A bioeconomic model of shrimp maricultural systems in the U.S.A.

Ecological Modelling, 25 (1984) 47-68 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

47

A BIOECONOMIC M O D E L OF S H R I M P MARICULTURAL S Y S T E M S IN THE U.S.A.

W.L. G R I F F I N l, W.E. GRANT 2, R.W. BRICK 3 and J.S. HANSON 4

i Department of Agricultural Economics, and e Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843 (U.S.A.) s The Oceanic Institute, Makapuu Point, Waimanolo, HI 96895 (U.S.A.) 4 165 North Old Orchard, Lewisville, TX 75067 (U.S.A.) (Accepted for publication 21 June 1984)

ABSTRACT Griffin, W.L., Grant, W.E., Brick, R.W. and Hanson, J.S., 1984. A bioeconomic model of shrimp maricultural systems in the U.S.A. Ecol. Modelling, 25: 47-68. A general conceptual model of a marine shrimp farming system representing important relationships between the engineering design of facilities, the environmental and managerial factors affecting shrimp growth and survival, and the factors affecting production costs and profit is presented. Based upon this conceptual model, a bioeconomic simulation model is developed to assess the economic feasibility of a projected penaeid shrimp maricultural operation along the Texas coast, and to evaluate the effects of changes in an important managerial variable rate of water flow, on the biological and economic productivity of the system. The conceptual model consists of five interconnected parts including environmental, production, engineering, marketing, and profit submodels. The bioeconomic simulation model is coded in FORTRAN to simulate system behavior with a daily time step on a digital computer. Results of simulations of a projected penaeid shrimp maricuttural operation along the Texas coast suggest that such an operation would be marginally economically feasible when based upon the particular assumptions of this study. Baseline simulations predict a mean annual profit of US $275/acre (1 acre = 0.4 ha) with a standard deviation of US $122/acre, which represents a 2% chance of economic loss. The predicted annual return on investment is 4.5%. The role of modeling in development of shrimp maricultural systems in the Unites States is discussed.

INTRODUCTION

Culture of marine shrimp (Penaeus spp.) has received considerable attention in Asia, Latin America and the United States as an alternative to

48

fisheries as a source of this most valuable of all seafood commodities (Bardach et al., 1972; Hanson and Goodwin, 1977; Hirasawa and Walford, 1979). Demand for all forms of shrimp is great, resulting in relatively high prices even near traditional sources, for example, U.S. South Atlantic and Gulf Coasts (USDC, 1982; U.S. Nat. Mar. Fish. Serv., 1982). Shrimp farming has long been promoted along the Texas coast because of generally favorable climate, abundant land and water, and proximity to relatively large markets (Parker, 1972; Parker and Holcomb, 1973; Hysmith and Colura, 1976). Though certain legal and institutional constraints exist (McGlew and Brown, 1979). these have not been insurmountable (J.C. Parker, personal communication, 1982). In spite of these and other favorable conditions, economically-feasible, commercial culture of marine shrimp has not been achieved in the United States. To date, only in certain tropical countries with natural populations of marine shrimp, abundant coastal areas suitable for construction and operation of ponds and year-round growing season has shrimp farming been profitable--and not always even then (Hanson and Goodwin, 1977; Pillay, 1979). Japan and Taiwan, in the temperate zone are notable exceptions to this generality, with shrimp farming being supported by very high market prices (Shigueno, 1975; Liao, 1977; Hirasawa and Walford, 1979). Commercial shrimp farming, as generally proposed for the United States, is based upon a relatively high technology involving control of reproduction of marketable products in ponds or raceways (Hanson and Goodwin, 1977; Adams et al., 1980; Griffin et al., 1981). A large number of research areas exist which could provide valuable information in support of commerical shrimp culture in the United States. Such areas include engineering design, environmental management, marketing analysis, and overall operation management. This paper presents a general conceptual model of a shrimp maricultural system representing important relationships within and among these various research areas. It also develops a bioeconomic simulation model to assess economic feasibility of a projected penaeid shrimp maricultural operation along the Texas coast. Use of the simulation model is demonstrated by evaluating the effects of changes in an important managerial variable rate of water flow, on biological and economic productivity of the system. CONCEPTUAL MODEL

A model of an aquacultural operation must incorporate information from several different disciplines including ecology, biology, engineering, and economics if it is to accurately reflect the reality of a practicing shrimp farm. The conceptual model developed for this study consists of the interconnected

49

submodels presented in Fig. 1. Those relationships indicated by a solid line have been incorporated into the simulation model that will be described in the next section of this paper. Those relationships indicated by a dashed line, although important conceptually, are beyond the scope of the present study and have not been represented explicitly in the simulation model. The environmental submodel represents different physical and biotic factors that affect shrimp growth either directly or indirectly. These factors include climate, weather patterns, dissolved chemicals in the water, water flow characteristics, and metabolic processes of plants and decomposers. The environmental submodel included in the simulation model represents three water quality parameters: temperature, salinity, and dissolved oxygen. Temperature and salinity are functions of geographical location and weather patterns. Dissolved oxygen is determined according to conditions within the body of water, in this case as a function of wind, water flow, photosynthesis, plant respiration, decomposition, salinity and temperature. .

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ENVIRONMENTALSUBMODEL

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:

!

..~~i

oflFeo,,°g , i __,__'r

i [~

Rate

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Production

•'i.... [

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: PRODUCTIONSUBMODEL

i

4 - - - - -

........ .I ................ -

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ENGINEERING ,, . . . . . . . . . . . . . . . .

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PROFITSUBMODEL

°=,°°, . . . . . • . . . . . . . . . . . .

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Fig. 1. Conceptual model of a shrimp mariculture system.

MARKETINGSUBMODEL;

°° . . . . . • . . . . . . . . . . . . . . . . . . . . . .

50 The production submodel represents growth of the entire population of shrimp. It includes the number of shrimp surviving as well as the growth in weight of individual shrimp. Although stocking density is a potentially important factor affecting survival rate and individual growth of shrimp, the relationships between stocking density, survival rate, and individual shrimp growth are now known. Output from the production submodel includes the total shrimp biomass in the system and the size of individual shrimp at any point in time. The engineering submodel is concerned primarily with size and design of the facility. Depending partially on these two factors, capital and operational expenditures are determined. In the simulation model, size of the facility directly determines specifications of equipment such as pumps, tractors, and trucks, and indirectly determines the volume of water flowing through the system. The marketing submodel determines the price of shrimp from demand and supply at the time of harvest. Shrimp supply is affected by fishery landings both inside and outside of the United States and by the amount of farm-raised shrimp harvested. Demand for shrimp is determined from the price of substitute goods, lobster and crab for example, and by consumer income within a given area. The marketing submodel is not developed in the present study. In the simulation model price is assumed to be fixed for the shrimp farmer depending upon the size of individual shrimp (number of tails per pound) and the harvest date. The profit submodel calculates annual profit or loss from the mariculture operation based on annual revenue and costs. Annual revenue is determined from the shrimp biomass and price by the production and marketing submodels, respectively. Annual costs are determined directly from the environmental submodel through maintenance of appropriate levels of dissolved oxygen, from the production submodel by feeding costs required for shrimp growth, and from the engineering submodel through the costs associated with water flow-rates, use of equipment, and maintenance of levees. SIMULATION MODEL DEVELOPMENT Based on the general conceptual framework presented above (Fig. 1), a simulation model designed to evaluate the effects of changes in management and environemental variables on the biological and economic productivity of a shrimp mariculture system is described below. The model was coded in F O R T R A N to simulate system behavior with a daily time step on a digital computer.

51

Environmental submodel Although most species of shrimp are relatively euryhaline and eurythermal, salinity, temperature and oxygen levels can greatly influence shrimp growth (Zein-Eldin and Griffith, 1969; Venkataramaiah et al., 1972; Stickney, 1979), and we have represented these three water quality parameters explicity in the model. Equations representing seasonal dynamics of these three factors are based on data from the Gulf coast of south Texas.

Salinity. Along the Texas coast, salinity varies from seasonal lows of 7 ppt a in some areas to seasonal highs of 50 ppt in other areas. In the model, salinity can fluctuate randomly between 15 and 32 ppt. It was assumed that salinity normally was at a level of 30-32 ppt, but had a random chance to decrease. This was accomplished by generating a random number between 0 and 1 that determined a day after the start of production season in which salinity would begin to decrease. Thus, a production season begins with salinity levels of 30-32 ppt, after which the model randomly determines on a day-to-day basis if the level decreases. If the salinity declines, it declines according to an equation that was estimated by fitting a linear regression to a typical decrease in salinity from approximately 30 ppt in mid-May to 15 ppt in mid-July that was observed along the Texas coast: salinity = 68 - 0.2(day of year)

(1)

Once salinity has begun to decrease, the model may randomly select for salinity to increase at a rate of 1 p p t / d a y up to the normal level. It is assumed that only one major decrease in salinity will occur per production season.

Temperature. Water temperature is much more predictable along the Texas coast than is salinity. During the growing season temperatures rise from early May (21 23°C) to late June or mid-July (29-31°C), remain stable through mid to late August, and decline through late October (18 21°C). In the model, temperatures increase linearly from the time that shrimp are stocked (early May) to a temperature of 28.5 °C in late June: temperature (o C) = 8.159 + 0.1159(day of year)

(2)

This temperature continues until the middle of August, at which point temperatures decrease linearly to 26 °C in early September: temperature (°C) = 111.18 - 0.3214(day of year) a ppt, parts per thousand. ppm, parts per million.

(3)

52 These equations were based on data from Angleton, TX. Linear regression gave a n R 2 of 0.82. The stocking and harvesting dates in this model were represented as functions of temperature; that is, the production season was allowed to occur only within those days in which temperature was above 18 ° C. Normal distributions of the dates of first and last occurrence of 18°C temperatures were generated using data from the Angleton area over the period 1968-1978. Dates of stocking and harvesting in the model were chosen randomly from these distributions.

Oxygen.

Dissolved oxygen in ppm was determined by using a modification of a model developed by Cassinelli et al. (1978). Sources of oxygen include photosynthesis, wind and external water flowing into the ponds. Oxygen is removed by decomposition, shrimp respiration and phytoplanktonic respiration: O2 (ppm) = OpH o q-- OWIND --t--OTURN -- ODEC -- OCRES -- OpRES

(4)

where Opn o is the oxygen input by photosynthesis, OWIND is the oxygen input from the air, OTURN is the oxygen input from inflowing water, ODEc is the removal of oxygen due to decomposition, OCRES is oxygen removal due to shrimp respiration, and OFRES is oxygen removal due to phytoplanktonic respiration (Cassinelli et al., 1978). Rate of photosynthesis was represented as a function of temperature and light intensity. The oxygen input by photosynthesis was represented by: OpH O =

F(t) × P

× 6.9434

(5)

where F(t) is the temperature-dependence factor, P is the photosynthetic rate and 6.9434 represents the number of grams of oxygen produced for every gram of carbon assimulated (Redfield, 1958). Temperature-dependence was estimated empirically by Park (1974): F ( t ) = vX e X('-o'

(6)

where o =

(Tma x -

r)/(Zma

x = W2(1 + ¢1 +

x -

Vopt)

40W)2/400

and W = ( l n Q,0l(rma× - ropt) F r o m these equations F ( t ) is the temperature-dependence factor for the time period t, T is the temperature (K), Tmax is the upper lethal temperature limit for phytoplankton, Topt is the temperature at which the maximum photosyn-

53

thetic rate occurs, and Q10 is the factor by which this process increases with a 1 0 ° C increase in temperature (Park, 1974). If T > Top', F(t) = 1. The light intensity dependence was estimated by Steele (1962): = P m e_ {1--(1 + 2 a I ) e

2al

2~1}

(7)

where P is the average photosynthetic rate, Pm is the m a x i m u m photosynthetic rate, ] is the average light intensity, and a is a constant determining the initial slope of a curve from plotting photosynthetic rate (as P/Pm) versus light intensity (Kester, 1975). Cassinelli et al. (1978) integrated this equation over the depth of the p o n d according to Beer's law (Cole, 1975): I z = I 0 e -*:z

(8)

where 1z is the light intensity at a point in the water column, I 0 is the light intensity at the surface, K is the absorption coefficient, and z is the depth. Integrating over the depth of the p o n d the photosynthetic rate equation becomes: p = KPmexp [/opt I°

exp

{ [ -- I0/Iopt] [exp( -- Kz)

-exp(-l/Iopt)]} ]

(9)

where P is the photosynthetic rate over the water column of the p o n d and /opt is the light intensity which gives the m a x i m u m photosynthetic r a t e . / o p t is assumed to 75% of the m a x i m u m intensity (with a 30-day lag). This causes /opt to vary between approximately 200 and 300 kcal b m - 2 h - I which gives conservative estimates for photosynthesis (Van Den Avyle, 1977). The maxim u m intensity is calculated as follows: /
(10)

where I w and I S are the intensities at winter and summer solstice, respectively (Lehman et al., 1975). This equation gives a m i n i m u m intensity at winter solstice and a m a x i m u m at summer solstice (Cassinelli et al., 1978). Light intensity through the day was predicted as: I0 = C(0.5)I0

....

{1 + cos(2"rrt)}

(11)

where C is the percent of light transmitted through clouds, t is a characteristic time of day calculated by dividing the hours from sunrise by the n u m b e r of hours of sunlight during the day and 0.5 is a constant (Vollenweider, 1965). The absorption coefficient, K is determined by the absorption due to pure water, turbidity, and dissolved substances within the water (Cole, 1975). In b cal, calorie -- 4.2 J.

54 this model, K was a function of the phytoplankton plus the particulate matter in the water (Van Den Avyle, 1977). Bannister (1974) considered the relation of phytoplankton to K to be a proposition of the concentration of chlorophyll-a. The relation of particulate matter to K was expressed as a function of water turbidity and the day of the year (Van Den Avyle, 1977) as:

E w = 0.064 ( 50 + 30(cos( v (day of year - 60) / 180) ) }

(12)

The final variable in calculating the photosynthetic rate was the depth of the pond, z. In this model, the average depth was 0.80 m. Oxygen produced by photosynthesis was predicted as a function of the level of chlorophyll-a, the maximum rate of carbon uptake, the light intensity at which the maximum rate occurs, and the percent of sunlight coming through the clouds. The level of chlorophyll-a was assumed to be 0.035 mg/1 because at this level, oxygen variation closely resembled that of actual data. The results of Van Den Avyle (1977) showed variation in chlorophyli-a around approximately this median level. After the production season began, the concentration of chlorophyll-a was constant except for fluctuations due to exchange with external water, which was assumed to have a concentration of 0.0236 mg/1 (E. Cox, Texas A & M University, personal communication, 1979). The maximum rate of carbon uptake was assumed to be representative of a variety of different phytoplankters and estimated to be 0.15 g carbon assimilated per h for every mg of phytocarbon (Van Den Avyle, 1977). The optimum light intensity for photosynthesis was assumed to be 75% of the light intensity at noon. The percent of sunlight coming through the clouds was assumed to be a random variable throughout the production season. The second source of oxygen input is the atmosphere, primarily due to wind. Kester (1975) presented an equation to represent the rate of gas exchange as: 0WIND = Ae~

(Pa--&) Kc

(13)

where A is the surface area of the pond, eG is the exchange velocity, Pa is the partial pressure of oxygen in the air, Pw is the partial pressure of oxygen in water, and K G is Henry's law constant for oxygen. Cassinelli et al. (1978) represented e G as a function of wind velocity: eG = 1.235 (exp[0.115(wind velocity] }/1000

(14)

In this relationship, wind velocity ( m / s ) is the meteorological standard at a height of 10 m. The partial pressure of oxygen in the water was represented by: Pw = M N T (15)

55 where M is the concentration of oxygen (mM/1), T is the temperature (K), and N is a conversion factor to express Pw (in atmosphere). The third source of oxygen is the rate of water flow through the ponds. In this model, the manager specifies the minimum level of oxygen desired; if the water in the pond decreases below that level, the flow is increased to obtain a more favorable oxygen concentration. The equation relating oxygen input to inflow is expressed as a function of the percent of water turnover per h: OTUR = turnover rate(ci~ - Cout)

(16)

where Ci, is the oxygen concentration of inflowing water and Co, ~ is the oxygen concentration of the outflowing water (Cassinelli et al., 1978). It is assumed that the external water source is at saturation concentration for the existing conditions, normally in the range of 6-7 ppm. In the model, decomposition reduces 02 concentration in the pond at a rate of 1.24 g oxygen per g carbon decomposed (Redfield, 1958): 0DEc = (mass decomposing)(1.24 g O : / g mass decomposed)

(17)

The mass decomposing in this model was 30% of the feed given to the shrimp, which was assumed uneaten (Cassinelli et al., 1978). It was arbitrarily assumed that, because of the mortality of phytoplankters, the rate of decomposition varied with the amount of chlorophyll-a present. If the chlorophyll-a concentration is less than 0.03 mg/1, the decomposition rate is 0.1 x 10 7% of food not eaten decomposing 1 i h - l . If the chlorophyll-a concentration is greater than 0.03 rag/l, the decomposition rate varies with the amount of cholorophyll-a present according to the linear equation: decomposition rate = 0.28 × 10 -8 + (0.4255 X ]0-6)m

(18)

where m is the concentration of chlorophyll-a (mg/1). Oxygen also is reduced in the pond by shrimp respiration. This model represents respiration as a function of weight: l o g OCRES =

a I + a 2 log w

(19)

where a 1 and a a are constants which are species-dependent and w is the weight of the shrimp (Alcaraz, 1974). This log value is then combined with the number of shrimp per 1 to give the change in oxygen due to the respiration by: 0CRES = n (10'°g o,,E~ )(4.464 × 10-14)

(20)

where n is the number of shrimp per 1. The density of shrimp was assumed to be uniform throughout the pond.

56 The survival rate of the shrimp was assumed to decrease according to the linear function: survival = 1 - 0.0022(day of year - 111)

(21)

Due to lack of knowledge of survival rates, various assumptions were made. It was assumed that survival would be a linear function from time of stocking to harvesting. In estimating this linear function it was assumed that at harvest the survival would be approximately 60% of the shrimp stocked. The amount of shrimp stocked was established in the model at 40000 individuals per acre c in accordance with current practices. As the production season continues, survival rate and, thus, the number of shrimp, fall according to eq. (21). At harvest, the number of shrimp in the ponds is determined according to this equation and all shrimp are assumed to be harvested. The final factor affecting level of oxygen in this model is loss of oxygen due to phytoplankton respiration. The method used to estimate this respiration was that developed by Van Den Avyle (1977) in which phytoplankton respiration is a proportion of the maximum respiration rate and is dependent upon temperature: CERES = (Rmax) X F ( t ) × m/0.0114

(22)

where F ( t ) is defined in eq. (6), the constant 0.0114 represents a conversion of chlorophyll-a to phytoplankton (Bannister, 1974), Rmax is the maximum total respiration rate (assumed to be 0.03 mg of carbon per mg phytoplankton per h; Lehman et al., 1975), and m is the concentration of chlorophyll-a. The Ql0 for phytoplankton respiration was assumed to be 2 (Cassinelli et al., 1978). Cp~ES, when multiplied by the number of moles of oxygen per milligram of carbon respired, gives 0pRES. Production submodel Growth of individuals.-- In this study, shrimp at 0.01 g were stocked directly into growout ponds, i.e., without being first reared in nursery ponds. Two types of ponds are represented, those that experience an oxygen-depletion and those that do not. This study models growth of P. vannamei because recent data are available from mariculture ponds along the Texas coast concerning this species. In developing the model, however, it is necessary to assume that research involving other penaeids applies generally to P. vannamei. Wendorf (1979) represented shrimp growth by incorporating the levels of c acre

= 0.4

ha.

57 different water quality parameters into a Von Bertalanffy equation developed by Ursin (1963). Following Wendorf (1979), three water quality parameters will be utilized in this growth model: temperature, salinity, and dissolved oxygen. The basic Von Bertalanffy equation may be written as: w = W~(1 - b e - k ' ) 3

(23)

where w is the weight of the animal (g), W~ is the asymptotic weight (g), k is an indication of the proportional growth of the animal, t is the "physiological age" of the animal, and b is a factor relating to the size of the animal at birth (Fabens, 1965). The modifications of the growth equation are in the parameters t and b, which will be discussed later. Twenty grams were used for W~ in this study. In the model, k is calculated using a computerized method by Fabens (1965). The partial derivative of eq. (23) is simplified to: ~ w / ~ k = F( k ) = dipir, ( ripi - si) = 0

(24)

where di is the time interval between lengths of an individual at different time periods, p, is substituted for the term e -kd,, rg is the difference between asymptotic size and the size of the animal at time period 1, and si is the difference between the asymptotic size and the size of the animal at time period 2. The function is solved in an iterative manner using the Newton Raphson method. Using 1972 data from the Angleton ponds, k for P. vannamei was estimated to be 0.0296. The parameter t in the modification of Von Bertalanffy's equation is the "physiological age" of the animal. It is an estimation of the number of days that the animal has been actually growing based on environmental conditions. By multiplying the actual number of days in a time interval by a ratio determined by dividing average level of some water quality factor over the time interval by level of the water quality factor that permits maximum growth, t is calculated. The levels of temperature, salinity, and oxygen at which maximum growth occurs are assumed to be 2 5 - 3 0 ° C , 24-30 ppt, 5.5 ppm, respectively (Hanson and Goodwin, 1977). If more than one of these water quality parameters differs from the optimal level, the value of t is determined by calculating t separately for each parameter and taking an average. The shrimp, therefore, may be growing in an optimal environment of temperature, salinity, and oxygen or in an environment where any of these parameters are less than optimal. The parameter b was estimated as in Fabens (1965): b-

pi(a-

xi)

(25)

58

where Pi is the same as in eq. (24) and x i is the weight of the animal in the previous time period. Using 1972 data from the Angleton ponds, b for P. vannamei was estimated to be 2.5729. As used here, b is not related to the size of the animal as Fabens (1965) suggests. To determine the growth of an individual shrimp, the modified Von Bertalanffy equation was used with the values of k, b, and asymptotic weight estimated from Angleton pond data. The initial weight of shrimp was 0.01 g. The model determines the value of t from the levels of temperature, salinity, and dissolved oxygen each day of the simulation. Each day the weight of the shrimp is determined according to eq. (23) on the basis of the environmental parameters mentioned above.

Calculation of the yield--To obtain total biomass produced from each pond, the number of shrimp surviving at the end of the growing season was multiplied by average weight of the individual shrimp. It was assumed that shrimp grow in two types of ponds; those with limiting oxygen and those with the oxygen level within optimal range. The number of ponds experiencing lower than optimal oxygen conditions were determined randomly. As many as 60% of the ponds were allowed to experience oxygen shortage. The biomass of shrimp from the two types of ponds was added to give the total biomass of the shrimp farm system. Marketing, engineering, and profit submodels Determination of price.

Temperature limits the growing season of shrimp in the United States to a maximum of 5-7 months. Generally, shrimp prices for all size classes are lower during the early production months and higher during the ending months (U.S. Nat. Mar. Fish. Serv., 1978, 1979, 1982). For this study, 1978 prices were used to determine revenue in a partial budgeting framework. Interactions between supply and demand were, therefore, ignored. In this model, a base price was determined by using the size-class containing 36-40 shrimp tails per lb d. The price for this size-class was averaged over the entire production season to derive a base price of $2.68/lb. A weekly price of each size-class was assigned a coefficient depending upon its percentage of the base price. Each size-class was then divided according to the ranges of the newly-assigned price coefficients. The coefficients were not allowed to exceed ranges of 0.15 before a division was made. The coefficients were then averaged for each division. The final price of shrimp was determined, according to the particular size-class of shrimp and the time of year, by multiplying the base price by the appropriate price coefficient. d lb, p o u n d (US) = 0.454 kg.

59

Since experimental farm-raised shrimp in Texas have yet to reach a large size in one production season, the size-classes used were 36-40, 40-50, 50-60 and 60-70 tails per lb. Calculation of reoenue. The number of pounds of each size-class of shrimp was multiplied by the appropriate price to determine revenue. The weight of the shrimp tail was taken to be 65% of the total weight of the shrimp. Therefore,the total biomass of shrimp tails multiplied by the current price per lb calculated the toal revenue. Determination of facility size and calculation of costs. In order to determine the annual costs, the system size and design must be known. The annual costs involved in this study included: postlarval shrimp, lubricant for pumps, p u m p repairs, pump fuel, fertilizer, feed, truck and tractor operation, utilities, ice, labor, interest, taxes, insurance, and depreciation. The facility in the present analysis consists of 22 6-acre ponds. Each pond receives new water and releases used water with no recycling. These features are representative of maricultural operations along the Texas coast today. The source of postlarval shrimp utilized in this model is from production and rearing of young shrimp within the operation. Cost of producing postlarval shrimp has been estimated as $2.50 per 1000 post-larvae (Adams et al., 1980). The amount of lubricant (grease and oil) required to maintain pumps (for the water flow in keeping oxygen at proper levels) was determined from equations used by Kletke et al. (1978). The following equation was used to estimated the amount of oil needed for the motor: oil = (LMULT)(WHP)(HOURS)($LUB)

(26)

where L M U L T is a multiplier in gallons of oil used for every water horsepower hour, WHP is the water horsepower of the motor used, HOURS is the number of hours used for pumping, and $LUB is the price of a gallon e of oil. The values used for the different factors of the equation were 0.0015 for L M U L T using a diesel engine (Kletke et al., 1978), $2.00 for a gallon of oil, and WHP and HOURS were determined from the flow of water required by the model. The cost of grease for the pumps was assumed to be 2 cents for every hour of pump use. Pump and pump motor repair cost were also calculated from equations given by Kletke et al. (1978). The repairs for the pump were determined from: p u m p repair cost

(0.5)($PUMP)(HOURS) 30 000

gal, gallon ( U S ) ~ 3.785 I.

(27)

60

where $ P U M P is the investment in the pump, H O U R S is the number of hours spent pumping, and 30 000 is expected life of the pump in hours. The repairs for the pump motor were determined from: motor repair cost = ( M M U L T ) ( H O U R S ) ( A M T R $ )

(28)

were M M U L T is the multiplier representing the cost of repairs per hour per dollar of engine purchase price and A M T R $ is the engine purchase price. In this model the investment in each pump was $1800 which is an approximate cost of a relatively small pump for pumping water from a well less than 20 ft f deep. Each motor cost was assumed to be $3750 which was the cost of a 75 horsepower g diesel engine in 1978. M M U L T was given by Kletke et al. (1978) as 0.0001 repairs per h per dollar of engine cost for a diesel engine. The major cost of pumping and, thus, the major cost of maintaining oxygen levels is the cost of the pump fuel. The method used by Adams et al. (1980) was used to determine the number of gallons of fuel needed for the operation: WHP = (GPM)(HEAD)/3960

(29)

amount of fuel = ( W H P ) ( 2 6 4 7 ) / ( P E ) ( E E ) ( B T U )

(30)

G P M represents the number of gallons of water to be p u m p e d per min, H E A D is the distance the water must be lifted vertically, W H P is the water horsepower, PE and EE represent the pump and engine efficiencies, respectively, and BTU is the number of BTU h in 1 gal of diesel fuel. G P M was determined by the model, H E A D was assumed to be 20 ft, PE and EE were both 75% (Kletke et al., 1978) and BTU was 136000. Pump costs, W H P , and H O U R S were determined by the model from the pumping requirements to maintain desired oxygen levels. As the oxygen level goes below the desired level specified by the manager, the model calculates the amount of new water needed within the hour to bring oxygen back to the specified level; that is, the pump is turned on. Once the number of gallons of water flowing through the system in 1 h is determined, g a l / m i n can be found to calculate W H P (eq. (26)). After the pump was turned on, it was assumed to run continuously at the speed set in the 1st hour for 24 h. H O U R S was then determined by keeping a running total of the number of hours each pump was run. In a system of this size, more than one pump is required to maintain oxygen at a specified level. It was assumed that each pump could not pump more than 3000 gal/min. The number of pumps being utilized over a given f ft, f o o t = 3 0 . 4 8 c m . g metric horsepower h BTU,

= 735.499 W.

British thermal

u n i t = 1 0 5 5 . 0 6 J.

61

24 h period was specified by dividing total number of gallons needed per minute by maximum g a l / m i n per pump. It was assumed in this model that ten pounds of urea and super-phosphate fertilizer were added to each acre of water prior to stocking. Another application of the same magnitude was added after the shrimp had been in the ponds for 2 weeks. The fertilizers added were assumed to cost 8 cents/lb. Marine shrimp require substantial amounts of protein (New, (1976; Colvin and Brand, 1977), and feed cost is one of the major costs of production. Amount of feed usually is determined as a percentage of total weight of shrimp estimated to be in the pond (Stickney, 1979). For this model, postlarval shrimp less than 2 g in size were fed 10% of the pond shrimp biomass per day, shrimp between 2 and 5 g were fed 7%, those greater than 10 g were fed 3% (Adams, 1978). The price of feed was assumed to be 17 cents/lb. In this model, the number of pick-up trucks used in the operation was based rather loosely on information from the Texas coast and was dependent upon the size of the system: number of trucks = 0.766 + (0.0195)(surface acres)

(31)

Cost of the average truck operation was determined from the gas cost plus the costs of maintenance (oil, grease, washing). The average truck was assumed to travel 1000 m i l e s / m o n t h ~ at 12 miles/gal with gas priced at 65 cents/gal. The costs of maintenance were assumed to be $ 2 0 / m o n t h for the average truck. Tractor usage on the shrimp farm centers around everyday chores. One tractor for every 40 surface acres of water was assumed to be the number of tractors used in the system. It was also assumed that a combination tractor and feedblower would utilize 240 gal of fuel and $10 of oil and maintenance per month. Three utility costs were represented in the model; telephone, electricity, and water. It was assumed that monthly telephone costs were $ 8 / m o n t h plus long distance charges of $20/month. During September the long distance telephone costs were increased to $50 due to increased effort for marketing an October harvest. It was assumed in this model that only a small electrical input was needed to maintain office and hatchery operations. Fifty kilowatt-hours occurred per day and charged at a rate of 4 cents per kWh. The water cost was assumed to be $ 2 0 / m o n t h . Ice is used primarily at harvesting to cool the shrimp and prevent bacterial decay of the meat and spotting of the shell. The weight of ice used in the

i mile ~ 1609 m.

62 model annually was equal to the predicted shrimp biomass at harvest, with the price per pound being 3 cents. The number of hired laborers was determined by size of the system; one man for every 30 acres. Each man was assumed to put in an 8-h day at a rate of $4.00/h. At the time of harvest, one man for every 20 acres of ponds was hired at a rate of $3.00/h for 6 days at 8 h / d a y . The owner-manager receiver a minimum salary of $16 0 0 0 / y e a r plus $70 for every acre of pond in production. This relationship was estimated to give a competitive salary as compared to owner-managers of other small businesses in the area. There are two types of loans involved in this model, both of which contribute to annual costs. One type involves the financing of long-term capital investments, the other involves financing short-term operating loans to be paid during the year. The long-term loan in this model is used for the purchase of equipment and buildings such as tractors, trucks, and hatchery facilities. The value of the long-term loan was estimated as a function of the size of the system, approximately $1000/acre. This value was arbitrarily chosen and thought to be a reasonable assumption considering the purchase involved. The annual payment was calculated as: A =

V

1 -(1 +

i)-l/i

(32)

where A is the annual payment, V is the loan value, i is the interest rate on the loan, and t is the number of years on the loan (Hopkin et al., 1973). Interest rate was assumed to be 9% and number of years to pay out the loan was 15. The loan was assumed to be equally ammortized with the payment year being the 3rd year of the loan. The short-term loan was assumed to be under a revolving line of credit in which the borrower could draw funds as long as a specified maximum was not exceeded (Hopkin et al., 1973). The loan was paid when the shrimp had been harvested and sold, usually by November. It was assumed in this model that the cost of feed and pump fuel would be under the revolving line of credit with an interest rate of 9% at the end of the production season. Since the type of shrimp farm being considered in this model is a sole proprietorship, the only taxes involved are real property taxes, social security taxes, and unemployment compensation. Real property taxes in the Angleton area were at a rate of $2.44 for every $100 or 20% of the total value of buildings, equipment, and land. The value of buildings was assumed to be $20000, the amount of land (ponds plus 5 extra acres) was valued at $800/acre and the value of farm machinery was $5550 for each pump and driver, $4000 for each truck, $8000 for each tractor and $5000 for each feedblower. The rate of social security tax was assumed to be 6.05% of each

63 employee's income unless that income was above $17700. The unemployment tax was 0.8% of the first $6000 of each employee's income. Income taxes were not employed in this model because they do not relate to the financial feasibility of the business, but rather to the private business of the sole proprietor. Varying degrees of insurance can be obtained for a mariculture operation. In this model three categories of coverage were assumed; buildings, equipment and employees. Rates for these coverages were those given by Adams et al. (1980). Buildings were insured at an annual rate of 4.5% of the appraised value covering fire, wind, and storm. Equipment was insured at an annual rate of 0.76% of replacement value and included tractors, pump, feedblowers, and trucks. Employee insurance was assumed to be Workman's Compensation and cost the employer $8.17 for every $100 of annual payroll. Depreciation is a noncash expense to the shrimp farm (Hopkin et al., 1973). The method of estimation for depreciation was the straight-line method computed as: D

O C - SV n

(33)

were D is the depreciation per year, OC is the original cost of the equipment or investment, SV is the salvage value at the end of the asset's useful life, and n is the number of years of useful life (Hopkin et al., 1973). The items being depreciated in this model included trucks, feedblowers, tractors, pumps, buildings, and pond levees. USE OF T H E M O D E L

The baseline version of the model, based on the parameter estimates presented in the previous section and representing a facility consisting of 22 6-acre ponds, was used to simulate a shrimp mariculture system along the Texas coast under 'normal' conditions. The model can be used to examine the effect of changes in several management and environmental variables on system productivity in terms of: (1) yield (lb); (2) revenue ($); (3) cost ($); (4) profit ($), and average price per pound ($/lb). Management variables than can be examined include: (1) stocking date; (2) harvest date; and (3) water-flow rate. Environmental variables that can be examined include: (1) water temperature; (2) salinity; and (3) oxygen level. For each situation examined, 25 stochastic simulations can be run. A different set of random numbers would be used to generate the various random variates in each replicate simulation. Each replicate, therefore, is unique in terms of the number of ponds that experienced oxygen depletion, length of the production season, weather conditions, and water quality. To demonstrate the use

64

of the model, a baseline model will be simulated. Then, a management variable, water flow rate, will be varied and results analyzed to demonstrate the usefulness of the model.

Basefine simulation results The 25 replicates of the baseline simulation had an average of seven (a standard deviation of four) ponds per production season experiencing low oxygen. The mean length of the production season was 151 (a standard deviation of 11) days, the mean yield was 927 (a standard deviation of 41) lb/acre, and the mean revenue $1725 (a standard deviation of 149)/acre (Table I). The mean cost was $1450 (a standard deviation of 96)/acre. The mean profit was $275 (a standard deviation of 122)/acre. The highest profit was $554/acre; whereas, the lowest profit was $102/acre.

Effects of changes in a management variable Four levels of water flow were examined. One, 2, 3 and 4% h, respectively, of the pond volume was constantly flowed through those ponds expected to experience low oxygen. Mean profits are reduced and the change of a loss increased as water flow rates are increased (Fig. 2). Although the higher flow rates produced higher revenues, costs increased at a much faster rate, reducing profits (Table I). The larger standard deviations in profit resulted from the higher flow rates producing more variable pumping costs due to

7~/...

"q:,,\

/ /" L,Y i -500

/ -400

-300

"l -200

-100

0

I 100

I 200

I 300

I 400

I 500

600

' 700

' 800

Profit/acre ($)

Fig. 2. Comparison of using different constant hourly water flow rates (1, 2, 3, and 4% of the total pond v o l u m e / h ) on the profit frequency distributions.

65

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66

whether few or many ponds had constant flow and whether there was a shorter or longer growing season.

Role of modeling in development of shrimp maricultural systems in the United States Currently the role of modeling in the development of shrimp maricultural systems in the United States is three-fold. (1) It serves to integrate information from such diverse disciplines as ecology, biology, engineering, and economics into a coherent systems framework. The formality introduced by the development of conceptual models such as presented in Fig. 1, facilitates effective communication between the different disciplines and thus helps to identify key structural and functional linkages between a diversity of system components. (2) The rigor required when quantifying function relationships within specific maricultural systems inevitably leads to identification of key areas where there is insufficient information to model system processes accurately. This helps in setting priorities for future research and also provides information regarding the relative usefulness of the model within a management framework. (3) Models developed to represent specific maricultural systems provide system managers with a means of examining a much larger number of alternative management schemes than possibly could be examined by experimentation with the real system. The current accuracy of such models probably is too low for managers to base final choice of a management scheme solely on simulation results. But accuracy is sufficient to base initial screening of management schemes on simulation results, thus, greatly reducing the number of schemes to be evaluated experimentally in the real system. As more experimental work is done within the framework established by modeling projects and as results of these experiments are incorporated into the models, use of and confidence in models of maricultural systems as an integral part of the manager's decision-making process will increase. ACKNOWLEDGEMENTS

This work is a result of a research program sponsored by the Texas A & M University Sea Grant College Program, supported by the National Oceanic and Atmospheric Administration, Office of Sea Grant, Department of Commerce, under Grant No. NA-81AA-D-00092 with the Texas Agricultural Experiment Station (Technical Article No. 18578).

67 REFERENCES Adams, C.M., 1978. A bio-economic model for penaeid shrimp mariculture systems. M.S. Thesis~ Department of Agricultural Economics, Texas A&M University, College Station, TX, 147 pp. Adams~ C.M., Griffin, W.L., Nichols, J.P. and Brick, R.W., 1980. Application of a bio-economic-engineering model for shrimp mariculture systems. South. J. Agric. Econ., 12 (1): 135-142. Alcaraz, M., 1974. Respiracion en crustaceos: influencia de la concentration de oxigeno en el medio. Invest. Pesq., 38(2): 397-411. Bannister, T.T., 1974. A general theory of steady state phytoplankton growth om a nutrient saturated mixed layer. Limnol Oceanogr., 19:13 30. Bardach, J.E., Ryther, J.H. and McLarney~ W.O., 1972. Aquaculture: The Husbandry of Marine and Freshwater Organisms. Wiley-Interscience, New York, NY, 868 pp. Cassinelli, R.D., Farnsworth, J.T., Sweat, V.E. and Stoner, D.L., 1978. Variations in dissolved oxygen concentration in mariculture p o n d s - - A preliminary model. In: R. Nickelson II (Editor)~ Proc. 3rd Annu. Tropical and Subtropical Fish. Techn. Conf. TAMU-SG-79-101, 23 26 April 1978, New Orleans, LA, pp. 310-330. Cole, G.A., 1975. Textbook of Limnology. Mosby, St. Louis, MO, 283 pp. Colvin~ L.B. and Brand, C.W., 1977. The protein requirement of penaeid shrimp at various life cycle stages in controlled environment systems. Proc. World Maricult. Soc., 8: 821-840. Fabens, A.J., 1965. Properties and fitting of the Von Bertalanffy growth curve. Growth~ 29: 265-289. Fishery Market New Report 0-102, 1978, 1979, 1982. Tri-weekly Report by the National Marine Fisheries Service. U.S. Dep. of Commerce, New Orleans, LA, 6 pp. Griffin, W.L., Hanson, J.S., Brick, R.W. and Johns, M.A., 1981. Bioeconomic modeling with stochastic elements in shrimp culture. J. World Maricult. Soc.~ 12(1): 94-103. Hanson, J.A. and Goodwin H.L.~ 1977. Shrimp and Prawn Farming in the Western Hemisphere. Dowden, Hutchinson and Ross, Stroudsburg~ PA, 439 pp. Hirasawa, Y. and Walford, J.~ 1979. The economics of Kurumaebi (Penaeusjaponicus) shrimp farming. In: T.V.R Pillay and W.A. Dill (Editors), Advances in Aquaculture. Fishing News (Books), Farnham, pp. 288-298. Hopkin, J.A., Barry, P.J. and Baker, C.B. 1973. Financial Management in Agriculture. Interstate, Danville, IL, 529 pp. Hysmith, B.T. and Colura, R.L., 1976. Effect of salinity on growth and survival of penaeid shrimp in ponds. Proc. World Maricult. Soc., 7: 289-304. Kester, D.R., 1975. Dissolved gases other than CO 2. Chem. Oceanogr.~ 2: 497-589. Kletke, D.D., Harris, T.R. and Mapp~ H.P. Jr., 1978. Irrigation Cost Program Users Reference Manual Oklahoma State University. Res. Rep., Agriculture Experiment Station, Oklahoma State Univ., Stillwater, OK, 790 pp. Lehman, J.T., Botkin, D.B. and Likens, G.E., 1975. The assumptions and rationales of a computer model of phytoplankton population dynamics. Limnol. Oceanogr., 20: 343-364. Liao, I.C., 1977. A culture study on grass prawn, Penaeus monodon in Taiwan. J. Fish. Soc. Taiwan, 5(2): 143-161. McGlew, P.A. and Brown, D.E.~ 1979. Legal and institutional factors affecting mariculture in Texas. Coastal Zone Manage. J., 6(1): 69-88. New~ M.B., 1976. A review of dietary studies with shrimp and prawns. Aquacuhure~ 9: 101 144.

68 Park, R.A., 1974. A generalized model for simulating lake ecosystems. Simulation, 23(2): 33-50. Parker, J.C., 1972. Commercial shrimp farming nearing reality. Tex. Agric. Prog. 18(3): 13 16. Parker, J.C. and Holcomb, H.W., 1973. Growth and production of brown and white shrimp (Penaeus aztecus and P. setiferus) from experimental ponds in Brazoria y Orange Counties, Texas. Proc. World Maricult. Soc., 4: 215-234. Pillay, T.V.R., 1979. The state of aquaculture, 1976. In: T.V.R. Pillay and W.A. Dill (Editors), Advances in Aquaculture. Fishing News (Books), Farnham, pp. 1-10. Redfield, A.C., 1958. The biological control of chemical factors in the environment. Am. Sci., 46: 205. Shigueno, K., 1975. Shrimp culture in Japan. Association for International Technical Promotion, Tokyo, 153 pp. Steele, J.H., 1962. Environmental control of photosynthesis in the sea. Limnol. Oceanogr., 7: 135-150. Stickney, R.R., 1979. Principles of Warmwater Aquaculture. John Wiley, New York, 375 pp. U.S.D.C., 1982. Fisheries of United States, Current Fishery Statistics No. 8200. NOAA, NMFS, U.S. Dep. Commerce, Washington, DC, 117 pp. Ursin, E., 1963. On the incorporation of temperature in the Von Bertalanffy growth equation. Denmarks Fish. Harrinder-Sogelser, 4(1): 1-16. Van Den Avyle, M.J., 1977. A modeling analysis of lake ecosystems responses to inorganic fertilization. Ph.D. Diss., Texas A&M University, College Station, TX, 209 pp. Venkataramaiah, A., Lakshmi, G.J. and Gunter, G., 1972. The effects of salinity, temperature and feeding levels on food conversion, growth and survival of Penaeus aztecus. In: Proc. Food-Drugs from the Sea. Marine Technology Society, Washington, DC, pp. 29-42. Vollenweider, R.A., 1965. Calculation models of photosynthesis-depth curves and some implications regarding day rate estimate in primary measurements. Primary productivity in aquatic environments. In: C.R. Goldman (Editor) Mem. 1st Ital. Idiobiol., p. 18. Wendorf, S.B., 1979. Influence of hydrobiological parameters on growth of Penaeus oannamei (Boone) in earthen ponds. M.S. Thesis, Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX, 125 pp. Zein-Eldin, Z.P. and Griffith, G.W. 2969. An appraisal of the effects of salinity and temperature upon growth and survival of post-larval penaeids. FAO Fish. Rep., 57(37): 1015-1026.