Spatial Variance of Mobile Aquatic O rganisms : Capelin and Cod in Coasta l Newfound land Waters

Capelinand Codin CoastalNewfound land Wat ers

By oJohnK.Home

A thesis submitted 10 theSchoolofGraduateStudies in partial fulfillmentofthe requirementsfor

thedegree ofDoctorofPhilosophy

ocean SciencesCentreand Departmentof Biology MemorialUniversityofNewfoundland

St.John' s,Newfoundland 1995

who alwaysthought Icoulddoit.

t"'eyjwtdidn ' tthinkitwouldtakethislong.

Patchy distributions of organismsare a long recognized attributeof terrestrialand aquatic ecosystems. Quantitativedescriptionsof spatialvarianceprovideclues 10 processesthat generatepatchiness.In aquaticenvironments,greater effort has focussed on quantifyingspatialvariancein distributionsof planktonthan on quantifyingspatial variancein distributionsof mobileorganisms. Toevaluate therelativeimportanceof biologicaland physicalprocessesthat generatevariance,a theoreticalframeworkwas developedthat combinesdemographic,growth,and kinematicrates in dimensionless ratios.Ratio valuesare then plottedas a functionoftemporal and spatial scale.

Applicationofthis techniqueidentifiedkinematicsas the dominantprocessinfluencing capetin(Mal/orus viffosus)distributionalong the coast duringthe spawningseason.

Hydroacousticdistributiondata of capelinand Atlanticcod(Gadus morhua)were analyzedto examinehow shoaling,schooling,and the aggregativeresponseof predatorscontributeto the spatialvarianceof mobile, aquaticorganisms. A characteristicscaleof patchinesswas not observedat the temporalscaleof a single transect (ca. I hour)orat the scaleof a survey(l,,'"2 weeks).On average, spatial varillncedecreasedslightlyover intermediatescales(10 km-0.5km) and then dropped rapidly at smallerscales.Data manipulationsand computersimulationsdemonstrated thatshoalingpotentiallyincreasesspatialvarianceat intermediate scales, andthai schoolingpotentiallyreducesspatialvarianceat scalessmallerthan aggregationsizes.

There was no evidenceof an aggregativeresponsebycod 10concentrationsof capelin throughoutthe analyzedscale range(20m-10km).This unexpectedlack of spatial associationbetweenpredatorandprey was explainedusingestimatesof foraging

iii

capclin spawningseason.

Theoreticaland empiricalresults of this study haveincreasedknowledge of scale-dependentspatialvariancein mobile.aquaticorganismsand providedinsightto the biologicalprocessesthat potentiallygenerate these patterns.Scale-dependentplots ofspatial variancecombinedwith ratediagramscan be used to evaluatethe relative importance of biologicaland physical processes that influenceorganismdispersionasa functionof spatialand temporalscale.

iv

I thankmysupervisorDr.DavidSchneider (oralwaysleading by example,for exposingme to hisquantitativeacumen,and forcontinuouslychallenging me just the rightamountThesearethequalitiesIhopeto emulate asa scientist.Ialsothank my committee membersDrs.GeorgeRoseandJoeBrown forhydroacoustictraining,for criticism at committee meetings,andfor commentson an earlierdraftofthis manuscript.

Thereisoneauthoronthetitle pageofthis thesisbulseveralpeoplemadethejob easier.Dr,RamMyersoriginallyinvitedmetogiveaseminarin Newfoundland . BrianBeckwarned meaboutalways being a bridesmaid,JimHiscock(captainofthe Naughty GalIII),ChesJackson,GordJackson,andTommy (captainsoftheMarie Louise)cheerfullylooktheirboats moreorlesswhereI wanted 10go.PaulNormore, CraigTuck,andDaleFraserhelpedout in thefield.I thankfriendsandcolleaguesat the placewecallNICOS-notablyK.S, Prasadand Marimar Villagarciamyoffice males, andDavidMethven mydinnercompanion onthenightshift.Dr.Richard Haedrich alwaysprovidedadvice(gardeningandotherwise),encouragement,andthe necessary computerhardware 10 getthejobdone.

Fundingforthisprogramwasprovidedby NationalCentres of Excellence.- OceanProduction Enhancement Network(OPEN),NaturalSciencesandEngineering Research CouncilofCanada(NSERC) throughD. Schneider,andan A.G.Hatcher MelTK)rialScholarship1(1 theauthor.

Chapter1. BackgroundandApproach 1 1.1Introduction...•••.•.••...••••..•.•••..•.••....••.•.•.••.•..••.•... .••••.••.••••••..1 1.2Characterizin& spatialvarianceiltorganism distribution ...•....S 1.3Scale-dcpendentpredator·preyinteractions 10 1.4 Cod-CapelininteractionsinthenonhwestAtlantic 12

Otapter2. EvaluatingSpatialVariance 16

2.1Introduction•.••••...•.••...•.•...•...•..••.•..•.••••..•.••...•••.•••.•••.•.16 2.2Methods..•...•..•.•..•...••.••....•••... .•... ... . ..•.•.••.. . .•.. .•.. .•... .•••. .. •.18

2.3Results 24

2.4Discussion 28

2.4.1IdentifyingAppropriateSamplingScales 32 2.4.2EvaluatingVariance Generating Processes 33

Appendix2.1:Spatial Dynamics of Biomass 38

Appendix2.2:Dimensional Analysis....•....•.•...•..•.•••••.•.••.•..••.••••. ..•.40

Chapter 3. InnuenceofFlow Gradients 42

3.1Introduction••••.••.•.••.•.•••.••..•••.•.•.•.••.•••.••.••••.••••.••...•••.••...••••.42 3.2Methods••••...•••.••.•.•..••••...••...•.••...•.•..•.••...•••..••...43 3.3Results..•••...••••.••••.••... ...••.... •. •....•.••....•...•.46 3.4 Discussion.••••••.••••.. ..•..•.•.•••••.•.••••.••..•••..••.•.••.•.•...•.•...•....59 Chapter4. Spatial VarianceofMobile AquaticOrganisms•••••.••.. •...•••.•••.•63 4.1Introduction.••.•••..•••••.. ....•.•••.. ...•••.... ••.. ••••. •.•.•...•••....••.•...63 4.2Methods••.••...•••... •...•••... .•••... •••••••••••.•.. ....•. ...•. . .•...65

4.2.1Sampling Procedure 65

4.2.2 Analysis•••..•..•.•.•..•.•....•..•...• •.••... .•..•.•••••••.••.•••..••.•••..•..66 4.3 Results.•...•.•••••••••.•...••...••.••..••.•.••...•...•.•.•...•..•••.•.70

4.3.1 SpatialvariancePatterns 70

4.3.2 Effect of Zeros 7S

Chapter 5. Spatial Coherenceof MobileAquaticOrganisms 86 5.1Introduction...•.•. ...•. .•...••...• ••••...•..•••....•..86 5.2Methods...•.•.•.•••.•.•••...•••.... ...•... .•.... . •... .. .. ....•...90

5.2.1Spatial Coherence 90

5.2.2BioenergeticCalculations 91

5.3Results 93

5.3 .1Spatial variance Pauems 93

5.3.2Bioenergeticcalculations 96

5.4Discussion .100

Chapter 6. Shoalingand SchoolingSimulation 106

6.1Introduction .106

6.2Mobile Particle InteractionModel 107

6.2.1Model Development 107

6.2.2Model domain 113

6.2.3Model parameters 114

6.2.4Simulations 117

6.3Results .118

6.4 Discussion .124

Appendix6.1List of symbols 131

Chapter 7. Spatial Variancein Ecology 133

7.1Introduction .133

7.2 Spatial varianceatsingle scales 134

7.3Spatialvarianceatseveralscales 140

7.4 The analysis of spatialvariance 143

7.5The next steps .146

Chapter 8. Summary .148

References .150

vii

Capelinrate diagrams .25

ZOOplankton rate diagrams 30

Acoustictransectlocations 44

Presentationof spectraldensity plots 50

Longshore and crossshorecapclinspectraldensityplots 51

Synopticcapelin spectral density plots 54

Surfacetemperaturespectraldensityplots 56

Averagecapclinand surfacetemperaturespectral densityplots 57 Absolute difference in capellaaggregation number in repealedtransects 59

Capelinand Atlanticcod spectraldensityplots 71

Averagecapelin,Atlantic cod, and surfacetemperaturespectral densityplots ..73 Cumulativefrequencyhistogramsof capelinand Atlanticcod•....•.... ...•.. ... 74 Spectraldensity plotsofmanipulated surfacetemperature 76 Averagespectral density plots of capelin,Atlanticcod,Atlantic puffin, commonmurre, Antarctic krill,and phytoplankton 82 Schematicdiagramof predatorand preyspatialcoherence 89 Powerspectra, coherence, and phaseof capelinand Atlanticcod 94 Averagepower spectra,coherence,andphaseof capelinand Atlanticcod 95 Schematicdiagramof attractiveandrepulsive forces 108 Attractive,repulsive, andnet force plottedas a functionofdistance 115 Velocities of 8 particlesfromthefirst 250time steps 119 Frictionofeight particlesfrom thefirst250 time steps 120 Positionsof800 particlesat timesteps0,SO,100,and?.50 122

viii

Spectraldensity plots of particles at time steps0,50,100,and 250 125 Spectral densityplotsof particles at time steps0, 2000, 4000, and 6000 126 Spectraldensity plots of particles at timesteps 0, 2000, 4000,and 6000,

reduced swath width .127

ix

Stan and endlocations of acoustictransects' 47 Stan and end locationsof acoustictransects(cont'd ) 48 Date,time, anddistanceof acoustictransects , ,.,....•_67 Spatialscales of maximumcovariation . ...•.••.•••••.•...87

Energeticcalculationsofcodglutfeeding 99

Simulationmodelparameters , 116

l.llnlroduclion

Heterogeneityin spatialdistributionsof organismsis along-recognized attribute of both terrestrial(Watt1925,1947) and aquatic (Hensen1911;Hardy1935. 1936) ecosystems.Quantifying spatial heterogeneity asa functionof scale has been used to judgethe applicability of smallscaleexperimentstolargerscale naturalsettings (Mercerand Hall1911),to identifydomainsof equivalentspatialvariability (Fairfield Smith1938),to identifyscalesofmaximumheterogeneity(Greig-Smith 1952;Kershaw 1957), andto providecluesto biological orphysicalprocessesthat generateobserved spatialvariance pattems (Greig-Smith1983; Denman and Powell1984:Legendreand Demers 1984;Mackas etal.1985).

Inaquatic ecosystems,well establishedtheory slates thatspatia lvariance of passiveparticles isdeterminedby the surrounding flow field.Energythatcreates spatial variance patternsoriginatesatlargescales (e.g. eddies,gyre s) andistransferred byturbulent advection to successivelysmallerscalesuntilviscousdissipationbecomes important(Kolmogorov1941;Okubo J980).Thiscascadeof energyis characterized by a powerfunctionwherethe spatial varianceof a passiveparticle is proportionalto the inverse of scale(wavenumberorfrequency) raisedto anegative exponent.When the logarithm ofvariance is plottedas a functionof'ogarithm of frequency,the slope of the line isequalto the exponent. A decreaseinspatialvariancewithscaleis commonly observed among passive particlesandorganismsin marineandfreshwater environments includingsurface watertemperature (Saunders 1972;Fashamand Pugh19'16; Estrada

1986), sea level(Wunsch1972), andphytoplankton(Plattet al. 1970;Platt1972;

Powell et al.1975: Fashamand Pugh1976;Denman1976; Estradaand Wagensburg 1977;Horwood1978: Weberetal.1986).

The spatialvariancepatternof atleastone mobileaquaticorganismwas foundto differ fromthat of passivetracers.The rate of changein spatial varianceof Antarctic krill(Euphausia superha)withchangein spatialscalewas on averagelowerthan that of surfacetemperatureorphytoplanktonover resolutionscalesof2 km to 100km (Fig.6, weberet aI.1986).The magnitudeof averagespatialvariancein krill was less atlarge scalesand greater at small scalesthansurfacetemperatureorphytoplankton. Weber et al.(1986)attributedthe increasedspatial variability of krill at smallerscalesto an unspecifiedbehavioural mechanism.Ina subsequentstudy, Levin et al.(1989) extended the samplingresolution to 200 m and observeda shallow negative slopein krill spatialvariancedownto scalesof1km. The slightnegative slopeof krillspatial varianceplotswasobservedinboth studiesbut processesinfluencingspatialvariance patterns and thegeneralityof these patternshavenot beensystematicallyinvestigated for mobileaquaticorganisms.

Earlystudiesthatquantifiedvariabilityin organismdistributionfocusedonspatial andtemporaldistributionsof phyto-andzooplankton(e.g.Gran and Braarud1935;

Riley and Bumpus1946; Bainbridge1957;Cassie 1960).Planktonwere treatedas passiveparticleswithshortturnover times.Statisticalindicesanddescriptive models usedto quantifyvariancein planktondistributions arenotdirectly applicableto long-lived organismsthat can moveindependentlyof the surroundingfluid.Spatial

environmentsasthey are limited to twodimensionsandoften assume homogeneous environments(e.g.Wiens1976;Hassell and Anderson 1988).As aresult, thereisa limitednumber ofmodels that quantifyspatialvarianceof mobile organismsin aquatic environments.

Spatialvariancestudies of mobile,predator-preysystemsin fluidenvironments are also rare.Spatial and temporal variabilityin the densityof preymay ultimately determine foragingsuccessof a predator. In the northwestAtlantic,predator-prey spatial variancestudiesarelimitedto seabirds-pelagicfish (SchneiderandPiatt 1986;

Schneider1989)and demersal-pelagicfish (Roseand Leggett1989, 1990) .These and other similarstudiesrlemonstratethatobservedspatialvariancein the distribution of mobileaquaticorganismsis dependentonthespatial and temporalscaleof measurement(Schneiderand Duffy1985;Schneider 1989;Piatt1990;Rose and Leggett 1990).Therefore,toexamine the spatialdynamicsof mobile predator-prey interactionsitis imperativetoquantifyspatialassociationsof predatorwithprey overa widerange of scales andto explicitlyreport spatialand temporal scalesof measurement.

These observationswere used to formulatean approachto evaluate scale-dependentspatialvariance in the distributionof mobile,interactingorganisms:

I) Use previous knowledge to evaluatethe relativeimportanceof biologicaland physicalprocessesthatpotentially generatespatialvarianceas a functionof scale.

analytictechniques.

3) QUMtifyspatialvarianceinthe quantityof interestas a function of scale.

4) Confirm hypothesized variancegeneratingprocesses.

~)Generalizeresults from specificcases andidentifythenext analyticsteps.

This thesisis dividedinto eightchapters.The remainderofthis chapterreviews effortsto characterize spatialvariancein distributionsof aquaticorganismsand in interactionsofpredators with their prey. Background is providedon Atlanticcod (Gadus morhua)andcapelin(Mallo/us villosus)whichare usedas an exampleofa mobilepredator-preypair. The secondchapterusesdimensionlessratiosof rates to quantify the relativeimportanceof processesthatpotentiallygeneratespatialand temporal varianceinallY biologicalquantityof interest.This method is then usedto identifydominant biological processesinfluencingspatialvariancepatterns ofcodand capelinat logistically feasiblesamplingscales. Chapters3 and 4quantify variancein the distributionof capelinandcodfrom relativedensitydatacollectedusing hydroacoustics inConceptionBay,Newfoundland.Spatialvariance patternsobserved inthedistributionofcodand cepelinare comparedtothose of driftingparticles and other mobile species. Chapter5 focuseson scalesof spatialassociationbetweencod as predatorand capelinas prey. Observedpatternsof spatialassociationbetweenthe two speciesare interpretedusingbioenergeticcalculations.A particlesimulatoris used in Chapter 6toconfirm the influenceofhypothesized biologicalprocesses fromChapters 3 and4on spatialvariancepatternsof mobileaquaticorganisms.Chapter7 reviews

prediction and analysisof spatial variance will continue.The final chaptersummari zes contributions of this thesis.

1.2 Char acteridng spatialvaria ncein organismdistr ibution Early efforts to verballydescribedistributionalpatternsof organismswereindirect methodsof examining spatialvariance at oneor morescales. Numeric techniques attempteda moreexact detectionand description of spatialvariancebycomparing empiricalindicesof aggregation toanexpectedvalue under theassumption of randomness.These indices assess variance atasinglescalefor each calculation.To quantify spatialvariance as a functionofscale, quadratsize can be sequentially increasedfrom the sample resolutionto one halfof the samplerange(Greig-Smith 1952).A chronologiedetailingof the developmentof statisticsmeasuringdeparture from randomnessand determiningscale will be reviewedin the penultimatechapter.

The ability todetectconcentrations of spatialvariancehaslargelybeen determined by availablesamplingtechnology.Earlysurveysbasedon net samplesfoundthat spatialvariance in planktondistributionspeakedatthe scale of tens of kilometers (Bainbridge1957;Cushingand Tungate1963;Steele1974).The developmentofin vivofluorometry(Lorenzen1966),theLongurst-Hardyplanktonrecorder(Longhurstet al.1966),and applicationof theCoullercounter(Sheldonand Parsons1967)10 planktonsamplingdramaticallyincreasedtheresolution ofhorizontal samplingin aquatic environments(cf.Fig.I,Denmanand Mackas1978).Subsequentanalysis resulted in areduction inestimatesof phytoplanktonpatch sizes (cf.Table I, Legendre

1972; Platt and Denman1975) facilitatedthe analysisof spatialvariance over a continuousrange of spatial scales. Spectral analyses of phytoplanktoncountsand other passive particledata confirmed that spatialvariancepeakedatlow frequencies(large scales) and monotonicallydecreasedto high frequencies (smallscales)(e.g .Denman and Platt1975;Fasham1978).

Efforts to explainbiologicalspatial variance commonly match characteristic scales of biologicalpattern to dominant physicalprocesses at the same scale. The hypothesizedcouplingof biological patterns to physicalprecessesis most common in pelagic communitiescomprised of phytoplankton(e.g.Denman and Powell1984), zooplankton(e.g .Legendre and Demers1984), and larval fish(e.g .Shepe rdetal, 1984;Stssenwine1984).One ofthe first studiesdirectlycoupling physicalto biologicalprocesseswasGran and Braarud (1935)whoexplainedthelow abundanceof phytoplanktonin the Bayof Fundybythelack of vertical stabilityinthe watercolumn.

This observationand other physical-blolcgicalcoupledstudies (Bigelow etal.1940;

Riley1942) wereused inthe developmentofthe criticaldepth concept(Sverdrup 1953).Theimportance of physical-bic logicalcouplingin marineecosystemshas been reviewed byWalsh (1981), Denman and Powell(1984),and Mackasetal.(1985).

An implicit assumptionin thismatchingapproach isthat biological patternis directly coupled to physicalprocessesatthesamescale.This hasbeen demonstratedin descriptions of plantcommunitieswithreferencetoenvironmental gradients(e.g.

Greig-Smith1952;Kershaw1958), and the couplingof spatial variance patternsin passive tracers toflow structuresin fluidenvironments (e.g.Denman and Powell 1984;

May1976)andexperimental(e.g.Dwyer andPerez1983)evidence10suggest that non-linear relationships occurbetween ecosystem components.Anaquaticexample is growth of phytoplanktonalteringthe transmission oflightinthewater column dueto selfshading (ShigesadaandOkubo1981).Theassumptionofdirectcouplingat a singlescalealsoexcludes multipleprocessesinfluencing pattern ata singlescale, and thepropagationof effects acrossspatial or temporalscales(e.g.adultcohortsize establishedalan earlylifehistorystage).

A second assumptionofthis matchingapproachis thatthe couplingof biological spa!ial variance to anyvariancegenerating processoccursata characteristicscale.

Singleplotsof variance as a function of scaleshow concentrations ofspatial variance among terrestrial(Greig-Smith 1952;Kershaw1957) andmarine (Grassle et aI.1975;

Schneider1989; RoseandLeggett1990)organisms.Butinall studies, scales or"

maximumspatial variance differamongtransects.Inthefewstudiesthatincrease the temporal scalebyaveraging multipleplots(Weberetal.1986;Schneider 1994a), these scale-dependent concentrationsofspatial varianceoftendonotoccur.Itremains unclear whether variance in thespatial distributionof mobileaquaticorganisms occurs atcharacteristicscales.

A thirdassumptioninthis matching approach isthatthecreationofbiological spatial varianceis generated exclusivelybyphysicalprocesses.Biological processes canalsoinfluencespatial variance overa rangeof scales. Phytoplanktoncriticalpatch sizeis a classic example.Onetheoryis thaturesizeof a phytoplanktonpatchis detennined bythe opposing forcesof horizontaldiffusionandphytoplankton

sizetheory waslater expandedto includeherbivoregrazing(O'Brien andWroblewski.

1973a;Wroblewskietal.1975).Theassumption thatspatialvarianceof passive tracers is generatedexclusivelyby physicalprocessesisalsocontradictedby theidea thatthe dominatingprocessdetenniningphytoplanktonspatialvarianceswitches betweenphysicaland biologicalprocessesovertime(Demersand Legendre1979, 1981). Relianceon matching biological patterntophysical processeswasdue,in part, to alack of analytictoolsthatquantify therelativeimportance of variancegenerating processes.The relativeinfluenceof biologicalandphysicalprocessesonspatial varianceofmobile aquaticorganismshasnot beenextensivelystudied.

Initialattemptsto describespatialvarianceof mobileaquatic organismsalso lookedfor characteristicscalesof maximumspatialvariance. Thefirstdiagrammatic portrayalofscale-dependentbiological variancewas Hauryet al.'s(1978)conceptual modelof macrozooptanktonbiomassdistribution.Dominantfeaturesin the zooplanktondiagram(cf.Fig.I, Haury ctal.1978)matched dominantphysicalfeatures inthe originalStommel diagram of sealevel(cf.Fig.I,StommeI1963). Magnitudes of zooplanktonbiomass varianceorsea levelvariance werenot quantifiedineither diagram. Oneof Stomme1's(1963) major points wasthatthis task was virtually impossiblegiventhe numberof required measurements.Hauryet al.(1978)includeda relative'measureof biological importance'whenestimatingmagnitudes of zooplankton variance. Theunitsof 'importance' werenot quantified.More recently,Marquetetal.

(1993)advocatethe useof Stommeldiagrams tocharacterize spatialand temporal variance of biologicalandphysicalquantities.Theyrecommend theuse of spectral

essumpuonsof the techniqueand difficultiescollectingsynoptic dataat largescales.

Evidence from spectralanalysesshows that spatialvariancepatternsof mobile organismsdo not matchthoseof passivetracersinthe surrounding fluid.Weberetal.

(1986)examinedspatialvarianceof Antarctickrill(Euphausiasuperba)in relation to surfacetemperatureand chlorophyllfluorescenceas a measureof phytoplankton abundance.This study was thefirstcomparison of spatialvariancepatternsof mobile organismsto passivetracersin an aquaticenvironment.11wasalsothe first exeminauonof scale-dependentspatialvariance at morethan onetemporal scale.The rate of changeinkrillspatialvariancewithchangein spatialscalewaslower thanthat ofeithersurface temperatureor phytoplanktonover resolutionscalesof2 kmto100 Jun.Themagnitudeof averagespatialvarianceinkrill was smalleratlowfrequencies (large scales)and greater at high frequencies (smallscales) thansurfacetemperatureor fluorescence.Weberetal.(1986)attributedincreasedspatialvarianceof krill abundanceatsmallerscalestoan unspecifiedbehaviouralmechanism.In a subsequent study, Levinetat.(1989)extendedsampleresolution to 200 m and observeda shallow negativeslopein krillspatialvariancedown to scalesof 1 km.Spatialvariance dropped rapidlyatscales smaller than 1 km (cf.Fig. 4, Levinetat.1989).The abrupt change inspectraldensityslopeimpliesthat different processes maybeinfluencing spatialvariance over different rangesof scales.Potentialvariancegenerating mechanismsincludephysicalas wellas biologicalprocesses.These two studiesclearly demonstratethe scaledependence of spatialvarianceand the necessityof muttl-scete observations indistributionalstudiesof aquaticorganisms.

SlUdiesof!hespatialvariance of mobile aquaticorganisms havelargelybeen limitedtosingletaxonomicgroups.Weberetat(1986)andLevin etal,(1989) quantified spatialvariance ofkrillbiomassoverawiderange of scales.Aseries of studies examinedscale-dependentspatialvarianceof marine birdsandthe association withpelagicschoolingfishand physical Ilowstruct ures (SchneiderandPiatt1986;

Schneider 1989;Piatt1990),Thisapproachwasusedtoexamine predator-prey associations of Atlanticcodwithcapelin asafunction ofspatial scale(Roseand Leggett 1990). To confirmthe generalityofpatterns obse rvedwithingroups of mobile organisms.acomparison isrequiredofscale-dependentspatial varianceacross taxonomic groupsattemporalscales greaterthan that ofa singletransect 1.3Scale-dependentpredator-preyinteractions

Thescale-dependence of spatialvarianceinthedistributionofasingle speciesalso appliestopredator-prey interactions.Analytictechniquesused10quantify interactions of predatorswithprey havelargelybeenadopted fromsingle speciesstudies.The traditionalgoalofthese studiesis to identifyscales ofmaximumassociationbetween predatorandprey.Havingidentifiedacharacteristic scaleofinteraction,dominant physicalprocessesatthe samescale are often proposedas mechanismsthat concentrate prey.Thismatching approach hasbeensuccessful when preyorganismsmove passivelywith thesurrounding fluidbut maynot applywhen organismscan move independentof fluid motions.

The temporalscaleof spatialsampling potentiallyinfluencesobservedspatial variancepatternsof predator-preyinteractions.Identificationof a characteristicscale

ofspatialassociationbasedonasingle or limitednumberof samplesimplicitly represents short temporalscales.Amongstudies thatpresentresults frommultiple transects(Schneider and Piatt 1986;WeberetaI.1986;Schneider 1989; Roseend Leggett1990) thescaleofmaximum spatial association differsamong transects.With theexception of the stud ybyWeber etaI.(1986),therehasnotbeena combiningof associationvalues fromanumberof transectsto examinespatialscalesofassociation betweenaquaticpredator sand preyat largertemporal scales.

Temporalandspatialscalesused intheoretical predator-preymodelsfrequently differfromthoseusedtotest predictions inthe laboratoryorfield(Kareiva1989.

1990).Thetemporal resolution ofpo putation-Imeracuonmodelsis implicitlysetat the generation time of thepredator.Butthe temporal scaleof surveytransectsis typically short relativetothe life spanofthepredatoror eventheprey.Field and laboratory observationsare commonly conductedattemporal scales equivalentto thatof a foraging bout. In addition, the rangeofspatialscales used to formulatepredator aggregative-responsemodels havealso differedfrom thosetestedin the field.

Theoreticaldescriptions of aggregattveresponsesbypredatorsarebasedon changesin preydensityat asinglespatialscale(e.g .Holling1965,1966;Murdochand Oaten 1975).Fieldstudies identifythe type ofresponse andrangeofspatialscales over whichaggregativeresponses occur(e.g. Headsand Lawton 1983;Piatt1990).To ensure compatibilitybetween theoreticalmodelsandempiricalexperiments the spatial andtemporal scaleof both theoryand observationmustbe explicitlystated when quantifyinginteractions betweenpredators andprey.

Predator-prey interactions amongmobileaquaticorganismspotentiallyoccur over

awiderangeofspatial andtemporalscales. Thereforescalesof maximumassociation between predator and preycanonlybeconfirmedbyanalyzingvarianceover a continuousrangeofspatialand/or temporal scales. Biological processesmustnot be excluded whendetermining mechanismsthat createobserved patternsof spatial variance.

1.4Cod·Capelin interactions in the northwestAtlantic

Capelinarea pelagic,schooling osmerid speciesinhabitingsub-ArcticandArctic watersintheAtlanticand Pacific oceans(Jangaard 1974).In thenorthwest Atlantic, adultcapelin(?3 yr) m'grate from offshoretocoastal waterstospawn on gravel beaches duringlateJune andJuly(Templeman1948;Carscadden 1983).Spawning mortality exceeds80%(CarscaddenandMiller1980).Eggshatch withinthe beach gravelin9·20days(Templeman 1948;Frank andLeggett 198 1)and larvae are transportedoffshore(Portierand Leggett19 82, 1983).Survivingadultsandjuveniles remainoffshoreduringfallandwinter(BigelowandSchroeder 1963;Baileyer aI.

1977).Duringthe spawningseasonAtlanticcod,asemi-demersalgadoid,complete a post-spawningmigrationtocoastalwatersto feedon capelinalongthe coastof Newfoundland(Templeman1979;Akenhead etal.1982; Lilly1987;Rose1993).

Capelinhaveformedthebasisof a multimillion dollarcommercialfishery (Anon.1980;

Carscadden 1983)andare akeyforagespecies formarine mammals, fish andmarine birds (WintersandCarsceddec1978; BaileyetaI.1977).

Capelinarea majorpreyofcodin offshore[Turuk1968;CampbellandWinters 1973;Stanek1975;MinetandPerodou1978;Lilly etal.1984;LearetaI.1986;Lilly

1986, 1987, 1991)and coastal (Thompson1943; Templeman1965;Aggettetal.1987;

Lilly 1987;Methven and Piatt1989)waters.Butthe proportion of capelinreported in coddiet studiesdiffers dependingonthegeographicarea and limeof yearthat samples were obtained.In NAFQ Divisions2Jand 3KLNO, Campbell and Winters (1973) estimatedIhatcapelin composed32%byvolumeof coddiet annually. Minetand Perodou (1978) found that capelin comprised56%byweightof cod diet froma set of stomachs samp ledduri ngwinterand summerin NAFO Divisions2Jand 3K.Annual consumptionof capelinbycod wasthenestimated tobe28%by weightunder the assumption that capelin are not consumed during springand fall.Thisestimateforms a minimumasLilly (1987)found thatcapelincomprised15%byweightof codstomach contentscollectedinNAFO Division 3L, and16% (1982) to 36% (1985)by weightof cod stomachssampledduringautumnin NAPO Divisions2Jand 3K.

Therearefewpublished studieson the food of cod from inshoreNewfoundland areas (Lillyand Botla 1984). Using a seriesofstomachsamplesfromcodcaughtin cod traps,Templeman (1965) found that capelinformed96% of codstomach contents byvolumeduringJuneto August,and 55%from May to November.Capelin represented99% by weight ofcod stomachcontentsfrom traps sampledinJuly 1968 and1969(Lillyand Flemming1981).

Thereis little doubt thatcodfeed heavilyon capelin but the dependenceofcod diet on capelinabundanceand availabilityhas not beenclearly demonstrated. Concern aboutthe impact of reductionsin capelinabundanceon cod dynamicsappearedas early as1835 (Akenheadetal.1982). The limitedresults thatindicatecapelinare important tocodgrowthand survivalare correlativeandlargely focusedon changesin

commercialcatchesorgrowthrates of cod in responseto changesincapelinabundance.

Usingcommercialcatchdata from197010 1978,Akenheadetal.(1982) found that fluctuations in capelin biomasswere notrelatedto catch or growthrates of cod in NAFO Divisions2J3KL.Indicesof capelinabundanceexplained35%of the variation incodinshorecatchesfrom1975 to 1984(Learetal,1986).Agge~tetaI.(1987) observed a correlation of 0.5 (25%ofexplainedvariance) betweencod catchesin inshore trapsandthe proportionof capeJinfoundin cod stomachs.Rose and Leggett (1989)foundthat correlationsbetweenhydroacousticabundanceestimates of cod and capelinranged from0.3to0.6.These valueswere withinthe 0,2to 0.9range of correlationsobservedbyLilly~1 99 1 )betweencodstomachfullnessindexand annual estimatesofcapeltn biomassfrom 1978 to 1986. Sheltonetal.(991) found no relationshipbetweencod growth and capelinabundancebut found a large probabilityof Type IIerror, failuretodetect arealresponse.A commonstatementat the endof all these correlativestudiesis a call for quantltauve, causalexamination of

e-

importance of capelinto the growthand populationdynamicsof cod.

Spatial associationsbetweenAtlanticcod and capelindensitieshavebeen examinedin thenorthern Gulfof 51. Lawrence.Roseand Leggett (1989) foundthat positivecorrelationsbetweenpredatorand prey were a functionof high preydensities (>100 capelin/lOSm^Jwater)and the presenceoffavourable watertemperatures (1-9 OC). Cod and capelindensitieswerenotcorrelated at temperaturesoutsideofthis range. At thetemporal scale of a day,spatialcoherencebetweencod and capelinwas positiveat spatialscales rangingfrom4 and 10 km and negativeatscaleslessthan

capelin aggregation dimensions (3-5 km) (Rose and Leggett1990). On a single occasionwhencodwere activelyfeedingon capelin,predator and prey were coherent at a scale of 3.5m (Roseand Leggett1990).

2.1Introduction

Recent publications(e .g.Wiens1989; MengeandOlson1990;Holling 1992;

levin1992)re-iteratetheimportance of scale inthedescriptionofecological variability.TIlescale-dependenceofbioJogicaJandphysical measurement iswell recognizedinbothaquatic (Stommel 1963;Smith1978:Steele 1978a) and terrestrial (Watt1925.1947;Greig·Smith1952; Urban etal.19 87) ecosystems.Many techniques havebeendeveloped toquantify scalc-dependentecological pattern (see reviews in Plait andDenman1975;Ripley1981:Greig-Smith 1983) andstandard datasets areregularly used10comparethe consistencyof spatialand temporal patternsamongtechniques(e.g.

O'Neilletal.1991;Cullinanand Thomas1992;Tumeret al.1992).Despiteeffortsto quantifyand comparescale-dcpendent spatialvariance, therehasnotbeena concomitant developmentof techniquesthatevaluate the relativeimportance of processesthaigenerate spatial variance patterns.

Scale-dependenlphysicalorbiologicalpattern canbesummarizedin a diagramby plotting varianceof a quantityas a functionof spatialandtemporalscale. The first diagrammatic descriptionsof scate-dep-ndentphysical variabilitywereestimatesof sea leveland deep ocean currentvariance(Stommel1963).Haury et el.(1978) usedthis presentation10developaconceptualmodelofzooplanktonbiomassvariability.This wasthe firstcomparisonof biologicalvariance acrossa wide rangeof scalesand remainstheonly published Stommel diagramof an ecologicalvariable (Marquet etal.

1993).Variations ofSlommeldiagramsshowconcentrations ofspatial and temporal

variabilityas a functionofspace and time scalefor aquatic(e.g.Steele 1978b,1989;

Harris1986;Dickey1990) andterrestrial (e.g.Delcourtetat.1983) ecosystems.

These are intuitivediagramswheretheboundariesof anyfeature ina plotindicatethe minimum andmaximumscalesofvariability for the quantity of interest.The construction ofa true Stommeldiagram requires simultaneousvariance estimatesatall spatialand temporal scales.Thisis rarely possibleat intermediateOflargespatial scales asthe passageof time during data collectionprecludes independentcalculationof spatial and temporalvariance.Stommel diagramssummarizescale-dependent variabilityin a quantityof interest.Theydo not indicatethe biologicalor physical processesthat generate observedpatterns.

As analtemative toinfeni ng process from statisticaldescriptionsofbiological variance,Iproposetheuseof dimensionlessratiosto evaluate therelative importance of variance generatingprocesses as a functionof scale.Comparisonofscale-dependent ratesin theform of a dimensionlessratio assessestheselativecontributionofbiological or physical processesinthe generationofbiological variability.Similarcomparisons using a completesetof ratiosidentifyall potential processes thatregulate variability in a biologicalquantity of interest.Dimensionlessratioshave beenused in ecologyto identifysourcesof planktonvariability(O'BrienandWroblewski1973b; Denmanand Platt1976;Okubo1978), examinegrowth and physiologicalratesas a functionof body size (Gunther 1975; Plaitand Silvert1981; Heusner1987),summarizespatial variabilityin marinenekton (Schneider 1991, 1994a),andevaluatecomplex problems inwildlifemanagement(Schneideretat1993).

In this chapterIuse dimensionless ratios tosummarizeknowledge ofvariance

generatingprocessesacrossspatial andtemporalscales.Thissummary identifies dominantvariance generatingprocesses at any scale of interestand canbeused to improve the design of field sampling programs.The application of dimensional reasoningto evaluatecompeting processescomplementsthe quantitative descriptionof scale-dependentbiologicalpattern.Itneitherreplacesstatistical techniques,nor isit directly comparable10them.

2.2Methods

Prior to any fieldsampling, a crucial task isto identifyvariablesto be measured and appropriatescalesof measurementfor each variable.A scaleof measurementhas two components•• a resolutionand a range.The resolutionor grainis the minimum sampleunit (e.g.quadrat size)while the range is the maximumextentofthe sample (O'Neill 1"1 al. 1986; Wiens 1989).To summarizetherelative importanceof biological or physicalprocessesthat generatescale-dependent biologicalvariability, I proposea 'generic' procedureconsistingof 4 steps:

1) State the quantityof interest.

2) Writean equationincorporatingallpotentialsourcesof variability for this quantity.

3) Calculatedimensionlessratios.

4) Plotand contour ratio values in rate diagramsusingexistingdata.

To illustrate this procedure,I examine thespatial and temporaldynamics of capelinbiomassdistributionin the northwestAtlantic.From the life historyof capelin describedin ChapterI, it is apparentthat changesinthe distributionof capelin biomass

are a result of demographic(recruitment, mortality), growth, and kinematic(activeand passive movements) processesacting within a widerangeof spatialand temporal scales.

The quantityof interestin thisexampleis the proportionalrateof change of capelinbiomassin the northwestAtlantic.Theraieof change of biomass has dimensionstime-r.The biomassBof a groupof organisms i is the productof the number of animalsNmultipliedbytheir individualmassM:

B =I~ NjM i

The concentration of biomassis definedas:

[B].NVM

(2.1)

(2.2)

whereVis thevolume occupied.Tosimplify thenotation a dot over a symbol is used to signifythe proportional rate of changein the quantityrepresentedbythe symbol.

Hence,the proportional rateof changein theconcentration of biomass[!J] is:

[ Li) '[ Br , d~~l

^(2.3)

The secondstep is 10write an equationcontainingpotentialprocessesthat affect the concentration of capelinbiomass. Changein theconcentration of biomass(IJ1is a functionof changein biomassdueto recruitmentand mortalityN •somaticgrowth

Nt.the divergencedue to fluid motionsVFand thedivergencedue to individual motionsrelativeto the fluidVIasshown in Appendix 2.1.Five researchareas are integrated by theequationthat expressesthe rate of changein biomassconcentration:

[Il] tV M biomass demographics growth distribution

V_F V/ (2.4)

fluid behaviour mechanics

Thethirdstep combinestermsfrom equation (2.4)to formdtmcnsiontessratios.

Ifvariables inan equation are dimensionallyheterogeneous, a completesetofratiosis obtainedbydimensionalanalysis(Bridgman 1922).Ifall termsin an equation have the sameunits thenratioscanbecombinedfrom any pair or group of terms.This flexibili ty enables theformationof ratios relativeeithertoa processof interest(e.g.

Schneider1992)ortothecombinationofmultipletermsinto functionallyimportant singleterms (Fischeret al.1979).Three ratios canbeformed fromequation (2.4) relative to the fluidmechanicstermOfcombine demographicand kinematicterms to form populationdynamicsand constructasingle ratio withsomatic growth.

Inthe capelin biomassexample,all termsin equation(2.4) have dimensions of time"so ratios were formed fromthe equation.Biologicalreasoningwas usedtoselect groups ofterms to compare.For example,I wasmore interestedin comparingthetwo kinematicterms,1/randVI,than comparingone of the kinematictermsto demographicsIVor somaticgrowthitt.A formalapproach illustratingthe use of dimensional analysisto formratiosfrom equation (2.4) is providedin Appendix2.2.

The formal approachensuresthat redundant ratiosare not included.

The firstdimensionlessratio comparessomaticgrowthM to the net result of demographicsIVand kinematicsV.

(2.5)

Biomassconcentrationincreasesifanimals grow(hi>0).increaseinnumber (til >0),or contract into a smallervolume

or

water(V<0).Atsmall timescales relativetothe life span ofthe organism,changes in populationbiomassdue 10somatic growth are limitedandthevalueof lhe ratioisexpectedto bemuchlessthan 1. Spatial ortemporalvariability ofa samplebecomesa functionofthe changeinnumberof individualsor the volume in which theyoccurrather thanachangein mass of organisms.Over longertemporal scales the value oftheratiois expected toapproach 1.LargepositivechangesingrowthMand a ratio greatlyexceeding I are typical for long-lived(tVsmalt)speciesthat are managedin large geographicareas(Vsmall).

SmallchangesinsomaticgrowthMcoupled with aratiomuchless than 1(IVlarge, Iismall) are expectedatspatial and temporal scalesassociated withthecapelin spawningseason.

Thedemographictokinematicratiorelates recruitment andmortalityto movements.

tV

iT

(2.6)

Ifthe ratio isgreaterthanI thendemographicsprevailoverkinematicprocesses.A ratio less than 1 indicatesthat kinematicswilldominate overdemographic processes.

Valuesof theratiocanbeexpected to benearunity attime scales ofacohort and at space scalescomparable to the rangeofthe population.In manypopulations,kinematic processesdominateatsmall temporal andspatialscales, whiledemographicprocesses

dominateatlargertemporalandspatialscales.

Thekinematicratiocompareslocomotory velocitiesof the organismtopassive velocitiesduetofluidmotions.

v, i/;

(2.7)

rrindividual motionsdominate,thekinematicratio will exceed1.Themagnitude of ItIis a functionof the locomotorycapacityand life historystageof the organism.An exampleis the relativemobility offishlarvae comparedto adults.As the mobilityof anorganismdecreases,VIapproachesO.Whenorganisms drift passivelywiththe fluid,the value of the ratio ismuch less than 1. ValuesofV^Fare sensitiveto study locationand spatialscale. Lcntieand lotic environmentswilldifferinthe potential for passivedrift of any organism.Passivedrift may also be importantto terrestrial organisms,includingseeds,small insects,and spiders.At largespatialscales, the range of a studymayencompass autonomouscirculationfeaturesassociatedwith the fluid (e.g. gyres), thereby makingIiFsmalland the kinematicratio large.Ifthe value of the ratiois approximatelyequal to 1, changesin the distributionof biomassdue to movement dependonthe interactionbetweenbiologicaland physicalprocesses. High, intermediate, and low valuesofthis ratio correspondtoWiebeand Flierl's (1983) biological,physical-biological,and physicaldistributionalmechanisms.

The demographicratio measuresthe importanceof recruitment]i.'rrelative to mortalityN..Incapelin,as in other commerciallyimportantspecies, mortalityN.

is partitionedintonaturalN",and harvestingNImortality.

(2.8)

Overshort timescales,thisratioisgreater than 1 during the breedingseasonof capelin and lessthan oneduring theremainderof the year. At thespatialscale of the populationrange(lOO' skm)andthe temporalscale of a cohort(5yr),the valueofthe ratio will approachunity.In unexploitedpopulations, maintenance of biomasslevelsat equilibrium isindicatedbyavalue ofI.Increased mortalitydue10predation or the onsetof harvestingreduces this valuebelow unity unless a compensatory increasein recruitment occursat lowdensities. Commercial fisheriesmanagers attempt to maintain the valueofthis rationear unityat time scalesof several yearsbyregulating harvestmortalityNJthrough quotasand gear restrictions.

The fourth step in the procedureisthe plottingof eachdimensionlessratio as a functionofspatial(x-axis) andtemporal(y-axis) scaleusingexistingdata.In many ecological systemsprecisionofcalculations may be limitedby a paucityofdata at large spatialand temporalscales.If data arelimited orunavailable, calculations can bemade at benchmarkspatiotemporal scales. Nominal«1,1,>I)contours are then drawn basedon these benchmarks.Ifdata areavailable overawiderange of scales, spatiotemporalscales where transitionsbetweendimensionlessratiovalues occur are marked.Contour lines are then drawn to connecttransitionpoints. Locationof dimensionlessratiocontours are refined asadditionaldataare obtained from field studies.The inabilityto calculatedimensionlessratiovaluesat a specific scaleindica~

a potentiallyimportantresearcharea.Thismethod canbeused by groups of researchersto make perceptionsof therelativeimportanceof competingprocesses

explicit. Comparisonsof rate diagramsfrom each individualcanbeused to highlight discrepanciesbetweenratio valuesand 10focus the discussionof large research groups on dominantscale-dependentprocesses.

Data from capelinassessmentdocumentsand publishedvelocitiesof the Labrador and Newfoundland inshore currents wereused10estimatescale-dependentratiosin rate diagrams. Order of magnitudecalculationsshowed whetherthe absolutevalue of any dimensionless ratio was less than, equal 10, or greater than I at a given spatiotemporal scale.Contour linesmarkedthe spatialand temporalscaleswhere dimensionlessratios changed value.

2.3 Results

The major feature in the rate diagramof capelingrowth to populationdynamics ratio (Fig. 2.1a) reflectsthe persistenceof Newfoundland-Labrador cape1inpopulations at large scales. At spatialscaleslarger than the continentalshelf and temporalscales larger than a year the valueof the ratio is greater than 1. This is a result of changes in the concentrationof biomassdue to somatic growth exceedingchangesdue to populationdynamics.On averagecapetlngrowth, as indicatedbylength,increasesa total of 40,900% or 10,225% ofinitial hatch length per year during the first 4 years of life (Templeman 1948). This rateexceedsthat of partial recruitmenttothe adult stock

··53% peryear (Carscaddenand Miller 1981), spawning mortality_. 80% of spawning stock per Yl',M (Carscaddenand Miller 1980),fishingmortahty-.0.05% of estimated biomassper year (Carscaddenetal.1991), and the net kinematicrate --0% because the populationremainson the continentalshelf. Recruitment,mortalityand kinematicrates

,"-I I b:=~ ^COVe

:~.""' o< ... ...., ...., ' : . • _{,~" ,~~, ,~.} ":, , ,,.

_;:'k • "

..

hour

] mlnul.

_ . .cond

j~~~:'.,. ,

^d

ll ' · ··

day • <'. '

<1 ,. p e n"9.

hou' • •••

mlnul•

• ""ond 10", lkm 1001",., <I 10... lkm IlJOkm

Spatia lScale

F1g.2.1Contoured rate diagramsof dimensionlessratio values for adultcapelin biomassdistribution inthe northwestAtlantic.Ratiosare contouredless thanI

«

1), equal to 1 (=1),and greaterthanI(>1).a) Growthto population dynamics (demographics -kinematics) ratio,

-h

b) Demographics (recruitment

+

mortality)to kinematic (locomotory

+

passivemotions)ratio,_~.Dolled line indicatesshiftin contourduring spawningseason.c) Locomotorytofluid (passive) motion ratio,~^{d)Recruitment}to naturalplusharvestingmonality ratio,

N ::N "

^Dottedlineindicates scalesof mortality duringspawningseason.

exceedsomaticgrowth ratesatsmallerscalesand the valueof the ratioislessthan I.

Valuesof the demographic10 kinematicratio(Fig.2.th)vary depending on capelio reproductivestatus.Attemporal scales of ayear and spatial scales ofthe continentalshelfchangesin the concentrationof capelinbiomassdue to demographic processesexceedchangesdue 10kinematicsand thevalue of theratioisgreaterIhanI.

Partialrecruitmenttotheadultpopulation (4years) is53%peryear (Car scadden and Miller1981).Natural mortality istypicallyassumed tobe 30% peryear incapelin (e.g.Carscaddenand Miller 1980). Changesin the volume occupiedbycapelin populationsare negligibleat thesescalesand ther eforethe valueofthekinematic term isnear zero.Atsub-annual scalespassiveand activemovementsofcapelins.crease the value of the kinematictermand the valueof the ratiodrops below I.During the spawningseason, thelocation of the unity contourshifts to the spatial scale ofa spawning beach or cove (100-1000m) on a daytoweeklyscale. This isa resultof increasedmortalitydue to spawning_. approximately 2%of spawning fishper day (Carscaddenand Miller1980) and inshoreharvesting--0.001%of total estimated biomassper day (Carscaddenetal.1991).Concentratedpredationon capelinbyfish, seabirdsand marine mammals also occursduring thisperiod(cf.Carscadden 1983)but lack ofdata prevented an estimateof mortalityratesdue to naturalpredation.

Theunity contour in the diagram of the kinematicratio(Fig.Z.lc) isalsolocated at the scaleof theentire population. Onthecontinentalshelfoveran annualcycle.

passivedriftassociatedwiththe LabradorCurreru-.typical surface speedofinshore branch 0.1mS·l(Helbiget el.1992),is balancedby the annual migratorycycleof adult fish (cf.Carscadden1983).Attemporal scaleslessthan ayear and aspatial scaleof

the contine ntalshe lf, changes in biomass concentra tionduetoswimmingexceed changes dueto passivedrift and thevalue of the ratio is greaterthan1.At spatial scalesof kilometresto metresand temporalscales of weeks to seconds, potential changesinthe concentrationofbiomassdue 10 passivedrift withtides,currentsand internal waves(Yao 1986,de Younget al.1993) exceed changesdue to active movements.Hence the valueofthe ratio isless than1.The dominanceof passive movementsat thesescalesdisappearsduringthe spawningseasonwhenaggregationsof adult capelin mig ra te to coastal waters.

Atthelargest scales in the rate diagram of the demographicratio(Fig.2.1d), persistenceof a populationrequires a balancebetweenrecruitment andmortality.The resulting valueof thedemographic ratio mustequal 1.On an annualscaleoverthe spatialrange of thepopulation,recruitmentgenerallyexceeds naturaland harvesting mortality.Largedecreasesin recruitmentcombinedwithincreasednaturaland harvesting mortalitymay reduce thevalue of theratio belowunityatthese scalesin any particularyear.For example,capelin recruitmentmeasured as 2-year-oldsdroppedby afactor of35 betweenthe 1973 and 1916year-classesin NAFO Division2J3K (CarscaddenandMiller1981).During the spawningseason, mortality exceeds recruitmentto theadultpopulation.This reducesthe valueof thedemographicratio to less than one atspatial scalesof hundredsof metrestotens ofkilometresand temporal scales ofhourstoweeks.Atthe scaleofanindividual capella (tessthan a metre,afew minutes), changesinbiomassdue tonatural andharvestingmortalityare greaterthan thosedueto recruitment.

2.4Discussion

Theproposedframework isnota panacea forevaluatingpattern generating processes.Itis a technique thatsummarizesand displaysexistingknowledgeof scele-depencenrprocessesin anyecological system. Ratediagramscan beused to evaluatet.herelative importanceofvariancegeneraling processesatany scaleofinterest and 10identifysampling scales in process oriented research.This isaniterative procedurewhereratio values and contourlocations arcrefinedas newdata are gathered.

A plot depictingbiologicalvariability asa function ofspaceand time combined with a set of ratediagrams synthesizesavailable knowledgeofscale-dependent pattern and processfor abiologicalquantity.Comparison of prominent variancefeatures to dimensionlessratio values atthesame scale identifiesprocesses thatar e likely to generatespatial ortemporalvariance in the quantityofinterest. Thispresentation avoidstheassumption that asingle biological or physicalprocessisdirectlylinked to pattern at anyscale,and that couplingof biological and physicalprocessesoccurat characteristicspatial and temporalscales.Tofurtherillustrate the advantagesof using dimensionlessratios,1constructed a setofzooplankton ratediagramsto identify potentialvariancegenerating processesin theHauryet al.(1978)Stommel diagramof zooplanktonbiomassvariability(Fig.2.2a).Dimensionlessratio valueswere estimated and nominal contours« I.I,>1)wereplotted across thesamerangeof scales in a column ofratediagrams (Fig.2.2b -2.2e). Zooplanktonwere assumedtobean unexpfoitedpopulationof mid-latitudezooplanktonicorganisms with the limited locomotorycapabilityof copepods.

1978).Nominal contouredratediagrams«1,=1,>I) of b)growthto populationdynamicsdimensionlessratio,~c)demographicto kinematic dimensionless ratio,~d) locomotory tofluid(passive) motiondimensionless ratio,~^{and e)}recruitment to naturaland harvesting mortalitydimensionless ratio,N",~·N,.Shadedregions indicatea ratiovaluegreaterthan1.

The rate diagramof thegrowth to population dynamics ratio(Fig. 2.2b)shows greater changeinthe concentration of biomass due to somatic growththa n dueto demographicand kinematicprocessesat spatial scalesup to a kilometre( 10' em) and temporal scales from days to a month(l()f s - lQ6s). Thevalue of the ratio isless than 1atall otherscales.In the demographictokinematic rate diagram(Fig.2.2c) atthe scale of the population,biomasschanges duetothe successionof generationsexceed biomass changes due to movement. At scales shorterthan annualcycles and smalle r than the continentalshelf,biomasschangesdue to swimmingand passive movements dominateoverdemographic changesand the valueof the ratiois lessthan I. The rate diagra m of the kinematic ratio (Fig.2.2d)reflects the locomotorycapacity of the organism. Changesin biomassdue to swimmingand diel migrationdominate at scales of days and hundredsof metres,resulting in a ratiovalue greater thanI. Atlarger scales passive motionsassociatedwithflow structures(e.g. currents,gyres,upweJling) determine the distributionof biomassand the valueofthe ratio is reduced belowI.In the rate diagramof the demographicratio (Fig. 2.2e),changesin biomass due to recruitmentand naturalmortalityare approximately equal at allspatial scalesover annualandlargertemporal scales.The valueof the ratiois greater thanI atspatial scales greaterthan a kilometreand attemporal scalesofweeksto monthsas a resultof the turnoverin generations.Changes in biomassdue to predation and natural mortality dominateat allotherscales,thereby reducing the valueof theratio below 1.

Comparisonof the ratediagrams withthe zooplanktonSlommeldiagram showed thatof the elevenfeaturesin the Stommel diagram(designatedby letters A·K), Sillwere attributableto dominantprocesses inratediagramsat the same spatial and temporal

scales. Theremaining five features(C,F,I,J,K)intheStommcl diagramareattributed 10fluid motions,whileplotsof rates indicate thatdemographicprocesses should prevail at[hespaceandlimescalesofthese features.Basedon the ralcdiag rams ,1 hypothesizethatvariabilityinzooplanktonconcentrationatthe spaceandtimescalesof featuresC,F.I,J,Kinthe Stommel diagramaredue moreto demographic than tofluid processes.Biomass distribution,locomotory capacityand passivedrift data atlarge temporal scalesareneed edtotestthis spec ulation.

2.4.11denti ryingAppropr iateSamplingScales

Ifa researchprogramisfocused ona particularprocess (e.g.somaticgrowth).

ratediagrams canbeusedtoidentifyrelevantsamplingscalesfora field program.For examplethe ratediagram ofthegrowth to populationdynamicsratio(Fig.2.la) indicatesthatsomaticgrowthexceedsdemographicandkinematicrates ata spatialscale ofhundreds of kilometresanda temporal scale ofseveralyears.nlisspatiotemporal scaleis a logicalchoiceof samplingresolutionwhen quantifyingthecontributionof somaticgrowthtochangain capelinbiomass concentratice.At smallerspatiotemporal scales,changesin capelin biomass concentrationare dominatedbydemographicand kinematicprocesses(i.e.ratio<I).Scales whereinteractionbetweencompeting processesmaybeimportant areindicatedbydimensionless ratio values approximately equal to1.Interactions betweengrowth and populationdynamicprocesses arelikelyto occur at annual and continental shelf scales (Fig.2.la).

The plottingofdimensionlessratioscanalsobe usedtoquantifytherangeof scales over which researchconclusions canbe generalized.Ecosystemprocessmodels

shouldnotbegeneralizedacrossscales,just asregressionmodels shouldnotbe extrapolatedbeyondlimitsof sampleddata. Forexample,thecapelinbiomassrate diagramsindicatethat a spatialvariance modelforthe eapelin spawningseason oyer spatialscalesless than 10 kilometresshouldincludefishingand spawningmortality (Figs.2.lb,2.ld).Ratediagrams indicatethatexpansion ofthe madel iaannual cycles over the continentalshelf would require theinclusion of recruitmentand growth processes (Figs. 2.1a,2.lh, 2. td).

2.4.2Evaluat ing Variance GeneratingProcesses

Comparisonof ratios derived from dimensionalanalysisprovides considerable insightintothe relativeimportance of pattern generatingprocesses.Aftersettingthe temporaland spatialscalesof interest,a set ofrate diagramsandorderofmagnitude calculationscan be usedto identifypotentiallydominantprocessesprior to field sampling.To illustrateby wayof example,what samplingscalesshouldbeused and whichprocessesshouldbemeasuredto quantifythespatialvarianceof capelin distributioninnearshore watersduringthe spawningseason? Fromcapelinlifehistory it is known thatthe spawningseasonlasts approximately six weeksevery year and occurs along most ofthe Newfoundlandcoast. Onsetof spawningmay follow a south tonorth latitudinaltrend(Templeman1948)butsuitablespawninghabitatis assumed alongtheentirecoast. Thereforethetemporal scaleatwhich to evaluatecompeting processes is approximatelysix weeks. Logisticsamplingconstrainu setthe spatial scaletothat of a bay (20-40km).At this spatiotemporelscale,therate diagram of the growthtopopulation dynamicsratio (Fig.2.la)indicatesthat demographic and

demographicto kinematicrates (Fig.2.lb )is near I,indicatingthat both demographic and kinematicprocesses maybe importantto capelinspatial dynamicsduringthe spawning season. Furthercomparisonshows thatkinematic processes are dominatedby divergenceduetoswimming motions (Fig.2.lc)and that mortalityexceedsrecruitment in thedemographic ratio(Fig.2.1d)at thistime or year.

Order ofmagnitudecalculationscanbeusedto compare therelative importance of individualmotionVItomortalityiii'"+iii1at this scale.Using therelation between body size andswimming speed(Okubo 1987),a IScm capelinbasa range of approximately24 kmday-t.Mortality averagesapproximately2%day·ldue to spawning (Carscaddenand Miller1980) and 0.00125%of thetotal biomass day. in NAFOdivisions2J3KLduring 1989duetoharvesting (Carscadden etal.1991).Using 20 and 40 kilometre.samplingranges,thereis a60%-119%day·l rateof capelin divergencecomparedto atotalmortalityof2% day·l. Atthe scaleof a bay^Iresearch effort on thespatialdynamics ofcapelinduring the spawningseasonshould beginby examiningkinematics.

Plouingdimensionlessratioswithinratediagramscanbe used10define time and space scalesrequiredto managerenewableresources.The ratioof growth to populationdynamics(equation 2.5)assessesthe effectsofresourcemanagementpolicy.

Large positivechanges in somaticgrowthMcombined with aratio greatly exceeding I indicateapotentialfor growthoverharvesting.Smallchangesinsomatic growth coupled witharatiomuchlessthan1 indicates recruitmentoverharvesting.

widely-usedfisherymodels(Ricker1954; BevertonandHolt 1957) weredevelopedfor

situationswhereMwaslarge and the ratio inequation(2,5)greatly exceededI. This istypicalfor100g.livOO,demersalspecies that are managed overlarge areas. 10 contrast,heavyfishingpressureon pelagic species increasesbothNandVas mortalityincreasesand the spatialrange is contractedtomaintain schooldensities (Murphy 1966;Winters andWheeler1985; Csirke 1988),The sizeofmanagement areas for demersalandsome pelagicfishstocks are typicallyon the order of hundreds of square kilometres.These arechosen to containpopulationmovements over an annualcycle.Thisreducesthe value of the demographictokinematicratio(eq ua tion 2.6) belowJ and the kinematicratio (equation2.7)becomeslarge asVFapproaches O.Wide rangingspecies(e.g.whales,tuna) clearlyrequiremuchlarger management areasto maintainsimilarvaluesinratios containing kinematicterms.

The managementof exploitedpopulationsissummarized, in part,bythe demographic ratio (equation2.8). Resourcepopulationsare regulated through the allocation of quotasIVt.Natural mortalityN",is rarely measuredfor commercial fish stocks.Itis traditionallyassigneda constantvalueinstock assessments,typically 0.2year-tfor demersalspecies.Fisheriesresearch haslargely focusedon recruitment processesNrin an effort to predict conditionsof high recruitment. Fluctuationsin annual recruitmentof fish specieshave rangedfrom a factorof 2 to a factorof 100 (Cushing 1982)but theprocess is not wellunderstood.The demographicratiocan also beused to calculateharvestingrates needed to maintainorincreaseresourcelevels.

The onset of harvesting dramatically increasesNIrelativetoN,.If the recruitment rate isknown,resource managerscan preventrecruitmentoverharvestingbylimiting harvesting atlevelsequaltoorbelow recruitmentrates duringthelong-term

management of the resource.

Contouringdimensionlessratiovaluesas a functionof spaceand timescales provides a comprehensivemethodtosummarizeknowledgeof pattern generating processesincomplexecologicalsystems.Itcanbeusedbyindividuals conducting researchprograms orbyagenciesmanagingrenewable resources.This technique summarizesthe spatialand temporaldynamics of any organism, evaluates the relative importanceof pattern generatingprocessesat singleor multiplescales,identifies potentialresearchareasand appropriatesamplingscales for field studies. andquantifies the range overwhichspatioternporal modelscanbegeneralized.Aquaticexamples wereusedto demonstrate the methodbutthe sameproceduresshouldbeapplicableto organismsinterrestrialor aerialenvironments.

As a brief terrestrialexample I examinefactorsaffectingtherate of change in the concentrationofseedproducingbalsamfir (Abiesbalsamea)trees.The rateof change inthe concentrationoftrees[N]isa functionof recruitmentN" naturalN'"and harvestingtil~mortality,and the lateraldivergenceof treesduetoseeddispersalAD.

orsimply:

[N ]..N,+NJ7I+ N,, - AD

INI-N-A

(2.9) (2.10) Aforestmanager 01" conservationistmaybe interestedin changesin the densityof sprucetrees.Changesin densityreflect therelative importanceof demographicand kinematicprocesses,indicated by the changeinnumberof trees relativetothe areal spread of a balsamstandor of thespecies~. Iffor examplerecruitmentto the balsam treepopulationN,is approximately 0.1%year-r,thenmortalityN",+tV~mightbe expectedto exceed recruitmentat smallspatiotemporalscales.At scalesgreaterthan

100kilometresand the lifespanof a tree (100years) recruitmentis expected10equal morta1ity.At spatialandtemporalscalesof asingle tree values of the ratio are predicted10equal1, although soil conditionsand stand successionstage willinfluence localvalues.Atannualscalesthe ratio will exceedunity due to blowdown,disease.

insectdamage,and seed movement.At the scale of centurieskinematic changesdue to lateraldivergencemightbeexpectedto exceedthose due to demographics and the ratio willbeless than I. Thissketch of therelativeimportance of competing processes in balsam tree distribution couldbedepicted in a ratediagram such as Fig.2.1 orFig.

2.2,based on estimatesof rates and the resulting dimensionlessratiosplotted as a function ofsca1e.

The useof dimensionless ratiosishighlyusefulto researchers collecting datain diverse ecosystems, such as the Long-Term EcologicalResearch (LTER) sites (d.

Magnuson et aJ. 1991). Variancegeneratingprocessesof severalspeciescanbe summarizedand comparedwithinoramongterrestrialand aquaticenvironments over a widerange of spatialand temporal scales.

Appendix 2.1: Spatia l Dynamicsof Biomass

OIanges intheconctnuationof biomass[!J]of an organism ina fluid environmentareafunctionof recruitmentN ••naturalfJ..andharvestingNJ mortality, somaticgrowthM•divergenceduetomolions within thefluidVF.. .,d divergence duetoindividual motionsrelativetothe fluidII,:

{B]-liIr-Nm-NI+M-11,-V, Definitionofterms:

IS] instantaneoustime rate of changeinconcentrationof biomass.

Dimensionsare time-t,

' d(NN)

IBJ-I Br'dl!!_

(NM) - --.2:..

dl V dt

til· tV,-N ..-IVIinstantaneoustimerate of changein biomassduetobirths( r ).

natural.mortality(m)andharvestingmortality(f ).Dimensions are time-I,

M instantaneoustime rateof changein populationbiomassdueto growth.Dimensionsareume-,

instantaneous timerale of changein volumeoccupiedbya groupof organismsdue to the velocityof the fluidIi"Fandthe velocityof individualsrelative to the fluidV^{I .}The divergencetheorem can beused to describethe kinematicsofbiomassin a fluid environment(Schneider1991). This theoremrelatesthelocal rate of changein a volume

7.-

occupiedbya groupof organisms10 horizontalu..

¥r.

u ...

t.-

and verticalw"~velocitiesin an x,y,z co-ordinatesystem. Incompactnotation, the rateof change in volumeoccupiedVisIi..(r::j •1I)whereuis thevectorof velocities (u,v,w),the dotIndicates scalarmultiplication,andvis the gradientoperator(seeDutton1976.chapterS).Dimensions are

Ji-v-I~ _~ +~ + ~-Q.t1

d! oX oy 02:

Thisequation statesthat rate ofchangein thevolume occupiedbya given populationi.:iequalto thedivergenceof thepopulation.where divergencecanbepositive(diverging)or negative(converging).

Movementof the populationin a fluidenvironmentis a resultof displacementduetomotions of thefluidUFandmovementof individuals relativeto the fluidu1. Formanyterrestrialorganisms

IiF ..0and divergenceisa function of organismlocomotion.

Appendix2.2: DimensionalAnalysis

Dimensionless ntiosarec:ak:ulatedbyconstructing atwo-waylablewherethe variablesofinterest are columll!andall funda mentaldimensions(e.g. mass,length , time,numberof organisms) arerows.Exponentsofeachvariableform the elementsof a dimensional matrix(e.g.volun.c:has dimensions lengthS).Variablesarethen combined usingthelinearalgebra(Langllaar 1980) or the successiveelimi nation method(Taylor 1974)tomake all valuesof exponents zero.Thisresultsina set of dimensionlessproducts.

In thecapelin biomass enmple,quantitiesofinterest are:demographicN • growth M. andkinematic V rates.The fundamenl.a.1quantities are:lengthL.mass

M•timeT.andnumberof organisms

'*.

The dimensional matrix is:

tV M V

Dimension L 0 0 0

M 0 0 0

T -1 -1 -1

•

^{0 0 0}

SinceaUquantities are rates, dimensionsotherthantimecanbe dropped.Dividing throughbyVtherevisedmatrixbecomes:

Dimension T

tV

V o

AI V

o

Dimensionallyhomogeneous termscanbecombinedtoformlogical groups(Fischeret al.1979).Demographicsand kinematicsan: combinedto formthe quantitypopulation dynamicsN-Vwithdimensionstime-t.ReplacingNandIibyN- Vand dividingtheoriginal matrixbyN - Iithe revisedmatrixbecomes:

Dimension

M

!i-v

T 0

Analysisresultsin tworatios:

fI

V

Ratioof demographics(recruitment,naturalmortality, harvestingmonality) tokinematics(activemovement,drift).

Ratioof growth to populetion dynamics(demographics,kinematics),

Two additionalratiosres ultif demographicand kinematicprocesses are examined individually.

tVr Ratioof recruitment to natural andharvesting mortality.

N",+N ,

IiI Ratiooflocomotoryto fluid(passive)motions.

i';

3.1Introduction

Theoryar.dobservationsuggesteasternand northeasternNewfoundland coastal watershaveananisoeoptchorizontalthermal structure^e-greaterspatialvariation acrossthanalongthe continentalshelf.Thelate springtoautumnpressuregradient caused bytheBermudahigh resultsin episodicupwelling throughlocal southwesterly winds(Frank and Leggen 1982; TaggartandLeggett1987;Schneiderand Merlwen 1988) andpropagatinginternalwaves(Yao1986;de Youngetal,1993).The anisotropicphysicalstructure ofcoastalwaters isalso augmentedbythesouthward flow oftheinshorebranchoftheLabradorCurrent(Petrieand Anderson1983).Anisotropic physicalgradientshave been showntoinfluencethe diszri"'ulionof phytop lankton (lversonetal.1979;Denman andPowell1984; Mackas et al.1985),zooplankton (Hermanetal.1981;Maclw 1984;IbanezandBoucher 1987),andseabirds(Schneider andDuffy1985;Briggs1986;Schneider etal.1988).

littlework has focused onanisotropicconcordanceof physicalgRdients wilhfish distributions(e.g .Olson andBackus 1985).Capelinareastenothermalspecies (fempleman 1948;ScottandScott1988;Rose and Leggett1989)andre.pond to displacementsofhorizontal(Buzdalin and Burmaldn 1976;Schneider andMethven 1988) andvertical (MethvenandPiatt 1991)thermalgradients Thereforea horizontal concentratingofcapelinis predicted at a warm/cold water frontTheresultingcapelin distributionishypothesiz.'"dtobe patchyat thescaleClfupwellingcross-shoreand patchy at thescaleofacapellnaggregationlongshore.SchneiderandMethven (1988)

and Schneider(1989)examinedcapelin distributionduring upwellingandnon-upwelling periodsin theAvalonChannel.Cape lin aggregationswere concentra tedatthe warm/cold water interfaceat the scale ofupwelling,butanalyseswere restrictedto c.ossshore transects.Thepotential anisotropicdistributionof capelin aggregationshas not been examinedincoastalNewfoundland waters.

This chapter quantifies spatial variancein capelindistributionas a functionof spatialscale.Long and cross shorespatialvariabilityis compared and contrastedto spatial variance patternsof coastal sea surfacetemperatures.Sea surface temperatures are used as anexample of a passive tracerof thesurrounding fluid.Spatialvariance patterns ofcapelinaggregationsinsynoptic long and cross shore transect pairs are then examined fo ranisotropy.

3.2Methods

Hydroacoustic surveywerecond ucted along the northwesternshoreof Conception Bay,Newfoundland, from Ochre Pit Cove toBaydeVe rde(Fig. 3. 1).Transectswere oriented paralleland perpendicular to shore,the majorityfor ming alarge letter-E"

(Fig.3.1).The locationoffishinggearin the area dictated the proxi mityoflo ng and cross shore transects to the coastline .Transec t lengthwasset at 10 kilo metres,a distance corresponding to approximately twicethe first internalradiusofdefor ma tion (Rossby radius)atthis latitude(Schneide rand Methven1988).

Sea surface temperatu re(±0.1"<:)wasrecorded at60 second intervals using a surfacetowedthermistor.Atthestart and endof eachtransect, wate rtemperature(±

0.1"C)was measuredalSm depthintervalsusingan ElLMCS Salinometer