Aquat. Liring Resour.. 1988, 1 , 14 1-15-1

Empirical modelling of the growth of Ruditapes philippinaricm by means of non linear regression on factorial coordinates

I'liilippc Coullctqucr and CCdric Baclicr

IFREJIER, Station de La Tremblade, .\lus de Loup, BP no 133,17330 La Tremblade (France).

Rcccivcd June 7 , 1 9 ; acmptcd Scptcmber 2 I, 1~~823.

Goulletquer P., C. Bacher. Aquat. Licing Resour., 1 , 141-154.

In order to highlight the main factors accounting for the growth of clams in Marennes-Oléron Bay, three locations were investigated in 1984-85. First, factor analysis provided information on fluctuations of the environment. Second, principal components analysis was used to study ecological phenomena. ï h e main axes explained the growth rate, which was included in an allometric model. Its properties were then studied by means of sensitivity analysis.

iieynorbs : Trophic relationships, Ruditapes philippinarum, principal components analysis, non-linear model, sensitivity analysis.

Aloclelisation empirique de la croissance de Ruditapes phillipinarum : utilisation de la rfgrcssion non linéaire sur coordonnées factoriclles.

Afin de dégager les principaux facteurs responsables de la croissance de Ruditapes philippinarum dans le bassin de hlarennes-Oléron, trois populations d'élevage ont été suivies en 198.1-85. Dans un premier temps, l'analyse factorielle permet d'étudier les fluctuations des paramètres environnementaux. L'analyse en composantes principales est utilisée pour représenter les phénomènes écologiques. Les axcs principaux expliquent le taux de croissance qui est introduit dans un modèle allométrique. Ses propriétés sont étudiées au moyen de i'analyse de sensibilité.

%lots-clés : Relations trophiques, Ruditapes philippinarum, analyse en composantes principales, modélc non linéaire, analyse de sensibilité.

Trophic characteristics of bivalves have been stud- ied by many authors, investigating the relationships bctween growth and environmental descriptors. For example, Wildish and Kristmanson (1985) rclatcd body wcight fluctuations to the flow of particulate organic malter (POAI X current spccd), and FrCchctte and Bourget (1985) related growth in length to parti- culate organic matter concentration (POAI as indi- cated by chlorophyll a and phaeopigments) for d l ~ t i l u s cdulis.

Wallacc and Reinsnes (1985) explained differcnces in growth of Chlamys islandica as the result of differ- ences in nutritional conditions for the scallops, defined by the relationship between particulate organic and inorganic matter in the \vater column. Besides, shell biometric data are often used (Kautsky, 1982; Page and ZIubbard, 1987), but winter emacia- tion, o r seasonal variations affecting condition have been scarcely treated. This study aims are to describe the relationship bctwccn scasonal variations in the wcight of Rudirapcs philippinarutrt and environmental descriptors (represented by hydrological and sedimen- tary temporal series, over a two years' pcriod).

Aquat. Lidng Resour., 1988, l, 141-154

Empirical modelling of the growth of Ruditapes philippinarumby means of non linear regression on factorial coordinates

Philippe Goullctquer and Cédric Bacher

IFRE.\/ER, Station de La Tremhlade, .\fus de Loup, BP nO 133, 17XJO La Tremhlade (France).

RcccivcdJune 7, 1983; acccp1cd Scptcmbcr 21, IgP,s.

Goulletquer P., C. Bacher. Aquat. Lidng Resour., l, 141-154.

Abstract

Résumé

ln order to highlight the main factors accounting for the growth of clams in Marennes-OléronBay, three locations were investigated in 1984-85. First, factor analysis provided information onfluctuations of the environment. Second, principal components analysis was used to study ecologicalphenomena. The main axes explained the growth rate, which was included in an allometric mode!.Ils properties were then studied by means of sensitivity analysis.

Ke)""ords : Trophie relationships, Ruditapes philippinarum, principal components anal}"sis, non-linearmodcl, sensitivity analysis.

Modelisation empirique de la croissance de Ruditapes phillipinarum: utilisation de la rél:ression nonlinéaire sur coordonnées factorielles.

Afin de dégager les principaux facteurs responsables de la croissance de Ruditapes philippinarumdans le bassin de Marennes-Oléron, trois populations d'élevage ont été suivies en 1984-85. Dans unpremier temps, l'analyse factorielle permet d'étudier les fluctuations des paramètres environnementaux.L'analyse en composantes principales est utilisée pour représenter les phénomènes écologiques. Lesaxcs principaux expliquent le taux de croissance qui est introduit dans un modele allométrique. Sesproprietés sont étudiées au moyen de l'analyse de sensibilité.

J\1ots-c1és: Relations trophiques, Ruditapes philippinarum, analyse en composantes principales, modèlenon linéaire, analyse de sensibilité.

Il'.'TRODUCTION

Trophic characteristics of bivalves have been stud­ied by many authors, invcstigating the rclationshipsbetween growth and cnvironmental descriptors. Forexample, Wildish and Kristmanson (1985) relatedbody weight lluctuations to the now of particulateorganic matter (PO:\1 X current spccd), and Fréchetteand Bourget (1985) related growth in length to parti·culatc organic malter concentration (PO:\1 as indi·catcd by chlorophyll a and phaeopigments) for.\fytilus cdulis.

~ ~ 7~_: n 00'1'\"1 .... 'A"'1I1"·~I'n'·•• '·n .LO __ '."II _

Wallace and Rcinsncs (1985) explaincd dirfcrenccsin growth of Chlamys islandica as the resu1t of differ­cnces in nutritional conditions for the scallops,derined by the relationship between particulateorganic and inorganic matter in the watcr column.Besides, shell biometric data are often used (Kautsky,1982; Page and lIubbard, 1987), but winter emacia­tion, or scasonal variations arrecting condition havebeen scarcc1y treated. This study aims are to describethe rclationship bctween seasonal variations in theweight of Ruditapes pllilippinarum and cnvironmentaldescriptors (rcpresented by hydrological and scdimen·tary temporal series, over a two years' pcriod).

P. Goulletquer and C. Dacher

The use of statistical methods has recently made it possible to describe trophic relationships (for a review, see Iiéral, 1987). Variability between spccies and the use of different cornputation methods may explain divergent results. Non-parametric methods, establishing rank-correlations, have presented the most divergent results (Soniat and Ray, 1985; Benin- ger and Lucas, 1983). hlore informative results are obtained when statistical methods are applied to rank the descriptors in order of importance (Bodoy and Plante-Cuny, 1983; Plante-Cuny and Bodoy, 1987; Iléral et al., 198.2; Page and Iiubbard, 1987). Since linear regression is the most comrnon method used, these results are only reliable as far as the relation- ships are consistent with the hypothesis of linearity. Our paper applies non-lincar statistical analysis and the idca of classification to evaluate relationships between environmental descriptors and bivalve growth. The property of prediction should be impro- ved, and the regression model is expected to be more general. It enables to classify the descriptors according to their effect on growth and to compare spatially separated areas. hloreover, the study of the properties of the model allows discrimination of the effects of environmental variability on growth among areas and arnong years.

Marennes-Oléron

1% 5 l01 5 1'5

Figure 1. - Geographical location and sample area.

The study was conducted in the Scudre river estuary in the bay of hlarennes-Olkron (jg. 1). The experi- mental design involved the survey of three areas defined by their intertidal level of exposure called low, medium, high level (12, 19, 46% emersion respec- tively). Substratum was a soft bottom (65% silt). Experirnental populations of filanila clams in eaeh area were sown in hlarch 1983, with an average length (28.4f 0.04 mm), total weight (5.15k0.01 g) and soft tissue weight (123.4k6.2 mg) at a density of 200 individuals. m-2.

AIULTIVARIATE I~NALYSIS OF ENVIRONAlENTAL DESCRIPTORS

Since benthic pigments constitute a part of the clam diet (Bodoy and Plante-Cuny, 1983; MantelCuny and Bodoy, 1987), the sediment was sampled using scdi- ment cores twice a month. The six following descrip- tors were surveyed in the upper centirnetre of cores: particulate organic matter (POhl), carbohydrates, proteins, Iipids, chlorophyll a and phaeopigments.

The amount of organic matter in the upper centime- tre of the cores was measured by weight difference on ignition at 450°C for 24 hours. Carbohydrate analysis was performed using the method of Dubois et al. (1956) and analysis of proteins using the method of Lowry (1956). After extraction (Bligh and Dyer, 1959), lipids were dosed by the hlarsh and Weinstein method (1966). Chlorophyll a and phacopigments, extractcd with 90% acctone, were measured by spectrophotometry (Lorenzen, 1967).

Data were averaged to filter short-term variability (i. e. less than a month). Thereby monthly growth could be related to the mean values of the descriptors during the month elapsed. According to Héra! et al. (1987), the variability of hydrological character- istics results from four sources: stratification between surfacc and bottorn; tidal fluctuation (daily cycle); fortnightly period (spring and neap tides); seasonal trends.

The sarnpling strategy aimed at estirnating an unbi- ased mean of each variable, averaged over the water column and over a month. Samples were collected at the surface and the bottom of the water column and averaged. Data were collccted twice a month on spring and neap tidcs. The times of sampling was dependent on the low tide hour and chosen to esti- mate the tidal mean. Nine descriptors were surveyed: temperature, POXI, particulate inorganic matter (PIhl), chlorophyll a, phaeopigments, proteins, lipids, carbohydrates, dissolved oxygen (0,P).

The temperature was measured in situ and dissolved oxygen was estirnatcd by the Winckler mcthod (Strickland and Parsons, 1972). To analyse the bio- chemical composition of particulate organic matter, water sarnples were pre-filtered through a 250 Fm,

Aquat. Living Resour.

142 P. Goulletqucr and C. Bacher

I\IATERIALS Al"'n METllOnS

The use of statistical methods has recently made itpossible to describe trophic relationships (for areview, see Héral, 1987). Variability between speciesand the use of different computation methods mayexplain divergent results. Non-parametric methods,establishing rank-correlations, have presented themost divergent results (Soniat and Ray, 1985; Benin­ger and Lucas, 1984). More informative results areobtained when statistical methods are applied to rankthe descriptors in order of importance (Bodoy andP1ante-Cuny, 1984; P1ante-Cuny and Bodoy, 1987;Héral et al., 1984; Page and Hubbard, 1987). Sincelinear regression is the most common method used,these results are only reliable as far as the relation­ships are consistent with the hypothesis of linearity.Our paper applies non-linear statistical analysis andthe idea of classification to evaluate relationshipsbetween environmental deseriptors and bivalvegrowth. The property of prediction should be impro­ved, and the regression model is expeeted to be moregeneral. It enables to classify the descriptors aceordingto their erreet on growth and to compare spatiallyseparated areas. Moreover, the study of the propertiesof the model allows discrimination of the effects ofenvironmental variability on growth among areas andamong years.

1°25

Bay of

f15

The study was eonducted in the Seudre river estuaryin the bay of Marennes-Oléron (fig. 1). The experi­mental design involved the survey of three areasdefined by their intertidallevel of exposure calied low,medium, high level (12, 19, 46% emersion respec­th'ely). Substratum was a soft bottom (65% silt).Experimental populations of Manila clams in eaeharea were sown in Mareh 1984, with an averagelength (28.4±0.04 mm), tolal weight (5.15±0.01 g)and soft tissue weight (123.4±6.2 mg) at a density of200 individuals.m- 2.

l\IULTIVARIATE ANALYSISOF ENVIRON:\lENTAL DESCRIPTORS

Sampling

Sinee benthic pigments constitute a part of the clamdiet (Bodoy and P1ante-Cuny, 1984; P1ante~Cuny andBodoy, 1987), the sediment was sampIed using sedi­ment cores twiee a month. The six following descrip­tors were surveyed in the upper centimetre of cores:particulate organie matter (POM), carbohydrates,proteins, lipids, chlorophyll a and phaeopigments.

The amount of organic matter in the upper centime­tre of the cores was measured by weighl differenceon ignition at 450"C for 24 hours. Carbohydrateanalysis was performed using the method of Duboiset al. (1956) and analysis of proteins using the methodof Lowry (1956). After extraction (B1igh and Dyer,1959), Iipids were dosed by the Marsh and Weinsteinmethod (1966). Chlorophyll a and phaeopigments,extracted with 90% acetone, were measured byspectrophotometry (Lorenzen, 1967).

Data were averaged to fil ter short-term variability(i. e. less than a month). Thereby monthly growthcould be related to the mean values of the descriptorsduring the month elapsed. According to Héralet al. (1987), the variability of hydrological character­istics results from four sources: stratification betweensurface and bottom; tidal fluctuation (daily cycle);fortnightly period (spring and neap tides); seasonaltrends.

The sampling strategy aimed at estimating an unbi­ased mean of each variable, averaged over the watercolumn and over a month. Samples were collected althe surface and the bottom of the water column andaveraged. Data were collected twice a month onspring and neap tides. The times of sampling wasdependent on the low tide hour and chosen to esti­mate the tidal mean. Nine descriptors were surveyed:temperature, POM, particulate inorganic matter(PIM), chlorophyll a, phaeopigrnents, proteins, Iipids,carbohydrates, dissolved oxygen (02P),

The temperature was measured in situ and dissolvedoxygen was estimated by the Winekler method(Strickland and Parsons, 1972). To analyse the bio­chemical composition of particulate organic matter,water samples were pre-filtered through a 250 ~m,

I-igure 1. - Geographicallocation and sample area. Aquat. Living R~our.

Alodelling of the growth of clams, R. philrjlpinarum

previously heated to 4503C for 1 hour. IQ3I and I'Ihl, were measured by weighing after ignition at 450'C (1 hour). Chlorophyll a and phaeopigrnents were measured by fluorometry (Yentsch and hlenzel, 1963) after extraction in acetone 90%. Pro- teins, lipids and carbohydrates were analysed using the methods describcd earlier.

Data analysis

For each descriptor of the sediment and water column, 48 observations were available on the three areas together. Using STATITCF software package, Principal Components Analysis ( K A ) was perfor- med on the correlation matrix of water column and sediment descriptors and yielded an ordination of ten independent principal axes ordered according to descreasing variance. Denoting X (48, 15) the matrix of normalized observations, X' the transpose of X and U, the eigenvector associated to the uth eigenvalue h, of the correlation matrix C=XrX, the coordinate of the ith observation on axis a., Y,(,, is equal to the ith element of the vector XU,. Thus the vcctor Y, represents the coordinates of observations on axis a, and Y =(Y,. . .Y ,,) is the new matrix of observations in the space generated by the eigenvec- tors (Volle, 1981).

Sampling

The growth of clams is described by changes of dry tissue weight, estimated from monthly sampling of 20 individuals from each area. Dry tissue weight was measured after lyophilisation (24 hours). The vari- ations in length or whole weight are not so informa- tive: these two parameters did not show any notice- able decrease during winter. Two periods of growth were considcred: from hlarch 1984 until July 1984 (class l), from September 1984 until July 1985 (class 2). Data collected during the spawning season (weight loss due to the release of gametes) were not included in the treatment.

Equation

Roth W and G are known to integrate past events. In general, W or G are expressed as a function of the environment and of the initial weight. Accordingly the model is written:

The parameters G and h are supposed to be depen- dent on the environment and the species respectively (Sebens, 1982).

Provided b # l and G is constant between t, and t,, integration yields:

In order to take into account the time of exposure in the explanation of the growth, the time elapsed betwcen two samples is corrected by a multiplicative factor defined as the fraction of daily immersion time. Thus:

Where At is correctcd for immersion time. The growth rate G may be related to the principal

axes Y, extracted from the factor analysis; the relationship is written:

I'arameter estimation

The model is an extension of the orthogonal regres- sion (Tomassone et al., 1983) to the nonlinear case. The simplex algorithm (Nelder and hfead, 1965; Schnute, 1982) was applied to estimate the parameters b, a,, a,. It is a direct search method which minimizes the residual sum of squares (RSS):

KSS = C (Wob,- WC,,)' t

The calculations are kept on running until any modification of the parameters have no more notice- able effect on the value of the RSS.

The Fisher test allows to compare it with the total sum of squares SY Y:

SYY =C (\vo,,-~v)2 t

in order to check the goodness of fit of the model. Since a11 the axes are independent, any axis Xi explains a part of the variability (contribution) of G: ci=aZ hi (hi is the ith eigen-value). The computation of c, allows one to rank the axes according to their importance in the cxplanation of the growth rate. Eventually, a new optimisation may be performed once axes of lesser contribution are excluded. The new criterion RSS, may be compared to the former one with the Fisher test:

(n,, n , = degrecs of freedom). Unless the loss of information is significant (at the

Ievel of 5 x IO-,) the trials are continued. Similar to a linear stepwise descendant regression process, this method decreases the number of variables to select the more significant ones. Derived from PCA, they may contribute to the explanation of G bccause of

Vol. 1. no 3 - 1988

Modelling of the gro"th of clams, R. philippinarum 143

IJaramcter estimation

(4)

(2)c=l-b

Providcd b #- 1 and G is constant between t 1 andl2' integration yie1ds:

Jn order to take into account the time of exposurein the explanation of the growth, the time e1apsedbetween two samples is corrected by a multiplicativefactor defined as the fraction of daily immersion time.Thus:

Where At is corrected for immersion time.The growth rate G may he related to the principal

axes Y, cxtracted from the factor analysis; therclationship is written:

The model is an extension of the orthogonal regres­sion (Tomassone el al., 1983) to the nonlinear case.The simplex algorithm (Nelder and Mead, 1965;Schnule, 1982) was applied to estimate theparameters b, ao, al' Il is a direct search methodwhich minimizes the residual sum of squares (RSS):

RSS= L(Wob.-WC8t)21

previously heated to 450'C for 1 hour. PO~f andPIM, were measured by weighing after ignition at450'C (1 hour). Chlorophyll a and phaeopigmentswere measured by nuorometry (Yentsch andMenzel, 1963) after extraction in acetone 90%. Pro­teins, Iipids and carbohydrates were analysed usingthe methods described earlier.

GROWTH MODEL

Da ta anal)'sis

For each descriptor of the sediment and watercolumn, 48 observations were available on the threeareas together. Vsing STAT1TCF software package,Principal Componcnts Analysis (PCA) was perfor­mcd on the correlation matrix of water column andscdimcnt descriptors and yicldcû an ordination often indcpendent principal axes ordered according todescrcasing variance. Denoting X (48, 15) the matrixof normalized observations, X' the transpose of Xand V.. the eigenvector associated to the cxtheigenvalue À.. of the correlation matrix C = X' X, thecoordinate of the ilh observation on axis ex, y .. (1) iscqual to the ith clemcnt of the vector XV... Thus thevcctor y .. rcprescnts the coordinatcs of obscrvationson axis cx, and Y =(Y l' •• y 10) is the new matrix ofobservations in the space generated by the eigenvec­tors (Voile, 1981).

Sampling

The growth of clams is described by changes of drytissue weight, estimated from monthly sampling of20 individuals from each area. Dry tissue weight wasmeasured after lyophilisation (24 hours). The vari­ations in length or whole weight are not so informa­tive: these two parameters did not show any notice­able decrease during winter. Two pcriods of growthwere considered: from March 1984 until July 1984(c1ass 1), from Scptembcr 1984 until July 1985(c1ass 2). Data collccted during the spawning season(weight 10ss due to the release of gametes) were notinc1uded in the treatment.

Equation

Both W and Gare known to inlegrate past events.Jn gencral, W or Gare expressed as a function ofthe cnvironment and of the initial weight. Accordinglythe model is written:

( 1)

The parameters Gand b are supposed to be depen­dcnt on the environment and the species respectively(Sehens, 1982).

The calculations are kept on running until anymodification of the parameters have no more notice­able effcct on the value of the RSS.

The Fisher test allows to compare it with the totalsum of squares SYY:

SYY = L (Wob.-W)2

in order to check the goodness of fit of the mode!.Sincc ail the axes are independent, any axis Xiexplains a part of the variability (contribution) of G:Ci =ar À; (À, is the ith eigen-value). The computationof c, allows one to rank the axes according to theirimportance in the explanation of the growth rate.Eventually, a new optimisation may he performedonce axes of lesser contribution are excluded. Thenew criterion RSS2 may he compared to the formerone with the Fisher test:

(RSS2 - RSS 1)/(n2 -nt)

RSStfn l

(ni' n2 =dcgrccs of frccdom).Vnless the loss of information is significant (at the

Icvcl of 5 x 10- 2) the trials arc continued. Similar to

a Iincar stepwise descendant regression process, thismethod decreases the number of variables to selcctthe more significant oncs. Dcrivcd from PCA, theymay contribute to the explanation of G bccausc of

V01. l, nO 3 • 1988

144 P. Coulletquer and C. Bacher

Table 1. - Correlation matrix between the 15 descriptors. Ilydrology PIIEQ phaeopigment, CI 1LA: chlorophyll a, TEMP: temperature, 0,P: dissolved oxygen, PROT protein. LIP: lipid. CARB: carbohydrate. Plhl: particulate inorganic matter, mlrf: particulate organic matter. Sediment PIIEO: phaeopigment, CIILA: chlorophyll a, PROT: protein, LIl? lipid, CARB: carbohydrate. POM: particulate organic matter.

Water Sediment

Water: PROï LI P CARB Mhf IQkf CIILA Pt 1 EO TEXlP O P

Sediment fQlrl 0.147-0.119 0.086-0.054-0.218 0.060 0.025 -0.142 0.029 1.000 CHLA -0.058 -0.022 0.024 -0.123 -0.160 -0.042 -0.075 -0.168 0.028 0.357 1.000 MIE0 -0.036 0.008 0.054 -0.014 -0.127 0.039 0.0dl 0.007 -0.041 0.726 0.658 1.000 PROT 0.174-0.068 0.161 -0.090 0.115 0.309 0.159 -0.032 0.032 0.146 0.254 0.148 1.000 LI P 0.196 -0.042 0.113 -0.064 0.011 -0.065 -0.198 -0.238 -0.045 0.531 0.182 0.394 0.464 1.000 CARB -0.127 -0.175 0.117 0.081 -0.056 -0.129 -0.143 -0.316 0.100 0.657 0.352 0.575 0.436 0.614 1.000

the high score of the cocfficicnt ai or the eigenvalue A,. Thereby the secondary axes in the analysis of the environmental descriptors (characterized by low value of Ai) cannot be removed because of their potential impact on growth.

Sensitivity analysis

Once the parameters of the model are determined, the influence of the environmental descriptors on the expccted weight may be estimatcd through a scnsitiv- ity analysis. A random fluctuation T of the one parameter ai around its true value leads to a final weight different from the one expected for each area and for each class. Given a normal distribution ,t'(O, a ) for T, the final weight will also follow a normal distribution whose standard deviation ai may be estimated by running n simulations with n values of T; the ratio a,/a highlights the sensitivity of the model with respect to parameter ai for each site and class. From an ecological point of view, the sensitivity of growth to natural fluctuations taken into account in principal axes equations, is outlined. In this study, values of n(50) and ~ ( 0 . 0 1 ) were chosen to remain in the validity domain of the model.

The model is then applied to compare sites or years at equal initial weights or times of exposure. Simultations are run with other initial conditions and the final weight expresses the growth potential in these cascs.

R ES ULTS

Principal Components Analysis (PCA) was perfor- med on hydrological and sediment descriptors. The examination of the partial correlations matrix showed

that these 2 groups were independent (table 1). This result obviously led to perform separate analyses for each set without altering the basic principle of global independence. Both analyses provided ten principal axes which explaincd 95% of the variability.

The growth model

The ten axes derivcd from the PCA were included in the growth model. After sorting, 5 were finally input into the growth equation (table 2). The simula- tions and observations are displayed onfigure 2. Since

Table 2. - Percentage of variance explained by the 5 axes finally entered into the model; regression coefficient of each axis; a,= 1.40 and 6=0.61 (see text).

Axis % variance ai

Water

the F test is grcater than the F(37, 7) given by tables at a level of 0.05, the goodness of fit of the model is probably to be correct.

Sensitivity analysis provides more information on the influence of each axis. From table 3 the percentage of total sensitivity accounted for by each axis was calculated for each area and class. The axes extracted

Aquat. Living Resour.

144 P. Goulletqucr and C. Bacher

Table 1. - Correlation matrix between the 15 descriptors. Ilydralogy PIlEO; phaeopigment, CillA: chlorophll1 o. TE~fP: temperature,0 11': dissolved oxygen, PROT: protcin, UP: lipid, CARn: carbohydrate, l'lM: particulate inorganie matter, PO~I: particulate organicmatter. Sediment PIIEO: phaeopigment, CillA: chlorophll1 a, PROT: protcin, L1P: lipid, CARn: carbohydrate, PO~I: particulate organicmatter.

Water Sediment

l'ROT L1P CARO l'lM PO~1 CilLA plIEO TEMp 0 11' PO~I CHLA pHEO l'ROT UP CARB

Water:l'ROTUPCARnPIMPO~1

CilLAPlIEQTEMp°lP

1.0000.154 1.0000.601 0.010 1.0000.133 0.062 0.702 1.000

-0.073 0.490 0.289 0.554 1.0000.391 -0.009 0.265 -0.136 -0.0260.271 -0.014 0.054 -0.316 -0.202

-0.133 0.074 -0.480 -0.270 -0.0630.117 0.284 0.258 -0.158 0.086

1.0000.7670.2450.432

1.0000.460 1.0000.577 -0.247 1.000

Sedimentl'mlCilLAPIIEOPROTUPCARn

0.147 -0.119 0.086 -0.054 -0.218 0.060 0.025 -0.142 0.029 1.000-0.058 -0.022 0.024 -0.123 -0.160 -0.042 -0.Q75 -0.168 0.028 0.357 1.000-0.036 0.008 0.054 -0.014 -0.127 0.039 0.004 0.007 -0.041 0.726 0.658 1.000

0.174 -0.068 0.161 -0.090 0.115 0.309 0.159 -0.032 0.082 0.146 0.254 0.148 1.0000.196 -0.042 0.113 -0.064 0.011 -0.065 -0.198 -0.238 -0.045 0.531 0.182 0.394 0.464 1.000

-0.127 -0.175 0.117 0.081 -0.056 -0.129 -0.143 -0.316 0.100 0.657 0.352 0.575 0.436 0.614 1.000

the high score of the coefficient a/ or the eigenvalue ')../.Thereby the secondary axes in the analysis of theenvironmenlal descriplors (characterized by low valueof ')..J cannot be removed because of their potentialimpact on growth.

that these 2 groups were independent (table 1). Thisresult obviously Ied to perform separate analyses foreach set without altering the basic principle of globalindependence. Both analyses provided ten principalaxes which explained 95% of the variability.

Table 2. - Percentage of variance explained by the 5 axes finallyentered into the model; regression coefficient of each axis; 0 0 = 1.40and b=0.61 (see text).

The gro\\,th model

The ten axes derived from the PCA wcre includedin the growth mode!. After sorting, 5 were finallyinput into the growth equation (table 2). The simula­tions and observations are displayed onflgure 2. Since

the F test is greater than the F(37, 7) given by tablesat a level of 0.05, the goodness of fit of the modcl isprobably to be correct.

Sensitivity analysis provides more information onthe inlluence of each axis. From table 3 the percentageof total sensitivity accounted for by each axis wascalculated for each area and c1ass. The axes extracted

RSS=13.5, SYY=170, n=35,p=7, F(7,35) =58.

0.30

-1.370.940.640.42

%variance

YI 67.9Y3 18.3Y4 6.4Yz 6.3

Axis

Water

Sediment Y8 l.l

RESULTS

Sensith'ity analysis

Once the parameters of the model are determined,the influence of the environmental descriptors on theexpected weight may be estimated through a sensitiv­ity analysis. A random lluctualion T of the oneparameter a/ around its true value Ieads to a finalweight different from the one expected for each areaand for cach c1ass. Given a normal distribution...i"(0, 0) for T, the final weight will also follow anormal distribution whose standard deviation (J/ mayhe estimated by running n simulalions wilh n valuesof T; the ratio (J//o highlights the sensitivity of themodel with respect to parameter a/ for each site andc1ass. From an ecological point of view, the sensitivityof growth to natural fluctuations taken into accountin principal axes equations, is outlined. In this study,values of n(50) and 0(0.01) were chosen to remainin the validity domain of the mode!.

The modc1 is then applied to compare sites oryears at equal initial wcights or times of exposure.Simultations are run with other initial conditions andthe final weight expresses the growth potenlial inthese cases.

Principal Componenls Analysis (PCA) was perfor­med on hydrological and sediment descriptors. Theexamination of the partial correlations matrix showed

Aquat. Living Resour.

ModePJixg of the growth of clams, R. philippinarum 10

figrre 2 - Growth mode1 (continu- ous line) and observations (squares): (1) high level area (46% emersion) and classes 1 and 2. (2) medium level area (19% emersion) and classes 1 and 2. (3) low level area (12% emer- sion) and classes 1 and 2.

L

1

O

O

Vol. 1, no 3 - 1988

Mo~em~g of t~e growth of cl8ms, R. pkilippinarum 14510

9 CDe

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(1) high level area (46% emersion)1- 5:r and classes 1 and 2. (2) medium level~w area (19% emersion) and classes 1~ 04- and 2. (3) low level area (12% emer·)- c ca: sion) and classes 1 and 2.c c

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O+-----r-----.-----"T"'"-----,-----r----;o 200

Vol. 1. nO 3·1988

P. Coulletquer and C. Bacher

Figure 3. - Simulation of growth potential(1/10 g) for the three areas corresponding to high (1). medium (2) and low (3) levels of emersion. (1) first class and different initial weights (1/10g). (2) first class and different immersion times (hourslday). (3) second class and different initial weights (1/10g). (4) second class and different immersion times (hourslday).

Table 3. - Sensitibity of the final weight to the regression coeffici- ents of the five axes retaincd. I'crcentages of sensitivity are Bven in parenthesis (see text for further explanation).

1st class 2nd class

Level 1 2 3 1 2 3 (high) (medium) (low) (high) (medium) (low)

Axis

y 1 1.27 2.49 4.49 3.16 5.88 9.08 (57) (63) (61) (52) (56) (55)

y 7. 0.11 0.22 0.40 0.14 0.26 0.40 (5) (6) ( 5 ) (2) (2) (2)

y3 0.01 0.03 0.05 0.19 0.36 0.56 (0) (0) (0) (3) (3) (3)

y, 0.56 1.09 1.96 1.48 2.75 4.25 (25) (28) (26) (24) (26) (26)

y, 0.28 0.12 0.54 1.10 1.27 2.26 (12) (3) (7) (18) (12) (14)

from the sedimentary analysis were rcsponsiblc for 7 and 14% of the sensitivity according to the class considcrcd (respectively first and second one). The

first class is more sensitive to hydrological conditions than the second onc.

Although the low level area carried out the highest weight during the survey, simulation and sensitivity analysis enable one to compare the growth pcrform- ancc of the two classcs. Figure 3(1) shows thc highcst growth potential of the low level area whatever the initial weight. Since hydrological characteristics are the same for the three areas, such differences may be attributcd to the scdimcntary characteristics or to the immersion time. The low sensitivity to sedimentary disturbances (7%) and the computations of growth potential related to immersion time [fig. 3(2)] intend to show that high immersion time is mainly respon- sible for growth of the first class. Howevcr the sensi- tivity to the sediment is greater than that expected from the computation of contribution (tables 2, 3). This difference must bc attributcd to the non-lincarity of the modcl.

Because of the differences in initial weights of clams in the second class, no direct information may be derived from the obscrvations. However, the simula-

Aquat. Living Resour.

146 P. Goullctqucr and C. Bacher

23

23

®15t y[.lll1 1/10 Dl

30

2

CD

2 nd ~HR

1 1/10 DI18

Fi~ure 3. - Simulation of growth potential (1/10 g) for the three areas corresponding to high (1). medium (2) and low (3) levels of emersion.(1) first c1ass and different inilial weights (I/I0g). (2) first c1ass and diffcrent immersion times (hours/day). (3) second c1ass and diIferentinitial weights (I/I0g). (4) second c1ass and different immersion times (hours/day).

Table 3. - Scnsiti\'Ïty of the final weight to the regression coeffici-ents of the five axes retained. Pcrcenlagcs of sensilivily are givenin parenthesis (see text for funber explanation).

Ist c1ass 2nd class

Level 1 2 3 1 2 3(high) (medium) (Iow) (high) (medium) (Iow)

Axis

YI 1.27 2.49 4.49 3.16 5.88 9.08(57) (63) (61) (52) (56) (55)

Yz 0.11 0.22 0.40 0.14 0.26 0.40(5) (6) (5) (2) (2) (2)

Y3 0.01 0.03 0.05 0.19 0.36 0.56(0) (0) (0) (3) (3) (3)

y. 0.56 1.09 1.96 1.48 2.75 4.25(25) (28) (26) (24) (26) (26)

Ys 0.28 0.12 0.54 1.10 1.27 2.26(12) (3) (7) (18) (12) (14)

from the sedimentary analysis were rcsponsible for 7and 14% of the sensitivity according to the c1assconsidered (respcctively first and second one). The

first c1ass is more sensitive to hydrological conditionsthan the second one.

Although the low level area carried out the highestweight during the survey, simulation and sensitivityanalysis enable one to compare the growth perform­ance of the two classes. Figure 3 (l) shows the highestgrowth potential of the low level area whatever theinitial weight. Since hydrological characteristics arethe same for the three areas, such differences may beattributed to the scdimentary characteristics or to theimmersion time. The low sensitivity to sedimentarydisturbances (7%) and the computations of growthpotential related to immersion time [fig. 3 (2)] intendto show that high immersion time is mainly respon­sible for growth of the first c1ass. However the sensi­tivity to the sediment is greater than that expectedfrom the computation of contribution (tables 2, 3).This difference must be attributed to the non-linearityof the mode!.

Because of the differences in initial weights of clamsin the second c1ass, no direct information may bederived from the observations. However, the simula-

Aquat. Living Rewur.

i1Iodelling of the growth of clams, R. philippinarum

tions of growth potential versus initial weight [fig. 3(3)] for each area show the high score of the mcdium lcvcl area compared to the low level one. The effect of immersion lime is also important [see simulations with different immersion limes on figure 3(4)] and growth would be still better with longer immersion time in the high and medium areas. The impact of scdimcntary conditions is more consist- ent for the second class than for the first one and inverts the classification of arcas.

We can return to the original descriptors by identi- fying factor axes with ecological dcscriptors. Analyses of the projections of descriptors and observations highlightcd the annual fluctuations, and the variability between years and between areas.

IIgdrological analgsis

Since hydrological parameters were the same for al1 three areas, a single analysis was carricd out and the differcnt areas were not discriminated.

The first three axes account for 72% of the total variability among the nine variables (table 4). By com- paring the projections of variables (correlations) and

Table 4. - Eigenvalues and percentage of variance explained by the principal axes of K A of hydrological and sedimentary descriptors.

PCA Water Sediment

Axis Eigenvalue % Eigenvalue %

YI 256 28 3.24 54 y 2 251 28 1.12 19 y 3 1.45 16 0.83 14 y4 1.09 12 0.36 6 y 5 0.80 9 0.27 5

of observations, periodical and single fluctuations may be identified. Points close to the center of the graph arc insufficiently reprcscntcd and are not taken into account in the analysis. Five axcs wcrc extracted by the analysis, but only the first thrce wcre plottcd; axes 4 and 5 may be investigated from the table 5a.

The first axis is correlated with 3 variables wg. 4 (1)) chlorophyll a -i- phacopigments, dissolved oxygen, protcins and appcars to be characteristic of the bloom period (June 1983, hlay 1985) Vg. 5(1)]. In contrast, earlicr and later periods (hlarch and April, Octobcr and November) are related to poorer waters and are projectcd on the other side of the first axis wg. 5 ( l)].

The second axis discriminates temperature and seston linked to carbohydrates which show a peak in winter.

The different origins of nutrients appcar on the first plane [fig. 4(1), 5(1)]: bloom in hlay and June, detritus in winter and show a one month lag betwecn 1983 and 1985. The time scale docs not allow to investigate the true lag within oscillations with a period lcss than 2 months.

The third axis is related to the concentration of lipids [ jg. 4(2), 5(2)]. A pcak is noticcd in February 1985 in contrast with January, Dcccmbcr and hlarch. This strenghthens the assessment of short tenn fluctuations.

Dissolved oxygen and tempcrature are opposed on the 4th axis which dcfines a second component of both variables related to January and August 1985. The fifth axis shows another component of protein fluctuations. As shown by the qualities of representa- lion (table 5b), this component corresponds to hlarch, hIay and July 1983; it disappears in 1985.

Finally, axcs 3 and 5 dcscribe short tcrm fluctu- ations related to specific amounts of nutrients. Axis 4 is only related to physical parameters.

Table Sa. - Correlations between hydrological variables and pnn- cipal axes.

Axis Y, Y i Ya Y4 Ys

PR (TT LI P CARB Pl hl M S I CIILA PIiEO TEhIP 0 , P

Table Sb. - Qualities of representation of observations on axes Y, and Y, extracted from the K A of hydrology.

Date Axis Y, Axis Y,

hlarch 1984 0.212 0.343 April 1984 0.002 0.215 hlay 1984 0.110 0.366 June 1984 0.034 0.106 July 1984 0.236 0.331 August 1984 0.017 O. 011 Oaober 1984 0.213 0.005 November 1984 0.020 0.039 Decem ber 1 984 0.66 1 0.050 Janvier 1985 0.423 0.001 February 1985 0.196 O. 000 hlarch 1985 0.01 1 0.039 April 1985 0.077 0.145 hlay 1985 0.063 0.005 June 1985 0.010 0.005 July 1985 0.340 0.095

Sedimcntary analgsis

54% of variability is cxplaincd by the first axis. Thc 5 axes of the analysis account for 98% of the original variability (table 4). Principal and secondary fluctu- ations are present.

Chlorophyll a, phaeopigment and POSl may be scen on the first axis [fig. 4(3), 4(4)]. The first two

i\lodcJlin~ of the gro~th of clams, R. philippinarum

tions of growth potential versus initial wcight[fig. 3 (3)] for each area show the high score of themedium level area compared to the low level one.The effeet of immersion time is also important [seesimulations with different immersion limes onfigure 3 (4)] and growth would be still belter withlonger immersion time in the high and medium areas.The impact of sedimentary conditions is more consist­ent for the second c1ass than for the first one andinverts the classification of areas.

We can return to the original descriptors by identi­fying factor axes with ecological descriptors. Analysesof the projections of descriptors and observationshighlighted the annual fluctuations, and the variabilitybetween years and between areas.

147

The third axis is related to the concentration oflipids [fig. 4 (2), 5 (2»). A peak is noticcd inFebruary 1985 in contrast with January, Decemherand March. This strenghthens the assessment of shortterm fluctuations.

Dissol\'ed oxygen and temperature are opposcd onthe 4th axis which dcfines a second component ofboth variables rclated to January and August 1985.The fifth axis shows another component of proteinfluctuations. As shown by the qualities of representa­tion (table 5 b), this component corresponds toMarch, May and July 1984; it disappears in 1985.

Finally, axes 3 and 5 describc short tcrm fluctu­ations rcJated lo specifie amounls of nutricnts. Axis4 is only rcJatcd to physical paramctcrs.

Table Sb. - Qualities of representation of observations on axesY. and Ys extraeted from the l'CA of hydrology.

Date Axis Y. Axis Ys

54% of variability is cxplaincd by the firs! axis. The5 axes of the analysis account for 98% of the originalvariability (table 4). Principal and secondary fluctu­ations are present.

Chlorophyll a, phaeopigment and PO~1 may besccn on the first axis [fiK. 4 (3), 4 (4)]. The first two

Table Sa. - Correlations bctween hydrologîcal \lariables and prin-cipal axes.

Axis YI YI Y3 y. Ys

PROT 0.35 0.11 0.10 0.05 0.36UP 0.03 0.07 0.62 0.03 0.22CARB 0.21 0.64 0.10 0.01 0.00PIM 0.00 0.72 0.00 0.13 0.07ro~t 0.00 0.38 0.44 0.02 0.05CilLA 0.74 0.03 0.00 0.04 0.03PIIEO 0.72 0.18 0.00 0.01 0.03THfP 0.01 0.38 0.16 0.41 0.00OzP 0.49 0.00 0.03 0.40 0.04

H)'drological anal)'sis

Sincc hydrological parameters were thc same forail threc areas, a single analysis was carried out andthe different areas were not discriminated.

The first three axes account for 72% of the totalvariability among the nine variables (table 4). Dy com­paring the projections of variables (correlations) and

Table 4. - Eigenvalues and percentage of variance explainedby the principal axes of l'CA of hydro1ogica1 and sedimentarydescriptors.

l'CA Water Sediment

AxisEigcm'alue % Eigenva1ue %

YI 256 28 3.24 54YI 25t 28 1.12 19Y3 1.45 16 0.83 14y. \.09 12 0.36 6Ys 0.80 9 0.27 5

of observations, periodical and single fluctuationsmay he identified. Points close to the center of thegraph arc insufficiently represented and arc not takeninto account in the analysis. Five axcs wcre cxtractedby the analysis, but only the first three were ploltcd;axes 4 and 5 may he invcstigated from the table 5 a.

The first axis is corrclatcd with 3 variables[fig. 4 (1)]: chlorophyll a +phacopigmcnts, dissolvedoxygcn, protcins and appears to be characteristic ofthe bloom pcriod (June 1984, t-.by 1985) [fig.5(I)J.ln contrast, carlicr and latcr pcriods (March andApril, Octobcr and NO\'cmher) are rcJated to poorcrwaters and arc projcctcd on the other side of the firstaxis [fig. 5 ( 1)].

The second axis discriminates tcmpcrature andseston Iinked to carbohydratcs which show a peak in....inter.

The diffcrcnt origins of nutrients appcar on thefirst plane [fig. 4(1), 5(1)]: bloom in May and June,detritus in winter and show a one month lag betwcen1984 and 1985. The time scale does not allow toinvcstigate the truc lag within oscillations with aperiod Jess than 2 months.

Vol. l, nO 3 -1988

March 1984Apri11984May 1984June 1984July 1984August 1984Oetobcr 1984NO\lember 1984Dcccmbcr 1984Jam'ier 1985February 1985March 1985Apri11985May 1985June 1985Jury 1985

Scdimcnlary anal)"sis

0.2120.0020.1l00.0340.2360.0170.213O.O~O

O.C610.4230.1960.0410.0770.0630.0100.340

0.3430.2150.3660.\060.3310.0440.0050.0390.0500.0010.00:>0.0390.1450.0050.0050.095

P. Goulletquer and C. Bacher

Figure 4. - Correlations between descriptors and principal axes. ( 1 ) axes 1, 2 extracted from the PCA of hydrology. (2) axees 1, 3 extracted from the PCA of hydrology. (3) axes 1, 2 extracted from the PCA of sediment. (4) axes 1, 3 extracted from the PCA of sediment.

variables are of major influence. The proteins are associated with the second axis, and are independent of the former set. The comparison with the results of hydrological analysis shows the impact on the axes of ending bloom periods (August, 1985; October, 1984; November, 1984). From April to June, high levels of proteins, lipids, carbohydrates are noticed. In con- trast, the summer periods correspond to low levels of proteins lipids, carbohydrates (July 1984, August 1984, 1985).

As already indicated in the hydrological analysis, higher order axes may bc analyscd as sccondary scasonal components (table 6). Only chlorophyll a, lipids and carbohydrates are concerned. The same peak of lipids appears in water and sediment in Febru- ary. Lipid and carbohydratc peaks occur mainly in winter.

Thc diffcrenccs between areas are easily visible in the plane of axes 1, 2 which shows a decreasing con-

Aquat. Living Resour.

148

CD ®

P. Goulletqucr and C. Bacher

1--n;;=:=====~)r-------4à1

®

figure 4. - Correlations between descriptors and principal axes. (1) axes l, 2 extracted from the l'CA of hydrology. (2) axees l, 3 extractedfrom the l'CA of hydrology. (3) axes l, 2 extracted from the PCA of sediment. (4) axes l, 3 extracted from the PCA of sediment.

variables are of major influence. The proteins areassociated with the second axis, and are independentof the former set. The comparison with the results ofhydrological analysis shows the impact on the axes ofending bloom periods (August, 1985; October, 1984;November, 1984). From April to June, high levels ofproteins, lipids, carbohydrates are noticed. In con­trast, the summer periods correspond to low Jevelsof proteins lipids, carbohydrates (July 1984,August 1984, 1985).

As already indicated in the hydrological analysis,higher order axes may be analysed as secondaryseasonal components (table 6). Only chlorophyll a,lipids and earbohydrates are eoncerned. The samcpeak of lipids appears in water and sediment in Febru­ary. Lipid and earbohydratc pcaks oeeur mainly inwinter.

The differcnces between areas are easily visible inthe plane of axes l, 2 which shows a decreasing eon-

Aquat. Living Resour.

hlodelling of thc g r o ~ t h of clams, R. philippinarum

Figure 5. - Principal components analysis of hydrology. (1) Projections of observations on the plane (1,2). (2) Projections of observations on the plane (1.3). First class: X I I 1 1: Marck APl: April, MA 1: hfay, JU 1: June. JL 1: July, AT 1: Augost 1984. Sewnd class: OC 1: Oaober, NO 1: November, DE 1: December 1983, JA2: January, FE2: Febmary, ?cl112 March, AP2: April, M A 2 May, JU2: June, JL2: July 1985

Table 6. - Correlâtions between sedirncntary variables and princi- pal axes.

Axis YI y, y, y., y,

CH LA PH1:O PR OT LI P CARB

ccntration gradient from the high level to the low level area, highly correlated with the first axis [fig. 6(4)].

Loiv lerel area Four well defined periods appear on the first plane

[fis. 6(3)1: - April, May, ;une with high concentrations in

protcins, lipids and carbohydrates; - July, August with low levels of IQhl;

Vol. 1, no 3 - 1988

- October, Novcmbcr considered as a post bloom period (chlorophyll a, phaeopigment); - Winter, a season with average concentrations. A slight time-lag discriminates the 2 ycars projccted

on the same plane. The plane 1-3 brings little informa- tion, sincc the J-coordinate of al1 the observations but one is negative [fig. 6(6)].

On the first bisector, the months of October and November coincide with a pcak of lipids. The third axis also discriminates the 2 ycars according to detri- tic materials. As a consequcncc, morc nutrients were available for food al1 over 1983 compared to 1985.

,lledium lerel area

This area differs from the others by both stability and low lcvels of nutrients no matter the organic compartment considercd [fig. 6 (2), 6 (91. Bloom pcriods are not very intense and arc shown in the plane 1-3 [fis. 6(5)].

Iligh lccel area

When first analysing the plane 1-2 organic matter flows occurrcd mainly in June 1983 [fig. 6(1)]. One can notice greater oscillations in 1985 with two main peaks of nutrients in June and hlarch corresponding to chlorophyll a, phrieopigments and proteins, lipids and carbohydratcs. A rapid succession of scston pcaks occurs in Junc and is an indicator of a grcat sensitivity of scdiment to cnvironmental fluctuations. In contrast with the low lcvcl arca, the third axis is far from being stable. For instance positive coordinates are observed in April, hlay 1984, in wintcr and June 1985 so that chlorophyll u and protcins vary rapidly i$s. 6(4)1.

DISCUSSION

Combining correlations and the classification, the following descriptors arc dcmonstrated to be of dccreasing importance: chlorophyll a + phacopigmcnts (axis l) , temperature (axes 2+4), lipids (axis 3), sedi- ment organic matter (axis 8).

Data on trophic rclationships have been compiled in table 7. Kautsky (1982) on ,lljtilus cdulis, Iléral et al. (1983) on Crassosrrcu gigus obtained such corre- lations in situ. The influence of temperature on bivalve physiology \vas demonstrated by many authors. For example, an effect of temperature on gro~vth, excre- lion and gametogenesis of Rudirapcs pltilippinurunt has been shown by hfann and GIomb (1978) and hlann (1979). Ventilation rate (Iscrnard, 1983) and respiration rate were also modificd by temperature (Bernard, 1983; Laing et al., 1987). Laing et al. (1987) showed that growth efficiency depended on temperat- ure and phytoplankton nutritional value. The con- tents in polyunsaturated fatty acids (I'UFA) wcrc underlincd by Waldock and IIolIand (1983). The quantity and quality of lipids appear to bc important to the growth of R. philippinarum, as suggcstcd by

Modellin:;: of the ~rol\th of clams, R. philippinarum 149

-2

Table 6. - Correlations betwccn scdimcntary variables and princi·pal axes.

Axis YI Yz YJ Y4 Y5

ro~1 0.67 0.04 0.09 0.01 0.07CHLA 0.39 0.19 0.36 0.02 0.02PHEO 0.69 0,20 0.00 0.00 0.01PROT 0.24 0.45 0.24 0.01 0.05UP 0.53 0.21 0.06 0.20 0.01CARB 0.72 0.03 0.02 0.12 0.01

figure S. - Principal components analysis of hydrology,(1) Projections of observations on the plane (1,2), (2) Projectionsof observations on the plane (1,3). Firs! c1ass: Mill: ~Iarch, API:April, MA 1: May, JU 1: June, JL 1: July, ATI: August 1984,Second c1ass: OC 1: Octobcr, 1':01: NO\'cmber, DE 1: December1984, JA 2: January, FE 2: February, M1I2: March, AP2: April,~IA 2: May, JU 2: June, JL 2: July 1985

DISCUSSION

Combining correlations and the classification, thefollowing descriptors are demonstrated to be ofdccreasing importance: chlorophyll a+phaeopigrnents(axis 1), temperature (axes 2+4), lipids (axis 3), sedi­ment organic matter (axis 8).

Data on trophie rclationships have bcen compiledin table 7. Kautsky (1982) on ."yti/us cdulis, Héralet al. (1984) on Crassostrca gigas obtained such corre­lations in situ. The innuencc of temperature on bivalvephysiology \Vas demonstrated by many authors. Forexample, an efrect of temperature on growth, excre­tion and gametogenesis of Ruditapes philippinarumhas been shown by Mann and Glomb (1978) andMann (1979). Ventilation ratc (Bernard, 1983) andrespiration rate \Vere also modified by tcmperature(Bernard, 1983; Laing et al., (987). Laing et al. ( (987)showed that growth efficiency depended on temperat­ure and phytoplankton nutritional value. The con·tents in polyunsaturatcd fatty acids (PUFA) wereunderlined by \Valdock and HolJand (1984). Thequantily and quality of lipids appear to be importantto the growth of R. philippinarum, as suggcstcd by

- October, Novcmber considered as a post bloomperiod (ehlorophyll a, phacopigment);

- \Vinter, a season .....ith average concentrations.A slight time-Iag discriminatcs the 2 years projccted

on the same plane. The plane 1-3 brings little informa­tion, since the y-coordinate of ail the ob~crvations

but onc is ncgativc [fig. 6 (6)].On the first biscctor, the months of October and

Novcmbcr coincide \Vith a peak of Iipids. The thirdaxis also discriminatcs the 2 ycars according to detri·tic matcrials. As a consequence, more nutrients wereavailable for food an over 1984 compared to 1985.

Medium let'el area

This area dirfers from the others by both stabilityand low levcls of nutrients no matter the organiccompartment considcred [fig. 6(2),6(5)]. DIoomperiods arc not very intense and are shown in theplanc 1-3 Ifig. 6(5)].

11igh lere! area

When first analysing the plane 1-2 organic matternows occurred mai nI y in June 1984 [fig. 6(1)]. Onecan notice greatcr oscillations in 1985 with two mainpeaks of nutrients in June and March corrcspondingto chlorophyll a, phaeopigmcnts and protcins, lipidsand carbohydrates. A rapid succession of seston peaksoccurs in June and is an indicator of a great sensitivityof sediment to cnvironmental nuctuations. In contrastwith the low level area, the third axis is far frombcing stable. For instance positive coordinates areobseT\'ed in April, May 1984, in wintcr and June 1985so that chlorophyll a and proteins "ary rapidly[fig. 6(4)].

l­l

-2

AT! CDI/AZ

~z ...,11><1

JP7. 1001

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1lA,

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Ali

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centration gradicnt from thc high level to the low Jevclarea, highly correlated \Vith the first axis [fig. 6 (4)].

Law let'el arca

Four wcU defincd pcriods appear on the first plane[fig. 6(3)]:

- April, May, June \Vith high concentrations inprotcins, lipids and carbohydrates;

- July, August \Vith low levels of PO~f;

Vol. l, nO 3 • 1988

-,

-2

-1

-4

-4

-2

150 P. Goulletquer and C. Bacher

Rgure 6. - Projections of observations on principal axes extracted from the K A of sediment. Axes 1,2: (1) high levei, (2) medium levei, (3) low level. Axes 1.3: (4) high levei, (5) medium level, (6) low level.

the sensitivity of the mode1 to this factor. Although no strong correlations were found between the meat production and the detritic organic matter in estuarine areas, growth in weight was correlated with chlorophyll a concentration. Similar results have been found with C. gigas (Héral et al., 1984). The correla- lions obsewed betwcen growth, water column and the interface between water and sediment, need to be confirmed by animal field studies to assess the influ-

W f a 1 m -8

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ence of each variable, and to avoid any casual correla- tion (Héral et al., 1984). The results of the present study show significant correlations for two classes at different tidal exposures, during two years. Even though explanatory variables are identical, the sensi- tivity varied between the 2 years, as demonstrated by the stronger sediment effect in 1985. Hbwever the winter conditions in 1985, which caused a more fre- quent resuspension of superficial sediment, could

-4 -# O 8 4

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Art w

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Aquat. Living Resour.

ISO P. GouIletquer and C. Bacher

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•-t

-1

Figure 6. - Projections of observations on principal axes extracted from the PCA of sediment. Axes 1,2: (1) high level, (2) medium Ievel,(3) low level. Axes 1,3: (4) high level, (5) medium level, (6) low level.

thc scnsitivity of the model to this factor. Althoughno strong correlations were found bctwccn thc meatproduction and the detri tic organie matter in estuarineareas, growth in weight was correlated withchlorophyll a concentration. Similar results have becnround with C. gigas (Héral et al., 1984). The correla­tions observed betwccn growth, water column andthe interface between water and sediment, need to beconfirmed by animal field studies to asscss the influ-

ence of cach variable, and to avoid any casual correla­tion (Héral et al., 1984). The results of the presentstudy show significant correlations for two classes atdifferent tidal exposurcs, during two years. Eventhough explanatory variables are identical, the sensi­tivity varicd bctwecn thc 2 years, as demonstrated bythc strongcr sediment cffeet in 1985. Hciwever thewinter conditions in 1985, which caused a more fre­quent resuspension of superficia1 sediment, could

Aquat. Living Resour.

Modelling of the growth of clams, R. philippinarum

. .

Table 7. - Review of factors and methods used for the study of trophic relationships. -- - -

Calculation used to

establish correlation

Dependent Variable

Positive factors

Negative factors

Authors

Benthic biomass Hargrave and Peer (1973) Lelong and Riva (1976) Vahl (1980) Héral et al. (1983) Deslous-Paoli and Héral (1 984) Fréchette and Bourget (1985) Wallace and Reinsnes (1985)

Biomass

Ruditapes philippinarum Length Phytoplankton, TO, salinity

- - -

Chlamys islandica Crassostrea gigas (adult)

Crassostrea gigas

Dry weight Dry weight Dry weight

PI M PIM PI M

Mytilus edulis Length Dry weight Dry weight

POM

Food quantity, PIM,

% W M . ATP

current speed, POM ATP

current speed, POM POM

current speed No correlation

with: temperature

salinity Proteins, Lipids,

Carbohydrates Log ATP

current speed T",

chlorophyll a Chlorophyll a,

carbohydr. T",

chlorophyll a, pheopigment

dissolved orga. (sediment and

water) Chlorophyll a,

primary production

(water + sediment) Chlorophyll a

(Ta. No significant)

Chlamys islandica

Wildish and Kristmanson (1979)

Biomass Biomass

Wildish and Kristmanson (1984)

Biomass Mytilus edulis

Wildish and Kristmanson (1985) Rrninocr and l i::.:: (l9Q4)

Mytilus edulis Wet weight

Dry weight Ruditapes philippinarum, Ruditapes decussatus

Non parametric

tests

Soniat et al. (1985) Crassostrea virginica Dry weight gonad

Temperature Non parametric

tests Linear

regression Linear

regression Factor

analysis Multiple

linear regression

Wildish et al. (1981) Biomass Erosion sediment -

Molluscs

Mytilus edulis Kautsky (1982) Length

Deslous-Paoli et al. (1982) Héral et al. (1984)

Crassostrea gigas Biochemical composition Dry weight Bacteria

Crassostrea gigas

Bodoy and Plante-Cuny (1984) Plante-Cuny and Bodoy (1987) Page and Hubbard (1987)

Ruditapes decussaf us

Donax trunculus

Length Multiple linear

regression

Length Multiple linear

regression Stepwise

regression Stepwise

regression

Mytilus edulis

Parache and Massé (1986) Parache and Massé ( 1987)

Length

Dry weight

Pheopigment proteins Lipids,

carbohydrates. T'. proteins

Mytilus galloprocincialis

Mytilus galloprovincialis (adults, juveniles)

explain' the difference in mode1 sensitivity. Further- The daily submersion time represents the more morc, the dominant phytobenthic species on muddy important factor in determining growth differences 1-;.:;dm are generally large diatoms (Rincé, 1978). between intertidal levels, such as demonstrated by the These species could represent a more easily available growth modcl. Thcse differences can be attributcd to food for the older clams. the difference of food availability. Tidal level has

Vol. 1. nQ 3 - 1988

Modclling of the growth of clams, R. philippinarum 151

Table 7. - RevÎew of factors and methods used for the study of trophic relationships.

Calculation

Authors SpeciesDependent Positive Negative used to

Variable factors factors establishcorrelation

Hargrave Benthic biomass Biomass Oorophyll a Noand Peer (1973)Lelong Ruditapes philippinarum Length Phytoplankton, Noand Riva (1976) T', salinityVahl (1980) Chlamys islandica Dry weight PIM NoHéral et al. (1983) Crassostrea gigas (adult) Dry weight PIM NoDeslous-Paoli Crassostrea gigas Dry weight P1M Noand Héral (1984)Fréchette and Mytilus edulis Length l'OM NoBourget (1985) Dry weightWallace and

Chlamys islandicaDry weight Food quantity, No

Reinsnes (1985) PIM,% l'OM.

Wildish and Biomass ATP NoKristmanson (1979) Biomass current speed,

l'OMWildish and

M ytilus edulisBiomass ATP No

Kristmanson (1984) current speed,l'OM

Wildish and Mytilus edulis Wet weight roM NoKristmanson (1985) current speedR.."i",?e'f lInd Ruditapes philippinarum. Dry weight No correlation Nonl ,:::: (t<)~4) Ruditapes decussatus with: parametric

temperature testssa\inity

Soniat et al. (1985) Crassostrea virginica Dry weight Proteins, Temperature Nongonad Lipids, parametric

Carbohydrates testsWildish et al. (1981)

Mol/usesBiomass Log ATP Erosion Linear

current speed sediment regressionKautsky (1982) Mytilus edulis Length T', Linear

chlorophyll a regressionDeslous-Paoli Crassostrea gigas Biochemical Chlorophyll a, PIM Factoret al. (1982) composition carbohydr. analysisHéral et al. (1984) Dry weight T', Bacteria Multiple

chlorophyll a, linear

Crassostrea gigaspheopigment regression

dissolved orga.(sediment and

water)Bodoyand Ruditapes decussatus Length Chlorophyll a, MultipleP1ante-Cuny (1984) primary \inearP1ante-Cuny Donax trunculus production regressionand Bodoy (1987) (water+sediment)Page and Length Chlorophyll a MultipleHubbard (1987) Mytilus edulis (T', No significant) \inear

regressionParache and

Mytilus galloprovincialisLength Pheopigment Stepwise

Massé (1986) proteins regressionP'drache and

Mytilus galloprovincialisDry weight Lipids, Stepwise

Massé (1987)(adults, juveniles)

carbohydrates, regressionT', proteins

explain· the difference in model sensitivity. Further­more, the dominant phytobenthic species on muddyh~:;l)m are generally large diatoms (Rincé, 1978).These species could represent a more easily availablefood for the older clams.

Vol. l, nO 3 - 1988

The daily submersion lime represents the moreimportant factor in determining growth differencesbetween intertidal levels, such as demonslrated by thegrowlh mode\. These differences can be attributed 10the dirferencc of food availability. Tidal level has

152 P. Goulletquer and C. Bacher

long bcen rccognized as an important factor in controlling growth [e.g. Glock and Chcw, 1979 on R. philippinarum, Griffiths (198 1) on Choromjtilus meridionalis, Gillmor (1982), Cracycrmcersh et al. (1986) on hfytilus edulis].

hlany authors have suggested that food deplction can occur, due to the activity of suspcnsion feeders during tidal cycles. Frfchcttc and Bourget (1985) show that deplction of organic particlcs limits thc growth of hl. edulis. In the same way, Cloern (1982) and Cohen et al. (1983) suggested that benthic organ- isms were prcscnt in quantities large cnough to rcducc the phytoplanktonic biomass. Pcterson and Black (1987) demonstratcd that potcntial food dcplc- lion in the water column is a "priority" effect of suspension fccdcrs in intcrtidal shore. Eléral et al. (1983) and Deslous-Paoli and IIéral(1984) found that C. gigas rctaincd bctween 0.1 and 0.5% of the water column energy, at a density of 200 g/m2 in the bay of Marennes-Oléron, while the current speed varied between 0.5 m. s-' and 1.5 m. s-'. The retention rate of R. philippinarum was 0.8 times the retention rate of C. gigas, with particlcs retained of ncarly the same size (Dcslous-Paoli et al., 1987). For thcsc rcasons, the deplction of P û X I due to 40 g/m2 biomass of clams remains usually lower than 1% and does not account for growth limitation. Ilowcvcr, at a major scale, depletion rates arc rclated to residual currcnts, water residence timc and biomass levels in the briy (IIéral, 1987; Bacher, 1987).

Since submersion tirne is thc most important factor which explains growth differences between sites, the filtration time is not the only factor affectcd by sub- mersion. Any increase in tidal exposure will have physiological cffccts (Bayne et al., 1976; Griffiths, 1981; Fang, 1982). A sensitivity of growth to the scdimcnt organic content has bccn shown. Thesc

results agree with those obtained by Plante-Cuny and ISodoy (1987), who observed a positive correlation bctwccn primary production in scdimcnt and growth

- of R. decussatus. A significant positive correlation between phytobcnthic primary production, chloro- phjll a concentrations and level of exposure was also found by Cadée and Iiegeman (1977). These results are supportcd by the work of Admiral and Pclcticr (1980) and Colijn and de Yongc (1983) in cstuarine areas. The high primary production resultcd mainly from a longer lighting at high elevation. Sediment organic content is correlatcd to the lcvcl of exposure. Thus the quality or quantity of available food in the higher levels of sediment may countcract the growth deficit due to increasing tidal exposure. Simulations of the growth model wcre pcrformed with equal immersion time or wcight. Thc largcr weight obtained at high or medium levels supportcd this phenornenon.

The value of the exponcnt b=0.6 shows that the model is really non linear. Consequently, Our model shoud be more precise than a lincar one and the comparisons more reliable. Theorctically, estimation of thc parameters requires cross combinations of the factors. This should have led to study the growth of diffcrcnt cohorts, since initial wcight is partly takcn into account. On the contrary, interdcpcndcnt csti- mators of the parameters results from the correlations between some factors (e. g. initial weight and lcvel of immersion). Rcsults do not allow generalization in that case, cvcn though computed values are consistent with observations. In this study, the experimental design encompasses somc heterogeneity since the spawning at the end of the first year leads to initial weight variability bctwccn the areas. Ilowever, the whole data set docs not support cxactly the cross effects hypothesis and the model parameters should not be applied to other sites without due precautions.

Acknow ledgemcnts

We thank Dr. P. Gros for his precious advice, Drs. B. hlesnil and A. Bodoy for corrections of the manuscript and the staff of the LEC for their help.

REFERENCES

Admiraal W., 21. Peletier, 1980. Influence of seasonal vari- ations of temperature and light on the growth rate of culture and natural populations of intertidal diatoms. Afar. Ecol. Prog. Ser., 2, 35-43.

Bacher C., 1987. hlodélisation de la croissance des huîtres dans le bassin de hlarennes Oléron In: Rapp. E.P.R. Poitou Charentes, 96 p.

Bayne B. L., R. J. Thompson, J. Widdows, 1976. 1. Physi- ology. In hfarine hlussels, their ecology and physiology, B. L. Bayne Ed., Cambridge Univ. Press., Cambridge, 12 1-206.

Iieninger P., A. Lucas, 1983. Seasonal variations in condi- tion, reproductive activity and gross biochemical compo- sition of two species of adult clam in a common habitat: Tapes decussatus L. (Jeffreys) and Tapes philippinarum (Adams and Reeve). J. Exp. hlar. Biol. Ecol., 79, 19-37.

Bernard F. R., 1983. Physiology and the mariculture of some northeasterm Pacific Bivalve hlolluscs. Can. Spec. Publ. Fish. Aquat. Sei., 63, 24 p.

Bligh J. G., W. F. Dyer, 1959. A rapid method of total lipid extraction and purification. Can. J. Biochem. Physiol., 37, 911-917.

Bodoy A., hl. R. Plante-Cuny, 1984. Relations entre I'évo- lution saisonnière des populations de palourdes (Rudi- tapes decussatus) et celles des microphj-tes benthiques et planctoniques (golfe de Fos, France). Ilaliotis, 14, 71-78.

Aquat. Living Resour.

152

long been recognized as an important factor incontrolling growth le. g. G10ck and Chew, 1979 onR. philippinarum, Griffiths (1981) on Choromytilusmeridionalis, Gillmor (1982), Craeyermeersh et al.(1986) on Mytilus edulis].

Many authors have suggestcd that food depletioncan oceur, due to the activity of suspension feedersduring tidal cycles. Fréchette and Bourget (1985)show that depletion of organic particles Iimits thegrowth of M. edulis. In the same way, Cloern (1982)and Cohen et al. (1984) suggested that benthic organ­isms were present in quantities large enough to reducethe phytoplanktonic biomass. Peterson andBlack (1987) demonstrated that potential food deple­tion in the water column is a "priority" effect ofsuspension feeders in intertida1 shore. Héra1 et al.(1983) and Deslous-Paoli and Héral (1984) found thatC. gigas retained between 0.1 and 0.5% of the watercolumn energy, at a density of 200 g/m2 in the bayof Marennes-Oléron, while the current speed variedbetween 0.5 m. s-1 and 1.5 m. s-1. The retention rateof R. philippinarum was 0.8 times the retention rateof C. gigas, with particles retained of nearly the samesize (Deslous-Paoli et al., 1987). For these reasons,the depletion of POM due to 40 g/m 2 biomass ofclams remains usually lower than 1% and does notaceount for growth limitation. However, at a majorscale, depletion rates are related to residual currents,water residence time and biomass levels in the bay(Héral, 1987; Bacher, 1987).

Sinee submersion time is the most important factorwhich explains growth differences between sites, thefiltration time is not the only factor affected by sub·mersion. Any increase in tidaI exposure will havephysiologicaI effects (Dayne et al., 1976; Griffiths,1981; Fang, 1982). A sensitivity of growth to thesediment organic content has been shown. These

P. GoulIetquer and C. Dacher

results agree with those obtained by Plante-Cuny andBodoy (1987), who observed a positive correlationbetween primary production in sediment and growth

• of R. decussatus. A significant positive correlationbetween phytobenthic primary production, chloro­phyll a concentrations and level of exposure was alsofound by Cadée and Hegeman (1977). These resultsare supported by the work of AdmiraI and Peletier(1980) and Colijn and de Vonge (1984) in estuarineareas. The high primary production resulted mainlyfrom a longer Iighting at high elevation. Sedimentorganie content is correlated to the level of exposure.Thus the quality or quantity of available food in thehigher levels of sediment may counteract the growthdeficit due to increasing tidaI exposure. Simulationsof the growth modeI were performed with equalimmersion time or weight. The larger weight obtainedat high or medium Ievels supported this phenomenon.

The value of the exponent b = 0.6 shows that themodel is really non Iinear. Consequently, our modelshoud be more precise than a linear one and thecomparisons more reliable. Theoretically, estimationof the parameters requires cross combinations of thefactors. This should have led to study the growth ofdifferent cohorts, sincc initial weight is partly takeninto account. On the contrary, interdependent esti·mators of the parameters results Crom the correlationsbetween sorne factors (e. g. initial weight and Ievel ofimmersion). Results do not allow generalization inthat case, even though computed values are consistentwith observations. In this study, the experimentaIdesign encompasses some heterogeneity since thespawning at the end of the first year Ieads to initialweight variability between the areas. However, thewhole data set does not support exactly the crosseffects hypothesis and the model parameters shouldnot be appIied to other sites without due precautions.

Acknowledgcmcnts

We thank Dr. P. Gros for his precious advicc, Ors. D. Mesnil and A. Bodoy for corrections of the manuscript and thestaff of the LEe for their help.

REFERE~CES

AdmiraaJ \V., H. Pelelier, 1980. Innuencc of seasonal vari­ations of temperature and Ijght on the growth rate ofculture and natural populations of intertidal diatoms.Afar. Ecol. Prog. Ser., 2, 35-43.

Bacher c., 1987. Modélisation de la croissance des huîtresdans le bassin de Marennes Oléron ln: Rapp. E.P.R.Poilou Charentes, 96 p.

Bayne B. L., R. J. Thompson, J. Widdows, 1976. 1. Physi­ology. In Marine Mussels, their ecology and physiology,B. L. Dayne Ed., Cambridge Univ. Press., Cambridge,121-206.

Beninger P., A. Lucas, 1984. Seasonal variations in condi­tion, reproductive activily and gross biochemical compo­sition of two species of adult clam in a common habilat:Tapes decussatus L. (Jeffreys) and Tapes philippinarum(Adams and Reeve). J. Exp. Afar. Biol. Ecol., 79, 19-37.

Bernard F. R., 1983. Physiology and the maricullure ofsorne northeasterm Pacifie llivalve Molluscs. Con. Spec.Publ. Fish. Aquat. Sei., 63, 24 p.

Bligh J. G., W. F. Dyer, 1959. A rapid method of total lipidextraction and purification. Con. J. Biochem. Physiol., 37,911-917.

Bodoy A., M. R. P1ante-Cuny, 1984. Relations entre révo­lution saisonnière des populations de palourdes (Rudi­tapes decussatus) et celles des microph)1eS benthiques etplanctoniques (golfe de Fos, France). llaliotis, 14, 71·78.

Aquat. Li\ing Resour.

l\Iodelling of the gro\\th of clams, R. p!zilippinarum

Cadée G. c., J. Hegeman, 1977. Distribution of primaryproduction of the benthic micronora and accumulationof organic matter on a tidal flat area. Balgzand, DutchWadden Sca. Neth. J. Sea Res., 11,24-41.

Cloern J. E., 1982. Does the benthos control phytoplanktonbiomass in South San Francisco Bay? .\Iar. Ecol. Progr.Ser.,9, 191-202.

Cohen R. 11., p. V. Drcslcr, E. J. p. phillips, R. L. Cory,1984. The effcct of the Asiatie clam, Corbicula jlumineaon phytoplankton of the Potomac River, Mar)·land. Lim­nol. Oceanogr., 29, 170-180.

Colijn F., V. N. de Yonge, 1984. Primary production ofmicrophytobenthos in the EMS. Dollard Estuary. Mar.Ecol. Prog. Ser., 14, 185-196.

Craeymeersch J. A., p. M. J. Hermann, p. M. Meire, 1986.Secondary production of an intertidal musse! (Mytilusedulis L.) population in the Eastern Scheldt (S.W.Netherlands). lIydrobiol., 133, 107-115.

Deslous-Paoli J. M., M. Héral, 1984. Transferts énergé­tiques entre l'huître Crassostrea gigas de 1 an ct la nourri­ture potentielle disponible dans l'cau d'un bassin ostréic­ole. lIaliotis, 14, 79-90.

Deslous-Paoli J. M., M. Héral, p. Goulletquer, W. Borom­thanarat, D. Razet, J. Garnier, J. Prou, L. Barillet. 1987.Évolution saisonnière de la filtration de bivalves interti­daux dans des conditions naturelles. Indices biochimiquesdes milieux marins nov. 86, L'Houmeau. Oceanis, 13,575-579.

Deslous-Paoli J. M. Héral, Y. Zanette, 1982. Problèmesposés par l'analyse des relations trophiques huÎtres­milieu. Indices biochimiques des milieux marins. Actescoll. CNEXO, 14, 335-340.

Dubois F., K. A. Gilles, J. K. Hamilton, p. A. Rebecs,F. Smith, 1956. Colorimetrie method for determinationof sugars and related substances. Anal. Chem., 28, 350­356.

Fang Y., 1982. Tidal zonation and cardiae physiology infour species of bivalves from Hong Kong. In: Procce­dings of the First International Marine Biological Work­shop: The Marine Flora and Fauna of Hong Kongand Southern China Hong Kong 1980, N. S. Morton,C. K. Tseng Eds. Hong Kong University l'ress, 849-858.

Fréchette M., E. Bourget, 1985. Food limited growth of.\Iytilus edulis L. in relation to the benthie boundarylayer. Cano J. Fish. Aquat. Sc., 42, 1166-1170.

Gillmor R. B., 1982. Assessment of Intertidal growth andcapacity Adaptations in Suspension Feeding Bi\·ahes..\Iar. Biol., 68, 277-286.

Glock J. W., K. K. Chew, 1979. Growth, recovery andmovement of l\Ianila clams, Venerupis japonica(Deshayes) at Squaxin island Washington. Proceed. Natl.Shellfish. Assoc., 69, 15-20.

Grirriths R. J., 1981. Population dynamics and growth ofthe bivalve Clloromytilus meridionalis (Kr) at differenttidallcvels. Estuar. Coast. SlIel! Sei., 12, 101·118.

Hamon p. Y., 19S3. Croissance de la moule Mytilus edulisprodneialis (Lmk) dans l'étang de Thau: Estimation desstocks de mollusques en élevage. 11Jèse âètat Univ.Montpellier, 331 p.

Hargrave B. T., D. L. Peer, 1973. Comparison of benthiebiomass with depth and primary production in sorne

Vol. l, nO 3 - 1988

153

Canadian east coast inshore waters. ICES C.M./K. 8,14 p.

Héral 1\1., 1987. Evaluation of the carrying capacity ofMolluscan Shellfish Ecosystems. Shellfish culture Devel­opment and Management. International Seminar inLa Rochelle (France), 4-9- mars 1985. Ed. IFREMER,297-318.

Héral M., J. 1\1. Deslous-Paoli, J. Prou, D. Razet, 1987.Relations entre la nourriture disponible et la productiondes mollusques en milieu estuarien: variabilité temporellede la colonne d'eau. IJaliotis, 16, 149-158.

Héral 1\1., J. 1\1. Deslou-Paoli, D. Razet, J. Prou, 1984.Essai de mise en évidence in-situ de paramètres biotiqueset abiotiques de l'eau et de l'interface eau-sédiment inter­venant dans la production de l'huître Crassostrea gigas.Oceanis, 10, 465-475.

Héral M., J. 1\1. Deslous.Paoli, J. M. Sornin, 1983.Transferts énergétiques entre l'huître Crassostrea gigas etla nourriture potentielle disponible dans le bassinostréicole: premières approches. Océanis, 9, 169·194.

Kautsky N., 1982. Growth and size structure in a BaltieMytilus edulis population. Mar. Biol., 68, 117-133.

Laing 1., S. D. Utting, R. W. S. Kilada. 1987. Interactiveeffect of diet and temperature on the growth of juvenileclams. J. Exp. Mar. Biol. Ecol., 113,23-38.

Lelong P., A. Riva. 1976. Relations entre croissance debivalves et phytoplancton en lagune et bassin fermé.IJaliotis,7, 104-109.

Lorenzen C. J., 1967. Determination of chlorophyll andpheophytin: spectrophotometrie equation. Limnol. Oce­anogr., 12, 343-346.

Lowry O. N., N. 1. Rosebrough, A. L. Farrand, R. J.Randall, 1951. Protein measurement with the folinphenol reagent. J. Biol. Chem., 193, 263-275.

Mann R., S. J. Glomb, 1978. The erfect of temperature ongrowth and ammonia excretion of the l\Ianila clam,Tapes japonica, Estuar. Coastl. .\Iar. Sei., 6, 335-339.

Mann R., 1979. The effects of temperature on growth,physiology, and gametogenesis in the Manila clam, Tapesphilippinarum, J. Exp. .\Iar. Biol. Eco!., 38, 121·134.

Marsh J. 8., D. Weinstein, 1966. Simple charring methodfor determination of lipids. J. Lipids Res., 7, 574-576.

Nelder J. A., R. Mead, 1965. A simplex method for functionminimi.ration Computer J., 7,308-313.

Page II. 1\1., D. M. Hubbard, 1987. Temporal and spatialpatterns of growth in mussels Mytilus edulis on an off­shore platform: relationship to water temperature andfood availability. J. Exp. .\Iar. Biol. Eco!., 111, 159-179.

Parache A., II. Massé, 1986. Croissance de Mytilus gallo­prodneialis sur filières en mer ouverte en MéditerranéeNord-Occidentale. IJaliotis, 15, 163-171.

Parache A., H. l\Iassé, 1987. Inl1uence des facteurs dumilieu sur le cycle biologique de .\Iytilus galloprodneialisen élevage sur corde, dans l'anse de Carteau (côte Médi­terranéenne Fran.;aise). IJaliotis, 16, 137-147.

Peterson C. IL, R. Black, 1987. Rcsource deplction byactive suspension-freeders on tidal flats: Influence oflocal density and tidal elevation. Umnol. Oceanogr., 32,143-166.

P. Goulletquer and C. Bacher

Plante-Cuny M. R., A. Bodoy, 1987. Relations trophiques entre microphytes benthiques ou planctoniques et mollus- ques bivalves endogés. Production et relations trophiques dans les écosystèmes marins. 2' colloque franco-soviéti- que Yalta, 1984. IFREMER Act. Coll., 5, 157-169.

Rincé Y., 1978. Intervention des diatomées dans l'écologie des claires ostréicoles de la baie de Bourgneuf. Thèse dr. 3' cycle, Univ. Nantes, 203 p.

Schnute J., 1982. A manual for easy non linear parameter estimation in Fishery Research with interactive Micro- cornputer Programs. Can. Tech. Rep. Fish. Aquat. Sci., 1140, 1-115.

Sebens K. P., 1982. The limits to indeterminate growth: an optimal size mode1 applied to passive suspension-feeders. Ecology, 63, 209-222.

Soniat T. M., S. M. Ray, 1985. Relationship between pos- sible available food and the composition, condition and reproductive state of oysters from Galveston Bay, Texas. Contr. Mar. Sci., 28, 109-121.

Strickland, J. D., T. R. Parsons, 1972. A practical hand- book of seawater analysis. Bull. Fish. Res. Board Can., 167, 1-310.

Tomassone R., E. Lesquoy, C. Millier, 1983. La regression, nouveaux regards sur une ancienne méthode statistique. Masson. !%ris, 180 p.

Vahl O., 1980. Seasonal variations in seston and in the growth rate of the Iceland scallop, Chlamys islandica from Bulsfjord 70" N.J. Exp. Mar. Biol. Ecol., 48, 195- 204.

Volle M., 1981. Analyse des données. Economica. Pnric

317 p. Waldock M. J., D. L. Holland, 1984. Fatty acid metabolism

in young oysters, Crassostrea gigas: polyunsaturated fatty acids. Lipids, 19, 332-336.

Wallace J. C., T. G. Reinsnes, 1985. The significance of various environmental parameters for growth of the Ice- land scallop, Chlamys islandica (Pectinidae). in hanging culture. Aquaculture, 44, 229-242.

Wildish D. J., D. D. Kristmanson, 1979. Tidal energy and sublittoral Macrobenthic Animals in Estuaries. J. Fish. Res. Board Can., 36, 1197-1206.

Wildish D. J., D. D. Kristmanson, 1984. Importance to mussels of the benthic boundary layer. Can J . Fish. Aquat. Sci., 41, 1618-1625.

- 1985. Control of suspension feeding bivalve production by current speed. Helgol. Meeresunter., 39, 237-243.

Wildish D. J., D. D. Kristmanson, D. Peer, 1981. Effect of tidal currents on suspension feeding benthos in the bay of Fundy. ICES C.M./L, 33, 7.

Yentsch C. S., D. W. Menzel, 1963. A method for the determination of phytoplankton chlorophyll and phae- ophytin by fluorescence Deep-Sea Res., 10, 221-231.

Aquat. Living Resour.

154

Plante-Cuny M. R., A. Bodoy, 1987. Relations trophiquesentre microphytes benthiques ou planctoniques et mollus­ques bivalves endogés. Production et relations trophiquesdans les écosystèmes marins. 2e colloque franco-soviéti·que Yalta, 1984. IFREMER Act. Coll., 5, 157-169.

Rincé Y., 1978. Intervention des diatomées dans l'écologiedes claires ostréicoles de la baie de Bourgneuf. Thèse dr.3e cycle, Univ. Nantes, 203 p.

Schnute J., 1982 A manual for easy non Iinear parameterestimation in Fishery Research with interactive Micro·computer Programs. Cano Tech. Rep. Fish. Aquat. Sei.,

. 1140, 1·115.Sebcns K. P., 1982. The Iimits to indeterminate growth: an

optimal size model applied to passive suspension-feeders.Ecology, 63, 209-222.

Soniat T. M., S. M. Ray, 1985. Relationship between pos­sible available food and the composition, condition andreproductive state of oysters from Galveston Bay, Texas.Contr. Mar. Sel., 28, 109-121.

Strickland, J. D., T. R. Parsons, 1972. A practical hand·book of seawater analysis. Bull. Fish. Res. Board Can.,167, 1·310.

Tomassone R., E. Lesquoy, C. Millier, 1983. La regression,nouveaux regards sur une ancienne méthode statistique.Masson. Paris, 180 p.

P. Goulletquer and C. Bacher

Vahl O., 1980. Seasonal variations in seston and in thegrowth rate of the Iceland scallop, Chlamys islandicafrom Bulsfjord 70Q N.J. Exp. Mar. Biol. Eco!., 48, 195­204.

Voile M., 1981. Analyse des données. Economira. Par;.317 p.

Waldock M. 1., D. L. Holland, 1984. Fatty acid metabolismin young oysters, Crassostrea gigas: polyunsaturatedfattyacids. Lipids, 19, 332-336.

Wallace J. c., T. G. Reinsnes, 1985. The significance ofvarious environmental parameters for growth of the Ice­land scallop, Chlamys islandica (Pectinidae), in hangingculture. Aquaculture, 44, 229-242.

Wildish D. J., D. D. Kristmanson, 1979. Tidal energy andsublittoral Macrobenthic AnimaIs in Estuaries. J. Fish.Res. Board Can., 36, II97·1206.

Wildish D. J., D. D. Kristmanson, 1984. Importance tomussels of the benthic boundary layer. Can J. Fish.Aquat. Sei., 41, 1618-1625.

- 1985. Control of suspension feeding bivalve productionby current speed. Helgol. Meeresunter., 39, 237-243.

Wildish D. J., D. D. Kristmanson, D. Peer, 1981. Effeetof tidal currents on suspension feeding benthos in thebay of Fundy. ICES C.M./L, 33, 7.

Yentsch C. S., D. W. Menzel, 1963. A method for thedetermination of phytoplankton chlorophyll and phae­ophytin by fluorescence Deep-Sea Res., 10, 221-231.

Aquat. Uving Resour.