Modelling, Instrumentation and Control in Marine Larviculture

Morten Omholt Alver

Modelling, Instrumentation and Control in Marine Larviculture DR.ING thesis

Norwegian University of Science and Technology

Thework onthis thesis hasbeenfunded throughan NTNU (NorwegianUni-

versity of Siene and Tehnology) sholarship, and has formed part of the

CODTECHprojet.

Iwouldliketo thankmysupervisors,JoArveAlfredsen,YngvarOlsenand

BårdHoland,forsharingtheirenthusiasm,knowledgeandgoodadvie.

ThankstoGunvorØieatSINTEFFisheriesandAquaultureforgreatlead-

ershipinrunningtheCODTECHexperiments,andforvaluableideasandfeed-

bak throughout these four years. Thanks to Atsushi Hagiwara at Nagasaki

University,forlettingmestayathislabinSeptemberDeember2005,andfor

ollaborationon rotifermodelling. This thesiswould nothavebeenwritten if

notforJensG.Balhen,whoinitiatedsheriesandaquaulturerelatedresearh

atourdepartmentmorethan35yearsago.

ThanksalsogotoTrygveSigholt,ToroddTennøy,OlavVadstein,ErikHøy,

Sunniva Kui, Tove Beate Leren, Ingrid Overrein, Werner Johansen and Per-

Arvid Wold,for good ooperationin variousexperimental work,andall kinds

ofhelpandadvie.

Aknowledgments i

ListofPapers v

1 Introdution 1

1.1 Objetives. . . 3

1.2 Outline . . . 3

2 The Marine LarviultureProess 5 2.1 EnvironmentalConditions . . . 7

2.2 Feeding . . . 9

2.2.1 FeedingRegimeandFeedIntake . . . 9

2.2.2 NutritionalRequirements . . . 11

2.3 LiveFeedProdution. . . 12

2.3.1 Algae . . . 12

2.3.2 Rotifers . . . 12

2.3.3 Artemia . . . 14

3 Methodsand Results 15 3.1 Instrumentation. . . 15

3.1.1 RotiferDensityMeasurement . . . 15

3.1.2 AutomatiFeeding . . . 18

3.2 RotiferPopulationModels . . . 22

3.2.1 Rotifersin FirstFeedingTanks . . . 22

3.2.2 RotiferCultures . . . 23

3.2.3 ModellingRotiferBodyComposition . . . 28

3.3 LarvalModel . . . 31

3.4 TheFirstFeedingSenario . . . 34

3.4.1 LiveFeedQualityAssessment. . . 34

3.4.2 LarvalBiomassEstimation . . . 36

4 Conluding Remarks 41

4.1 SummaryofContributions. . . 42

4.2 SuggestionsforFurtherWork . . . 42

5 Errata 45

Referenes 47

1. Alver, M. O., Alfredsen, J. A. & Olsen, Y., 2006. An individual-based

population model for rotifer(Brahionuspliatilis) ultures. Hydrobiolo-

gia560,93108.

2. Alver, M. O., Alfredsen, J. A. & Olsen, Y. An individual-based model

for prediting body omposition of ultured Brahionus pliatilisrotifers.

CanadianJournalofFisheries andAquati Sienes,submittedpaper.

3. Alver, M. O., Tennøy, T., Alfredsen, J. A. & Øie, G. Automati mea-

surement of rotifer Brahionus pliatilis densities in rst feeding tanks.

AquaulturalEngineering,inpress.

4. Alver,M.O.,Alfredsen,J.A.&Øie,G.,2005. Asystemfor model based

biomass estimation of larvae in intensive od larviultures. Aquaulture

International13,519541.

5. Alver,M.O., Alfredsen,J.A. &Øie,G.Estimating larval densityinod

(Gadus morhua) rst feeding tanks using measurements of feed density

andlarval growth rates. ProeedingsoftheLarvi2005onferene,Aqua-

ulture,submittedpaper.

6. Alver,M.O.,Tennøy,T.,Alfredsen,J.A.,Øie,G.&Olsen,Y.Automati

ontrolofrotiferdensityinlarvalrstfeeding tanks. ControlEngineering

Pratie,submittedpaper.

Introdution

Theold-watermarineshspeiesAtlantiod(Gadusmorhua L.)andAtlanti

halibut(Hippoglossushippoglossus L.)arerelativelynewaquaulturespeiesin

Norway(Olsen,1997). Thedevelopmentofulturemethodsforthesespeieshas

beenfaedwithsignianthallenges,partiularlybeauseoftheomplexityof

the larval rearing proess (Moksnes et al., 2004, pp. 15). Juveniles of both

speieshavebeenproduedinNorwaysinearound1990,but duetoproblems

with produtivity and preditability, the progressin prodution volumes was

poor in the period 19902000 (Engelsen et al., 2004). Sine year 2000, od

produtionhasinreasedstrongly,whilethevolumesoffarmedhalibut arenot

expetedtoinreaserapidlyduring thenextdeadeowingtotheslowprogress

ofjuvenileprodutiontehnology(Engelsenetal.,2004).

Preditableprodutionandlowprodutionostsarekeysforsuess,andin

Norwegianmarinelarviulturethere isstillalotto begainedin bothrespets.

Hatheriesoftenrelyonthepersonalexperieneofkeyemployeestoensuresta-

ble prodution. Monitoringand ontrol tehniques have played animportant

partin improving preditability and reduingosts in other industries (Haley

and Mulvaney, 1995; Jämsä-Jounela, 2001; Findeisen et al., 2003), but have

apparentlynotbeenwidelyappliedin aquaultureprodution. Dynami mod-

ellinghasalsonotbeenapplied veryextensivelyin aquaultureresearh, with

someexeptionssuhasSlagstadetal.(1987),Coneiçãoetal.(1998),Balhen

(1999)andAlveretal.(2004). Thepresentthesisispartofaneorttoaddress

theseissues.

This work is part of the university programme CODTECH A proess

oriented approah to intensive prodution of juveniles with emphasis on od.

Figure 1.1: Overviewof theprodution proess from eggs to metamorphosed

od larvae.

Theativitieswithin CODTECHaredividedinto fourprojets: 1. Modelling,

instrumentation,ontrolandoptimizationofhatheryproesses. 2. Larvalfeed

omponents. 3. Mirobialinterationsandontrol. 4. Controlledintensiverst

feeding and weaning of od larvae. The present thesis ontributes primarily

to Projet 1,whose title impliesthe appliation of yberneti methods to the

juvenileprodutionproess. Thebasiproessesinvolvedin theprodutionof

juvenilemarinesharesummarizedinFigure1.1. TheboxlabeledMonitoring

&ontrol indiateswhihelementsoftheprodutionproessthat this workis

primarilyfousedon.

Mathematial modelling hasanimportantrolein thiswork,and aswill be

learfromtheenlosedpapers,themodelsareusedfortwopurposes. First,they

serveastoolsfor desribingproess dynamis. Modelsimulationsanprovide

preditions for appliation in prodution planning and in assessing the eet

of model based ontrol systemsand state estimators. In this appliation, the

models are run in parallel with the atual proess and with instrumentation,

providing estimates of the urrent proess state beyond what an be readily

measured.

1.1 Objetives

Themain objetivesofthisworkareto:

ˆ Developpreditivemodelsofentralproesses,suhaslarvalrstfeeding

andtheultivationandenrihmentoflivefeed.

ˆ Use instrumentation in ombinationwith models to extrat information

from the prodution proess for variables that are diult to measure

diretly.

ˆ Implementautomationtrol inordertoimprovepreditability, optimize

produtionandreduemanuallabour.

1.2 Outline

ˆ Chapter 2 provides bakground on the marine larviulture proess, and

highlightsthehallengesinvolvedinthevarioussubproesses.

ˆ Chapter 3desribes themethods that have been developed, in the form

of mathematial models or physial equipment, and presents the main

resultsthathavebeenahieved. Theontentsofthis hapter aremainly

extrated fromthe enlosedpublished papers,whihgo into moredetail

onthevarious methodsandresults.

ˆ Chapter 4ontainsonluding remarks,asummary of theontributions

ofthisthesis,andsuggestionsforfurtherwork.

The Marine Larviulture

Proess

Itisreasonabletodrawomparisons betweenmarineaquaultureandtheul-

tureof salmonand trout, whih has been aremarkably suessfulindustry in

Norway,withaprodutionofnearly600.000tonnesin2005(Anon.,2005). De-

spite the great amount of knowledge obtained and tehnology developed for

salmonidaquaulture, and forthe ultureof other marinesh speiessuh as

sea bass (Dientrarhus labrax) and sea bream (Sparus aurata) (Oliva-Teles,

2000),thedevelopmentofulturetehniquesforold-watermarinespeieshas

posed signianthallenges.

Thehallengesofultivatingtheinitiallifestagesofmarinesharedierent

fromthose ofsalmonid prodution. Themostimportantdierenesarein the

sizeanddevelopmentalstage ofthelarvaeathathing,asmarineshtypially

hath at asmallersize (Moksneset al.,2004, Figure1.2)and anearlierdevel-

opmental stage. Forinstane, od larvaeat thetime ofhathing havenotyet

developedastomah,andthedigestivetratisonlypartlydeveloped(Kjørsvik

etal.,1991).

Marine sh larvae in aquaulture generally require live feed in the initial

phase,forreasonsthatanbeexplainedbyseveralharateristisofthelarvae.

First,feedingestion is triggeredby visualand hemialstimuli(Cahu andIn-

fante,2001),andbeauseofthelarvae'slimitedvisualrangeandmovementat

theearlieststage(AksnesandUtne,1997;Fiksenetal.,1998),thefeedpartiles

havetobesuspendedinthewaterolumninordertobeavailable.Formulated

feedstendtohaveahighsinkingrate,andmustthereforebedistributedinlarge

exessto overthe larvae's requirements (Cahu and Infante,2001). Livefeed

organisms,ontheotherhand,haveativeloomotion,andthusabetteravail-

abilityin thewaterolumn. Seond,verysmallfeedpartilesizes arerequired

to maththe larvae's mouthsizes, and thismaypose problemsin formulating

feeds. Forseabassatrstfeeding,CahuandInfante(2001)useddryfeedpar-

tiles of50150

µ

^{m in diameter. Preventingnutrient leakagefrom partilesof}

these sizes withoutreduing the digestibility of the feed is a signiantman-

ufaturing hallenge (Baskerville-Bridgesand Kling, 2000; Cahu and Infante,

2001). Third, sine the larvae's digestive systemis under developmentin the

initial larval stage,thediet must ontainthe requiredomponentsto support

theindution ofenzymeseretorymehanisms(Cahu and Infante,2001). The

live feed requirement may have other auses in addition to those mentioned

here.

The requirementfor livefeedis notabsolute, and someexperimental diets

havebeen shown to sustain growth and survival of larvae (Cahu and Infante,

2001). However,inthe nearfuture,it isnotpratiallyfeasibleto run aom-

merialfarming proessbasedonformulatedfeed only.

For several reasons, the use of live feed makes the ulture proess more

ompliated andostly.

1

First,the prodution oflive feedrequires signiant

amounts of tank spae, equipment, feed and manual work. Hatheries need

tobepreparedthatrotiferulturesansometimesunexpetedlysuer massive

mortality,inreasingtheoverallost(Papakostaset al.,2006).

Seond, live feed diers from formulated feed in that the organisms have

theirownmetabolismandthereforeamorevolatilebiohemialompositionor

nutritionalvalue. Therearefewavailablehoiesoflivefeedorganismssuitable

for intensive ulture, and therefore the body omposition of the organisms in

ulture typially mathes the requirements of the sh larvae poorly. This is

espeially trueforold-waterspeies withahigh requirementfor

n − 3

^HUFA

(highlyunsaturatedfattyaids)(Olsen etal.,2004,pp. 282284). Toompen-

sate for this the farmer needs to enrih the live feed with essentialnutrients

beforeusebyprovidingafeeddosageontainingtheneessarynutritionaladdi-

tions(Rainuzzoetal.,1997). Theeetofsuhanenrihmentlastsforalimited

timeonly,asthelivefeedorganismsmetabolizethenutrientsafterenrihment.

Third, live feed organisms arry their own baterial ora into the larval

rearing environment, and ontribute in this wayto a heavy mirobialload in

1

Onestudyshowsthatforseabassthelivefeedostswere79%ofthetotalostsduring

thetanks(Skjermo andVadstein,1999). Thedigestivesystemof thelarvaeis

initiallysterile,andisolonizedbybateriafromtheeggs,thewaterandfrom

ingestedfood(Vineet al.,2006). Shorttermenrihmentproeduresbeforeuse

of the live feed provides an energy-rih environment whih may inrease the

numberoffastgrowingbateriaarriedbythelivefeed. Someofthesebateria

may be harmful to the sh. However, ontrol of the miroora an also be

utilizedtotheadvantageofthelarvaethroughtheuseof probioti tehniques,

whihisurrentlyaeldofativeresearh(SkjermoandVadstein,1999;Huys

etal.,2001;Shields,2001;Planaset al.,2004;Vineetal.,2006).

2.1 Environmental Conditions

Marineshlarvae areulturedin ylindrialtankswith onialbottoms, with

sizesrangingfromjust afewlitersin researhfailitiesupto30m

3

ormorein

ommerialhatheries. Dierentinsidewalloloursareused,andtheolouran

infat haveanimportanteetonthelightonditionsandthelarvae's ability

to detet prey. For instane, Downing and Litvak (2000) found signiantly

better growth andsurvivalfor haddok (Melanogrammus aeglenus)larvae in

whitetanks ompared to blak tanks. Commerial sale tanks may be tted

withautomatileaningarmsthatsweepdeadlarvaeandfeedpartilesintothe

drain.

Abioti water quality parameters inlude temperature, salinity, dissolved

oxygenandammonia. Withinlowerandupperlimits,therateofbiologialpro-

essesinreaseswithtemperature,butabovetheoptimumtemperaturedeleteri-

ouseetsbeomemoresigniantandtheratefalls(HowellandBaynes,2004).

Highertemperatureanallowfasterlarvalgrowthupto anoptimumlevel,but

beauseof dereasingfeed utilizationand survival,thetemperaturegivingthe

mosteientgrowthistypiallylowerthanthatgivingthefastestgrowth(Jor-

daanandKling,2003). Forod,theoptimumtemperatureforgrowthratehas

been shown to inrease from 9.7 to 13.4‰ aslarvae grow from 73 to 251

µ

^g

(HowellandBaynes,2004).

Thesalinityofseawateristypiallyaround35pptoshore,andanbe3233

ppt in oastal areasaeted by freshwaterrun-o from the land (Howell and

Baynes, 2004). Salinity aets both the energy required for osmoregulation,

andthebuoyanyofeggsandlarvae(HowellandBaynes,2004). Aninreasein

salinityfrom 32.3ppt to35.5ppt hasbeenshownto haveanegativeeeton

themorphologial developmentof halibut yolksa larvae (Bollaand Ottesen,

Dissolved oxygen is required for the larvae's respiration, and the onen-

tration needs to be above aertain minimum level, dependent on speies. A

onentrationof5mgl

−1

isonsideredaeptabletoaquatiorganismsingen-

eral(HowellandBaynes,2004). Thesolubilityofoxygenisstronglyaetedby

aombinationoftemperatureandsalinity,withhighertemperatureandhigher

salinity giving lowersolubility. Theoxygenlevel alsodepends on thebalane

betweenonsumptionandsupply,withonsumptionbeingespeiallydependent

onfeedingrate.

Ammonia(NH

3

^{)andammoniumions(NH}

+

4

^{)areexretedbytheshlarvae,}

and these twoforms exist in a hemial balaneaeted bypH in partiular,

butalsobytemperatureandsalinity(HowellandBaynes,2004). BothNH

3

^and

NH

+

4

^{are toxi, but NH}

3

^{to amuh higherdegree. Inreasing pH leadsto an}

inreasein theonentrationofunionizedammonia,whihmustbeheldbelow

aspeies-dependentlimit.

The exhange rate of water is typially in the interval 18 tank volumes

perday, inreasing throughout the rst few weeks after hathing. The water

exhangerateisimportantfortheadditionofoxygenandremovalofammonia,

butahigherexhangerateleadstofasterdepletionoffeedorganisms,andauses

strongermehanial fores at theinow andoutow points. These fores an

ause damage to the larvae, and may put a limiton the maximum exhange

ratethatanbeused.

Water treatmentsystemsanbedividedinto ow-through systemsandre-

irulation systems. In the former, water is mehanially ltered, heated or

ooled to theorret temperature, aerated,and de-gassedto avoidgas super-

saturation. Forreduing baterialnumbers,the water maybetreatedby UV

radiation or ozone injetion. Thewater is only used one. Ina reirulation

system,aertainfrationoftheoutletwaterisreused. Thisreduestheamount

ofwaterenteringthefaility,andtherebytheloadontheinitialwatertreatment

system. Nitrogenousompoundsaumulatinginreirulationsystemsarenor-

mallyremovedbybiologialltering(vanRijn,1996). Reirulationanallow

amoreonstantandontrollablewaterqualitythanow-throughsystems(At-

tramadal,2004). There is urrentlynogeneralonsensusastowhih strategy

ispreferable,andtheoptimalhoiedependsonwhihspeiesisultured.

Developmental deformities are oftenenountered during the proess of es-

tablishingulturemethodsfor newspeies(BrownandNúñes, 1998),andthis

has also been the ase with od and halibut (Bollaand Ottesen, 1998; Olsen

etal.,1999;Grotmoletal.,2005;Imslandetal.,2006). Thesuseptibilityoful-

tivatedshtodeformitiesmaypartlybeausedbyahighsurvivalrateoflesst

deieniesinthefeed(BrownandNúñes, 1998).

2.2 Feeding

Under favorablerearing onditionsod larvae anshowahigh growthrate of

morethan20%weightinreaseperday(Otterleietal.,1999;Finnetal.,2002).

Thisgrowthratenaturallyleadstoarapidinreaseinfoodrequirements,whih

onthe population level is ountered by a relatively high mortality rate. The

food requirementfor eah larval tankis a funtion of both larval growth and

development,and thenumberofsurvivinglarvae.

2.2.1 Feeding Regime and Feed Intake

Atatemperatureof6‰,theyolksaofodlarvaeisabsorbedinabout6days

afterhathing(Finnetal.,1995a).Feedingwithrotifersisinitiatedonday35

post-hath,andtherotiferfeedingstagenormallylastsbetween20and40days

(Brown et al., 2003). If Artemia is used, its introdution is made gradually,

replaing rotifers when the larvae reah about 89 mm in length (Rosenlund

etal.,1993). However,itisalso possibletointrodueaformulatedfeedatthe

endoftherotiferphase,exludingtheuseofArtemia(Baskerville-Bridgesand

Kling,2000). The majority of od hatheriesin Norwaydo not useArtemia.

Forhalibutlarvae,eventhelargestrotifersarenearthesmallestaeptablefeed

partilesize,andArtemiaisommonlyappliedastherstandonlytypeoflive

feed(Olsenetal.,2004).

Intherotiferperiod,odlarvaeanbefedeitherinseveralbathesperday,or

moreontinuously. Bathfeedingwith34feedingsperdayisthemostommon

method,bothinommerialhatheriesandresearhfailities. Feedavailability

isstronglyaetedbythewaterexhangerate. Theout-owingwaterisltered

to retain the sh larvae, but the rotifers ow out freely. Together with feed

ingestionbythelarvae, thisausestherotiferdensitytodereaserapidly after

eahfeeding. Figure2.1 showsameasurementseries demonstratingthehighly

dynamionentrationof rotifersin larvaltanks. The waterexhange ensures

alimitedresidenetimefortherotifersin thelarvaltank,eveniftheingestion

rateofthelarvaeislow.

Underabathfeedingregime,theoptimalrotiferdensityforodlarvaewith

regardto larvalsurvivalandgrowthhasbeen foundto be4000l

−1

(Puvanen-

dranandBrown, 1999;Puvanendran et al.,2002). It isworthnotingthatthe

−1

9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 0

1000 2000 3000 4000 5000 6000 7000 8000

Days

Rotifers l −1

Figure 2.1: Automati measurements of rotifer density in a od larval rst

feeding tank. The gray lines indiate feeding times. The measurements are

fromdays9and10ofanexperimentwhihispresentedinPaper5.

meaningthat theaveragedensitywill be signiantlylower. Theuseofbath

feeding has probably been motivated mostly by pratial onsiderations, and

there is noevidene of bath feeding beingthe optimalstrategy for ahieving

high growth and survival. For red porgy (Pagrus pagrus), whih has a high

feedrequirement,Papandroulakiset al.(2004)ahievedfavourableresultswith

automatedontinuousfeeding.

Fish larvae are believed to be number maximizers, whih means that feed

intakeinreaseswithpreydensityevenathighdensities,asopposedtoreahing

asaturationlevel(Lubzensetal.,1989;Hoehne-Reitanetal.,2001;Olsenetal.,

2004). There ismost likely anupperlimit tothe feedingestion rate, andthis

limitis an eet of the minimumtime required to apture andhandle a prey

organism. Severalmathematialmodelshavebeenpublishedthat desribethe

foragingbehaviourofpelagishlarvae (Fiksen etal., 1998,2002;Fiksenand

Folkvord,1999;FiksenandMaKenzie,2002)basedonsuhvariablesasvisual

tendedforlarvaeinthewild,wherefoodlimitationisasigniantrisk,andmay

notbeappliablefortheaquaulturalsetting, wherefoodisabundantmostof

thetime. Whenfoodisabundant,theeetofhandlingtimeismoresigniant,

andthis elementis typiallyignored by thefeed ingestion models. There is a

limitedamountofdatafrombehaviouralstudiesontheatualingestionrateof

livefeedbyodlarvaeinulturetanks(Munk,1995;Puvanendranetal.,2002).

2.2.2 Nutritional Requirements

The sh larvae require an adequate supply of the major nutrient lasses to

overenergyrequirementsandsupportgrowth,but thefeedmustalsoontain

anumberofspeiessentialomponents. Thereisasigniantamountofdata

ontheatualbodyompositionofthelarvae,e.g. Finn etal.(1995a)andFinn

et al.(1995b), whih an beexpeted to providelues abouttheir nutritional

requirements. The sh larvae an to aertain degree metabolize omponents

toovertheirneeds,butsomefattyaids,aminoaidsandmironutrientssuh

asvitaminsand minerals,annotbesynthesized bythelarvae,andneedto be

suppliedin thefeed. As mentionedearlier, deformities anoften be linked to

deieniesinthenutritionalvalueofthefeed(BrownandNúñes, 1998).

Thenaturaldiet ofthe shlarvae, onsistinglargely ofopepods for old-

watermarinespeies,anbeexpetedtoprovideanearperfetnutritionalvalue.

Copepodshavebeenharvestedandutilizedasfeedinextensiveulturesystems,

buttherehassofarbeenslowprogresstowardsmass-ulturetehniquesforthese

organismsexeptinsmall-salelabulturesoflimitedduration(Støttrup,2000).

Beauseofthesediulties,rotifersandArtemiaarethemostviablehoiesfor

intensiveulture,andfarmersmustoveromethehallengeofproduingrotifers

andArtemiamanipulatedtoontainsuientamountsofessentialomponents.

Researhonthenutritionalrequirementsofmarineshlarvaehastoalarge

extentfousedonlipids,andespeiallyontwoessentialfattyaids: doosahex-

aenoiaid,22:6

n − 3

^(DHA),andeiosapentaenoiaid,20:5

n − 3

^(EPA).These

fattyaidsareabundantinthetissueofthelarvae(Rainuzzoet al.,1992),and

itappears that both ahigh ontentofDHA andahigh ratioof DHAto EPA

in the feed appearto beimportant for the developmentof old-watermarine

larvae (Sargentet al., 1999;Kjørsviket al.,2004). Oneverystrikingeet of

lowDHAontentandlowDHA:EPAratioismalpigmentationofatshlarvae

suh as turbot (Reitan et al., 1994). Arahidoni aid, 20:4

n − 6

^{(ARA), is}

anotheressentialfattyaid. BoththeontentofARAandtheEPA:ARAratio

2.3 Live Feed Prodution

2.3.1 Algae

Miroalgae suh as Isohrysis galbana, Nannohloropsis oulata, and Chlorella

vulgarisareusedintheprodutionoflivefeed. However,theyanalsobeadded

to thelarvaltanks in what isknownasthegreen water tehnique,to serveas

feedbothfortheshlarvaeandforthelivefeed(Reitanetal.,1997). Addition

ofmiroalgae hasbeenshownto improvebothgrowthand survivalforturbot

(Shophtalmus maximus)andhalibutlarvae(Reitan etal.,1993,1997). There

are probably several reasons for this eet, inluding the stabilization of the

nutritionalvalueofthelivefeedthroughpreventingstarvation,diretingestion

of algae by the sh larvae, and apositive eet of the algae on the baterial

oraof thetanks (Reitanet al.,1997). Themoderateturbidityaused bythe

algae analso be afator in enhaningthe ontrastofprey organismsagainst

thebakground(Shawet al.,2006).

Miroalgae aretypiallyprodued in large,shallowtanks orin transparent

tubes. The supply of lightis an important growth regulator,along with pH,

salinity,temperature,turbuleneandthequalityandquantityofnutrientspro-

vided. The ombination of all these fators determine the maximum growth

rate andthe arryingapaityof a miroalgaulture. Thegrowthurveof a

bathulturefollowsseveralphasesfromtheinitiallagandexponentialgrowth

phases,untiltheulturestagnatesand nallyollapsesbeauseofnutrientde-

pletion. The nutritional value of the algae hanges with the growth phases,

andisbetterintheinitialphasesthanafter growthstagnatesattheendofthe

exponentialphase(Coutteau,1996). Algaeanbegrownsemi-ontinuouslyin

ultureswith regulardilution andharvesting, whih animprovethestability

oftheirnutritionalvaluebyprolongingtherapidgrowthphase.

There arewellestablishedtehniquesfortheprodutionofmiroalgae,but

itislabourintensiveandexpensive. Farmersommonlypurhasealgaepasteor

ommerialondensedChlorella ratherthanproduingtheirownalgae.

2.3.2 Rotifers

Rotifers of the speies omplex Brahionus are used asthe rst feed for od

larvae and numerous other marine speies (Lubzens et al., 1989; Papakostas

etal.,2006). Rotifersarelter-feedingplanktoniorganismsfoundin salinities

from fresh water to seawater, in a wide range of temperatures. They vary

signiantlyinsize,withlengthsof150270

µm

^{beingtypialforrotifersusedin}

aquaulture. Rotifersingeneralanreproduebothasexuallyandsexually,with

thelattermoderesultingintheprodutionofrestingeggs(PourriotandSnell,

1983). The frequenyof sexual reprodution varies between strains, however,

andthestrainsusedaslivefeedforodreprodueasexuallyonly. Manyrotifer

strainslose thesexualreprodution mode after sometime in ulture, beause

theommonulturemethodsfavorasexualreprodution(Hagiwara,1994).

Rotifer tanks are supplied with strong aeration, and feed is added either

ontinuously orin bathes. Theulturegrowthdynamis anbedesribed as

havingalagphasewithlowgrowthinthebeginning,thenanexponentialgrowth

phase before growth stagnates due to food or other limitations. Maximum

spei ulture growthrates an reah 0.41.6 (Hagiwara et al., 1998; Olsen,

2004)dependingontherotiferstrainandultureonditionssuhastemperature

andsalinity. Toahievesteadygrowthoneanharvestrotifers andreplaethe

ulturewatereitherontinuouslyorperiodially. Thealternativeistorunpure

bathultures,whihareharvestedompletelyonetheyreahtheendoftheir

exponentialgrowthphase.

The body omposition of rotifers is inuenedstrongly bothby their feed

and by the ulture growthrate (Frolov et al., 1991; Øieet al., 1997; Øie and

Olsen,1997;Lieetal.,1997),andtheirnutritionalvaluemustbeensuredtobe

adequatefortheshlarvaebeforeuse. Baker'syeasthasalowost,andisoften

used asthe main feed. However, asthe sole feed it leadsto rotifers with too

lowlipidontentandashortageofessential

n − 3

^{HUFA(Lubzensetal.,1989).}

Typially, yeastis usedwith a10%addition ofanoilemulsion toimprovethe

ompositionandamountoflipids(Olsen,2004,pp. 8081).

There are two main strategies suggested for obtaining a suient nutri-

tionalvalueofrotifers,alledshort-term enrihment andlong-termenrihment

(Rainuzzoet al.,1994;CoutteauandSorgeloos,1997). Whenusingshort-term

enrihment,the rotifersanbeulturedusing aheapdiet, andenrihedwith

aarefully seletedand formulatedfeed for aperiodof 224hours before use.

Thedisadvantagesofshort-termenrihmentareanexessivetotallipidontent,

shortretentiontimeofthenutrients,andpossibleproblemswithwaterquality

when adding the rotifers to the larval tanks (Dhert et al., 2001). Long-term

enrihmentis aombinationof growth andenrihment, where

n − 3

^{HUFA is}

inorporatedduring growth. Long-termenrihmentgenerally leadsto a more

2.3.3 Artemia

Artemia,orbrineshrimp,isarustaeanwithanadaptationtoextremelyhigh

salinity levels. Innature,Artemiaare foundonlyat high salinitylevelswhere

theirpredators annotsurvive(vanStappen, 1996),but despite this, Artemia

anbeulturedatthesalinitylevelofnormalseawater. Oneadaptationtotheir

extremenaturalenvironmentistheabilitytoprodue restingeggsalledysts

in preparationofadverseenvironmentalondition. Theystsanlaydormant

for years before hathing, and an be spreadto other loationswith the help

ofmigratingbirds. Artemiaystsareharvestedfrom theshores ofhypersaline

lakesatseveralloationsintheworld,andareavailableasaommerialprodut

(vanStappen,1996).

Artemia ysts used in prodution of larvalsh are disinfeted and deap-

sulatedbefore beinginubated for upto 24 hours, depending ontemperature

andhathing synhrony(vanStappen, 1996). Afterhathing, theyneedto be

enrihed foranother1224hoursbeforeuse. Artemiaanbegrownfor longer

periodsinordertoobtainlargersizes. UseofsuessivelylargersizesofArtemia

during theperiod 060dayspost-hathhasbeenfoundto improvetherateof

ompletepigmentationandmetamorphosisofhalibutlarvae(Olsenetal.,1999).

Ahieving asuientrelativeontent ofessentialfattyaidssuh asDHA

andEPAinArtemiaisdiult,andalsoleadstoaveryhightotallipidontent

omparedtothefeedorganismsofthelarvaein nature(Evjemo,2001,p. 25).

Methods and Results

3.1 Instrumentation

3.1.1 Rotifer Density Measurement

Intheperiodwhenodlarvaearefedwithrotifers,asuientdensityofrotifers

isimportanttoahieveahighgrowthrate. However,withmanualsamplingand

ountingonlyitisalabourintensivetasktomonitorthisvariable. Aordingto

thedynamisoftherotiferdensityinrstfeedingtanksthiswillrequirefrequent

measurements,asthedensityhangeswith atimesaleontheorderof 1hour

(seeFigure 2.1). Monitoring therotiferdensityouldbeequallyimportant in

rotiferulturetanks,wherethedensitiesarefarhigher.

AutomatiountingandsizemeasurementofrotifersusingaCoulterounter

has been applied by Boraas (1983) and Walz et al. (1997) in hemostat and

turbidostat ulture systems for rotifers. However, a general-purpose oulter

ounterisexpensive,andisnotaonvenientinstrumentforuseinaommerial

shhathery. A dediatedinstrumentformeasurementof rotiferdensitieshas

been developed under the CODTECHprojet, providing asystem forregular

measurements in a set of tanks without manual intervention (Tennøy, 2003).

Theounterisfurtherdesribedin Paper3.

Figure 3.1 shows anoverview ofthe rotiferounter. It is equipped with a

numberoftubesforextratingsamples,andusesomputerontrolledmagneti

valves to open for one tube at a time. Eah tube is tted with a 0.5 mm

lterat the end to prevent shlarvae from being extrated. Thepump pulls

waterfromthetankthroughtheobjetglass,whereaknownvolume

V

^[ml℄is

Figure3.1: Overviewoftherotiferountersystem. Thegureisfrom Paper3.

photographedbyadigitalamera. Lightingisprovidedbyyellowlightemitting

diodesmountedinasquarewithfourdiodesalongeahside. Thesquareisset

belowtheobjetglassinaplaneparalleltotheglassplates,atadistanehosen

sotheamera'sangleofvisibilityfallsbetweentheLEDs(seeFigure2inPaper

3). Thissetupprovidesdarkeldlighting,wherelightisreetedbypartilesin

thewater,ausingrotifersandotherpartilestoappearintheimagesasbright

spots againstadarkbakground.

Imagesareaptured ingraysale. Tolteroutstationaryrotifers orother

partiles, thepreviousimage issubtrated from eah newimage, removingall

thelightareasandpartilesthat werealsopresentin thepreviousimage. The

image is then thresholded (onverted to binary form), and partiles loated

and ltered by area, elongation and roundness. The remaining partiles are

ounted,and theresultdividedbythevolume

V

^{toahieveanestimateof the}

to representthesize and shape of therotifers,and haveto beadapted to the

rotiferspeiesused.

Theounter takesimages in rapid sequene, runningthe pump briey be-

tweeneah imagetoreplaethesamplevolume. Afterasequeneof

N

^images

(determinedby theoperator),thepumpis runforalongerperiod toushthe

entire tube. The meandensity found in those

N

^{images is logged asasingle}

datapoint.

The statistial properties of the measurements are derived in Paper 3. If

the truerotifer density is

ρ

^{[rot. ml}

⁻¹

^{℄ and the number of pituresused per}

measurementis

N

^{,thesamplingvarianewillbegivenas:}

σ ² = ρ

N V

^(3.1)

whih means that the standard deviation is inversely proportional with

√ N

andwith

√ V

^,andinreasesproportionallywith

√ ρ

^{. Theoeientofvariane}

isinverselyproportionalto

√ ρ

^{, andthe} measurementsare thereforerelatively moreaurateat higherdensities. Wean inuene auraybyadjustingthe

N

^and

V

parameters.

Afteraseriesoftestounts,themeanvaluesandthesamplevarianesanbe

studiedto determine thepreisionand therepeatabilityof themeasurements,

respetively. Figure 3 in Paper3 shows the automatimeasurements plotted

againstthemanualontrolounts. Theresultsfromtheounterfallfairlylose

tothemanuallyountedvalues. Figure4showsthesamplestandarddeviation

of the same measurements plotted againstthe theoretial minimum standard

deviation. The observed variane is as expeted, apart from asmall positive

bias. Thebiasindiatesthatsomeadditionalerrorisintroduedintheounting

proess,butthestatistialunertaintydue tosamplesizelearlydominates.

Highdensity rotifer ultures

Whentheounter isused for monitoringrotifer ultures, densitiesmaybeon

theorderof 1000rotifers ml

−1

orhigher. Fordensitiesof this magnitude,the

proessofountingrotifersasindividualpartilessuersinreasingerrorsdueto

severalrotifersforminglustersinthepitures. Iftheseannotbeidentiedas

suh,themeasurementwillunderestimatethedensityforhighdensitysamples.

To address this error soure, several alternative algorithms for high density

3.1.2 Automati Feeding

Formanualfeedingofshlarvaeintherotiferperiod,thestandardproedureis

toestimatethenumberneededineahtankinordertoreahapredenedfeed

density. An experiened operator anmakean eduated guess of theurrent

densitybyvisualinspetion,andalulatetheapproximatenumberofrotifersto

add. Thedensityofrotifersintheenrihmenttankismeasured,andtheorret

amountextratedandwashed,typiallywithanadditionof10%toaountfor

handlingloss. Finallytherotifers areadded to eah ofthe tanksby manually

measuringouttheorretamounts.

This proedure an be automated to onsiderably redue the amount of

manualworkandthevariabilityinrotiferdensity. Oneexampleofanautomati

feedingsystemisthatpresentedbyPapandroulakisetal.(2002),whihprovided

ontinuousfeedingin apurely feed-forwardmannerbasedonfeedrequirement

tablesormanualdosagesetup.

Paper 6 desribes the appliation of feedbak ontrol in order to ahieve

appetite-basedfeeding. Theadvantageoffeedbakontroloverafeed-forward

systemis that thefeed will notbedepletedregardlessof theingestion rateof

theshlarvae. Thefeedbakontrollertherebydeouplesfeedsupplyfromfeed

density,andprovidesahighdegreeofexibilityinthehoieoffeedingregime.

Figure 3.2 showsanoverviewof theontrol system. Theautomatirotifer

ounter desribed in Setion 3.1.1 provides measurementsof the urrent feed

density,usingavalvemanifoldtopullsamplesfromeah ofthelarvaltanksin

turn. Theontrollerpumpsrotifersfromareservoirintothelarvaltanks,using

asimilarvalvemanifoldtodirettheow. Theonlymanualworkinvolvedisthe

regularrellingofthereservoir.Therotiferdensityinthereservoirismeasured

manually,butthismeasurementouldalsobeautomated.

The density ontroller is implemented using a model-based approah, for

three reasons. First, when ontrolling several tanks using the same ounter,

new measurements are only available a few times per hour. The ontroller

should beableto omputeinputvaluesmorefrequently. Seond,thereanbe

signiantmeasurementerrorineahsinglesample(seePaper3),andamodel

based approah makesit possible to lter the data and redue the impat of

errors. Third,this strutureallowstheestimationofthe totalfeedintakerate

ofthelarvae,whihisanimportantmetriforthestatusandprogressoflarval

growth.

The proess model of the ontroller is very simple, orresponding to the

rotiferdensitymodeldesribedin Paper5,butdisregardingbothreprodution,

Figure3.2: Overviewoftheontrolsystem. Solidurvesrepresenttubes,while

dashedlines representdata transmissionand ontrollines. The ounter and

ontroller are both implemented in the same omputer. The gure is from

Paper6.

therotiferlossdueto dilutionand ingestionbythelarvae. Thedilutionlossis

assumedtobeproportionaltothemeasurablewaterdilutionrate. Theingestion

termisnotdiretlymeasurable,butanbeestimatedbytheontroller. Adding

the feed ingestion rate asa seond model stateresults in thefollowinglinear

model:

R(t) = ˙ u(t) − q(t)R(t) − I(t) + v D (t)

^(3.2)

I(t) = ˙ v I (t)

^(3.3)

where

R

^{is the rotifer density,}

I

^{is the larval ingestion rate,}

q

^{is the water}

exhangerateand

v D

^and

v I

^{arerandomnoiseterms.}

Ifwedenethestatevetor

x = [R I] ^T

^{andthenoisevetor}

v = [v D v I ] ^T

^,

weanexpressthesystemasfollows:

˙

x = f (x, u) + I 2×2 v

^(3.4)

where

I 2×2

^{isthe2x2identitymatrix,and:}

f (x, u) = 1

0

u + Ax

^(3.5)

A =

− q(t) − 1

0 0

(3.6)

We need to dene a measurement model

y(t)

^{to represent the predition of}

measurementsfromthemodel. Ouronlymeasurementisoftherotiferdensity:

y(t) = R(t) + w(t) = Dx(t) + w(t)

^(3.7)

where

D = [1 0]

^and

w

^{is the} measurement noise. Given this measurement model the system is observable(see Paper 6), and by use of a Kalman lter

(Jazwinsky, 1970)the deviationbetween preditedmeasurements

y(t)

^anda-

tualmeasurementsanbeusedtoadjustthemodelandobtainestimatesofthe

rotiferdensity

R(t)

^{andtheingestionrate}

I(t)

^{loseto thetruevalues.}

The ontroller omputes the input value based on the urrent estimated

rotiferdensity, denoted

R(t) ˆ

^{. Theontrol algorithm isaPI ontrollerwith an}

addedfeed-forwardtermtoaountforthelossofrotifersthroughtheestimated

ingestionrate(

I(t) ˆ

^{)andthewaterexhangerate. Finally,theinputisrestrited}

tononnegativevalues:

u(t) = max 0, h

I(t) + (q(t) + ˆ K p )r(t) − K p R(t) + ˆ h(t) i

(3.8)

where

r(t)

^{is thereferenedensity,}

K p

^isthe proportionalgainand

h(t)

^{is the}

integratorvalue.

The ontrol systemhas been tested in aomplete rst feeding experiment

with9tanks (80l)keptat dierentrotiferdensityset points(19 rot. ml

−1

).

To verify the atual rotifer densities in the tanks, 50 ml samples were taken

from eah tanktwotimesperday,and analyzedforrotiferdensity. Figure3.3

showsboththemanualmeasurementsandtheontroller'smeasurementsforall

the9tanks.

The resultsdemonstratedthat theontroller performed satisfatorily,with

theexeptionofsomedeviationsobservedinonnetiontopratialproedures

suh asadditionofalgaetothewater,andleaningofthetankbottoms. Both

theseproeduresdisturbedtheontroller'smeasurementstemporarily.

Theontrolsystemallowsaredutioninmanuallabourbyautomatingthe

feeding. Itsusageisnotrestritedtoonstantfeeddensitiesasused intheex-

5 10 15 0

0.5 1 1.5 2 2.5

Days 1/ml

5 10 15

0 1 2 3 4 5

Days 2/ml

5 10 15

0 2 4 6 8

Days 3/ml

5 10 15

0 2 4 6 8 10

Days 4/ml

5 10 15

0 5 10

Days 5/ml

5 10 15

0 5 10 15

Days 6/ml

5 10 15

0 5 10 15

Days 7/ml

5 10 15

0 5 10 15 20

Days 8/ml

5 10 15

0 5 10 15 20

Days 9/ml

Figure3.3: Manual rotiferdensitymeasurements(X)and automatimeasure-

ments (gray dots) in eah of the experimental tanks. Tanks are ordered by

inreasingreferenedensity. Foromparison,astraightlineshowsthereferene

densityforeahtank.

bathwisefeedingorotherpatterns. Inadditiontobeingatoolforommerial

farmers, the ontroller provides wide opportunities for researhers in investi-

gatingfeed ingestionpatternsoftheshlarvae, andinndingoptimalfeeding

3.2 Rotifer Population Models

Mathematialmodelsdesribingpopulationdynamisofrotifers havebeende-

veloped for two dierent settings that impose dierent requirements: rotifer

produtionulturesandrotifersafteradditiontorstfeedingtanks. Intherst

feedingsenario,thetemperatureislow,andthereisstrongpredationpressure

in addition to rotifers beingremoved due to water dilution. As a result, the

residene time of eah individual rotifer is low, and the dominant dynamial

variable is the population density. In rotifer ultures the environmental and

feeding onditionsareoptimizedfor fastpopulationgrowth, andthe eggratio

and agestruture of thepopulationhave amarkedinuene on theexpeted

growthrateforthenear future.

3.2.1 Rotifers in First Feeding Tanks

Rotifersinrstfeedingtanksaremodelledusingasimplemodelthatdisregards

mostindividualdierenesandinternaldynamisoftherotifers.Thismodelis

usedin Paper4and Paper5, andin asimplied formin Paper3. Themodel

has4statevariables:

ˆ

N c

^{: Thenumberofrotifers inthewaterolumn.}

ˆ

N w

^{: Thenumberofrotifersattahedtothetankwall.}

ˆ

E c

^{: Thenumberofeggsarriedbyrotifers inthewaterolumn.}

ˆ

E w

^{: Thenumberofeggsarriedbyrotifersattahedtothetankwall.}

The separationbetween rotifers in the water olumn and on the tank wallis

madebeauserotifersattahedtothewallarenotsubjettowaterdilution.

The state equations for the rotifermodel, as presented in Paper 5, are as

follows:

dN c

dt = u + (E c + E w )h e − M w + M c − p c − q c

^(3.9)

dN w

dt = M w − M c − p w

^(3.10)

dE c

dt = ue u − E c h e − E c

N c (M w + p c + q c ) + E w

N w M c

^(3.11)

dE w

dt = − E w h e + E c

N c

M w − E w

N w

(M c + p w )

^(3.12)

wheretheontrolledvariablesare

u

^{,theadditionrateofrotifersintothewater}

olumn,

e u

^{,theeggratiooftheaddedrotifers,and}

Q w

^{,theexhangerateofthe}

tankwater(theturnoverrateofthewatervolumeperday).

Q w

^determines

q c

^,

thelossrateofrotifers fromthewaterolumnausedbythewaterexhange.

Themodeldisregardsmortalitythatisnotausedbypredation,beausethe

shortresidene timeeliminatesany signianteet ofthis fator.

1

Predation

by sh larvae is onsidered a disturbane, and aets all states through the

variables

p c

^{, predation rate in the water olumn, and}

p w

^{, predation from the}

tankwall. Migrationrateofrotifersbetweenthewallandwaterolumn states

isrepresentedby

M w

^and

M c

^{. Rotifer}reprodutionisrepresentedthroughthe hathing rate

h e

^{of eggs, but produtionof new eggs is} disregarded. Paper 4 inludes a termrepresenting eggprodution, but due to the low temperature

andshort residenetime this fatorisof minorimportanein astandardrst

feedingsettingwithold-watersh.

TheexperimentdisussedinPaper3providesdataforevaluatingtherotifer

model. A163ltankwasset upwithtemperature,lighting,aerationandwater

exhange rate similar to that of a rst feeding tank, but without sh larvae.

Rotifers were added to the water olumn several times. The rotifer ounter

was set up with sampling tubes at four dierent loations within the tank,

andmademeasurementsthroughoutthewholeexperimental period. Wemade

theassumption that the arithmeti meanof the density measuredat the four

measurement loations was representative of the overall density in the water

olumn,andplottedthemeaninomparisontothemodel'soutput(Figure3.4).

Twomodelsimulationsareshown,oneusingthemodelasdesribedabove(solid

line),andonewhererotifersattahingtothewallweredisregarded(dashedline).

Theomparison showsa very good t forthe omplete model. It also shows

thatthedensityislearlyoverestimatedintheinitialperiodwhendisregarding

the wall state. Obviously, the signiane of the wall state depends on the

surfae-area-to-volumeratioofthetank(inthisasea. 0.1m

2

/m

3

),andwill

belessimportantforlargertanks thantheoneusedinthisexperiment.

3.2.2 Rotifer Cultures

Amodeldesriptionofarotiferulturewherepredationandwaterdilutionare

not dominant fators an be found by introduing fators suh as maximum

growth rate, arrying apaity and steady-state mortality rate (Olsen, 2004).

Toinvestigatepopulationtransients,however,suh amodelisinsuient. For

1

0 5 10 15 20 25 30 35 40 45 50 0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Hours

Rotifers l −1

Modelled values, original model Modelled values w/o wall state Measured values

Figure3.4: Automatimeasurementsmadeina48hourexperiment,ompared

with model simulations with and without a state value representing rotifers

attahed to the wall. Thevalues are averages of measurements made at four

dierentloationsina163ltank. Thegureis fromPaper3.

instane, MNairet al.(1998)demonstratetheinabilityof lassialhemostat

populationmodelsto aountfor transientonditionsand phenomenadealing

with population struture. The authors also present a simple physiologially

struturedpopulationmodel.

InPaper1,anindividual-basedpopulationmodelforrotiferulturesis de-

rivedbasedondynamienergybudget(DEB)theory,asdesribedbyKooijman

(2000). Inthemodel, aseparationis madebetweenstrutural volume anden-

ergyreserve. Theenergyreserveisenergyavailableformaintenane,growthand

reprodution,whilethestruturalvolumerepresentstheirreversibleinvestment

inbodystruture. Figure3.5showsanoverviewoftheindividualmodel.

Thestateequationforthestruturalvolume

V

^isasfollows:

dV

dt = (κ p ˙ C − p ˙ M )/[E G ]

^(3.13)

where

p ˙ M = [ ˙ p M ]V

^(Jm

⁻³

^day

⁻¹

^{)is the}temperatureorretedmaintenane rate, and

[E G ]

^{(J m}

⁻³

^{) is the} volume-spei ost of growth. The ux

p ˙ C

representstheonsumption rateof energyfrom thereserve, andis referredto

astheatabolirate:

˙

p C = [E]([E G ] ˙ vV ^{2 / 3} + ˙ p M )

[E G ] + [E]κ

^(3.14)

Thisexpression ishosento obtainsimple rst-orderdynamis forthereserve

density

E/V

^{(Kooijman, 2000). The rate of hange of the energy reserve}

E

equalsthedierenebetweentheassimilationrate

p ˙ A

^{andtheatabolirate:}

dE

dt = ˙ p A − p ˙ C

^(3.15)

wheretheassimilationrateismodelledasaHollingType2funtionalresponse

(Holling,1965)withamaximumrateproportionalto

V ^2/3

^:

˙

p A = X

X + X K { p ˙ Am } V ^2/3

^(3.16)

where

X

^{is the feed density and}

X K

^{is the} half-saturation onstant for feed intake.

Ifthe ataboli rate

p ˙ C

^{is toolowto support growth, i.e. Eq. (3.13) gives}

negativegrowth,theindividualisonsideredtobestarving. Starvationismod-

elledbyassumingthatallgrowthandreprodutionisstopped,andenergyisonly

expendedtoovermaintenane. Thus,

dV

dt = 0

^,and

^dE _dt = ˙ p A − ([ ˙ p M ] + [ ˙ p J ])V

^,

where

[ ˙ p J ]V

^{representsmaturity maintenane (Kooijman,2000). If}

E

^reahes

zero,theindividualdies.

The rotifers attain theirnal size within the rst oupleof days(Korstad

etal.,1989),andshowlittlegrowthduringtheirremaininglifetime. Wethere-

fore assume that one they reah a maximum strutural volume

V p

^{, growth}

stops andthe rotifers start investing energy in reprodution. Theenergy ux

investedin reprodutionin thisphaseis:

˙

p R = (1 − κ) ˙ p C − [ ˙ p J ]V

^(3.17)

Theux

p ˙ R

^entersareprodutivebuer

R

representingtheprodutionofeggs.

One

R

^{reahestherequiredamountofenergyfortheprodutionofasingleegg,}

thebuerisemptiedandaneggisprodued. Eaheggisarriedbythefemale

Figure 3.5: Overviewof theindividualrotifer model. Arrowsrepresentuxes,

squaredboxesrepresentenergyorstrutureompartments,whileroundedboxes

representthemodelled relationsbetweenuxes. ThegureisfromPaper1.

eggsarried by eah female (the egg ratio) is auseful indiator of thegrowth

rateofarotiferulture.

Seneseneandnaturalmortalityisimportantforthepopulationdynamis,

and is modelled by the method of Kooijman (2000): respiration is assumed

to ause the prodution of damage-induing omponents whih in turn ause

damagetoDNA.Agingisexpressed throughthehazardrate,whihrepresents

aumulated ell damage, and inreasesas a funtion of the onentration of

damage-induing omponents. The amount of damage-induing omponents,

M Q

^{,hasthefollowingstateequation:}

dM Q

dt = η QC p ˙ C

^(3.18)

where

p ˙ C

^{isthe atabolirateof therotifer,} representingtherespiration rate, and

η QC

^{is theparameterdening itslife expetany. Thehazard rate}

h

^{, rep-}

resentingtheprobabilitypertimeunit ofentering thesenesentphase,hasthe

followingstateequation:

dh dt = M Q

V

^(3.19)

A senesentindividual ingestsless feed, andno longerprodueseggs. After a

Theindividualmodel isusedinaLagrangiansimulationto omputepopu-

lationdynamis,bysimulatinganumberofparallelinstanesoftheindividual

model. Eah instanerepresentsanumber

N

^{ofatualrotifers,andis referred}

toasasuperindividual. Thisprinipleisoutlined bySheer et al.(1995). It

isassumedthat the rotifersin aulturedo notinterat, exeptfor ompeting

forthe samefeed resoure. The availabilityof feed is modelled under the as-

sumptionthatthefeedishomogeneouslydistributedinthewaterolumn. This

meansthat asinglestatevariable

X

^{anrepresentthefeed}onentration:

dX

dt =

^addition

−

^ingestion

tankvolume

−

^{dilution (3.20)}

wheretheingestion termisthesumoftheingestion ofallsuperindividuals.

Loss of rotifers due to mortality or water dilution an be handled in one

oftwoways;either superindividualsliveor dieasaunit,determinedbytheir

probabilityofdeath,ormortalityanberealizedbyreduingthe

N

^valueofa

superindividualatarategivenbytheprobabilityofdeath. Thelatterstrategy

avoidstheintrodutionof randomnessinthesimulation,andis agoodwayof

representinge.g. waterdilution, butleadsto amonotonousdereasein the

N

valuesofthepopulation. Forapopulationofstabledensitythisausesaorre-

spondinginreaseinthenumberofsuperindividualsneededtorepresentit,and

thusagradualslowdownin simulationspeed. Toounteratthistheomputer

analyzesthepopulationat regularintervals,ombiningsuperindividuals that

aresuientlysimilar,thusreduingthemodeldimension.

2

Modelparametershaveto behosenwith aspei rotifer strainin mind,

beausedierentstrainshavedierenesin size,growthrateandotherhara-

teristis. InPaper 1,we havehosenaset of parametervaluesfor this model

basedonvariouspublishedresultsfortheSINTEFstrainofBrahionuspliatilis

(aNevada strainwhihhas been held in ultureforalongtime, and whih is

usedinanumberofodhatheries).Figure3.6showsasimulationofthepopu-

lationdensityandtheeggratioofabathulturepopulation,omparedtothe

measurementsfrom6ultures.

2

Fortwo individualstobeonsideredsuientlysimilar,werequirethattheyhavethe

samenumberofeggs,andthatthesumofrelativedierenesinstatevaluesdoesnotexeed

athreshold level. Thisthreshold levelan bedynamiallyadjustedto keep the number of

0 1 2 3 4 5 6 7 8 10 ²

Rotifers ml −1

0 1 2 3 4 5 6 7 8

0 0.2 0.4 0.6 0.8 1

Days

ER

Simulation Tank 1 Tank 2 Tank 3 Tank 4 Tank 5 Tank 6

Figure3.6: Growthandeggratioofabathulture,omparedwithexperimen-

talresultsfrom6ultures. ThegureistakenfromPaper1.

3.2.3 Modelling Rotifer Body Composition

Themodel desribedin Paper 1doesnot takefeed omposition into aount,

exept for the onsideration of the energy ontent of the feed. Beause the

nutritionalvalue of rotifers is aeted by feed omposition (Maruyamaet al.,

1988;Lubzensetal.,1989;Frolovetal.,1991;Fernandez-Reirizetal.,1993;Lie

et al.,1997; Castell et al.,2003) andultureonditions (Øieand Olsen,1997;

Øieet al.,1997),weseek amodelformulationthatantakethisintoaount.

In Paper 2, the model of Paper 1 is expanded to expliitly represent the

balanebetweenprotein,lipidand arbohydrateinreserves. Thereserveom-

partment

E

^{fromPaper1isreplaedbythree}ompartments,

E P

^,

E L

^and

E C

^,

representing energy reserves in the form of protein, lipid and arbohydrate.

Figure3.7: Overviewof the individualmodel. Arrowsrepresentenergy ows,

and rounded boxes represent modelled relations between these. The shaded

squaresrepresentmodelstates. Thegrayarrowsrepresentthereturnedfration

κ R

^{ofrejeteduxes. ThegureistakenfromPaper2,wherethedetailsofthe}

modelarepresented.

struturehasanapproximatelyonstantompositionin termsof themainnu-

trient lasses. The body omposition of the rotifers depends on the balane

betweenthestatevalues

E P

^,

E L

^,

E C

^and

V

^.

Feedintakeandassimilationistreatedthesamewayasintheoriginalmodel,

exept that dierent assimilated frations are allowed for the three nutrient

lasses. Themain diereneis inthedetermination ofmaintenaneuxesand

growthorreprodutionbasedonthebalanebetweentheenergyreserves.

Analogoustotheataboliratein theoriginalmodel,wedeneaataboli

rateforeah ofthe threereserveompartments. These ratesare proportional

to the reserve densities(reservelevelsdivided by strutural volume). Part of

eah ataboliux isused foroveringmaintenanerequirements. Theontri-

butionfromeah dependsontheirrelativemagnitude,weightedbytheanity

parameters

ρ P

^,

ρ L

^and

ρ C

^{(Eqs. (11)(13)in Paper 2). A higher anityfor}

onenutrientlassmeansthat agreaterpartoftheorrespondingataboliux

After subtrating themaintenaneuxes from theataboliuxes, there-

maindersareavailable forgrowthoreggprodution. Theseproessesareboth

modelled in the same way, with the omposition of struture (

P V

^,

L V

^and

C V

⁾representingtherequiredontributionfromeahnutrientlassperunitof growth. In addition, anoverhead fration ofenergy is required,whih anbe

overedby any ombination of nutrient lasses. A sideeet of the overhead

requirementistorelaxthestoihiometribalaneditatedby

P V

^,

L V

^and

C V

^,

beausea limiting nutrientlass will not beutilized to overoverhead. This

prinipleisspeiedinEqs. (14)(27)in Paper2.

Themodel presentedinPaper2isstill fairlybasi,andtreatsallthethree

nutrientlassesidentially exept fordierenes in parametervalues. Despite

this, the model an provide fairly good preditions after adapting parameter

valuesto a spei rotiferstrain. Figure 3.8 showsthe model's preditionsof

rotiferdryweightandproteinandlipidontentafterthreedierenttreatments,

in omparison with measured values (Øie et al., 1997). In the

P

^treatment,

rotifers are short-term enrihed after being grown at 20% dilution. In the

L

treatment, rotifers are short-term enrihed, but dilution rate is only 5%, and

in the

N

^{treatment,dilutionrateis 5%andthere isnoenrihment. Themain}

weakness ofthe model preditionsasfound in Paper 2is atendeny to exag-

geratetheeet offeedomposition onbodyomposition.

Aountingfortheeetoffeedompositionongrowthrateandbodyom-

positionhas valuein preditingthefuture stateofrotiferultures, but is also

important when studying the nutritional value of rotifers in the rst feeding

senario. Setion3.4.1disussesthisappliationofthemodel.

Rotifer resting egg prodution

In the model presented in Paper 1, it is assumed that the rotifers reprodue

onlyasexually,and this istrueforthe SINTEF strainfor whih it isadapted.

However,mostrotiferstrainsfoundinnatureinitiatesexualreprodutionunder

ertainonditions, resultingin resting eggsthat anliedormantfor extended

periodsunder unfavorableonditions(PourriotandSnell,1983).

Commerialprodutionofrestingeggsasinoulumforrotiferulturesmight

be an interesting ativity in the future (Lubzens et al., 1989), partly for the

purpose of mirobial ontrol, sine resting eggs an be disinfeted before use

(Dhert,1996). ProdutionmethodsforrestingeggshavebeenstudiedinJapan

(Hagiwaraet al.,1993;Balompapuengetal.,1997;Hagiwaraetal.,1997),and

somemodellingworkhasbeenundertakenfortherestingeggformationproess

P L N 0

10 20 30 40

Protein DW fraction (%)

P L N

0 5 10 15 20 25

Lipid DW fraction (%)

P L N

0 100 200 300 400

DW per ind. (ng)

Measured Modelled

Measured Modelled

Measured Modelled

Figure3.8: Relativeproteinontent,relativelipidontentand dryweightper

individualofrotifersafterthethreedierenttreatments

P

^,

L

^and

N

^(Øieetal.,

1997),ompared tothemodeloutput. ThegureisfromPaper2.

themodelofPaper1hasbeenexpandedtodesribetheompletereprodutive

yleleadinguptotheprodutionofrestingeggs(Alver,M.A.&Hagiwara,A.,

An individual-based population model for thepredition of rotifer population

dynamisandrestingeggprodution. Hydrobiologia,submittedpaper).

3.3 Larval Model

Thereisawiderangeofpublishedworkwithinmathematialmodelling ofsh

physiology and behaviour, suh as Balhen (1979), Olsen (1989), Olsen and

Balhen (1992),Beerand Anderson(1997)andFiksenandMaKenzie(2002).

A large amount of modelling work, suh as Aksnes and Utne (1997), Leising

and Franks (1999)and van der Veer et al. (2003), has been motivated by an

Figure 3.9: Overviewof the larvalmodel. Arrowsrepresentenergyows,and

roundedboxesrepresentmodelledrelationsbetweenthese. Theshadedsquares

representmodelstates.

insheries.

In Paper5, an energetimodel forod larvae in aquaulture tanks is pre-

sented. ThismodelisbasedonthesameDEBpriniplesastheindividualrotifer

modelpresentedinsetion3.2.2,butwithseveraldierenes. Figure3.9 shows

thebasistrutureofthemodel.

Feedingestion

p ˙ I

^{ismodelledasaHollingType2funtionalresponse(Holling,}

1965):

˙

p I = { p ˙ Im } V ^2/3 f

^(3.21)

f = X X + X K

(3.22)

where

{ p ˙ Im }

^isthemaximumsurfae-speifeedintake,

X

^{isthefeeddensity}

and

X K

^isthehalf-saturationonstantforfeedintake. Thisformulationassumes that the feeding behaviour of the larvae is not appetite regulated, whih is

onsistentwiththegeneralbeliefthatmarineshlarvaearenumbermaximizers

(Lubzensetal.,1989;Olsenetal.,2004).

p ˙ I

^{representsanenergyux,andgiven}

theamountofnutritionalenergyperindividualrotifer,

E r

^{,weanalulatethe}

numberofrotifersingested as:

p = p ˙ I

E r

(3.23)

Ingestedfeed enters a gut ompartment

S

^{, whih is assumedto be evauated}

exponentiallywith

k g

representingtherelativegutemptyingrate:

dS

dt = ˙ p I − k g S

^(3.24)

Theterm

k g S

^{representstheenergyuxavailablefordigestion, andtheassim-}

ilated ux

A

^{is a variable fration of}

k g S

^{in the interval}

(0, k as )

^{, with higher}

energyux resultingin lowerassimilationeieny(seePaper5fordetails).

Cod larvae arry a yolksa at their point of hathing, whih serves as a

soureofnutritionforashortperiod. Whentheyolksaisdepleted,thelarva

mustbeabletoathpreyanddigesttheingestedfood(Kjørsviket al.,2004).

Theyolksaismodelledasaompartment

Y

^{that isgraduallyemptied:}

dY

dt = − p ˙ Y =

−{ p ˙ Am,yolk } V ^{2 / 3}

^if

Y > 0

0

^{otherwise (3.25)}

where

{ p ˙ Am,yolk }

^{is the surfae area-spei yolk} assimilation rate. Energy drained from the yolk sa is available in the sameway as energy assimilated

from food, sothetotalenergyaquisitionrateis:

˙

p A = A + ˙ p Y

^(3.26)

Themaintenanerequirementisassumedtobeproportionaltothestrutural

volume

V

^withproportionalityonstant

[ ˙ p M ]

^{. Theenergybudgetoftheenergy}

reserve

E

^{andthestruturalvolume}

V

^{areasfollows:}

dE

dt = ˙ p A − p ˙ C

^(3.27)

dV

dt = κ p ˙ C − [ ˙ p M ]V

[E G ]

^(3.28)

wheretheparameter

[E G ]

^{speiestheenergyexpendedperunitofvolumetri}

growth. Theparameter

κ

^{setsaxedproportionof}

p ˙ C

^{thatisspentongrowth}

plusmaintenane(theremainingportion

1 − κ

^{isavailablefor}developmentplus investmentin reprodution).

Both

dV dt

^and

dE

dt

^{depend on}

p ˙ c

^{, whih is referredto asthe atabolirate,}

andrepresentstheonsumptionrateofenergyfromthereserve.

p ˙ c

^isalulated

asfollows:

˙

p C = [E]([E G ] ˙ vV ^2/3 + ˙ p M )

[E G ] + [E]κ

^(3.29)

whih isanalogoustoEq. (3.14)fortheindividual-basedrotifermodel.

Thedrymatterontentoflarvaedependsonalllarvalstates:

W d = [W V ]V + (E + Y )/µ E + S/µ S

^(3.30)

where

[W V ]

^{relatesstruturalvolumetodryweight,and}

µ E

^and

µ S

^areenergy

densitiesofreservesand gutontents,respetively.

In Paper5, theenergeti modelis used to represent theentire larvalpop-

ulationof atankby simply addingthe numberof larvae,

N

^{, asan additional}

statevalue. Thisimpliestheapproximationthatalllarvaeareequal,orthatthe

energetimodeldesribesarepresentativeaverageindividual. Itisalsopossible

to runmultiple instanesofthis model in aLagrangiansimulationin orderto

studytheimpatofdierenesinmodelparametersorstatevalues(forinstane,

onsideringlargevs. smallindividuals).

Figure 3.10showsthestatevaluesof thelarvalmodel, aswell astheom-

puted dry weight, in a simulation of tank B1 in the experiment presented in

Paper5. Energyreservesinreaseastheyolksaisdepleted,and theguton-

tentinreasesgraduallyfromtheonsetoffeeding. Dryweightdereasesslightly

initially,butstartsinreasingafterfeedingisinitiated.

3.4 The First Feeding Senario

3.4.1 Live Feed Quality Assessment

Thenutritionalvalueofenrihedrotifersisvolatile,andtheatualbalaneand

amountofnutrientsaquiredbytheshlarvaedependsbothontheenrihment

proedureandtheresidenetimeoftherotifersintherstfeedingtank. Paper

1and Paper2 go along way towarddening a model whih an beused for

prediting these dynamis, although they do not provide a desription of the

rotifers' ontent of individual fatty aids or amino aids. This model an be

used in ombination with thelarval growth model of Setion 3.3 to represent

theentirefood hain of therotifer feeding phase. This approah allowsloser

investigationof bothenrihment eets, and theeets of parameterssuh as

waterexhangerateandalgaladditiononthenutritionoftheshlarvae.

We illustrate thismethod with simulationof arstfeeding senariowhere

the results for lear water are ompared to the resultsfor green water. The

followingstepsareused:

ˆ Simulate pre-treatment of therotifers using themodelfrom Paper2. A