Management ability and the economics of recirculating aquaculture production systems

Management Ability and the Economics ofRecirculating Aquaculture Production Systems RICHARD F.. Abstract A bioeconomic model offish growth in recirculating aquaculture systems was constr

Management Ability and the Economics of

Recirculating Aquaculture Production Systems

RICHARD F KAZMIERCZAK, JR AND

REX H CAFFEY

Department of Agricultural Economics and Agribusiness

Louisiana State University Agricultural Center

Baton Rouge, LA 70803-5604 U.S.A

Abstract A bioeconomic model offish growth in recirculating aquaculture

systems was constructed by developing a bioenergetic model comprised of metabolic sub-models for growth, ammonia production, and oxygen consump- tion Metabolite accumulations are determined by exogenous control variables for filtration and aeration and used to indirectly represent management ability Numerical solutions to model parameters were obtained using a two point boundary shooting algorithm within a dynamic profit maximization frame- work Optimal trajectory, isoquant, and bioeconomic optimization analyses describe specific tradeoff relationships existing between nutrition, density, and technology Results demonstrate the economic importance of these relation- ships changes over time in response to fish weight, and not always in ways suggested by the physical importance of individual factors Specifically, eco- nomically viable tradeoffs between dietary protein and stocking density occur over relatively narrow regions of management ability Without highly experi- enced and capable management, the biological realities of recirculating sys- tems may preclude profitable system operation.

Keywords aquaculture, recirculating bioenergetic, bioeconomic,

optimiza-tion, dynamic, model

Introduction

The U.S aquaculture industry has benefited from over three decades of researchaimed at developing technically viable production systems (Trosclair 1994) Im-proved nutrition, species selection, disease prevention, and water quality man-agement have allowed not only widespread establishment of pond facilities, butalso the emergence of recirculating production systems (Brune and Tomasso1991) Recirculating systems are defined as production units that recycle water bypassing it through filters that remove metabolic waste products Recirculatingsystems have many potential advantages over pond systems, including bettercontrol of the production environment and the ability to locate production facil-

The authors would like to thank Drs Gregory Luiz and Ronald F Malone for helpful

comments during development of the biological model The United States Department ofAgriculture funded this research through an Aquaculture Special Grant Approved forpublication by the Director of the Louisiana Agricultural Experiment Station as manuscriptnumber 94-86-8411

187

188 R F Kazmierczak and R H Cajfey

ities near major markets (Spotte 1979; Lawson 1991) In addition, the relativelysmall land and water requirements of recirculating systems make them attractive

in an era of increasing environmental regulation of aquaculture (Rosenthal 1994).But, in order to operate successfully, recirculating systems and their critical fil-tration components must be effectively managed

While the potential advantages of recirculating systems led to research in filterdesign, the existence of technically advanced filters has not generated widespreadeconomic success for commercial producers (Losordo, Easley, and Westerman1989) The aquaculture industry has come to realize only too well that the eco-nomic viability of recirculating systems is not guaranteed by technical feasibility(Weaver 1992) Profitable operation of a recirculating system requires not only theability to manage complex biophysical interactions over long periods of time, but

to do so in an economically efficient manner Despite an abundance of biologicaland engineering studies, there is a shortage of useful information on the interac-tions among management, technology and the economics of recirculating systems

Of course, it can be difficult and expensive to conduct economic experiments oncommercial-size recirculating systems One way to avoid this problem and stillgenerate the needed information is through the use of bioeconomic models thataccurately describe the underlying bioenergetic operation of the system (Allen et

al 1984)

Bioenergetic models have been widely used to examine the time dynamics ofspecies growth in pond aquaculture systems (Paloheimo and Dickie 1%5, 1966a,1966b; Machiels and Henken 1986; Cacho 1990) Some investigations have evenincluded the impact of metabolic feedbacks on growth (Cuenco, Stickney andGrant 1985) Less common are bioeconomic models that combine bioenergeticsand the economics of producer decision making Cacho, Kinnucan, and Hatch(1991) developed a bioeconomic model of pond catfish production and used it todetermine cost-effective feeding regimes Researchers have also used bioeco-nomic models of varying degrees of sophistication to examine open system rearing

of shrimp (Karp, Sadeh, and GrifTm 1986) carp (Talpaz and Tsur 1982), lobster(Botsford, Rauch, and Shieser 1974), and tilapia (Liu and Chang 1992) To ourknowledge, however, no study has examined a recirculating production systemfrom a complete bioeconomic framework, incorporating not only realistic metab-olite-constrained growth over time, but also the economic constraints faced byprofit-seeking producers

This study investigates the importance of management ability and filter nology on the economic viability of a recirculating system To this end three mainobjectives are pursued; development of a theoretical bioeconomic model of re-circulating systems, parameterization of the economic and biophysical compo-nents of the theoretical model, and optimization of the empirical model Thispaper begins by presenting a conceptual model that identifies the important rela-tionships in a generic recirculating system Next, the economic framework, bioen-ergetic growth, and metabolic feedback components of an empirical bioeconomicmodel are discussed Specifically, a differential equation model of recirculatingtilapia production is developed and validated from published information andexpert opinion After a brief explanation ofthe optimization strategy, simulationresults are analyzed to identify the levels of management ability necessary toprofitably operate a recirculating system The paper concludes with implicationsofthe results for actual recirculating system management

tech-Conceptual Model

A conceptual recirculating system mode! can be developed using bioenergeticrelationships, the principles of ecosystem dynamics, and the energy circuit lan-guage advocated by Odium (1989) Considering only the bioenergetic portion ofthe model (lower half of Figure 1), flows in the system are primarily driven by fishweight as mediated through metabolism and appetite Variables potentially underproducer control, such as water temperature and feed quantity and quality, can beused to adjust the various flows and thus the time path offish growth Feeding andgrowth lead to the generation of waste products and the consumption of oxygen,but most bioenergetic models assume that these components are assimilated orsupplied by the open environment Recirculating system models, however, need

to fully account for these feedbacks because of their potential impact on individualfish growth, mortality, and the overall expansion of total biomass in the produc-tion system

Metabolic waste products take two forms in the conceptual model; solids anddissolved total ammonia nitrogen (TAN) (Figure I) The toxic portion of TAN,unionized ammonia nitrogen (UAN), serves as one component of a feedbackmechanism that can inhibit fish growth through changes in appetite or if largeenough, cause fish mortality Biological filtration controls the buildup of UAN in

y- X

Figure i Conceptual Model of the Interactions Among Control Variables (Circles), cess Variables (Arrow Polygons), and Storage Variables (Peaked Half Circles) in a Recir-culating Production System

Pro-R F Kazmierczak and Pro-R H Caffey

the conceptual model, but this activity adds to the biological oxygen demand(BOD) generated by fish respiration and solids decomposition Open flow-throughsystems mitigate both UAN and BOD buildup by water dilution, but recirculatingand some pond systems must supply oxygen to meet BOD through mechanical orliquid oxygen aeration Suspended solids are removed from the system with me-chanical filters Failing adequate filtration, it may be possible to control the effects

of UAN and BOD by emergency water dilution, depending on the laws andregulations governing a specific species culture

The operation of biological and mechanical filters are critical to the growth offish and the stability of a recirculating system over the growout cycle Only whenboth filters are 100 percent efficient will there be no growth or mortality feed-backs Because perfect filter management is unlikely under commercial condi-tions, questions arise as to how filter inefficiency affects the potential for profit-able system operation Given the objectives ofthe study and the generic structureofthe conceptual model, the causes of less than perfect filter efficiency are mosteasily interpreted as management difficulties and not different technology pack-ages This approach allows us to compare varying management abilities and theireffects on the profitable operation of recirculating systems

Bioeconomic Model

The empirical economic application of the conceptual model to a recirculatingtilapia production system required specific bioenergetic and metabolic feedbacksub-models, as well as the integration of these submodels within an overall eco-nomic framework This section describes these model components, their param-eterization and validation,' and the way in which they interact during numericaloptimization.^

Economic Framework

Over a growout cycle, management ability primarily affects the variable costsassociated with short-run decision making In addition to the direct monetarycosts associated with stocking, feeding, and electrical power use, indirect costscan arise when a producer does not adequately manage a recirculating system'sfiltration technology These indirect costs show up in the form of reduced fishgrowth and increased mortality Considering the short-run nature ofthe problemand the assumption that producers seek to maximize returns above variable costs,the decision making problem can be expressed as

maximize "" = PQ ' Q ~ Cf - C^ - C^ (1)

' The empirical equations used in this study were generally not statistically estimated due

to the lack of adequate data sets on many critical biophysical relationships Instead, merical calibration was employed using the limited available data and expert opinion con-cerning functional relationships, ranges, and domains Within this context, validation fo-cuses on qualitative model performance relative to existing knowledge, especially wheninsufficient data exist for statistical validation (Law and Kelton 1982)

nu-^ The following discussion focuses on important model comjwnents and highlights criticalrelationships A complete description of the model's derivation can be found in Caffev

(1994) '

where PQ is the price of tilapia ($/gram), Q is the quantity of fish harvested (grams/liter), Cf is feed cost ($/Iiter), Q is electricity cost ($Aiter), and C, is total

fingerling cost ($/liter) The model was constructed on a per liter basis to avoid theneed for explicit description of the types, sizes, and configuration of variousphysical system components While this approach allows the study to proceedwithin a generic framework, it does assume an input divisibility and constantproportional returns that may not exist across the spectrum of real system de-signs How lumpy inputs and variable proportional returns might affect the anal-ysis of management ability are left to future research

The growth function required for equation (1) can be expressed as

(2)

where Wfj is the terminal fish weight at harvest (grams), /)„ is the numerical

density offish in the system at harvest (numbers/liter), WQ is the initial fish weight

at stocking (grams), /Q is the stocking day, /„ is the harvest day, and W, is thegrowth rate on day t (grams/day) The variable production costs can be defined as

Cf=Pf {'" RU) • F, • D{t) dt (3)

Ce = Pe- ('" E, dt (4)

C, = Ps- Do, (5)

where Pfis feed price ($/gram), R{t) is ration size relative to appetite on day t (0

=s R(0 =e 1.0), F, is fish appetite on day t (grams/day), D{t) is fish density on day

t (numbers/liter), P^ is electricity price ($/kilowatt hour), E, is rate of electricity use for aeration and pumping on day t (kilowatt hours/liter day), Ps is fingeriing price ($/gram), and D^ is the initial stocking density (numbers/liter) Prices were

obtained from surveys of major suppliers, budget-based analyses of recirculatingsystems, trade journals, and industry reports (Table I)

Given the desire to include UAN and dissolved oxygen feedbacks in themodel, the technical relationships can be expressed as

W, = g{VAN{t),DO{t),W{t)Mt),DC\ (6)

E, = j\W{t), Dit), R{t) DC] (7)

F, = h[W{t)] (8) UAN, = k[Wit), Rit), Dit) DC BE] (9)

192 R F Kazmierczak and R H Caffey

Table 1

Description of Constant, State, Fixed, and Free Control Variables for any

Individual Simulation ScenarioVariables Variable Description (value where appropriate)Constants

Feed price ($0.00026/gram $0.00030/gram, and

$0.00034/gram for low, medium, and high protein feeds,respectively)

Electricity price ($0.07/kilowatt hour)Fingerling price {S0.05/one gram fish)

Individual fish weight on day t (grams)Concentration of unionized ammonia nitrogen on day t(mg/liter)

Concentration of dissolved oxygen on day t (mg/liter)Biological oxygen demand on day t (mg/liter)

Oxygenation capacity of the water on day tIndividual fish appetite on day t (grams)Numerical fish density on day t (numbers/liter)Numerical fish density at harvest (numbers/liter)

Individual fish stocking weight (I gram)Terminal fish weight at harvest (700 gram market size,live weight)

Initial numerical stocking density (0.07, 0.09, 0.11, or 0.13fish per liter, depending on the simulation)

Feed quality (20%, 30%, or 40% crude protein feed,depending on the simulation)

Biological filter efficiency (0.7 to 1.0, depending on thesimulation)

Standard aeration efficiency (2.0)Ration size relative to appetite on day t (0 ^ R(t) «Electricity used for aeration and pumping on day t(kilowatt hours/liter day)

1.0)

where VAN, is the rate change in UAN concentration on day / fmg/liter/day), DO,

is the rate change in DO concentration on day / (mg/liter/day), and other variables

are defined in Table 1 The relationships that determine these equations of motionjointly compose the bioenergetic and metabolic feedback sub models Given thatmost recirculating systems are housed in climate controlled buildings, tempera-

ture is not included as a growth-related variable.^ In addition, water dilution isexcluded as a possible control variable because many state regulations governingtilapia culture ban water exchanges in order to prevent the escape of tilapia intonatural fisheries.

Given the description of the bioeconomic model in equations (lHlO), it isobvious that the biological relationships in a recirculating system significantlyinfluence the ultimate economic operation ofthe system Thus, before examiningthe impact of management ability, the biophysical relationships embedded in themodel need to be more fully described and empiricized

Bioenergetic Sub-Model

The bioenergetic model used in this study was an adaptation of Ursin's (1967) andLiu and Chang's (1992) generalized metabolic growth model Physical growth isdefined by the difference between energy intake and energy expenditure;

dw/dt = p • dr/dt - a • p • dr/dt - k • w'^ (11)

where dw/dt is the daily weight gain, p is the efficiency of food assimilation, dr/dt

is the daily feed ration, a is the fraction of assimilated food lost to active olism, k is the coefficient of resting metabolism, and T) is an exponent relatingbody weight (w) to resting metabolism Within this framework, daily ration can bedescribed by

metab-dr/dl = a-f-w^ (12)

where <T is the coefficient of food consumption, / i s the ration size relative to

appetite, and p is an exponent relating body weight to synthesis Thus, the firstterm on the right hand side of equation (11) represents the amount of consumedfood that is digested and initially incorporated into body weight The second andthird terms of equation (11) measure the amount of digested food energy that islost to active and resting metabolism, respectively The growth model is quiteflexible and capable of depicting concave, convex, or sigmoidal growth patternsover time depending on the specific parameter values However, it is generallybelieved that unconstrained fish growth should follow a sigmoidal pattern (Hop-kins 1992)

Although equation (11) is capable of tracking the growth effects of differentration quantities, it does not explicitly incorporate feed quality This can be ac-complished by defining the tilapia-specific assimilation efficiency as

^ While temperature can have important impacts on growth and other biophysical cesses in both extensive and intensive aquaculture production, the mode! assumes a grow-out period over warm spring, summer, and autumn months when heating costs are not afactor In addition, simulations with a fixed temperature assume that extremely high tem-peratures, and the resulting impairment of metabolic activity, are not encountered Ingeneral, these conditions are met in recirculating aquaculture systems in the lower South-east United States Extensions ofthe current model can easily include explicit incorpora-tion of fluctuating temperature in the bioeconomic model

pro-R F Kazmierczak and pro-R H Caffey

where P.E is the protein-energy to total-energy ratio contained in the food, with

average tilapia assimilation efficiencies being approximately 70% for protein and51% for total energy contained in a ration (Bowen 1982) Given this formulation,assimilation efficiency is primarily a function of feed protein levels

Assuming a constant water temperature of 3 0 ^ , equations (II) and (12) werecalibrated using a wide range of data from published and unpublished experiments(Caffey 1994) Final parameter values are presented in Table 2 Verification andvalidation ofthe bioenergetic model, a critical step in any simulation study, wasaccomplished with data used in model calibration and data independent of themodel structure Resulting simulations demonstrate that the bioenergetic modelaccurately depicts experimentally observed tilapia growth over a wide range offeeding conditions (Figure 2) The upper bound on modeled growth was approx-imately 1.4 kilograms over a 600 day period, a weight that was considered feasibleunder ideal conditions (Lutz 1994) Additional simulations suggest that the timepath of individual tilapia growth was relatively insensitive to the range of feedprotein levels commercially available (Figure 3a) This result might be expectedfor a fish like tilapia that feeds low in the food chain However, changes in theallowed percent of satiation feeding had considerable effects on simulated growth(Figure 3b) In order to avoid protracted juvenile development, the high metabolicrates of fish under 50 grams needed to be satisfied by maximum, or satiation,feeding Thus, the daily feeding rate was one ofthe free control variables numer-ically optimized in this study

UAN Feedback Sub-Model

The buildup of ammonia compounds in recirculating systems results from theaccumulation of excreted metabolic byproducts, fecal waste, and uneaten feed

Final Parameter Values

Table 2Used in the Bioenergetic ModelParameter

synthesisExponent of resting

metabolismCoefficient of food

consumptionCoefficient of

restingmetabolism

Fraction of

assimilated foodlost to activemetabolism

Value in Model0.67

1.000.980.018 + 0.034sech[0.01 W(t)] +0.018

tanhtlOO-O.OIW(t)]

0.269 + 0.513sech[0.141 W(t)]

+ 0.017

tanh[0.141 W(t)]

SourceCalibration; Liu andChang 1992Calibration; Liu andChang 1992Liu and Chang 1992Calibration (seeCaffey 1994)

Calibration (seeCaffey 1994)

in the ration (Meade 1973; Liao and Mayo 1974; Drennan and Malone 1990) But,TAN is only of interest because of its relationship to UAN the most toxic form

of aqueous ammonia UAN levels are generally dependent on system pH andtemperature, and are usually calculated as a fraction of the TAN in the system(Drennan and Malone 1990) Given a fixed pH of 8.0 and a temperature of 30°C,approximately 7.5 percent of TAN will be in unionized form (Emerson et al 1975).Using this information and converting to an average daily concentration, a UANproduction relationship was defined as

UAN, = 0.075 • CP • D(t) • dridt (14)where UAN, is in mg/liter/day, CP is the percent crude protein of the ration, and

D is the fish biomass load in g/liter.

Of course, recirculating systems employ biological filters to restrain the

196 R F Kazmierczak and R H Cajfey

200 300 Time (days)

400 500 600

1600 140011200

percent-to the following day's simulation and provide a mechanism by which metabolitescould buildup in the system Thus, the final relationship for UAN concentrationswas defined as

UAN{1) = (I - BE)(UAN, + UAN(t - 1)) (15)

where UAN(t) is the concentration at time / and UAN(t - 1) is the residual UAN carried over from the previous time period BE is used in the model to represent

the varying ability of producers to effectively manage the available biological filtertechnology

If the possibility of UAN buildup exists, then the resulting feedback effectsneed to be defined Mortality from UAN toxicity varies significantly amongwarm-water fishes Tilapia have survived at UAN levels as high as 3.4 mg/liter instudies involving long acclimation periods (Redner and Stickney 1979) While nocomplete information exists on tilapia mortality for various levels of UAN expo-

sure over time, the acute toxic UAN levels for channel catfish {Ictaluras

punc-tatus) closely resemble those reported for tilapia." Using catfish data from Colt

and Tchobanglous (1976), an expression for daily percent UAN-induced mortality( M ) derived:

Given equation (16), mean daily mortality increases gradually as UAN trations rise to 3.0 mg/liter and then increases rapidly for UAN concentrationsbetween 3.0 and 5.0 mg/liter (Figure 4a)

concen-In another article, Colt and Tchobanglous (1978) provide data on catfish thatcan be used to estimate the impact of UAN concentrations on growth Convertingthe author's information into a relationship for the mean daily UAN-induced

growth reduction (GRu^^) yielded

= 100(1.035 • UANU)) (17)

With this relationship, growth reductions increase linearly for UAN tions between zero and 1.0 mg/liter (Figure 4b) While UAN concentrations lead-ing to negative growth (individual fish weight loss) are possible, the suppression

concentra-of UAN levels caused by falling growth rates and small levels concentra-of mortality vents growth reduction from exceeding 100 percent as long as acute UAN shocks

pre-do not occur

BOD Feedback Sub-Model

The consumption of oxygen in a recirculating system, or BOD, arises from threesources; fish respiration, oxidation of ammonia compounds by autotrophic bac-teria, and the decomposition of organic solids by heterotrophic bacteria(Wheaton Hochheimer and Kaiser 1991) The BOD generated by fish respiration

is usually determined by the sum of the oxygen required for active and standardmetabolism Using data in Watten, Colt, and Boyd (1992), total respiratory BODfor tilapia can be expressed as

BODf, = 0.0043 - Dit) • W{tr^^ (I8)

where BODf, is grams of oxygen consumed/liter/day.

Additional oxygen demand can be linked to the nitrifying autotrophic bacteriathat colonize available substrate within a recirculating system Due to its highspecific surface area, most nitrification occurs within the biological filter Nitri-fying bacteria require approximately 4.65 grams of oxygen for every gram of TANoxidized (Wheaton 1977), or in terms of unionized ammonia, approximately 0.062

** Tilapia are generally considered more tolerant than channel catfish of poor water tions, both in terms of potential mortality and growth effects Thus, use of catfish data forunavailable tilapia information yields impacts of varying management ability that are biasedtowards the theoretical upper bounds

condi-198 R F Kazmierczak and R H Cajfey

grams of oxygen for every milligram of UAN Combining this information withequation (14) yields the relationship

BODn, = 0.00465 • CP • D{t) • drtdt (19)

where BODn, is in grams of oxygen consumed/liter/day.

The residual portion of BOD is associated with the oxygen demanded byheterotrophic bacteria that break down organic solids Malone and Drennan(1994) developed expressions for oxygen consumed during filtration in experimen-tal systems Their studies suggest that BODr can range from one to four times thelevel of BODn depending on the solids removal efficiency (SRE) of a mechanicalfilter Using this relationship and equation (19) yields

BODr, = (0.00465 • CP • D{t) • drldt)ISRE (20)

where BODr, is in grams of oxygen consumed/liter/day and 0.25 ^ SRE ^ 1.0.

SRE is used in the model to represent the varying ability of producers to tively manage the available mechanical filter technology

effec-The sum of equations (18)-(20) represent the daily per liter oxygen demand inthe modeled system In terms of validation, Colt and Orwicz (1991) developed a

2 3 4 5 6

UAN Concenlration (mgfl)

B UANIndui •dGrMrthRadiK Uon

0 2 0.4 0.6 UAN ConcentfatKm (mg/1)

0.8

Figure 4 Unionized Ammonia Nitrogen (UAN) Induced Mortalily (Panel A) and Growth

Reduction (Panel B) Feedback Effects Used in the Bioenergetic Model