Illlllllill}ll‘llllllllllflu ' 3 1293 00655 2818 LIBRARY Michigan State University This is to certify that the dissertation entitled GROWTH AND PRODUCTION CONTROL OF GOLDEN SHINER NOTEMIGONUS CRYSOLEUCAS (MITCHILL) BY MANIPULATING TEMPERATURE AND DENSITY presented by Sha Miao has been accepted towards fulfillment of the requirements for Doctor of Philosophy degreein Fisheries and Wildlife m l/ fiél‘éftp Major professor Date JULY 7, 1987 MS U is an Affirmatiw Action/Equal Opportunity Institution 0-12771 MSU RETURNING MATERIALS: Place in book drop to remove this checkout from LIBRARIES w your record. FINES will be charged if book is returned after the date stamped below. ‘“mem~ ' £333 2 was. 3 3 3 GROWTH AND PRODUCTION CONTROL OF GOLDEN SHINER NOTEMIGONUS CRYSOLEUCAS (MITCHILL) BY MANIPULATING TEMPERATURE AND DENSITY BY Sha Miao A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Fisheries and Wildlife 1987 ABSTRACT GROWTH AND PRODUCTION CONTROL OF GOLDEN SHINER NQIEHIQQHQ§ QBXSQLEQQAS (MITCHILL) BY MANIPULATING TEMPERATURE AND DENSITY BY Sha Miao Better control of the growth and production of the golden shiner to meet market demand is needed. An experimental study evaluated the simultaneous effects of two factors (temperature and fish density) with three treatment levels each. Three thermal regimes Consisted of one constant temperature (24C) and two daily thermocycles. The temperatures of two thermocycles increased respectively from 22.7C to 26.8C and from 24.6C to 28.8C on a 12-hour- cycle, and then declined to their respective origins on the following 12-hour-cyc1e. Three fish densities were created by stocking five fish per 10-, 15-, and 30-gallon aquaria. This investigation was accomplished using the systems analysis involving three modeling stages in sequence: a statistical, a deterministic, and a computer model. Data indicated that density was not a dominant factor during the 80-day experiment. However, the results suggested that two out of the three thermal treatments, 24C and 22.7C - 26.8C, should be alternatively applied to this conditioned system of four 20-day periods to control golden shiner production for market needs. The temperature of the dynamic system should be constant at 24C for the first and last periods but cyclicly between 22.7C and 26.8C for the other periods. TO MY WIFE Tu, Shunchi iv ACKNOWLEDGEMENTS I am deeply indebted to my parents and sister, without whose encouragement and support I would never have been able to accomplish this project. Dr. Niles R. Kevern, my major professor, contributed unselfishly of his time and his concern throughout the project. I can never express enough of my gratitude for his guidance, friendship, and the opportunity to maintain an assistantship under his supervision. Drs. Robert O. Barr, Ivan Mao, and Donald L. Garling also contributed significantly with constructive suggestions and encouragement. My special thanks go to my wife, Shunchi, for her great contribution to the completion of this document. TABLE OF CONTENTS Page LIST OF TABLES ......OOOOOOOOO......OOOOOOOOOOOOOOOOOO Viii LIST OF FIGURES 00.000.000.000.........OOOOOOOOOOOOOOO Xi INTRODUCTION 0 o o o o o o oooooooooooooooooooooo o 00000000000 ’ 1 MATERIALS AND METHODS O O O O O O 0 O O O O O O O O O O O O O O O O O O O O O O O O O 11 Stochastic Modeling ............... ................ 11 Tests Of Assumptions 0 I O O O O O O O O O O O O O O O I O O O O O O O O O 15 Analysis of Variance (ANOVA).................... 18 Tukey's Tests ....................... ........ ... 23 A Development and Performance Evaluation of the Experimental System ............................... 24 Deterministic Modeling by Computer Simulation ..... 32 RESULTS O0....I...O......OOOOOOOOOOOOOOOOOO0.00.0.0... 39 StOChaStiC MOdeling o o o o o o o o o o o o o ccccc ' ooooooooooooo 39 Tests of Assumptions ...... ........ . ........... . 39 Analysis of Variance (ANOVA).. ..... . ............ 43 TukeY's Tests .........OOOOOOIOOOOOOOO0.00...... 43 Performance of the System's Operation ............. 49 Deterministic Modeling by Computer Simulation ..... 49 DISCUSSION ........................................... 70 LISTOFREFERENCES OOOOOOOOOOOOO.......OOOOOOOOOOOOOOO 76 vi APPENDICES Appendix Appendix Appendix Appendix Appendix Appendix 1. 2. Michigan bait minnow supply survey .... The formulas of respective sums of squares regarding the weight/weight ratio ......OOOOOOOO......OOOOOOOOOOOOO Obtaining the simple regression line for the four individual tanks during four individual 20-day intervals ...... The formulas of testing hypotheses in Figure 2 and of computing common slope as well as intercept .................. Program of computer simulation ........ Original printouts of 4 selections of computer simulation ................... vii 80 80 84 85 86 88 92 LIST OF TABLES Table Page 1. Michigan bait minnow supply in 1982-survey summarization 00............OOOOOOOOOOOOOO....... 3 2. Michigan bait minnow demand in 1982-survey summarization O0.0...IO....OOOOOOOOOOOOOOOOOOO.I0 4 3. ANOVA of the weight/weight ratio ................ 19 4. The demonstration of the numbered Tukey's tests in Figure 1 on the weight/weight ratio .......... 25 5. The distribution in number of heater(s) with correspondent wattages per aquarium for each thermal treatment ........ ..... .................. 26 6. Total required items and the related quantities of the system's facilities ...................... 28 7. One way ANOVA with variable Y denoting the production cycle of reaching a desired size ..... 37 8. The weight observations per treatment combination at 4 periods (P) of 20-day ...................... 40 9. The weight ratio observations per treatment combination at 4 periods (P) of 20-day .......... 41 10. Random errors, E(tdp)a’ of the weight ........... 42 11. Random errors, E(tdp)a' of the weight ratio ..... 44 12. Bartlett's test on homogeneity of variances regarding the weight ............................ 45 13. Bartlett's test on homogeneity of variances regarding the weight ratio ...................... 46 14. ANOVAOf theweight ...O.......OOOOOOOOOOOOOOOOOO 47 15. ANOVA of the weight ratio .......... ............. 48 viii Table Page 16. The means of thermal treatments of the weight at eaCh time periOd ......OOOOOOOOOOOOOO0.0.0.0....O 50 17. The means of thermal treatments of the weight ratio at each time period ....................... 51 18. Tukey's test on thermal treatments of the weight within each time period ......................... 52 19. Tukey's test on thermal treatments of the weight ratio within each time period ................... 53 20. Quality controll of the constant thermal treatment (24C) ......OOOOOOOO......OOOOOOOOOOOO. 54 21. Quality control of the cyclic thermal treatment (22.7C to 2608C) ......OOOOOOOOOOOOOOOO0.0.0.0... 55 22. Quality control of the cyclic thermal treatment (2406C to 2808C) ..........OOOOOOOOOOOOOOOOOOOOOO 56 23. Linear regression of cyclic thermal treatment (22.7C to 26.8C) at various time interval ....... 57 24. Linear regression of cyclic thermal treatment (24.6C to 28.8C) at various time interval ...... 58 25. Carrying capacity of a single fish associated with producing thermal treatment at 4 periods Of zo-day 0.00.00.00.00.....OOOOOOOOOOOOOOOOOOOO. 60 26. Daily growth rate of a single fish associated with producing thermal treatment at 4 periods Of 20-day 0.00.00.00.00.........OOOOOOOOOOOOOOOOO 61 27. The dynamic inputs of computer simulation based on the selection of optimum daily growth rate ... 62 28. The dynamic inputs of computer simulation based on the selection of optimum carrying capacity ... 63 29. Production cycles of reaching a desired size, 2.03 grams, Of 4 Simulations ......OOOOOOOOOOOOOO 64 30. Maximum yields of a fixed production cycle (Bo-day) of 4 simulations ....................... 65 ix Table Page 31. 32. 33. 34. ANOVA of computer modelings for reaching a desired size with shortest production cycle ..... 67 ANOVA of computer modelings for obtaining a maximum harvest over 80 days .................... 67 Tukey's test on computer modelings of reaching a desired size with shortest production cycle (days, O.......OOOOOOOOOO......OOOOOOO0.......... 68 Tukey's test on computer modelings of obtaining a maximum harvest over 80 days .................... 69 LIST OF FIGURES Figure Page 1. Flow chart of hypotheses tests on the weight/weight ratio followed by appropriate deCiSions 0.0............OOOOOOOOOOOO0.00.0000... 20 Flow chart of the comparison of regression lines to evaluate the system's performance in cyclic thermal treatments .............................. 31 xi INTRODUCTION The minnows (Cyprigiggg) are one of the characteristic families of North American fishes and are of economic importance since they constitute the major portion of the food for game and commercial fishes (Markus, 1934). The advent of minnow farming was preceded by many years of harvesting of wild minnow stocks (Brown and Gratzek, 1979). A major problem of the bait industry is that it can not catch enough minnows during the summer when the sport fishery reaches its peak (Gordon, 1968). Hedges and Ball (1953) also pointed out that throughout Michigan there is a high summer demand for bait minnows, often considerably in excess of the supply. Bait dealers depend on natural supplies and are often forced to travel considerable distances in search of streams where bait fishes are available (Hedges and Ball, 1953). As wild stocks became more difficult to find and harvest, as a result of overharvesting, pollution, and other factors, interest grew in raising bait fish (Brown and Gratzek, 1979). In pond operations, however, the fish can be harvested as they are needed and a faster turnover between dealer and fisherman results (Hedges and Ball, 1953). In February, 1983, Dr. Donald L. Garling surveyed the Michigan bait minnow supply. One hundred and fifty letters were sent to the wholesale bait dealers in Michigan. Three main questions were included in the survey (Appendix 1): (1) What is the status of the bait minnow industry in Michigan? (2) What are the needs of the Michigan bait minnow industry? (3) Can Michigan minnow farms be developed to meet those needs? Forty-nine responses were received including nine without answers. While many species were mentioned in the survey, my analysis concentrated on the five species having the highest production rates. The results are summarized in Tables 1 and 2. This survey showed that of the respondents annual production rates of minnows among these five species varied from a high of 1.8 million gallons to a low of 8.6 thousand gallons (1 gallon = 8 pounds) which were sold at $27 million and $199 thousand, respectively. Of the total production, the majority of bait minnows came from "purchasing" as compared to "netting and raising". Also, out-of-state producers played an important role in providing Michigan dealers with bait minnows. Seasonal shortages were evident throughout the year but were especially critical in July and August. The survey also showed that bait minnow dealers in Michigan will pay premium prices for a guaranteed constant supply of farmed raised minnows. The percentages of the dealers that will pay premium prices varied from a high of 89.0% for golden shiner to a low of 0.2% for emerald shiner. The .nmwu 00H non mumHHop 6cm .cmflu pom mucmo .couoo mom mucmo OCHUSHocfl .moflum gawaamm no mafia: nonuo ocfluoowmcoo usocuws AcoHHmo pom mumHHocv dodge ocwaamm monum>m >2 AmcoHHmov cofiuozpoua Hmuou vcfixaafiuase >3 pmcfimuno mums mmscm>mu Hospw>wch .c .mpcsom m u coHHmo H .0 .mcoHHmv em >Hcmsou mos cofluozpoum onu man» “coHHmv Hoe wo.m~m was wofium onwaamm oomuo>c mnu “oo.mmmw um cHom mes “coach was cofluospoum no women: may .uocwcm copaou you mamaoxm nocuoc< .mcoHHmm an 0» Hedge >Hcm=ou mm: cofiuosooue on» ououmumnu “coHHom you vo.mmm um owumeflumo mm3 mOqu mafiaamm momu0>m on» “oo.omcw um Odom was one comm mm; msoccws pmmnueu couscoum no bones: on» .wocmumcfi uom.mmo«ue mcwaaom ommum>w on» we mmscm>mu ufionu mcficfi>wc we pmumsflumo mums mamspfl>flc:w u0m mcoHHmv no mucosa: ecu .msze .pflc: cofiuospoum o no =cmwu mo Hogans: pom: muoamop 039 .b .>m>u:m mama mcwusc cwmflcon CH coHuospoue awesome on» nude wsoCCME pawn ecu mums nocwnm >mum can pmcwnm vacuosm .um:wnm condom .uoxosm muflc3 .BoccflE coonumm .c NH mm o.wm v.H thqmmw.m wwmkmma umcflsm xwuo on Om w.mm N.o mvoloooqu «HHJémJ meflcm cannoem mm mm o.vm 0.00 cah.mofi mmoqw pocflcm cocaoo mm me o.wm o.mv vuo.vhm omw4mfi Logosm mums: m5 mm o.¢m o.w mwm.0mm omm~va 30ccfiz pmocumm mucoscoum mumospoum AcoHchv mumumnuouuzo oumumncH ommzonsm mmwmm no uoz AumHHoov o wscm>mm c0wuoscoum mofiommm “we Scum meoo msoccw: vamaoccfiz ufimm mo mmousom p namuoa cofiumufiumfiesm >o>usmu~mma cfl wandsm Boccfle uflmn :cm«20wz .H mam AeOMuQ saweeum m awn >Hmcfiauu3 ocz emocu ha ceospoumv c0uuoscoua Hauuumm ecu mo Ouumu ecu ac ceCuEueuec we: =we»: mo eomuceouem ecu .mewoemm Hespw>wpcu Mom .w v.wm n.H om I I I I I I I I om cm on I I I I om mm ha I I I I I uechm heuu w.mm m.o mm I I mm mm ee .3 I I mm mm mm B” I I ha be om ha I I ha 5H 5H Mecflcm camuesm oi: o.mm on OH OH I om ov Om om Om om ov ov om OH OH ov ov ov 0m ON ON 0m On On heCHcm cecaou o.mm o.m Hm N. h N. on am «a h h am am am HH I I mm mm mm mm HA .2 mm mm mm Mexosm euucz o.mh oém OH OH OH I I I OH I OH OH OH oa mm I I Ha mm mm I I I mm mm mm 30532 II. onecymm oz we» NH as OH m m a o m s m m H NH us 0H m w s MI m. s m m H msocCuz cemumm ceEumm we maummcousm >c m3occuz mauuuez >2 m3occu: mefladasm uceumcou peeucmu sumuco ou mcucoz uHDOMLHuc aueuco ou mcucoz uH50uuuuo meuoemm Imsu MOM meOuum Esueeum ocu>mm Awe mueawmeaocz oeu>mm va mueawmeaocz sad sumcusuuz mcwvmumummo cOuumNuumEEDm >e>u5mI~mmH Cw pcmeec 30ccwE uumc cmmucoflz .m eacmB results indicated an unmet demand for bait minnows that might be satisfied by an increase in minnow farming in Michigan. In aquaculture, two variables that may influence recruitment to fish stocks are temperature and population density, both of which could influence growth and fecundity. Everhart and Youngs (1981) reported that the growth rate of fish depends to a large extent on temperature and most species of fish do not spawn unless the water temperature is within certain limits. A temperature fluctuating between 10 and 20C and averaging 15C does not necessarily have the same effect on organisms as a constant temperature of 15C (Odum, 1959). Biette and Geen (1980) demonstrated that the growth of young sockeye is greater under cyclic than constant temperatures. For brown trout, a fluctuating temperature could significantly increase their feeding, growth, and lipid deposition compared with constant temperatures at the mean of the fluctuations (Spigarelli et al., 1982). Odum (1959) stated that organisms normally subjected to variable temperatures in nature (as in most temperate regions) tend to be depressed, inhibited or slowed down by constant temperature. However, depending on the time of day the thermocycle was initiated, weight gain and testicular growth could be either stimulated, inhibited, or equal to that in fishes subjected to constant heat or constant cold (Spieler et al., 1977). Le Cren (1965) stated that population density and growth rate are inversely related (cited by Smith et al., 1978). As population density increases, competition for nutrients, food, and living space usually intensifies, providing one of the most effective controls of both plant and animal populations (Odum, 1959). Meanwhile, metabolic wastes, which are directly proportional to population density, have been implicated as inhibitory to growth and toxic to fishes (Yu and Perlmutter, 1970). Smith et a1. (1978) reported that high population density appeared to limit growth and gamete development regardless of food abundance. Water volume also appeared to limit numbers (tolerance density) of fish which can be supported in a specific volume of water (Smith et al., 1978). As a partial explanation for the reduction in reproduction and growth under crowded conditions, several investigators have suggested the presence of a water-borne, fish-produced represser that inhibits reproduction (Swingle, 1953; Rose and Rose, 1965, cited by Smith et al., 1978) and reduces growth rate (Yu and Perlmutter, 1970; Francis et al., 1974). However, Glaser and Kantor (1974) showed that spawning rate in medaka (grygiag latipes) can be inhibited by social factors of crowding, irrespective of chemical conditions of the water (cited by Smith et al., 1978). The golden shiner is an excellent bait minnow (Cooper, 1937; Prather, 1957; Scott and Crossman, 1973; Pflieger, 1975) and is well suited for pond culture (Forney, 1957; Scott and Crossman, 1973; Pflieger, 1975). Table 2 shows that there is a high shortage of golden shiners throughout the year. It also indicates that 89% of the dealers were willing to pay a premium price for a guaranteed constant supply of farmed raised golden shiners. The objective of this research was to control the growth and production of the golden shiner ugtgmiggnus grysgleugas (Mitchill) under two factors' stimuli. This demonstration has been illustrated by utilizing three related models; a linear stochastic model, a nonlinear deterministic model, and a computer simulation model. A linear stochastic model based on a split-plot design (Gill, 1978b; Petersen, 1985; Myers, 1979; Winer, 1971; Cochran and Cox, 1957) was designed to investigate the effect of interaction between temperature and stocking density on the growth of golden shiner. Each factor consists of three fixed levels. Two thermocycles and a constant temperature (24C) were introduced with respect to the temperature factor. Twenty-four C was determined by averaging the temperatures of spawning initiation (21C or 70F) and spawning cessation (27C or 80F) for golden shiner (Scott and Crossman, 1973; Pflieger, 1975; Brown and Gratzek, 1979). For density, 10-, 15- and 30-gallon sizes of aquarium were chosen. Five fish were stocked in each volume. It was reported by Hickman and Kilambi (1974), and Roseberg and Kilambi (1975) that a stocking density at 5 golden shiners per 15-gallon-water produces the best growth. There were a total of nine treatment combinations. This study lasted eighty days. Individual fish weights were taken at the beginning of the study and at intervals of twenty days. As a result, the growth rate and carrying capacity were estimated at the end of each twenty-day interval. Carrying capacity here is defined as the growth potential or the maximum growth that is attained during the time period and under the conditions of this experiment. The growth rate and carrying capacity are a pair of parameters in the Logistic Equation (Ricker, 1975; Wilson and Bossert, 1971; Spain, 1982). Their magnitudes are affected with the intensity of the treatment combination. A better growth rate or carrying capacity reveals that a given treatment combination is more effective. There is no causal correlation between the paired parameters. This implies that a better growth rate is not necessarily accompanied by a better carrying capacity, or vice versa. Consequently, several sets of treatment combinations in a time sequence were statistically determined as optimum considering only growth rate. Likewise, other sets of treatment combinations might be accepted as optimum considering only carrying capacity. Computer modeling was used to clarify such a controversy. In computer modeling, a mean and a standard deviation were computed from the initial body weights of the fish. With the mean and standard deviation, one million normal- random deviates were generated through Monte Carlo simulations (Rubinstein, 1981; Hewlett-Packard Company's Manual, 1984; Sobol', 1974; Hammersley and Handscomb, 1964). The generated one million deviates represented equivalently one million fish body weights at the initial stage. Accordingly, the generated golden shiners were then simulatively stocked into a pretend "production system" described by the Logistic Model. A set of consecutive treatment combinations provided this production system with a series of dynamic inputs. In practice, however, the system's dynamic inputs were substituted with a sequence of the paired parameters; growth rate and carrying capacity. They were repeatedly estimated in four consecutive periods of twenty days. Secondly, the fourth-order Runge-Kutta method (Stiefel, 1963; Davis and Robinowitz, 1975; Todd, 1962; Weeg and Reed, 1966; Stark, 1970; Scraton, 1984) was selected to deal with the computer modeling because of its lower cost in terms of computer time while describing the Logistic Model more precisely. With the generated initial weights and the system's dynamic inputs (i.e. growth rate and carrying capacity), the computer modeling continuously predicted not only the total yield but the individual size of the one million generated golden shiners on a daily basis. The production cycle in number of days was determined under a desired yield or desired size. An optimum production cycle in terms of minimum time was thus identified according to desired yield, size or both. As a result, a particular set of the consecutive treatment combinations was finally screened as an optimum based on 10 the best production cycle. However, a less effective treatment combination does not always indicate a nuisance input. Such inputs, especially from the management point of view, may act as control valves to reduce an unwanted growth and production at different rates, and therefore to provide positive effects for the system. For example, sport fishermen may require various sizes of bait minnow in fishing. Our objectives are to provide neither a shortage nor an oversupply, but rather a supply that meets the demand of the market place. This research therefore demonstrates a feasible way by interchanging the system's inputs over time to periodically adjust the rates of growth and production. Eventually, the system's operation can be controlled at a desired pace to satisfy the market demand. MATERIALS AND METHODS Three stages in sequence were involved to develop and carry out this research. In conducting a stochastic modeling for the first stage, an experimental system was designed and its model was statistically examined. An indoor operational system was then built for the second stage and the system's performance in terms of exactness of temperatures control was statistically evaluated. In the final stage, a nonlinear deterministic model was studied using a computer simulation. The outputs of the computer modeling were statistically compared with one another. Consequently, a series of treatment inputs were determined as most suitable for serving market demands. STOCHASTIC MODELING The stochastic modeling formulates a linear statistical equation with split-plot design as follows: =p+T +Dd+(TD)td Ytdap t + A(td)a + Pp + (TP)tp + (DP)dp + (TDP)tdp + (AP)(td)aP + E(tdap) where t = 1, 2, ; d = 1, 2, 3; a = 1, 2; and p = 1, 2, 3, 4. 11 12 The right hand side of the above equation is composed of varieties of a system's inputs. These inputs represent average effects resulting from a particular factor or combination of factors at a certain quantitative level. The p is described as the true mean of the distribution of Y for a population defined by the experimental conditions as a whole. The capital letters T and D represent temperature and density, respectively. The three treatment levels (t) in temperature were: (1) constant temperature of 24C, (2) low cyclic temperature from 22.7C to 26.8C, and (3) high cyclic temperature from 24.6C to 28.8C. Three density levels (d) were created by randomly distributing groups of five fish into aquaria of 10-, 15-, and 30-gallon. The (TD)td indicate the average effects of the interaction of temperature at level t and density at level d. The t levels of temperature and d levels of density are combined in all possible ways to make t x d = 3 x 3 = 9 treatment combinations. And for each treatment combination, there were two aquaria, or two replicates (a). The A(td)a denote random effects of aquaria nested within a treatment combination. Also known as "Error One", the A(td)a correspond to the E(td)a of the model for a completely randomized design without the repeated measurement. As a result of the fish weight samplings repeatedly taken at intervals of twenty days, the Pp are effects of time at the various sampling points in the process of repeated measurement, where the sampling intervals are p = 13 1, 2, 3, 4. The (TP)tp and (DP)dp are the effects of the interactions of time with temperature and time with density, respectively. The (TDP)tdp are the effects of the interaction of three factors temperature, density, and time at the combined levels tdp. The interaction of an aquarium with time; (AP)(td)ap is not separable from the residual error within an aquarium; . The E E(tdap) (tdap) is the residual error or net effect on Y of all unspecified factors of influence peculiar to aquarium a at interval p under the treatment combination td. The left hand side of the equation is the system's output symbolized by Y. Y is also a collective variable being repeatedly sampled every twenty days. By modeling the same equation, this collective variable Y may represent two different variables depending on what parameters are under study. If carrying capacity, a parameter in the Logistic Equation, is being estimated then variable Y are the total weights of 5 fish from each experimental unit. 0n the other hand, variable Y represents the weight ratio of the 5 fish as long as the growth rate, another parameter in the Logistic Equation, is being estimated. The weight ratio is the final weight divided by the initial weight over the study time periods (i.e., 20, 40, 60, 80 days). Therefore, the sampled variables Ytdap' corresponding to a particular parameter, are the measurements being taken from aquarium a at interval p under the (td)th treatment combination. The total observations per estimated parameter, or sample size, 14 are N = t x d x a x p = 3 x 3 x 2 x 4 = 72. In order to prevent a possible influence on the experimental estimates, a few nuisance factors had to be eliminated or systematically controlled. The system's illumination included nine fluorescent light fixtures with four 34-watt bulbs each regulated to a light period from 0800 hours to 2000 hours each day. The aquaria were filled with cold tap water one week prior to the addition of fish to allow for aeration, iron precipitation, and chlorine removal. The water came from the Michigan State University water supply system originating in deep groundwater sources. The experimental fish were shipped by air from Arkansas (Finley Company Farmsa). On arrival, five fish were randomly chosen and distributed into each aquarium and acclimatization begun. The system's conditions of acclimatization were identical to those of the experiment. The research began after twenty days of acclimatization. The fish received a daily diet of 3% of their body weights. This ration was divided into two equal parts given at 1000 hours and 1600 hours each. A commercial diet (Purina Trout Chowb) was the food source utilized for this feeding scheme and was kept refrigerated. The feeding activities were periodically terminated one day before to one day after the sampling date when the measurements of the fish a' The address is P. 0. Box 317, Lonoke, AR. 72086. b‘ Purina Trout Chow, Diet CR 6-30 #4 GRAN, manufactured by Glenooe Mills INC., Glencoe, Minnesota 55336. 15 weights and lengths were taken. Weights were determined to tenths of a gram using a top-loading Mettler balance. To avoid fish flapping and reduce the stress, the following method of handling each individual fish was used. This procedure showed no adverse effects on the fish: (1) prebalance the weight of a sandwich bag containing about a gram of water, (2) place an individual fish into the bag, and (3) weigh the entire bag. Meanwhile the aquaria's clean-ups were repeatedly performed during the weighing periods. This cleaning scheme consisted of (1) scrubbing walls of the heaters and aquaria, and (2) syphoning the metabolic wastes and feed residuals. After syphoning, each aquarium was refilled (about one-third of its volume) with conditioned water previously stored in a reservoir. This study was followed by a statistical analysis performed in the following three consecutive steps: (1) tests of assumptions, (2) analysis of variance (ANOVA), and (3) Tukey's tests. Every test or analysis was repeated twice but alternatively with one of the two variables, weight and weight-ratio. sts o Assum ons The assumptions underlying this statistical modeling may be summarized by E ~ NID(0,02). That is, the tdap experimental errors are distributed "normally" and "independently", with mean zero and "homogeneous variance" 02 common to all treatment combinations. 16 The normality was examined by the Shapiro-Wilk test (Gill, 1978a) described as follows. 1. Determine individual random errors by E(tdp)a = Ytdpa ' Ytdp. ’ where Ytdpa denote the weight or weight-ratio observations of five fish; and gtdp are the means of the observations Ytdpa through a = 1, a = 2. 2. Order the N random errors by value (E1 5 E2 5 ... 5 EN); where N = total sample size = 72. 3. Compute M G 3 1:1 i,N (EN-1+1 ’ Bi) ’ where M = N / 2 = 36; and the values of B. are found 1,N in the extended tables of Appendix A.13.1 (Gill, 1978c). 4. If the test statistic, w=——, SSE is less than the critical value W; from the extended ,N tables of A.13.2 (Gill, 1978c), one may reject the hypothesis of normality with probability of Type I error less than a; where SSE = sum of squares of the random experimental error; a a 0.1. The test of independent errors can be omitted because the random experimental errors are no longer independently related due to repeated sampling. This problem resulting from the assumption's violation was internally solved by this particular modeling use of a split-plot design. The 17 hypothesis of homogeneous variance was then examined by Bartlett's test (Gill, 1978a; Zar, 1984). In other words, we wish to test if the variance of weights or weight ratios is the same for all nine treatment combinations within each time interval. The test statistic within each period of time is 2 td td 2 where ”i = A1 - 1 and AJ.- is the number of duplicated aquaria per treatment combination 1. The pooled variance, 2 Sp , is calculated by 2 td td s = ( 2 ss.) / ( 2 u.) , p i=1 1 i=1 1' where td = the number of total treatment combinations 2 9, and SSi = the sum of the squares of the deviations from the sample's mean for a given treatment combination 1. The Si2 is the sample variance corresponding with treatment combination i. The distribution of B is approximated by the Chi-Square distribution, with td-l degrees of freedom, but a more accurate Chi-Square approximation is obtained by computing a correction factor, 1 tdl 1 c = 1 + ( 2 3(td-1) i=1 Vi td with the corrected test statistic being 18 and the critical value is x2 1, with a = 0.2. a,td- s 'a V ANOVA is a term of process for partitioning the variance of a random variable (Y) into orthogonal (independent) parts caused by treatments and experimental error. Namely its objectives are :(1) to obtain the precision (variance) of estimates of treatment means or differences, as well as (2) to test hypotheses about equality of treatment means and existence of interactions among factors. Table 3 details the ANOVA. Appendix 2 demonstrates the associated formulas to quantitatively determine the individual sums of squares. The F ratios listed in Table 3 indicate that a series of corresponding hypotheses were being alternatively tested. Then Figure 1 shows the procedure of testing these hypotheses in a flow chart. Any hypothesis tested should be rejected if Fi < Fa df df ; where Fi = F F ...F , 1 , 2 1' 2' 7 (Table 3); a = 0.05; df1 = associated numerator's degrees of freedom, and df2 = associated denominator's degrees of freedom. A rejection or acceptance of any hypothesis test is then followed by making an appropriate decision. Table 3. ANOVA of the weight/weight ratio. 19 Source of Variation Degrees of Sum of Mean F Ratio Freedom (D.F.) Squares Square Total (tdap)-l SSY MSY Temperature (T) t-l SST MST MST/MSA/TD=F7 Density (D) d-l SSD MSD MSD/MSA/TD-FG Interaction T-D (t-l)(d-l) SSTD MSTD MSTD/MSA/TD-FS Aquaria/TDa td(a-l) SSA/TD MSA/TD Period (P) p-l SSP MSP MSP/MSE-F4 Interaction T-P (t-1)(p-1) ssTP MSTP MSTP/MSE-F3 Interaction D-P (d-1)(p-l) SSDP MSDP MSDP/MSE-F2 Interaction T-D-P (t-l)(d-l)(p-l) SSTDP MSTDP MSTDP/MSE-Fl Residualsa td(a—l)(p-l) SSE MSE a'(Aquaria/TD) is A Recalling the model's equation, A is also known as (td)a. (td)a Error I for a completely randomized design without repeated measurement. The residuals, or Error II, consist of (AP) and E and are inseparable (td)ap (tdap) due to the model 5 limitation. In fact we may separate (AP)(td)ap from E(tdap) by tagging all the fish. As a result, a new model containing two new components of (FP)(tda)fp and E(tdafp) (F denotes fish effect and f is the number of fish) would be used for the purpose of separating (AP)(td)ap from E Again (tdap)' and E are inseparable due to the new model's limitation. (tdafp) (FP)(tda)fp Therefore, to what extent the partition of total variation should reach is a function of an acceptable precision in modeling from biological concerns. For example, without excluding the quantity (AP)(td)ap from Error II, which is the interaction effect of aquarium and time period, should not affect the model's precision significantly from biological considerations. Besides, tagging itself may possibly introduce unexpected physical effects into the system. ‘ 20 | I H01:Interaction TDP=0 HA1:Interaction TDP¢0 F1 compare Fa,df 1,dfg4 I Accept H01 Yes H02:Interaction DP=0 HA2:Interaction DP¢0 ‘Tukey's Test 1 F2 compare Fa,df df Tukey's” Test(2) H03:Interaction TP=0 HA3:Interaction TPuO F3 compare Fa,df ,df 1 2 I I (D Figure 1. Flow chart of hypotheses tests on the weight/weight ratio followed by appropriate decisions. (BE-+— -+— Figure l (cont'd.). Tukey's est 3 21 | Yes H04: Effect P=0 HA4: Effect P¢0 F compare Fa 4 ,df df Tukey's Test(4) H05: Interaction TD=0 HA5: Interaction TD¢0 F5 compare Fa'dfl'dfz Tukey ' s _< Test(5 HA6: Effect D¢0 F6 compare Fa,dfl,df2 l I'K (a Tukey's Te§t(6) 22 Tukey's L{_— GEE: ITest(7) Temperature Density Period ’UCJH "ll" Figure 1 (cont'd.). H07:Effect T=0 HA7:Effect T¢0 F com are P 7 p a,df1,deL | Yes | No T,D and P are trivial factors in this model I Y (END) 23 W Tukey developed an honestly significant difference (HSD) test that utilizes a t-like statistic based on the distribution of the Studentized range, that is, distribution of the ratio of the sample range to the sample standard deviation for K items from the normal distribution (Gill, 1978a). For the K(K-1)/2 possible comparisons of two means among a group of K means, the joint probability of Type I error may be set at a. Compare the difference between each pair of means from a balanced experiment (i.e. equal number of replicates for individual treatments) with a selected HSD. If the difference between two means, in absolute magnitude, exceeds a predetermined HSD, it may indicate that one correspondent treatment is significantly more effective than the other. However, my HSD may be computed in two different ways according to different decisions made through the flow chart shown in Figure 1. I. HSD for split-plot design (Gill, 1986). I??? HSD = [(qa K V)J_—— 1 / J5 I I I r 02 - [MSA/TD + (p - 1) MSE] / P , u = (a2)2 / {[MSA/TD K = number of compared means (i.e. treatments' 2 + (P - 1) MSEZJ / [KP2(r - 1)]l . means), r = number of conditioned replicates, 24 P = 4 time periods, and a = 0.05 II. HSD for completely randomized design (Gill, 1978a). - 355122. HSD " (qa,K,N-K) ' r K = number of compared means (i.e. treatments' means), r = number of conditioned replicates, N - total sample size = 72, and a 8 0.05 Table 4 demonstrates how the numbered Tukey's tests shown in Figure 1 are individually performed by using an appropriate HSD. In addition, the numerical numbers of both R and r are also given to each numbered Tukey's test (Table 4). A DEVELOPMENT AND PERFORMANCE EVALUATION OF THE EXPERIMENTAL SYSTEM Based on the previous model, an indoor operational system was built as follows. Three aquaria with respective sizes of 10-, 15-, and 30-gallon were assigned to a constant temperature at 24C, and to the other two cyclic thermal treatments. In order to maintain the desired temperatures, the aquaria were individually equipped with heaters at various wattages. All the heaters have an automatic electronic thermostat. Table 5 summarizes how the heaters were distributed into the aquaria according to the 25 Table 4. The demonstration of the numbered Tukey's tests in Figure 1 on the weight/weight ratio. Numbered Tukey's HSD K r Test from Figure 1 Remark Tukey's Test (1) I 9 2 Compare 9 means of treatment combinations within each time period. Tukey's Test (2) I 3 6 Compare 3 means of density treatments within each time period. Tukey's Test (3) I 3 6 Compare 3 means of thermal treatments within each time periods. Tukey's Test (4) I 4 18 Compare 4 means of time periods. Time is no longer a factor below here Tukey's Test (5) II 9 8 Compare 9 means of treatment combinations. Tukey's Test (6) II 3 24 Compare 3 means of density treatments. Tukey's Test (7) II 3 24 Compare 3 means of thermal treatments 26 Table 5. The distribution in number of heater(s) with correspondent wattages per aquarium for each thermal treatment. Aquarium Size Thermal Treatment 10-gallon 15-gallon 30-gallon 1 heater 1 heater heater 1 heater 2 24C 50-watt 75-watt loo-watt 50-watt Heater # 22.7C to 1 2 1 2 1 2 26.8C 50- 50- 100- 50- 200- 100- watt watt watt watt watt watt Heater # 24.6C to 1 2 1 2 1 2 28.8C 100- 75- 200- 50- 300- 200- watt watt watt watt watt watt 27 desired temperatures and the aquaria sizes. For each cyclic temperature, the three sizes of aquaria were placed into a tank. Inside each tank, the 10- and 15- gallon aquaria were seated on 4-leg steel frames, and as a result, were able to stand as high as the 30-gallon aquaria. After filling the tanks, the 3 aquaria emerged from the tanks' water level by 1-inch in height. With two BOO-watt heaters installed diagonally in the tanks, the waterbath cyclicly controlled the temperatures of the aquaria at smoothly changing rates. Aeration was additionally applied inside of the tanks and their aquaria to facilitate the thermal circulation. For the 24C constant temperature aquaria, each was aerated with two air stones placed in its diagonal corners. The entire operational system was replicated twice. Table 6 details the items and the related quantities of the system's facilities. The heaters used in aquaria receiving constant thermal treatment were adjusted to be continuously on to maintain the temperatures at 24C during this study. The heaters of the other tanks and their associated aquaria cycled on daily from 0800 hours to 2000 hours and then off during the next 12-hours. Such on-and-off activities therefore generated two thermocycles. Like feeding activities, the heating process was also periodically interrupted beause of cleanings and measurings. The aquaria's temperatures were monitored by a 28 Table 6. Total required items and the related quantities of the system's facilities. Item Size Quantity Tank length x width x height 4 = 79" x 21.5" x 22" 10-gallon Aquarium 20" x 10.5" x 12.25" 6 lS-gallon Aquarium 24.25" x 12.75" x 12.5" 6 30-gallon Aquarium 30" x 12.75" x 18.75" 6 Emergent Heater 50-watt 12 Emergent Heater 75-watt 4 Emergent Heater loo-watt 8 Submersible Heater 200-watt 6 Submersible Heater BOO-watt 10 Air Compressor 0.5HP, 1725RPM 1 Tank-Air Stone 6"-stripe 24 Aquarium-Air Stone marble shape 36 Air Tubing regular accordingly 29 thermistor usually four times daily: 8:00 AM, 8:00 PM, and before each feeding. Consequently, the accuracy of the temperature control was statistically evaluated through the recorded temperatures. The evaluation was performed in the following two ways: (1) one-sample Student's t test (Zar, 1984; Gill, 1978a), and (2) comparing simple linear regression (Zar, 1984). The test statistic of one-sample t test is T r n t = , S /./NT where N denotes a number of the total temperature T samplings from an individual aquarium receiving 24C- treatment throughout the experimental duration. Compute the mean temperature (T) and standard deviation (S) of the NT readings, followed by a hypothesis test of the aquarium temperature being controlled at p = 24C. The hypotheses test for an individual aquarium receiving constant thermal treatment is no : p = 24C and HA : p # 24C, if |t| z t , then reject HO; where a(2) refers to a(2) ,NT_1 the two-tailed probability of a = 0.01. Comparing two simple regression lines was used to examine the efficiency of the cyclic thermal treatments. The simple linear regression, A Y = a + bx , was determined (Appendix 3) for each individual tank at 30 every interval of 20-days to reduce the possible variation in room temperature due to seasonal changes. Variables X and Y (Appendix 3) represent heating hours and averaged temperatures, respectively. Heating started daily at 8:00 AM and ended at 8:00 PM. Variable X ranges from 0 to 12 hours after coding. Practically speaking, there were no temperatures measured "exactly" at X = 0, or 8:00 AM. In other words, the true range of X, statistically speaking, should never include the point at X = 0. For each tank, the variable Y was computed by averaging the temperature readings taken from three sizes of aquaria at time X. Intercept "a" is the lowest point of a cyclic temperature estimated at X = 0, or 8:00 AM. Slope "b" denotes an increasing rate of temperature change per unit time. Variable Y differing from the observation variable Y, are the tank's temperatures predicted at hours X by the regression equation. The thermal similarity of tanks is evaluated by comparing two treatment-related regression lines for the same time interval. The two compared regression lines thus correspond to two thermal-duplicated tanks. Therefore we may conclude that any two duplicated tanks are thermally alike at a given time interval when their corresponding regression lines possess statistically equal intercepts and slopes. Figure 2 demonstrates the testing procedure in comparing two regression lines. The related test statistics 31 (START) I :0: £1332 A' 1 2 Yes Compute Common Accept HO ‘_"—-%” Slope bc II HO: The two regression8 lines have the same elevation. 5 No HA: The two regression I lines do not have the; same elevation. I I No \\ Accept HO l' Yes Compute Common Intercept ac II’ Common Regression Equation Y = aC + ch | I I l I | I | | | I I l I | l I I I I I I I \I/ I Figure 2. Flow Chart of the comparison of regression lines to evaluate the system's performance in cyclic thermal treatments. ’%=STOP The test of difference between elevations may be considered the same as asking wether the two intercepts are different. However, it is not advisable to test H 'a — a because no temperatures were able to be measdred Exactly at 8:00 AM (i.e. x=0). Therefore, the point of x=0 is statistically beyond the x's range. 32 as well as the computations of common slope (be) and intercept (ac) are detailed in Appendix 4. Finally the common equation of linear regression A Y = ac + bc X is obtained if no hypotheses are rejected when quantitatively describing the qualities of the thermal treatments at a given time interval. DETERMINISTIC MODELING BY COMPUTER SIMULATION The nonlinear justification for Logistic Model was used to determine the optimum from the few selected sets of treatments according to the comparisons among their associated productions. The Logistic Equation is one well- accepted model proposed to characterize the growth of both individuals and populations. Some researchers sought to define the Logistic Model as a universal law of growth, others recognized it as a logical explanation for growth provided certain assumptions were met. This production model is mathematically expressed as dW K-W —=GW( dt K ) I with two assumptions: (1) the studied population is homogeneous; and (2) the growth increases exponentially, when W is small. 33 The instantaneous output of the model, dW/dt, is the derivative of weight (W) with respect to time (t). The system's parameter G is the daily growth rate estimated by the natural logarithm of the ratio of final weight to initial weight for a time interval: Wt G = [1n ( )]/t , where t = 20 days. Wo The Wt/WO' in fact, is the variable of weight ratio being repeatedly monitored at intervals of 20 days. K is the system's carrying capacity of a single fish, that is K = Wt/S. Wt is the weight of 5 fish in individual aquaria at time t, where t = days 20, 40, 60, and 80. Obviously Wt is the weight variable having been studied in stochastic modeling. Apparently the system's output, dW/dt, is directly proportional to its own parameters, G and K. Meanwhile, a few sets of treatments in a time sequence may be all viewed as same optimum if they induce statistically equal G's and K's. Therefore, to compare the system's outputs (dW/dt's) associated with the sets of treatments in a statistical tie is a way to further determine the most optimum set. To do this, we must go to an approximate numerical (computer) technique for solution because of the nonlinearity in the Logistic Model. That is, changing the differential equation 34 into a difference equation which we can solve recursively with a computer. The fourth order Runge-Kutta, a time efficient computer method with a high degree of precision, was selected to transform the Logistic Model into a difference equation, W(t + At) = W(t) + 1/6 (f1 + 2:2 + 2:3 + f4), K -W(t) f1 = (At) G W(t) [——E—————] p K p f K -[W(t)+f /2] f2 = (At) op [W(t) +— 1]{ P 1 } 2 K p f K -[W(t)+f /2] f3 = (At) GP mm + 2H p 2 } 2 K p K -[W(t)+f3] f4 = (At) 6 [W(t) + f ]( p I P 3 K p where W(t) = individual weight of the fish at time t. t is initially set at 0, i.e. day zero; and At = 1 day. Gp and Kp are pairs of the system's parameters, growth rate and carrying capacity, respectively, constrained by a set of treatments associated with a sequence of time periods denoted by p = 1, 2, 3, 4. The system's initial condition is given by W(t=0) = W(0), that is, the initial weight of a fish at day zero. One million values of W(O) were generated from Monte Carlo Simulations using a given mean and standard deviation. The given mean and standard deviation 35 were the mean and standard deviation of the initial weights of the studied fish. A computer simulation based on the difference equation was therefore used with the one million initial weights of fish and a series of paired Gp and KP. In other words, the total biomass production in grams from the system under a given set of sequential treatments was continuously generated on a daily basis. Appendix 5 presents a complete program of the computer simulation. By comparing the various outputs due to the various sets of treatments, we may approach a determination regarding the optimum set of sequential treatments. The optimum set may be defined by the following two ways with respect to the market demand: (1) it is a set of sequential treatments capable of producing fish at a certain desired size in grams with the fewest operating days; or (2) it is a set of sequential treatments capable of producing the greatest biomass in grams under a selected number of operating days, i.e. 80 days. Two ways of analyzing the outputs were therefore designed. Based on the shortest production cycle in days to reach a desired size, a statistical model was designed as follows, Yij = p + SRi + Eij . Y.. is the jth observed production cycle, or the number of 13 th days to reach a desired size using the i selection in the computer simulation. p, a constant, is the true mean of the 36 distribution of variable Y. SRi is the average effect of the ith selection of the simulation. Eij is the random error associated with Yi" Perform Hartley's F-max test 3 (Gill, 1978a) first, a test of homogeneous variance, involving the ratio of the largest to the smallest of the variances within the total simulations. As long as the assumption of equal variances is met, the ANOVA is conducted (Table 7). If the F ratio of the ANOVA is significantly large, then Tukey's test is applied to the multiple comparison. If not, the analysis ends. In Tukey's test, the HSDa (Honestly Significant Difference) is again used as an index to compare with any difference between two means, Yi. and Yi'.’ where i i i'. If the difference between Y1. and §i'. exceeds the HSD, we may conclude that simulation run 1 is better than simulation run i', or vice versa. This test thus indicates which of the two compared sets of sequential treatments is the best for producing fish of a desired size in the shortest time. To determine the optimum treatments to produce the largest biomass production in grams under a given number of operating days, the statistical model is Yij = p + SR1 + Eij . Yij is the jth observed mean weight in grams of the one a. MSE ———— , where a = 0.05; n = i x j ”SD = (qa,i,n-i) j = sample size; i = a number of the simulation runs; j = a number of the observations (replicates) per simulation run. 37 Table 7. One way ANOVA with variable Y denoting the production cycle of reaching a desired size. Source of Variation Sum of8 Degrees of Mean F‘b Squares Freedom Square Ratio Total SSY 1 x j - 1 MSY Simulation Run 33 i - 1 MS M333 SR SR MS Residuals ssE i(j - 1) MSE E a. 1 j 2 1 j 2 . . SSY = E 2 Yif - ( 2 2 Y.i') / (1 x j) , 1=1 j=1 3 i=1 j=1 3 i 2 . i 3 2 . . SSSR — (.2 Yi /3) ' (.2 Z ij ) ./ (1 X 3) r 1=1 ° 1=1 j=1 SSE = SSY - SSSR , where i the number of computer simulations, 3 = the number of observations in production cycle per simulation. A critical value of F is chosen at a = 0.05, i'e" Fa,(i-1),i(j-1) = Fo.os,(i-1),i(j-1)' 38 th million fish under the i simulation run. p, a constant, is the true mean of the distribution of the variable Y. SRi is the average effect of the ith selection of the simulation run. Eij is the random error associated with Yij' This modeling, design and analysis, is similar to the former, except that the variable Y is now defined differently. RESULTS The discussion of results is divided into three areas: (1) stochastic modeling, (2) performance of the system's operation, and (3) deterministic modeling by computer simulation. STOCHASTIC MODELING The experimental observations of weight and weight ratio are contained respectively in Tables 8 and 9. The results of this modeling are separately presented in the following sections: (1) tests of assumptions, (2) ANOVA, and (3) Tukey's tests. Tests of Assumptions In testing the hypothesis of normality, the 72 random errors with weight variable are shown in Tables 10. The test statistic is 2 G (9.20738) = = 5.38 , a 33 15.76 W which is much greater than a critical value of WO 1 72 = ' I ' SSE = 15.76 is quoted from Table 14. 39 40 .cm0u m we unowma mnu m0 c00um>uwwno comm .0 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.00 00.00 00.00 00.00 :00: 00.00 00.00 00.00 00.00 000: 00.00 00.00 00.00 00.00 :00: 00.00 0.00 0.00 0.00 0.00 500 0.00 0.00 0.00 0.00 2:0 0.00 0.00 0.00 0.00 5:0 o0wW0 0.00 0.00 0.00 0.00 .000 0.00 0.00 0.00 0.00 0000 0.00 0.00 0.00 0.00 000 0.00 0.00 0.00 0.00 0000 0.00 0.00 0.00 0.00 0000 0.00 0.00 0.0 0.0 000 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.00 00.00 00.00 00.00 0002 00.00 00.00 00.00 00.0 :00: 00.00 00.00 00.00 00.0 :00: 00.00 0.00 0.00 0.00 0.00 000 0.00 0400 0.00 0.00 200 0.00 0.00 0.00 0.00 2:0 000W0 0.00 0.00 0.00 0.00 0000 0.00 0.00 0.00 0.0 0000 0.00 0.00 0.00 0.0 000 0.00 0.00 0.00 0.00 0000 0.0 0.0 0.0 0.0 000 0.00 0.00 0.0 0.0 000 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.0 00.0 00.0 00.0 00 00.00 00.00 00.00 00.00 :00: 00.00 00.00 00.00 00.00 :00: 00.00 00.00 00.00 00.00 000: 0.00 0.00 0.00 0.00 000 0.00 0.00 0.00 0.00 5:0 0.00 0.00 0.00 0.00 0:0 000 0.00 0.00 0.00 0.00 0000 0.00 0.00 0.00 0.00 000 0.00 0.00 0.00 0.00 000 0.00 0.00 0.00 0.00 .000 0.00 0.0 0.0 0.00 000 0.00 0.00 0.00 0.00 000 00 0m 0m 0m 000002 00 00 0m 0m 000202 00 0m 0m 0m 000502 6:0umsq4 5:0005U4 EsHumso< 000000-00 000000-00 000000-00 pummwmmwa ucwEuwmuB >u0mcwo .xmo-om 00 Amy m600uma 0 um c00u020nsoo ucmsummuu you w mc00um>ummno unq0m3 028 .w m0nma .0000 0 0o 00000 020003 0:» m0 c0000>0mmno comm Al .w -00x0 0000.0 000.0 000.0 00 000.0 0000.0 000.0 000.0 00 0-00x0 000.0 0000.0 000.0 00 000.0 000.0 000.0 000.0 0002 000.0 000.0 000.0 000.0 0002 000.0 000.0 000.0 000.0 :00: 00.00 00 000.0 000.0 000.0 000.0 2:0 000.0 000.0 000.0 000.0 5:0 000.0 000.0 000.0 000.0 5:0 00.00 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 .000 000.0 000.0 000.0 000.0 000 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 .000 000.0 000.0 000.0 000.0 000 00.0 0000.0 0000.0 -00x0 00 000.0 000.0 000.0 000.0 00 0-00x0 000.0 -00x0 000.0 00 000.0 000.0 000.0 000.0 :00: 000.0 000.0 000.0 000.0 0002 000.0 000.0 000.0 000.0 000: 00.00 00 000.0 000.0 000.0 000.0 0:0 000.0 000.0 000.0 000.0 000 000.0 000.0 000.0 000.0 0:0 00.0 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 000 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 200 000.0 000.0 000.0 000.0 000 -00x0 0000.0 0000.0 000.0 00 000.0 000.0 000 0 000.0 00 000.0 0000.0 000.0 000.0 00 000.0 000.0 000.0 000.0 0002 000.0 000.0 000.0 000.0 :00: 000.0 000.0 000.0 000.0 :00: 000.0 000.0 000.0 000.0 2:0 000.0 000.0 000.0 000.0 2:0 000.0 000.0 000.0 000.0 2:0 000 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 000 000.0 000.0 000.0 000.0 000 000.0 000.0 000.0 000.0 0000 000.0 000.0 000.0 000.0 .00 000.0 000.0 000.0 000.0 000 00 00 00 00 000502 00 00 00 00 000002 00 00 00 00 000502 5:0005U4 8:0003U4 530003U4 ucme nummua c0000wnon c0000u-00 c0000o-o0 0050029 ucmeumwue 0000:00 .xmp-om 00 “my 0000009 0 um co0um:0neou acmeumouu 00a mch0um>0wmno 00u00 uno003 one .0 m0n09 42 .m an m . 00w u 000 u 02 0000 .0 00.0 00.0 00.0 00.0 2000 00.0 00.0 00.0 00.0: 2000 00.0 00.0 00.0 00.0 200 00.00 00.0- 00.0: 00.0- 00.0- 2000 00.0: 00.0- 00.0- 00.0 2000 00.0- 00.0: 00.0: 00.0- 200 00 00.00 00.0: 00.0 00.0 00.0 2000 00.0 00.0 00.0 00.0: 2000 00.0 00.0 00.0 00.0 200 00.00 00.0 00.0- 00.0: 00.0- 2000 00.0: 00.0: 00.0: 00.0 200 00.0- 00.0: 00.0: 00.0- 200 00 00.00 00.0- 00.0- 00.0: 0.0- 2000 00.0 00.0 00.0 00.0 200 00.0- 00.0: 00.0- 00.0- 200 00.0 00.0 00.0 0.0 2000 00.0- 00.0- 00.0- 00.0: 200 00.0 00.0 00.0 00.0 200 000 00 00 00 00 000502 00 00 00 00 000502 00 00 00 00 000502 5:0003U4 50000034 5:0000v4 050E ceaammuon ceaamocma cofiammuoH :00009 H050mce ucmeummua >uflmcmo .ucm003 may no . mflmnuvm .000000 Eoocmm .oH manna w 43 0.9725. Therefore the random errors are normally distributed. Table 11 contains the other 72 random errors with the variable of weight ratio. The test statistic is 62 (0.5605007)2 SSE 0.275311 which exceeds the critical value of W = 0.9725. The 0.1,72 hypothesis of normality in weight ratios is still accepted. The homogeneity of variances associated with the nine treatment combinations was examined within each time period. Tables 12 and 13 indicate that the assumption of equal variances is met. Analysis of Variance (ANOVAL Both of the ANOVA tables (Tables 14 and 15) reveal that the time factor (period) has a significant effect on the growth of fish. However, the multiple comparison among the three thermal treatments must be done for the same period of time because of the significant interaction effect between period and temperature (Tables 14 and 15). 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Amy mamsuflmmm m¢¢.o thmvoo.o momvmo.o NH Amoev :ofluomumucH ma¢.o mmnmmoo.o meomo.o m Amov cofluomumucH Ho.ovmvmoo.o mmoo.v mnmmovo.o mmomvm.o o Amev :ofluomumucH mmoo.ovmvHoo.o m¢ma.n movmmno.o mmmwflm.o m Amy noflumm mmwmmoo.o mommho.o m Aoe\uwaflnwnoum caumm m cums no saw no mmwumwo newumwum> mo wousom .oflumu unoflms mnu mo <>oz< .mH mHnma 49 treatment. As a result, Tables 16 and 17 respectively display the rearranged data with related treatment means of the weight and weight ratio. By applying Tukey's method, the means of thermal treatments were compared at every time interval. Tables 18 and 19 present the optimum treatment(s) in terms of temperature on the basis of the ZO-day-cycle. PERFORMANCE OF THE SYSTEM'S OPERATION Table 20 shows that the quality control of the constant thermal treatment (24C) was satisfactory. Additionally, each pair of duplicated tanks, receiving the same assigned cyclic thermal treatment, statistically possess equal slopes (b) and intercepts (a) for the same time interval (Tables 21 and 22). As a result of the equivalences, a common linear regression of temperature versus time for each cyclic thermal treatment is described on the basis of 20 days' cycle (Tables 23 and 24). DETERMINISTIC MODELING BY COMPUTER SIMULATION The stochastic modeling has identified some significant thermal treatments according to the variables of weight and weight ratio on the cycle basis of 20 days (Tables 18 and 19). By further processing the results of Tables 18 and 19, 50 Table 16. The means of thermal treatments of the weight at each time period. Thermal Aquaria Size P0 P20 P40 P60 P80 Treatment (Gal) 10 15.1 13.5 12.8 13.8 14.5 10 7.4 10.2 10.4 10.8 12.2 15 7.5 11.3 9.1 8.9 10.1 24C 15 10.1 12.1 11.8 12.4 12.8 30 10.7 13.9 12.2 12.9 14.9 30 9.0 11.3 10.2 10.5 12.2 mean = 10.0 12.050 11.083 11.550 12.783 10 7.6 8.7 9.9 10.8 11.4 10 10.0 9.5 10.7 12.7 13.4 22.7C 15 9.6 9.9 9.1 9.3 9.5 to 15 10.3 9.5 11.1 11.9 12.9 26.8C 30 10.6 11.6 13.0 14.0 16.5 30 11.4 12.5 13.7 14.5 14.2 mean = 9.9 10.283 11.250 12.200 12.983 10 7.9 9.6 9.5 10.3 11.6 10 11.2 10.9 11.1 11.3 12.7 24.6C 15 10.6 13.6 11.5 12.0 12.8 to 15 10.1 12.0 13.0 13.3 15.3 28.8C 30 8.5 10.4 10.0 11.0 11.5 30 11.1 12.8 13.5 14.4 15.0 mean = 9.9 11.550 11.433 12.050 13.150 51 Table 17. The means of thermal treatments of the weight ratio at each time period. Thermal Size of Aquarium P20 P40 P60 P80 Treatment (in Gallons) 10 0.894 0.948 1.078 1.051 10 1.378 1.020 1.038 1.130 15 1.507 0.805 0.978 1.135 24C 15 1.198 0.975 1.051 1.032 30 1.299 0.878 1.057 1.155 30 1.256 0.903 1.029 1.162 mean 1.255 0.922 1.038 1.111 10 1.145 1.138 1.091 1.056 10 0.950 1.126 1.187 1.055 22.7C 15 1.031 0.919 1.022 1.022 g to 15 0.922 1.168 1.072 1.084 26.8C 30 1.094 1.121 1.077 1.179 30 1.096 1.096 1.058 0.979 mean 1.040 1.095 1.084 1.062 10 1.215 0.990 1.084 1.126 10 0.973 1.018 1.018 1.124 24.6C 15 1.283 0.846 1.044 1.067 to 15 1.188 1.083 1.023 1.150 28.8C 30 1.224 0.962 1.100 1.045 30 1.153 1.055 1.067 1.042 mean 1.173 0.992 1.056 1.092 52 Table 18. Tukey's test on thermal treatments of the weight within each time period. Time Thermal Treatment Difference Determination Period Treatment Mean Between According to Means HSD=1.62 Period I 24C 12.050 Treatments 0.500 24C and 24.6C Day 1 24.6C~28.8C 11.550 to 28.8C are to 1.267 effective. Day 20 22.7C~26.8C 10.283 Period II 24.6C~28.8C 11.433 0.183 There is no Day 21 22.7C~26.8C 11.250 . significant to 0.167 difference. Day 40 24C 11.083 Period III 22.7C~26.8C 12.200 0.150 There is no Day 41 24.6C~28.8C 12.050 significant to 0.500 difference. Day 60 24c 11.550 Period IV 24.6C~28.8C 13.150 0.167 There is no Day 61 22.7C~26.8C 12.983 significant to 0.200 difference. Day 80 24c 12.783 53 Table 19. Tukey's test on thermal treatments of the weight ratio within each time period. Time Thermal Treatment Difference Determination Period Treatment Mean Between According to Means HSD=0.0975 Period I 24C 1.255 Treatments 0.082 24C and 24.6C Day 1 24.6C~28.8C 1.173 to 28.8C are to 0.133 effective. Day 20 22.7C~26.8C 1.040 Period II 22.7C~26.8C 1.095 Treatment 0.103 22.7C to Day 21 24.6C~28.8C 0.992 26.8C is to 0.070 effective. Day 40 24C 0.922 Period III 22.7C~26.8C 1.084 0.028 There is no Day 41 24.6C~28.8C 1.056 significant to 0.018 difference. Day 60 24c 1.038 Period IV 24C 1.111 . 0.019 There is no Day 61 24.6C~28.8C 1.092 significant to 0.030 difference. 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Period I Initial Final (Day 1 to Day 20) Temperature Temperature Range at X = 0 at X = 12 Y = 21.552 + 0.434X 21.6C 26.8C 5.2C Period II (Day 21 to Day 40) A Y = 22.989 + 0.336X 23.0C 27.0C 4.0C Period III (Day 41 to Day 60) ; =22.776 + 0.327X 22.8C 26.7C 3.9C Period IV (Day 61 to Day 80) A Y = 23.542 + 0.254X 23.5C 26.6C 3.1C Mean 22.7C 26.8C 4.1C Standard Deviation 0.8057 0.1708 0.8660 a. A Y are temperatures predicted at time X according to a regression line. 58 Table 24. Linear regression8 of cyclic thermal treatment (24.6C to 28.8C) at various time interval. Period I Initial Final (Day 1 to Day 20) Temperature Temperature Range at X = 0 at X = 12 Y = 23.656 + 0.403X 23.7C 28.5C 4.8C Period II (Day 21 to Day 40) Y = 24.791 + 0.356X 24.8C 29.1C 4.3C Period III (Day 41 to Day 60) Y = 24.705 + 0.341X 24.7C 28.8C 4.1C Period IV (Day 61 to Day 80) Y = 25.149 + 0.307X 25.2C 28.8C 3.6C Mean 24.6C 28.8C 4.2C Standard Deviation 0.6377 0.2450 0.4967 8. A Y are temperatures predicted at time X according to a regression line. 59 the carrying capacities and daily growth rates, influenced by various thermal treatments in a time sequence for a single fish, are summarized respectively in Tables 25 and 26. Tables 27 and 28 summarize four sets of dynamic computer inputs, determined by selecting the optimum thermal treatments through time periods from Tables 25 and 26, according to the optimums in daily growth rate and carrying capacity, respectively. By providing the simulation system (Appendix 5) with the inputs (Tables 27 and 28) in order, the computer made printouts of mean and variance of the one million weights on a daily basis. These primary printouts are collected in Appendix 6. Tables 29 and 30 show the rearranged data extracted from the primary printouts to proceed ANOVA in the simulations. The statistics in Hartley's Fma test are x 2 9 1666667 maximum ' Fmax = = = 1.00 (Table 29), 2 S minimum 9.1666667 and 2 0 0000277 maximum ' Fmax = = = 1.17 (Table 30). 2 0.0000236 minimum 60 Table 25. Carrying capacity of a single fish associated with producing thermal treatment at 4 periods of 20-day. Time Thermal Treatment, Carrying Remark Period Treatment Mean(W Capacity(K) Period I 24C 12.050 2.410 Optimum (Day 1 to 24.6C~28.8C 11.550 2.310 Optimum Day 20) 22.7C~26.8C 10.283 2.057 Viewed as Period II 24.6C~28.8C 11.433 2.287 optimum (Day 21 to 22.7C~26.8C 11.250 2.250 Day 40) 24c 11.083 2.217 Viewed as Period III 22.7C~26.8C 12.200 2.440 optimum (Day 41 to 24.6C~28.8C 12.050 2.410 Day 60) 24c 11.550 2.310 Viewed as Period IV 24.6C~28.8C 13.150 2.630 optimum (Day 61 to 22.7C~26.8C 12.983 2.597 Day 80) 24c 12.783 2.557 a . t = days 20, 40, 60 and 80. b. K is carrying capacity of a single fish, Wt is a weight of 5 fish per aquarium at time t; where 10e. K = Wt/S. 61 Table 26. Daily growth rate of a single fish associated with producing thermal treatment at 4 periods of 20-day. Time Thermal Treatment Daily Growth Remark Period Treatment b Mean(Wt/We) Rate (G) Period I 24C 1.255 0.0113568 Optimum (Day 1 to 24.6C~28.8C 1.173 0.0079782 Optimum Day 20) 22.7C~26.8C 1.040 0.0019610 Period II 22.7C~26.8C 1.095 0.0045377 optimum (Day 21 to 24.6C~28.8C 0.992 —0.0004016 Day 40) 24C 0.922 -0.0040605 Viewed as Period III 22.7C~26.8C 1.084 0.0040329 optimum (Day 41 to 24.6C~28.8C 1.056 0.0027244 Day 60) 240 1.038 0.0018648 Viewed as Period IV 24C 1.111 0.0052630 optimum (Day 61 to 24.6C~28.8C 1.092 0.0044005 Day 80) 22.7C~26.8C 1.062 0.0030077 a. former time; W t time t or the latter time. b. G = 1n (—E)/t , W 0 G is the daily growth rate of fish, that is, W where t = 20 days. W0 is the fish weight of an aquarium at time zero or the is the fish weight of an aquarium at 1‘ 62 Table 27. The dynamic inputs of computer simulation based on the selection of optimum daily growth rate. Simulation 1 Simulation 2 Period I Thermal Treatment 24C 24.6C~28.8C (Day 1 to Produced G 0.0113568 0.0079782 Day 20) Produced K 2.410 2.310 Period II Thermal Treatment 22.7C~26.8C 22.7C~26.8C (Day 21 to Produced G 0.0045377 0.0045377 Day 40) Produced K 2.250 2.250 Period III Thermal Treatment 22.7C~26.8C 22.7C~26.8C (Day 41 to Produced G 0.0040329 0.0040329 Day 60) Produced K 2.440 2.440 Period IV Thermal Treatment 24C 24C (Day 61 to Produced G 0.005263 0.005263 Day 80) Produced K 2.557 2.557 G and K respectively denote daily growth rate and carrying capacity of a single fish. 63 Table 28. The dynamic inputs of computer simulation based on the selection of optimum carrying capacity. Simulation 3 Simulation 4 Period I Thermal Treatment 240 24.6C~28.8C. (Day 1 to Produced K 2.410 2.310 Day 20) Produced G 0.0113568 0.0079782 Period II Thermal Treatment 24.6C~28.8C 24.6C~28.8C (Day 21 to Produced K 2.287 2.287 Day 40) Produced G -0.0004016 -0.0004016 Period III Thermal Treatment 22.7C~26.8C 22.7C~26.8C (Day 41 to Produced K 2.440 2.440 Day 60) Produced G 0.0040329 0.0040329 Period IV Thermal Treatment 24.6C~28.8C 24.6C~28.8C (Day 61 to Produced K 2.630 2.630 Day 80) Produced G 0.0044005 0.0044005 K and G respectively denote carrying capacity and daily growth rate of a single fish. 6A .comwwu umHsofluumm wcm usonufiz coeumuuwCOEDU you do omxofld ma mo.~ .m soemmmH.m u moemHum> soeemeH.m n 00cmHum> sommmeH.m u mucmHum> seememH.m u mocmHum> m.me u cam: m.mv u cam: m.Hw u cmmz m.sn u new: oH u mumoHHemm oH u mumuHHdmm eH u mumoHHemm 6H u mumoHHemm oeoommo.~ an mmmeemo.~ em emHesmo.~. mo emammmo.m Ne Hemmemo.~ ms . mememmo.~ mm mHeemmo.~ mm meemHmo.~ He mHHsemo.~ ms ommemmo.m mm omemmmo.~ em s~m60mo.~ oe ~H66mmo.~ He emaeHno.m Hm OHmommo.~ me enm40mo.~ an meoeHmo.~ on awesome.m om son6mo.~ mo smHoomo.m mm enmeamo.~ a6 maHsamo.~ me memmmmo.~ H6 eaemamo.m em mmmowmo.m mo HHthmo.m we movhomo.m oo mmmommo.m on Amneemo.~ he eHeasmo.~ he amaemmo.~ am maHemmo.~ mm mansemo.~ 66 MHmaemo.N ea memeemo.~ mm memHmmo.N an Hmonmo.~ me eoeammo.~ me amoemmo.m em . semesmo.~ mm amHe eoHHHHz “mean we we emHe eoHHHHz .msme do my :mHe coHHHHz Amsmn Do we :mHe coHHHHz Amsma to we mco mo maoxo mco mo mHoxo mco mo mao>u mco mo mauxo ucmflmz com: COwuosooud unmflmz cow: coHuosooum ucqwmz com: COwuosooum ucmfimz coo: newuosooum e sawumHsEfim n cowumHSEHm m cowumHSEHm H cofiumHDEwm EOMDMHSEMW MO MCOHUUNHOW .mcoHumHseflm a no .meu@ mmo.m .muflm omuflmmo m mcflnummu mo mmaoxo cowuosooum .mm magma .mocmficm>coo you swam coHHHME mco mo ucmflw3 some onu daem: >n ommmmumxm Hawum mH name» Essflxwz .0 65 bvmoooo.o u moccaum> ommoooo.o u mocmflum> bbmoooo.o H mocmflum> Homoooo.o H mocmflum> wowvoeo.~ u cows mbbwmmo.~ u :00: memoemo.~ u :00: mbbbo.~ u :00: OH H mumowammm OH H mumowammm OH H oumoflammm OH H mumoflamom ow omnwbvo.m ow Hobwmbo.m om mmmwawo.m ow emmmmwo.m mb moomowo.m . mb HmwNHbO.N mb wwmaomo.m mb womommo.m wb mmomvvo.m wb mbwomoo.m mb maovmmo.m mb vommawo.m bb bmmmmvo.~ bb emwowoo.m bb weboomo.m bb webmomo.m 0b womNHvo.N ob wwwvooo.m ob wommvmo.m 0b mbmmwbo.m mb omvommo.m mb bmmwvoo.m mb vmmammo.m mb ©0000b0.m Vb omoommo.m vb Nowmmoo.m 6b owm¢Hm0.N Vb moammbo.m mb Hommmmo.m Mb NNboHoo.N Mb vabmvo.N mb ooameo.m Nb wHHbvmo.N Nb baboooo.w Nb moombwo.m Nb mmeHb0.N Hb NHbOmmo.m Hb mwvvwmo.m Hb Hoamovo.m Hb meHObo.m Amsmev wHoso Ame 6HOH> Amsmnc mHoso Ame 6H0H> Amsmec wHoso Ame 6H0H> Amsmec mHoso Ame 6H0H> COHHUSUOHD EDEMXMZ cOHUODUOMm EDEHXGE COMUODGOHQ ESEHXGZ COMUUDUOHQ EDEMXGZ ¢ COHHMHfiEMW M COHHMHDEHW. N COflUMHDEHm H COMfiMHDEflm cowumHDEwm mo mcofluowamw .mcofiumasefim e no Aboouowv maobo cowuosooua owxwu a mo mmoamflb EDwamz .om manna 66 Both of the Fmax's are much smaller than the critical Fmax,a,i,j-1 = 3.648. As a result, the assumption of homogeneous variance is met. Moreover the ANOVAs (Tables 31 and 32) indicate that the overall tests are significant. Tukey's test is then used on the comparisons of means from Tables 29 and 30. The results of Tukey's test, summarized in Tables 33 and 34, conclude that the first selection of simulation enables the production of golden shiners to reach the management goals. Fmax,a,i,j-1 = 3.64; where a = 0.25; 1 = a number of the simulation runs = 4; j-l = (a number of the replicates) - 1 = 10 - 1 = 9. 67 Table 31. ANOVA of computer modelings for reaching a desired size with shortest production cycle. Source of Variation Sum of D. F. Mean F Ratio Squares Square Total 6210 39 Simulations 5880 3 1950 213.8188 (p<<0.0005) Residuals 330 36 9.1666666 Table 32. ANOVA of computer modelings for obtaining a maximum harvest over 80 days. Source of Variation Sum of D. F. Mean F Ratio Squares Square Total 0.008454 39 Simulations 0.007624 3 0.0025413 110.49130a (p<<0.0005) Residuals 0.00083 36 0.000023 a' The effects due to the simulation runs are significantly different from one another. 68 .ufi 000Hmwu s s o s s 0 on ammono ma mew.m u on 6 mo ow .muoumumcu .0H20Hw0>0 uoc we on v mo ow s s o H'Csds‘ 00>0som .6H\000000H.mfi Aem 4 me owe n “\mms_ A. . as n am: 0:00 was .0 H000 acmemo0c0s buHuoHum cuusom mflnu ocfiob0omu . . m.mo 0 H000 ucmswqmcme buHuoHum ouHcB o.w mwcu ocfiob0mmu . . . m.Ho m H000 ucmsmo0c0s o.mH many magnummmu bufluoflnm ocoowm m.mv m H0oo ucmewomc0s o.mH was» gawou0mmh bufluoHum umuflm m.bm H m:0mz c003u0m cofiUOHDEHm COwumasfiwm 0Hw6.m u owm o» mcfionoooc comeHocoo mwocmumuufio mo mammz mo mcowuomamm .Amb0ov 0H0>0 cofluosooum pmwuuocm nuws muflm omnwmwo 0 ocwcommu mo nonwamoos u0u5m500 co umwu m.>0x58 .mm 0HQ0B 69 s s 0 on ammoco ma mew.m n on a mo 00 .muoumumnu .wHD0Hfl0>0 uoc ma .uw momammu ~ s 0 on v mo DU . . . ch.H. 00>0zo= .Omemoooo.ofi Ron 4 mo owe u “\mmz_ A. . u we n am: 0:00 0:9 .0 Hmom ucwswm0c0E buwuoflum nuusom menu mcHob0omu moovovo.m v HMMWDDMNWMWMMMM >0H00Hbm nuHce mmomMHo.o oemoemo.m m HMMMDDMWMMWMMMM suHuoHue 0:0000 emmoHHo.o msbomoo.~ m Hmmmuummwmwmmmw suHuoHue umuHe smmomHo.o mnbso.~ H mammz cmwiwnvwm COHUMHDEHW COHHMHDEHW 0~Hnmmoo.o n 000 cu ocHepoooe :onsHocoo mmoemumeeHo mo mc0mz uo mcowuomamm umm>hmn Boswx0s 0 vcwcfl0uno mo mmcwamoos nmuzmsoo .mbmo ow um>o :0 ummu m.>0xse .em 0Hbme DISCUSSION Discussion of this research is focusd on two areas: (1) quality of the experimental system's operation; and (2) application and promotion of the research concept. The intensities of the three thermal treatments were consistent over the duration of this research. Thus the system's performance in thermal control was highly satisfactory. However, the two studied cyclic temperatures as a secondary design differed from the primary desires. The primary desires were intended to be 24 i 2C and 24 1 4C with daily fluctuations of 4C and 8C, respectively. Budgetary constraints did not allow using the desired temperature cycles, forcing the use of a secondary design. In addition, the electrical supply to the laboratory only allowed each treatment combination to be replicated 2.5 times in terms of the needed heating and aeration. Constrained to two replicates per treatment combination, this experiment ran the risk of low statistical power. The replication used was the maximum attainable with the facilities available. While the factor of density was shown to be insignificant, the thermal factor did have a significant 70 71 effect on the growth and production of fish. The constant temperature, 24C, was the most effective treatment for the first and last periods of 20 days. The cyclic temperature, fluctuation between 22.7C and 26.8C, appeared to be the best treatment from day 21 through day 60. These results suggests that the two effective thermal treatments should be interchanged with each other over the four consecutive intervals to achieve the management goals. The statistical information from this experiment enables scientists to conduct a series of additional studies efficiently. That is, with referred mean square error (MS scientists can estimate the replication E). required per treatment (or treatment combination) in related studies to obtain expected statistical power (1 - B) of detecting treatment (or treatment combination) effects of specified magnitude at a specified level of significance (1 - a). Moreover, the results can be applied to at least two other aspects of aquaculture development: (1) utilizing the heated effluent waters of power plants as a substitute water source, and (2) introducing the modeling technique into the field of aquaculture. The aquaculture industry in the United States today is facing an increasing problem of water supply. More and more farming systems are getting less and less water out of deep wells because of lowered water tables. Such declines expose the serious fact of overpumping resulting from the high water demand by 72 industrial plants and a vast increase in farming activities. In fact, overpumping is a common and inevitable means used to gain more profits in the management of aquaculture businesses for those farmers in developing countries. Consequently, water tables fall rapidly and usually contribute to environmental deterioration. The west coast of southern Taiwan, for example, has attracted thousands of aquaculture businesses and is now suffering from degeneration of water quality. The local scientists warn that overpumping is a major factor and must be prohibited immediately, otherwise the water table will continue to drop. As a result of the lowered water tables, the local stratum will be encroached upon by the sea and the ground water will be salinized. Another problem is heated effluent waters released from the cooling systems of power plants. These effluents cause concern among limnologists. The heated effluents may disturb the normal thermal structures of the aquatic environments and result in degradation of the system. Therefore, limnologists suggest that water used in the power-generating process should be returned to receiving waters after being cooled in pools, reservoirs, or cooling towers. But, as viewed by aquaculturists, such heated effluents are valuable resources providing tremendous amount of warm water for fish culture. By mixing waters properly, several desired temperatures (constant or cyclic) could be generated to produce fish to meet market demands. The application of 73 "waste-heat aquaculture" may provide for efficient production and reduce ecological problems. The three types of modeling introduced into this study contribute to a future trend in developing aquaculture using systems analysis. Statistical modeling is a commonly used routine for experimental design and analysis. This type of modeling is applied to investigate systems which can be only described by predictive models. Scientists from fields, such as biology, economics, and sociology, must accept the use of predictive models that are only approximately correct because of unknown factors. The unknown effects on the trait of interest are collectively referred to as random error, sometimes called experimental error. Studies of physical and chemical systems, on the other hand, can be described with related deterministic models. The input-output relationship of a given electronic system, for example, may be exactly expressed by a deterministic model without considering random error because of the certainty of the physical world. Computer modeling, in fact, is an extension from previous modelings; that is, scientists study a system by translating the original form of a mathematical model into a computer program. Future life scientists may be characterized more by their ability to use the computer for data analysis and simulation than by their ability to use the traditional microscope. This results from the fact that living systems involve a complex interaction of chemical 74 and physical processes all of which are capable of being described in mathematical terms. These systems being more complex than any devised by the mind of man have for the most part resisted mathematical analysis by the classical methods so successfully employed by physicists and chemists. with the advent of computers, scientists have been able to use numerical methods to deal with these complex, multi-component systems. The problems of managing aquaculture systems grow in magnitude and complexity as the mass production of fish involves environmental conditions which have physical, nutritional, physiological, and pathological manifestations. Each species of fish has specific environmental requirements in which it can best grow and reproduce. Because of this, anyone interested in raising fish for profit should make every effort to obtain all available information concerning the environmental requirements of the fish of interest and should attempt to maintain such an environment for the fish. In addition, a recognition of the intricacy of aquaculture development has grown with the expanding awareness that nothing in this world exists by itself. Everything is interrelated, and no longer is there any excuse for considering the farming of aquatic systems, the overproduction by agriculture accompanied by changing markets, the fluctuating of financial interest rates, the tumbling of agricultural land values, the increasing or decreasing of oil-prices, or a 75 national deficit as a single, simple activity or phenomenon. By facing the complexity within and among systems, successful stewardship of aquaculture must rely deeply on systems analysis. Systems analysis through modeling, therefore, provides us with quantitative techniques and a methodological approach in dealing with planning, development, and management problems in real world systems. Aquaculture is now in a transitional stage evolving from reliance on crudely subsistent production techniques to more highly developed technologies. Unlike the past, modern aquaculture scientists are now making an endeavor at introducing systems and modeling concepts into the aquaculture area. Eventually they will use the systems at their disposal to manage aquaculture operations as effectively as a driver controls the course of an automobile to reach one's destination. The development of aquaculture will proceed more rapidly and efficiently if we apply the analytical techniques that have been developed for other fields to aquaculture. Appreciation of the whole may seem to make aquaculture management more difficult, but it also makes real and satisfactory solutions more certain. LIST OF REFERENCES LIST OF REFERENCES Biette, R. M., and G. H. Geen. 1980. Growth of underyearling salmon (Oncorhvnchus nerka) under constant and cyclic temperatures in relation to live zooplankton ration size. Can. J. Fish. Aquat. Sci. 37:203-210. Brown, E. E. and J. B. Gratzek. 1979. Fish Farming Handbook. Avi Publishing Company INC., Westport, Connecticut, 391pp. Cochran, W. G. and G. M. Cox. 1957. Experimental Designs. 2nd. ed., John Wiley and Sons, New York, Chichester, Brisbane, Toronto, Singapore. 611pp. Cooper, G. P. 1937. Food habits, rates of growth and cannibalism of young largemouth bass (Micropterus salmoides) in state-operated rearing ponds in Michigan in 1935. Trans. Amer. Fish. Soc. 66:242—266. Davis, P. J. and P. Rabinowitz. 1975, Methods of Numerical Integration. Academic Press, Inc., New York, San Francisco, London. 459pp. Everhart, W. H. and W. D. Youngs. 1981. Principles of Fishery Science (2nd ed.). Comstock Publishing Associates, Cornell University, Ithaca and London, 349pp. Forney, J. L. 1957. Bait fish production in New York ponds. N. Y. Fish and Game J. 4(2):150-194. Francis, A. A., F. Smith and P. Pfuderer. 1974. A heart- rate bioassay for crowding factors in goldfish. Prog. Fish-Cult. 36, 196-200. Gill, J. L. 1978a. Design and Analysis of Experiments in the Animal and Medical Sciences, Volume I. The Iowa State University Press, Ames, Iowa. 409pp. 76 77 Gill, J. L. 1978b. Design and Analysis of Experiments in the Animal and Medical Sciences, Volume II. The Iowa State University Press, Ames, Iowa. 301pp. Gill, J. L. 1978c. Design and Analysis of Experiments in the Animal and Medical Sciences, Volume III. The Iowa State University Press, Ames, Iowa. 173pp. Gill, J. L. 1986. Repeated measurement: sensitive tests for experiments with few animals. J. Anim. Sci. 63:943-954. Glaser, M. J. and R. A. Kantor. 1974, Effects of crowding on the spawning rate of the medaka (Oryzias latipes). Northeast. Fish Wildl. Conf. McAfee, N. J. 17pp. (Unpubl. ms.) Gordon, W. G. 1968. The Bait Minnow Industry of the Great- Lakes. United States Department of the Interior Fish and Wildlife Service Bureau of Commercial Fisheries. Fishery Leaflet. 608:1. Hammersley, J. M. and D. C. Handscomb. 1964. Monte Carlo Methods. John Wiley and Sons Inc., New York. 178pp. Hedges S. B. and R. C. Ball. 1953. Production and Harvest of Bait Fishes in Michigan. Michigan Department of Conservation Institute for Fisheries Research. Ann Arbor, Michigan, Miscellaneous Publication No. 6:3-29. Hewlett-Packard Company's Manual, 1984. HP 98820A Statistical Library for the HP 9000 series 200 computers (Manual Part No. 98820-13112). Hewlett- Packard Company, Fort Collins, Colorado. 399pp. Hickman, G. D. and R. V. Kilambi. 1974. Growth and production of golden shiner (Notemigonus grysoleucas) under different stocking densities and feeding rates. Proc. Arkansas Acad. Sci., Vol. 28:28-31. IMSL (International Mathematics Statistics Library) Library 1984. Volume I. FORTRAN Subroutines for mathematics and statistics. IMSL, Inc., Houston. Le Cren, E. D. 1965. Some factors regulating the size of populations of freshwater fish. Mitt. int. Verein. theor. angew. Limnol. 13, 88-105. Markus, H. C. 1934. Life history of the blackhead minnow (Pimephales promelas). Copeia, 1934(3):116-122. Myers, J. L. 1979. Fundamentals of Experimental Design. 3rd. ed., Allyn and Bacon, Inc., Boston, London, Sydney, Toronto. 524pp. 78 Odum, E. P. 1959. Fundamentals of Ecology. 2nd. ed., W. B. Saunders Company, Philadelphia and London, 546pp. Petersen, R. G. 1985. Design and Analysis of Experiments. Marcel Dekker, Inc., N. Y. Pflieger, W. L. 1975. The Fishes of Missouri. Missouri Department of Conservation, 343pp. Prather, E. E. 1957. Preliminary experiments on winter feeding small fathead minnows. Proc. 11th Ann. Conf. S. E. Assoc. of Game and Fish Comm. :249-253. Ricker, W. E. 1975. Computation and Interpretation of Biological Statistics of Fish Populations. Bull. Fish. Res. Board. Can. 191 : 382pp. Rose, S. M. and C. F. Rose. 1965. The control of growth and reproduction in freshwater organisms by specific products. Mitt. int. Verein. theor. angew. Limnol. 13, 21-35. Roseberg, R. B. and R. V. Kilambi 1975. Growth and production of golden shiner (Notemigonus grysoleucas) under different stocking densities and protein levels. Proc. Annu. Conf. Southeast. Assoc. Game and Fish Comm. 28: 385-392. Rubinstein, R. Y. 1981. Simulation and the Monte Carlo Method. John Wiley and Sons. New York, N. Y. 278pp. Scott, W. B. and E. J. Crossman. 1973. Freshwater Fishes of Canada. Fisheries Research Board of Canada, Ottawa, 966pp. Scraton, R. E. 1984. Basic Numerical Methods, An introduction to Numerical Mathematics on a Microcomputer. Edward Arnold, London, Baltimore, Caulfield East. 92pp. Smith, H. T., C. B. Schreck and O. E. Maughan. 1978. Effect of population density and feeding rate on the fathead minnow (Eimephales promelas). J. Fish Biol. 12(5):449- 455. Sobol', I. M. 1974. The Monte Carlo Method. University of Chicago Press, Chicago and London. 63pp. Spain, J. D. 1982. Basic Microcomputer Models in Biology. Addison-Wesley Publishing Company, Inc., London, Amsterdam, Don Mills, Ontario, Sydney, Tokyo. 354pp. 79 Spieler, R. E., T. A. Noeske, V. DeVlaming and A. H. Meier. 1977. Effects of thermocycles on body weight gain and gonadal growth in the goldfish (Carasgius auratus). Trans. Am. Fish. Soc. 106:440-444. Spigarelli, S. A., M. M. Thommes, and W. Prepejchal. 1982. Feeding, growth, and fat deposition by brown trout in constant and fluctuating temperatures. Trans. Am. Fish. Soc. 111:199-209. Stark, P. A. 1970. Introduction to Numerical Methods. Macmillan Company, New York, Toronto. 334pp. Stiefel, E. L. 1963. An Introduction to Numerical Mathematics. Academic Press, Inc., New York, London. 286pp. Swingle, H. S. 1953. A repressive factor controlling reproduction in fishes. Proc. Pacific Sci. Congr. 8(IIIA), 865-871. Todd, J. 1962. Survey of Numerical Analysis. McGraw-Hill Book Company, Inc., New York, San Francisco, Toronto, London. 589pp. Weeg, G. P. and G. B. Reed. 1966. Introduction to Numerical Analysis. Blaisdell Publishing Company, Waltham, Toronto, London. 184pp. Wilson, E. o. and W. H. Bossert. 1971. A Primer of Population Biology. Sinauer Associates, Inc., Sunderland, Massachusetts. 192pp. Winer, B. J. 1971. Statistical Principles in Experimental Design (2nd. ed.). McGraw-hill, Inc., New York, St. Louis, San Francisco, Dusseldorf, Johannesburg, Kuala Lumpur, London, Mexico, Montreal, New Delhi, Panama, Rio De Janeiro, Singapore, Sydney, Toronto. 907pp. Yu, M. and A. Perlmutter. 1970. Growth inhibiting factors in the zebrafish (Brachvdanio rerio) and the blue gourami (Trichoqaster trichopterus). Growth 34, 153- 175. Zar, J. H. 1984. Biostatistical Analysis (2nd ed.). Prentice-Hall, Inc., Englewood Cliffs, N. J. 718pp. APPENDICES Appendix 1. Michigan bait minnow supply survey. 1) 2) 3) 4) 5) What is your source of bait minnows? (please check one) I net or raise minnows for sale (please go to question 2) I purchase minnows for resale (please go to question 6) A combination of both (please go to question 2) My answers for the numbers of minnows netted or raised in the following section will be in (check one) dozens , pounds , or other (please specify other as ), Please list below how many bait minnows you netted last year: Small Medium Large Type spr/sum/fall/wint spr/sum/fall/wint spr/sum/fall/wint Golden shiner Fathead minnow White sucker Other (list) When was it difficult to obtain minnows by netting during the year? Never or fill in below: Small Medium Large Type months in short supply mo. short supply mo. short supply Golden shiner Fathead minnow White sucker Other (list) How many bait minnows did you raise last year? None or fill in below: Small Medium Large Type spr/sum/fall/wint spr/sum/fall/wint spr/sum/fall/wint Golden shiner Fathead minnow 80 81 Appendix 1 (cont'd.). *~k* 6) 7) 8) 9) White sucker Other (list) IF YOU DID NOT PURCHASE ANY MINNOWS FOR RESALE, PLEASE GO TO QUESTION 17*** My answers for the numbers of bait minnows purchased for reslae in the following section will be in (check one ) dozens , pounds , or other (please specify other as ). Please list the numbers of bait minnows you purchased for resale last year: Small Medium Large Type spr/sum/fall/wint spr/sum/fall/wint spr/sum/fall/wint Golden shiner Fathead minnow White sucker Other (list) Have minnows been harder or easier to obtain (please check one and explain in the space below). During what months are minnows difficult to obtain ? Never or fill in below: Small Medium Large Type months in short supply mo. short supply mo. short supply Golden shiner Fathead minnow White sucker Other (list) 82 Appendix 1 (cont'd.). 10) ll) 12) 13) 14) 15) 16) Please list percentages of your minnows which come from in-state and out-of- state producers below: In-state Producers Out-of-state Producers Type netted (%) minnow farms (%) (%) Golden shiner Fathead minnow White sucker Other (list) Have your sources of bait minnows changed significantly in the last few (3-5) years: No Yes (please explain yes answers below). Please list your in-state sources of farmed bait minnows. Please provide addresses if available. (use separate sheet if necessary) Do you know of any other in-state sources of farmed bait minnows?: Please provide names and addresses if available. (use separate sheet if necessary) Are there any specific reasons why you do not buy minnows from the bait farms listed in question 13? Please explain. Please list your average purchase prices per dozen , pound , or other (please specify other as ) bait minnows: Small Medium Large Type months in short supply mo. short supply mo. short supply Golden shiner Fathead minnow __ White sucker Other (list) Do you expect prices for bait minnows to increase , remain about the same , or decrease in the coming year? 83 Appendix 1 (cont'd.). 17) Please list your average se1ling prices per dozen , pound , or other (please specify other as ) bait minnows: Small Medium Large Type months in short supply mo. short supply mo. short supply 18) 19) 20) Golden shiner Fathead minnow White sucker Other (list) Have your sales of bait minnows improved , remained about the same or declined over the last few (3-5) years. Please explain. Do you expect bait sales will increase , remain about the same , or decline over the next few (3-5) years. Please explain. Would you be willing to pay premium prices for a guaranteed constant supply of farmed raised bait minnows ? Yes No (explain no). 84 Appendix 2. The formulas of respective sums of squares regarding the weight/weight ratio. 3 3 2 4 2 2 a as = 2 z z 2 Y - Y /N Y t=1 d=1 a=1 p=l tdap .... 3 2 2 $8 = 2 Y /(dap) - Y /N T t. I O O O O O t=1 3 2 2 SS = E Y /(tap) - Y /N D .d. O O O O O d=1 3 3 2 2 SS = 2 2 Y /(ap) - Y /N - SS - SS 3 3 2 2 3 3 2 SS 2 2 2 Y /p - Z 2 Y /(ap) A/TD t=1 d=1 a=1 tda t=1 d=1 td ' 4 2 2 ssP = 2 Y /(tda) - Y /N p=1 '10 3 4 2 2 SS — E 2 Y /(da) - Y /N - SS - SS TP t=1 p=1 t..p . T P 3 4 2 2 SS = z E Y /(ta) - Y /N - SS - SS DP d=1 p=1 d.p . D P 3 3 4 2 2 $5 = z z 2: Y /a - Y /N TDP t=1 d=1 p=1 td.p . - [SST + ssD + ssP + ssTD + ssTP + ssDP] ssE = ssY - [SST + ssD + ssTD + SSA/TD + ssp + ssTP + ssDP + SSTDP] a’N = total sample size = t x d x a x p 3 x 3 x 2 x 4 = = 3 72, where t = 3 thermal levels, d density levels, a = 2 aquarium replicates, and p = 4 time intervals (peiods). 85 Appendix 3. Obtaining the simple regression line for the four individual tanks during four individual 20-days intervals. N(EXY) - (EX)(ZY) Slope b = 2 2 NZX (2X) where X = heating hours; Y = averaged temperature of tank; and N = number of (X,Y). Intercept a = Y - bX Total 88 = 2Y2 - (2Y)2/N (EXY - ZXZY/N)2 2X2 Regression SS 2 (2X) /N Residual SS Total SS - Regression SS, Residual DF Total DF - Regression DF N 2 where DF = degrees of freedom. r = Correlation Coefficient = Jr2 2 Regression SS r = Total SS 86 Appendix 4. The formulas of testing hypotheses in Figure 2 I. II. and of computing common slope as well as intercept. Comparing two slopes. The test statistic is, b - b2 b = b otherwise 1f |t| 2 O: 1 2; ta(2),(N1fN _4), reject H 2 accept HO: bl = b2; 0 = 0.05. 2 2 _ (SY.X )P (SY.X )P Sb - b ‘ 2 2 + 2 2 1 2 2X1 - (2X1) /N1 2X2 - (2X2) /N2 Residual SSl + Residual SS 2 Residual DF1 + Residual DF2 is accepted, then the common slop is H m m U H 0‘ 1 b2' leyl - (2x1)(2Y1)/N1 + >3sz2 - (2X2)(2Y2)/N2 c 2 2 2 2 2X1 (2X1) /N1 + 2X2 (2X2) /N2 and then; Comparing two elevations. The test statistic is, _ (Y1 - Y2) — bc(X1 — x2) t _ ](s 2) [l/N + (1/N) (i J )Z/A] Y.X C l 2 1 2 C if |t| 2 ta(2)’(leN2_3), reject HO: the same elevation; otherwise accept HO: the same elevation: a = 0.05. _ 2 _ a 2 2 _ 2 AC - 2x1 (1x1) /N1 + 2x2 (2x2) /N2 BC = leyl - (2X1)(ZYl)/Nl + >3sz2 - (2X2)(ZY2)/N2 87 Appendix 4 (cont'd.). _ 2 _ 2 2 _ 2 cC - 2Yl (2Y1) /N1 + 2Y2 (2Y2) /N2 _ 2 ssC - cC BC /AC 2 SSc (SY.X )c = . N1 + N2 — 3 If HO: the same elevation, is accepted then the common intercept is aC = Yp - bC Xp, N X + N X where X = l l 2 2 , p + N 1 2 N Y + N X Yp: l 2 o Nl+N2 Thus, the common regression equation at a time interval of 20-day is Y = aC + bC X. This linear equation describes a thermal characteristic of the cyclic temperature treatment in a quantitative way; where X = heating hours with a range of 0 to 12; b c thermal increasing rate (C per hour); the lowest point of the cyclic temperature, namely a temperature at x = 0; and a Y = a predicted temperature at a given X. 88 Appendix 5. Program of computer simulation. *JOBCARD*,RG2,JC500,CM370000. FTNS. HAL,L*IMSL5. LGO. *EOS PROGRAM SHA REAL K DIMENSION W(lOOOOOO, 0:80),R(1000000,0:1) DOUBLE PRECISION DSEED OPEN (2,FILE='OUTPUT') c=0.0 K=0.0 Fl=0.0 F2=0.0 F3=0.0 F4=0.0 WMEANPD=0.0 WVARPD=0.0 DSEED=999999999.D0 WBAR=1.9855556 WSD=0.5661939 NR=1000000 WRITE (2,303) 303 FORMAT ('0',1OX,"MEAN AND VARIANCE OF lOOOOOO FISH 89 Appendix 5 (cont'd.). 313 404 100 -FOR EACH DAY") WRITE (2,313) FORMAT(25X,"[FIRST SELECTIONJ") WRITE (2,404) FORMAT('0',14X,"MEAN",25X,"VARIANCE") CALL GGNMLa (DSEED,NR,R) Do 10 J=1,80 s=0.0 WTOTAL=0.0 WSQRTOT=0.0 DO 20 I=1,1000000 IF (J .GE. 2) GO TO 100 W(I,J-1)=R(I,J-l)*WSD+WBAR IF (J .LE. 20) THEN G=0.0113568b K=2.410b ENDIF IF ((J .GT. 20) .AND. (J .LE. 40)) THEN c=0.0045377b K=2.250b ENDIF IF ((J .GT. 40) .AND. (J .LE. 60)) THEN G=0.0040329b ? K=2.44OJ 90 Appendix 5 (cont'd.). 20 30 505 ENDIF IF ((J .GT. 60) .AND. (J .LE. 80)) THEN G=0.005263b K=2.557b ENDIF Fl=G*W(I,J-1)*((K-W(I,J-l))/K) F2=G*(W(I,J—l)+F1/2)*((K-(W(I,J-1)+F1/2))/K) F3=G*(W(I,J-1)+F2/2)*((K-(W(I,J-1)+F2/2))/K) F4=G*(W(I,J-l)+F3)*((K-(W(I,J-1)+F3))/K) W(I,J)=W(I,J-l)+(F1+2*F2+2*F3+F4)/6 S=W(I,J) WTOTAL=WTOTAL+S WSQRTOT=WSQRTOT+S**2 CONTINUE CONTINUE WMEANPD=WTOTAL/(I—1) WVARPD=(WSQRTOT-WTOTAL**2/(I-l))/(I-2) WRITE(2,505) WMEANPD,WVARPD FORMAT('0',llX,F10.7,21X,F9.7) a 0 Generate Standard Normal Deviates (GGNML) is a computer subroutine program from IMSL Library (1984). During the computer simulation, the numerical values of G and K may be changed periodically depending on the selection of simulations. 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