Ecophysiological dynamic model of individual growth of Ruditapes philippinarum

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Ecophysiological dynamic model of individual growth of

Ruditapes philippinarum

Jonathan Flye-Sainte-Marie, Fred Jean, Christine Paillard, Susan Ford, Eric

Powell, Eileen Hofmann, John Klinck

To cite this version:

Jonathan Flye-Sainte-Marie, Fred Jean, Christine Paillard, Susan Ford, Eric Powell, et al..

Ecophysio-logical dynamic model of individual growth of Ruditapes philippinarum. Aquaculture, Elsevier, 2007,

266 (1-4), pp.130-143. �10.1016/j.aquaculture.2007.02.017�. �hal-00452257�

growth of Ruditapes philippinarum

⋆

Jonathan Flye Sainte Marie

a

, Fred Jean

a

,

_∗

, Christine Paillard

a

, Susan Ford

b

, Eri Powell

b

, Eileen Hofmann

c

, John Klin k

c

a

IUEM- LEMAR,Pla e Coperni , 29280 Plouzané, Fran e

b

HaskinShellsh Resear h Laboratory, Rutgers University, 6959 Miller Avenue,

PortNorris, NJ08349 USA

c

Center for CoastalPhysi al O eanography, Old DominionUniversity,Crittendon

Hall, Norfolk, VA 23529, USA

Abstra t

A bioenergeti s model of the Manila lam (Ruditapes philippinarum) was built

to simulate growth,reprodu tion and spawning in ulture and sheryeld sites in

MarennesOléron Bay (Fren h Atlanti oast). The model is driven by two

envi-ronmental variables:temperature andfoodsupply.The foodsupplyand the lam's

ltrationratedeterminesofttissue onditionindex,whi hinturndrives lamgrowth

andreprodu tion.Themodelwas alibrated andthenvalidatedusingtwo

indepen-dentdatasets.

Thispaperdis ussesthe di ultyof omparingexperimentaldataandindividual

modeloutputswhenasyn hronousspawningeventso urinthestudiedpopulation.

In spite of this di ulty, the simulations reprodu e the typi al pattern of growth

and reprodu tion ofthe Manila lam.

Simulationsshowedthatwater olumn hlorophylla on entrationisnotaperfe t

estimatorof foodresour es for anear bottom suspensionfeeder su hastheManila

lamandemphasizethe la kofknowledgeaboutRuditapesphilippinarumnutrition.

The individual growth model presented in this paper will be integrated into a

numeri al population model des ribing the host-parasite-environment relationship

inBrown RingDisease, aused bytheba terium Vibrio tapetis.

Key words: model, individualgrowth, energy balan e,reprodu tion, foodinput,

Brown RingDisease

⋆

SupportedbyNSF-CNRSjointprogram

The Manila lam (Ruditapes philippinarum) was introdu ed for aqua ulture

purposes to Fran e between 1972 and 1975 (Flass h and Leborgne, 1992). In

Fran e, this venerid ulture be ame in reasingly widespread, and sin e 1988

natural populations have olonized most embayments along the Fren h

At-lanti oast, resulting ina shery of a1500 tons inthe Gulf of Morbihan at

the end of the 1990s. R. philippinarum is often ae ted by high mortalities

inlate winter, whi h onsiderably limitaqua ulture and sheries produ tion.

These mortalitieswere rst asso iated with unfavourable environmental

fa -torssu haslowtrophi resour es, oldtemperaturesandlowsalinity

(Goullet-quer,1989b;Bower,1992).Later,theywere attributedtoBrownRingDisease

(BRD), a ba terial disease indu ed by the pathogen Vibrio tapetis (Paillard

etal.,1989;PaillardandMaes, 1990),in onjun tionwithlow onditionindex

and lowbio hemi alreserves (Goulletquer,1989a).BRDprogression in lams

andV.tapetis strategiesforinfe tionhavebeendes ribed indepthbyPaillard

etal.(1994)and Paillardand Maes(1994).Infe tions maytheoreti allyo ur

any time of the year, but BRD development may be modulated by

environ-mental onditions (Paillard et al., 2004) and lam's defen e system (Allam

and Paillard,1998;Allametal.,2000).Inadditiontheseauthorsshowed that

BRD developmentis modulatedby the energy balan eof the lam.

Asa rststep indeveloping anumeri almodeldes ribing the

host-pathogen-environmentrelationshipsinBRD,thisstudypresentstheindividual

e ophys-iologi almodel ofgrowth and reprodu tionofthe Manila lam.The aimisto

des ribe the variability in energy balan e for an individual without BRD as

a fun tion of the two main environmental fa tors presumed to ontrol BRD

development:the trophi resour es(Goulletquer,1989a)andthe temperature

(Paillard etal.,2004).

2 Materials and methods

2.1 Basi on ept and state variables

The modelisbased ona thewidely applied(see reviewinBayne,1998)s ope

for growth (

SF G

) on ept. The

SF G

on ept assumesthat energy ormatter

gained by food a quisition is equal to the energy or matter lost for

mainte-nan e,growth and reprodu tion.

SF G

an be al ulated asfollowsa ording

SF G = Gg + Sg + Sh = Cons − (P p + F p + Resp + U)

where:

Gg

isgonadalgrowth;

Sg

issomati growth;

Sh

isshellgrowth;

Cons

is onsumption(retained organi matter);

P p

ispseudofae es produ tion;

F p

is fae esprodu tion;

Resp

isrespirationand

U

isureaandaminoa idex retion.

If

SF G < 0

, energy or matter is mobilized, rstly from gonad, then from

somati tissue, and the lam loses weight while using energy reserves. If

SF G > 0

,energy ormattergainedispartitionedintoshell, soma,and gonad.

Partitioning among those three ompartments is ontrolled both by

environ-mental parameters (quantity and quality of food, temperature, salinity, ...)

and by endogenous fa tors su h asgenotype, size and physiologi al ondition

(see e.g. Shafee and Lu as, 1982; Lu as, 1993; Goulletquer, 1989a;Pérez

Ca-ma hoetal., 2003).

The on eptual design is des ribed in Fig. 1. The stru ture and formulation

of this model is based on the Hofmann et al. (2006) Mer enaria mer enaria

growth model.The twostate variables are the shelllength and the total esh

weight in ludingsomati weight and gonadalweight.

Ingestion

Assimilation

Respiration

Reproduction

Filtration

Net Production

Division

Net Production

Trophic

Ressource

Temperature

Condition

Index

Somatic

Growth

Shell

Growth

(length)

LEGEND:

Negligible energy flow

Influence

Spawning

Energy flow

Three data sets (Fig. 2) were extra ted from Goulletquer (1989a), a survey

of Manila lam aqua ulture in the Marennes-Oléron basin (Fren h Atlanti

oast, see Fig. 3):

(1) atimeseriesfromNolestation(Mar h1984toSeptember1985)of

hloro-phyll a (

Chla

) on entration was used for alibration. Temperature (

T

;

◦

C) was obtained from the same study site duringa 1986 survey;

(2) two time series, one from Nole station and the other from Lilleau

sta-tion,both extendingfromMar h1985 toMay 1986,were used formodel

validation.Both onsistedof

Chla

on entrationandtemperatureseries.

Datafromalltimeserieswerelinearlyinterpolatedtoobtaindailyvalueswhen

ne essary.

In order to evaluate trophi resour es,

Chla

on entration was onverted to

ingestible dry organi matter (trophi resour e

F ood

,

g L

−1

) to take into

a ount the pseudofae es produ tionstep, followingthe equation:

F ood = Chla × F oodCoeff

where

F oodCoef f

in

g DW µg

−1

_Chla

is the oe ient that onverts

Chla

toingestibledry organi matter.

2.3 Physiologi al me hanisms formulations

2.3.1 Net Produ tion

Netprodu tionofdryorgani matter(

P net

;

g day

−1

)was al ulatedwiththe

following equation, whi h ree ts energy gain from assimilationand lossdue

torespiration:

P net = Ingest × Assim − Resp

(1)

Food a quisition Using data from literature (Goulletquer et al., 1989;

Goulletquer,1989a), theltrationrate ofa 1-

g DW

individualwasestimated asa fun tion of temperature using the followingempiri alequation:

F ilt

T

(T ) = −5.62 10

−3

× T

2

0

2

4

6

8

10

12

14

16

18

50

100

150

200

250

300

350

400

450

500

Chlorophyll a (µg.l−1)

Time (Days)

A

0

2

4

6

8

10

12

14

16

18

50

100

150

200

250

300

350

400

450

500

Chlorophyll a (µg.l−1)

Time (Days)

B

0

2

4

6

8

10

12

14

16

18

20

22

24

50

100

150

200

250

300

350

400

450

500

Temperature (°C)

Time (Days)

C

0

2

4

6

8

10

12

14

16

18

50

100

150

200

250

300

350

400

450

500

Chlorophyll a (µg.l−1)

Time (Days)

D

0

2

4

6

8

10

12

14

16

18

20

22

24

50

100

150

200

250

300

350

400

450

500

Temperature (°C)

Time (Days)

E

Fig. 2. Environmental data sets used for alibration and validation, interpolated

from Goulletquer (1989a). Data sets A and B and C were usedfor the alibration

at Nole station. Data sets Band C were used for validation at Nole and datasets

1°25

1°20

1°15

1°10

1°05

46°05

46°00

45°55

45°50

France

Marennes−Oléron

basin

B

A

Fig. 3. Lo ation of the the two stations studied by Goulletquer(1989a) in

Maren-nes-Oléronbasin(Atlanti oast,Fran e).Nole(A),anestuarinestationandLilleau

(B),an o eani station.

F ilt

T

in

L h

−1

rea hes itsmaximum (

F ilt

T

(16) = 1.16 L h

−1

) at16

◦

C.

Filtrationratewasestimatedasafun tionofdryweight(

F ilt

W

(W )

in

mL min

−1

)

following the empiri alequation:

F ilt

W

(W ) = a

f

× W

bf

(3)

with

a

f

= 20.049

and

bf = 0.257

.

Usingequations(2)and(3), ltrationratewas nallyexpressed as afun tion

of individualweight and temperature(

F ilt

;

L day

−1

)followingthe equation:

F ilt(W, T ) = (a

f

× W

bf

×

F ilt

T

(T )

F ilt

T

(16)

) × 1.44

(4)

Ingestion (

Ingest

;

g day

−1

) of dry organi matter an be then al ulated

a ording tothe equation:

Ingest = F ood × F ilt

(5)

Assimilation Aminoa idand ureaex retionisverylow omparedtoother

parametersandwasthusomittedfromthemodel.Therefore, assimilationwas

onsidered equal to absorption. Assimilation rate (

AE

) was estimated as a

fun tion of weight a ording to aMi haelisMenten formulation:

AE = AE

0

+

AE

1

× W

K

A

+ W

(6)

where

AE

0

= 0.1

and

AE

1

= 0.6

arethe minimumandmaximum additive

as-similationratesrespe tively,and

K

A

= 2.74 g

is the half-saturation onstant. Assimilation(

Assim

;

g day

−1

) wasthen al ulated following :

Assim = AE × F ood × F ilt

(7)

Respiration Respiration was also al ulated, using data from Goulletquer

et al. (1989) and Goulletquer (1989a), as a fun tion of temperature for a

1-g DW

individualas

Resp

T

(T ) = −4.75 10

−4

× T

2

+ 2.02 10

−2

× T + 2.43 10

−2

(8)

Resp

T

(

ml O

2

h

−1

) rea hes its maximum

Resp

T

(21) = 0.24 ml O

2

h

−1

at

21

◦

C. Respirationforindividual lams wasestimated fromweight (

Resp

W

in

Cal day

−1

)following the empiri alequation:

Resp

W

(W ) = a

r

× W

br

(9)

where

a

r

= 27.88

and

br = 0.85

.

Using equations (8) and (9), respiration (

Resp

;

g DW day

−1

) was nally

expressed asa fun tionof weight and temperaturefollowingthe equation:

with

2.177 10

−3

being the oe ient to onvert alories to

g DW

.

2.3.2 Condition index

In bivalve studies, ondition index is usually the ratio between shell and dry

esh weights(see review inLu asand Beninger, 1985).In our modela

ondi-tionindex,basedonvariationoftotaleshweightinsideinternalshellvolume,

likethatused inoyster studies(Lawren e andS ott, 1982),was al ulated as

follows:

C =

W − W

o

W

max

− W

o

(11)

wheretherelationshipbetweenthemeaneshweight(

W

o

)andtheshelllength (

L

)is

W

o

= a

o

× L

bo

(12)

and

a

o

= 8.52 10

−7

and

bo = 3.728

.The values were

a

o

and

bo

were evaluated

using a omposite data set (Paillard et al., unpublished data;

n = 921

,

r

2

=

0.904

), and

W

max

= a

om

× L

bo

(13) where

a

om

= 1.70 10

−6

.

C

is related to the shell weight-based ondition index (

CI

) using a linear relationship:

C = 0.0124 × CI − 1.0562

(

n = 558

,

r

2

= 0.95

).

2.3.3 Length growth

Theorgani matrixisonly2to3%ofshellweightoftheManila lam

(Goullet-quer and Wolowi z,1989) and generally a ounts for onlya small fra tionof

SF G

inbivalves(Thompson,1984;Dame,1996;Pouvreauetal.,2000);inthe present model,energy allo ationtoshellgrowth wasthusomitted.Therefore,

shelllengthgrowthrate

LgrowthRate

(

day

−1

)isaMi haelisMentenfun tion

of ondition index (

C

)and is saturated as afun tion of the maximum length (

L

):

LgrowthRate(L, C) = dl

o

×

L

max

− L

L

max

×

C − C

S

K

l

+ C − C

S

(14)

where

dl

o

is maximum daily growth rate,

L

is the individual length,

L

max

is the maximum lam length,

K

l

is the half saturation onstant and

C

S

is

the minimum value of

C

for

LgrowthRate > 0

. Parameters of the Mi haelis Mentenequationwereevaluatedusinga ompositedatasetfrom(Goulletquer,

1989a)in MarennesOléron Bay.

2.3.4 Resour es allo ation to reprodu tion

As in most venerids, the gonad of R. philippinarum is a diuse organ in the

vis eralmass.Thisisthemainreasonwhyrulesspe ifyingtheprioritiesfor

re-sour epartioningbytheManila lamhavenotbeenextensivelystudied

(Laru-elle, 1999;Laruelleetal.,1994;Calvez, 2003). However, availableinformation

was used to make assumptions on erning energy allo ation. Most of the

in-formationisbasedonvarious ondition index andhistologi alstudies,aswell

as re ent investigations using enzyme-linked immunosorbent assays (ELISA)

toquantifyegg weight(ParkandChoi,2004;NgoandChoi,2004).Thegonad

is almost never developed in lams less than 20 mm, whi h is assumed to be

the minimum size for reprodu tion (Laruelle, 1999, Calvez omm. pers). R.

philippinarum isknown tohavea reprodu tiveperiodextendingfrom

Mar h-April to O tober on western European and Korean oasts. This orresponds

to a period when water temperature rises above 12

◦

C, whi h is onsidered

as the minimum temperature allowing gametogenesis (Laruelle et al., 1994;

Mann,1979; Park andChoi,2004; Ngoand Choi,2004).Conditionindex and

histologi alstudies showed that most of net produ tionis allo atedto

repro-du tion frommid-June to the end of O tober (Laruelle, 1999; Calvez, 2003).

Thisphenomenonisobservedatallstationsmonitoredbythoseauthorsalong

theFren hAtlanti oastando urswhen onditionindexisaboveathreshold

value.

Reprodu tive eort

RepEf f

is the adimensional fra tion of net produ tion

allo ated to gonadal tissues.

RepEf f

be omes positive, and gametogenesis

possible, when lam length is above a minimum (

LengthRepMin = 20

mm;

Laruelle,1999)andtemperatureisaboveaminimum(

T empRepMin = 12

◦

C;

Laruelle,1999;ParkandChoi,2004;NgoandChoi,2004;Mann,1979).Below

those thresholds,

RepEf f = 0

. Above the thresholds, reprodu tion eort is

al ulated asa fun tion of temperature a ording to

RepEf f = RepEf f

M ax

×

1

2

× (1 + tanh(

T − 13.8

with

RepEf f

M ax

, the maximum fra tion of net produ tion allo ated to the gonad.

2.3.5 Gamete release

Fa torstriggeringspawningarealsonotwellknownorintensivelystudiedinR.

philippinarum,forthesamereasonsmentionedforresour eallo ation.Spawns

o ur from May to O tober (Laruelle, 1999; Goulletquer, 1989a; Meneghetti

et al.,2004). Spawnings and rapid rematuration after spawning are observed

during the whole breeding period. Individuals are well syn hronized during

the rst springmaturation ofgametes, whi his orrelatedtotemperature

in- rease,butthis syn hrony may belostduringsubsequentspawnings(Laruelle

et al., 1994; Toba et al., 1993; Meneghetti et al., 2004). Asyn hronous

par-tial spawnings o ur fromend of May until the end of August. During these

partialspawnings events, onlya fra tion of the gonad ontent, orresponding

to the mature ovo ytes, is released. The main spawning is observed in late

AugustorSeptember, when almostallindividualsreleasetheir entire gonadal

ontent. Under good environmental onditions, late spawning events an

o - ur until end of O tober (Goulletquer, 1989a; Laruelle, 1999; Calvez, 2003).

In the model, partialand major spawning events are distinguisheda ording

tothe following riteria:

•

a lam is ready for a partial spawning event if its ondition index and

gonado-somati index(gonadtoeshweightratio,GSI)rea hthreshold

val-ues (

P arIC

and

P arGSI

, respe tively). After the partial spawning event,

the ondition index drops to a value (

P arP ostIC

) orresponding to the weight lostby gameterelease.

•

a lam isready foramajorspawningeventif itsGSIis abovethethreshold

value (

SpawnRatio

) and it has experien ed a minimal number of days of

gametogenesis,whi hisevaluatedas119daysfromthedaythetemperature

denitively rises above 12

◦

C.

Threshold values for spawning events were estimated using data sets from

Calvez (2003) for the Gulf of Morbihan.

2.4 Parameter evaluation and model adjustment to experimental data

Mostof the parameters of the modelwere rst estimated frompublished

val-ues for individualswithout BRD symptoms ( Table 1), however, some of the

parameters ould not be evaluatedthis way and were evaluated by adjusting

On e parameters were evaluated, the model was then validated using one

data set from Nole station and one from the Lilleau station. Chlorophyll a

and temperature time series are shown in Fig. 2. Both data sets are from

Goulletquer(1989a) (see se tion2.2).

Forboth alibrationandvalidation,thetbetweenexperimentalandmodeled

results was as ertained using a linear regression through the origin for ea h

state variable (length, weight and ondition index). The slope of regression

line of modeled vs experimental values was ompared to 1 (t-test) and the

oe ient of determinationwas al ulated.

3 Results

3.1 Model evaluation

Results of a simulation after adjustment of the model to experimental eld

data are shown in Fig. 4. This simulation was obtained using the parameter

values in Table 1. For all state variables, the slopes of the regression lines

between observed and simulatedvalueswere not signi antly dierent from1

(t-test, p-value >0.05).

The simulated lengthtraje toryof a standard individualfollowed that of the

average length observed in the eld (Fig. 4A). Length growth was almost

ompletely explained by the model (

r

2

= 0.98

). Simulated dry weight (Fig.

4B) and ondition index (Fig. 4C) were also lose to eld observations, even

though oe ients of determination were lower (

r

2

= 0.77

and

r

2

= 0.66

,

respe tively).Theselowervalues an beattributed tothe simulatedspawning

pattern: the model simulated partial spawning events at days 140 and 153

(end of May and begining of June respe tively). Spawning at this time was

notnotedbyGoulletquer(1989a),who olle tedthedataset usedto alibrate

and validate the model, but they are in a ordan e with observed spawning

patterns ontheFren hAtlanti oast (Laruelle,1999; Calvez, 2003).Amajor

spawningwassimulatedatday230(lateAugust)atthedatewherethisgamete

are expresedinthe model onditionindex (

C

)experimentalequivalentvalues

(

CI

) are shown in parenthesis.

Parameter Explanation Value Unit Evaluatedfrom

F ilt

T

(16)

Maximumofthe

F T

(T )

fun tion(at16

◦

C)

1.16

L h

−1

Goulletqueretal.(1989);Goulletquer(1989a)

a

f

Allometri oe.oftheeq.relatingltrationratetoDW

20.049

nounit Goulletqueretal.(1989);Goulletquer(1989a)

bf

Allometri exponentoftheeq.relatingltrationratetoDW

0.257

nounit Goulletqueretal.(1989);Goulletquer(1989a)

AE

0

Minimumadditiveassimilationrate

0.1

nounit Goulletqueretal.(1989)

AE

1

Maximumadditiveassimilationrate

0.6

nounit Goulletqueretal.(1989)

K

A

Half-sat. onst.oftheM.-M.eq.relatingassim.ratetoDW

2.74

g

thisstudy

Resp

T

(21)

Maximumofthe

RT

(T )

fun tion(at21

◦

C)

0.24

ml O

2

h

−1

Goulletqueretal.(1989);Goulletquer(1989a)

a

r

Allometri oe.oftheeq.relatingrespirationratetoDW

27.88

nounit PowellandStanton(1985)

br

Allometri exponentoftheeq.relatingrespirationratetoDW

0.85

nounit PowellandStanton(1985)

a

o

Allometri oe.oftheeq.relatingaverageDW(

W

0

)tolength

851.88 10

−9

nounit Paillard(unpublisheddata)

bo

Allometri exponentoftheeq.relatingaverageDW(

W

0

)tolength

3.728

nounit Paillard(unpublisheddata)

a

om

Allometri oe.oftheeq.relatingmax.DW(

W

max

)tolength

1703.76 10

−9

nounit Paillard(unpublisheddata)

L

max

Maximum lamlength

60

mm

MortensenandStrand(2000)

dl

o

Maximumlengthgrowthrate

0.0045

day

−1

Goulletquer(1989a)

K

l

Half-sat. onst.oftheM.-M.eq.relating

C

tolengthgrowthrate 0.123 nounit Goulletquer(1989a)

C

S

Minimumvalueof

C

for

R

L,C

>

0

-0.45(

49

) nounit Goulletquer(1989a)

LengthRepM in

Minimum lamlengthforreprodu tion

20

mm

Laruelle(1999),Calvez(unpublisheddata)

T empRepM in

Minimumtemperatureforreprodu tion

12

◦

C Laruelle(1999)

P arGSI

GSIthresholdvalueforpartialspawning

0.30

nounit thisstudy

P arIC

Conditionindexthresholdvalueforpartialspawning

0.50

(

125

) nounit Calvez(2003)

P arP ostIC

onditionindexvalueafterapartialspawningevent

0.23

(

104

) nounit Calvez(2003)

SpawnRatio

GSIthresholdvalueforprin ipalspawning

0.42

nounit ParkandChoi(2004)

C2F

Chla

todryingestibleorg.mat. onversion oe.atNolestation

0.2552

g DW µg

−1

thisstudy

C2F

Chla

todryingestibleorg.mat. onversion oe.atLilleaustation

0.3432

g DW µg

−1

thisstudy

Nole

Validation simulations at Nole station are shown in Fig. 5. For length and

weight,the slopesof the regressionlines between observed and simulated

val-ues were not signi antlydierent from1 (t-test, p-value >0.05). The

simu-latedlengthtraje tory(Fig.5A)was losetoobserved dataandthe oe ient

of determinationwas very high (

r

2

= 0.95

). Simulated traje tories for weight

(Fig.5B)and ondition index(Fig.5C) werealsonearthe observed data;two

partial spawnings were simulated at days 154 and 187. Laruelle (1999) and

Calvez (2003) showed that partial spawnings indu ed asyn hrony of gonadal

state, resulting in in reased variability of esh weight within a ohort. The

two large standard deviations for weight in the eld data between days 154

and day 187 tend to onrmthe o urren e of su h spawnings.

During the whole gamete release period, from day 150 (late May) to day

240(beginingofSeptember),the simulatedtraje torydivergedfromobserved

data be ause of spawnings. The importan eof the prin ipalspawning in the

fall indu ed a divergen e of the model ompared to observed data. These

di-vergen es indu ed lower oe ients ofdeterminationbetween simulationand

elddataforweight(

r

2

= 0.63

)and onditionindex(

r

2

= 0.78

).For ondition

index,slopeoftheregressionlinebetweenexperimentalandmodeleddatawas

0.84 and signi antly dierent from 1 (t-test, p-value < 0.05). Nevertheless,

for both weight and length, simulations were within the observed standard

deviationrange.

Lilleau

Validation simulations for the Lilleau site are shown in Fig. 6. For all state

variables, the slopes of the regression lines between observed and simulated

values were not signi antly dierent from 1 (t-test, p-value > 0.05). The

simulated length traje tory followed losely the observed values at Lilleau

(

r

2

= 0.89

) andlaywithin standard deviationrange(Fig. 6A).Condition

in-dexwaswellexplainedbythemodel(

r

2

= 0.72

)andtheweightsimulationwas

better explained than in the Nole validation simulation(

r

2

= 0.77

). Like the

Nole simulation, the rst gamete emissions were simulated at the end of the

spring (day 144, late May) and ontinued duringthe summer. The simulated

prin ipal spawning o ured at day 227 (mid August), whi h was onsistent

with the observation of Laruelle (1999) and Calvez (2003) for the oast of

Brittany,Fran e. In earlysummer, many (8) partialspawnings are simulated

whi h are not des ribed in the eld dataset of Goulletquer (1989a), thus

26

28

30

32

34

36

38

40

42

44

50

100

150

200

250

300

350

400

450

500

Length (mm)

Time (Days)

A

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

50

100

150

200

250

300

350

400

450

500

Weight (g DW)

Time (Days)

Spawning

B

20

30

40

50

60

70

80

90

100

110

120

130

50

100

150

200

250

300

350

400

450

500

Conditon index

Time (Days)

Spawning

C

Fig.4.Results oftheadjustment of themodelto experimentaldataof Goulletquer

(1989a)for(A)length (mm);(B)weight (gDW)and(C) onditionindex.

Continu-ouslines: modeloutput.Crosses(+):observeddatapoints.The arrowindi atesthe

datewhere spawning wasobservedbyGoulletquer(1989a).Time (days) is ounted

fromthe1st ofJanuary 1984.

partial spawnings are in a ordan e with Laruelle (1999) and Calvez (2003)

observations.A simulatedlate spawningevent o uredatday 285(mid

O to-ber). This gameterelease event wasnoted inthe eld dataset ofGoulletquer

(1989a) who emphasized that at Lilleau station the reprodu tion eort was

26

28

30

32

34

36

38

40

50

100

150

200

250

300

350

400

450

500

Lenght (mm)

Time (Days)

A

0

0.1

0.2

0.3

0.4

0.5

0.6

50

100

150

200

250

300

350

400

450

500

Weight (g DW)

Time (Days)

B

20

30

40

50

60

70

80

90

100

110

120

50

100

150

200

250

300

350

400

450

500

Condition index

Time (Days)

C

Fig.5.Resultsofthevalidationofthemodelusingtemperatureand

Chla

timesseries

at theNole Sation for length (A), weight (B) and onditionindex (C).Continuous

lines: model output; rosses (+): observed datapoints; errorbars indi ate standard

deviationforelddata(Goulletquer,1989a).Standarddeviationsfor onditionindex

werenot available. Time(days) is ountedfrom the 1stof January1985.

4 Dis ussion

Shell growth

An important and original aspe t of this model, whi h is derived from the

Hofmannetal.(2006)hard lam growthmodel, omparedtootherindividual

growthmodelsbasedontheS opeForGrowth on ept(e.g.Barilléetal.,1997;

Grantand Ba her, 1998; Pouvreau etal., 2000; Hawkins et al.,2002;

Gangn-eryetal.,2003;Fré hette etal.,2005),isthat ondition indexdrivesbothnet

24

26

28

30

32

34

36

38

40

42

44

46

48

50

100

150

200

250

300

350

400

450

500

Length (mm)

Time (Days)

A

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

50

100

150

200

250

300

350

400

450

500

Weight (g DW)

Time (Days)

B

20

30

40

50

60

70

80

90

100

110

120

130

50

100

150

200

250

300

350

400

450

500

Condition index

Days (Jours)

C

Fig.6.ResultsofthevalidationofthemodelatLilleauforlength(A),weight(B)and

onditionindex(C).Continuouslinesshowmodeloutput, rosses(+)showobserved

data points and errorbars indi ate standard deviation for eld data (Goulletquer,

1989a). Standard deviations for ondition index were not available. Time (days) is

ountedfromthe1st ofJanuary 1985.

bivalves, length is al ulated from weight through an allometri equation. In

present study weight and length are two state variables independently

al u-lated. Su h a formulation for the Manila lam allowed un oupling of length

growth in rements and weight growth in rements. This is in agreement with

observationsofLewisandCerrato(1997)onMyaarenaria,whi hshowedthat

shell growth ould be un oupled from somati growth. Simulationswere in a

very good agreement with eld data as the oe ient of orrelation values

were very high (

r

2

= 0.89

at Lilleauand

r

2

= 0.95

atNole). This formulation

also allowed our model to simulate post-spawning shell growth stops, whi h

For both Nole and Lilleau sites, the simulated reprodu tive pattern

devi-ated somewhat from eld observations. The aim of most studies on growth

of R. philippinarum is to assess the best ultivation strategy for

maximiz-ing growth. Most often, authors monitor the evolution of biologi al variables

(length,weight and ondition index are amongthe most ommon) of aset of

homogeneously sized individuals (i.e. a ohort  Maître-Allain,1982; Bodoy

etal.,1980; Goulletqueretal.,1987;Goulletquer, 1989a;Robertetal.,1993).

Onea hsamplingo asion,allindividualsinthesampleare sa riedtoassess

thosevariablesand anaveragelength,weightor onditionindex is al ulated.

Usingsu h amethod,oneobtainsthe traje toryofthe averageweight,length

and ondition index of a ohort through time. It is often said to be the

tra-je toryof an"averageindividual"(i.e. anindividualthat has average

physio-logi al features),although noreal individual traje tories are involved in su h

adata set.

The o urren e of asyn hronous events, likepartial spawnings, may indu e a

dieren ebetweenthetraje toryofan"averageindividual"andthetraje tory

of the average of a ohort.In order toexplain this dieren e, two theoreti al

ases arehypothesized both of whi hlead tothe same average ohortweight

time series (Fig.7).

Weight

Weight

Time

Time

Time

Weight

Time

Weight

Case 1

Case 2

Cohort average trajetory

Individual trajectories

Fig.7.Twohypotheti al asesoftheinter-individualvariabilityofspawningstrategy

ina ohort.Case 1:the ohort is omposedofindividualspresentingsimilar

spawn-ing eorts, with ea h individual spawning four times, but not simultaneously. The

individualtraje tories graphshowstheevolution ofweightsoftwoindividuals

( on-tinuousanddotted lines). Case2 :the ohortis omposedofindividuals presenting

dierentspawningstrategies.One lassofindividualsspawnsfourtimes( ontinuous

line in individual traje tories) and the other doesn't spawn at all (dotted lines in

individual traje tories). In both ases,be ause of theasyn hronous spawnings, the

averageweight ofthe ohort mayremain onstant.

spawn-the individual weight traje tories. If these spawnings don't o ur

simulta-neouslyinalltheindividualsofthe ohort,the average weightofthe ohort

may remain onstant.

•

Case 2 is a situation where the ohort is omposed of two kinds of

indi-viduals: some of them spawn with a high frequen y and the other ones

don't spawn at all. As in ase 1, if spawnings, when they o ur, are not

syn hronous, the average weight of the ohort may alsoremain onstant.

Inboth ases, one mayobtainthe same evolutionof averageweight;however,

theweightvarian ewillbehigherin ase1.Itisimpossible,however, tomake

assumptionsabout thebehaviorof individualsand todistinguishbetween the

two asesjustbyexaminingthemeanandvarian eoftheweightofthe ohort.

Pro esses of reprodu tionin bivalves are mu h more omplex than these two

examples;however, these twotheoreti al ases illustratethat if asyn hronous

events o ur in a ohort, the average traje tory of the ohort doesn't allow

any assumption about individual behavior.

Consequently, simulations of individual variables annot easily be ompared

toobserved data when asyn hronous events o ur within a ohort.Tryingto

ta modelsimulatingthe evolution ofmean weightof the ohortwhen

asyn- hronous partial spawning events o ur would not in lude these events thus

resultingin a large underestimate of the reprodu tiveoutput be auseit does

not take into a ount the peak reprodu tive output of individuals lams. In

su h a ase, a high value of the oe ient of orrelation (i.e. tending toward

1)between simulatedand elddatamaya tuallyrevealapoorrepresentation

of individual behavior. This points out (1) the di ulty of omparing

mod-eled toobserved dataduring the reprodu tiveseason and (2)the di ulty of

evaluatingquantitatively the reprodu tiveoutput of an"average individual".

For allthese reasons, deviations of the modelfrom observed weight and

on-dition index values during the gamete-emission season appear relevant: they

explainthelowervaluesofthe oe ientsofdeterminationobtainedforweight

and ondition index inthe validationsimulationsatNole(

r

2

= 0.64

and

0.77

,

respe tively) and at Lilleau (

r

2

= 0.77

and

0.71

, respe tively); they also

ex-plain the weak value of the slope of regression line between observed and

modeled ondition indexatNole.During the spawning season,goodness oft

of thesimulated weight and ondition index an't bevalidated:poort ould

beattributedtoboth(1)highvariabilityamongindividualweightsand

ondi-tionindexesor(2)poormodelrepresentationoftheindividualenergybalan e.

Thusthemodel shouldbevalidatedoutsideof thereprodu tiveseason.When

ex luding the main spawning season (i.e. from mid May to mid September),

simulationsofboth variableswerevery lose tothe observeddata; oe ients

ofdetermination al ulatedforweightwere higher(

r

2

= 0.86

atNoleand

0.84

simu-allstatevariables.Thisindi atesthatourmodelproperlyestimatestheManila

lam energy balan eunder for ing by temperatureand trophi resour e.

Several population dynami s models have been built for bivalves, whi h use

bioenergeti equations to simulate bivalves standing sto k transfers among

size lasses (Powell et al., 1992; Hofmann et al., 1992). They are not

indi-vidually based. This strategy allows a dire t omparison between the model

outputs and the experimental data means. Nevertheless, the present study

learly shows that observation at the ohort (or the population) s ale may

hide some individuals ale pro esses. As individuals an be onsidered the

basi entity of populations (Kooijman, 1995), the individuals ale pro esses

inuen epopulationspro esses.Thisproblemofs aletransferwasemphasized

by Kooijman(1995). The Manila lam model has been developed in order to

buildapopulationdynami s,individual-basedmodelfollowingthatdeveloped

by Hofmann et al. (2006) for Mer enaria mer enaria. This strategy permits

a ounting for the inuen e of individuals ale pro esses at the population

level.

Trophi resour e

The problem of estimating food resour es available to suspension feeding

bi-valves is well known and re ognized as a major problem in modelling

bi-valve energeti s (see e.g. Bayne, 1998; Grant and Ba her, 1998). The Manila

lam uses food resour es available at the sediment-water interfa e, and may

have a very omplex diet : it is known for ltering prey items as diverse as

ba teria, pi o yanoba teria (Nakamura, 2001) and diatoms, as well as

de-triti parti ulate organi matter and small rotifers (Sorokin and Giovanardi,

1995) fromthe water olumnand the sediment surfa e. The Manila lam has

alsobeen des ribed asingesting toxi and non toxi dinoagellatesby Liand

Wang (2001).Moreover, growth ofmi rophytobenthosis very ee tiveonthe

MarennesOléron mudats (Guarini et al., 2000), and was shown to be an

importantfoodsour eforoysters Crassostreagigas (Rieraand Ri hard,1996)

on e resuspended by tidal urrents (Blan hard et al., 1998, 2001). In su h

mudats, we an hypothesize that mi rophytobenthos is an important food

sour e fornear-bottomsuspension-feeding bivalves su has R. philippinarum.

Fegleyetal.(1992)haveshownthatshort-termvariabilityinthequantityand

nutritionalqualityoffooditemsavailabletointertidalnear-bottomsuspension

feeders like R. philippinarum may be of parti ular importan e for assessing

their growth and reprodu tion.

Insu ient information is available on erning these diverse potential food

sour esandthe asso iatedvariabilityoffeedingrateforthemtobe onsidered

a rough estimate of the food input (

Chla × C2F

) for lams exhibiting su h a omplex diet. Following Grant and Ba her (1998) with Mytilus edulis, our

simulations demonstrate that simple formulation of food and feeding may

su ein predi ting Manila lam energeti s. A areful study of the lam diet,

using arbon and nitrogen isotope ratios (Kasai et al., 2004) and pigment

analysis of bottom interfa e water POM, shouldimproveour knowledge.

5 Con lusion

Despite thedi ulty of omparing eldaveraged datasets tomodeloutputs,

simulationofgrowthand reprodu tionforanaverage individual lam under

naturalfoodand temperaturegaverealisti results.The model an beusedto

predi tlengthandweightgrowthaswellasgameteprodu tionofManila lams

in temperate e osystems. Further work will fo us on modelling intera tions

between environment,host and pathogenusing our results,whi hprovidethe

environment lam oupling.

A knowledgements

This study was nan ed by a NSF-CNRS joint program. It was also

sup-portedbythe ConseilRégionalde Bretagnewithinthe MODELMABregional

resear h program. The authors thank Me Fola e and B. Le aunar for their

te hni al help. Thisis IUEM ontributionNo 1023.

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