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Ecological Modelling 222 (2011) 1743–1755

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

alculating ecological carrying capacity of shellfish aquaculture usingass-balance modeling: Narragansett Bay, Rhode Island

arrie Byrona,b,∗, Jason Linkc, Barry Costa-Piercea,d, David Bengtsona

University of Rhode Island, Department of Fisheries, Animal and Veterinary Sciences, Kingston, RI 02881, USAGulf of Maine Research Institute. 350 Commercial Avenue, Portland, ME 04101, USANational Marine Fisheries Service, Northeast Fisheries Science Center, 166 Water Street, Woods Hole, MA 02543, USARhode Island Sea Grant College Program, University of Rhode Island, Narragansett, RI 02882, USA

r t i c l e i n f o

rticle history:eceived 3 September 2010eceived in revised form 3 February 2011ccepted 8 March 2011vailable online 31 March 2011

a b s t r a c t

Increasing growth in the aquaculture industry demands ecosystem-based techniques for managementif that growth is to be ecologically sustainable and promote equity among users of the ecosystems inwhich it occurs. Models of carrying capacity can be used to responsibly limit the growth of aquaculturein increasingly crowded coastal areas. Narragansett Bay, Rhode Island, USA is one such crowded coastalregion experiencing a rapid increase in bivalve aquaculture. An ecosystem mass-balance model was used

eywords:arrying capacityquaculturehellfishodeling

to calculate the ecological carrying capacity of bivalve aquaculture. Cultured oyster biomass is currentlyat 0.47 t km−2 and could be increased 625 times without exceeding the ecological carrying capacity of297 t km−2. This translates to approximately 38,950 t of harvested cultured oysters annually which is 4times the total estimated annual harvest of finfish. This potential for growth is due to the high primaryproductivity and large energy throughput to detritus of this ecosystem. Shellfish aquaculture has potential

is un

copatharragansett Bay

for continued growth and

. Introduction

Growth of bivalve aquaculture worldwide (Costa-Pierce, 2008a;AO, 2009) presents new challenges in coastal management. Thisrowth is happening in both developing and industrial countries inearshore coastal environments where user conflict is high (Costa-ierce, 2008a; Hamouda et al., 2004). Over 50% of the humanopulation lives within 100 km of the coast and several industriesompete for use of coastal resources (Martínez et al., 2007).

One such bay with increasing aquaculture and high user con-ict is Narragansett Bay, Rhode Island (RI), USA. Approximately halff Rhode Island’s aquaculture takes place in Narragansett Bay. Inhe matter of 6 years (2001–2007), the industry grew exponentiallyrom a $300,000 to a $1,600,000 industry doubling the number of

arms and submerged land under lease (Alves, 2007). Ninety-nineercent of the aquaculture in Rhode Island is oysters (Crassostreav-

rginica). On a global scale, this industry is quite small. However,iven that Rhode Island (RI) is the smallest and second most denselyopulated state in the United States, the rate of growth is notable.

∗ Corresponding author at: University of Rhode Island, Department of Fisheries,nimal and Veterinary Sciences, Kingston, RI 02881, USA. Tel.: +1 401 874 2668;

ax: +1 401 874 7575.E-mail addresses: carriebyron@my.uri.edu, cbyron@gmri.org (C. Byron),

ason.link@noaa.gov (J. Link), bcp@gso.uri.edu (B. Costa-Pierce), bengtson@uri.eduD. Bengtson).

304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2011.03.010

likely to become food limited due, in part, to the large detritus pool.© 2011 Elsevier B.V. All rights reserved.

Over the past decade, bivalve aquaculture has progressedin technological, political, and social sustainability (Costa-Pierce,2008a,b; National Research Council, 2010). Rearing and harvestingtechniques are more efficient (Costa-Pierce, 2008a,b). Technolo-gies and policies aimed to mitigate the spread of disease haveincreased (Bushek et al., 2004; Forrest et al., 2009; Sapkota et al.,2008; Sindermann, 1984). Society’s acceptance of bivalve aqua-culture continues to grow in part due to educational campaignsaimed at increasing awareness to the ecosystem services providedby shellfish (Coen et al., 2007). Additionally, bivalve aquacultureis one of the most ecologically sustainable types of aquaculture(Shumway et al., 2003). Bivalve aquaculture has little negativeimpact on the benthos (Crawford et al., 2003; Forrest et al., 2009;Grant et al., 1995). Bivalves act as a benthic-pelagic link makingplanktonic nutrients available for benthic deposit feeders and sub-merged aquatic vegetation (Newell, 2004; Peterson and Heck, 1999,2001) and improve water quality (Newell et al., 2002). Cages andother gear provide structure and habitat for a suite of other organ-isms thereby increasing biodiversity (Dealteris et al., 2004; Tallmanand Forrester, 2007).

As social acceptance of bivalve aquaculture continues to

increase, management strategies that promote sustainable indus-tries become critical. The most important question managers needto ask is; “How much aquaculture can the system support?” Thisquestion can be addressed by calculating the carrying capacity ofthe system for bivalve aquaculture. Limiting aquaculture within the

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arrying capacity is the most straightforward and obvious way toontinued sustainability.

If we fail to manage within carrying capacity guidelines, theres potential to cause degradation of the system function. Tracadieay, PEI, is operating above its carrying capacity (Waite et al., 2005).lthough a further increase in bivalve production may be possible,

t would stress the system outside its normal range of variationFilgueira and Grant, 2009). Similarly, river basins (rias) of the Gali-ian area in northern Spain are operating at carrying capacity witho room for growth of the industry (Duarte et al., 2008; Smaal,002). Systems such as these threaten the ecosystem sustainabilityor, not only their own, but other industries as well. Social equitys likely to decline as user-conflict increases with environmentalegradation.

.1. Carrying capacity

The definition of carrying capacity has been extended to fourypes of carrying capacity that can be applied directly to bivalvequaculture (Inglis et al., 2002).

. Physical—“total area of marine farms that can be accommodatedin the available physical space”

. Production—“the stocking density of bivalves at which harvestsare maximized”

. Ecological—“the stocking or farm density which causes unac-ceptable ecological impacts”

. Social—“the level of farm development that causes unacceptablesocial impacts”.

While physical and production carrying capacity are useful onfarm-scale, acknowledging that the farm is only a part of a largercosystem requires consideration of ecological and social carryingapacities. In order to take an ecological approach to aquacultureSoto, 2010), it is helpful to consider ecological carrying capacity.

Both the ecological and social carrying capacities are defined byhe acceptability of change and, therefore, depend on social val-es (Mckindsey et al., 2006). Mckindsey et al. (2006) explainedhat society defines the variables of interest and how much thoseariables can change. Therefore, society has a part in definingcceptability. Society can determine the acceptability of alterationso sustained ecological function, species biomasses and energyows between trophic levels. This information can be used toetermine ecological carrying capacity using mass-balance mod-ling (Jiang and Gibbs, 2005; Mckindsey et al., 2006). Stakeholdersn RI wanted to calculate ecological carrying capacity for currentonditions in Narragansett Bay and were therefore, unwilling toccept any change in ecosystem function, biomasses, or energyows.

.2. Modeling

Ecopath is static, mass-balance, ecosystem-based modelingoftware that focuses on energy transfer between trophic levelsnd is widely used in fisheries management (www.ecopath.org).copath has been used for modeling a wide range of systems andanagement scenarios (Christensen, 1995; Christensen and Pauly,

993; Monaco and Ulanowicz, 1997; Vasconcellos et al., 1997)ncluding the carrying capacity of bivalve aquaculture (Jiang andibbs, 2005). It differs from other modeling approaches because itncompasses the full trophic spectrum, which is what makes it truly

n ecosystem model appropriate for determining ecological carry-ng capacity. Most other shellfish carrying capacity models are athe production or farm scale (Bacher et al., 1998; Carver and Mallet,990; Nunes et al., 2003; Raillard and Ménesguen, 1994) whichails to incorporate all trophic levels equal to and higher than the

ing 222 (2011) 1743–1755

bivalves. This approach is useful on a farm scale but is shortsightedfor ecosystem management where several user groups depend onthe stability and sustainability of other trophic levels across theentire ecosystem. Furthermore, Ecopath provides a methodologyto standardize model outputs thereby making it easy to compareacross systems.

Since Ecopath is a foodweb-based model, special emphasis isplaced on predator–prey interactions and they are handled as theywould be in a foraging arena (Walters et al., 1997). Overall, Ecopathis a good balance between simplicity and the complexity of otherecosystem models. Some applications of shellfish carrying capac-ity models only consider nutrients, plankton, detritus, and bivalves(Bacher et al., 1998; Hawkins, 2007; Raillard and Ménesguen, 1994;Smaal et al., 1998) which limit the scope of the model. Ecosystemmodels are more appropriate in scope, but can have unrealistic datademands and require advanced computer programming skills tooperate (Plagányi, 2007). Ecopath provides a structured, yet flexi-ble, framework for ecosystem modeling.

Ecopath, like any model, has shortfalls and limitations (Plagányiand Butterworth, 2004). Most shortcomings are attributed to usererror such as uncritical use of Ecopath default settings. It is up tothe modeler to change default settings so that they are appropriatefor each functional group. Failure to do so treats all groups equallywhich can lead to erroneous conclusions (Plagányi, 2007). Perhapsthe most unavoidable shortfall of any ecosystem model is the quan-tity and quality of data available to feed the model. We attempted tominimize this shortfall by using data collected at the model locationto calculate input parameters and by employing a series of diag-nostic tests to evaluate data parameterization and identify areas ofdata weakness that may need further investigation prior to modelbalancing (Link, 2010).

An ecosystem model of Narragansett Bay, consisting of 14functional groups, has been previously defined by Monaco andUlanowicz (1997). It was originally designed and used to comparetrophic structure and sustainability of three major Atlantic bays;Narragansett Bay, Chesapeake Bay, Delaware Bay. These originalmodels included no fisheries or aquaculture. Including both activi-ties in the model are essential to fully understand the dynamics andfunction of the system. In order to aid the development of a long-term plan for aquaculture in Rhode Island, a working group of thestate aquaculture regulatory agency recommended that the ecolog-ical carrying capacity of Narragansett Bay (and other coastal waters)for oyster aquaculture be determined. The purpose of this studywas to update the Ecopath model of Narragansett Bay developedby Monaco and Ulanowicz (1997) and to use the updated modelto calculate that ecological carrying capacity by increasing farmedoyster biomass until the model became unbalanced. A similar mod-eling effort was conducted for Rhode Island’s coastal lagoons (Byronet al., 2011a). A noteworthy aspect of these efforts is the inclusion ofa wide variety of stakeholders in the development and applicationof the models (Byron et al., 2011b).

2. Methods

2.1. Study area

Narragansett Bay (355 km2) in Rhode Island, USA (W71◦20′

N40◦35) is an eutrophic, well-mixed estuary with relatively lit-tle fresh water input (Saarman et al., 2008), residence timeof 26 days, an average depth of 9 meters (Boothroyd and

August, 2008; Nowicki and Nixon, 1985a,b) and average yearlytemperature of 11.24 ◦C (Oviatt et al., 2002; Pilson, 2008;http://www.narrbay.org/physical data.htm). Narragansett Bay hasbeen well studied and modeled over the past 3 decades (Desbonnetand Costa-Pierce, 2008; Kremer and Nixon, 1978; Monaco and

odelling 222 (2011) 1743–1755 1745

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lanowicz, 1997). Recently (2007), 50 hectares of Narragansett Bayere leased for oyster aquaculture which is a sharp increase from

.2 hectares in 1995 and exponentially less than the 8436 hectareseased in 1911 when peak production biomass was approximately44,562 t (Alves, 2007; Beutel, 2009; Pietros and Rice, 2003; Rhode

sland Commissioners of Shellfisheries, 1912). Several anthro-ogenic and environmental factors contributed to the decline inquaculture in the 1920s–1950s (increased raw sewage inputs,umulative effects of continued soil erosion, increased metal fin-shing effluents, hurricane of 1938, labor shortages during WWII,nd several state socio-political changes) and continued lack ofrowth in the 1950s–1990s (lingering pollution, rise of tourism,uburbanization of coastal zone, robust capture fisheries, and fear ofeturning to a “mill town” social system) (Rice, 2006). Wild harvestf clams (Mercenariamercenaria), wild capture of finfish, tourism,nd recreational fishing are additional industries vying for spacend resources in Narragansett Bay. The environmental impact ofncreased aquaculture is only one of several concerns for stakehold-rs including nutrient control and periodic bloom-initiated hypoxiavents occurring in patches of the upper Bay (Desbonnet and Costa-ierce, 2008).

.2. Input parameters

Calculating ecological carrying capacityusing a static mass-alance ecosystem model is an iterative process that was donehrough several steps to ensure the validity and quality of theutput. In order to calculate carrying capacity, a cultured shell-sh group and fisheries removals were added to Monaco andlanowicz (1997) model. The biomass parameters were updatednd improved to reflect current conditions in Narragansett Bay ashanges in the ecology have been documented over the past decadeCollie et al., 2008; Nixon et al., 2008; Oviatt et al., 2003). The orig-nal Monaco and Ulanowicz (1997) diet matrix (Table 1a), with theddition of cultured oysters, was used for this study. All parameterseflect a time-lapsed snapshot of the ecosystem so that seasonal andemporal variability are included, but expressed as a yearly average.

.3. Data

Multiple data sources were available for several of the func-ional groups in the model. Due to the extent of these sources,nly the most recent and accurate sources are mentioned in thiseport. Further details on data sources and model parameterizationere reported by Byron (2010). Not all functional groups have beeneasured with equal intensity and precision, despite centuries

f surveys and examination in Narragansett Bay (Desbonnet andosta-Pierce, 2008). Top trophic levels were measured more oftennd more accurately than lower trophic level consumers. On-goingurveys and monitoring efforts were targeted as current sourcesf data for all model input parameters. Only when recent (≥2003)ata within Narragansett Bay were not available were older dataets considered.

None of the various data sources used for parameterization wereollected for the sole purpose of constructing this model. Otherrojects that measured or surveyed the biota used different unitsf measures at different spatial and temporal scales. To unify theseiffering units, data were converted into standard units (gramsry weight per square meter per year; g DW m−2) and then re-valuated before they were considered appropriate for this model.ry weight was calculated from wet weight assuming 0.20 con-

ersion coefficient for most species (Baird and Ulanowicz, 1989).enthic invertebrate species biomasses were converted to dryeights according to Mckinney et al. (2004). Algae were converted

o dry weight assuming 87% moisture (Thornber and Guidone,npublished data). Carbon was converted to dry weight assuming Ta

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g dry weight = 0.4 g C (Baird and Ulanowicz, 1989; Jørgensen et al.,991; Parsons et al., 1984).

Ecopath requires input of at least three parameters (biomass (B),roduction/biomass (P/B), consumption/biomass (C/B)) for everyefined functional group in the system (Christensen et al., 2005).rom these three parameters the fourth main parameter requiredor balancing, ecotrophic efficiency (EE), which is a measure of themount of production used in the system, can be calculated auto-atically by Ecopath. The final two input components, which must

e entered into the model for every functional group, are diet com-osition and fisheries removals (i.e. aquaculture harvest or wildatch).

Biomass estimates for fish and invertebrate carnivores groupsriginated from 2003 to 2006 Rhode Island Department of Envi-onmental Management (RIDEM) trawl survey of Narragansett BayLongval, 2009) (Table 1b). Finfish species caught were categorizednto carnivorous fish or planktivorous fish. Invertebrate carnivoresre primarily comprised of squid and ctenophores (Monaco, 1995).

Benthic invertebrates were comprised of several groups eacheasured using different techniques. Benthic invertebrate carni-

ores were primarily comprised of lobsters and crabs (Monaco,995). The primary sources of data for biomass of benthic inverte-rate carnivores were from bottom trawl surveys by RIDEM, bottomrawl surveys from the University of Rhode Island’s Graduatechool of Oceanography (GSO), and subtidal sampling in Greenwichay (Thornber and Guidone, unpublished data). Infauna (benthiceposit feeders and benthic suspension feeders groups) were sam-led from four stations throughout Narragansett Bay on the sameay in July 2006 (Table 1b). Parabenthos were primarily comprisedf Crangon and Palaemonetes shrimp (Monaco, 1995). Shrimp wereounted in June 2006–August 2008 in the subtidal region of Green-ich Bay in Narragansett Bay (Thornber and Guidone, unpublishedata) (Table 1b). The biomass of cultured oysters was estimatedsing planting and harvest estimations from the farmers and usingllometric conversions derived from a 2008 survey conducted onultured oysters in RI coastal lagoons (Markey, 2009). Length andet weight measurements were taken on 647 individual oysters

etween 35 and 100 mm and used to allometrically infer a biomassrom counts.

Mesozooplankton and microzooplankton biomass remainnchanged from Monaco and Ulanowicz’s 1997 model (Table 1b).he two dominant mesozooplankton species are Acartiahudson-

ca and A. tonsa (Durbin and Durbin, 1981; Durbin et al., 1983;ulsizer, 1976; Kremer and Nixon, 1976; Monaco and Ulanowicz,997; Smayda and Borkman, 2008). The dominant microzooplank-on are ciliates and microflagellates (Monaco and Ulanowicz, 1997;mayda and Borkman, 2008). Monaco and Ulanowicz (1997) zoo-lankton estimates were primarily based on work done in the late970s (Durbin and Durbin, 1981; Durbin et al., 1983; Hulsizer,976; Kremer and Nixon, 1976). Zooplankton work from this timeeriod remains the most comprehensive and precise to date. Recentstimates of mesozooplankton were considered, but proved toe an order of magnitude too low during the diagnostics andere confirmed by E.G. Durbin (personal communication). Micro-

ooplankton has not been given much attention in Narragansettay (Durbin and Durbin, 1998) and no current estimates arevailable.

Pelagic bacteria in Narragansett Bay were measured weeklyrom September 1999 to June 2000 at two stations (Staroscik andmith, 2004) (Table 1b). Bacteria particulate organic carbon (POC)n the sediment has not been directly measured in Narragansett

ay. Typical benthic bacteria abundances in estuarine systemsange from 5 to 50 g DW m−2 (Mann, 2000) (Table 1b). Detritusas estimated using an empirical relationship that relates detritus

iomass to primary productivity and euphotic depth (Pauly et al.,993) (Table 1b).

ing 222 (2011) 1743–1755

Benthic macroalgae were surveyed monthly between Jan-uary 2006 and December 2007 intertidally and between June2006 and August 2008 subtidally in Greenwich Bay—a smallbay located within Narragansett Bay (Thornber and Guidone,unpublished data) (Table 1b). Chlorophyll fluorescence was mea-sured monthly (20 surveys) from December 2006 to October2007 using a sampler that undulates through the water columnwhile being towed along a transect through East and West Pas-sages, Rhode Island Sound, Mount Hope Bay, and the ProvidenceRiver (NOAA Narragansett Bay, RI Lab). Survey methods and datawere available (as of December 2010) at http://www.narrbay.org/d projects/nushuttle/shuttletree.htm (Table 1b). Each monthly sur-vey takes over 100,000 measurements which were averaged from20 surveys to get a current biomass estimate of phytoplankton.

Vital rates (P/B and C/B) for all species groups originated fromthe Monaco and Ulanowicz (1997) model. The same P/B and C/Bvalues used for the filter feeders group were also used for thecultured oysters group, 46.92 and 103.64, respectively (Table 1b).Respiration was calculated for each functional group as 65% ofassimilated consumption (Link et al., 2006). Respiration, althoughnot a required Ecopath input, is a useful parameter for diagnostics.

Major species landed from fisheries in the bay includeStenotomuschrysops, Paralichthysdentatus, Brevoortiatyrannus,Homarusamericanus, Mercenariamercenaria, Myaarenaria, Spisu-lasolidissima (SAFIS–Standard Atlantic Fisheries Information Sys-tem, queried December 2009). Commercial and recreational catchwere based on the NOAA Fisheries Vessel Trip Reports (VTRs), theRhode Island Department of Fish and Wildlife Harvester Catch andEffort Logbook and allocations set by the RIDEM. The harvest loca-tion of the clams was precisely recorded whereas finfish and lobstercatch in Narragansett Bay were deduced from harvest of a large area(statistical area 539) both in and out of the Bay (Table 1c).

2.4. Diagnostics

Prior to balancing the model, additional non-Ecopath deriveddiagnostics were performed to evaluate the validity of the inputparameters. Diagnostics check and aid in balancing the model inde-pendent of Ecopath assumptions prior to the mandatory Ecopathautomated balancing routine. Diagnostic tests allow evaluation ofthe cohesiveness of the data despite the natural discrepancies thatoccur when using a multitude of data sources collected across vary-ing temporal and spatial scales. Pre-balancing diagnostics allow themodeler to look at the system holistically instead of piecemeal inthe way the individual data sources were collected.

Diagnostic tests were performed on: biomass, the ratio ofbiomass to primary production, the vital rates (production (P), con-sumption (C), respiration(R)), the ratios of vital rates (e.g. P/C) andthe total consumptive removals. For detailed description on diag-nostic testing see Link (2010). In brief, each functional group wasplotted along the x-axis in order of decreasing trophic level to alloweasy visualization of trophic relationships (Link, 2010).

• Biomass and vital rates should decrease with trophic level.• Ratios of biomass to primary production should remain less than

one.• Vital rate ratios should be within ecologically acceptable limits

(i.e. P/C < 0.5).• Within each functional group, consumption should be higher

than production.• Total consumptive removals should be lower than production.

When simple ecological and physiological ‘rules’ were not metas evident from these diagnostic tests, parameters were correctedfor improved ecological integrity and validity. The parameter inquestion was increased or decreased by a multiple of 2/3, 1/2, 3/2,

C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755 1747

Fig. 1. Pre-balancing diagnostics. See Tables 1 and 2 for abbreviations. In some cases, groups were summed; all primary producer groups (PP), all zooplankton groups (Zoo).B s. (a) Tt tes sha onsum

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2

tibegaewd(pet(

iomass, P/B, and C/B values depicted were used as initial Ecopath input parametero total primary production showing all levels remained at or below one. (c) Vital rand respiration. (d) Vital rate ratios. (e) P/C remaining less than P/R rates. (f) Total c

, 3, 10, or 25 until the parameter conformed to the expectationsf the diagnostic test (Fig. 1). Performing diagnostic tests allowedmanual check of the validity of data sources and greater controlver the mass-balancing of the model by manually bringing thearameters closer to mass-balance instead of relying solely on theutomated Ecopath mass-balance routine.

.5. Model outputs

In addition to diagnostic tests, Ecopath is equipped with toolshat can be used to address uncertainty in the data, thereby furthermproving the quality of the parameter inputs through the mass-alancing routine. The Pedigree routine allows entry of a range forach parameter input which evaluates statistical uncertainty. Pedi-ree allows the user to mark the sources of data for each parameternd has a ranking scheme for the ‘goodness’ of those data givingach parameter confidence intervals. These confidence intervalsere then used by the Ecoranger module to give a probabilityistribution for each parameter using a Monte-Carlo parametric

Christensen et al., 2005). Additionally, a sensitivity analysis waserformed to evaluate the effect of each of the entered input param-ters on all of the ‘missing’ basic parameters for each group inhe system by varying each input parameter from −50% to +50%Christensen et al., 2005). Data were not always available for every

rophic decline in biomass across species groups. (b) Biomass and production ratiosowing relative decline with trophic level and higher consumption than productionptive removals which are less than production and consumption.

parameter and the sensitivity analysis was a way to identify thoseparameters and, subsequently, functional groups that were mostlikely to be impacted by slight modeling perturbations.

Mixed Trophic Impact Analysis was used to evaluate whichfunctional groups were most likely to be impacted by slight per-turbations by measuring the impact of an infinitesimally smallincrease in group biomass on other groups (Christensen et al.,2005). Mixed Trophic Impact is the measure of direct or indirectinfluence a group (on the left of the matrix) has on another group (atthe top of the matrix) based on food web characteristics. Ecopathproduces a matrix that reports the measured direct and indirectincrease or decrease in every groups’ biomass parameter caused byan infinitesimally small increase in every other groups’ biomass.

Ecopath Summary Statistics provide informative systems mea-sures such as throughput, cycling index, and pathways that can beused to characterize the system. Total system throughput is the sumof all flows in a system: consumption, export, respiration, and flowsto detritus (Christensen et al., 2005). It represents the size of thesystem expressed as a flow (Ulanowicz, 1986). Cycling index is the

percentage of energy throughput in the system that is recycled andcorrelates to system maturity, resilience and stability (Christensenet al., 2005; Finn, 1976; Odum, 1969). The number of pathways isindicative of the redundancy and stability of the system.

1748 C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755

Table 2Ecopath Model Outputs. (a) Pedigree Index. Higher numbers signify greater confidence. See Table 1 for abbreviations. (b) Information analysis of balanced model outputs.

Pedigree index Group name Information analysis

B P/B Q/B Diet Catch Ascendency Overhead Capacity Info. ThroughputgDWm−2y−1*bits gDWm−2y−1*bits gDWm−2y−1*bits bits gDWm−2y−1

4 2 2 1 4 Carnivorous Fish (CF) 2.566 23.407 25.973 0 1.494 2 2 1 4 Planktivorous Fish (PF) 41.56 178.083 219.644 0 15.3934 2 2 1 4 Benthic Invertebrate Carnivores (BIC) 43.287 271.198 314.485 0.001 24.0014 2 2 1 – Benthic Deposit Feeders (BDF) 172.115 429.003 601.118 0.002 45.7684 2 2 1 4 Benthic Suspension Feeders (BSF) 557.899 3971.221 4529.121 0.007 551.1394 2 2 1 – Parabenthos (Par) 167.577 949.081 1116.658 0.002 99.724 2 2 1 – Invertebrate Carnivores (IC) 279.254 1955.309 2234.563 0.003 231.751 2 2 1 – Mesozooplankton (Mes) 1946.625 9883.553 11830.18 0.023 1585.9721 2 2 1 – Microzooplankton (Mic) 2415.679 13636.42 16052.1 0.029 2181.584 2 2 1 – Pelagic Bacteria (PB) 7118.605 18955.1 26073.7 0.084 42002 2 2 1 – Bacteria Sediment POC (POC) 17705.37 41618.1 59323.46 0.21 186905 1 1 0 5 Cultured Oysters (CO) 3.169 12.982 16.152 0 0.9844 2 – – – Benthic Algae (BA) 1333.879 5606.105 6939.984 0.016 1022.814

23.9292.3203.83

502

2

asie2

P

C

EbcwF2ivaTa

2

fbintNm

aatrmv

5 2 – – – Phytoplankton (Phy) 229Ecopath Pedigree index: 0.3 Detritus (D) 433Number of living groups: 14 Total 981Measure of fit: 1.09 Percent of Total (%) 35.

.6. Model considerations

All modeling was done using EwE5 software package (avail-ble at www.ecopath.com). Ecopath mass-balances the model bylightly adjusting the input parameters within their confidence lim-ts according to two master equations (Equation 1–2) so that thenergy input and output are equal for each group (Christensen et al.,005).

roduction = predation + catches + net migration

+accumulated biomass + other mortality. (1)

onsumption = production + respiration + unassimilated food.(2)

Energy between groups is linked through the diet matrix.copath provided a range of setup options for the automated mass-alancing routine. Five thousand (5000) iterations per run werehosen and the EE goal was forced to 0.95. The confidence intervalsere set by the Pedigree with a lower limit 10% of the original value.

or perturbation method, neighborhood perturbations of 10% B,0% DC (diet composition), 10% P/B and 10% C/B were chosen. The

nitial conditions for each run were set to continue with B and DCalues at end of last run. Finally, both “reduce sum of excess EE”nd “reduce max EE” were selected for the iteration design logic.he model was considered balanced when all EEs were below 1.0,ll P/C were below 0.5, and there was no negative respiration.

.7. Carrying capacity calculations

Ecological and production carrying capacities were calculatedollowing the methods of Jiang and Gibbs (2005). Cultured oysteriomass and proportional cultured oyster harvest were increased

n consecutive models until the system became unbalanced ando longer represented its present condition. The point just prioro any change in the system was the ecological carrying capacity.o parameters other than cultured oyster biomass and catch wereanually altered while calculating ecological carrying capacity.Zooplankton are major competitors with oysters for food (Jiang

nd Gibbs, 2005). Removing zooplankton from the system would

llow greater food source for oyster thereby maximizing oys-er production. Production carrying capacity was calculated byemoving all zooplankton groups from the models, rebalancing theodel using current levels of cultured oyster biomass and har-

est, and then iteratively increasing cultured shellfish biomass and

27921.23 50845.14 0.272 20130.6852818.09 96210.41 0.514 35583.44178228.9 276332.7 1.163 84364.7364.498 100 – –

proportional cultured oyster harvest until the model became unbal-anced. The biomass value just prior to causing the zooplankton-lessmodel to become unbalanced was the production carrying capac-ity.Because the two zooplankton groups were removed from thediet matrix, effectively that meant the proportion of each prey itemconsumed by zooplankton predators needed to be redistributed sothat all prey items consumed by a given predator would still addto 100% of their diet. The percentage of zooplankton in each preda-tor’s diet was redistributed evenly among other prey groups priorto re-balancing.

2.8. Carrying capacity analysis

Robustness of biomass parameters while the system was atecological carrying capacity was examined by changing individualbiomass values of each group by factors of 0.01, 0.5, 2, 10 and 100of their original value when the model was balanced at ecologi-cal carrying capacity. Only one value was changed at a time whileall other biomass values remained constant. The degree to whichthe biomass value could vary while the model remained balancedwas an indicator of the robustness of the biomass of that functionalgroup at carrying capacity against perturbations. Additionally, bal-anced biomass parameters at ecological carrying capacity werethen rebalanced using EE as primary constraint (<0.95) under vary-ing cultured oyster biomass scenarios: 0.001, 0.01, 0.1, 10, 100,and 1000 times the ecological carrying capacity biomass (i.e. Linket al., 2009). This scenario testing allowed a visual representation ofthe influence of different levels of oyster culture on other speciesgroups in the system. Finally, the ecological carrying capacity ofcultured oysters in Narragansett Bay was compared to filter feederbiomasses in other Ecopath models of similar estuarine ecosystems.

3. Results

3.1. Parameter quality

The Pedigree index scored 0.3 with a measure of fit equal-ing 1.09 implying a reasonable quality of data sources (Table 2a)(Morissette, 2006). Confidence was highest in biomass input

parameters and lowest in diet matrix (Table 2a). Biomass inputparameters mostly originated from current surveys conducted inthe study area whereas diet composition originated from a pre-vious model of the same study system (Monaco and Ulanowicz,1997). Pedigree confidence was lowered in cases where no recent

C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755 1749

biom

ibv

swrtistf

Fbl

Fig. 2. Sensitivity analysis of balanced model. Biomass (B), production/

nformation was available from Narragansett Bay or when the pre-alancing diagnostics varied greatly from the data-derived inputalue.

At current levels of cultured biomass, the Sensitivity Analysishowed that the greatest impact of altering an input parameteras that of biomass and C/B of microzooplankton on EE of bacte-

ia sediment POC (Fig. 2). However, at ecological carrying capacity,

he Sensitivity Analysis showed that the greatest impact of alter-ng an input parameter was that of biomass and C/B of benthicuspension feeders group on the C/B of benthic algae (Fig. 2). Cul-ured oysters were not sensitive to changes in input parametersrom any group other than itself. For instance, altering the biomass

ig. 3. Mixed trophic impact index of balanced model. An infinitesimally small increase iar extending downwards symbolizes a negative impact and an upwards rising bar symb

obsters (pots), and oysters (farmers).

ass (P/B), ecotrophic efficiency (EE), ecological carrying capacity (ECC).

and C/B of cultured oysters impacted the EE of cultured oysters(Fig. 2). Cultured oysters also did not alter input parameters ofany group other than itself under current conditions. However,at ecological carrying capacity, altering the cultured oyster inputparameters did have an impact on other groups. Specifically, thebiomass input parameter of the cultured oysters group impactedthe EE of the microzooplankton, pelagic bacteria, bacteria sediment

POC, and cultured oysters groups and the C/B of the phytoplanktongroup. Similarly, altering the C/B input parameter of cultured oys-ters altered the EE of the microzooplankton, pelagic bacteria, andbacteria sediment POC groups and the C/B of the phytoplanktongroup.

n biomass of the groups on the left column impact the groups across the top row. Aolizes a positive impact.Catch is noted for finfish (trawl), wild clams (harvesters),

1750 C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755

Table 3Changes in Narragansett Bay Ecopath model while estimating carrying capacity using the automated mass-balancing routine.The bold-type numbers are the calculatedecological carrying capacity and production carrying capacity biomass values for cultured oysters. Any biomass value below the carrying capacity did not affect the balancedmodel. Any biomass value above the carrying capacity unbalanced the model by unrealistically increasing the ecotrophic efficiency (EE) of another group to one (1) or highersignifying that the entire group was consumed.

Multiplier Biomass (g DW m−2) Catch (37% of biomass) Mass-balance changes in model

1 (current conditions) 0.00949 0.00353

Ecological Carrying Capacity2 0.0189 0.00706 Balances

10 0.0949 0.0353 Balances100 0.949 0.353 Balances500 4.745 1.765 Balances600 5.694 2.118 Balances624 5.92176 2.20272 Balances625 5.93125 2.20625 Balances626 5.94074 2.20978 Microzooplanton EE = 1630 5.9787 2.2239 Microzooplanton EE = 1.001

1,000 9.49 3.53 Microzooplanton EE = 1.0995000 47.45 17.65 Microzooplanton EE = 2.153, Pelagic Bacteria EE = 1.357

Production Carrying Capacity6000 56.94 21.18 Balances7000 66.43 24.71 Balances7300 69.277 25.769 Balances7330 69.5617 25.8749 Balances7336 69.61864 25.89608 Balances7337 69.62813 25.89961 Balances

3

MMatlfi(daaoiogc

lc1lwtaT(

3

ctofa

7338 69.63762 25.903147340 69.6566 25.91029000 85.41 31.77

10000 94.9 35.3

.2. Ecopath summary statistics

As Sensitivity Analysis measures the impacts of parameters,ixed Trophic Impact Analysis measures the impacts of groups.ixed Trophic Impact is the measure of direct or indirect influencegroup (on the left of the matrix) has on another group (at the

op of the matrix) based on food web characteristics (Fig. 3). Theargest positive impact of any group is that of benthic suspensioneeders on wild clam harvesters (“harvesters”). Similarly, benthicnvertebrates have positive impact on crab and lobster pot harvests“pots”). The second largest impact is that of planktivorous fish onetritus. Detritus has a large positive impact on pelagic bacteriand a slightly smaller positive impact on benthic sediment POCnd benthic deposit feeders. The largest negative impact is thatf benthic sediment POC on detritus. Parabenthos has a negativempact on benthic deposit feeders (Fig. 3). The biomass of culturedysters is low compared to its harvest (“farmers”) relative to otherroups (Table 1, Fig. 3). As such, the impact of changes in biomassofultured oysters on every other group is negligible (Fig. 3).

Carnivorous fish were at the top of the food web (TL 3.71) fol-owed by invertebrate carnivores (TL 3.66), benthic invertebratearnivores (TL 3.33), and planktivorous fish (TL 3.19). There were73 relatively short (3.99) pathways that linked these high trophic

evel groups to lower trophic levels. This system also has 232 cycleshich are linked pathways starting from a group and returning

o it (Christensen et al., 2005). The cycling index was low at 27%nd the throughput was high at 84,364 g DW m−2 y−1 (Table 2b).he complete suite of Ecopath outputs were reported by Byron2010).

.3. Carrying capacity

Cultured oyster biomass is currently at 0.0095 g DW m−2 and

ould be increased 625 times to 5.93 g DW m−2 without exceedinghe ecological carrying capacity (Table 3). Assuming a conversionf 2% live to dry weight based on measurements made on oystersarmed in Rhode Island (Rheault, unpublished), that translates tolive weight of 0.47 t km−2 currently and 297 t km−2 at ecological

Pelagic Bacteria EE = 1Pelagic Bacteria EE = 1Pelagic Bacteria EE = 1.028Benthic Deposit Feeders EE = 1.058, Pelagic Bacteria EE = 1.334

carrying capacity. Given the total area of Narragansett Bay, the totalpotential ecological carrying capacity for bivalve aquaculture was105,279 t. Initial harvest of cultured oysters was 0.18 t km−2 whichis 37% of the total biomass. Maintaining this proportion, harvestof cultured oysters could be 110.1 t km−2 or 38,953 total t at eco-logical carrying capacity. This potential shellfish harvest is morethan 4 times that of reported finfish harvest in Narragansett Bay(ecological carrying capacity of oysters/trawled biomass of finfish;Table 1c).

Production carrying capacity estimated maximum productionwithout zooplankton in the ecosystem and irrespective of the sta-bility of the system and is typically thought about on a farm scale.The production carrying capacity was calculated to be 69.63 g DWm−2 or 3481 t km−2 which equates to 1,235,897 t in NarragansettBay. Cultured oyster biomass at production carrying capacity was7337 times that of its current biomass. If farming at this high pro-duction biomass (3481 t km−2) was restricted to only 9% of surfacearea, the Bay on average would still be operating below ecologicalcarrying capacity for aquaculture.

When cultured oysters surpassed ecological carrying capacityin Narragansett Bay, microzooplankton were overgrazed, result-ing in an EE equal to or greater than one (Table 3). Ecotrophicefficiency was the constraining parameter indicating model imbal-ance. Microzooplankton and benthic deposit feeders were limitingfactors when Narragansett Bay was at ecological carrying capacityfor cultured oysters. This means that a slight change in biomassof either microzooplankton or benthic deposit feeders unbalancedthe model indicating “unacceptable” change to the system. Otherbiomass parameters in the model at ecological carrying capacitywere more robust. The model remained balanced when any oneof 11 functional groups where halved or any one of 7 groups werereduced 10-fold (Table 4). The model also remained balanced whenany one of 6 groups was doubled or any one of 3 producer groups

was increased 10-fold (Table 4). Keeping in mind that there area total of 15 groups, most groups in the model could withstand aperturbation in biomass without influencing the balance of the sys-tem while at ecological carrying capacity. Benthic algae and detrituswere the most robust groups at ecological carrying capacity.

C. Byron et al. / Ecological Modell

Tab

le4

Rob

ust

nes

sof

biom

ass

(B)

valu

esat

ecol

ogic

alca

rryi

ng

cap

acit

yan

dp

rod

uct

ion

carr

yin

gca

pac

ity.

Bio

mas

sva

lues

ofea

chgr

oup

wer

em

ult

ipli

edby

fact

ors

of0.

01,0

.1,0

.5,2

,10

and

100.

On

lyon

eva

lue

was

chan

ged

ata

tim

ew

hil

eal

lot

her

biom

ass

valu

esre

mai

ned

con

stan

t.V

alu

esin

ital

ics

ind

icat

eth

efa

ctor

atw

hic

hth

em

odel

beca

me

un

bala

nce

dan

dre

pre

sen

tslo

wro

bust

nes

s.V

alu

esin

bold

insh

aded

boxe

ssi

gnif

yth

atth

em

odel

rem

ain

edba

lan

ced

rep

rese

nti

ng

hig

hro

bust

nes

sin

thos

egr

oup

sat

carr

yin

gca

pac

ity.

Ecol

ogic

alca

rryi

ng

cap

acit

yG

rou

pn

ame

Prod

uct

ion

carr

yin

gca

pac

ity

=0.0

1*B

=0.1

*B=0

.5*B

Bio

mas

s(g

DW

/m2)

=2*B

=10*

B=1

00*B

=0.0

1*B

=0.1

*B=0

.5*B

Bio

mas

s(g

DW

/m2)

=2*B

=10*

B=1

00*B

0.00

385

0.03

850.

1925

0.38

50.

773.

8538

.5C

arn

ivor

ous

Fish

0.00

385

0.03

850.

1925

0.38

50.

773.

8538

.50.

0124

0.12

40.

621.

242.

4812

.412

4Pl

ankt

ivor

ous

Fish

0.01

240.

124

0.62

1.24

2.48

12.4

124

0.03

167

0.31

671.

5835

3.16

76.

334

31.6

731

6.7

Ben

thic

Inve

rt.C

arn

ivor

es0.

0316

70.

3167

1.58

353.

167

6.33

431

.67

316.

70.

0290

30.

2903

1.45

152.

903

5.80

629

.03

290.

3B

enth

icD

epos

itFe

eder

s0.

0319

30.

3193

1.59

653.

193

6.38

631

.93

319.

30.

0531

80.

5318

2.65

95.

318

10.6

3653

.18

531.

8B

enth

icSu

spen

sion

0.05

318

0.53

182.

659

5.31

810

.636

53.1

853

1.8

0.02

770.

277

1.38

52.

775.

5427

.727

7Pa

rabe

nth

os0.

0277

0.27

71.

385

2.77

5.54

27.7

277

0.02

032

0.20

321.

016

2.03

24.

064

20.3

220

3.2

Inve

rteb

rate

Car

niv

ores

0.02

032

0.20

321.

016

2.03

24.

064

20.3

220

3.2

0.07

550.

755

3.77

57.

5515

.175

.575

5M

esoz

oop

lan

kton

0.02

260.

226

1.13

2.26

4.52

22.6

226

Mic

rozo

opla

nkt

on0.

0525

0.52

52.

625

5.25

10.5

52.5

525

Pela

gic

Bac

teri

a0.

0525

0.52

52.

625

5.25

10.5

52.5

525

1.05

1.5

7.5

1530

150

1500

Ben

thic

Sed

imen

tPO

C0.

151.

57.

515

3015

015

00.

0593

10.

5931

2.96

555.

931

11.8

6259

.31

593.

1C

ult

ure

dO

yste

rs0.

6962

86.

9628

34.8

1469

.628

139.

256

696.

2869

62.8

0.03

627

0.36

271.

8135

3.62

77.

254

36.2

736

2.7

Ben

thic

Alg

ae0.

0362

70.

3627

1.81

353.

627

7.25

436

.27

362.

72.

4676

24.6

7612

3.38

246.

7649

3.52

2467

.624

676

Phyt

opla

nkt

on2.

4676

24.6

7612

3.38

246.

7649

3.52

2467

.624

676

0.12

891.

289

6.44

512

.89

25.7

812

8.9

1289

Det

ritu

s0.

1289

1.28

96.

445

12.8

925

.78

128.

912

89

ing 222 (2011) 1743–1755 1751

When cultured oyster biomass surpassed the production carry-ing capacity, pelagic bacteria were overgrazed, resulting in an EEgreater than one (Table 3). Planktivorous fish were also sensitive atproduction carrying capacity and were not able to withstand anychange in biomass. However, the model could withstand a halv-ing in biomass of any one of 9 functional groups and a 10-folddecrease in biomass of any one of 6 groups (Table 4). The modelalso remained balanced when any one of 8 groups was doubledor one of 5 groups was increased 10-fold (Table 4). Benthic algaeand detritus were the most robust groups at production carryingcapacity.

Changing the oyster biomass resulted in minor changes in modeloutputs of other groups. Scenarios of oyster biomass two to threeorders of magnitude above the ecological carrying capacity resultedin perturbations of less than one order of magnitude in other groups(Fig. 4). All groups were affected at the 1000× scenario wherebenthic and zooplankton groups decreased slightly and detritus,primary producers, and fish groups increased slightly. This patternsuggests that cultured oysters have little impact on the system atvarying biomass scenarios.

4. Discussion

4.1. Ecopath summary statistics

Cycling index is the percentage of system throughput that isrecycled and corresponds to system maturity, resilience and stabil-ity (Christensen et al., 2005; Finn, 1976; Odum, 1969). The cyclingindex calculated by this model (27%) is much lower than thatcalculated by the Monaco and Ulanowicz (1997) model (48%). Fur-thermore, the path length calculated by Monaco and Ulanowicz(1997) model was much longer (6.01 compared to 3.99). Thedecrease in cycling and path length in the last decade suggests thatNarragansett Bay is becoming less efficient at recycling energy andretaining material. Increasing the biomass of bivalves may improveefficiency of energy cycling by increasing the benthic pelagic link byfiltering material out of the water column and repackaging it so itis biologically available for plants and benthic consumers (Newell,2004; Peterson and Heck, 1999, 2001).

Narragansett Bay is a large system with high overall activity, asindicated by the high throughput (84,364 g DW m−2 y−1) (Table 2b& 3). Throughput represents the size of the system’s energy flow(Christensen et al., 2005; Ulanowicz, 1986) and was higher thanMonaco and Ulanowicz (1997) estimate of 5,147,600 mg C m−2 y−1

(equivalent to 12,869 g dry weight m−2 y−1 using the conversioncarbon to dry organic matter, 1:2.5). Twenty eight percent (27.79%)of total throughput was cycled (23,019 g DW m−2 y−1 includingdetritus and 426.97 g DW m−2 y−1 excluding detritus). Most of theenergy in the system (42%) was diverted to detritus or consumedby predators (32%). Only 3.24% of the total cycled throughput (w/odetritus) constitutes predatory cycling. Low trophic levels con-tribute most to detritus and also had the highest throughput andexport which makes sense since low trophic levels also had themost biomass. The largest flows were through the primary produc-ers (Table 2b). More than half (51.5%) of the primary productionwas consumed by zooplankton which were direct competitors withcultured oysters for food.

4.2. Carrying capacity

Currently, cultured oysters are not a significant part of ecosys-tem, despite rapid increase in the industry. As an exercise, thisNarragansett Bay model was balanced twice; once with the cul-tured oysters group, and once without cultured oysters as it wasin the original Monaco and Ulanowicz (1997) model structure. The

1752 C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755

unde

dfiitluStihdoe

cfnschthusncpiltaoe

ot

Fig. 4. Changes in biomass of key groups

iagnostics, automated mass-balance routine and the final outputsor both models with and without cultured oysters were almostdentical. Additionally, the impact analysis showed little to nompact of cultured oysters on other groups (Fig. 4). Those groupshat were most impacted, although minimally, by oysters were theower trophic levels, specifically plankton groups. Although bottomp effects on higher trophic levels are possible (Steele et al., 2007;teele, 2009), the model results suggest that they are weak. Higherrophic level groups are not feeding on oysters thereby eliminat-ng a potential mechanism for a direct impact between oysters andigh trophic levels. Indirect impacts are possible, but unlikely to beetected, due to the low biomass of oysters. As such, the culturedysters group is functionally a very small and redundant part of thecosystem.

At or below the ecological carrying capacity, there are nohanges to the ecosystem in the model (Table 3). One reasonor Narragansett Bay’s high carrying capacity potential is its highutrient loading and primary productivity. The effects of exten-ive terrestrial nutrient inputs are exacerbated by its extensiveoastline and shallow depth (Boothroyd and August, 2008). Sincealf of primary production is consumed by zooplankton alone, cul-ured oysters and other filter feeders are competing for the otheralf. The high throughput of energy to detritus suggests a largenused source of food for oysters. Typically attention to bivalvehellfish nutrition is focused on plankton; however, detritus shouldot be overlooked. In the Irish Lough system, it is estimated thatultured shellfish remove four times as much detritus as phyto-lankton (Ferreira et al., 2007).There is no indication that shellfish

n Narragansett Bay are currently food limited or will become foodimited with continued growth of the shellfish aquaculture indus-ry. According to the model, high oyster biomass does not have‘trickle’ effect through the ecosystem and on the biomasses of

ther species groups except at extremely high biomasses above thecological carrying capacity (i.e. 100×–1000× scenarios; Fig. 4).

Oyster aquaculture has potential to continue on its current trendf increase (Alves, 2007; Beutel, 2009) and is capable of returningo peak historic biomass levels (144,562 t) without altering major

r different scenarios of cultured oysters.

energy flows or ecological structure of Narragansett Bay (Pietrosand Rice, 2003). The potential production biomass calculated inEcopath (3481 t km−2) was much higher than current productionbiomass reported by RI farmers of 1121 t km−2 (converted fromRheault, 2008). This suggests that farms are currently not operat-ing at maximum potential. Regulatory constraints, limited use ofvertical structures, and reliance by most growers on bottom cul-ture for part of the life cycle all contribute to current levels of lowerproduction.

If growers continue to use current production techniques andmaintain biomass densities at or below 1121 t km−2, managerscould theoretically allow expansion of shellfish farming to cover26% of the surface area of the Bay without exceeding the ecologi-cal carrying capacity. In other words, oyster biomass could exist at1121 t km−2 in isolated patches totaling 26% of the bay while stillremaining below the ecological carrying capacity on average acrossthe entire bay. This 26% is very close to the 24% bay area that wasleased in 1911 when the RI shellfish aquaculture industry was atits peak (Pietros and Rice, 2003). Notably, 1911 oyster farmers alsoused bottom culture and therefore were presumably operating atsimilar biomass densities as today’s farmers.

The ecological carrying capacity in Narragansett Bay exceedsthat of some of the major shellfish aquaculture producing loca-tions worldwide. New Zealand is the primary global exporter ofGreenshellTM mussels and harvests 97,000 t annually (New ZealandMinistry of Fisheries, 2008). The estimated ecological carryingcapacity of Tasman and Golden Bays in New Zealand is 65 t km−2

(Jiang and Gibbs, 2005) which is only about one-fifth that of cal-culated for Narragansett Bay. Tasman and Golden Bays are oneof the primary shellfish aquaculture locations in New Zealandand encompass 4500 km2 surface area compared to the relativelysmall Narragansett Bay (355 km2) ecosystem. Furthermore, Tas-

man and Golden Bays are comparatively oligotrophic and have alower standing stock of primary production.

Although the carrying capacity in Narragansett Bay is high, itis similar to historic oyster biomass levels (Pietros and Rice, 2003)and within the range of bivalve filter feeder biomasses in similar

C. Byron et al. / Ecological Modelling 222 (2011) 1743–1755 1753

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ig. 5. Final biomass input parameters from similar systems with bivalve filter feet al., 2008; Link et al., 2006; Monaco and Ulanowicz, 1997; Rybarczyk and Elkaim,ivalve groups were combined. Original units were converted to gDWm2 assuming

ystems (Fig. 5). In fact, the ecological carrying capacity of oys-ers in Narragansett Bay is similar to the standing stock of oystersn near-by Chesapeake Bay and Delaware Bay and a fraction ofhe standing stock in Long Island Sound and the Bay of Sommen the Seine Estuary (Fig. 5). All of these estuarine systems shareommon characteristics as shallow water estuaries with tidal influ-nce at one end of the bay and riverine-input at the other endf the bay. Narragansett Bay, Long Island Sound, Delaware Baynd Cheseapeake Bay are all located on the urbanized easternoast of the USA and are open to the Atlantic Ocean. Narragansettay, like many estuarine bays, is capable of hosting high bivalveiomass.

However, a slight increase beyond the ecological carrying capac-ty does have dramatic ecological implications for the biomasses ofther groups as demonstrated by the robustness tests (Table 4).rophic cascade effects are apparent in that the model will sup-ort a doubling in the biomass of planktivorous fish (Table 4), aajor consumer of zooplankton who inturn compete with oysters

or phytoplankton, detritus, and bacteria food sources. The modelecomes unbalanced if there is a doubling of biomass of most otherroups besides food groups of oysters. Increases in biomass up to00× of food sources of oysters (phytoplankton, detritus, bacteria)o not unbalance the model.

.3. Ecology

Using mass-balance models to calculate production carryingapacity allows for scientific questioning of ecological processesuch as competitive species interactions. Removing zooplanktonroups from the system is comparable to oysters outcompetingooplankton for food thereby starving them to death. The question

f whether cultured oysters are better competitors than zooplank-on has not been experimentally tested. However, modeling suchnteractions is a useful academic exercise to simulate possible out-omes should cultured oysters exceed their ecological carryingapacity.

Byron et al., 2011a; Christian and Luczkovich, 1999; Jiang and Gibbs, 2005; LeloupRybarczyk et al., 2003; Wolff, 1994; Zajac et al., 2009). Models with more than oneoisture (Mckinney et al., 2004) and 0.4 gC to dry weight (Jørgensen et al., 1991).

The role of zooplankton in Narragansett Bay is important andmay contribute to the uniqueness of Narragansett Bay relative toother coastal systems such as the neighboring lagoons. Zooplanktonwere a major stabilizing species in Narragansett Bay, more so thanin the lagoons. Zooplankton limit phytoplankton (Deason, 1980;Durbin and Durbin, 1981; Durbin et al., 1983) thereby reducing theamount of primary production available for cultured oysters andother species.

Invertebrate carnivores (ctenophores) are major predators inNarragansett Bay. Biomass was lower than what the diagnosticssuggested so the value at the maximum end of the calculated rangewas used. Kremer (1976, 1979) and Sullivan et al. (2008) showedthat ctenophores have strong impact on controlling zooplanktonin Narragansett Bay. However, this model conversely shows thatzooplankton have more of an effect in stabilizing the system thanctenophores through grazing. Experimentally removing zooplank-ton using modeling gives us the ability to measure the effects ofthese extreme changes in the system.

Based on the model, oyster biomass at or below the ecologi-cal carrying capacity will not change the impact on the ecosystemfrom that of the current biomass. These results have implicationsfor management of aquaculture. High ecological carrying capacityhas strong implications for management and ecosystem models,such as this one, are useful tools towards that end (Héral, 1993). Itshould be stressed that modeled carrying capacity is a theoreticallimit and should be viewed with caution. A suggested precaution-ary approach is to limit aquaculture to half the calculated carryingcapacity value. Half of carrying capacity is the maximum sustain-able yield (MSY) where growth rate is high and is an acceptedmanagement target for many fin fisheries (Mace, 2001). Manag-ing at MSY will also allow for the inherently dynamic variabilityof carrying capacity that is not described by static models. Natural

and anthropogenic perturbations, temporal and spatial scales atwhich populations are measured, and climatechange contribute tothe variability of carrying capacity. Climate change in coastal zones,predicted to be characterized by increase in temperature, possi-ble decreases in salinity, and decrease in pH (Anthony et al., 2008;

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PCC, 2007), will greatly influence the vital rates of bivalves (Davis,958; Miller et al., 2009; Motes et al., 1998) and subsequently theirarrying capacity.

As the aquaculture industry continues to grow, carrying capacityechniques using mass-balance modeling can be used to guide theevelopment of the industry in an ecologically sustainable manner.he ecology of Narragansett Bay may be unique, but the methodspplied here to calculate carrying capacity are easily transferableo other coastal habitats experiencing rapid aquaculture growthnd user conflict issues. Understanding the uniqueness of thearticular system is imperative for responsible ecosystem-basedanagement and mitigating user conflict between industries and

takeholders.

cknowledgements

Robert Rheault, David Beutel and David Alves provided valu-ble assistance. This work was possible through the cooperationnd support of all the agencies and labs that shared the datahat were used to parameterize this model. This work wasunded by the NOAA National Marine Aquaculture Initiative grantNA08OAR4170838, NSF IGERT grant #DGE-0504103, and a Johnald Science Grant.

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