey slightly before thaiß (see Muller & Osse, in press, Fig. 17). These features will decrease the initial prey distance, but increase ü'prey and u'tp b(se e also page 106).A n opposite effect was observed for Platichthys. Amia and Gadus showed a quite variable behaviour. In Amia the deviation may be caused by the relatively early opening of thecauda l valves.Also , at a slow forward body speed the initial prey distance and u'tpb may be about equally affected by the phase relationship. We found that Amia quite often expands its mouth aperture to the maximal width and keepsthi spositio n for sometime ,whil eexpandin gcaudally .A nexampl ei sgive n in Fig. 10. 5.3. INFLUENCE OFMOUT H GAPEO N INITIATION DISTANCE AND PREY VELOCITY The initial prey distance and ultimate prey velocity are evidently dependent on the size of the mouth aperture, as already suggested in Fig. 3. h\ influences esuction and eSwimming and hence u'prey. The influence of mouth gape will now be further investigated. distance 60 (mm) Î .y 't .y 30 hi y / / V ./ J_ 1—• J 30 60 90 120 -»time (msec) Fig. 10. Movements of mouth aperture and opercula during a feeding event of Amia calva (SL 365mm) , hi ismeasure d ashal f the height of the mouth aperture and fois half the distance between the caudal bony edges of the opercula. A plateau phase is present in hi. Here hi is maximal at the end of the plateau phase, but it may also be maximal at the start of this phase. This largely influences the measured relative timing of thaifi and thimax. Generally thaifi is larger thanthimax in Amia, in contrast to the situation in Pterois. The dashed vertical line denotes the actual time of theopenin g ofth eopercula r valves. 98 (mm) î 45 60 75 90 105 120 135 150 165 180 45 60 75 90 105 120 135 150 165 180 ->tha n2 (msec ) thaif2 (msec) 45 60 75 90 105 120 135 150 165 180 -60-30 0 30 60 90 120 150 180 210 -> thaif2(msec) -»than 2(msec ) Fig. 11. Plots of diprey against thalfi,usin g the data of the pike shown in Fig. 2. thalfl andhimax arevarie d to study theirinfluenc e on diprey- Thepre yi sassume d to enter themout h at thimax. A. Usw = 0.0 m/sec. Contours show values of himax. The contour without symbols shows the actual h\max = 10.3 mm. Each point on a contour represents a single simulation of a feeding act. tri was given the actual value (32.6 msec) for each simulation. Therefore, a bigger h\max represents also a bigger mean expansion rate.di preyincrease s withhimax. B. As (A), but now Usw = 0.61m/sec, equal to the actual mean swimming speed. Now, dipreyin creases with himax for low values of thalfl and high values of thalfi. At intermediate values of thalfi, about 110 msec, diprey is hardly influenced by the choice of himax. The position of the actual feeding event isdenote d with an asterisk. C. As (A) and (B), but with Usw = 2.0 m/sec. Now dipreyincrease s with a decreasing himax, except for very lowvalue so fthalfl. 99 D. Usw = 0.61 m/sec. Contours show values of h\max. The expansion rate of hi is equal for all contours, so that tn is different for successive contours. This means that the time available for prey capture is proportional to himax.Th e moment thimax is chosen to be equal for all mouth opening curves. So, M decreases with a larger h\max. The start of the caudal expansion, tv2,wa s varied from Ui to thimax.Thu s the range of thaip. for which simulations were made decreases with a smaller h\max. The contour without symbols shows the actual h\max.Th e actual feeding event of the pike is again denoted with an asterisk. The trend of an increasing diprey withhimax was also found for other swimming velocities than 0.61 m/sec. (A) prey- -14 • h imax (mm) prey- velocity D 20.6 velocity -12 (m/sec) /""\ O 14.4 (m/sec) Î -10 / ^ A 8.2 Î -10 X 4.1 - 8 ; / \ - 6 \ " U'prey 1 X^ "CS 4. 45 60 75 90 105 120 135 150 165 180 45 60 75 90 105 120 135 150 165 -• than2 (msec ) -» thaif 2(msec) (D) prey- _-|4 Prey- -13.5 r h max (mm) velocity velocity D 20.6 (m/sec) (m/seç)-120 O 14.4 * î î -10.5 A 8.2 \ X 4.1 1 - 9.0 - 7.5 - 6.0 - 4.5 - 3.0 - - 1.5 Uprey 1/ 1(K 1 1 f/^~Z\\ 0.0 45 60 75 90 105 120 135 150 165 180 -60-30 0 30 60 90 120 150 180 -> than2 (msec ) -> thalf 2(msec ) Fig. 12. Plots of u'ipb and U'prey against thal/2, using the data of the pike as done in Fig. 11. Fig. 12Acorrespond s to Fig. IIA, Fig. 12Bt o Fig. IIB, etc. Contours in (A)-(C) show values ofhimax, with tri kept equal to the actual tn for each simulation. Contours in (D) show again values of himax,bu t now with the mean expansion rate kept constant. Contours without symbols denote 100 5.3.1.Initial prey distance Figs. 11A-C shows plots of diprey against thai/i for three different swimming velocities and different h\max. himax and M are kept constant at each contour. Fig. 11D shows similar contours for Usw = 0.6l m/sec, but now h\max and Ah\max\{th\max—U\), i.e. the expansion rate of the mouth aperture, are kept constant. A larger h\max increases the intial prey distance at a low swimming speed iftr\ is kept constant, whereas the reverse is truefor high swimming speeds (above 0.7 mlSec). This effect is also illustrated in Fig. 13, see below, diprey was found to increase in all cases if the expansion rate of h\ is kept constant. This isno t a surprise as the time available for prey capture increases too. Note that the difference in initial distance is again quite small if tn is constant (19 percent for a doubling of the actual hlmax if Usw = 0, for a higher Usw this is even less).A comparison with the results of Figs. 7 and 8 suggests again that the ultimatepre y velocity isa more important quantity to be optimized. 5.3.2. Ultimateprey velocity The effect of a change in h\max, with tr\kep t constant, on u'tpbi s shown in Fig. 12. The increase in u'tpb is considerable if h\max is kept smaller and the correct thaifi is chosen (so that u'tpbi s maximal). The range of h\max that can be used depends on the swimming speed, the generated pressure and the size of the prey. Theswimming speedlimits themaximal h\max, whereas thepres sureand the size of theprey set alimit to theminimum h\max. Theabove results suggest that itmight beadvantageous for a fish, if it isfeeding in the open water, to open its mouthfaster and wider when it swims slower (and vice versa). Fig. 13 shows a plot of u'prey against USw, using the movement curves of the pike shown in Fig. 2 and thaifi = thimax = 100 msec. It is assumed that Uswi s constant during each simulated feeding attempt. Simulations were made for three different mouth apertures, as shown by the contours in Fig. 13. If Uswi s zero the initial prey distance is only influenced by suction. The obtained distance in this case for the actual mouth aperture is about 32 percent of the fish's head length, slightly more than the approximate 25 percent estimated by Alexander (1967). As expected, u'prey almost equals — Uswfor hig h values of Usw- At a large distance the prey will be approached with the swimming velocity (if protrusion is absent). Thus u'prey= —U swi n this case. Close to the mouth swimming induces stagnation, which may lead to forward pushing of the prey inth eearth-boun d frame ifstagnatio n isno tcompensate d bysuction .A n overall the actual hi. Asterisks in (B) and (D) denote the positions of the actual feeding attempt of the pike. The bunch of curves plotted over each other in (A) to (D) show u'prey. The curves with clear maxima represent u'tpb- Little is gained by maximizing u'prey (or diprey) compared to a maximiza tion of u'tpb- u'prey increases with Usw (compare (A), (B) and (C)). The fish should chose its h\maX such, that u'tpb Fig. 13. Mean velocity of the prey against Usw.thaifi was chosen to equal fMma*= 100 msec, and tpb = th\max.Usw is assumed to be constant during each (simulated) feeding act. Contours show values of h\max and tri kept constant. Other parameters equal those given for the pike in Fig. 2. Again, each point on a contour represents a single simulated feeding act. The actual h\max is 10.3 mm (contour without symbols) and the actual mean swimming velocity is 0.61 m/sec. The actual position of the feeding act of the pike is denoted by an asterisk. Black dots denote contour with h\max is twice the actual h\max. Circles denote contour at which h\max is 0.4 times the actual himax- Along the dashed line u'prey = —U sw, so that the mean speed of the prey in the earth-bound frame is zero. The shaded area denotes the range of an overall pushing effect in the earth-bound frame. Further explanations aregive ni n the text. stagnation effect occurs when u'prey is greater than — Usw.I n Fig. 13 this feature is present in the area enclosed by the abscissa and the dashed line (shaded area). For high swimming velocities the contour at which h\maxi s twice the actual h\maxlie s in this area. To avoid stagnation effects the caudal valves can be opened. Valve opening is particularly important for feeding with a high swimming velocity (as in the rainbow trout, see page 91), as otherwise the prey sizewoul d belimite d by the necessarily smaller mouth aperture. For the pike we found indeed a feeding behaviour in this direction (see Fig. 14). The valves tended to be opened at a smaller mouth gape when swimming faster. But also the maximal mouth aperture tended to be reduced. The experi mental results obtained by Rand and Lauder (1981) for Esox niger are also in accordance with this theory. 102 (A) (B) 1.5 50 hi at Ta hiTatTa (mm) *a Î (m/sec) 40 Î 1.0 30 20 0.5 - 10 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 -•Usw at ia (m/sec) -• Uswa t Ta(m/sec ) Fig. 14.A .mout h radiushi a t xa, theactua lmomen t ofth eopenin go fth eopercula r and branchioste- gal valves,agains t Uswat xa. h\ ismeasure d as half the height of themout h aperture. B. Mean expansion rate till Taagains t Uswa t za. The black dots in these graphs represent data of a pike of SL 485 mm, the circles are data of a pike of SL 195 mm. Each datum represents a separate feeding act. (A) indicates the tendency of a reduction of M at xa with a higher Usw. (B) indicates a tendency of a reduction of the mean expansion rate of themout h opening before Tawitha higher Usw. 5.4. THE INFLUENCE OFTH E PRESSURE ON THEMOUT H EXPANSION The pressure inside the mouth cavity varies asa function of time and position inside the mouth. The pressure is influenced by the mouth expansion, but also by swimming movements (see e.g. Muller et al., 1982). Now, one may wonder how a fish should expand itsmouth , so that with the delivered effort (not neces sarilymaximal ) thechanc e ofpre ycaptur e is maximized. The pressure inside the mouth can be calculated for each combination of ros tral and caudal expansion usingth emode l ofMulle r et al.(1982 ,se ethei r formu la 43). For each initial prey distance in Fig. 7 the combination of ai and thaifi wasdetermine d for whichth econtributio n ofth ecauda l expansion to themagni tude of the negative pressure was lowest. The obtained curve intersects the con tours in Fig. 7. The magnitude of the pressure shows a strong, non-linear, in crease with the initial prey distance and thus the mean velocity of the prey (see Fig. 15).A similar calculation was carried out for the relation between the mini mal possible pressure and the prey velocity in the mouth aperture (see Fig. 8B and Fig. 15). Here a similar relation was found, but the pressure increase was a lot slower. Again, the fish gains more if it tries to optimize the ultimate velocity than it wouldgain in optimizing the initialprey distance. Fig. 8B shows that the optimal phase relationship, i.e. the situation with the highest ultimate velocity with a given pressure, overlaps themaxim a of each contour. 103 10 g pressure (kPa) 8 î t. _1_ J_ ^ 200 —0.205 —0.210 —4 —5 û'prey (m/sec) > u'tpb(m/sec ) Fig. 15. Graph of the extra pressure halfway inside the mouth due to the caudal expansion against u'tpb and u'prey- Calculations were done using the model of Muller et al. (1982). The movement data of the pike, shown in Fig. 2 were used as input data for the simulation, with the exception that (X2 was varied (and thus Ui) to obtain the variation in u'tpb- thalfi was chosen such that each simulation was positioned on the heavy curves shown in Fig. 8, denoting the feeding acts with the minimal possible magnitude of the pressure. (B) tpb (msec) diprey 25.5 r pb(msec) D 73.2 (mm) D 73.2 | 24.0 O 86.6 O 86.6 A 113.4 22.5 A 113.4 x 126.8 126.8 21.0 19.5 • «// yS\ \\\ 18.0 16.5 / \ \ \\\ 15.0 • ^ \ V^, > 13.5 12.0 X« 45 60 75 90 105 120 135 150 165 180 45 60 75 90 105 120 135 150 165 -> than2 (msec ) -»thai f2 (msec ) Fig. 16. Graphs of diprey against thalfi,obtaine d by simulations, using the movements data of the pike shown in Fig. 2.Th e contours show values of tpb. The contours without symbols represent tpb = thimax. Note that each point on a contour represents a simulation of a single feeding event. Heavy curvesconnec t maxima of contours. A. Usw = 0.61 m/sec, the actual mean swimming velocity. The maximal possible diprey increases with a larger tpb(a t least inth e simulated range). B. Usw = 0.0 m/sec. Now diprey is maximized if tpb is chosen slightly larger than th\max,wit h the proper thalfi. Both (A) and (B) show that a change in tpb has only little influence on diprey if thalfi is chosen properly. 104 The optimal thatfia s shown by the heavy curve in Fig. 8B is little influenced ifth emout h opening curve changes, asi sapparen t from Fig. 12. 5.5.Pre y uptake before and after peak mouth gape The above considerations were made with the assumption that tPb = thimax. Now, we will consider the effects on diprey and u'tpbo f other moments of prey passage through the mouth. 5.5.1.Initial prey distance The contours in Fig. 16A show again graphs of diprey against thaifi. Now, each contour shows the situation for a particular tpb.Usw = 0.61 msec, the actu al mean swimming speed. The hi and hi shown in Fig. 2 were again used as input functions, with the exception that thai/i (and thus tvi) were varied. The maximum diprey that can be achieved increases with a higher tpb-Thi s may not be a suprise as tpb shows the time available for prey capture. This is however notgenerally truefor a verylow swimming speed (see Fig. 16B). (B) tpb(msec ) prey- - 14 tpb(msec ) velocity D 73.2 - 12 • (m/sec) O 86.6 Î - 10 A 113.4 X 126.8 - 8 - 6 - 4 - 2 V prey 0 2 '/ 4 ' --~». 45 60 75 90 105 120 135 150 165 180 45 60 75 90 105 120 135 150 165 180 ->thaif2(msec) -» thaif2 (msec ) Fig. 17. Graphs of u'tpb and ~ü'prey against thaifi. Input data for simulations equal those used for Fig. 16. The contours show again values of tpb. The contours without symbols represent tpb = th\max. Each point on a contour represents a simulation ofa particular feeding event. A. Usw =0.6 1 m/sec, the actual mean swimming velocity. This plot corresponds to Fig. 16A. The bunch of curves plotted over each other represent data oîû'prey,othe r curves, of which the maxima are connected via the heavy curve, represent u'tpb- B. Usw = 0.0 m/sec. Contours are similarly ar ranged asi n (A). (A) and (B) show that if tpb is changed the fish should shift thaifi into-the same direction, because than u'tptca n be kept maximal. If thaifi < thimax both h\ and hi are expanding and a high u'lpb can be acnieved if tpb is chosen likewise smaller than thimax.A tpb greater than thimax seems to beunfortunate , as than hii scontracting , sotha t a large gain in u'tpbi simpossible . 105 5.5.2. Ultimateprey velocity Generally, the maximum u'prey that can be achieved increases with a lower tPb(a t least in the simulated range, Fig. 17A,B). The magnitude ofu'tpbincreases witha lower t Pb, iftpb < thimax. The tpbtha t can be used by the fish depends on the size of the prey and diprey. If theprey can be approached closely, e.g. whilefeeding near substrates, it may be advantageous to use a tpb less than thxmax- If this is done the fish should preferably decrease its thatfi too, to optimize u'tpb. This simultaneous shift of tpb and thai/2 towards a value below thimax was observed for Pterois russelli (seeals opage s 98 and 108). 6. Generaldiscussio n Several authors have discussed the prey capture mechanisms in bony fish. The first quantitative treatment was given by Alexander (1967), who estimated the distance from which a prey can be sucked into the mouth. As mentioned by Alexander, the estimates were quite rough, as no account was taken of for wardmotion ,protrusio n and thevariatio n ofth emout h radius,apar t from other simplifications. Nyberg (1971) made estimates of the effect of protrusion on diprey, but took only account of the translation effect of protrusion. Weihs (1980, using steady flow assumptions) calculated particle trajectories in a flow field consisting of a sink and a uniform flow. In this approach the velocity is infinite at the mouth aperture ('the sink') and a reverse calculation of diprey as carried out in the present paper is impossible. Webb (1976) discussed the predator-prey interaction, usingth emode l of Howland (1973).H e took account of the accelerations and possible turning radii ofpredato r and prey. He omitted, however, the final suction act, a possible effect of protrusion and stagnation effects due to forward motion. Muller et al. (1982) presented the most useful quantitative model of suction feeding in fish to date. Attention has already been paid to this model in the methods. The present paper is an extension of this model. The present paper provides calculations of the initial prey distance and the velocity of the prey as a function of time and position. It takes account of the unsteady nature of the flow and the variation of the mouth radius. The effects of movements of the expanding mouth, forward motion of the fish and protru sion on u'preyar e quantitatively assessed. The present approach is limited to an analysis along the Z'-axis, away from the substrate, and a mouth cavity with closed opercular and branchiostegal valvesbefor e tpb. Also,escap e movements of the prey were omitted in the analy sis. A treatment of the complete field of flow shows that the analysis along the A"-axis is a valid procedure (see Muller & Van Leeuwen, in prep.). An exact calculation of u'preyafte r valve opening could not be achieved for reasons men tioned in Muller &Oss e (inpress) . Escape movements of elusive preys are hard to predict for us. This may also 106 bedifficul t for a prey capturing fish. An elusive prey may elicit a more powerful prey capture act than a sluggish prey (see Elshoud-Oldenhave, 1979). A more powerful feeding act increases ~ü'prey and u'tpban d hence decreases the time of prey capture. This will decrease the effect of a possible escape response. It seems difficult for the fish to correct beforehand for the direction of an escape response. Most suction acts are so fast that an in between adjustment of the predator asa response topre y behaviour seemst o beimpossibl e (Osse& Muller , 1980). An escape along the A"-axis can be easily incorporated in the present approach. The present paper discusses three different options to increase the relative velocity of the prey towards the fish's mouth: suction by mouth expansion, pro trusion of thejaw s and swimming. The contributions of these options to u'prey vary among different species of fish and among different feeding events of one species. In the open water full advantage can be taken of swimming. Suction remains important to compensate for stagnation effects due to swimming. Stag nation effects can also be avoided by opening of the caudal valves (seee.g . Van Leeuwen, in prep.). Swimming will be necessarily unimportant in feeding from substrates. Here protrusion isa n important means to obtain the prey. The acquisition of a large diprey will be rather unimportant under these circumstances, as the prey can be more closely approached. It is probably more important to generate a high velocity of the prey,especiall y ifth epre y has a higher density than water. There fore, a small mouth aperture at / = tpb is probably advantageous, as this in creases u'tpb. This may be obtained by a reduction of h\max, as in Esox (see Rand & Lauder, 1981) or by a reduction of tpb, so that the prey is captured before thimax, asi n Pterois (seepage s 98 and 106). This paper is mainly concerned with the problem of how a fish should move (i.e. translation of the body, expansion of the head and protrusion of the jaws) if it seeks to maximize the chance of prey capture. An adequate morphological basis isrequire d for an (close to) optimal performance. Consider e.g. the follow ingexample .Th emai n power for the expansion of themout h cavity is generated by the trunk and sternohyoid muscles. A substantial fraction of this power is mediated via the hyoids to lower the mandible and to abduct the suspensoria and gill covers. The position of the hyoids during mouth expansion changes so that first the depression of the mandible is effected most and thereafter the abduction of Suspensorium and hyoid (see Osse, 1969). Barel (in prep.) found that the power of the trunk is most effectively transmitted for the abduction of the Suspensorium and gill cover if the angle of the hyoids with the medial plane(/? )i sabou t 45degrees .W esugges t that shorter hyoidsma y allowa n earlier achievement of this situation, so that thaifica n be shortened. First, shorter hyoidsca n bepositione d at alarge r ß at thestar t ofmout h expansion and second ß can be increased relatively faster. The consequence would be that the feeding act is shortened and the possible volume increase of the mouth reduced. On page 92 it was argued that protrusion allows less water to be sucked and the feeding act to be shortened. So, the presence of relatively short hyoids, with 107 a well developed protrusion apparatus and the use of a relatively small thai/2 seems to be aprofitabl e combination, especially suitable when the prey can be approached closely.A tpresen tw ehav eno tenoug hdat a for arigorou s verifica tiono fthi shypothesis ,althoug h thedat a ofPterois giv ealread ysom esupport . The consequence of a small thai/2ma yb etha t thecauda l valveshav e to open relativelyearly ,a sth eexpansio n rateo fth emout hapertur edrop searlie r under thecritica l rate(Va n Leeuwen,i nprep.) .Thi sma yexplai n whyprotrusio n and anearl ymomen to fvalv eopenin gar eofte n found tocombin e(i.e . low-r-suction withprotrusion , seeMulle r& Osse ,i npress) . This example shows that different structures within the fish's prey capture apparatusar efunctionall y interrelatedwit heac hother .A chang ei non eelemen t requiresals ochange si nothe relements .Othe rexamples ,als obase do na quanti tative approach can be found in Muller & Osse (in press) and Van Leeuwen (inprep.) . 7.Summar y The separate contributions of forward body motion, mouth expansion and jaw protrusion to preycaptur e infish wer ederive d quantitatively (see formula (8)).Thes econtribution swer eshow nfo r feedingevent sofSalmo gairdneri, Pla- tichthysflesus an d Pterois russelli. Protrusion appeared to be a very effective meanst oobtai n ahig hspee do fth epre yrelativ et oth e fish. Model simulations showed maximization of the initial prey distance by an exactadjustmen t ofmout hexpansio n tob erathe ruseles sfo r afish. Muc hmor e isgaine d by an optimization of the prey velocity whilei t enters the mouth (at tpb). To achieve this, thefish shoul d abduct its operculars at the maximal rate at tpb. A high swimming speed increases the danger of pushing the prey forward ina nearth-boun d frame. Alarge rmout h aperture increasesthi seffect . Stagna tion effects can, however, be avoided by decreasing the maximal mouth gape when swimming faster and by opening of the opercular and branchiostegal valves.Thi s last possibility permits preys of a considerable sizet o be captured ata hig hswimmin gspeed . Thepik e(Esox) seem st ous ebot hoptions . For big preys, it seems favourable for the fish to let the prey pass through the mouth aperture when it is opened widest. A smaller mouth gape allows a higher velocity of the prey to be generated at the moment of prey seizure. If thepre yca nb eapproache d closely,i tca n beadvantageou s to capture thepre y before peakmout h gape,becaus ethe nth espee do fth epre yca nb eincreased . Wethan k Prof.Dr . J.W.M. Ossefo r hiscritisis m on themanuscrip t and many discussions about suction feeding. Miss Ineke Oomen carried out the analysis presentedi nFig .9 .Ja nKremer scarrie dou tth eanalysi so fFig .14 .Ari eTerlou w gavetechnica l assistance.Wi mVale nprepare d somefigures. Th e contributions madeb yal lthes epeopl ear egratefull y acknowledged.Th eFoundatio n for Fun- 108 damental Biological Research (BION, 14.90.18),subsidize d byth e Netherlands Organization for the Advancement of Pure Research (ZWO), is thanked for agran t toJ.L .va nLeeuwen . 8.Reference s Alexander, R.McN. (1967).Th e function and mechanisms of the protrusible upperjaw s of some acanthopterygian fish.J. Zool., Lond. 151:43-64. Barel.C.D.N ,(i nprep.) .Titl estil lunknown . Elshoud-Oldenhave,M.J.W .(1979) . Preycaptur ei nth epike-perch ,Stizostedion lucioperca (Teleos - tei,Percidae) : Astructura lan dfunctiona l analysis.Zoomorphologie 93 : 1-32. Howland,H.C .(1973) . Optimalstrategie sfo r predatoravoidance .Th erelativ eimportanc eo fspee d andmanoeuvrability .J. theor. Biol. 47: 333-350. Kremers,J.J.M .& Leeuwen ,J.L .va n(i nprep.) .Th einfluenc eo fgrowt ho nth epre ycaptur emecha nismo fth epik e(Esox lucius). Lauder,G.V .(1980) .Th esuctio nfeedin gmechanis mi nsunfishe s(Lepomis): anexperimenta lanaly sis.J. exp. Biol. 88,49-72. Leeuwen, J.L. van (in prep.).A quantitativ e study of flow in prey capture by rainbow trout, with generalconsideratio no fth eactinopterygia n system. Leeuwen, J.L. van &Muller , M. (in prep.).Th e recording and interpretation ofpressure s inpre y suckingfish . Muller,M & Leeuwen ,J.L .va n(i nprep.) .Titl estil lunknown . Muller, M.& Osse,J.W.M ,(i npress) .Hydrodynamic s ofsuctio n feeding infish . Trans. Zool. Soc. Lond. Muller, M., Osse, J.W.M. &Verhagen , J.H.G. (1982).A quantitative hydrodynamical model of suctionfeedin gi nfish ./ . theor. Biol. 95:49-79. Nyberg,D.W .(1971) .Pre ycaptur ei nth elargemout h bass.Am. Midi. Nat. 86:128-144. Osse, J.W.M. (1969). Functional morphology of the head of the perch {Percafluviatilis L.) : an electromyographic study.Neth. J.Zool. 19(3): 289-392. Osse,J.W.M .& Muller ,M .(1980) .Amode lo fsuctio nfeedin gi nteleostea nfishes wit hsom eimplica tions for ventilation. In: Environmentalphysiology offishes (ed . M.A. Ali) NATO-ASI. Series A.Lif eSciences ,p p335-352 . PlenumPublishin gCorporation ,Ne wYork . Rand, D.M. &Lauder , G.V. (1981).Pre y capture in the chain pickerel, Esoxniger: correlations betweenfeedin gan dlocomoto rbehavior .Can. J. Zool. 59(6) : 1072-1078. Webb,P.W .(1976) .Th eeffec t ofsiz eo nth efast-star t performanceo frainbo wtrou tSalmo gairdneri, anda consideratio no fpiscivorou spredator-pre yinteractions .J. exp. Biol. 65:157-177 . Weihs,D .(1980) . Hydrodynamicso fsuctio nfeedin goffis h inmotion .J. Fish Biol. 16:425-433. 9.Appendix :mathematica lequation s Thevelocit y in themout h aperture due to suction at x' = Ifo r a, posteriorly closed,expandin gcon ei s(fro m formula 18 ofMulle re tal. ,1982) : u'mk + u'mprot= -j^2 |(2Ai + h2)hi + (2h2 + h\)h2\ (11) where/ = l0+ lprot- Notetha tl prot isa functio n oftime . Theinitia lpre ydistanc ed iprey isobtaine db ysolving : 109 o "•iprey = I ?+ 3 dr (12) t}b Jid'prey +hSY (J J (cPprey+ A,*) " with dprey — O at r^. 110 HOOFDSTUK 3/CHAPTER3 Therecordin g andinterpretatio no fpressure s inprey-suckin g fish 111 Therecordin gan dinterpretatio no fpressure s inprey-suckin gfis h J. L. VAN LEEUWEN AND M. MULLER* (Department of Experimental Animal Morphology and Cell Biology, Agricultural University, Marijkeweg 40, 6709 PG Wageningen, The Netherlands) Keywords:Fish , Pressure,Suctio n feeding. Summary Possible pitfalls of techniques used to record pressures in prey-sucking fish have been analysed by applying control systems and hydrodynamic theory. Fourier analysis re vealed a bandwidth of 1 kHz to be generally sufficient for an accurate recording of the overall pressure waveform. The exact bandwidth needed depends on the species, speci men sizean d intensity of thefeedin g act.A bandwidth greater than 1 kHz mayb e needed when secondary fluctuations (e.g., due to vortices) are also to be recorded accurately. Large errors (i.e.o f the same order of magnitude as the real pressure) due to the dimen sions of the transducer itself cannot be excluded on theoretical grounds. Most reliable pressure records were made with catheter tip pressure transducers, possessing small di mensions and a broad bandwidth (about 3kHz) . Pressure records were made for Amia calva, Salmo gairdneri, Esox lucius, Gadusmor- hua and Perca fluviatilis. The largest negative pressure peak was measured in Gadus (-42 kPa). Accurate simulations of the pressure records were made using the hydrody- namic model of suction feeding of Muller, Osse and Verhagen (1982), to which new boundary conditions were added. This model takes into account the unsteady nature of the flow. The good correlation between measured and simulated pressures strongly suggests that: 1.th emode l isa verygoo d description of theproces s of suction feeding. 2. the errors in the pressure records obtained with catheter tip pressure transducers are small. The pressure inside the mouth of a prey-sucking fish has velocity and acceleration components due to head expansion and forward motion of the fish. Forward motion strongly influences the pressure profile in feeding events of the two fast-swimming fish studied, Salmo gairdnerian d Esox lucius. The literature on pressure measurements in prey-sucking fish is reviewed. * Authors listed alphabetically. No priority of author isimplied . 113 Contents Summary 113 1. Introduction 115 2. Materials and methods 115 2.1 The acquisition and interpretation of pressure records: some prin ciples 115 2.1.1. Dampingcoefficien t and resonance frequency 116 2.1.2. Distortions in pressure records due to inadequate band widthan dphas erelationshi p 117 2.1.3. Effects of the dimensions of the transducer on pressure re cords 120 2.1.4. Effects ofa boundar y layeraroun d apressur etransduce r . . 122 2.1.5. Effects of hydrostatic components on the recording of pres sures 122 2.1.6. Effects of accelerations of the transducer system on pressure records 122 2.1.7. Temperature effects onth etransduce r output signal .... 123 2.1.8. Interpretation of pressure records;earth-boun d and moving frame 123 2.2. Experimental procedure 124 2.2.1. Experimental setu p 124 2.2.2. Testingo fth etransducer s 125 2.2.3. Pressuremeasurement s inprey-suckin g fish 126 3. Results 128 3.1. Transducer characteristics 128 3.2. Pressurean dmovemen t records 136 3.3. Interpretation ofpressur erecord s 144 3.3.1. Themode lo fMuller ,Oss ean dVerhage n(1982 ) 144 3.3.2. Thechoic eo fth emomen t ofvalv eopenin g 144 3.3.3. Formulationo fa ne wboundar yconditio n 146 3.3.4. Simulation ofpressur ecurve s 148 3.3.5. Thecomponent s ofth epressur e 152 4. Discussion 153 4.1. Pressure transducers 153 4.2. Arevie wo fpressur emeasurement s 153 4.3. Interpretation ofpressur erecord s 156 5. Conclusions 158 6. References 158 7. Appendix 159 7.1. Nomenclature 159 7.2. Formulae 160 114 1.Introductio n At least half of the more than 20.000 species of teleost fish capture their prey bysuctio n feeding: arapi d expansion and compression ofth ebucca l and opercu lar cavities causing water, containing the prey, to flow into the mouth. During this very unsteady process (with a duration time in the order of 50 msec) water velocities of about 10m/ s (Muller and Osse, in press) can occur, while the pres sure inside the mouth cavity may vary from -65 to +10 kPa relative to the ambient pressure (Alexander, 1969 and 1970; Casinos, 1973an d 1974; Lauder, 1980a and b; Lauder and Lanyon, 1980; Muller et al., 1982; Osse and Muller, 1980an d Osse, 1976). Knowledge of the pressures generated can give insight into the mechanical loading to which the head of the fish is subjected. Therefore predictions and measurements of thepressure s inside the buccal and opercular cavities (together denoted asth emout h cavity)durin g the suction event areimportan t inth e study of the functional design and evolution of the fish head. The continuously work ingrespirator y pumps (Hughesan d Ballintijn, 1963)als ocreat epressur e fluctua tions in the mouth cavity. These fluctuations, however, are generally less than 1kPa , so the load on the fish's head caused by these pressures isnegligibl e com pared to the load generated during feeding. The present paper deals with problems met in measuring and interpreting pressures inside the fish's mouth cavity during feeding. In addition it evaluates previous work, discusses a new technique with catheter tip pressure transducers and presents newdat a for perch (Percafluviatilis), cod (Gadusmorhua), rainbow trout (Salmo gairdneri),pik e (Esox lucius)an d bowfin (Amia calva). Thehydrodynamica l model offish feeding, asdesigne d byMulle r etal .(1982) , provides an important tool for predicting the pressure from the fish's mouth cavity expansion and forward motion. 2. Materialsan dmethod s 2.1. THE ACQUISITION AND INTERPRETATION OF PRESSURE RECORDS: SOME PRINCIPLES Several reviews about physiological pressure measurement can be found in the literature. These papers are mostly concerned with recordings in the cardio vascular system (e.g. Gabe, 1972). The pressure fluctuations in this system are of a low frequency (<5 Hz) and amplitude (< 15 kPa). In the fish's sucking system, however, we are concerned with a completely different region of fre quency, ƒ, and amplitude, p (\0 Hz/?>-70 kPa). So recording techniques suitable for the cardiovascular system are not, a priori, applicable to the sucking system. We willno w discuss theprerequisites , from both a control systems and a hyd rodynamical viewpoint, necessary for obtaining accurate records of the pres- 115 surestha toccu ri nth emout h ofa prey-suckin g fish. 2.1.1.Damping coefficient and resonance frequency Theprinciple s from control systemstheor y willb eexplaine d usingth esingl e degreeo ffreedo m systema sa nexampl e(man ytransduce r systemsca nb echar acterized adequately by such a system). For that system the following second orderdifferentia l equationhold s(se efo r symbolsth eAppendix) : 2 d y0 „„ dy0 , , , ,,, dr dt (DiStefanoetal., 1967) where t is time,xt i s the input signal, y0 is the output signal, Ç is the damping ratio and o)„ is the undamped natural angular frequency of the system. The relation between thefrequency,/ , (expressed inHz )an d theangula r frequency, co, (expressed in rad/s) is: co— Inf. Th e time constant of the system is given by: *-{= <2) Three important frequencies are associated with a system for which 0< Ç < 1 (anunderdampe d system):th eundampe d natural frequency, thedampe d natu ral frequency and the resonance frequency (seee.g . Jones, 1961).Th e damped natural frequency occurs asa reactio n to aste po r impulseshape d input signal, andi sgive nby : (Od = (onsJ\-Q (3) For C> 1 codha s no real value; the system is overdamped. An example of the step response of an underdamped system is given in Fig. 1A. The resonance frequency (that frequency atwhic ha force d oscillation hasmaxima l amplitude) isgive nby : 2 (Or = (onyJ1-2Ç (4) For systems with £> 1/^/2a real value for cordoes not exist and resonance is impossible.A si sclea rfro m (3)an d(4) :(o r 2.1.2.Distortions in pressure records due toinadequate bandwidth anaphase rela tionship The Bode magnitude plot of a particular system shows its bandwith, often defined as that range of frequencies over which the magnitude ratio does not differ by more than -3 dB from its value at a specified frequency. The plot is ameasur efo rth espee do frespons eo fa syste m(DiStefan o etal. , 1967). General lyth efollowin g rulei saccepte di nth eliteratur et odesignat ea signa la sa naccur atereproductio n ofa nevent : "Therecordin gequipmen tshoul db eabl et orepro duce frequencies up to the 10thharmoni c of the fundamental frequency of the event, otherwise the records will be seriously distorted" (see e.g. Gabe, 1972). Therefore, knowledgeo fth eexpecte d frequency content ofth eeven t isa prere quisite for the choice of appropriate equipment. The fundamental frequency ofth efeedin geven tgenerall ylie si nth eorde ro f 10t o 100Hz ,a swil lb eillustrat ed in theresult s (determined by Fourier analysis, seee.g . Fig. 6).Thu s a band width of 1 kHzwil lb esuffien t inmos tcase st orecor d theoveral lpressur e faith fully. The complex formula of the pressure in a fish's mouth obtained by Muller et al. (1982)show s that the pressure depends upon the intensity of the suction act, the position in the mouth cavity, the acceleration of the fish's body and upon the species and sizeo f the predator. These effects, computer simulations and experimental results(e.g .Fig . 16)sho wtha t highfrequencies , upt oa tleas t 100time sth efundamenta l one,occu ri n the records.Thes ema ycontribut eim portantly toth eloa dexerte d onth esystem .A bandwidt h ofgreate r than 1 kHz willgenerall yb erequire d for accuratemeasuremen t ofmino rfluctuation s (freq. > 100Hz) . Distortions in thepressur e recordsmigh t bedu e alsot o aninadequat e phase relationship of the recording system. Ideally thephas e angle should bezer oi n the required bandwidth, as no distortions or time shift will occur in thiscase . To avoid distortions the natural frequency of the transducer should be ashig h aspossibl e (about 50time sth efundamenta l frequency to beanalysed) ,an d the damping ratio l/N/2 or very lowi n higher order systems.Conside r e.g. the fol 4 lowing transducer. Let con be 4*10 .7i rad/s and Ç be 0.1. The time shift, At, at a frequency co, equals -> Normalizedtime , -» Normalized frequency, co/a>n Fig. 1.A . Unit step response of a single degree of freedom system (equation 1),fo r different values of the damping ratio C (denoted near each curve). y0 is the output signal and cont the normalized time. B. Bode magnitude plot of a single degree of freedom system. Note that dB = 20 l0log \P\, where \P\is the magnitude of the transfer function of the system. The normalized frequency, (ojœ„, is set at logarithmic scales.Contour s show values off . 118 -120° 0 -90° î -60° -30° 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -* Normalizedfrequency ,co/to n 0.5 1 2 10 Normalizedfrequency ,a>/io n C.Plo to fphas eangl eagains tnormalize dfrequency , bothse ta tlinea rscales . Contourssho wvalue s ofJ .Not etha t analmos tlinea rrelatio nbetwee n 2.1.3.Effects of the dimensions of the transducer on pressure records Other distortions in the pressure recordsca n because d by an inappropriate form ofth epressur etranducer .Ideally ,th evelocit yo fth eflo wnea rth esensitiv e part of the transducer isno t affected by the presence of the transducer. In this casen odistortion swil loccu ri nth erecord sdu et oth epresenc eo fth etransducer . Asa nexampl ew ewil ldiscus sth e flow past our Millar transducers (see2.2.1.) . The sensitive part of the transducer is mounted in a ditch at the side of the tipo fa draco ncathete r (Fig.2A) . Theflo w pastth etransduce r canb emodelle d asth eflo wpas t aspher ean d ablun tnose d body (Fig.2B) .Th estrea m function ofthi sconformatio n ina unifor m stream,U, i sgive ni nth eAppendix .Evidently , Fig.2 .A .Cathete rti ppressur etransducer ,diamete ro fcathete ri s1.6 7mm . B.Th eflow pas tth etransduce ri smodelle da sa flow pas ta spher ean da blun tnose dbody .Furthe r explanationsar egive ni nth etext . 120 this stream function does not hold when Umake s an angle with the .Y-axis, i.e., when the flow is not parallel to the dracon catheter. In the fish's mouth thevelocit yaroun d thetransduce r alongit slon gaxi si sgive nby : up = Ufc(x,&) (5) where u/i s the velocity of the water in the fish's mouth without a transducer andc(x,m) afunctio n ofth epositio n and thedimension s ofth etransduce r(se e Appendix). To calculate the change in pressure due to the introduction of a pressuretransduce r onecoul dprocee d asfollows . Mullere tal .(1982 )modelle d the suckingfish a s anexpandin g and compressing cone.The y solved theequa tion of continuity and motion and obtained values for «/, C//(the velocity of thecone )and/ ?(th epressur einsid eth econe) .Th eerro ri nth epressur emeasure ment could be calculated by subtraction of the extra pressure component due to the presence of the transducer from the recorded pressure. However, this procedurewoul d bever ylaborious ,an d theresult swoul d probably not bever y accurate,a sslightl ydifferen t orientationso fth etransduce rma ygiv ever y differ entpressur evalues .Therefor e wewil ltr yt ogiv ea goo destimat eo fth emaxima l error that might occur. From Bernoulli's equation it follows that the deviation inth evelocit ycomponen t ofth epressur eequal s llip(\ — c2)u2/. At thesensitiv e part of the transducer, (1— c 2)ha s afixed valu ewhic h can becalculate d from thedimension so fth etransducer .( 1— c 2)i sabou t0.02 5 for ourMilla rtransduc ers. Hence,larg edeviation s inth evelocit y component ofth epressur e do occur when ufi s high. For instance, with u/=— 1 m/s the pressure deviation is only 13 Pa,whil ewit h u/=— 5 m/san d w/=—1 5 m/s thisvalu ebecome srespectivel y 0.3kP a and 2.8kPa . This last valuerepresent s an error of about 10%.Highes t velocitiesgenerall yoccu ra t themout h aperture (generallyles stha n 10m/s ,se e Muller and Osse, in press), so that largest errors are to be expected here (as fara sth e"stead ypart "o fth epressur ei sconcerned) .Th eerror si nth eopercula r regionwil lb enegligible . In calculating the pressure, not only the velocity, but also the accelerations should be taken into account. Changes in the acceleration of the water near thetransducer' smembran ewhic har ei nth eorde r ofmagnitud e ofth eaccelera tions generated by the fish cannot be excluded. This means that errors in the ordero f100 %migh tb epresen ti nth epressur erecords .Th eerror smigh tincreas e when the transducer's membrane is rotated from a parallel to a perpendicular position relativet oth eflow . Anextensiv emode lwoul d benecessar yfo r agoo d estimate of the errors that do occur in the acceleration part of the pressure, irrespective of which transducer type is used. This, however, has not been ac complished and wasjudge d tob eto ofarfetched . However,i nou r opinionpres sure measurement is still worth doing, although the errors might be as large as 100%.I nth efirst plac eth emeasurement sar eth ebes tindication so fth epres surestha t occuri nth emout h ofa suckin gfish. Secondly ,the yca nb ecompare d withcompute rsimulation susin gth emode lo fMulle re tal .(1982) .A goo dagree mentbetwee nth etw omethod swoul dsugges ttha tth eerror sar erelativel ysmall . 121 2.1.4.Effects of aboundary layeraround a pressure transducer Muller et al. (1982) derived a formula for the thickness ô of the boundary layer: Ô = J^f (6) were v is the kinematic viscosity and T the duration time of the feeding act. Taking 10-5 m2/s and 5x10~ 2 s as characteristic values for Dan d T gives an estimate of 0.7m m for the thickness of the boundary layer. The boundary layer might influence the frequency response of the transducer by the additional mass of water it represents. Consider e.g. the analogy of a spring hanging, on a rigid wall, with a mass m^ attached to it. Let the spring constant be K. Then the undamped natural frequency of the system equals y/K/ml (Jones, 1961). Addi tion of a second mass m2 results in a decrease of the damped natural frequency byN /wi/w1+m2). Asimila r phenomenon might alter thebandwidt h ofa cathe ter tip pressure transducer during the gradual formation of the boundary layer. In the worst case the additional mass iscomparabl e to the mass of the sensitive membrane.Hence ,a decreas e of0. 7time sth eorigina ldampe d natural frequency would occur if the effect of the additional mass is similar as for the spring.This should not seriously influence our measurements as the damped natural fre quency of our catheter tip pressure transducers is very high (about 25kHz , see also paragraph 3.1.). Clearly, the frequency response of pressure transducers with fluid filled catheters willb ehardl y influenced byth epresenc e of a boundary layer. 2.1.5. Effects ofhydrostatic components onthe recording of pressures Generally, the difference in height between the sensitivepar t of the transducer and the water surface in the aquarium will add to the pressure record. This hydrostatic pressure has a constant value when transducers connected via a liq uid filled tube to the measuring point are used. In this case the height between the transducer and the water surface is constant and can even be eliminated (through choice of position or by electronical means). In case of a catheter tip pressure transducer the hydrostatic component is determined by the depth of the transducer in theaquarium . During the feeding attempt thisdept h may vary a few centimeters due to the displacement of the fish. This will obviously result in a slightdistortio n of the pressure record (error in the order of a few percents). Care must be taken that the signal to bemeasure d falls within the sensitive range of the transducer after addition of thehydrostati c pressure. 2.1.6.Effects ofaccelerations of the transducersystem onpressure records During feeding thepressur e transducer or the fluid filled cannula will beacce lerated. The effect of the acceleration will be quite small when catheter tip pres sure transducers are used whose sensitive membranes are of low mass. As an example consider a membrane with mass m and surface A that is accelerated (perpendicular to itssurface ) with am/ s . Then therewil lb ea deviatio n of (m.a)j A in the pressure record due to the acceleration of the transducer. Substituting 122 some characteristic values of the three parameters, e.g. a = 100m/s 2, m = 10~6 kg and A = 2xl0~6m2, a value of 50 Pa is obtained for the deviation, which represents an error of lesstha n 1%i nmos t cases. Errors due to acceleration are more serious when fluid filled catheters are used.Conside r e.g. apressur e transducer to which isconnecte d a stretched water filled catheter of length /<•. Suppose that this system is accelerated with a m/s along a line making an angle a with the long axis of the tube. The pressure measured due to this acceleration will be (/c.a.cosa) kPa. Taking lc = 0.1l m, a = 100m/s 2an d a = 0ra d one obtains 10kP a for the acceleration pressure, a value comparable to the pressure generated by the sucking fish. Thus, considerable errors are likely to be present in pressure records from moving fish made with liquid filled catheters connected to an external transducer. 2.1.7. Temperature effects on the transduceroutput signal When transducers are used in combination with liquid filled catheters (e.g. Statham tansducers or related types) a temperature effect will be negligible, as no water flows along the sensitive membrane. However, in the case of catheter tip pressure transducers the fluid flow along the transducer might decrease the operating temperature of the strain gauges, and hence change their resistance. Thiscoolin geffec t might strongly influence thetransduce r output when no effec tive temperature stabilizing system is present. When a pressure transducer with a fixed air filled volume behind the sensitive membrane is used, cooling might result in a positive deviation of the recorded pressure relative to the actual one (thela wo fBoyle-Gay -Lussa cca nb eapplie d to thevolum e ofair) .A s thisdevia tion is large, catheter tip pressure transducers must have an open connection between the inner sidean d the atmosphere. 2.1.8.Interpretation ofpressure records;earth-bound andmoving frame An important aspect to be considered in interpreting pressure records is the frame of reference in which pressures are measured. Pressure recordings in an earth-bound frame will give other results than those in a frame fixed to the suc king fish, the moving frame (seeMulle r et al., 1982an d Muller &Osse ,i npress) . In the moving frame the pressure is measured with respect to the fish, i.e. the position of the pressure transducer remains constant relative to the fish, but itspositio n in the aquarium changes with time.Analogously , when the pressure transducer is fixed in the aquarium the fish sucks itself (generally supported by swimming) over the pressure transducer (e.g. in the measurements of Alex ander, 1969) and so the pressure is successively measured at different sites in the fish's mouth. It is clear that the two methods lead to completely different pressure-time curves. 123 2.2. EXPERIMENTAL PROCEDURE 2.2.1. Experimental set up Feeding events by two specimens of Salmo gairdneri and Amia calvaan d one specimen each of Gadus morhua, Perca fluviatilis and Esox lucius were studied by pressure measurements inside their mouth cavities. Table 1 summarizes their dimensions and thecondition s in which theywer ekept . During experimentation they were fed with live cyprinids (young Cyprinus carpio, Barbus conchonius or Carassius auratus). Earliest experiments were done with two almost identical Statham P23 Db strain gaugetyp emanometers ,connecte d toth emeasurin gpositio n by polyethy lene tubes (o.d. 1.63 mm, i.d. 1.14 mm) filled with boiled, air free water. Care was taken that the system was air bubble free. The output voltages of the trans ducerswer eamplifie d usingElema-Schonande rEM T 311amplifier s (bandwidth 0-700 Hz).Th e pressure curves were photographed from a storage oscilloscope screen(bandwidt h 0-10kHz) .Alternatively , theinformatio n wasstore d on mag netic tape, using a Bell and Howell instrumentation recorder (bandwidth 0-2.5 kHz in FM-mode) and played back through a Siemens EMT 311 oscillomink (bandwidth 1 kHz) for analysis. The Statham transducers were the limiting fac tor in the frequency response of the recording equipment (seeparagrap h 3.1.). In later experiments MillarP C 350an d PC 340cathete r tippressur e transduc ers (semi-conductor strain gauge types) attached to woven Dracon catheters (filled with air and having an open end outside the aquarium, o.d. 1.67 mm or 1.33 mm) were used. Here the output voltages were amplified with Grass PI5 preamplifiers. The lower frequency limit was set at 0.1 or 0.3 Hz and the upper frequency limit wastake n to be 50kHz .Th e amplified signalswer e stored using the B&H recorder (speed 30inch/s ,bandwidt h 0-10kHz ) and played back (at 7.5inch/s ) to bevisualize d on a storage oscilloscope (set at a frequency range of 0-10 kHz). In several cases the pressure records were filtered at 2 kHz (12 dB/oct.) to eliminate high frequency events, probably due to vortices (see para graph 4.3.). An Entran EPA-125E-10SW miniature pressure transducer (strain TABLE 1. Fish specimen used.S Li sstandar d length,/ i shea d length, Prot, isprotrusio n ofuppe r jaws.T i stemperatur eo fwater ,LA ,W Aan dH Aar elength ,widt han dheigh to faquarium . species SL / Prot. T LA WA HA (mm) (mm) (mm) (°Q (m) (m) (m) Amia calva 365 92 0 17 .9 .5 .4 Amia calva 395 100 0 19 .9 .5 .4 Salmo gairdneri 240 56 0 14 .8 .5 .4 Salmo gairdneri 230 53 0 15 .7 .5 .3 Esox lucius 253 73 0 15 .8 .5 .3 Gadus morhua 225 58 1 13 .9 .5 .4 Perca fluviatilis 160 48 5 15 .8 .5 .3 124 gaugetype )wa sinitiall y tested,bu t found to beunsuitabl e for our experiments (see paragraph 3.1.)- The fishes were filmed (200-400 frames/sec) and trained asdescribe db yMulle ran dOss e(i npress) .Measurement so fth emout hopening , suspensorial abduction, hyoid depression and opercular dilatation were made asdescribe d byMulle ran dOss e(se ethei r Fig. 11). 2.2.2.Testing of the transducers Beforeexperimentatio n severaltest swer ecarrie d out withth etransducers : A.Al ltransducer swer ecalibrate d hydrostatically. B.A "transien t test" wascarrie d out for both the Statham and Millartrans ducers, using a metal cylinder (height 1 m, wall thickness 7mm , i.d. 82mm) . Thepressur etransducer swer einserte d intoth ecylinde ra t0. 7m fro m theclose d bottom. Thecylinde rwa sfilled wit hwater , upt oabou t 0.99m an d closedwit h a cellophanemembrane .Th epressur ewa sincrease d toabou t 40kP a viaa hol e just underneath the membrane. The membrane was punctured with a knife to produce a sudden change in the pressure. In some cases the cylinder wall was hitwit hth eknif eafte r rupturingth emembrane .Th erecording so fth etransduc ers were displayed on a storage oscilloscope screen (bandwidth 1 MHz), or at firstinstan t stored onmagneti c tape (speed 60inch/s ,bandwidt h 20kHz) .Th e length of the polyethylene tube attached to the Statham transducer was 1 m, 0.5 m and 0m i n these experiments. The frequency content of the response of thetransducer swa sdetermine d byFourie ranalysis ,usin ga Mine-1 1computer . Thedampin gratio san dth edampe d natural frequencies ofth etransducer swer e calculated from thetes tresult susin gth emetho d ofGab e(1972) . Theresonanc e andundampe d naturalfrequencie s werecalculate d from equations(3 )an d(4) . C.Th e effect of the position of the pressure cannula aperture relative to the flow direction wasteste d in thecas e of the Statham transducers in a flow tube. The aperture of one transducer was positioned parallel to the flow direction, whereas the other was orientated perpendicular (either facing the flow or in theopposit edirection ) and pressureswer erecorde d simultaneously. Thecathe ters used were of equal length. In vivo a similar experiment was performed in the buccal cavity of a specimen of Salmo gairdneri. The tube with the parallel aperturewa smounte d through theethmoi d regiona sdescribe d byLie m(1978) . Theothe rtub ewa sfastene d toth efirst one . Bothaperture swer ekep tperpendic ular(se eFig .8A) .Th elatte rtub eentere dth emout hcavit ythroug hth eopercula r slit. In contrast to theflow tub e experiment the tubes were accelerated in this experiment. The acceleration ofth etube s would havediffere d as theywer eno t orientatedi nth esam eway . D.Artefact sintroduce db ytub emovemen twer estudie dfurthe r bytub eshak ing,keepin gth etub eapertur ei na fixed position . E.Th eeffec t of tube length wasinvestigate d in vivob ymountin g two tubes on the head of a specimen of Salmo gairdneri, parallel to its longitudinal axis and connected to the Statham transducers (see Fig. 10A).Measurement s were taken with equal tube length (890mm ) and a length difference of 50m m (890 and 840mm )an d 100m m(89 0an d 790mm) . 125 F. The Statham, Millar, and Entran transducers were put in a calibration tank to investigate the effect of cooling. Both the pressure and the velocity were varied (related to each other via Bernoulli's equation). G. The frequency content of pressure records of Amia calva obtained with the Millar transducers wasdetermine d using Fourier analysis. 2.2.3. Pressuremeasurements inprey-sucking fish Statham transducers were used in the pressure measurements during feeding in Amia calva, Salmo gairdneri and-Percafluviatilis. In Salmo (specimen of 240 mm SL.) and Perça (SL. 160mm ) pressures were recorded in the buccal cavity. The cannulas were mounted as described by Liem (1978). In Amia (SL. 395 mm) one cannula was placed in the opercular cavity and another in the buccal cavity, and the pressures were recorded simultaneously. Both cannulas entered the mouth cavity medially from the supra-cleithrum in the dorso-caudal corner of the opercular cavity. The aperture of the opercular cannula was more or less fixedt oth eshoulde r girdlean d parallel to theflo w direction. The buccal cannula was bent distally to position the aperture parallel to the flow direction. The flared end of this cannula was not firmly fixed to one of the buccal walls. All measurements with Statham transducers in Amia calvawer ecarrie d out in 1970 byProf . Dr. Osse and used for comparison with the results obtained with cathe ter tippressur e transducers. Millar transducers were used in measuring pressures in a specimen of Amia calva (SL. 365 mm), a specimen of Salmo gairdneri (SL. 230 mm), a specimen of Esox lucius (SL. 253 mm) and a specimen of Gadus morhua (SL. 225 mm). The specimen of Amia calva was trained to feed with a battery of filming lights (power input of 12 kW, effectively, however, almost equivalent to 24 kW due to focussing) and 400 fr/s films were made of about 30 feeding events, with or without pressure transducers.A transducer wasmounte d in theopercula r cavity or in both the buccal and opercular cavities. The catheters were fastened to the outer side ofth e cleithrum, directly ventral to the supra-cleithrum, such that the opercular cavities could be closed completely. The buccal transducer was sewn to the roof of the mouth, directly lateral to the parasphenoid. In Esox pressure measurements and training were performed similar to those in Amia. Fig. 3. "Transient test" for a Millar PC 350cathete r tip pressure transducer and a Statham P23 Dbpressur etransducer . A. Response of Millar transducer. Oscillations in the record are due to oscillations of the metal testcylinder plus itswate r content (see text). Soth e "test" cannot bedesignate d as "transient" for thistransducer . B.Respons eo fStatha m transducer, connected viaa polyethylen etub eo f0. 5m lengt h to themeta l testcylinder .Oscillation sa si n(A )ar eno tpresent ,owin gt oth ever ylo wfrequenc y response(mainl y aresul to fth eflui d filledcannula) . C.A s(A) ,bu twit ha differen t timescale . D^Respons e of the Statham transducer of (B)(t o another transient test), but now connected via a needle to the test cylinder. This system is less damped than in (B). The cylinder has the same resonance properties as in (A) and (B);not e the similarities in the oscillations between (A) and (D). 126 In Salmoan d Gadus pressures were only recorded in the opercular cavity. In Salmo thetransduce r entered the opercular cavity directly anterior to thebasi s of the pectoral fin, whereas in Gadus a position dorsal to the pectoral fin was preferred. Theseposition swer eselecte dt oallo wcomplet eclosur eo fth eopercu larcavit yb yth eopercula ran dbranchiostega lvalves . To illustrate the effect of the acceleration of the fish on the pressure inside '1^11* i^lli^^^l^—M»—M»W—— 40kPa (C) 40kPa 1 1 \, A A; A , /\ V \ \ \t \l \J 1.25 msec I / 40kPa ^WVywvW*w»*wWVW»w « 127 the mouth cavity a tube was mounted on the head (screwn to the parietals) of Amia, parallel to the longitudinal axis of the body. The tube was opened at itsanterio ren dan dclose da tth eposterio rend .A pressur etransduce rwa sposit ioned posteriorly inside the tube at 4c m from its rostral end. When the tube is accelerated along its axis a pressure of lP.a kPa will be recorded, where lp is the distance between the transducer and the rostral end of the tube and a the acceleration. Another transducer was brought into the opercular cavity. Pressureswer erecorde d simultaneously. Inal lexperiment scar ewa stake ntha tth etub eaperture s(i ncas eo fth eStath - amtransducers )o rth esensitiv emembrane swer eorientate d parallelt oth eflow . Ineac hcas eth efish coul dswi m freely. 3.Result s 3.1. TRANSDUCER CHARACTERISTICS The results of the transducer tests will be presented in the sequence of their previousmethodologica ldescriptio n (seeparagrap h 2.2.2.). A.Al ltransducer s tested showed alinea rpressure-voltag e relationship inth e required range(-6 0 kPat o +10kPa) ,whe nhydrostaticall y tested. B. The results of the transient tests for the Statham and Millar transducers areillustrate di nFigs .3, 4an d 5. Fromthes etest sth eresonance ,dampe dnatura l and undamped natural frequencies are calculated or estimated, as well as the dampingratios .Thes evalue sar esummarize di nTabl e2 ,togethe rwit hth euppe r frequency limit for accurate recording. The Statham transducers have a very limited frequency response (about 8t o 15Hz , dependent on the tube lenght) as is apparent from Figs. 3Ban d 4. They are largely damped when a catheter oflengt h0. 5m i sconnecte d tothe m( £> 1). Theyar eles stha ncriticall ydampe d when this cannula is absent (see Figs. 3D and 4B, £i s about 0.35). At first, thedampe dnatura lfrequenc y ofth eMilla rtransducer sseeme dt ob eonl yabou t 1 kHz (Figs. 3A and 3C). However, the same oscillations were registered (al thoughhighl ydamped )b yth eStatha mtransducer swhe nconnecte dt oth ecylin der via a needle instead of a polyethylene tubing. Without the tubing a higher TABLE 2.Dynami c properties of Statham P23 Db and Millar PC 350pressur e transducers. The PC34 0transduce r hassimila rpropertie s asth eMilla rP C35 0transducer . ft = resonance frequency, fd = damped natural frequency, ft, = natural frequency, £= damping ratioand/ / = upperfrequenc y limitfo r accurate recording. transducertyp e ft fd ft f ft StathamP23D b - - 46H z » 1 8H z + tubeo f0. 5m idem,withou t tube 40H z 43H z 46H z 0.35 15H z MillarP C35 0 27kH z 27kH z 27kH z 0.025 3kH z 128 T (A) (B) 20kPa 20kPa ||||l/|*~~-<.-~-". 50 msec 50 msec i- i ( (C) -VMJ 20kPa iyw^ 50 msec I 1 (E) (F) 5kPa 5kPa i— I r r— r— 0 150 300 450 0.0 50 100 -» frequency (Hz) »frequency (Hz) Fig. 4.Transien t test asi n Fig. 3,wit h the Statham pressure transducer attached via a needle to the test cylinder. The resonance properties of the test cylinder were slightly different from those showni n Fig.3 .Th emai nfrequenc y wasles stha n 300Hz . A.Respons eo fMilla rtransducer ,P C350 . B.Respons eo fStatha mtransducer .Th eoscillation spresen ti nth eMilla rrecor dar eals orecorded , buthighl ydamped . C. The response of the Millar transducer, but with the amplitudes of all frequencies above 200 Hz removed. The curve starts to oscillate before the moment of the "transient". Thus, the high frequency componentsar eneede d tofollo wth etransient . (Continuedpag. 130) 129 frequency responsei spossibl e(Figs .3 Dan d4B) .Thi sshow stha tth eoscillatio n of about 1kH z has to be ascribed to oscillations of the fluid and air in the metal testcylinder . Similar oscillationswer erecorde d byGab e(1972) .H emen tioned that their origin is not clear, but suggested that they could be the result of longitudinal wave transmission in the catheter wall. The recording of these oscillationswit hcathete rti ppressur etransducers ,withou ta flui d filled catheter, shows this suggestion to be incorrect. Also, the frequency of these oscillations waseasil yreduce db yputtin gsom egrave la tth ebotto m ofth ecylinder . Fourier analysis wasapplie d to the recordings of Figs.4 A and 4B(obtaine d with a test cylinder with different resonance properties than in Fig. 3). Figs. 4E and 4F show the amplitude spectra of the response of the Millar and the Statham transducers.Th erespons eo fth eMilla rtransduce r containsmor ehig h frequency components than that of the Statham transducer. Figs. 4C and 4D showth etransduce r responsesafte r removalo fth ehig hfrequenc y components. The pressure drop induced by rupturing the membrane cannot be regarded as a transient test for the Millar transducer. The Statham transducer reactsmuc h more slowly and starts to oscillate around the new mean pressure level. These oscillations areabsen t whena polyethylen e tubing isconnecte d to the transdu cer;the nth esyste mi shighl ydampe d (seeTabl e2) . In Figs. 5A,Ba n examplei sshow n in which thecylinde r wall ishi tjus t after therupturin go fth emembran e(se earrow) .Thi simpac teven tcause da seconda ry oscillation in the output of the Millar transducer. This oscillation of about 27kH zmus tb eregarde da sth erea ldampe d naturalfrequenc y ofth etransduce r system.(Th eamplitud eo foscillatio ni sdiminishe dbecaus eo fth eprimar ystora ge on magnetic tape with a frequency response of 20kHz) . The damping ratio of the transducer wascalculate d from a similar (submerged) impact event,wi thout a preceding pressure drop, displayed directly on a storage oscilloscope (see Fig. 5C). The calculated value was 0.025. It can be concluded (by using Fig. 1)tha tth eMilla rtransducer sar esuitabl efo rmeasurin gpressure saccurate lyu pt oa tleas t3 kHz . The importance of an adequate bandwidth of the pressure recording equip menti sillustrate di nFig .6 .Fourie ranalysi swa sapplie d toa bucca lan da noper cular pressure record obtained for Amiacalva with Millar transducers. In Fig. 6Ath e twopressur e records arelow-pas sfiltered (1 2dB/octave ) at 2kHz , 500 Hz, 100H z and 20Hz .A considerabl e amplitude decrease and phasedisplace mentoccur sa tlo wfrequencies . Thefundamenta l frequency ofthi sfeedin geven t lies in the order of 10 Hz. However, secondary oscillations up to 1kH z are D. Theremain s of the response of the Statham transducer after removal of the frequencies above 50Hz .Th e main frequency of oscillation left approximates the damped natural frequency of the transducer system(abou t 45Hz) .Fro m thisfigur e thedampin grati oca nb edetermine d (seeTabl e 2). E. Amplitude spectrum of the frequency content of the response of the Millar transducer. Above 350H zal lamplitude sar evirtuall yzero .Th eseparat epoint so fth eamplitud espectru mar econnecte d witha splin e function. F.Amplitud espectru mo fth efrequenc y contento fth erespons eo fth eStatha m transducer. 130 40kPa H v (B) 4#% it ?• ."• "J'.. T ™ 40kPa (C) 40kPa Fig. 5.Respons e of a Millar PC 350transduce r to rupture of a membrane enclosing a metal test cylinder. After the membrane was ruptured the cylinder wall was hit with a knife (see arrows in (A) and (B)), causing a secondary oscillation of about 27 kHz in the output of the transducer. The real amplitudes of these oscillations were not recorded, as the recording equipment had only a bandwidth of 20 kHz. (B) shows a part of (A) at a different time scale. (C) shows the impulse response of the Millar transducer when hit against a solid. This record wasmad e using a storage oscilloscoop with a MHz bandwidth. The frequency of oscillation is the same as in (A) and (B). Thistes twa suse dt ocalculat eth edampin grati oo fth eMilla rtransducers . 131 500H z 100H z 20 Hz 100mse c \j opercular (B) 3.5 buccal 3.5 opercular pressure amplitude 0- î (kPa) 0 250 500 750 0 250 500 750 •frequenc y (Hz) -»frequency(Hz ) 5kPa 100mse c /J**~~- •ƒ—~ , A opercular 2 kHz 100H z 20H z Fig. 6. A. Buccal (upper curves) and opercular pressure records of the bowfin (Amiacalva, SL. 365mm) ,low-pas s filtered at 2kHz , 500Hz , 100H z and 20H z (12dB/oct) . Filtering at 500H z hardlyaffect s thecurves ,contrar y toth esituatio n at 100 Hzan despeciall y2 0Hz ,wher ea decreas e inamplitud ean da phas eshif t occurs(denote db yth edashe dlines) . B. Amplitude spectra of the curves shown in (A).Th e main frequency components are less than 100Hz .Greate r amplitudes are present in the buccal record at high frequencies compared to the opercularrecord . C.Th e samerecord s asi n(A )bu t nowfiltere d at 2kHz , 100H zan d 20Hz .Thi smean s that after all frequency components in the amplitude spectra were set to zero above the mentioned levels, thecurve swer etransforme d from thefrequenc y domain to realtime .I t isimpossibl e to filter very sharplyi felectroni cfiltering is use d asi n(A) .Filterin g likei n(C )ha sth edrawbac k of adisturbe d balance between the components of the Fourier series, so that the curves start to oscillate even before the "actual" pressure drop. A time shift of the moment of the largest amplitude is absent by thismetho d (seedashe d lines in opercular records). Low-pass filtering resembles the situation ofa pressur etransduce rwit ha lo wfrequenc y responsebette rtha nfiltering b yremovin gcomponent s ofth eFourie rseries . 132 present in the records. The amplitude spectra of the recorded pressures are showni nFig .6B .Th ebucca lrecor d containsmor ehig hfrequenc y components than the opercular record. Frequency components up to 750 Hz are present, but above25 0H z theamplitude s arehardl y visible.A remova l ofal l frequency components above 100 Hz and 20 Hz results in a decrease of the amplitude and oscillations even before theactua l pressure drop,bu t no delay of thepea k negativepressure . Theanalysi so fth efrequenc y responseo fth etransducer s showstha t theSta - tham transducers are unsuitable for the recording ofpressure s in prey-sucking fish,du e to their limited frequency response (0-15 Hz). This is even true for alarg especime no fAmia calva fo r whichth esuctio nac tlast srelativel ylong . C.Fig .7 show stha tdifferen t orientationso fth etub eaperture so fth eStatha m transducers had noappreciabl eeffec t on themeasurement si na flo w tube.Thi s resultsuggest stha t thedistortion si nth epressur erecord sdu et oth edimension s of thetransduce r might beles sseriou s than expected on theoretical considera tions. The oscillations are, however, of a low frequency (about 2 to 18Hz) , so that conclusions for the situation of the fish's sucking system can not be drawn.Fig .8 showsth eresult so fa nequivalen texperimen ti nviv owit ha speci menofSalmo gairdneri. Different orientationso fth epolyethylen etubing sresul ted inmarkedl y different pressure records.Togethe r with theresul t of theflo w tube experiment this suggests that the records are very seriously distorted by accelerationso fth etubes . D.Fig .9 show sth eeffec t oftub eshakin go nth eoutpu t ofth eStatha mtrans ducers.Pressur e fluctuations ofabou t 10 kPa can easily beevoke d byshaking . Thisfeatur e stressesth e sensitivity ofth e Statham transducers to accelerations. The suckingfish als oproduce s movements with high accelerations. Therefore, the use of this type of transducers for the study of suction feeding should be accompanied withgrea tcar ean di fpossibl eavoided . (B) 20 •• (A) pressure (kPa) Î o 20 i> L>i 0.5 1.0 1.5 *15m m ->tim e (sec) Fig. 7. Records of pressure fluctuations in a flow tube simultaneously made with two identical Stathamtransducers ,connecte dvi apolyethylen etubing st oth etube . (A) shows the orientations of the apertures of the tubings in theflow. Heav y arrows denote the flow direction. Thepressur e in the tube wasvarie d by a periodical opening and closingo f avalv e inth eflow tube . Curve 1 in(B )i sth erecor dwit hth eapertur eparalle lt oth eflow . Curve2 show sth erecor dwit hth eapertur eperpendicula r toth e flow. Curves 1 and 2ar ever ysimilar .Se etex tfo rfurthe r explanations. 133 (B) yv 100mse c 7.5 kPa Fig. 8.Pressur e recordings during feeding in the buccal cavity of a rainbow trout (Salmo gairdneri, (SL. 240mm), using Statham transducers and tube orientations as shown in (A). Record 1i n (B) isobtaine d with the tube through the ethmoidial region, whereas 2i s obtained with a tube through the opercular slit. The records differ a great deal. Tube orientation and mounting have a strong influence on the measurements. 40mse c i 1 Fig. 9. Effect of shaking of the polyethylene tube connected to a Statham transducer on the output signal. The end of the polyethylene tube was fixed. This record shows that pressure fluctuations of a magnitude comparable to the maximal amplitude of the pressure generated inside the mouth during feeding may occur ifth e tube isaccelerated , e.g. by swimming. (B) 10 •• pressure 10 •• Kv^/U-,y^yAAA^ n A^v,. xt^ 0.5 1.0 -> time (sec) 134 .-** 15- ,''*' 18°C Vout it (mV) '(\ I \ \\ » 2.5 J J --JC-' \\ X ,-**"" - -*" * -X' ' _ -• "' • \ -*-- -•«-' ,-*''"*" ,.--< „ .-*-' .«--' 7°C P\ ,-*-" ' -x-. —»-- -*- --W-- — rf*' _-*• "" K ---*" " s .*- _-*'" »c^ --*1-'__* -- ~X- --«^" 10 —I \ 10 20 ->•pressur e(kPa ) Fig. 11.Result so fa calibratio n ofa nEntra n pressuretransduce ri n aflo w tubefo r three different water temperatures. Apressur e increasei saccompanie d by an increase in the velocity of the flow alongth e transducer (astead y flow regimewa sused) . Kouti sth eoutpu t voltage of the transducer. Alowe rtemperatur eo fth ewate rdecrease sth eoutpu to fth etransducer .Th enon-linea r behaviour atlo wpressur elevel si sdu et ocoolin geffect s byth eflow . E. Fig. 10illustrate s the effect of tube length on the output of the Statham transducers.Equa ltub elength sresulte di nidentica lrecordings ,wherea sa lengt h difference of 100 mm gavever ydifferen t results. Even a doubling of the input frequency mayoccu rwit hparticula r tubelenghts . F.Th eStatha man dMilla rtransducer sappeare d tob estabilize dfo r tempera tureeffects .Th eEntra npressur etransucers ,however ,showe da stron gtempera ture effect. Acalibratio n whereby a laminar stream of increasing strength was applied to the transducer did not give a linear relationship between pressure and output voltage (Fig. 11). The initial decrease of the output voltage might be due to a cooling effect of the fluid flow on the strain gauges. This effect could be minimized using a lower input voltage, accompanied of course by a lossi nth esensitivit yo fth etransducer . Soa distinctio n hast ob emad ebetwee n the dynamical properties of a pressure transducer responding to variations in the hydrostaticpressur e and suchpropertie s when a dynamically varying flow isapplied . Fig. 10.Pressur e records made simultaneously with two Statham transducers. The polyethylene tubings were mounted on the head of a rainbow trout, as shown in (A). The tubings were glued together, to ensure equal movements. Curve 1 in (B)represent s a record made with a tube length of0.8 9m ,wherea scurv e2 i sobtaine d witha tub elengt h of0.7 9m .Th erecord sar ever y different. Theywere ,however ,identica li fth elength so fth etube swer etake nequa l(no tshow ni nthi sillustra tion). 135 (A) _ opercularpressur e opercularpressur e 0 pressure (kPa) Î -5 -10 A /^\ -5 buccalpressur e -10 100 200 100 200 ->tim e(msec ) -•time(msec ) Fig. 12.Record s of the pressure in buccal and opercular cavity of a bowfin (Amiacalva, SL. 395 mm,hea d length 100mm )durin g prey capture. The records weremad e with a Statham pressure transducer, connected via polyethylene tubings to the fish's mouth. Large errors may be present in these records as these transducers have a very low frequency response, besides their extreme sensitivity for accelerations ofth etubes .Th escal eo fth epressur ei n(B )equal stha to f(A) . 3.2. PRESSUREAN DMOVEMEN TRECORD S Anadequat einterpretatio n ofpressur erecord srequire sknowledg eo fth epo sitions of the pressure transducers inside the mouth cavity. They will be given as a percentage of head length (opercular valve= 0 % and mouth aperture= 100%). Fig. 12show s pressure records obtained for a specimen of Amia calva (SL.39 5mm) ,usin g Statham P23D b transducers.Pressure swer erecorde d si multaneously inth ebucca l and opercular cavity (head length is 100 mm,trans ducers at 10an d 60%).Pea k negativepressure s areslightl y larger inth ebucca l cavity than in the opercular cavity. The buccal negative peak lasts about 70 msec, in the opercular cavity this is 65 msec. In the records of both cavities a positivephas ei spresen t after themai nnegativ eone .A ninitia lpositiv ephas e ispresen tbefor eth emai nnegativ eon ei nal lrecords .Not eth esimilarit ybetwee n theserecord san dthos eo fFig .6 A whic hwer elow-pas sfiltered a t2 0H z(origina l recordsobtaine dwit hMilla rtransducer swit ha hig hfrequenc y response). Anotherspecime nof Amia (SL .36 5mm )wa suse dfo rpressur emeasurement s with Millar transducers. Fig. 13show s three opercular pressure records (head length 93 mm, transducer at 14%).Th e first record shows the most negative pressure peak obtained (-13.6 kPa). Note the initial rapid fluctuations in the twoothe rrecords .Also ,a tth een do fth erecords ,rapi dfluctuation s often occur. Figs. 14 and 15 show similar records correlated with movement graphs of the mouth opening and opercular abduction. Fig. 14 shows a record of two 136 Fig. 13.Thre e records of the pressure in the opercular cavity of a bowfin (Amiacalva, SL. 365 mm,hea dlengt h9 3mm )durin gpre ysuction .Thes erecord sar eobtaine d withMilla rP C35 0trans ducers.(A )show sth erecor dwit hth elarges tobtaine damplitud e(13. 9kPa) .Not eth einitia lfluctua tionsi nth epressur ei n(B )an d(C) . 50 distance height mouth aperture (mm) Î 0 opercular abduction 75 50 displacement predator 25 0 displacement prey 25 - 0- pressure o *£ (kPa) opercular pressure Î -5 \ I \l -10- V 100 200 300 400 500 -• time (msec) Fig. 14. Records of the height of the mouth aperture, the distance between the caudal edges of theoperculars ,th edisplacemen to fth epredator , thedisplacemen t ofth epre y(earth-boun d frame) and the pressure inside the opercular cavity, during feeding in the bowfin (Amiacalva, SL. 365 mm).Th efirs t suction act isa failure. In thesecon d attempt thepre ywa scaught . Themovement s and thepressur efluctuation s arever y similar to thoseo f thefirst suctio n event.Th evertica l lines denoteth emoment so fth eopenin go fth eopercula rvalves . 137 height mouth aperture 25 0 distance ^5 s opercular (mm) î abduction 50 displacement predator 25 0 displacement prey 25 -^ pressure „ (kPa) opercular î pressure -5 A/ 1 1 ( 50 100 150 -•time (msec) Fig. 15.Record so fhea dmovement san do fpressur efluctuation s inth eopercula rcavit yo fa bowfi n (Amia calva, SL.36 5mm) ,a si n Fig. 14. Thesuctio n acts ofFig . 14 arefaste r and thevalve sope n earlier(momen tdenote db yth evertica lline) . attempts to capture the prey of which the first is a failure. Note the striking similarity between the movements and pressure fluctuations of both suction events. In several cases the pressure drops already slightly (in the order of 0.5 kPa) before any movement of themout h or opercula can be detected. Suction startswhe nth emout h opens.A tth esam etim eth epressur edrop sver y rapidly. Initially, the opercula move slightly inwards,thereb y decreasing the volumeo f the opercular cavity.Afte r this initial phase the gillcover smov eoutward s and theopercula r cavity isver ymuc henlarged . Duringpre ycaptur e thefis hmove s forward duet oth eimpuls egive nt oit sbod yb yth eexpandin gmout h andaddi tional swimming.A t acertai n moment (t= x) the opercular and branchiostegal valves(cauda lvalves )open .Th erelativ etim eo fopenin gdepend so nth eintensi ty of the suction act. In rapid suction events the valves open relatively early and themeasure d pressurei sstil l slightly negative at i (seee.g . Fig. 14,th e first 138 height mouthapertur e 25 distance O (mm) depression of hyoids î 50 25 suspensorial abduction 75 - 50 opercular abduction 75 50 pressure (kPa) Î -10 •• /\j -10 —I— 50 100 150 200 250 •time (msec) Fig. 16. Graphs of the height of the mouth aperture, the depression of the hyoids, the abduction of the suspensoria and the abduction of the opercula, together with records of the pressure in the buccal and opercular cavity during a feeding event of a bowfin (Amia calva, SL. 365 mm). The movement records wereobtaine d asdescribe d in Muller &Oss e(i npress) .Th epressure s were recor ded with Millar pressure transducers. The rapid fluctuations in het buccal pressure record may be due to vortices passing along the transducer. Note that the negative phase in the buccal record lasts longer than in the opercular record. The opercular and branchiostegal valves start to open when the opercular pressure crossesth e zero-level, denoted by the vertical line.Th emovemen t data of this feeding act were used for a simulation of the pressures and velocities in the fish's mouth, see Fig. 24D. 139 attempt).I nslo wsuctio nact s(e.g .Fig . 15)i fallsrelativel ylat ean d thepressur e isalread ypositive .A negativ epressur ea tth etim eo fvalv eopenin gi nth eopercu larcavit ydoe sno tnee dt oimpl ytha t aninwar dflo w ofwate rthroug hth eoper cularslit soccurs ,a sth esuctio neven ti sa highl yunstead yprocess . Fig. 16 showssynchroneou srecord so fth epressur ea t positionsi nth ebucca l and opercular cavity (transducers at 80%an d 9% of head length) correlated withkinemati cdat a (mouth opening,hyoi d depression, suspensorial abduction and opercular abduction).Hyoi d depression, suspensorial abduction and oper cularabductio nar edelaye drelativ et omout hopenin gan dstar ti nth ementione d sequence. Opening of the valves occurs when the opercular pressure (at 9%o f the head length) is almost equal to the ambient pressure. The negative phase lasts longer in the buccal pressure record than in the opercular one. After this phase a positive phase can be observed in all records, reaching higher values inbucca lrecord stha n inthos eo fth eopercula rcavity . Fig. 17 showssimultaneou s recordsfo r Amiao fa n opercular cavitypressur e (at 5%o f the head length) and the pressure at 40m m from the rostral end of thetub emounte do nit shea d(se eparagrap h2.2.3.) . Beforesuctio nstarte dswim mingoccurre d (unfortunately, nofilm wa smade) ,reflecte d byth epositiv eacce leration pressure in the tube. It was calculated that the maximal value of the forward accelerationwa s5. 5m/s 2(usin gth eformul a onpag e 126).Whe nsuctio n starts thisacceleratio n pressure iseve n increased, probably due to an extraim pulsecause d bymout h expansion.Thereafte r thepressur ecurv ebecome smor e difficult to explain. The rotation of the neurocranium makes the movements of the tube very complicated. The high frequency events later on in the record may be caused by a bouncing effect within the tube. This experiment shows (A) Fig. 17. Synchroneous records of the pressure in the opercular cavity of a bowfin (Amia calva, SL. 365mm ) and in a tube mounted on its head. The records are made with Millar transducers. In (A) the way of mounting is shown. Curve 1i n (B) is the opercular record; curve 2 represents the pressure in the tube. Note the different pressure scales.Th efish accelerate d towards thepre y by swimmingmovements . Thisresult s in a positive pressure in thetub e on the fish's head. From this pressure the forward acceleration of thefish ca n be calculated (see text). The maximal value was5. 5m/s 2.Thereafte r theneurocraniu mi srotate dupwards ,resultin gi nquit eunpredictabl epres sure fluctuations. 140 (A) 7.5kP a 100mse c 200mse c (B) 50mse c Fig. 18.A . Record obtained with Statham transducers of the pressure in the buccal cavity of a rainbowtrou t(Salmo gairdneri, SL .24 0mm) .Th erainbo wtrou tuse sconsiderabl eswimmin gdurin g feeding. This causes accelerations of the fluid in the polyethylene catheter. These records do not givea realisti cpictur eo fth epressur einsid e themout h cavityo fth efish. Actually ,a positiv einitia l pressurepea ki sgenerall yabsen ti nvali drecord so fth epressur eclos et oth emout haperture . B. Records of the pressure in the opercular cavity of another specimen of Salmo gairdneri (SL. 230mm) ,obtaine d with a MillarP C 350transducer . Curves 2t o 4hav eth e samescales .N o films weretake ndurin gth efeedin gacts .Anothe rfeedin gac twa suse dt omak ea simulatio no fth epressur e fluctuations inth e mouth. Astrikin g similarity wasobtaine d withcurv e2 .Th efirst negativ epea k incurv e 1 representsth epressur efluctuatio n duringpre ycapture .Th etw oothe rpeak swer egenera teddurin gpre yhandling . that the acceleration of thefish ha s a significant influence on the value of the pressurei nth emout hcavity . Fig.18 Ashow sbucca lpressur erecord so fa specime nof Salmogairdneri (hea d length 56 mm, transducer at 80%), obtained with a Statham transducer. The tube aperture was positioned perpendicular to the flow direction. Quite large positivepressur epeak si nth erecord sar epresent ,probabl ymainl ydu et oswim mingmovements ,causin gth eflui d inth ecatheter st ob eaccelerated . Fig. 18B shows opercular pressure records for another specimen of Salmo gairdneri(hea dlengt h5 3mm ,transduce ra t25%) . Quiteofte n considerableposi tive pressures occur at the start of the pressure waveforms, probably mainly caused by swimming. (Nofilms wer e made synchroneously with the pressure records,bu t swimmingplay s an important rolei n the prey capture mechanism of the rainbow trout as pointed out by Van Leeuwen, in prep.). During the negativephas esecondar y fluctuations mightb epresent . Peak negative pressure equals-8. 8 kPa (curve 1).I tmus tb estresse d that thepressur erecord s obtained 141 (A) 2.5 kPa 2.5 kPa 0.5se c Fig.19 .Bucca l(A )an dopercula r(B )pressur erecord so fth epik e(Esox lucius, SL .25 3mm) ,obtaine d with a Millar PC 340 transducer. The forward acceleration of the fish is reflected by the strong positivepea k in the opercular record.Th epea k acceleration ofth e fish would havebee n 120 m/s2 if thispositiv e pressure peak is only to beattribute d to forward motion. Afil m wastake n during measuremento fth ebucca lpressure .Th emovement so fth efish wer emeasure dan duse dt osimulat e thepressur ei nth emout hcavity . Theresult sar eshow ni nFig . 24B. 10 msec 5mse c Fig.20 . Opercular pressurerecord sfo r aco d (Gadusmorhua, SL.22 5 mm),obtaine d witha Milla r PC 350transducer . Note thedifferen t time scalesi n (A)an d (B).I n (A)th epre y wasno t caught. Preycaptur eeven t (B),however ,wa ssuccesful . Nofilms wer etake ndurin gthes efeedin g acts.Th e movementsdurin gfeedin go fanothe rco dwer euse dt osimulat eth epressur einsid eth efish's mout h (seeFig . 24C). for Salmoar eno tdirectl ycomparabl et othos eo fAmia a sbot hth ehea dlength s andth erelativ eposition so fth etransducer sar e different. Fig. 19show s a buccal and an opercular pressure record of the pike, Esox lucius (head length 73mm , transducer at 80%an d 10%respectively) . This fish generallyaccelerate stoward sth epre yb ypowerfu l swimmingmovement s(Web b and Skadsen, 1980). Thisi sreflecte d byth ehig hpositiv epressur ei nth eopercu lar record (8.5kPa )durin gth efirst par t ofth efeedin g act.Thi srecor d strongly supports the suggestion that movements of the predator as a whole influence significantly thepressur e insideth emout h cavity. Thepea k acceleration ofth e fish musthav ebee nabou t 120m/s 2i fth epositiv epressur epea kwa sonl ycause d byforwar d motion. 142 Fig.2 0show stw o opercular pressurerecord sfo r Gadusmorhua (hea dlengt h 58mm , Millar transducer at 5%). The first record represents a relatively slow suction act,wherea sth esecon d represents an extremelyfas t one.Th eduratio n time of the negative phase of the second attempt is only 5mse c and the peak negative pressure is-4 2 kPa. Obviously, such pressure fluctuations cannot be recorded accuratelywit hStatha m transducerso rrelate dtypes . Fig. 21show s twobucca l pressure records obtained for a specimen ofPerca fluviatilis withStatha m transducers(SL . 160mm ,hea dlengt h4 8mm ,transduce r at 80%).N o initialpositiv ephas ei spresent . Thepea k negativepressur e is-7. 5 kPa. The negative phaselast s about 90msec .Probably , these feeding attempts should beregarde d asrelativel y slow for aperc h of this size. Large errors may bepresen t inthes erecord sdu et o theunreliabl epropertie s ofth e measurement system(se eabove) . 7.5kP a 300mse c 100mse c Fig.21 . Buccalpressur erecord sfo r theperc h (Percafluviatilis, SL . 160mm) ,obtaine d witha Sta tham P23D b transducer (connected via apolyethylen e catheter to themout h cavity. Largeerror s mayb epresen ti nth erecord sdu et oacceleration so fth ecathete ran dth elimite dfrequenc y response. 143 3.3. INTERPRETATION OF PRESSURE RECORDS 3.3.1. Themodel of Muller, Osseand Verhagen (1982) Muller et al. (1982)discusse d a mathematical model of suction feeding in te- leostfish. Thei rmode lconsist s of aconica l profile along theX-axi swit h dictated radial movements. Fig. 1 of chapter 2 of this thesis illustrates the model ap proach. At oneen d ofth eprofil e (x = 0)a valv e("th e opercular and branchioste- gal valves") was defined, opening at t= x. The equations of continuity and mo tion for the expanding and compressing profile were solved to obtain the veloci tiesan d pressures inside the mouth. The formulae of thevelocitie s and pressures are giveni n the Appendix. Before t= x the velocity at x =0 i s zero, which is a valid boundary condition for calculating thevelocitie s and pressures inside the profile. To obtain thevelo cities and pressures for t> x the velocity or the pressure at a particular point for which 0 3.3.2. Thechoice of themoment of valve opening The ideal moment of valve opening depends on the forward velocity of the profile (the "fish's velocity") £//and the expansion of the head as pointed out by Van Leeuwen (in prep.). Once the mouth expansion rate is less than a certain critical value the valves should be open, otherwise the fish would push water forward in themout h aperture in theearth-boun d frame. Thepresen t resultso f theexperiment s with Amia calva(Figs . 15t o 17)sugges t that two other conditions should be fulfilled before valve opening is likely to occur: 1. The pressure at x =0 insid eth eprofil e ("the most caudal opercular pressure") 144 shouldb eclos et oth eambien tpressure .I nAmia th edeviatio n from theambien t pressurei sles stha n 10% ofth eamplitud eo fth epea knegativ epressure . 2. The profile has to expand to a certain amount before the valve is able to open.Experimenta levidenc efo r thisaspec ti sals ogive nb ysevera lothe r papers sucha sMulle ran dOss e(i npress) . Athir d condition wasformulate d on thebasi so fsimulation s with themode l of Muller et al. (1982) and the analysis given by Van Leeuwen (in prep.), and from the need of the formulation of an adequate boundary condition for /> x (seeparagrap h 3.3.3.): 3. The acceleration of the water in the mouth aperture should be equal to or greatertha nzer o(u' v{l,x) ^ 0).Whe nu' v(l,x) <0 th ewate ri nth emout hapertur e is sucked caudally with an increasing rate. Hence any pushing problems are stillabsen tan d therei sn onee dt oope nth evalve s(se eVa nLeeuwen ,i nprep.) . Wewil lillustrat eth efeasibilit y ofconditio n 3furthe r withth eai do fth esimu lationo fa profil ewit ha napparen tcone-lik emovemen t(se eFig .22) . Theveloci ty at the mouth aperture is double peaked and divided for convenience into 4phases .I nphas e3 thepressur ebecome smor enegativ ewhil ewate ri saccelera ted backwards (This is not generally true during phase 1a s the acceleration component due to forward motion ofth efish i n the pressure isver y important at that time).Th e same feature was found for 20othe r simulations, indicating that condition 3 ascertains that thepressur e isno t significantly decreasing after valve opening. This depends also on the boundary condition for t>x, to be discussedi nth enex tparagraph . Effectively, conditions 1t o 3allo w the valve to open during phases 2 and 4 of Fig. 22. In case of a single peaked velocity curve at the mouth aperture phases 3an d 4 are absent and valve opening is possible in phase 2. In actual simulations of feeding events the movement curves of the mouth opening and opercular abduction, found bycinematographi c analysis,wer efitted wit he-po - wer functions (see Muller et al., 1982 and Muller and Osse, in press). These 8.52 Uv(l.t) -8.52 time (msec) Fig. 22.Velocit yfluctuation i n themout h aperture for a profile with a cone-like expansion equal totha t of Fig. 23 (i.e.ther ei sa clea r delay timebetwee n theexpansio n at x = /an d theexpansio n at x = 0).Th e velocityi n themout h aperture isgive n relative to theprofile . Thephase snumbere d 1 to 4 are discussed in the text. The caudal valve is assumed to be continuously closed, so that waterleave sth eprofil e anteriorlywhe nit svolum ei sagai ndecreasing . 145 functions were used in the calculation of the velocity and pressure inside the conicalprofile . From thefil m theamoun t ofopercula r abduction h2 wasdeter mined at t= x. In simulations valve opening was often chosen to occur at the instant that h2>h2(x). This only leadst o slight differences between experimen tally determined x and x used in the simulations. Following this approach no caseswer efoun d wherex fel li nphas e3 . 3.3.3.Formulation ofa new boundary condition Van Leeuwen (in prep.) was able to calculate the boundary value for t>x for acylinde r modelwhe n themotio n ofth efish i sals oprescribed . Hepointe d out that the mean velocity with open valve in A"-direction in an earth-bound frame iszer ohalfwa y insideth ecylinde r (atx = 0.5*/ )i fn oinertia leffec t ispre sent due to thepreviou sclose d situation. From conservation ofmas si t follows thatafte r valveopening : Un(ß,t) =y h'- Uf (7) where h is the radius of the cylinder, and h' its expansion rate which can be substituted in(14) : Un (x,t) = Uv-Uf+-- h' (8) Hence, the velocity after valve opening can be completely deduced from the continouslyclose dphas ei ncombinatio n withth evelocit yo fth e fish. Thepositio n ofa poin t ofzer oflo w insidea conica lprofil e with independent anterior and posterior expansions and an open valvecanno t be easily derived duet ounstead yeffect s (Van Leeuwen,i nprep.) .Althoug h someimportan t fea tureso fth esuctio nfeedin g mechanismca nb eexplaine dwit hth ecylinde rmode l iti sa les saccurat erepresentatio n ofth esuckin gsyste mtha n thecone ,especiall y duringmout hclosure .Therefor ew etrie dt odevelo pals oa reasonabl e boundary condition for thecon ealthoug h anexac tcalculatio ni sno tye tpossible . Obviously, the velocity at the mouth aperture iszer o after mouth closure at t= td. Thus a valid boundary condition for t> td is:u n(l,t) = 0 .Generall y td>x, thus aboundar y condition for x< t < td ha s also to beformulated . Asw ecoul d not formulate solid arguments for a boundary condition during this phase,w e decided to keep the boundary condition as simple as possible. Condition 3o f paragraph 3.3.2. made sure that wedi d not have to define a function starting witha negativ evalue ,a negativ efirst tim ederivativ ean dendin gwit hzer ovalue s for both functions (Besides,whe n u'v<0 weha d noargument s for the formula tion of a minimum). In fact, computer simulations showed that u'v(l,x) > 0i n everycase . Foru'„(l,x) = 0w eformulate d thefollowin g boundarycondition : Unfit) = Uv(l,t)\ V2+ 72 cos j-^-^-j ,for x^t^td I andUn (l,t) =0 ,for t^ td ) 146 giving the required values for un (J,t) and u'n(l,t) at x and td.Unfortunately , a simple trigonometric function with a positive first time derivative during x \ \ \ \l u(l,t) (m/sec) -7.51 29.6 150 time (msec) time (msec) Fig. 23.Velocit y (in the moving frame) in the mouth aperture (x= f)an d the pressure near the valve(x = 0)fo r theprofil e chosen by Muller et al.(1982 ,se ethei r Fig. 11).Th emovement swer e keptth esame ,bu tdifferen t valuesfo r zan dth eboundar yconditio n for t >% ar eused . A. Situation with continuously closed valves.Th e velocity is double peaked. The initial positive valueo fth epressur ei scause d bya forwar d acceleration ofth eprofile .Wate ri sblow nou t through themout h aperturea t theen d ofth esuctio n act.Arrow sdenote d with (b)an d (c)depic tmoment s ofvalv eopenin gi n(B )an d(C) . B. Situation with moment of valve opening at the first minimum of the velocity (T= 6.3msec) . Thecosin efunctio n isuse da sa boundar ycondition . C.A s(B )bu tno wth evalve sope na tth esecon dminimu m (T= 25.6msec) . The dashed parts of the pressure curves denote the non-valid range of the calculations. Further explanationsar egive ni nth etext . 147 This function has the required values for un(/,/ ) and u'n(l,t) at x but not at td. However, it wasconclude d from an analysis of 20simulate d feeding events that: 1. The velocity at t= x is always less than 20% of the minimum velocity for velocitycurve swit hon eminimum , resultingi nonl ysmal ldeviation s from zero (afe wcm/sec )fo r t> td. 2. The valves open very shortly after the second minimum has been reached for the velocity curves with two minima. Hence, the first boundary condition can be used in this case,wit h xchose n to fall at the second minimum. It must bestresse dtha tsimulate dpressure swil ldepen do nth echoic eo fthes efunctions , as in the calculations they are compared with the chosen movement functions ofth emouth .A carefu l choice,base do nth eobservatio no fman ysuctio nevent s istherefor e requiredt oavoi dunrealisti cresults . Exampleso fsimulate d feedingevent swil lb ediscusse d inth enex t paragraph. 3.3.4.Simulation of pressure curves Fig. 23B shows a simulation with the new boundary condition (the cosine function was used) for the profile chosen by Muller et al. (1982), leaving all movements and parameter a the same. The valve was chosen to open at the firstextrem e of uv(l,t)a t t= 6.3 msec.Mout h closure waschose n to fall at 8*T, thustd— 50. 4msec .Th epressur ei nth eprofil e becomesles snegative ,compare d to the value obtained by Muller et al. (-50.5 kPa versus -58.5 kPa at x= 0) . The main advantage is the better form of the velocity curve (including mouth closure). However, several disadvantages still exist. The valve opens when the pressure in the opercular cavity is still largely negative (p(0,r)=-25 kPa) and decreases even more after t= x. Also,valv e opening occurs even before theex pansiona tx = 0 ha sbee nstarted .Thes eunrealisti cfeature s resultfro m anunap - propriatechoic eo fx. Fig.23 Cshow sa simulatio n withth esam eprofil e and movements,bu tvalv e opening was chosen to coincide with the second minimum of uv(/,/) , and td= 2x = 51.3msec .Th e new choice of xresult s in pressure curves with two minima, corresponding to the two minima in the velocity curve at the mouth aperture (uv(l,t)). The pressure near the valve at t= x is less negative than in thefirst exampl e (p(0,x) = —7 kPa) . After t= xth e pressure at x - 0become s positivewithi n 1.5msec . Starting with movement data obtained from films, simulations of velocities and pressures in themout h cavity weremad e of four different fish species. For Amiaan d Esoxsynchroneou s recordso fmovement san d pressureswer eavaila ble,s otha t measured and simulated pressurescoul d becompare d for thesam e feedingevent .Fo rSalmo an dGadus suc hdat awer elacking .W euse dmovemen t data of feeding acts of different specimens to simulate the measured pressures. The movements were fitted with e-power functions shown in chapter 2o f this thesis.Th evalue so fth eparameter suse di nth esimulation sar egive ni nTabl e3 .I n allcase sth ee-powe r function waschose nfo r theboundar ycondition s for t > x. Fig.24 Ashow sa simulatio nfo ra rainbo wtrou t {Salmogairdneri). Theobtai - 148 Salmo -1.5- -3.0- -4.5 - opercular halfway buccal -i h 40 80 120 80 160 240 320 -•lime (msec) Fig.2 4A , B • time (msec) 149 (C) Gadus Amia radiusi7.4 (mm) 40 80 120 -»time (msec) ned double peaked pressure at x= 0. 2 / is very similar to the pressure curve 2 of Fig. 18.Th e second negative peak is caused by the caudal expansion. The velocityi nth emout h aperturean dth evelocit ya tth evalv eresembl eth evelocit y records obtained by Muller and Osse (in press), using hot-film anemometry. The valves generally open very early in Salmo (seeVa n Leeuwen, in prep.). In thesimulatio n valveopenin gwa schose n tooccu rslightl ybefor e theactua lmo ment of opening. The lowest simulated pressure in the entire mouth is found atx = 0.5/ an dequal sabou t —5 kPa. Fig.24 Bshow sa simulatio nfo ra pik e(Esox lucius). Synchroneousmovemen t data belonging topressur e curve(A )i n Fig. 19 wereuse dfo r the simulation.A positive initial pressure peak is present in the opercular pressure curve due to a forward acceleration of the profile (parameter a was chosen to be 3). The measured andsimulate d buccalpressur ear ever ysimilar ,althoug ha large rpres suredro p was simulated than measured. Mouth expansion at x= 0 doe s result ina platea uphase ,bu tno ti na secon dnegativ epressur epeak . Fig. 24. Simulations of feeding acts of four different fish species. These simulations were obtained by assigning values measured from movie pictures to the parameters of the model. Starting from these values the pressures generated by the model were compared to pressures measured in the sameo r another individual.Th emode lparameter s then wereadjuste d within therang eo f experimen tal error untill the simulated pressure waveform and magnitude resembled the measured values. The dashed lines indicate pressure values which are strongly influenced by the chosen boundary conditions and thus are not realistic. A survey of the model-parameters used can be found in Table 3. Valveopenin g isdenote d by arrows. A. Salmo gairdneri.Th e measured movement and pressure data were obtained from different snaps of the same animal. In the simulation the opercular valveopen s up rather early, viz. 35mse c (actual time4 5msec) .Th ecalculate d and measured pressures arever y similar. The velocity curve islikewis e in good agreement with the actual velocity curve. Muller & Osse (1982) have published velocity data showing that the actual velocities can be of the same form and magnitude. To compensate for an overestimate of the mouth volume by the model the length of the simulated mouth was taken less than the actual mouth length. Note the similarity between the simulated pressure curve in the opercular region and curve 2i n Fig. 18B. B. Esox lucius. This simulation is based on a feeding event of which both movement and pressure data were obtained. The recorded pressure waveform in the buccal cavity is shown in Fig. 19A. Again a good similarity between measured and simulated pressure waveform exists. The amplitude of the simulated pressure is greater than the amplitude of the measured pressure. This presumably is due to an overestimate of the volume sucked and slight differences in the area of the mouth aperturejus t after the start of mouth expansion. Again the mouth length was taken smaller in the simulations.Th e actual moment ofvalv eopenin g fell 3 msec later than the simulated moment. C. Gadus morhua. The pressure record shown in Fig. 20B should be compared with the simulated pressure in the opercular region. The movement data of another (larger) specimen were used for this simulation, after having reduced the amplitudes of the movements, the mouth length and the duration time to the required scale. A very good resemblance was found between simulated and measured pressures, both inamplitud e and waveform. D. Amia calva. The movement data shown in Fig. 16 were used for this simulation. In this case two synchroneously recorded pressure waveforms wereavailabl e (opercular and buccal cavity). The mouth length was taken smaller than the actual one, to compensate for an overestimate of the volume of the mouth by the cone. Experimentally a lower pressure was found in the buccal cavity than in the opercular cavity. The reverse effect was found in the simulation. The simulated pressure waveforms resembleth eexperimentall y obtained waveforms quiteclosely .Th echose nboundar y con dition hasquit e a big influence on thecalculate d pressure after valve opening. 151 TABLE 3.Value s of parameters used in the simulations shown in Fig. 24.Symbol s are explained inth eAppendix .Th eactua lvalue sfo r /ar egive nbetwee n brackets. species Esox Amia Salmo Gadus code 100190 100189 100187 100188 h\nul(mm ) 1.6 8 4.5 6.5 hlmax (mm ) 10.3 20 13 9.3 «i 5 3.2 8.3 3.9 /Alma*(msec ) 11.5 5.65 4.5 0.65 U\ (msec) 0 0 0 0 fom/(mm) 15 27 16 17.4 famax(mm) 24 46.5 23.5 20 <*2 3.5 3.35 2.5 2.5 towax(msec) 15.5 8.8 7.5 1.4 tV2(msec ) 4.75 1.03 2.85 0.235 hkiep(ram) 1.94 3.8 1.70 1.772 T (msec) 100.4 51.15 37.9 4.63 /(mm) 62(73) 85 (92) 47 (53) 48(58) a 3 5 5 5 pressure shownat : 0.1/0.5/0.8 0.1/0.5/0.8 0.2/0.5/0.8 0.1/0.5/0.9 (../) Fig. 24C shows a simulation ofa feeding event ofa cod(Gadus morhua). The simulated pressure should becompare d to thesecon d pressure curveo f Fig.20 .Th emovemen tdat awer eobtaine dfro m adifferen t specimen.Th elowes t pressuredro p isfoun d halfway along thelengt h ofth emouth . Experiment and simulation showa strikin g similarity, both in form and amplitude. Evena pla teauphas ea si nth erecor d wassimulated ,althoug h ata differen t position. Fig. 24D shows a simulation of the feeding event ofAmia calva showni n Fig. 16. Thefor m ofth epressur ecurve sclosel yresemble sth emeasure d pressu res.Th emeasure dpea kbucca lpressur ei smor enegativ etha nth epea kopercula r pressure.A revers eeffec t wasobtaine d in thesimulation . Sometim eafte r valve openingth epressur ecalculation sar eno t realisticanymore ,becaus eo fth elarg e influence ofth echose nboundar y condition. Wema yconclud etha t themode lgive sa goo d description of the hydrodyna- micevent sdurin gfeeding .Th eshow nsimilaritie sbetwee nmeasure dan dsimula tedpressure sar egenerall y not present in thefirst simulatio n ofa feedin g event, as it is impossible to obtain the accelerations of themovement s accurately enough from the 16 mmfilms. Adjustmen t ofth e parameters within the range ofexperimenta lerro rgives ,however ,ver ysatisfyin gresults .Th evolum eincreas e ofth efish's mout hi sgenerall yoverestimate d withth econ emodel .W ecompen satedfo r thiseffec t bydecreasin gth evalu eo f/ (th elengt ho fth emouth) . 3.3.5. Thecomponents of the pressure Severalfeature s ofth epressur efluctuatio n canb eunderstoo d whenth esepa rate components offormul a (15) arelooke d at (see e.g.Mulle r andOsse ,i n 152 press).I nth e opercular pressure recordsi nAmia (Figs . 13 and 14) fluctuations are often visible at thestar t of the suction act.Term s (b)an d (c)o f equation (15)ar ever yimportan t inth e opercularcavit y asx issmal li nthi sregion .Ter m (b)i salway spositiv ean dparticularl yimportan t whenth efish ha sa hig haccele ration. The other terms of equation (15) areal l negative in the initial phase. The sumo f all terms might easily fluctuate like thepressur e records actually do.Suc hfluctuation s wereals oobtaine d insimulation so fpressur e waveforms. Insevera l ofth eopercula r pressure recordso fSalmo gairdneri positiv epeak s are present inth epressur e curves. Thetrou t isa rapid swimmer andmuc ho f thepositiv epeak sma yb ecause db yswimmin gmovements .Slo wpressur echan ges mayb e caused by swimming in a vertical direction. In theco d a clearly definable positiveacceleratio npea kcoul dno tb edemonstrated . Nearth emout hapertur eterm s(a) ,(b )an d(c )o fequatio n (15)ar ever ymuc h reduced and positive acceleration pressures duet o themovement s of the fish wereindee dno tmeasured .Th eresult so fth epressur emeasurement si nth etub e on thehea d ofAmia calva show theinfluenc e offorwar d movement ofth e fish onth epressur einsid eth emouth . More attention will be paid to the pressure components in our version of thispape rtha twil lb esubmitte d toth eNeth. J .Zool . 4.Discussio n 4.1. PRESSURETRANSDUCER S The present results show that pressure measurement systems consisting of fluidfilled catheter si ncombinatio n withstrai ngaug etyp emanometer sar euns uitable for recordings in the teleost feeding apparatus. Thelimite d frequency response of these systems isclearl y shown byth e results of the transient tests (see paragraph 3.1.). Another disadvantage is the distortions in the pressure records duet oacceleration s ofth e catheters. Catheter tippressur e transducers lackthes edisadvantages . We do not know exactly theinfluenc e of the dimensions of the transducer itself on themeasure d pressure. Thestrikin g similarity between measurements and simulationssuggests ,bu tdoe sno tprove ,tha ti ti ssmall . The acceleration ofth e sucking and swimmingfish contribute s significantly toth epressur ei nth emout h cavity. Hence,i ti simportan t tofix th etransduce r rigidlyt oth e fish. 4.2. A REVIEWO FPRESSUR E MEASUREMENTS Before discussing thepresen t pressure data wewil l review theliteratur e on pressuremeasurent si nsuctio nfeeding .Remarkably ,dat aabou tth ehea dlength , standard length andbod y mass ofth e experimental animals areofte n lacking inth eliterature .Also ,detail sabou t theexac tposition so fth etransducer sinsid e 153 themout har egenerall yabsent .Therefor en oreliabl esimulation swit hou rmode l couldb emad efro m theseliteratur e data. Thefirst pressur emeasurement si npre ysuckin gfish wer eperforme d byAlex ander(1969,1970) ,usin ga S E4-8 1 pressuretransducer .Th efishe swer etraine d to suck food from a nylon tubing connected via a thicker copper tubing to the transducer. Alexander measured a damped natural frequency of 100Hz ,whe n thesyste mwa sfilled wit hwater . Before experimentation hedampe d thesyste m critically(£ = 1, adampin grati oo f \\-Jl would havebee nbetter , seeparagrap h 2.1.2.) by replacing a certain amount of water by glycerol. Alexander (1969) stated that the transducer wasdesigne d to respond to pressuresfluctuatin g up to 100Hz .However ,a t 100H zther ei salread ya dro pi nth eamplitud erespons e ofabou t 50%(se eFig . 1A),assumin g that histransduce r functioned asa singl e degreeo ffreedo m system.A mor eaccurat eestimat eo fth ebandwidt ho fAlexan der's system is 0-30 Hz. In this range the amplitude response is flat and the phaserelationshi pi salmos tlinea r(se eFig .1) . Another disadvantage ofAlexander' s system istha t it may evoke unnatural feedingmovements .Mulle re tal .(1982 )pointe d out that thepressur e waveform is highly sensitive to only small alterations in the movements of the structural elements of the head of thefish. Furthermore , the prey and tubing might seal themout hapertur edurin gmuc ho fth esuctio nevent ,resultin gi nth eproductio n of abnormal high negative pressures.Als o theinitia l pressure waveform islac king as the pressure in the mouth cavity is only recorded after the mouth has openedt oa certai ndegree .Alexande rmeasure d thepressur ei nth eearth-boun d frame (seeparagrap h 2.1.8.). Although the measurements of Alexander only gave a rough indication of the pressures that act in reality during the suction event, they were valuable at the time they were made as they showed that pressure calculations based onstead yflo wassumption s(Osse , 1969) areinvalid . The peak negative pressures measured by Alexander ranged from -7.5 kPa inIctalurus t o-4 0kP ai nPterophyllum. Casinos (1973, 1974) used the technique of Alexander (1969). Some of his peak negative values are: Gadus: -15 kPa; Pollachius: -6 kPa and Mottella: -7 kPa. Several authors used Statham transducers in combination with fluidfilled polyethyelenetubing st omeasur epressure si npre ysuckin gfish. Th edisadvanta geso fthi ssyste mar edetailedl ydiscusse di nth epresen t paper. Osse(1976 )measure d synchroneouslypressure sinsid eth ebucca lan dopercu larcavitie si npre ysuckin gAmia calva. Fig. 12i nth epresen tpape rshow sexam pleso fth epressur ewaveform s obtained. Therecorde d maximal peak negative valuesb yOss ewere :buccally :-1 7 kPaan d opercularly:-9. 5kPa . In thebucca l recordsa smal lpositiv epressur epea k at thestar t ofth esuctio neven ti svisible . Such a positive phase has not been recorded with the Millar transducers and mightb ecause db yth eacceleratio no fth eflui d inth ecatheter ,du et oswimmin g andhea dmovements . Liem (1978) recorded pressures inside the buccal cavity of Serranochromis 154 robustus and Haplochromis compressiceps, using the Statham P23 Db pressure transducer. He implanted the tubing (diam. 2mm ) through the ethmoid bone and orientated the tube aperture parallel to the flow direction. Liem gave no information about acalibratio n procedure, nor about the bandwidth of hisre cording equipment. The properties, however, will be similar to those given for our Statham transducers (seeparagrap h 3.1.). Liem presented a few graphs of hismeasurements , showing curves with an amplitude of-6 m water (or about -60 kPa) or more in amplitude. The duration time of the negative peak given was in the order of 300 to 500msec . Probably the real duration times should be in the order of 30 to 50 msec, as no fish of the sizes used by Liem (about 20 cm of standard length) is able to create such low pressures during such a longtime . Elshoud-Oldenhave (1979) reported pressure measurements in Stizostedion luciopercawit h Statham P23D b pressure transducers (the sametransducer s as used by Osse;tes t report in paragraph 3.1.o f the present paper). Polyethylene tubings( d= 1-1. 2mm )wer eimplante di nbot h thebucca lan d opercularcavit y andpressure swer erecorde dsynchronously .Pea knegativ epressure svarie d from -5t o-11. 5kP ai nth ebucca lcavity ,wherea s 10 to 15%lowe rvalue swer efoun d inth eopercula rcavity . Lauder and Lanyon (1980)measure d pressuresi nth eopercula r cavity ofLe- pomismacrochirus, synchronouslywit hstrai ngaug emeasurement s onth eoper culum.Agai nStatha mP2 3D btransducer swer euse di ncombinatio nwit hpolye thylene tubings. Calibration was performed using the method of Gabe(1972) . Adampe d natural frequency of7 0H z was found, in combination with adam ping ratio, C» of 0.138. In certain experiments the viscosity of the fluid in the tubingwa sincrease d byexchang e ofwate r byglycerin e (method of Alexander, 1969)whic hresulte di nÇ = 0.524 .Th eauthor sdi dno tpa yattentio nt oresonanc e properties of their test cylinder. The catheter was mounted through a hole in thecleithru m(afte r Liem,1978) . FromFig . 1 itappear stha twit h£ = 0.13 8accu - rated recording is only possible up to about 30 Hz. With £= 0.52 4 this limit is only slightly higher. The inadequate frequency response isillustrate d by the time delay of 15t o 20mse c (seethei r Fig. 5)betwee n the strain gauge records and thepressur erecords . Lauder (1980a) shows pressure fluctuations in Lepomis, recorded synchro nously in the buccal and opercular cavity. Statham P23 Gb transducers were used in combination with plastic cannulae (out. diam. 1.52 mm, inner diam. 0.86 mm), filled with a mixture of 53% boiled glycerine and 47%boile d water to adjust C to 0.65.Accordin g to Lauder the frequency response of the system was7 5Hz .Th emaxima lnegativ epressure srecorde di nth ebucca lan dopercula r cavitywer eabou t-6 5 kPaan d-1 3 kPa respectively. Lauder(1980b )use dth esam eequipmen t asLaude r(1980a) .Thi stim ea mix ture of 55% glycerine and 45%wate r was used to obtain a damping ratio of 0.65.Th edampin grati oi sobviousl yno tonl ydependen to nth emixtur eo fglyce rine and water, but also, importantly, on the length of the catheters as shown in paragraph 3.1.Wit h Ç= 0.05 4a damped natural frequency was obtained of 155 250Hz .Laude rpai dn oattentio n toth einfluenc e ofth eresonanc eo fth etestin g cylinder on his calibrations. From Fig. 1 it is apparent that measurements up to 100H z (with £=0.65) have to be regarded as faithful if no troubles existed with resonance of the testing cylinder. Large errorsar ecause d by accelerations ofth ecatheter s(se eth epresen tpaper) . Lauder'smeasurement s givea nimpressio n ofth eoveral lpressur e waveform. However, the bandwidth of his equipment was insufficient to record pressure fluctuations occuringwithi n 10mse caccurately . Osse and Muller (1980) published simultaneous records of the pressure in the buccal and opercular cavity in Amiacalva, obtained with Statham P23D b transducers. Details of their technique are given in the present paper. The au thors stated that the response time of their system was 10 msec.A s shown the actual response time is about 50msec . Thus the curves obtained by Osse and Muller alsogiv eonl ya nindicatio n ofth eoveral lpressur ewavefor m (thedura tiontim eo fth enegativ ephas ei nth epressur ecurve si sonl yabou t 50msec) . 4.3. INTERPRETATION OFPRESSUR ERECORD S The Statham pressure records resemble the filtered Millar records (20 Hz, 12Db/oct, see Fig. 6A). Pressure curves obtained by Statham transducers are alwayssmoot hwherea s theMilla r records often showrapi d secondary fluctua tions (duration in the order of 1 msec).Thi s isparticularl y true for the buccal recordsof Amia calva. Apossibl eexplanatio n for thisphenomeno n isth epassa geo fsmal lvortice salon gth e transducer. At the start of the suction process water flows more rapidly in the anterior part of themout h cavity than in theposterio r part.Thus ,pressur e fluctuations due to passing vortices will occur first in the buccal cavity and only later on in the opercular cavity. This indeed is observed in most of our Amiarecords . An estimate can bemad e of the dimension of the vortex. For instance, in the mouth aperture one pressure oscillation lasts about 0.5 msec. Taking for the velocity a characteristic value of 1m/ s one obtains 0.5 mm for the diameter ofth evortex . Other causes of the rapid pressure fluctuations can be thought of, e.g. influ ences of the prey on the water flow and impact events on the catheters by the prey(i nth ebucca lcavity) . Lauder'sexplanatio n(1980a,b )o fhi spressur erecord si sbase do nstead yflo w assumptions, although the author claimed that inertial effects are important (Muller et al., 1982an d Muller and Osse,i n press). He tried to explain thebi g difference betweenbucca lan dopercula rpressur ei nLepomis b yassumin ga hig h resistance of the gills.Th e second negative peak in the buccal pressure records ofLepomis i sconsidere d to because d bymout h closing(Lauder , 1980a,b:"wa - terhammer effect"). Several objectives can be formulated against Lauder's ideas about suction feeding(Mulle ran dOsse ,i npress) .Firs ti ti simpossibl et oderiv eth eflo wdirec tionfro m thepressur eregim ei na nessentiall yunstead yflo w(Mulle re tal. ,1982) . 156 Second, without the assumption of any gill resistance our simulated pressures arever ysimila rt oth emeasure d pressuresa sdemonstrate d for Amiacalva, Sal- mogairdneri, Esox lucius and Gadus morhua. Thus gill resistance plays only a minor role in the suction process. Third, the initial positive opercular pressure peaki smainl ycause db yforwar d motiono fth efish an dno tb ya nactiv eopercu lar adduction. When thefish' s forward velocity isbelo wa certai n critical value acauda linflo w intoth eopercula rcavitie swoul doccu ri ncas eo fope nopercula r and branchiostegal valves as pointed out by Van Leeuwen (in prep.). The gill covers are an important tool to prevent such an inflow. The generally found slightinitia l activity ofth eM .adducto r operculi (asmeasure d for thefirst tim e by Osse, 1969) is necessary to seal the valves as both the threshold swimming speedan d thepressur e near thevalve sma yinitiall y(th efirst 1 0msec ) fluctuate rapidly (seeVa n Leeuwen, in prep, and Muller and Osse, in press). It islikel y thatthi ssligh tinitia lactivit ydoe sno tcontribut esignificantl y toth einitia lposi tive pressure peak nor to the initial adduction of the operculars, found in e.g. Lepomis and Amia. The initial adduction will be mainly caused by the more powerful buccal expansion in combination with the small mouth aperture at this instant, forcing the gillcover s to move inwards.Va n Leeuwen and Muller (inprep. )pointe d out that the initial opercular adduction reduces the negative pressurepea kan dhenc eallow sa faste r openingo fth emouth . An initial internal reverse flow in the opercular cavity will definitely occur, as the opercula move inwards. It has, however, to be considered as being of minorimportanc ei nth esuctio nprocess . Volumeenlargemen t ofth eopercula r cavity iscouple d with suspensorial ab duction and thus with hyoid abduction, in addition to theenlargemen t created by the activity of the M. dilatator operculi (abducting the opercula) and the M.hyohyoideu sinferio r (fanning out thebranchiostega l rays).Th erelativ eim portance of the opercular cavities in suction feeding varies throughout the te- leosts. In two extreme types of prey suction, viz. low-z-suction with protrusion and low-T-suction with swimming (seeMulle r and Osse,i n press), the opercular cavities are only slightly enlarged before the moment of caudal valve opening. Before that moment the main function of the gill covers is the sealing of the opercularcavity ,s otha ta cauda linflo wi sprevented .A significan t caudalinflo w couldrui nth egil lfilaments. Afte r valveopening ,however , suctionb ygil lcove r abduction canstil lb econtinue deffectivel y whenth ethreshol d swimmingspee d isattaine d (seeVa nLeeuwen ,i nprep.) . Inhigh-x-suction (seeMulle ran dOsse ,i npress) ,anothe r extremetyp eo fsuc tion, the valves open relatively late and at a large abduction of the opercula. Hence, thesuctio n function before valveopenin gi sincrease d relative tolow-T - suction. The term "waterhammer effect" used by Lauder is invalid (see also Muller &Osse ,i nprep.) .Thi s term isuse d for theevent soccurin gi na flo w tubewhe n theflo w issuddenl y stopped bya closin gvalve .I n afish th ewall so fth emout h cavity move towards each other after mouth closure. Mouth closing does not occur instantaneously. Quite complicated flow patterns may occur during this 157 phase (seeVa n Leeuwen, in prep.). The present survey of pressure recording techniques and the interpretation of the experimental results demonstrates the need of a physical approach in stu dying hydrodynamic events in prey-sucking fish. It shows that pressures should be calculated from the movements of the fish, and not vice versa. In this way accurate simulations ofpressure s generated by fishes during suction feeding can be made. The effect of changes in movements or dimensions of the fish on the pressuresan dvelocitie sca nb estudie d ingeneral ,providin gquantitativ e require ments for optimized prey capture mechanisms (seeals oVa n Leeuwen & Muller, in press). 5. Conclusions 1. Pressure transducers, connected via fluid filled tubes to the mouth cavity of the fish, are unsuitable for measurements during prey uptake because of their limited frequency response and distortions owing to accelerations of the fluid in the tubes. 2. At present, catheter tip pressure transducers offer the most useful measuring devices,owin g to their large bandwidth and small dimensions. 3. The pressure inside the fish's mouth is built up of velocity and acceleration components due to mouth expansion and forward motion (caused by suction forward and swimming). Therefore, the velocity of the water cannot be derived from the pressure. 4. Positive pressure peaks caused by forward acceleration of the fish do often occur during feeding by Salmo gairdneri and Esox lucius. 5. The striking similarity between simulated and measured pressures strongly suggests that the model of Muller et al. (1982) provides a valid description of hydrodynamic eventsdurin g suction feeding in fish. Special thanks aredu e to Prof. dr. J.W .M . Osse for many discussions and critisism on the manu script. He also gave permission for publication of his Statham pressure data of Amia (Fig. 12). The advices concerning hydrodynamic problems by Ir. J.H.G. Verhagen from the Delft Hydraulic Laboratory were of great benifit. Mrs. A. Ramakers, J. Kremers, Ir. M. R. Drost and especially Mr. A. Terlouw gave skillful technical assistance. Mr. W. Valen made some drawings and assisted with photographic work. We aregratefu l for thecontribution s of all these people. 6. References Alexander, R.McN. (1969). Mechanics of the feeding action of a cyprinid fish. J. Zool., Lond. 159, 1-15. Alexander, R.McN. (1970).Mechanic s of thefeedin g action ofvariou s teleost fishes. J. Zool., Lond. 162.145-156. Casinos, A. (1973) .E lmechanism e dedegluci od el'alimen t a Gaduscallarias, Linnaeu s 1758(Dade s preliminars). Bull,de la Soc. Catalana deBiologia, (1),43-52 . 158 Casinos, A. (1974). Registres de la chute de pression de la cavité buccale chez quelques gadiformes deno s cotes.XXIV- e Congr. Ass. Plen. deMonaco, pp. 1-4. DiStefano,J .J. ,Stubberud ,A.R .& Williams ,I .J . (1967). Theoryandproblems offeedback andcontrol systems, Schaums outline series.Ne w York. McGraw-Hill. Elshoud-Oldenhave, M.J.W. (1979).Pre y capture inth epike-perch , Stizostedion lucioperca (Teleos- tei,Percidae): Astructura l and functional analysis.Zoomorphology. 93,1-32. Gabe, I.T.(1972) .Pressur emeasuremen t inexperimenta l physiology. In: CardiovascularFluid Dyna mics (ed. D.H. Bergel),pp . 11-50. London. AcademicPress . Hughes, G.M. & Shelton, G. (1958). The mechanism of gill ventilation in three freshwater teleosts. J. exp. Biol. 35(4),807-823 . Jones, D.S.(1961) .Electrical andmechanical oscillations. Plymouth. LatimerTren d Co. Ltd. Lauder, G.V. (1980a). Hydrodynamics of prey capture by teleost fishes. Proceedings of the second Conference onBio-Fluid Mech. 2,161-181 . New York. Plenum Press. Lauder, G.V. (1980b).Th e suction feeding mechanism in sunfishes (Lepomis): an experimental ana lysis.J. exp. Biol. 88,49-72. Lauder, G.V. &Lanyon , L.E. (1980).Functiona l anatomy offeedin g inth ebluegil l sunfish, Lepomis macrochirus: in vivomeasuremen t ofbon e strain.J. exp. Biol. 84,33-55 . Leeuwen, J.L. van (in prep.). A quantitative flow study of prey capture in the rainbow trout with generalconsideration s ofth eactinopterygia n mechanism. Leeuwen, J.L. van & Muller, M. (in press) Optimum sucking technigues for predatory fish. Trans. Zool. Soc. Lond. Liem, K.F. (1978). Modulatory multiplicity in the functional repertoire of the feeding mechanism incichli d fishes. J. Morph. 158,323-360. Milne-Thomson, L.M. (1968). Theoretical hydrodynamics, 5th edition. London. MacMillan Ltd. Muller, M. & Osse, J.W.M, (in press). Hydrodynamics of suction feeding in fish. Trans. Zool. Soc. Lond. Muller, M., Osse, J.W.M. & Verhagen, J.H.G. (1982). A quantitative hydrodynamical model of suction feeding in fish. J.theor. Biol. 95,49-79. Osse, J.W.M. (1969). Functional morphology of the head of the perch (Perca fluviatilis L.): an electromyographic study. Neth. J. Zool. 19(3) ,289-392 . Osse, J.W.M. (1976). Mécanismes de la respiration et la prise des proies chez Amia calva Linnaeus. Rev. Trav. Inst. Peches Marit. 40,701-702. Osse,J.W.M . &Muller , M.(1980) .A mode lo fsuctio n feeding inteleostea nfishes wit hsom e implica tions for ventilation. In: Environmental physiology of fishes (ed. M.A. Ali) NATO-AS Series A. Life Sciences. Trans.Zool. Soc. Lond. Webb,P.W . &Skadsen , J.M. (1980).Strik e tactics of Esox. Can. J. Zool. 58,1462-1469. 7.Appendi x 7.1. NOMENCLATURE a acceleration, or parameter inmode l of Muller et al.( 1982 ) A surface area c(x,<3) function relatingvelocit yaroun d pressure transducer to velocity without pressure transdu cer d distance between source and sphere (seepag e 120) ƒ frequency hi profile radius at 'mouth aperture' (x'= I) h2 profile radius at 'opercular region' (x' =0 ) h-max maximal value ofprofil e radius, *= 1 or 2 h*min minimal value of profile radius, *= 1 or 2 k spring constant / length ofprofil e (or fish's mouth cavity) lc length of catheter 159 lp position of transducer intub e mounted onth e head of Amia m mass p pressure / time tc time constant td time at which mouth aperture closes th'max time at h'max, *= 1o r2 rv» delay time, *= 1 or2 T characteristic duration of feeding event uf velocity of water in the fish's mouth used forcalculatin g up Up velocity around a pressure transducer Un(x,t) velocity inth e mouth cavity in fish-bound frame after valve opening uv(x,t) idem, but before valve opening ui = UvQ.t) U velocity in uniform flow Uf velocity of fish's body x coordinate of long axis in fish-bound frame X.Y.Z axes of fish-bound frame Xi input signal ya output signal x angle between long axis of tube and the direction of acceleration of the tube a* shape coefficient of profile movement, *= 1 or2 6 thickness of boundary layer Afamax =h'max-h'nui,*=l or 2;amplitud e of movement ( damping ratio p density of water (j> phase angle T moment of opening of opercular valve u kinematic viscosity f stream function w =Inf, angular frequency (od damped natural frequency Wn undamped natural frequency (Or resonance frequency x, œ cylindrical coordinates 7.2. FORMULAE The stream function of a uniform flow — U past a sphere (radius, r) and a blunt nosed body, max. diam:4b, (seeFig . 2B)i sgive n by: «P = \UG>2 I ,_ r2 U (x+ WU nn (x1 + (b1)il1!^ ((x + d)2 + &2)1!2' (ll) a combination of the formulae of Milne-Thomson (1968) for a sphere and a source in a uniform stream, U, written in cylindrical coordinates. The centre of the sphere is positioned at x=0 and the source atx=~d. The velocity inth e A'-direction in this field of flow isgive nby : 3 2 2 3 3 3 2 i 1 5 2 up= -k~=-U{\-r (x +a) )~ l* + /2r w (x +a )~ l + (12) (O ceo -b1(x +d)((x + d)1 + à1) _3/2} The part between braces in (12) is equal to c(x, c5)i nformul a (5). Muller et al. (1982) derived the velocity in the X-direction inside anexpandin g rotationally symme tric profile of length /: 160 1 I* r\A uv(x,t) = --jj — àx ,(taz) (13) 0 and U (0 A 0 t) u„(XJ) = ur(X,)+ " ^x /) - .(t>r) (14) These velocities were used by these authors to calculate the pressure (derived from the equation of motion): ;+ (a) " (b) (c) (15) (UihJ' a+1 (d) (e) The symbols areexplaine d in paragraph 7.1. 161 Curriculumvita e Ik ben geboren te Delft op 13 januari 1956. Vanj ejeug d moetj e genieten, vandaarda ti kbe nbegonne n omd ekleuterschoo l overt eslaan .Septembe r 1963 benik ,n aeni gprotest ,da ntoc hbegonne no pd elager eschool .Daa rmoe t"reke nen" mijn sterkste kant zijn geweest, althans dat suggereren de zorgvuldig be waarde rapportboekjes. Augustus 1968 ben ik overgestapt naar het Christelijk Lyceum voor Delft en Rijswijk. De sport (basketbal, volleybal en vooral atletiek) heeft gedurende mijn middelbare school periode een minstens even belangrijke rol gespeeld als hetleren .A lvroe ginteresseerd ei kmi jvoo rhe tfunctionere n vanhe tbewegings apparaat, eenbelangstellin g diegevoe d werdvanui t mijn sportieve aktiviteiten. Dezebelangstellin gbreidd ezic ha lsne lui tto tee nbreder ebiologisch einteresse . Nahe tbehale nva nmij natheneum- bdiplom ai nme i 1974, beni kda noo kbiolo giegaa n studeren aand eLandbouwhogeschoo l teWageningen . Na een min ofmee r afsluitende daad gesteld tehebbe n in het sportgebeuren door universitair kampioen te worden op de 800m hardlopen, heb ikjanuar i 1978mij n kandidaats-diploma behaald "met lof'. Inmij n doctoraal hebi kee n drietalonderwerpe n bewerkt: 1. Defuncti e van het branchiostegaal-apparaat in dezuigend e voedselopname doorvisse no.l.v .Prof .dr .J .W .M .Oss ee nDrs .M .Muller . 2. De ontwikkeling van de m. adductor mandibulae van Barbus conchonius o.l.v.Prof .dr .L .P .M .Timmerman se nDrs .P .M .G .Barends . 3. De rol van de pootspieren in de locomotie van Testudo o.l.v. Prof. dr. R. McN. Alexander en Mr. A. Jayes (University of Leeds, U.K.). Het ingenieursdiploma in de biologie heb ik op 23 januari 1980 "met lof" be haald. 1 december 1979be ni kgestar tme tee n3-jari gpromotie-onderzoek , waar van dit proefschrift een resultaat is.No g deze zomer hoop ik te beginnen met eennieu wonderzoeksprojec t aanhe tZoölogisc h laboratorium vand e Rijksuni versiteitt eLeiden . 163