Linking biokinetics and consumer–resource dynamics of zinc
accumulation in pond abalone Haliotis diversicolor supertexta
Chung-Min Liao
a,*, Ming-Chao Lin
b, Jui-Sheng Chen
c, Jein-Wen Chen
aa
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan 10617, ROC b
Life Science Division, General Education Center, Nanhua University, Chiayi, Taiwan, ROC c
Department of Environmental Engineering and Sanitation, Foo-Yin Institute of Technology, Kaohsing, Taiwan 831, ROC Received 16 May 2001; received in revised form 30 April2002; accepted 20 May 2002
Abstract
A dynamic model that links biokinetics and consumer–resource dynamics for describing zinc (Zn) accumulation in abalone Haliotis diversicolor supertexta has been developed and then applied to Zn data from real abalone farms. The biokinetic parameters used in this study, uptake and depuration rate constants of abalone and their food source, red alga Gracilaria tenuistipitata var. liui, were obtained from a laboratory 14-d exposure experiment. We carried out a sensitivity analysis of the model by using the fractional factorial design technique, taking into account the influence of consumer–resource-related parameters such as growth and death rates and biomass and biokinetic parameters characterized by bioconcentration factor. Results indicate that the response time of biomagnification dynamics of Zn accumulation in abalone was influenced mainly by the growth rate of algae and biomass and the death rate of abalone and by interactions algae biomass and abalone death rate and abalone and algae biomass. New algae production results in substantially higher values of biomagnification factor. The linked model was then applied to field observations from a real-life situation of variable Zn concentrations occurring in abalone farms. Simulation results show that the predicted values are within a factor of 2 of the measured values (% errors range from 5.374% to 44.178%). Both modelanalysis and model application to the abalone farms suggest that the linking influences between biokinetics and consumer– resource dynamics support Zn accumulation in H. diversicolor supertexta and in G. tenuistipitata var. liui as functions of Zn concentration in water and abundance of food occurring in abalone farms. r 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Abalone; Algae; Bioaccumulation; Consumer–resource dynamics; Zinc
1. Introduction
Abalone are common gastropod molluscs that inhabit the coastalreefs in tropicaland subtropicalareas [1]. The herbivorous gastropod, Haliotis diversicolor super-texta, is the most abundant abalone species in Taiwan. The red alga Gracilaria tenuistipitata var. liui is the major forage for culturing the abalone H. diversicolor supertexta. These two species are commercially
impor-tant for fisheries and aquaculture in Taiwan [2]. H. diversicolor supertexta is also appreciated for its delicacy and high market value, the aquaculture of H. diversico-lor supertexta thus is a promising business [2,3]. However, the coastalregions of Taiwan where the abalone and algae aquaculture facilities are located are subjected to polluted discharges from rivers.
Zinc (Zn) is an essentialmicronutrient found at high levels in the algae and in the tissues of fish/shellfish [4,5]. Zinc is available to abalone from both the dissolved phase (e.g., gill uptake) and the diet (e.g., algae ingestion). If waterborne Zn levels are elevated, how-ever, toxicity can occur and have severe effects on the *Corresponding author. Tel.: 2-2363-4512; fax:
+886-2-2362-6433.
E-mail address:cmliao@ccms.ntu.edu.tw (C.-M. Liao).
0043-1354/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 3 - 1 3 5 4 ( 0 2 ) 0 0 2 3 0 - 0
health of abalone, which will reduce the market price and cause closure of abalone farms [1,6,7]. Previous investigations indicated that Zn have been detected in many rivers in that maximum Zn concentrations in contaminated aquacultural waters are reported to range from 60 to 300 mg L1in different areas of Taiwan [8]. At these levels, Zn specifically disrupts calcium uptake by the gills [9,10], leading to hypocalcemia, which may end with the death of the fish within a few days, depending on the Zn concentration.
Abalone/algae uptake and consumer–resource inter-actions are the two most relevant processes affecting the fate of waterborne Zn in aquacultural ecosystems. Abalone/algae uptake is the first step in the bioaccumu-lation of waterborne Zn in aquacultural food webs and also plays a major role in the occurrence and biogeo-chemicalcycles of Zn in the aquatic environments.
Bioconcentration occurs by means of passive diffusion of waterborne metals from the ambient water via gills into circulatory fluid and then deposition in the tissues, whereas biomagnification is the transfer of metals from lower trophic level to higher trophic level [11–13]. Therefore, bioconcentration of toxic metals in consumer biomass through uptake represents a ‘‘top-down’’ disturbance, whereas biomagnification showing the alteration of resource availability represents a ‘‘bot-tom-up’’ perturbation of aquatic ecosystems. An under-standing of how bottom-up and top-down processes influence the dynamics of aquacultural communities is necessary for effective management of aquacultural ecosystems in the face of environmentalvariability and multiple human impacts. It is difficult, however, to determine the effects of resource availability and food webs interactions in open highly variable aquacultural systems.
To assess the feeding and growth rates that influence metals accumulation to the abundance of resources and consumers, we adopted the consumer–resource model from population biology, incorporating the bioaccumu-lation model to make quantitative predictions about the effects. There are a number of observations regarding the occurrence of waterborne metals in aquatic food webs in pristine environments that suggest that bioac-cumulation kinetics and consumer–resource dynamics are linked [14–17].
The objectives of the present paper are to study the mutualinfluences between biokinetics and consumer– resource dynamics of Zn accumulation in H. diversicolor supertexta and to determine whether consumer–resource dynamics can support Zn concentrations observed in real abalone farms. A model for linking biokinetics and consumer–resource dynamics is developed, allowing the linkages between abalone/algae uptake and population-dynamic component of the system to be elucidated. We conducted a 14-d laboratory exposure experiment to determine the biokinetic parameters from
bioconcentra-tion and depurabioconcentra-tion bioassays. The integrated bioaccu-mulation–consumer–resource model will then be applied to field data collected from real abalone farms located in different sites of Taiwan region in order to determine whether it can describe Zn concentrations in abalone and algae as a function of Zn concentration in pond water and the abundance of food occurring in those farms.
2. Experiments
2.1. Sampling, acclimation and exposure conditions The most important farming areas for the production of abalone H. diversicolor supertexta are in Toucheng on the north coast, Kouhu on the western coast, and Anping on the south cost of Taiwan. All the abalone farms use seawater from polluted coastal areas. Thus we collected the samples of the abalone, the algae G. tenuistipitata var. liui and ambient water from nine farms in the three locations mentioned above. Three abalone, three algae and three 500 mL water samples per site were collected. The abalone and algal samples initially were washed in seawater to remove epiphytes and kept at 41C during transfers to the laboratory. The water samples were fixed by adding 5 mL 1 N HNO3.
Living abalone H. diversicolor supertexta, and the alga G. tenuistipitata var. liui were collected from Toucheng for the laboratory exposure experiments, because this place was the most Zn-contaminated area of the three sites. Abalone with a shell length of 4 cm were selected for the experiments. The algal samples selected were mature, whole and healthy. An amount of 200 abalone was transferred into four aquatic tank of approximately 54 L volume, containing 50 L of artificial seawater. In order to imitate the environment of the abalone farms, the abalone were held in baskets. Each tank contained 10 baskets. Four abalone per basket were used for analysis. To assure that at least four abalone would be alive at the end of the experiment, we put one extra abalone in each basket. Dissolved oxygen was main-tained close to saturation by aeration throughout the experiment. The temperature was maintained at 2571.51C under constant illumination [18]. The salinity was maintained at 35. The pH remained fairly constant during the assays (7.7570.24). Abalone were fed daily with G. tenuistipitata var. liui. The abalone and algae were acclimatized for 2 weeks before they were exposed to Zn.
2.2. Bioconcentration and depuration assays
In two tanks Zn (ZnCl2) was added to the seawater; in
one tank the abalone were fed with algae (water/food-exposed), and in the other tank the abalone were kept
without food (water-exposed). The Zn contamination level was determined by a preliminary test exposing abalone to different Zn concentrations of 0.25, 0.5, 1, 2, 4, and 6 mg L1. The median lethal tolerance (LT50) of
abalone atp1 mg L1 Zn was longer than 21 d. Thus, the organisms were exposed to 1 mg L1Zn for 7 d. The algae and the abalone were reared in the contaminated environment for 7 d uptake, then transferred to clean seawater and reared for 7 d of depuration. To examine if starvation affects Zn depuration in abalone, the same procedure with abalone and algae was followed over 14 d using the other two tanks, but without Zn in the sea water.
Abalone, algae and water samples were collected at day 0, 1, 2, 4, and 7, starting from the day the organisms were exposed to the contaminated seawater and from the day the organisms were transferred to clean sea-water. Every time we took one basket along with 500 mL water out of each tank. From this basket four pieces of algae and four abalone were collected. Because pre-liminary observation showed that H. diversicolor super-texta only feeds at night and has empty gut in the evening, we collected the abalone at night to make sure the contents of gut would not influence the results. The experiments in the four tanks, described above, were repeated again. The water samples were fixed with 5 mL 1 N HNO3, and the samples of abalone were stored in
the dark at 201C untilthey were analyzed. 2.3. Metal analysis
The algae and dissected abalone were freeze-dried overnight, and then grounded to a fine powder in a grinder (Tai-Hsiang S36-89, Taiwan). The 500 mg portions of the ground samples were digested in 10 mL of 65% concentrated HNO3 (v/v) overnight at room
temperature. The resulting solution was evaporated and redissolved in 0.1 N HC1 [19]. Zinc analysis was carried out by atomic absorption spectrophotometry using a Perkins Elmer model 5000 atomic absorption flame spectrophotometer equipped with a graphic furnace. The detection limit was 5 mg Zn/L water and 0.5 mg Zn/g tissue. Externalquality controlwas achieved by digest-ing and analyzdigest-ing identical amounts of rehydrated (90% water) standard reference materials (DORM-2, Dogfish Liver-2-oganic matrix, provided by the NRC-CNRC, NationalResearch CouncilCanada). Recovery rates ranged from 95% to 97%.
2.4. Data analysis
Bioconcentration is assumed to follow a well-estab-lished first-order one-compartment model as dCb=dt ¼ k1bCw k2bCbin that the solution at the constant Cwis CbðtÞ ¼ Cbðt ¼ 0Þ þ BCF Cwð1 ek2btÞ (referred to as the UD model), where Cb is the Zn concentration in
biota (mg g1), Cw is the Zn concentration in water (dissolved phase) (mg L1), k1b is the uptake rate constant from dissolved phase by biota (L g1d1), k2b is the depuration rate constant for Zn in biota (d1), and BCF (mL g1) is a generalequilibrium bioconcentration factor that is calculated as BCF ¼ k1b=k2b¼ Cb=Cw: Equilibrium biomagnification factor of abalone (BMFm)
was calculated from the concentration of the Zn accumulated in the abalone (Cm) divided by the Zn concentration in the algae (Ca) as BMFm¼ Cm=Ca:
The k1bs and k2bs that characterizes Zn bioconcen-tration/depuration process in H. diversicolor supertexta and G. tenuistipitata var. liui contaminated from food and water can be estimated by nonlinear regression fitting the UD modelto the measured Zn concentration data from the 7-d uptake experiments. The depuration rate constants ðk2bsÞ can also be calculated by the linear regression of log-transformed tissue Zn concentration on depuration days from the 7-d depuration experiments as ln CbðtÞ ¼ ln Cbðt ¼ TÞ k2bt; where T is the time when depuration begins. Variances in k2bs derived from two methods were tested for homogeneity using an F -test. Values were then compared using t--test.
All curve fittings were performed using the nonlinear regression option of the Statisticassoftware (StatSoft, Tulsa, OK, USA). The Statisticas was also used to calculate the coefficient of determination (r2) and statistical analyses (analysis of variance and Student’s t-test).
3. Mathematical model 3.1. Model description
Traditionalpredator–prey models are introduced in the original models of Lotka [20] and Volterra [21]. It has been refined in a number ways, notable via the introduction, by Holling [22,23], of the notion of a predator functionalresponse. The basis of much predator–prey theory will have the structure
dN
dt ¼ f ðNÞN gðN; PÞp; ð1Þ
dP
dt ¼ egðN; PÞP mP; ð2Þ
where N denotes the prey density, P the predator density, f ðNÞ the per capita prey growth rate in the absence of predators, and gðN; PÞ the rate at which an individualpredator consumes prey. The function gðN; PÞ is the functionalresponse of the model. The parameter e describes the efficiency of the predator in converting consumed prey into predator offspring, whereas m is the predator mortality rate. The functional response in
Eqs. (1) and (2) is said to be Holling type II prey dependent if gðN; PÞ ¼ gðNÞ:
The assumptions underlying in our approach are that (i) the algae satisfy a logistic growth function and (ii) the functional response of the model follows the Holling type II function in that the saturation effect affects the functional response of the abalone to change in the algae density.
In our notation, the derivation in Eqs. (1) and (2) yields a consumer–resource dynamics of abalone and algae: dAðtÞ dt ¼ ra 1 AðtÞ K AðtÞ g AðtÞ AðtÞ þ D MðtÞ; ð3Þ dMðtÞ dt ¼ fg AðtÞ AðtÞ þ D MðtÞ mmMðtÞ; ð4Þ
where rais the growth rate of algae (d1), K is the algae carrying capacity (g L1), AðtÞ is the algae biomass as a function of time t (g L1), MðtÞ is the abalone biomass as a function of time t (g L1), D is the half-saturation for algae ingestion (g L1), f is the biomass conversion efficiency of ingested algae (dimensionless), g is the grazing rate of algae by abalone (g g1d1), and mm is the abalone death rate (d1). The ðA=ðA þ DÞÞM terms can also be thought of as representing the conversion of energy from one source to another: gðA=ðA þ DÞÞM is taken from the algae and f gðA=ðA þ DÞÞM accrues to the abalone.
The scenario that we considered is (i) the exchange of Zn between abalone and dissolved Zn was modeled as a first-order process, with additionalZn accumulation from ingested algae, (ii) abalone ingest only algae and other suspended particles, bacteria and detritus uptakes are negligible, (iii) tissue concentration of Zn per unit biomass of abalone increases as a result of direct uptake from water and through assimilation of contaminated algae, and (iv) tissue concentration tend to decrease as a result of elimination from the whole body and growth dilution.
The dynamic modeldescribing the Zn accumulation in abalone and algae can be expressed by reconsidering from the viewpoint of consumer–resource dynamics in Eqs. (3) and (4) as dCmðtÞ dt ¼ k1þ k1f AðtÞ AðtÞ þ D BCFa Cw k2þ k2fþ fg AðtÞ AðtÞ þ D CmðtÞ; ð5Þ dCaðtÞ dt ¼ k1aCw k2aþ k1f MðtÞ AðtÞ BMFm CaðtÞ; ð6Þ where CmðtÞ is the time-dependent Zn concentration in abalone soft tissue (mg g1), t is the time of exposure (d), Cwis the dissolved Zn concentration in water (mg g1), k1 is the uptake rate constant from dissolved phase by
abalone (mL g1d1), k1f is the uptake rate constant
from algae by abalone (g g1d1), BCFa is the
bioconcentration factor for Zn in algae (mL g1), k2 is the depuration rate constant for Zn in abalone (d1), k2f is the depuration rate constant for Zn from food in abalone (d1), CaðtÞ is the time-dependent Zn concen-tration in algae (mg g1), k1a is the uptake rate constant from dissolved Zn by algae (mL g1d1), k2a is the depuration rate constant for Zn in algae (d1), and BMFmis the biomagnification factor for Zn in abalone
(dimensionless). 3.2. Numerical issues
The system of Eqs. (3)–(6) is a nonlinear, first-order system of coupled differential equations. Integration over time is straightforward in principle but is compli-cated by existence of a large number of widely differing time scales. The numerical integration scheme used to solve the system dynamic Eqs. (3)–(6) is a subroutine DIVPRK based on the Runge–Kutter–Verner 5th-order and 6th-order method that is provided by IMSL Subroutines Library [24] and done in double precision with FORTRAN 90. The algorithm is stable provided the error and the convergence criteria are carefully monitored. We used numericalscheme to solve Eqs. (3)– (6) under a number of biokinetic parameters obtained from 14-d exposure experiment and field data from nine abalone farms as well as parameters related to feeding rate and population dynamics, which are estimated in the following section.
3.3. Values used in consumer–resource dynamic model The values of the parameters used in the consumer– resource dynamic modelare indicated in Table 1. Some more important parameters will be discussed briefly below. Properties such as biomass conversion efficiency for ingested algae, algae growth rate, abalone death rate and grazing rate of algae by abalone were directly adopted from the literature. Certain other parameters that could not be easily measured have been estimated and, in some cases, the influence has been tested varying their values in the model simulations. The estimated parameters are the algae carrying capacity and half-saturation biomass for algae ingestion.
Algae carrying capacity (K): Typicalgrowth rates for algae are around 0.01–0.04 g g1d1, corresponding to instantaneous growth rates of 0.005–0.026 [25]. Pre-liminary simulations showed that grazing at realistic zooplankton biomass had little effect on algae biomass. We therefore used the observed long-term average algae biomass of 150714 g L1(ranging from 90 to 210 g L1) [26] as an approximation to algae carry capacity.
Half-saturation biomass for algae ingestion (D): The determination of half-saturation biomass for algae
ingestion, D; can be approximately obtained by fitting the Holling type II function of Eqs. (3) and (4) with the known values of grazing rate of abalone (g), death rate of abalone (mm) and growth rate of algae (ra) given in Table 1, to the biomass observations for algae and abalone collected from abalone farms in Toucheng area. The resulting value is D ¼ 61 g L1.
4. Results
4.1. Results of 14-d exposure experiments
The uptake and depuration rate constants used in this study were obtained from laboratory experiments designed to maintain constant Zn concentration in the water in order to properly apply the UD model and to treat them mathematically. Fig. 1 shows the results from the exposure experiments of Zn in soft tissue of H. diversicolor supertexta and in algae G. tenuistipitata var. liui. The nonlinear regression equations resulting from the best fits of the UD modelto data of uptake and depuration phases of Zn by abalone (Fig. 1A) were for food exposed, CðtÞ ¼ 111 þ 180:40ð1 e0:636tÞ (r2¼ 0:99) and for water exposed, CðtÞ ¼ 111 þ 166:01ð1 e0:611tÞ (r2¼ 0:98). Fig. 1B shows the uptake/depura-tion experiment results of Zn by algae in that the optimal fit to the data results in a nonlinear regression equation of CðtÞ ¼ 98:3 þ 163:9ð1 e0:588tÞ (r2¼ 0:98). A simple UD model was thus successfully fitted by the nonlinear technique to the uptake/depuration curves of the 14-d exposure data in that coefficients of determina-tion generally were high (r2> 0:95). Results suggest that
the fitted first-order equation is an appropriate model for the data set. Estimates of k2 and k2f were also determined from the depuration-phase experiments (Fig. 1). All of these regressions were significant (po0:05), with r2 values that ranged from 0.7 to 0.85. The k2 and k2f values determined in depuration
experiments were also statistically significant (po0:05) from their corresponding k2and k2f values derived from nonlinear curve fitting the UD model to the uptake data. Table 2 summarizes the experimentally determined biokinetic parameters for the UD modeldescribing Zn
50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 Time (d) Zn in abalone ( µ g g − 1) Uptake Depuration 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 Time (d) Zn in algae ( µ g g − 1) Uptake Depuration (A) (B)
Fig. 1. Laboratory 14-d exposure experiment results: (A) uptake and depuration of Zn by soft tissue of H. diversicolor supertexta during a 7-d exposure and then a 7-d depuration period. The measurements (mean7s.d.) are shown with symbols ((’) fed with algae; (E) kept without algae); and the model fittings are shown in lines ((—) fed with algae; (- - -) kept without algae) and (B) uptake and depuration of Zn by algae G. tenuistipitata var. liui during a 7-d exposure and then a 7-d depuration period. The measurements (mean7s.d.) are shown with symbols and the model fitting is shown in solid line.
Table 1
Parameters values (mean7s.d.) used in the consumer–resource dynamic model
Parameter SymbolValue
Initialabalone biomass Mi(g L1) Varied
Initialalgae biomass Ai(g L1) Varied
Dissolved Zn Cw(mg g1) Varied
Growth rate of algae ra(d1) 0.03870.013a
Grazing rate of abalone g (g g1d1) 0.2570.05b Biomass conversion rate for
algae ingested by abalone
f (g g1) 3.5070.81b Death rate of abalone mm(d1) 0.28670.17
c Algae carrying capacity K (g L1) 150714.2b Half-saturation for algae
ingestion
D (g L1) 61d aAdopted from Lee et al. [25].
b
Adopted from Chen and Lee [26]. c
Adopted from Shepherd [27]: at age 8 months to 4 years. d
bioaccumulation process in H. diversicolor supertexta and G. tenuistipitata var. liui contaminated by Zn from food and water.
4.2. BMF dynamics
A typical example of the dynamic simulation carried out for the dynamics of algae and abalone biomass and Zn concentrations in algae and abalone is shown in Fig. 2. The Zn concentration in algae attained a steady state by the end of the simulation, whereas the Zn concentration in abalone increased rapidly up to day 3 then decreased and attained a steady state by the end of
the simulation (Fig. 2A). Fig. 2B indicates that over 30 d, algae biomass decreased rapidly but abalone biomass increased slightly and has a peak occurring at day 5. Fig. 3 illustrates the BCFaand BMFmdynamics,
showing the response times toward 95% equilibrium during the simulation. The Zn concentration in algae increases with time and couples the whole Zn bioaccu-mulation process of water–algae–abalone in that BCFa
increases with time and reach equilibrium much shorter than that of BMFmwhich decreases with time (Fig. 3).
5. Discussion
5.1. Sensitivity analysis
The 2k factorialoptimization, an experimentaldesign approach, was used for sensitivity analysis. Factorial design allows the determination of the effects of different variables and their interactions with a mini-mum number of runs [28,29]. Interactions of three or more variables are usually negligible and/or hard to interpret; therefore, a fractionalfactorialdesign was used. Details on factorial experimental design and their applications to sensitivity analysis can be found else-where [30–33].
All the variables related to biokinetic properties are considered as one variable since they cannot be modified independently. This variable will be the bioconcentra-tion factor for Zn in algae (BCFa) since this biokinetic
parameter can be expressed as the ratio between the Table 2
Experimentally determined values (mean7s.e.) of uptake rate constants and depuration rate constants for the UD model describing Zn bioaccumulation process in abalone and algae contaminated from food and water
Uptake rate constants Abalone
Foof-exposed k1f¼ 113:84724:4 (g g1d1)
Water-exposed k1¼ 102:04723:2 (mL g1d1)
Algae k1a¼ 100:1722:8 (mL g1d1)
Depuration rate constants Abalone Food-exposed k2f¼ 0:63670:21 (d1) Water-exposed k2¼ 0:61170:43 (d1) Algae k2a¼ 0:58870:23 (d1) 0 200 400 600 0 5 10 15 20 25 30 Time (d) Zn concentration ( g g − 1 ) 0 60 120 180 0 10 20 30 Biomass (g L -1 ) Algae Abalone 0 5 10 18 22 26 30 Abalone Algae (A) (B)
Fig. 2. Typical example of the simulations carried out for the model predictions of (A) Zn concentration in algae and abalone and (B) biomass of algae and abalone. The initial conditions used were as: Cw¼ 80 mg L1, Að0Þ ¼ 100 g L1, Mð0Þ ¼ 80 g L1, equilibrium
equilibrium conditions of Zn concentration in algae and Zn concentration in water. In addition to different BCFa
values, we accounted for biomass of algae and abalone, algae growth rate, abalone grazing rate, and abalone death rate. With six variables (Table 3), a full factorial design requires 64 (26) experiments. With fractional factorialdesign the sensitivity analyses can be performed with 32 (261) runs of the model. Table 3 shows data from a complete 25fractionalfactorialdesign for the 32
runs of the sensitivity analysis of the model. The time to reach 95% of equilibrium for the BMFmdynamics was
chosen as the response time since the dynamics of this processes can be compared independent of the initial conditions (Fig. 3). The time required to reach 95% of equilibrium of BMFmðt95%;BMFmÞ is the response time of the system to changing Zn concentration accumulation in abalone. Response times for equilibrium BMFm
dynamics are listed in Table 3.
The effect of each variable on the response was determined using the following equation [28]:
t95%;BMFm¼ aA þ bM þ craþ dg þ emmþ fBCFa þ hAM þ iAraþ jAg þ kAmmþ lABCFa þ mMraþ nMg þ oMmmþ pMBCFa þ qrag þ rrammþ sraBCFaþ tgmm
þ ugBCFaþ vmmBCFaþ w; ð7Þ where a2w are the parameters obtained by fitting the response times by multiple linear regression. The Student’s t-test of these parameters allowed the deter-mination of significance of each variable and the interactions between variables [28,33]. The significant variables with a confidence level higher than 95% are (a) the main effects: algae growth rate (ra), abalone biomass (M), and abalone death rate (mm) and (b) the
interac-tions: algae biomass/abalone death rate (Amm), abalone biomass/algae biomass (MA), and algae growth rate/ abalone death rate (ramm). Response times for biomag-nification dynamics of abalone are dependent on algae growth rate as well as biomass and death rate of abalone in a complicated way since they are interacting. There-fore, algae growth rate as well as biomass and death rate of abalone explain the majority of the variability of the abalone Zn accumulation dynamics, whose correlation coefficient was also significant.
No significant effect of Zn concentration in water was observed, although the importance of uptake kinetics for the higher Zn concentration in water has been reported. Explanation for this could be that the differences in uptake kinetic properties among different Zn concentrations in water are not sufficient to provide significantly different response times. The higher Zn in water, however, may have very different uptake dynamics. A second complementary sensitivity analysis was performed for Zn in water and modifying all other variables one at a time. This allowed the determination of interactions between different Zn concentrations in water and the variables related to abundance of food in determining the 95% equilibrium BMFmvalues. Fig. 4
shows that 95% of equilibrium BMFm values were
affected by the growth rate and the biomass of algae. Higher values of BMFm were obtained for higher
growth rate of algae. The effect on the BMFm due to
increasing algae biomass depends on the growth rate, which led to lower values of BMFmat constant biomass
(zero growth rate) and larger BMFm values for higher
growth rates.
Higher growth rates yield higher BMFmvalues since
new biomass needs to reach equilibrium with the dissolved Zn concentration in water. Fig. 4 also implies that higher algae biomass in the absence of algae growth depletes the water Zn concentration faster, achieving lower equilibrium BMFm values. When the algae
biomass is increasing (ra> 0), however, response time of BMFm values achieving equilibrium are longer
(Table 3) due to the equilibrium requirements of the new biomass introduced in the system. An important result of the present study is the influence of algae uptake of dissolved Zn on the biomagnification dynamics of abalone.
Higher BMFmvalues are obtained for higher values of
algae growth rate and lower algae biomass since the effects of algae biomass and growth rate depend on the dissolved Zn concentration in water (Fig. 4). Further-more, a dramatic increase of BMFmvalues was observed
for raother than zero. Therefore, algae growth rate has such a big influence on BMFm values that, for Zn in
water with 102–103order of magnitude, algae biomass remains the same (Fig. 4). Algae uptake of Zn concen-tration by new biomass induces a depletion of the water Zn concentration, retarding and even preventing the
0 50 100 150 200 250 3 6 9 12 15 18 21 24 27 30 Time (d) BCFa 0 20 40 60 80 100 120 140 BMF m 0 t95%,BCFa t95%,BMFm Ca/Cw Cm/Ca
Fig. 3. Typical example of the simulation carried out for BCFa and BMFm dynamics, showing an approach to 95% equilibrium response time for BCFa ðt95%;BCFaÞ and
BMFm ðt95%;BCFaÞ: The initialconditions used were as:
achievement of equilibrium between the Zn concentra-tion in abalone and in water.
5.2. Model application to abalone farms
The simulations were performed using measured concentrations of Zn in pond water (Table 4) as initial conditions. Then the measured equilibrium BCFa and
BMFm values (Table 4) associated with experimentally
determined biokinetic parameters (Table 2) were in-corporated into the model. Other variables needed to perform the calculations were biomass of algae and abalone observed in abalone farms (Table 4) and parameters of consumer–resource dynamics (Table 1). Zn concentrations in the algae and abalone were predicted by the output of the model.
The comparison of the predicted Zn concentrations in algae and abalone with measured concentrations in nine abalone farms is given in Figs. 5 and 6, respectively. Calculations indicate that the coupled dynamic model predicts the measured Zn concentrations with average relative differences ranging from 17% to 55% in algae and from 1.3% to 47% in abalone, respectively, where the relative difference or errors were determined as, error ¼ ðCpred CobsÞ=Cobs
100; in which Cobsis the observation data and Cpred is the predicted concentra-tion. The predicted values are always within a factor of 2 of the measured values and are thus within the expected accuracy of the modeldue to uncertainties in the system variables.
The coupled dynamic model predicts the measured Zn concentration in algae with average relative differences Table 3
A 25fractionalfactorialdesign for the runs of the sensitivity analysis of the modeland response times obtained for achieving 95% of equilibrium for BMFm(t95%;BMFm) a Run M (g L1) A (g L1) ra(d1) G (g g1d1) mm(d 1) BCFa(L g1) t 95%;BMFm(d) 1 20 50 0.04 0.25 0.3 167 25.9 2 80 50 0.04 0.25 0 167 35.2 3 20 100 0.04 0.25 0 167 39.4 4 80 100 0.04 0.25 0.3 167 17.6 5 20 50 0 0.25 0 167 43.4 6 80 50 0 0.25 0.3 167 32.9 7 20 100 0 0.25 0.3 167 37.6 8 80 100 0 0.25 0 167 37.2 9 20 50 0.04 0.5 0 167 32.8 10 80 50 0.04 0.5 0.3 167 14.8 11 20 100 0.04 0.5 0.3 167 17.1 12 80 100 0.04 0.5 0 167 28.7 13 20 50 0 0.5 0.3 167 33.3 14 80 50 0 0.5 0 167 47.3 15 20 100 0 0.5 0 167 49.8 16 80 100 0 0.5 0.3 167 17.6 17 20 50 0.04 0.25 0.3 16.7 24.7 18 80 50 0.04 0.25 0 16.7 32.8 19 20 100 0.04 0.25 0 16.7 36.3 20 80 100 0.04 0.25 0.3 16.7 16.9 21 20 50 0 0.25 0 16.7 40.2 22 80 50 0 0.25 0.3 16.7 28.4 23 20 100 0 0.25 0.3 16.7 33.3 24 80 100 0 0.25 0 16.7 35.4 25 20 50 0.04 0.5 0 16.7 29.8 26 80 50 0.04 0.5 0.3 16.7 13.1 27 20 100 0.04 0.5 0.3 16.7 14.9 28 80 100 0.04 0.5 0 16.7 26.3 29 20 50 0 0.5 0.3 16.7 27.6 30 80 50 0 0.5 0 16.7 43.7 31 20 100 0 0.5 0 16.7 45.9 32 80 100 0 0.5 0.3 16.7 16.7 a
Here, A is the algae biomass, M is the abalone biomass, rais the algae growth rate, g is the grazing rate of algae by abalone, mmis
of 44.178.4%, 25.777.9%, and 26.474.5% for aba-lone farms in Toucheng, Kouhu, and Anping, respec-tively (Fig. 5) and the average relative differences of 41.176.1%, 5.374.3%, and 22.9712.3%, respectively, between the measured and predicted Zn concentrations in abalone for abalone farms in Toucheng, Kouhu, and Anping (Fig. 6). Simulation results show that the model accurately reflects the variations of Zn concentrations accumulation in algae and abalone, pointing out the importance of consumer–resource dynamics in real abalone farm when modeling the metal bioaccumulation process.
Even though the simulations for the real abalone farms were using time-independent uptake and depura-tion rate constants for Zn accumuladepura-tion in H. diversi-color supertexta and G. tenuistipitata var. liui obtained from a laboratory exposure experiment, an excellent fit between experimentalobservations and modeloutputs was obtained. This suggests that species allometric-dependent kinetic factor may play a secondary role in the interaction between abalone diets, population dynamics, and Zn accumulation.
The simulations suggest that some policy issues regarding water quality management in abalone farms may be reconsidered. The controlof Zn loadings from polluted coastal areas is not a sufficient measure to controlwater Zn concentrations since trophic status plays a major role on the mid- and long-term pollution trends. Therefore, water quality management requires a multi-disciplinary approach. Water pollution issues must be addressed together with food web structure issues and account for the ecological complexity of the aquacultural environment.
6. Conclusions
The following conclusions can be drawn from this study: 1. Sensitivity analysis of the model indicates that the response time of biomagnification dynamics of Zn accumulation in abalone was influenced mainly by the growth rate of algae and biomass and the death rate of abalone and by interactions of algae biomass Fig. 4. Effects of algae biomass (A) and growth rate (ra)
depending on Zn concentrations in the water for the sensitivity analysis of 95% equilibrium BMFmvalues.
Table 4
Measured values of dissolved Zn concentration in water (mean7s.d., n ¼ 3), biomass of algae G. tenuistipitata var. liui and H. diversicolor supertexta, equilibrium binconcentration factor for Zn in algae (BCFa), and equilibrium biomagnification factor for Zn in abalone (BMFm) used in the simulations for nine abalone farms in Toucheng, Kouchu and Anping, respectively
Abalone farm Zn in water (mg L1) Biomass (g L1) BCFa(L g1) BMFm(—)
Algae Abalone Toucheng Pond T-A 94.57750.22 150 120 559 1.8 Pond T-B 144.17732.48 180 100 757 1.1 Pond T-C 154.38728.87 180 100 721 1.1 Kouhu Pond K-A 53.33747.59 120 80 408 2.2 Pond K-B 85.03711.72 120 120 260 2.4 Pond K-C 43.76711.10 140 150 740 1.2 Anping Pond A-A 106.06737.42 150 60 434 1.3 Pond A-B 57.75712.60 140 60 503 1.6 Pond A-C 44.95725.01 100 90 216 2.2
and abalone death rate and abalone and algae biomass.
2. New algae production results in substantially higher values of biomagnification factor of abalone. Algae uptake-induced depletion of Zn concentration main-tains Zn concentration in abalone and in water out of equilibrium. The model results also point out the relevant role of algae, which is a dominant source of organic matter in abalone farms, in removal of Zn concentrations from polluted coastal areas by bioac-cumulation process.
3. Model application to the abalone farms confirms our hypothesis that the consumer–resource dynamics effectively supports the Zn concentrations accumula-tion in algae and in abalone and suggests that bioaccumulation kinetics and consumer–resource dynamics are constrained by the same factors.
Acknowledgements
The authors would like to express their appreciation for the financialsupport of the NationalScience Council of Republic of China under Grant NSC 88-2313-B-002-070. The authors appreciate the contributive comments by anonymous referees. Sincere thanks also go to abalone farm owners for providing the valuable infor-mation and for the use of their abalone farms, without which this research work would have not been possible. References
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0 20 40 60 80 0 10 20 30 40 % error 0 20 40 60 80 100 0 10 20 30 40 % error Toucheng Kouhu Anping Zn in algae ( gg − 1) Zn in algae ( gg − 1) Zn in algae ( gg − 1) T-A T-B T-C K-A K-B K-C
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A-A A-B A-C
(A)
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