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A MASS BALANCE MODEL TO ASSESS FOOD LIMITATION IN COMMERCIAL OYSTER NURSERIES.

INTRODUCTION

Bivalves accounted for 21% of global aquaculture production by volume (excluding seaweeds) in 2015. of which oysters represent 36% of the bivalve total (FAO 2017). Aquaculture is the main source for oyster production worldwide (~97%, FAO 2017). According to FAO (2017) datasets, in 2015, Asia contributed around 95% of the global oyster farming volume (corresponding to about 81% in value); the remaining 5% of the oyster aquaculture production is from North and South America and Europe. Oyster farming is generally regarded as a sustainable sector within the aquaculture industry, and it is widely recognized that oyster production provides a set of ecosystem services such as nutrient cycling, reduction of eutrophication symptoms, habitat provision to other marine species, and restocking of wild populations (Coen et al. 2011. Ferreira et al. 2011, Gallardi 2014, Rose et al. 2014, Baker et al. 2015, Depiper et al. 2017). In addition, it can integrate the organic extractive component of integrated multi-trophic aquaculture systems. Furthermore, shellfish farmers who grow these extractive species have a major interest in promoting good water quality to ensure industry sustainability (Dewey et al. 2011). Shellfish farming is promoted and recognized by some governmental stakeholders as providing social and economic benefits, as well as ecological benefits, e.g.. NOAA established in 2011 the USA National Shellfish Initiative.

Most oyster farming practices depend on the natural environment, and like many other farmed species, oyster growth and production hinges on a complex interaction of factors such as temperature, salinity, freshwater flow/rainfall, current speed, density, food concentration and phytoplankton species composition, food partitioning with other species, and disease outbreaks. Modeling can be useful for understanding the feedback between the farming and environmental systems, and the effects on production. As an example, carrying capacity models are often applied for management and spatial planning of filter feeder production, as reviewed by Byron and Costa-Pierce (2013) and by Filgueira et al. (2015). Many other model applications exist for production management of oysters and other shellfish both at ecosystem and farm scales (Ferreira et al. 2008, 2011, Gangnery et al. 2011, Nobre et al. 2011, Saurel et al. 2014. Filgueira et al. 2015). Farmers are seldom the end users of these models. A strategy to make available simulation models that embed scientific research to farmers is to shift from (1) complex models (in terms of spatial and temporal resolutions, processes simulated), which allow detailed simulations but require datasets that might not be feasible to gather by a commercial unit, to (2) simple models or at least with simple interfaces that can be directly used by farmers and provide estimates of key questions for production; e.g., http://www.farmscale.org/ and Nobre et al. (2017).

Most developments of shellfish models are for adult animals, and there arc only a few models that are suited to simulate initial development stages (Rico-Villa et al. 2010). Mass balance models can help estimate food requirements for a given spat stock (the initial seeding stock or the expected stock to harvest). Furthermore, spat are commonly reared in extensive nurseries that rely on natural seston concentration to feed the stock or are coupled with tanks designed to promote algal blooms (Helm & Bourne 2004). For these systems, it is more difficult to provide guidance on seed stock density given that local food concentration is variable, by contrast to hatcheries. For hatcheries and nurseries fed with algal cultures, there are manuals of oyster culture that include guidance for feed ration calculations (Breese & Malouf 1975, Helm & Bourne 2004, Wallace et al. 2008. Tetrault 2012). Guidance for cultivation practice in spat nurseries is provided based on rules of thumb about the typical number of seed per area or stock biomass to hold in each system, based on expert knowledge. On the other side of the spectrum is extensive research about the effects of body weight, temperature, food concentration, and feeding strategy, among others, on the filtration rate, assimilation efficiency, and growth of bivalves (Walne 1972, Winter 1978, Gerdes 1983a, Bacher & Baud 1992. Bougrier et al. 1995, Ward & Shumway 2004. Cranford et al. 2011, Tamayo ct al. 2014).

Mass balance models that use simple user interfaces can help translating scientific knowledge into practical guidance for commercial nurseries. The goal of this article is to develop and evaluate this concept using Pacific oyster (Crassostrea gigas Thunberg) spat as a case study for model implementation and evaluation for structures such as a floating upweller system (FLUPSY) or land-based tanks, silos, or trays. The authors aim to make the model available online for wider use and to ensure it tackles two questions that arise when planning or managing an oyster nursery: (1) how much food is required to sustain a given stock and/or (2) for a typical range of food available in the surrounding environment, what is the maximum biomass that can be stocked.

METHODOLOGY

Conceptual Model Description

This model consists of a single-compartment mass balance at steady state for a given nursery (Fig. 1):

[MF.sub.Food_in] + [MF.sub.phyto_Growth] = [MF.sub.Food_out] + [MF.sub.Food_Cleared], (1)

where, the mass fluxes (MF) are defined as [MF.sub.Food_in] (Eq. 2) is the food inflow which can be an external natural food resource or feed ration; [MF.sub.phyto_Growth] (Eq. 4) is the phytoplankton community net growth rate to accommodate the case of nurseries with natural blooming ponds (as illustrated by Helm & Bourne 2004), otherwise [MF.sub.phyto_Growth] is set to zero; [MF.sub.Food_out] (Eq. 5) is the food outflow; and [MF.sub.Food_Cleared] (Eq. 6) is the food cleared by oysters. To allow model generality, the MF are expressed using several optional oyster food indicators, such as phytoplankton (using chl-a as a proxy), particulate organic matter (POM), or particulate organic carbon (POC). The corresponding units are shown in Table 1.

[MF.sub.Food_in] (Eq. 2), is given by the external food concentration ([[Food].sub.External], units defined in Table 1) multiplied by the water inflow rate (WaterInflow, in [m.sup.3][??][day.sup.-]):

[MF.sub.Food_in] = [[Food].sub.External] * WaterInflow * M3toL. (2)

The user can define WaterInflow as the average flow rate or by the operational turnover rate (TurnoverRate, [day.sup.-1]) multiplied by the nursery volume (Eq. 3):

WaterInflow = TurnoverRate * [V.sub.nursery]. (3)

[MF.sub.phyto_Growth] (Eq. 4) is given by the phytoplankton community net growth rate ([Growth.sub.phyto], [day.sup.-1]) multiplied by the phytoplankton mass inside the nursery:

[MF.sub.phyto_Growth] = [Growth.sub.phyto] * [[Food].sub.nursery] * [V.sub.nursery] * [fraction.sub.phyto/food] * M3toL. (4)

Here. [[Food].sub.nursery] (units defined in Table 1) is the food concentration inside the nursery which is a constant because of the steady-state assumption. The sinks and sources of the mass balance are therefore solved to give that concentration in the nursery system. As reviewed by Cranford ct al. (2011), it appears that several bivalve species regulate clearance rate to maximize energy. In accordance with their review, several authors indicate that a bivalve's clearance rate depends on food concentration, showing an initial peak at low concentrations followed by a decline with increasing seston concentrations. Thus, [[Food].sub.nursery] is a key model parameter used in the model as the optimum concentration to maintain in the production unit. Depending on the available data. [[Food].sub.nursery] can be parameterized as the minimum food concentration that maximizes ingestion or as the optimum concentration for growth, [V.sub.nursery] ([m.sup.3]) is the nursery water volume, and [fraction.sub.Phyto/food] is the fraction of phytoplankton in the food. For the cases where the food indicator is POM or POC, the average fraction of phytoplankton in the food must be defined (otherwise [fraction.sub.phyto/food] = 1).

[MF.sub.Food_out] (Eq. 5), is given by [[Food].sub.nursery] multiplied by the water outflow rate (WaterOutflow, in [m.sup.3][??][day.sup.-1]), which is considered equal to the Waterlnflow:

[MF.sub.Food_out] = [[Food].sub.nursery] * WaterOutflow * M3toL. (5)

[MF.sub.Food_Cleared] (Eq. 6) is given by the [[Food].sub.nursery] multiplied by the water volume cleared by the standing stock in a given period of time ([ClearanceRate.sub.oyster] * Stock * DWtoFW * kg_to_mg):

[MF.sub.Food_Cleared] = [[Food].sub.nursery] * [ClearanceRate.sub.oyster] * Stock * DWtoFW * kg_to_mg. (6)

Here, [ClearanceRate.sub.Oyster] (L*mg D[W.sup.-1]*[h.sup.-l]) is the oyster-specific clearance rate. Stock (in kg) is the spat total biomass in the tanks, and DWtoFW (-) is the conversion ratio of dry weight (DW):fresh weight (FW) with shell. [ClearanceRate.sub.Oyster] is a function of seed weight and water temperature (Eq. 7) which must be parameterized per species (or if data are available for a strain within a line):

[ClearanceRate.sub.oyster] = f(WaterTemperature, SeedWeight). (7)

M3toL, kg_to_mg. and kg_to_g are conversion factors for unit consistency in Eqs. 2-8.

The overall aim of this model is to estimate (1) the required food inputs for a given stock biomass: and (2) the maximum stock biomass for a given typical external food concentration. To address that objective Eqs. 2-6 are replaced into the mass balance equation (Eq. 1) and solved for [[Food].sub.Exterrnal] (Eq. 8) and for TotalStock (Eq. 9) as follows:

[[Food].sub.External] = [[Food].sub.nursery] * (1 - [Growth.sub.phyto] * [[V.sub.nursery]/[WaterInflow]] * [fraction.sub.phyto/food] + [[ClearanceRate.sub.oyster]/[WaterInflow]] * Stock * DWtoFW * kg_to_g) (8)

Stock = [[[[Food].sub.External]*WaterInflow + [[Food].sub.nursery] * ([Growth.sub.phyto] * [V.sub.nursery] * [fraction.sub.phyto/food] - Waterlnflow)]/[[[Food].sub.nursery] * [ClearanceRate.sub.oyster] * DWtoFW * kg_to_g]] (9)

To be useful for real farms, the model was extended to consider the simultaneous cultivation of several spat grades. Equations 8 and 9 are thus respectively replaced by the following equations:

(1) Equation 10 to estimate the required external food concentration considering the summation of the volume cleared per grade ([SIGMA][ClearanceRate.sub.Oyster_PerGrade] * [Stock.sub.PerGrade]):

[[Food].sub.External] = [[Food].sub.nursery] * (1 - [Growth.sub.phyto] * [[V.sub.nursery]/[WaterInfolw]] * [fraction.sub.phyto/food] + [[SIGMA][ClearanceRate.sub.Oyster_PerGrade] * [Stock.sub.perGrade]/[WaterInflow]] * DWtoFW * kg_to_g) (10)

(2) Equation 11 to estimate the total maximum stock (TotalStock. in kg) considering a weighted clearance rate ([SIGMA][ClearanceRate.sub.Oyster_PerGrade] * [Stock.sub.%PerGrade]):

To provide outputs of interest to farmers, the final model equations (Eqs. 10 and 11) are solved for two values of phytoplankton growth ([Growth.sub.phyto]) and two values of external food concentration ([[Food].sub.External]). With this approach, the outputs encompass the range of scenarios within which a nursery operates, given that these two parameters are highly variable within a day.

All the model parameters are given in Table 2.

As a case study, in this work, the model is applied to the Pacific oyster. Parameterization for this species is presented in Table 3.

Model Parameterization and Evaluation for the Pacific Oyster

[[Food].sub.nursery], DWtoFW (-), and [ClearanceRate.sub.Oytser] are species specific and were parameterized (Table 3) for the Pacific oyster based on the published data of spat growth experiments.

[[Food].sub.nursery] was parameterized for the Pacific oyster spat based on Tamayo et al. (2014) which tested three feed concentrations (0.5. 3, and 6 [mm.sup.3]*[L.sup.-1]); the medium level was chosen, given it corresponded to the highest clearance rate (for the biological meaning of [[Food].sub.nursery], see Conceptual model description). That concentration level (which converts to 44 algal cells [micro][L.sup.-1] as per rationale explained herein) is comparable with the range indicated by Walne (1972) as the optimum for growth, around 30-40 algal cells*[micro][L.sup.-1]. Tamayo et al. (2014) provide the conversion of the algal biovolume into POM and POC. Conversion into mg algal*[L.sup.-1] considered that the algal cell has the same density of water following Suthers and Rissik (2009). For converting the biovolume ([mm.sup.3]*[L.sup.-1]) into algal cell count (algal cells*[micro][L.sup.-1]), the average cell biovolume for the species used in the work by Tamayo et al. (2014), Isochrysis galbana Parke, of around 68 [micro][m.sup.3]*[cell.sup.-1] (Ishiwata et al. 2013) was considered. Finally, conversion into Chl-a was carried out using the general conversion ratio of C:Chl-a of around 50 (Reynolds 2006). All values arc shown in Table 3.

TotalStock = [[[[Food].sub.External] * WaterInflow + [[Food].sub.nuesery] * ([Growth.sub.phyto] * [V.sub.nursery] * [fraction.sub.phyto/food] - WaterInflow)]/[[[Food].sub.nursery] * [SIGMA][ClearanceRate.sub.Oyster_PerGrade] * [Stock.sub.%PerGrade] * DWtoFW * kg_to_g]] (11)

Gerdes (1983a) carried out a set of experiments to study-clearance rates of small-size oysters ranging from 0.005-0.811 g DW and considering three different algal concentrations (50. 75, and 100 cells[??][micro][L.sup.-1]). In this work, the clearance rate allometric function defined by Gerdes (1983a) is used for a food concentration of around 50 cells[??][micro][L.sup.-1] (see function in Table 3). given that this is the concentration nearest to the assumption adopted in the model for [[Food].sub.nursery] (around 44 cells[??][micro][L.sup.-1]. Table 3). For conversion between tissue DW and oyster total FW, the following were considered: (1) the value from Gerdes (1983b) of shell weight of about 97.3% of total DW and (2) an average conversion factor of live FW to total DW of around 0.5 based on Walne and Millican (1978). The resulting ratio of dry tissue weight:total fresh weight (DWtoFW) is around 0.014 (Table 3). The effect of temperature on clearance rate was included in this model (Table 3) based on a function by Bougrier et al. (1995). The Bougrier function for clearance rate (L[??][h.sup.-1]) is [a - (b x [(T - c).sup.2])] x D[W.sup.d]', a to d are constants where c is the temperature that corresponds to the maximum clearance rate (a = 4.825, b = 0.013, c = 18.954. d = 0.439; Bougrier et al. 1995). The Bougrier allometric function with the temperature effect was converted into a dimensionless function to account only for the effect of temperature, by dividing this general form by the function at optimum temperature (thus T=c). The resulting temperature dependence function [1 -a/b x [(T-c).sup.2]] is herein multiplied by the individual clearance rate as a function of seed weight ([CR.sub.W] in Table 3) that results in a function of both temperature and weight ([CR.sub.W,T] in Table 3) and defines the following behavior: (1) the temperature for maximum clearance rate is around 19[degrees]C, which is within the range from other references for Pacific Oyster, e.g., literature revision by Barrett (1963) indicates the optimum at around 20[degrees]C and (2) the clearance rate at 5[degrees]C is about 50% of the clearance rate at 20[degrees] C, which is supported by the findings of Walne (1972). According to Barrett (1963), at around 3[degrees]C, the Pacific oyster ceases feeding, so the lower limit for model input for temperature is set to 4[degrees]C. The higher temperature limit for model input was set to 30[degrees]C.

The model was evaluated using data presented by Langton and McKay (1976). Langton and McKay (1976) experiments include feed supply at two levels: (1) daily supply of 180 algal cells[??][micro][L.sup.-1] x 250 L tank in Exp A and (2) 120 algal cells[??][micro][L.sup.-1] x 250 L in Exp B. Each daily algal cell concentration (Exp A and B) was supplied following four feeding regimes, ranging from all feed supplied at once or distributed continuously over 1 day as per Langton and McKay (1976) description. In this work, the model was applied to simulate the feeding regime that provides the two feeding levels with a 6-h interval. Within this regime, the feed is supplied in a concentration (180/4 = 45 algal cells [??][micro][L.sup.-1]; 120/4 = 30 algal cells[??][micro][L.sup.-1]) that is most similar to the [[Food].sub.nursery] set in the model (44 algal cells[??][micro][L.sup.-1], Table 3). To mimic the experimental setting, the model application includes only a single oyster grade whereby in each model run. the seed size is set to the same size obtained by Langton and McKay (1976) weekly observations for the 6 h on : 6 h off feeding regime (values taken from plots presented in Figs. 1 and 2 in Langton & McKay 1976). The slock biomass was calculated considering the density of 50 spat per liter multiplied by the tank volume (250 L) and by the seed size. An average temperature of 21[degrees]C was considered. A summary of the parameters used to drive the model that simulates Langton and McKay (1976) experiments is presented in Table 4. The model outputs for food requirement and maximum stock considering the settings for each of Langton and McKay's (1976) experiments were compared with the feed given and the stock of tanks and are presented in Results. The indication of whether feedd was limited was compared with the experimental outcomes and discussion carried out by Langton and McKay (1976).

MODEL APPLICATION AND USER INTERACTION

To promote widespread use, the model described in this work for Pacific oyster nurseries is made available online al http://seaplusplus4.com/oysterspatbud.html. It simulates several typologies of nursery systems such as a FLUPSY or land-based nurseries as reviewed by Helm and Bourne (2004). Nurseries that arc interconnected with large natural blooming ponds (Helm & Bourne 2004) are also simulated because the mass balance includes, as an option, a source of food because of phytoplankton primary production. This model does not simulate field nursery systems, e.g., spat floating bags sitting in intertidal areas of coastal ecosystems.

This work describes the model user interface, including the menus for nursery setup (Fig. 2). output for food requirements (Fig. 3), output for optimum stock (Fig, 4). and advanced settings (Fig. 5). Examples on how to use the model for different case studies are also provided.

(1) The nursery setup menu (Fig. 2) is where the users enter their farm inputs such as How rate (or turnover rate), water volume, water temperature, and if the nursery includes blooming tanks. This model simulates the nursery system as a single compartment, which means for instance, if the nursery has blooming tanks, the user should insert (a) in the "System volume" the sum of the volume of the oyster-holding unit and of the bloom tanks, (b) in the "Flow rate" or "Turnover rate" the water exchange with the surrounding waterbody. and (c) choose "Yes" in "With phytoplankton blooming tanks" box. Alternatively, that user can simulate only the oyster stock pond by inserting (a) in the "System volume" the volume of that pond, (b) in the "Flow rate" or "Turnover rate" the water exchange with the bloom tanks, and (c) choose "No" in "With phytoplankton blooming tanks" box. If the model is used to simulate a FLUPSY in an estuary, the user should insert (a) in the "System volume" the volume of the FLUPSY. (b) in the "Flow rate" or "Turnover rate" the water flow rate forced by the paddlewheel into the entire FLUPSY, not of the individual silos, and (c) choose "No" in "With phytoplankton blooming tanks" box. Alternatively, the user can simulate the individual silo inserting in the model its water volume and individual flow rate. Examples about system definition arc provided in Table 5.

Besides system definition, the nursery setup menu (Fig. 2) is where the user inserts the average seed weight per grade. Default seed grades and average weights are provided, but the user can customize any of these by changing any of the boxes under "Oyster grades" and "Seed weight." "Choose food indicator" allows the user to select his preferred food indicator for model inputs outputs.

(2) In the output for food requirements menu (Fig. 3) is presented the result regarding the food required for a given stock, which is expressed in the units chosen by the user in the previous menu. The user should insert in this menu below "Stock per grade (x[10.sup.3] seeds)" the amount of seeds per grade. If the nursery includes blooming tanks, then two outputs are shown that encompass a low and a high phytoplankton growth scenario.

(3) In the output for optimum stock menu (Fig. 4). the results are presented concerning the maximum stock sustained, expressed as overall biomass and as the number of seeds per grade, for two scenarios of available food. The model needs to "know" the oyster biomass distribution per grade that the farmer aims, for instance. 100% of small 0.04 g spat or 50% of the biomass slock with small spat and 50% with bigger 0.9 spat. The user can insert that input under "Biomass % per grade" or the model calculates distribution per grade based on data about "Stock per grade (x [10.sup.3] seeds)" inserted in the previous menu (Fig. 3). To test the effect of different food levels at the water intake from the surrounding ecosystem, the user must specify a lower and an upper food concentration. If the nursery includes blooming tanks, then two outputs that encompass a low and a high phytoplankton growth scenario are shown for each food concentration.

(4) The advanced settings menu (Fig. 5) allows the user to change the optimum food concentration for oyster filtration. That parameter ([[Food].sub.nursery]) is detailed in the model description and it is not foreseen that the common user will have the data required to change this value. This menu also presents the model estimates for the clearance rate based on an allometric filtration rate function (Gerdes 1983a) and the temperature dependence effect that assumes optimum filtration rale for the Pacific oyster al 19[degrees]C (Bougrier et al. 1995). If the nursery includes blooming tanks, the user can change in this menu the phytoplankton growth rate values. The model allows the user to specify a low and a high phytoplankton growth rate to test the range of community net primary production scenarios typical of the nursery's blooming tanks. Also in this menu is where the user specifies the value for the phytoplankton fraction in POM or POC. for the cases that POM or POC concentration were chosen as food indicator.

Model limitations include the following:

(1) Important effects that occur at smaller scale are not simulated in the model, e.g., changes in the water flow rate due to oyster size densities or tank shape.

(2) The option with bloom tanks assumes these arc interconnected with the oyster-holding tank, which together are the simulated unit. In this case, the water flow is the water that enters from the outside (an adjacent ecosystem for instance) into the bloom tanks forced by tidal height or pumped.

(3) The salinity effects on filtration rate are not simulated and thus it is assumed that water salinity is higher than 20.

RESULTS

Model Evaluation

The model settings to simulate the Langton and McKay (1976) experiments are systematized in Table 4 and the results are presented in Table 6.

For a spat of 0.75 mg and a stock of approximately 9 g in the 250-L containers, which corresponds to the conditions at the beginning (week 0) of both experiments (A--high and B--low feed level), the estimated food requirement is around 70 algal cells[??][micro][L.sup.-1]. For this spat weight and considering the two feed levels supplied, i.e.. 180 algal cells[??][micro][L.sup.-1] in Exp A and 120 algal cells[??][micro][L.sup.-1] in Exp B. the model estimates a maximum stock of 50 g and 28 g. respectively. The outputs of this model run indicate that at week 0, the feed supplied is much higher than the stock requirements.

The model outputs for the run that simulates week 2 indicate a food requirement around 139 algal cells[??][micro][L.sup.-1] for the 50 g stocked in the 250 L containers (spat around 4 mg). According to the outputs of this simulation, the feed level supplied in Exp A is still enough: nevertheless, oysters in the containers of Exp B are fed less than the optimum.

In week 3, the feed level supplied is near the threshold in Exp A and does not meet the oyster requirements in Exp B. which according to the model outputs should be 175 and 158 algal cells[??][micro][L.sup.-1] in Exp A and B. respectively. According to Langton and McKay (1976). the spat average weight in week 3 (6 and 5 mg in Exp A and B. respectively) already exhibits a slower growth for Exp B. In subsequent weeks, the higher feed limitation experienced in Exp B (since week 2) is translated into lower weights, in week 4. the spat weight is around 7.5 mg in Exp B compared with 13 mg in Exp A. and by week 6. the weight is around 11 mg in Exp B compared with 19 mg on Exp A (Langton & McKay 1976). These different growth rates measured in Exp A and B (Langton & McKay 1976) support the model predictions for food limitation. The model results also agree with Langton and McKay (1976). according to which in the first 2 wk. the oyster spat are not feed limited.

Model Application to Farms

The fact that the model implementation allows testing of ranges of values for the external food concentration ([Food) External) :and the phytoplankton growth rate ([Growth.sub.phyt]) means that model outputs provide a range of possible scenarios within which the nursery is operating. This facilitates model application into a given nursery whereby the user needs to provide the boundaries for this highly variable parameter (when dependent on food concentration in the surroundings). In extensive oyster nurseries, such seston concentration is unlikely to be monitored frequently. Therefore, in spite of the model simplification, it can still provide guidance for managing stock and food limitation in natural feeding oyster nurseries. These model functionalities contribute to support management of oyster nurseries. In particular, this model allows quantification of general rules of thumb regarding the spat-holding capacity for a given nursery. For instance, according to Helm and Bourne (2004). determining the biomass of spat that can be held in a pond system is largely a matter of trial and error. A general rule is that 1 hectare surface area of shallow pond will support the production of between 1 and 3 tons biomass of seed, depending on levels of algal productivity, over the course of a growing season. This represents the maximum sustainable biomass that can be maintained with careful management." To apply the model for the described rule of thumb, the following assumptions are made: (1) a water renovation with the external system of around 10%, (2) a system volume of about 10.000 [m.sup.3] corresponding to a surface area of 10.000 nr for the bloom pond +1.000 [n.sup.2] for the stock pond and a I m water depth. (3) a water temperature around 19[degrees]C, (4) a phytoplankton concentration in the external waterbody within the range of about 0.5-1 [micro]g Chl-a-[L.sup.-1]. and (5) phytoplankton growth rate that ranges between 0.5 and 1.2 [day.sup.-1]. The total biomass stock that can be sustained will depend on the spat grades. In accordance with the model outputs for this setup (Fig. 6A). if the farmer aims to slock spat of about 0.38 g. the nursery can hold in those conditions between 1 and 3 tons (Fig. 6B) of total seed biomass (corresponding to around 3 8 million seeds). These estimates lit well within the rule of thumb described by Helm and Bourne (2004): however, considering the same conditions but targeting to stock smaller spat of around 0.04 g. the biomass stock sustained is lower (Fig. 6C). between 0.7 and 2 tons (corresponding to around 17-47 million seeds). The application of the model allows to improve the rule of thumb for a given set of conditions and thus to lower the set of trials and errors required to determine the biomass of spat to hold in a pond system.

A wide range of other scenarios can be tested by any user in the online model (hup://seaplusplus4.com/oysterspatbud.html) to better adjust a general rule of thumb to their own nursery conditions: for instance, and considering the aforementioned example, what are the changes regarding the stock biomass or number of seeds per grade that can be sustained due to lower or higher temperatures, typical of the local winter/summer? What if the local phytoplankton community growth rate can be as low as 0.2 [day.sup.-1]?

DISCISSION

The inclusion in the model of a minimum concentration at the tanks that must be ensured to maximize ingestion ([[Food].sup.nursery]) is one of the key elements in solving the mass balance at the steady state. The practical implications of this assumption are that the model outputs provide (1) the food input requirements to ensure minimum concentration in the nursery: considering a given water inflow, oyster filtration rate at a given stocking and seed weight, and if applicable. phytoplankton natural production within the nursery: and (2) the maximum biomass that can be stocked to ensure that minimum concentration at the nursery and thus ensure an optimized growth; considering a given food input, oyster seed weight and distribution among the oyster grades, and if applicable, phytoplankton natural production within the nursery. The value adopted in the Pacific oyster model (3 [mm.sup.3]-[L.sup.-1] as per rational explained in Model Parameterization and Validation for the Pacific Oyster) was chosen from within a set of three tested concentrations (0.5. 3. and 6 [mm.sup.3][L.sup.-1]) from Tamayo et al. (2014). It is possible that within the interval between these values, other solutions maximize ingestion. Further research should be developed to more accurately estimate the [[Food].sup.nursery]. Given that other factors influence filtration efficiency dependence on food concentration, such as the algae size (Winter 1978). further research should also include different feeds. For nurseries that provide cultivated algae, they can improve their own model application by changing the [[Food].sub.nurscry] parameter (in http://seaplusplus4.com/oysterspatbud.html) and inserting the value that best suits their own facility.

Nevertheless, the value adopted in the model parameterization for the Pacific oyster for the minimum food concentration that maximizes ingestion, i.e., [[Food].sup.nnrsery] (44 algae cells [micro][L.sup.-1]. Table 3) is also in agreement with experiments by Langton and McKay (1976) whereby the growth was maximized for the feed supplied (120 or 180 algae cells [micro][L.sup.-1]) with 6-h intervals, which corresponds to 30 (=120/4) and 45 (=180/4) algae cclls [micro][L.sup.-1].

CONCLUSIONS

The model presented provides an assessment of the seed stock boundary ranges within a commercial extensive oyster nursery which can operate regarding food limitation. This model is built based upon a simplification of the oyster biological processes, the nursery systems and timescales of interaction. The model evaluation for the Pacific oyster using an experimental dataset (Langton & McKay 1976) indicates that it can provide valid guidance on boundaries for maximum stock at a given nursery setting or feeding requirements for a given seed stock for optimum rearing conditions. In this work, it is also exemplified how to use the model to improve the application of general rules of thumb for planning the oyster spat holding capacity within a nursery. Although there is extensive literature on ecological models, these are seldom used directly by farmers. This model is targeted to managers of commercial operations and can be used online: http://scaplusplus4.com/oyslerspatbud.html. Shellfish farmers arc major stakeholders for the sector sustainability and thus can benefit with the application of models to manage production and understand environmental interactions. Further developments to the model can be made based on feedback from farmers regarding usefulness of the model. Moreover, other features they find important could be included, as well as other oyster species, such as eastern oyster (Crassostrea virginiea Gmelin). European flat oyster (Osirea edulis Linnaeus). Olympia oyster (Ostrea lurida Carpenter). Portuguese oyster (Crassostrea angulata Lamarck), slipper cupped oyster (Crassostrea iredalei Faustino), and Sydney rock oyster (Saccostrea glomerate Gould).

ACKNOWLEDGMENTS

Financial support was provided by the Portuguese Foundation for Science and Technology (FCT) as a Postdoc scholarship to Ana Nobrc (SFRHBPD 109442 2015).

LITERATURE CITED

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ANA M. NOBRE, (1 *) FILIPE SOARES (2) AND JOAO G. FERREIRA (2)

(1) CIMAR/CIIMAR--Centra Interdisciplinar de Investigacao Marinha e Ambiental. Terminal de Cruzeiros do Porto de Leixoes, Avenida General Norton de Matos, S/N. 4450-208 Matosinhos, Portugal;

(2) DCEA, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Qta Torre, 2829-516 Monte de Caparica. Portugal

(*) Corresponding author. E-mail: anobre@ciimar.up.pt

DOI: 10.2983 035.036.0323
TABLE I. Oyster food indicators and corresponding model units.

                                                   Food concentration:

Oyster food indicator   [[Food].sub.External]      [MF.sub.Food_out]
                        and [[Food].sub.nursery]   and
                                                   [MF.sub.Food_Cleared]

Phytoplankton           Algae biovolume            Per water volume
(or a proxy chl-a)      Cell count
                        Algal mass
                        Chl-a mass
POM                     Mass
POC                     Mass

                        Corresponding
                        model units
                        Food fluxes:
                        [MF.sub.Food_in],
                        [MF.sub.Phyto_Growth],
Oyster food indicator

Phytoplankton           [mm.sup.3] algae*           Per time
                        [L.sup.-1]
(or a proxy chl-a)      algal cells*[micro]
                        [L.sup.-1]
                        mg algae*[L.sup.-1]
                        [micro]g Chl-a*[L.sup.-1]
POM                     mg POM*[L.sup.-1]
POC                     mg POC*[L.sup.-1]

Oyster food indicator

Phytoplankton           [mm.sup.3] algae*
                        [day.sup.-1]
(or a proxy chl-a)      [10.sup.6] algal cells*
                        [day.sup.-1]
                        mg algae*[day.sup.-1]
                        [micro]g Chl-a-
                        [day.sup.-1]
POM                     mg POM*[day.sup.-1]
POC                     mg POC*[day.sup.-1]

TABLE 2. List of model parameters.

Parameter type          Parameter (Unit)          Description

Farm parameters         General settings          [V.sub.nursery]
                                                  ([m.sup.3])
                                                  WaterInflow ([m.sup.3]
                                                  [??][day.sup.-1])
                                                  TurnoverRate
                                                  ([day.sup.-1])
                                                  WaterTemperature
                                                  ([degrees]C)
                                                  [SeedWeight.sub.
                                                  PerGrade] (g)
                                                  Food indicator
                        Model solved              [Stock.sub.perGrade]
                                                  (kg)
                        for
                        [[Food].sub.External]
                        Model solved for          [Stock%.sub.PerGrade]
                                                  (-)
                        TotalStock
                                                  [[Food].sub.External]
Biological parameters   Species specific          [[Food].sub.nursery]
(advanced)
                                                  DWtoFW (-)
                                                  [ClcaranccRate.sub.
                                                  Oyster](L[??]mg
                                                  D[W.sup.-1]*
                                                  [h.sup.-1])
                        Site specific             [Growth.sub.phyto]
                                                  ([day.sup.-1])
                                                  [fraction.sub.phyto/
                                                  food] (-)

Parameter type

Farm parameters         Water volume of
                        the nursery. The
                        boundaries of the
                        system can be the
                        volume encompassed
                        by the
                        FLUPSY area or
                        can further include
                        adjacent ponds
                        for naturally grown
                        phytoplankton communities.
                        Average water flow
                        rate into the nursery.
                        Number of volume
                        renewals per day.
                        Should be
                        consistent with the
                        system boundary.
                        An average value
                        should be provided.
                        Temperature
                        inputs are limited to
                        the range between
                        4 and 30[degrees]C.
                        To choose from Table 1.
                        Stock biomass per grade.
                        Fraction of the stock
                        for a given grade
                        relative to the
                        total biomass.
                        Typical external food
                        concentration or feed
                        supplementation. The model
                        implementation allows
                        testing of two values.
                        Units depend on the food
                        indicator chosen (Table 1).
Biological parameters   Optimum food concentration
                        for oyster filtration. Units
(advanced)              depend on the food
                        indicator chosen (Table 1).
                        Conversion ratio of
                        DW:FW weight with shell.
                        The clearance rate
                        is a model parameter
                        that in fact is
                        a function of seed
                        weight and water
                        temperature and
                        is species specific.
                        Specific local phytoplankton
                        community growth rate. If
                        values are not known,
                        a range within two
                        values can
                        be tested.
                        Average typical values
                        of the fraction of
                        phyto in the
                        food applicable for the
                        cases where food indicator is
                        POM or POC. When
                        food indicator is
                        algae, this
                        parameter is one.

TABLE 3. Model parameterization for Pacific oyster
(Crassostrea gigas Thunberg).

Parameter                     Value/function

[[Food].sub.nursery]          ([mm.sup.3] algae[??][L.sup.-1])
                              (algal cells[??][micro][L.sup.-1])
                              (mg algae[??][L.sup.-1])
                              ([micro]g Chl-a[??][L.sup.-1])
                              (mg POM[??][L.sup.-1])
                              (mg POC[??][L.sup.-1])
[ClearanceRate.sub.Oyster]    (mL[??]mg D[W.sup.-1][??][h.sup.-1])
Individual clearance
rate as a function of:
Seed weight--[CR.sub.W]       (mL[??][h.sup.-1])
Seed weight and               (mL[??][h.sup.-1])
temperature (T)--
[CR.sub.W,T]
DWtoFW                        (-)

Parameter                    Source

[[Food].sub.nursery]          3.0                   Tamayo et al. (2014)
                             44                     Tamayo et al. (2014)
                                                    and cell biovolume
                                                    from Ishiwata et al.
                                                    (2013)
                              3.0                   Tamayo el al. (2014)
                                                    and conversion
                                                    factor from Suthers
                                                    and Rissik (2009)
                             12.5                   Tamayo el al. (2014)
                                                    and conversion
                                                    factor from Reynolds
                                                    (2006)
                              1.037                 Tamayo el al. (2014)
                              0.63                  Tamayo et al. (2014)
[ClearanceRate.sub.Oyster]                          [CR.sub.W,T]
                                                    ([SeedWeight.sub.
                                                    PerGrade] x DWtoFW x
Individual clearance                                1,000)
rate as a function of:
Seed weight--[CR.sub.W]      17.8 x                 From Gerdes (1983a)
                             TissueDryWeight
                             [(mg).sup.0.79]        for a feed
                                                    concentration
                                                    of 50 cells. [micro]
                                                    [L.sup.-1]
Seed weight and              [CR.sub.W]*            Based on Bougrier
                             [1 - 0.002694 x        et al. (1995)
temperature (T)--            [(T- 18.954).sup.2])
[CR.sub.W,T]
DWtoFW                        0.014                 Gerdes (1983b) and
                                                    Walne and Millican
                                                    (1978)

TABLE 4. Model sellings to simulate the Langton and McKay (1976)
experiments.

                                          Model setting to simulate
                                          Langton and McKay
                                          (1976) experimental
                                          conditions at:
                                                Week 0
                                                Exp. A

[V.sub.nursery] ([m.sup.3])                      0.25
TurnoverRate ([day.sup.-1])                      1
WaterTemperature ([degrees]C)                   20.5
Food indicator                                  algal cells[??][micro]
                                                [L.sup.-1]
[[Food].sub.nursery]                            Pacific oyster
                                                parameterization
                                                (in Table 3)
DWtoFW (-)
[ClearanceRate.sub.Oyster]
[Growth.sub.phyto]                               0
([day.sup.-1])
[fraction.sub.phyto/food] (-)                    1
Seed Weight (mg)(*)                              0.75
Estimated Stock (g)                              9.4
in the 250 L tanks
Feed given ([[Food].sub.External])             180                  120
algal cells[??][micro]
[L.sup.-1]

                                                         Week 2
                                              Exp. B     Exp. A   Exp. B

[V.sub.nursery] ([m.sup.3])
TurnoverRate ([day.sup.-1])
WaterTemperature ([degrees]C)
Food indicator
[[Food].sub.nursery]
DWtoFW (-)
[ClearanceRate.sub.Oyster]
[Growth.sub.phyto]
([day.sup.-1])
[fraction.sub.phyto/food] (-)
Seed Weight (mg)(*)                   4                  6        5
Estimated Stock (g)                  50                 75       63
in the 250 L tanks
Feed given ([[Food].sub.External])       180     120   180      120
algal cells[??][micro]
[L.sup.-1]
                                         Week 3           Week 6
                                         Exp. A   Exp. B  Exp. A  Exp. B

[V.sub.nursery] ([m.sup.3])
TurnoverRate ([day.sup.-1])
WaterTemperature ([degrees]C)
Food indicator
[[Food].sub.nursery]
DWtoFW (-)
[ClearanceRate.sub.Oyster]
[Growth.sub.phyto]
([day.sup.-1])
[fraction.sub.phyto/food] (-)
Seed Weight (mg)(*)                  19     11
Estimated Stock (g)                 238    138
in the 250 L tanks
Feed given ([[Food].sub.External])  180    120
algal cells[??][micro]
[L.sup.-1]

(*) Wet weight taken from plots shown in Figure 1 (Exp A) and Figure 2
(Exp B) of Langton and McKay (1976) for feeding regime 6 h on : 6 h
off.

TABLE 5. Examples of nursery system definition for different types of
nurseries (FLUPSY, land-based with blooming tanks and closed systems).

Type of nurseries       FLUPSY in an estuary      (10% renovation with
                                                   external watcrbody)
Simulation options:     All system                Only one of the silos

"System volume"         Oyster-holding units      1 of the silos
"Flow rale" "Turnover   "Flow rate" = flow rate   "Flow rate" = Water
rate"                   forced by paddlewheel     flow rate into one
                                                  silo
"With phytoplankton     No                        No
blooming tanks"

                        Land-based with blooming tanks
Type of nurseries       Closed system

Simulation options:     All system
"System volume"         Oyster-holding unit +
                        blooming tanks
"Flow rale" "Turnover   "Turnover rate"
rate"                   = 0.1 [day.sup.-1]
"With phytoplankton     Yes
blooming tanks"

Type of nurseries
                        Only the seed holding   (Renovates the
Simulation options:     pond                    water every-one day)

"System volume"         Oyster-holding unit     Oyster-holding unit
"Flow rale" "Turnover   "Flow rate" = Water     "Turnover rate" =
rate"                   flow rate from the      1 day"'
                        blooming tanks
"With phytoplankton     No                      No
blooming tanks"

TABLE 6. Model outputs for Langton and McKay (1976) experiments.

Langton and McKay
(1976) experimental           (*)Seed weight   Simulated clearance
conditions:                    (mg)             rate (L[??] [h.sup.-1].
                                               mg D[W.sup.-1])

Week 0                Exp. A     0.75              0.047
                      Exp. B
Week2                 Exp. A     4                 0.033
                      Exp. B
Week 3                Exp. A     6                 0.031
                      Exp. B     5                 0.032
Week 6                Exp. A    19                 0.024
                      Exp. B    11                 0.027

                      Model outputs: Food                      Model
                      requirements                             outputs:
                                                               Max stock
Langton and McKay     Minimum algal
(1976) experimental   cells[*][micro]       (*)Considering a   Maximum
conditions:           [L.sup.-1] required   stock (g) of:      stock (g)

Week 0                 70                     9                  50
                                                                 28
Week2                 139                    50                  71
                                                                 40
Week 3                175                    75                  78
                      158                    63                  42
Week 6                370                   238                  99
                      256                   138                  49

Langton and McKay
(1976) experimental   (*)Considering a
conditions:           feed level
                      (algal cells[*]
                      [micro]L-1) of:

Week 0
Week2                    180
                         120
Week 3                   180
                         120
Week 6                   180
                         120
                         180
                         120

(*) Settings from Langton and McKay (1976) experiments
(6 h on/off feeding).
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Author:Nobre, Ana M.; Soares, Filipe; Ferreira, Joao G.
Publication:Journal of Shellfish Research
Article Type:Report
Date:Dec 1, 2017
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