The effect of food composition on Pacific oyster Crassostrea gigas (Thunberg) growth in Korea: a modeling study

Aquaculture 199 Ž2001. 41–62 www.elsevier.nlrlocateraqua-online

The effect of food composition on Pacific oyster Crassostrea gigas žThunberg/ growth in Korea: a modeling study Kyung-Hoon Hyun a,) , Ig-Chan Pang a , John M. Klinck b, Kwang-Sik Choi a , Joon-Baek Lee a , Eric N. Powell c , Eileen E. Hofmann b, Eleanor A. Bochenek c a

b

College of Ocean Science, Cheju National UniÕersity, Cheju-Do 690756, South Korea Center for Coastal Physical Oceanography, Old Dominion UniÕersity, Norfolk, VA 23529, USA c Haskin Shellfish Research Laboratory, Rutgers UniÕersity, Port Norris, NJ 08349, USA Received 29 June 2000; accepted 12 December 2000

Abstract A population dynamics model, originally derived for the Eastern oyster Crassostrea Õirginica and later modified for the Pacific oyster C. gigas in Japan, is applied to investigate the effect of food composition on the growth rate of C. gigas, which is in aquaculture in Kamakman Bay, Korea. Annual environmental cycles of temperature, salinity and particle concentration as well as various measures of food are used in the model. The model reproduces the general features of observed oyster growth in the different regions of the bay. Simulations show that chlorophyll-a is an inadequate measure of food for oysters. Using labile lipidq proteinq carbohydrate as a food source results in higher growth rates than observed, suggesting that a surplus of potential food is available in the water column, but that much of it is not utilized by oysters and that little of it is present as chlorophyll containing cells. Assuming that most of the food is available as small particles, which are filtered at low retention efficiency by oysters, results in simulated growth rates that are similar to observed field growth rates. The oyster model used in this research is shown to be generally applicable to the Pacific oyster, C. gigas. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Crassostrea gigas; Population dynamics model; Aquaculture; Food composition; Retention efficiency

) Corresponding author. Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, VA 23529, USA. E-mail address: [email protected] ŽK.-H. Hyun..

0044-8486r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 4 - 8 4 8 6 Ž 0 1 . 0 0 5 0 9 - 9

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1. Introduction Korea is one of the largest oyster exporters in the world ŽRana, 1998.. Oyster production in Korea peaked in 1987, but has decreased during the 1990s. Interest in the quality of the environment in areas of oyster aquaculture and the interactions between cultured oysters and their environment has been growing for the last decade. Empirical approaches have been used to maximize oyster production ŽYoo and Yoo, 1973; Yoo and Park, 1981. and then to assess the interactions of oysters with their environment ŽLee, 1993.. During the last decade, the use of ecological models for managing shellfish fisheries and improving shellfish aquaculture has increased ŽSmaal, 1991; Dowd, 1997.. Several numerical models have been developed for the Pacific oyster, Crassostrea gigas ŽThunberg; Kim, 1980; Kishi and Uchiyama, 1993; Kim, 1995; Kobayashi et al., 1997.. These models have contributed to our understanding of the role of biological and environmental factors in the growth of cultured oysters. In this study, we use an oyster population dynamics model to investigate the effect of food composition in controlling oyster growth in a bay in Korea. The model was originally developed for the Eastern oyster, C. Õirginica ŽKlinck et al., 1992; Hofmann et al., 1992. and was adapted to the Pacific oyster C. gigas in Japan ŽKobayashi et al., 1997.. Recently, Soniat et al. Ž1998. examined the effectiveness of various measures of food supply in modeling oyster population dynamics for C. Õirginica and concluded that a measure of carbohydrate, lipid and protein was vastly better than alternatives such as chlorophyll-a. In this contribution, we Ž1. evaluate the C. gigas population dynamics model in a second location, Kamakman Bay, Korea, to determine the generality of its application and Ž2. evaluate the usefulness of several measures of food supply in modeling C. gigas population dynamics by comparing various measures of food for oysters.

2. Materials and methods 2.1. Field measurements The site chosen for this evaluation is Kamakman Bay located on the southern coast of Korea ŽFig. 1a. at a latitude 28 south of Chesapeake Bay, USA and at about the same latitude as Seto Inland Sea in Japan, where the same species, C. gigas ŽThunberg., is cultured. Oysters are cultured by hanging culture with lines Žlan. of rope and rifters Žbuoys.. The oyster culture facility consists of two long lines that are 100 m in length, and are held 40 cm apart by buoys. Each facility contains 20 buoys, which are at 5-m intervals. The data used in this study are from samples taken at the oyster facility areas shown in Fig. 1b. Kamakman Bay is certified as a Aclean seaB for oyster production by the U.S. FDA ŽFood and Drug Administration.. The bay is semi-closed, being surrounded by land on the east, west and north. It has an average depth of 9 m with the deepest part at 40 m near the bay mouth in the south. Aside from local rainfall, the bay receives little freshwater input. Circulation is strongly dominated by semi-diurnal tidal currents flowing in and out in a north–south direction ŽLee et al., 1995..

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Fig. 1. Ža. Location of the study area, Kamakman Bay, southern Korea. Žb. Sampling sites in the major oyster mariculture area of the Bay. Oysters were sampled monthly at Sites A, B and F from March 1997 to May 1998 for determining annual oyster growth. Also, four replicate samples of oysters Ždots in figure. were taken at Sites B, C, D, E and F on 7 September 1997 and 2 March 1998 to compare local variation in oyster growth.

The annual variation in oyster production in Kamakman Bay varies over a wide range. In 1987, oyster production reached 83,400 metric tons but declined to 13,200 metric tons in 1993. The decrease in production in the 1990s has been ascribed to a number of causes including worsening water quality, high oyster density, and such biological factors as increasing competitors and oyster disease. However, the major cause for the decrease in production remains unknown. Lee Ž1993. suggested that regional differences in oyster production depend on the availability of phytoplankton to oysters as determined by phytoplankton concentration and the speed of wind-driven currents. The lower production in the eastern region of the bay was thought to be caused by slow water flow, low salinity and wide diurnal variations in water temperature and salinity. In order to evaluate this hypothesis, a physical–biological coupled model is needed to test the environmental conditions and their biological effects. Verification of an oyster population dynamics model is an essential first step towards a more complicated model, which includes the dynamics of water flow.

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Table 1 Significant equations and relationships used in the population dynamics model for the Pacific oyster C. gigas in Korea Žmodified from Hofmann et al. Ž1995. and Powell et al. Ž1995.. GoÕerning equation NPj s Pg j q Pr j s A j y R j

j, size class ŽTable 3.; NPj , net production; Pg j , somatic production; Pr j , reproductive tissue production; A j , assimilation; R j , respiration

dOj rd t s Pg j q Pr j qŽgain from jy1.y Žloss to jq1.qŽgain from jq1.y Žloss to jy1. Feeding and assimilation Filtration rate as a function of temperature FR t j s FR w j T 0.5 r4.47 FR w j s 2.51Wj 0.279 at Wj ) 2.09 g FR w j s 0.117Wj 3 y1.05Wj 2 q3.09Wj q 0.133 at Wj F 2.09 g Filtration rate as a function of salinity at S G 20 psu FR s j s FR t j at 10 - S- 20 psu FR s j s FR t j Ž Sy10.rŽ20y10. at S F10 psu FR s j s 0 Filtration rate as a function of TSS t ty 1 s Ž4.17=10y4 .Ž10 0.0418 x .

FR t j s FR s j w1y0.01 ŽŽlog 10 t ty1 q3.38.r0.0418.x FR j s Feff FR t j Ingestion I j s f ) FR j Assimilation A j s I j A eff Respiration Respiration and temperature R j s Ž69.7q12.6T .Wj by 1 Respiration and salinity at T - 208C at T G 208C at S G 20 psu at 15 psu - S- 20 psu at S F15 psu Reproduction Juvenileradult boundary Pr j s R eff j NPj R eff j s 0.8 at T G 278C R eff j s 0.2T y4.6 at 238C -T - 278C R eff j s 0.8 at T - 238C

Filtration rate ŽFR t j . Žml filtered individualy1 miny1 .; Wj , the ash-free dry weight Žin g.; T, temperature. S, ambient salinity

t , total particulate content Žinorganicqorganic. Žg ly1 .; x, the percent reduction in filtration rate. Feff , filtration efficiency f ) , the measured food value Žmg ly1 .; I j , ingestion A eff , the assimilation efficiency s 0.75

R j Žml O 2 consumed hy1 g dry wty1 .; bs 0.75 R r s 0.007T q2.099 R r s 0.0915T q1.324 Rjs Rj R j s R j Ž1qwŽ R r y1.r5xŽ20y S .. R j s R j Rr 0.39 g ash-free dry weight, about 50 mm long for adult size classes

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Table 1 Ž continued . Reproduction when NPj - 0 Spawning Malerfemale ratio f ratio s 0.021 L b y0.62 Eggs spawned R f s 0.50Oj

preferential re-sorption of gonadal tissue when the reproduction biomass exceeds 50% of total biomass fratio , the ratio of females to males; L b , length Žmm. when the reproductive biomass exceeds 50% of total biomass

No. eggs spawneds R f 1r6133 Wegg s 2.14=10y14 Vegg

Vegg , oyster egg volume Žmm3 .

LarÕal recruitment

larval life span: 20 days

Mortality Post-settlement population No. dying per time s k d Žno. living., for js k, l

Caloric conÕersions Oysters Food Oyster eggs Model solution

k d , the daily mortality rate Ždayy1 .; k and l, the inclusive size classes being affected by mortality 21,388 J g dry wty1 . 21,622 J g dry wty1 . 25,660 J g dry wty1 . Crank–Nicolson tridiagonal solution technique

Time step for integration: 0.5 day

2.2. Model The C. gigas population dynamics model is based on a standard energy flow equation in which net production ŽNP. is calculated from the difference between assimilation Ž A. and respiration Ž R . and where net production is the sum of somatic Ž Pg . and reproductive tissue Ž Pr . production. Significant equations and relationships used in the population dynamics model are shown in Table 1. The time-dependent model of oyster population dynamics Žoyster model, henceforth. has been described in detail by Kobayashi et al. Ž1997.. Relationships include filtration rate as a function of total suspended solids ŽTSS., temperature and salinity, respiration as a function of temperature and salinity, and an assimilation efficiency of 75%. Also, the model includes a temperature-dependent division of net production into growth and reproduction and spawning when the gonadal fraction of dry weight reaches 50%. All calculations with the oyster model were done in terms of energy ŽJ my2 . and converted to biomass using 21,389 J g dry wty1 ŽKim, 1980.. The food available to the oysters was converted to joule equivalents by using 21,623 J g dry wty1 ŽPowell et al., 1992.. The oyster model used to simulate the growth of the Pacific oyster C. gigas in

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Korea is similar to that used by Kobayashi et al. Ž1997., with the exception of an added variable describing retention efficiency and a length-to-biomass relationship typical of Korean C. gigas. Both modifications are described in later sections. The oyster model calculates growth in terms of energy ŽJ. and weight Žg.; however, output for verification is normally most easily rendered as a size frequency ŽTable 2.. Oyster growth is highly variable so that the conversion from weight to length typically must be changed to conform to local growing conditions. 2.3. EnÕironmental conditions Growth of oysters generally depends on water temperature, salinity, TSS, and food concentration. These environmental factors were measured at all oyster sampling sites ŽFig. 1b, Table 3. from March 1997 to May 1998. The annual variation of water temperature in Kamakman Bay ranged between 78C and 278C with a high in August and a low in January ŽFig. 2a.. Salinity was always above 28 psu and reached a maximum of 34 psu during the winter ŽFig. 2b.. Temperature and salinity curves show that warm and less saline waters occupy the bay in summer and colder and more saline waters are present during the winter. The TSS concentration in Kamakman Bay was normally below 0.03 g ly1 ŽFig. 2c. and followed a seasonal pattern rather different from chlorophyll-a ŽFig. 2d., suggesting that phytoplankton contributes little to TSS. Chlorophyll-a concentration ranged between 1 and 6 mg ly1 ŽFig. 2d.. A spring bloom occurred in March–May when mean values near 3.0 mg ly1 were observed. A distinct fall bloom occurred in November. Values fell to seasonally low levels in JunerJuly and during the winter. Lipid, protein and carbohydrate concentrations were measured in the Bay from July 1997 to June 1998 ŽFig. 3.. The concentration of total food computed as the sum of these three measures Žhereafter LPC. reached yearly highs in September–October, January and June. During this time, food supply, estimated from

Table 2 Oyster size classes in the model. Biomass is converted to size using the relationship between shell length and dry meat weight given in Eq. Ž2. Size class

Biomass Žg dry wt.

Shell length Žmm.

1 2 3 4 5 6 7 8 9 10 11 12 13

0.946=10y9 –0.703=10y7 0.703=10y7 –0.228=10y5 0.228=10y5 –0.209=10y4 0.209=10y4 –0.155=10y2 0.155=10y2 –0.193=10y1 0.193=10y1 –0.115 0.115–0.275 0.275–0.589 0.589–0.933 0.933–1.291 1.291–1.941 1.941–3.120 3.120–5.736

2–4 4–7 7–10 10–20 20–30 30–40 40–48 48–52 52–56 56–59 59–63 63–68 68–75

Site

20 Mar. 1997

27 Apr. 1997

20 May 1997

25 Jun. 1997

24 Jul. 1997

24 Aug. 1997

28 Sep. 1997

28 Oct. 1997

28 Nov. 1997

22 Dec. 1997

20 Jan. 1998

2 Mar. 1998

2 Apr. 1998

28 Apr. 1998

25 May 1998

A B F Total

128 108 110 346

82 61 152 295

62 68 112 242

253 295 183 731

289 209 361 859

196 111 188 495

419 223 453 1095

51 176 369 596

221 378 267 866

236 324 260 820

59 121 147 327

495 117 235 847

134 288 403 825

331 165 238 734

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Measurements has been carried out monthly at three sites in the bay from June 1997 to May 1998.

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Table 3 Sampling dates and the number of oysters measured for biological characteristics

47

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Fig. 2. Time series of the averaged Ža. water temperature Ž8C., Žb. salinity Žpsu., Žc. total suspended solid ŽTSS, g ly1 . and Žd. chlorophyll-a concentration Žmg ly1 .. Averaged values were computed using observations from the three sampling sites ŽFig. 1b.. Vertical bars indicate the standard deviation of the mean values.

LPC, routinely exceeded 4 mg ly1 , about a factor of 10 more than the estimate from chlorophyll. 2.4. Oyster growth for Õerification Shell length and biomass of oysters were measured at three sites ŽA, B and F in Fig. 1b. from March 1997 to May 1998 to determine the annual growth of oysters in the bay. Also, gonadal index of oysters was measured to determine the gametogenic cycle. The Kamakman oysters with a shell length of 17 mm that were planted in June 1997 increased to 73 mm by May 1998 ŽFig. 4a.. Shell lengths increased most rapidly from June to October 1997, reaching 56 mm by October’s sampling. Biomass increased slowly after the June planting through February of the next year, then at a much accelerated rate through May ŽFig. 4b.. The measured oyster dry weight shows similar trends ŽFig. 4c.. Yoo and Park Ž1981. also reported that meat weight of oysters

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Fig. 3. Change of concentration of lipid, protein, labile carbohydrate Žmg ly1 . and their sum ŽLPC. in Kamakman Bay from July 1997 to June 1998.

increased slowly from time of planting to February of the next year and then increased rapidly into May. The rate of increase in shell length is slow compared to growth rates in Japanese mariculture fields reported by Kobayashi et al. Ž1997.. The ratio of dry weight to wet weight ŽFig. 4d., which ranges between 0.14 and 0.27 with an average of 0.2, corresponds well to those in Klinck et al. Ž1992. and Choi et al. Ž1993.. Spatial variations in oyster growth were compared using oysters sampled at five sites ŽB, C, D, E and F in Fig. 1b. on 9 September 1997 and 2 March 1998. No significant spatial variation in oyster growth was observed over the Bay. 2.5. Shell length–biomass The model calculates oyster growth in joules and gram dry weight using a standard conversion of J Žg dry wty1 .. Comparison to field data is most easily done using a conversion from weight to length. Therefore, a relationship between the mean shell length Žthe distance between the hinge and the bill. and the mean wet meat weight Žg. was calculated as ŽK 1 in Fig. 5a.: SL s 39.60 Ww0.231

Ž 1.

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Fig. 4. Observed changes in Ža. mean shell length Žmm., Žb. mean wet meat weight Žg., Žc. mean dry meat weight Žg. and Žd. variations in the ratio of dry weight to wet weight. Solid line represents the averaged growth curve and bars represent the number of sampled oysters in each size or weight class.

where SL is shell length in millimeters and Ww is wet meat weight in grams. Lee Ž1993. also derived a relationship of oysters in Kamakman Bay ŽK 2 in Fig. 5a.: SL s 19.97 ln Ww q 29.21. The same species in Seto Inland Sea, Japan, produced the relationship ŽJ in Fig. 5a.: SL s 44.2 Ww0.340 . Compared to oysters from Seto Inland Sea, the Kamakman oyster has a higher biomass at a given shell length ŽFig. 5a.. A relationship between the mean shell length and the mean dry meat weight was derived as ŽK 1 in Fig. 5b.: SL s 56.65 Wd0.161

Ž 2.

where Wd is dry meat weight in grams. Eq. Ž2. was used as a size conversion relationship between length and weight in the model. A relationship between the mean wet meat weight and the dry meat weight was calculated as ŽK 1 in Fig. 5c.: Wd s 0.270 Ww y 0.208. Ž 3.

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Fig. 5. Reported relationships between mean shell length Žmm., SL, and Ža. mean wet meat weight Žg., Ww , Žb. dry meat weightŽg., Wd and Žc. between dry and wet meat weight. K 1 and K 2 refer to relationships for Kamakman oysters obtained from this study and from Lee Ž1993. respectively. J refers to Japanese oyster from Seto Inland Sea, Japan ŽKobayashi et al., 1997.. G1 and G2 refer to C. Õirginica in Galveston Bay, TX ŽHofmann et al., 1994.. Ža. G1 , SL s 31.877q60.170 log Ww ; G2 , SL s 39.594q30.429 log Ww ; J, SL s 44.2Ww0.340 ; K 1 , SL s 39.60Ww0.231 ; K 2 , SL s19.966 ln Ww q29.210, Žb. J, SL s 77.9Wd0.291 ; K 1 , SL s 56.65Wd0.161 , Žc. J, Wd s 0.225Ww y0.193; K 1 , Wd s 0.270Ww y0.208; K 3 , Wd s 0.2324Ww q0.0028 ŽYoo and Yoo, 1973..

2.6. Food measures What food supply to use in simulating oyster population dynamics has received considerable attention. Soniat et al. Ž1998. evaluated the use of total organic carbon, chlorophyll-a and a correction to chlorophyll-a for non-chlorophyll food source. The latter was obtained by measuring total lipid, labile carbohydrate and protein ŽSoniat et al., 1984; Soniat and Ray, 1985.. Accordingly, we evaluated four food estimates. First,

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Fig. 6. Relationship between the sum of lipid, protein and labile carbohydrate ŽLPC, mg ly1 . and chlorophyll-a Žmg ly1 ..

chlorophyll-a concentration was used as an index of available food. chlorophyll-a Žmg ly1 . was converted to food after Wilson-Ormond et al. Ž1997. as: Food s 0.085 chlorophyll-a.

Ž 4.

Second, Soniat et al. Ž1998. proposed the following equation to include non-chlorophyll food based on information obtained in Galveston Bay, Texas and Barataria Bay, Los Angeles, USA; Food s 0.088 chlorophyll-aq 0.520

Ž 5.

Third, food was directly measured as the total of lipid, protein and labile carbohydrate: Food s lipid q proteinq carbohydrate.

Ž 6.

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Table 4 Summary of the model conditions for the simulations of the time development of C. gigas populations Case no.

Food supply

Retention efficiency Ž%.

Eq. no.

Fig. no.

1 2 3 4 5 6 7

0.085 Chl-a 0.088 Chl-aq0.520 LPC LPC LPC LPC LPC from Chl-a correction

100 100 100 30 15 10 20

Eq. Ž4. Eq. Ž5. Eq. Ž6. Eq. Ž6. Eq. Ž6. Eq. Ž6. Eq. Ž7.

Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 Fig. 13

LPC refers to lipidqproteinqlabile carbohydrates concentration Žmg ly1 .. Chl-a refers to chlorophyll-a concentration Žmg ly1 ..

Fourth, a relationship between observed LPC Žmg ly1 . and observed chlorophyll-a Žmg ly1 . concentration were used to estimate food supply from chlorophyll-a ŽFig. 6.. The relationship is given by: Food s 0.66 ln chlorophyll-aq 3.88

Ž r 2 s 0.33 . .

Ž 7.

The correspondence between Eq. Ž7. and the monthly mean LPC and chlorophyll-a values is given in Fig. 6. 2.7. Model implementation The model was solved numerically using an implicit ŽCrank–Nicolson. tridiagonal solver with a 0.5 day time step. Each simulation was run for 10 months from June to April of the next year, which corresponds to the period from planting to harvest for oysters in Kamakman Bay. The Kamakman oysters are moved to the farming site from a seed area in early June and are harvested in spring ŽMarch to May.. Thus, the model was evaluated only between June 1997 and April 1998 for comparison to the growout data ŽFig. 4.. The simulated oyster population was initialized with oysters in size class 4 on Julian day 150 in accordance with the size at planting ŽFig. 4.. A summary of model conditions for each model simulation is given in Table 4.

3. Results The simulated C. gigas growth rate obtained when just chlorophyll-a is used as the food supply is too low, compared to the observed growth of Kamakman oysters ŽFig. 7.. A linear relationship between chlorophyll-a and food concentration is not likely to be representative of actual conditions in Kamakman Bay. This suggests that oysters feed not only on phytoplankton but also on other organic materials Žsee also Quayle, 1988; Soniat et al., 1998..

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Fig. 7. Simulated time-dependent growth of C. gigas obtained using food supply estimated from chlorophyll-a concentration ŽEq. Ž4... Contours are the logarithms of the number of oysters Žlog 10 N . with a contour interval of 0.5. Hence, the zero contour corresponds to one individual. Population values less than one are indicated by lines with negative values; positive values indicate population values greater than one individual. Size class boundaries are defined in terms of biomass Ždry meat weight. as shown in Table 3. The dashed line with circle indicates the time development of C. gigas populations, which was obtained from measurements of oyster dry meat weight measured for populations at the mariculture sites in Kamakman Bay.

The food conversion of Soniat et al. Ž1998. Žgiven by Eq. Ž5.. gave simulated C. gigas growth rates in the Bay that agree with observed growth rates ŽFig. 8.; however, chlorophyll-a values are so low in Kamakman Bay that the use of the Soniat et al. Ž1998. equation is effectively the use of a constant value for food supply. Accordingly, it is possible that the promising fit between simulation and observation ŽFig. 8. is an artifact. Food supply certainly should vary through the year. Using the measured time series of lipid, protein and labile carbohydrate ŽFig. 3. as an estimate of food supply ŽEq. Ž6.. results in a substantial overestimation of C. gigas growth ŽFig. 9.. The chlorophyll observations from Kamakman Bay suggest that much

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Fig. 8. Simulated time-dependent growth of C. gigas populations obtained using food supply estimated using a conversion of chlorophyll-a obtained by Soniat et al. Ž1998.. Sea Fig. 7 for further explanation.

of this organic matter must be present as small particles. Haven and Morales-Alamo Ž1970. noted that the retention efficiency of C. Õirginica for particles smaller than 3 mm was less than 50% of that for particles larger than 7 mm. Small particles might be of significance in the nutrition of oysters because of the abundance of suspended material less than 3 mm in estuarine waters. Palmer and Williams Ž1980. reported that C. Õirginica can retain particles between 3 and 6 mm with efficiencies as high as for particles larger than 6 mm. Conversely, Riisgard Ž1988. reported that C. Õirginica retains particles smaller than 6 mm with a lower efficiency than found for many other bivalve species. Ropert and Goulletquer Ž1999. reported that C. gigas showed 18–40% retention efficiency for 2-mm particles. Thus, in estuarine waters like Kamakman Bay, retention efficiency for small particles appears to be important. Consequently, particle retention efficiencies between 10% and 30% were evaluated to determine this effect on C. gigas growth rate.

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Fig. 9. Simulated time-dependent growth of C. gigas populations obtained using lipidqproteinqlabile carbohydrate concentration as a measure of food supply with a 100% retention efficiency. Otherwise same as Fig. 7.

Simulated growth rates using a retention efficiency of 30% are too high ŽFig. 10., whereas the simulated growth with a retention efficiency of 15% closely reproduces the observed growth ŽFig. 11.. A retention efficiency of 10% is too low ŽFig. 12.. Thus, abundant food is present in the water column of Kamakman Bay, but most of it must be present as small particles that are filtered by C. gigas with low retention efficiencies around 15%. Chlorophyll-a is much easier to measure than labile carbohydrate, lipid and protein. Soniat et al. Ž1998. obtained a regression between chlorophyll-a and LPC that permitted an estimate of total food from the more easily measured variable. The food supply, estimated from the relationship between LPC and chlorophyll-a ŽEq. Ž7.. observed in Kamakman Bay, and a retention efficiency of 20% reproduce observed C. gigas growth ŽFig. 13. despite the low r 2 obtained from the regression. This result suggests that LPC

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Fig. 10. Simulated time-dependent growth of C. gigas populations obtained using lipidqproteinqlabile carbohydrate concentration as a measure of food supply with 30% retention efficiency, assuming that most of the food is available as small particles by oysters. Otherwise same as Fig. 7.

concentration estimated from chlorophyll-a can be used to estimate total food supply. This, combined with the appropriate retention efficiency, then allows simulation of C. gigas growth. 4. Discussion Environmental and biological data were used to simulate and verify growth relationships of C. gigas in Kamakman Bay, Korea. The oyster model used in this study was developed using growth data obtained for the Pacific oyster C. gigas ŽThunberg. in Japan ŽKobayashi et al., 1997.. The same model was applied to the growth of the same species in Korea with three variations, length–weight relationship tailored to the local site, the use of LPC as an estimator of food supply, and the provision for a reduced retention efficiency for small particles.

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Fig. 11. Simulated time-dependent growth of C. gigas populations obtained using lipidqproteinqlabile carbohydrate concentration as a measure of food supply with 15% retention efficiency. Otherwise same as Fig. 7.

The oyster model reproduced observed growth curves only when a non-chlorophyll food source was included, suggesting that chlorophyll-a in isolation is a poor representative of food for oysters in this bay. Soniat et al. Ž1998. used LPC directly as a measured food supply and found it to provide reliable simulations of oyster growth in Gulf of Mexico bays. In contrast, using lipid q proteinq labile carbohydrate ŽLPC. as a food source in simulations of Kamakman Bay oysters results in higher growth rates than observed, suggesting that a surplus of potential food is available in the water column but that much of it is not readily accessible to the oyster because of small particle size. Reducing retention efficiency by assuming that most of the food is available as small particles results in simulated growth rates that are similar to field conditions. Thus, the retention efficiency would seem to be important in understanding the feeding behavior of the oyster, especially in coastal waters where small particles contribute significantly

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Fig. 12. Simulated time-dependent growth of C. gigas populations obtained using lipidqproteinqlabile carbohydrate concentration as a measure of food supply with 10% retention efficiency. Otherwise same as Fig. 7.

to total food supply. The model shows that a retention efficiency greater than 30% is too high and that an efficiency below 10% is too low. Thus, the Kamakman Bay oysters seem to filter particles from the water column within the range of 10% to 30% in retention efficiency. Chlorophyll-a, however, is much more easily measured than LPC. The regression relationship between LPC and chlorophyll-a concentration worked well as a measure of food supply once a proper retention efficiency was incorporated into the model. Thus, as Soniat et al. Ž1998. established for C. Õirginica, chlorophyll-a can provide the basis for estimating oyster food supply, once a relationship with nonchlorophyll explained food is available. Simulations have been shown to conform to observed conditions using LPC and a low retention efficiency. The question that needs to be addressed is whether an alternative exists that would permit chlorophyll-a estimates of food supply to provide

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Fig. 13. Simulated time-dependent growth of C. gigas populations obtained using the relationship between LPC and chlorophyll-a ŽFig. 6. as a measure of food supply, using a 20% retention efficiency. Otherwise same as Fig. 7.

adequate simulations of growth rates. This latter condition would exist if phytoplankton were, in fact, the principal food resource, despite the low concentrations measured. In practice, LPC with a 15% retention efficiency provides a realized food supply about two to three times higher than chlorophyll-a. Thus, the alternative would need to increase phytoplankton assimilation rates by two to three times. Assimilation efficiency is already assumed to be 75%, thus increasing this value cannot contribute substantively to the issue. Filtration rate for C. gigas is already considerably higher than that observed for C. Õirginica ŽKobayashi et al., 1997., and in fact, the C. gigas filtration rate is relatively high in comparison to all bivalves ŽPowell et al., 1992.. Certainly a doubling of filtration rate cannot be justified. Thus, varying ingestion or assimilation rate in the model to allow chlorophyll-a to provide an adequate food resource would take either or both the filtration rate and assimilation efficiency outside of the known physiological range. Reducing respiration rate is also not an alternative as the respiration rate being used is

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already among the lowest measured for this species ŽKobayashi et al., 1997.. Thus, model construction agrees with observations that observed growth rates require an alternate, substantial food resource, besides phytoplankton, in Kamakman Bay. What we cannot discriminate, however, is the alternative of a lower assimilation efficiency instead of a low retention efficiency. Small particles may well be less digestible and a reduction in assimilation efficiency to, say, 50% with an increased retention efficiency to, say 30%, would provide results that also closely approximately field observations. This research is the first attempt at using the Pacific oyster, C. gigas, population dynamics model in Korea. C. gigas is known to be highly variable and a number of races are described ŽArakawa, 1990.. The model developed by Kobayashi et al. Ž1997. worked well in the Korean site with minor changes in length–weight conversion. Once the proper estimate of food supply was obtained, the model appears to be generally applicable to the Pacific oyster despite the known geographic variability in the species. It is likely that the model can be applied to other mariculture areas where the Pacific oyster is grown with only minor modifications.

Acknowledgements The authors wish to acknowledge the financial support of the Korea Research Foundation. The authors appreciate the computer resources provided by the Center for Coastal Physical Oceanography ŽCCPO., Old Dominion University ŽODU.. Also, the authors are grateful to the students who helped in making the field measurements and samplings.

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