SIMULATION OF VOYAGE ECONOMICS FOR SALMON SEINE FISHING BOATS IN BRiTISH COLUMBIA by WILLIAM DAVID MOLYNEUX B. Sc. (Hons.) The University of Newcastle-Upon-Tyne, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in FACULTY OF GRADUATE STUDIES (Department of Mechanical Engineering) We accept this thesis as conforming to the required standard THE UNWERSITY OF BRITISH COLUMBIA September © 1992 William David Molyneux, 1992 In presenting this degree at the thesis in partial fulfilment of the requirements for an advanced University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of Jc’c I The University of British Columbia Vancouver, Canada Date DE.6 (2/88) 5 CcLl>-.4 CD) 11 Abstract It is important to know the likely income to a fishing vessel, so that it can be operated as a profitable concern for its owner. Most work on fishing vessel design optimization has used average catch size and income as the measure of performance. economic Whilst this analysis adequate is when cost minimization is being considered, it is deficient for developing strategies for maximizing income. One analysis method which allows the for observed random variation in fishing operations is system simulation. It is the intention of this thesis to demonstrate that simulation modelling can be developed into a useful same analysis model tool can predicting for then be fishing incorporated vessel into operating expert system economics. based The design techniques. A simulation model for salmon seine fishing in British Columbia was developed which allowed for variation in catch rates with fishing locations, the distance between the locations and constraints on the fishing process. vessel The operational profile used in the simulation was based on a review of previous research, discussions with previously unpublished specific fishermen and industry data on vessel representatives as mobility and well as fuel consumption for a boat. The other data used in the simulation were developed from records of catches, kept by the Department of Fisheries and Oceans. These data were analyzed by each geographic area, to give the distribution of catch per day, income per day, length of voyage and number of trips per year for the four years 1987 to 1990. 111 The of the model decision rules. Model), to These voyage were select the area was economics to always fish developed one for three alternative geographic area (Stationary which had the best performance during the last opening (Forecast Model) and to select the areas at random (Random Model). The simulation was run for each rule and the results were compared to observations derived from the performance of the actual fleet, for one year of observations. It was found that each simulated decision method was reflective of certain parts of the actual fleet. The results of additional simulations gave valuable insights into the most profitable methods of operating salmon seine fishing vessels. It was predicted that the Forecast Model provided an income 37 percent higher than average, based on four years of real catch data. However, a lower than average performance was predicted when the profit at each area was close to the mean value for all the areas in the model. The simulation quantifies the observed reluctance of skippers to change fishing locations. It was predicted that the vessels in the fleet had hold sizes which were between 60 and 100 percent bigger than was required, based on the most probable fishing trip. It was also predicted that the rate or return, based on the catch data and the investment in the boat, was much lower than would be expected for a high risk venture. When two or more boats operated together and pooled the operating expenses and income, the simulations showed that the risk of the income for the voyage being less than the expenses was considerable reduced. was for two boats to be fishing together. The biggest benefit This factor is important when the number of opportunities to fish are small, as observed in the British Columbia Salmon Season. iv TABLE OF CONTENTS ii Abstract List of Tables List of Figures Acknowledgements Chapter 1. Introduction Chapter 2. Salmon Seine Fishing in British Columbia viii xi xvi 1 7 2.1 Development of Fishing Techniques 7 2.2 Common Vessel Operating Practices 9 2.3 Constraints on Fishing Operations 12 2.3.1 Location & Openings 12 2.3.2 Fishing Gear 14 2.3.3 Vessel Dimensions 15 2.4 Current Fleet Size and Vessel Dimensions 17 2.5 Trends in Vessel Income with Time 19 2.6 Effect of Vessel Parameters on Income 28 2.7 Effect of Motivation and Mobility on Income 29 2.8 Important Factors to Include in a Simulation Model 33 Chapter 3. Operational Analysis of a Salmon Seine Vessel Based on Catch and Voyage Data 35 3.1 Data Collection for Voyage Profile Analysis 37 3.2 Voyage Profile Analysis 38 3.2.1 Overall Operation 39 3.2.2 Detailed Analysis of Transit Portion of Voyage 44 3.2.3 Fishing Portion of Voyage 46 3.2.4 Fuel Consumption 51 3.3 Summary of Observations on a Seine Vessel 52 V Chapter 4. Determination of Catch and Income Data for Salmon Seine Fishing Boats 54 4.1 Data Required for Simulation Model 56 4.2 Summary of Data Available for All DFO Areas 57 4.3 Translation of Catch Data to Income 62 4.4 Discussion of DFO Data 67 4.5 Nature of Distribution of Daily Catch 74 4.6 Variation in Mean Catch per Day Over Full Season 80 4.7 Simplification of Daily Catch Distributions 84 4.8 Summary of Catch and Income Data 91 4.9 Discussion of Analysis in Relation to Simulation 93 Chapter 5. Development and Testing of a Simulation Model for Salmon Seine Fishing 95 5.1 Information Required for Simulation Model 96 5.1.1 Vessel Technical and Operational Parameters 95 5.1.2 Spatial Distribution of Fishing Grounds 98 5.1.3 Openings and Other Constraints on Fishing 99 5.1.4 Catch Data for Fishing Areas 100 5.1.5 Operational Profile of Vessel 101 5.2 Development of Stationary Model 104 5.2.1 Data Available from Observations on the Fleet 105 5.2.2 Validation of Stationary Model against Observations 108 5.3 Development of Simulation of Mobile Boats 112 5.3.1 Random Model 112 5.3.2 Forecast Model 116 5.3.3 Validation of Forecast Model 119 5.4 Summary 125 vi Chapter 6. Sensitivity of Forecast Model to Catch Rate at Furthest Area 128 6.1 Parameters for Study 128 6.2 Results of Sensitivity Study 130 6.3 Discussion of Results 136 6.4 Conclusions 139 Chapter 7. Sensitivity of Forecast Model to Number of Boats Operating Together 141 7.1 Modifications to Simulation Model 142 7.2 Discussion of Simulation Results 143 7.2.1 Voyage Economics 143 7.2.2 Transportation Capacity 149 7.3 Conclusions Chapter 8. Performance of Forecast Simulation Based on Four Years of Observed Catch Data 8.1 Results of Simulations for Four Years of Catch Data 158 160 162 8.1.1 Variation in Profitability 163 8.1.2 Variation in Risk 167 8.1.3 Variation in Size of Vessel 168 8.2 Comparison of Results of Simulation with Observations 170 8.3 Vessel Design Features Derived from the Simulations 173 8.3.1 Fuel Consumption and Mobility 173 8.3.2 Empirical Relationships Between Mean Catch and Hold Size 174 8.4 Long Term Economic Predictions 178 8.4 Summary 182 Chapter 9. General Discussion and Further Work 184 9.1 Summary 184 9.2 Discussion on the Use of Simulation for Studying Fishing Boat Economics 190 9.3 Future Uses of Simulation in Fishing Vessel Analysis 191 vii References Appendix 1. Methods for Fitting Observed Catch Data 195 Probability Density Functions to 197 Appendix 2. Description of SLAM II Computer Program for Stationary Model 201 Appendix 3. Description of SLAM II Computer Program for Random Model 211 Appendix 4. Description of SLAM II Computer Program for Forecast Model 217 viii LIST OF TABLES Table I Comparison of Average Dimensions for Salmon Seine Vessel Fleets Table II 19 Summary of Annual Performance, Salmon Seine Fleet, 1979 to 1988 20 Table III Summary of Operating Economics, Salmon Seine Vessels, 1988 26 Table IV Summary of Measurement Methods for Voyage Data 38 Table V Summary of Voyage Times 41 Table VI Summary of Vessel Activity 43 Table VII Voyage Profiles for Seine Fishing Vessel 44 Table VIII Detailed Analysis of Transit Data 46 Table IX Detailed Analysis of Fishing Portion of Voyages, 1989 47 Table X Total Catch for DFO Geographic Areas, by Species, 10 Year Averages, 1979 to 1988 Table XI Summary of Annual Catch Data for Each Fishing Area, by Year 1987 to 1990 Table XII 55 59 Summary of Length of Season and Average Vessel Activity, by Fishing Area, 1987 to 1990 61 Table XIII Summary of Length of Trip for Each Fishing Area, 1987 to 1990 63 Table XIV Average Dollar Value for Salmon by Species, 1987 and 1988 64 Table XV Average Length of Vessels Fishing in Each Area, 1987 to 1990 73 Table XVI Summary of Parameters for Probability Density Functions, Daily Catch Data Table XVII 79 Summary of Fitted Distributions to Seasonal Catch Data, for Each Fishing Area, 1987 to 1990 81 ix Table XVIII Variation in Shape Parameter, X, Between Years, for Three Fishing Areas, 1987 to 1990 86 Table XIX Summary of Variation in Catch Rate with Time, 1987 to 1990 90 Table XX Distance Between Port and Fishing Locations Used in Simulation Model Table XXI Stationary Model, Comparison of Observed Daily Catch Rate with Simulated Results Table XXII 100 106 Stationary Model, Comparison of Observed Daily Income Rate with Simulated Results 106 Table XXIII Observed Catch and Income Data, All Fleet 113 Table XXIV Simulated Catch and Income Data, Random Model 113 Table XXV Simulated Catch and Income Data, Forecast Model 113 Table XXVI Observed Catch and Income Data, Boats Avoiding Area 12 113 Table XXVII Results of Simulation Models, 1988 Data 127 Table XXVIII Data Used in Sensitivity Study for Forecast Model 130 Table XXIX Sensitivity Study, Results of Forecast Model 132 Table XXX Sensitivity Study, Results of Stationary Model 132 Table XXXI Sensitivity Study, Results of Random Model 134 Table XXXII Effect of Number of Boats Fishing Together on Operating Economics 144 Table XXXIII Fitted Probability Density Functions to Catch Data, Single Boat 151 Table XXXIV Estimated Parameters for Fitted Distributions for Different Numbers of Boats Table XXXV Summary of Simulation Results for Stationary Models, Four Years, 1987 to 1990 Table XXXVI 155 161 Summary of Simulation Results for Mobile Models, Four Years, 1987 to 1990 162 x Table XXXVII Simulated Catch Data for Four Years, 1987 to 1990 Non-dimensionalized by Random Model 163 Table XXXVIII Comparison of forecast Model with Best Possible Area, 1987 to 1990, Non-dimensionalized by Random Model 165 Table XXXIX Proportion of Total Trips to Each Area, Forecast Model 174 Table XXXX Parameters Fitted to Maximum Catch Distribution, Assuming a Gumbel Distribution 177 Table XXXXJ Calculation of Payback Period 179 Table XXXXII Calculation of Internal Rate of Return 181 xi LIST OF FIGURES Figure 1 Statistical Area Map, Northern British Columbia 11 Figure 2 Statistical Area Map, Southern British Columbia 13 Figure 3 Variation in Overall Length with Time, Salmon Seiners 16 Figure 4 Variation in Brake Horsepower with Time, Salmon Seiners 16 Figure 5 Variation in Overall Length with Time, Salmon/Herring Seiners Figure 6 Variation in Brake Horsepower with Time, Salmon/Herring Seiners Figure 7 23 Regression of Normalized Dollars per Delivery against Year, Salmon Seine Vessels, 1979 to 1988 Figure 11 21 Regression of Average Catch per Delivery against Year, Salmon Seine Vessels, 1979 to 1988 Figure 10 21 Regression of Number of Deliveries by Salmon Seiners against Year, 1979 to 1988 Figure 9 18 Regression of Total Catch by Salmon Seiners against Year, 1979 to 1988 Figure 8 18 23 Average Number of Deliveries per Year, Salmon Seine, 1979 to 1988 25 Figure 12 Seine Fishing Boat Voyages, September/October 1989 40 Figure 13 Vessel Activity Profile, Ship Speed and Engine RPM against Time 42 Figure 14 Histogram of Vessel Speed, Sampled at Five Minute Intervals 42 Figure 15 Ship Movement During Fishing Activity, Latitude and Longitude, Juan de Fuca, 89-09-05 Figure 16 45 Ship Movement During Fishing Activity, Latitude and Longitude, Johnstone Strait, 89-09-05 45 xii Figure 17 Ship Movement During Fishing Activity, Latitude and Longitude, Bella Bella, 89-09-05 Figure 18 Fuel Consumption against RPM, Based on One Hour Averages for All Voyages Figure 19 49 49 Comparison of Regression Equations for Converting Catch to Income, Johnstone Strait, 1987 65 Figure 20 Fishing Vessel Activity Profile, 1987, All Areas 70 Figure 21 Fishing Vessel Activity Profile, 1988, All Areas 70 Figure 22 Fishing Vessel Activity Profile, 1989, All Areas 72 Figure 23 Fishing Vessel Activity Profile, 1990, All Areas 72 Figure 24 Gamma Distribution Fitted to Catch/Day, August 10, Johnstone Strait, High Catch Rate Figure 25 Gamma Distribution Fitted to CatchJDay, August 24, Johnstone Strait, Medium Catch Rate Figure 26 82 Comparison of Observed and Fitted Cumulative Distributions for Johnstone Strait Figure 31 82 Comparison of Observed and Fitted Cumulative Distributions for Juan de Fuca Figure 30 78 Comparison of Observed and Fitted Cumulative Distributions for Butedale Figure 29 78 Comparison of Probability Density Functions Fitted to Observed Data Figure 28 76 Gamma Distribution Fitted to Catch/Day, September 23, Johnstone Strait, Low Catch Rate Figure 27 76 83 Mean Catch per Day against Standard Deviation, Johnstone Strait, 1987 to 1990 85 xiii Figure 32 Mean Catch per Day against Standard Deviation, Juan de Fuca, 1987 to 1990 Figure 33 Variation in Shape Parameter, X, with Mean Catch per Day, Johnstone Strait Figure 34 85 87 Variation in Shape Parameter, a, with Mean Catch per Day, Johnstone Strait 87 Figure 35 Variation in Mean Catch per Day with Day, Butedale 1987 89 Figure 36 Variation in Mean Catch per Day with Day, Juan de Fuca 1987 89 Figure 37 Variation in Mean Catch per Day with Day, Johnstone St 1987 92 Figure 38 Comparison of Mean Catch per Day, Observations for Each Area and Stationary Simulation Figure 39 Comparison of Distribution of Observed Catch per Day with Simulated Values, Butedale, 1988 Figure 40 115 Overall Fleet Performance, 1988, Comparison of Distribution of Observed Catch per Day with Random Simulation Figure 46 111 Comparison of Number of Trips to Each Area, 1988, Total Fleet with Random Simulation Figure 45 111 Comparison of Average Catch per Day and Average Income per Day, Total Fleet with Random Simulation Figure 44 109 Comparison of Mean Income per Day, Observations for Each Area with Stationary Simulation Figure 43 109 Comparison of Distribution of Observed Catch per Day with Simulated Values, Johnstone Strait, 1988 Figure 42 107 Comparison of Distribution of Observed Catch per Day with Simulated Values, Juan de Fuca, 1988 Figure 41 107 115 Comparison of Mean Catch & Income per Day, Random and Forecast Simulations, 1988 118 xiv Figure 47 Comparison of Number of Trips to Each Area, Random and Forecast Simulations Figure 48 118 Comparison of Average Catch and Income per Day, Subset Avoiding Johnstone Strait and Forecast Model Figure 49 120 Comparison of Number of Trips to Each Area, Subset Avoiding Johnstone Strait and Forecast Model Figure 50 120 Comparison of Distribution of Observed Catch per Day, Subset of Fleet with Simulated Values, Forecast Model Figure 51 122 Comparison of Mean Peak Catch, 1988 Data, All Simulation Models Figure 52 Variation in Number of Trips/25 where Income was 122 < $6000, Stationary Models Figure 53 Variation in Number of Trips/25 where Income was 124 < $6000, Mobile Models 124 Figure 54 Variation in Number of Trips/25 to Each Area, Random Model 126 Figure 55 Variation in Number of Trips/25 to Each Area, Forecast Model 126 Figure 56 Sensitivity of Forecast Model and Overall Average Performance to Catch Rate at Butedale Figure 57 Sensitivity of Forecast Model and Stationary Models to Catch Rate at Butedale Figure 58 131 Number of Trips to Butedale against Catch Rate at Butedale, Forecast Model Figure 59 131 135 Histograms of Profit, Juan de Fuca, Johnstone Strait and Largest of Two Sampled Simultaneously 137 Figure 60 Histograms of Profit for Various Catch Rates at Butedale 137 Figure 61 Variation of Catch and Income (per Boat) with Number of Boats Fishing Together 146 xv Figure 62 Variation in Profit/Boat with Number of Boats Fishing Together Figure 63 Variation in Fuel Consumption and Risk at $6000 per Trip for Vessels Fishing Together Figure 64 157 Comparison of Forecast Model with Stationary Models, 4 Years of Data, Income Figure 70 - Fuel Cost, 1987 to 1990 74 172 Comparison of Mobility Between Observation and Simulation, 1987 to 1990, Johnstone Strait Figure 75 169 Comparison of Mobility Between Observation and Simulation, 1987 to 1990, Juan de Fuca Figure 169 Comparison of Mobility Between Observation and Simulation, 1987 to 1990, Butedale Figure 73 164 Comparison of Average Peak Catch for Different Decision Methods, 1987 to 1990 Figure 72 164 Comparison of Forecast Model with Stationary Models, 4 Years of Data, Risk at $6000, 1987 to 1990 Figure 71 157 Observed Cumulative Distribution of Hold Volume for Salmon Seine Vessels Figure 69 153 Estimated Peak Catch for 25 Openings, Based on 99 Percentile of Distribution of Maximum Catch Figure 68 153 Variation in Scale and Shape Parameters for Fitted Distributions with Number of Boats Figure 67 148 Comparison of Observed and Fitted Distributions for Daily Catch and Extreme Value for 25 Trips Figure 66 148 Histograms of Profit per Boat for One, Two and Three Boats Fishing Together Figure 65 146 172 Relationship Between Mean Catch per Day and 99 Percentile for 25 Consecutive Trips 175 xvi Acknowledgements I would like to thank Dr. S. Calisal, Dr. F. Sassani and Ms. N. Hofmann for their academic guidance and advice and the staff of the Pacific Region Department of Fisheries and Oceans who provided the catch data. of the Advisory Technical extremely development helpful and Committee commentary many of their on this on Replacement work suggestions have at several been of the The members Rules provided stages included. in Finally its I would like to thank my family for their eternal patience and moral support throughout this project. Dynamics) provided The National Research Council (Institute for Marine the financial support for this work, through Agreement for Collaboration with the University of British Columbia. an 1 Chapter 1 Introduction Industrial fisheries economic are activities, economic principles as other businesses. and are subject the to same However, constraints in the form of input controls are placed on fishing operations in order to preserve the fish stock for sustainable fisheries development. If these constraints are successful, then there is a limit to the growth of the industry, since there is a maximum total amount of fish which can be caught. It is therefore important for fishing vessel owners, designers and regulators to be able to predict the economic performance of alternative fishing vessel designs within a wide range of possible operating scenarios and constraints. A full understanding of the expected catching power of a fishing vessel is required before capitalized. it is built, to ensure it is not severely under or over In order to obtain this understanding, the analysis methods used must include estimates of the expected income to the vessel from the value of the fish caught, together with the cost of owning and operating the vessel. The expenses associated with the vessel are the capital cost of the hull and fishing gear, together with the variable costs (such as fuel and other consumable supplies) and the share of the income paid to the skipper and crew. include the cost of the fishing licence, harbour fees and other Fixed costs incidental expenses. A well constructed model will allow the vessel designer to optimize the initial design for a new boat, or an owner to optimize the operation of one or more existing boats fishing together. 2 have There costs operating deterministic many been vessels. of fishing studies lot A of methods has of emphasis for been reducing given to optimizing design for minimum fuel cost or minimum overall operating cost based on combined capital cost and operating cost [1, 2, 3]. These methods give results which are amenable to linear and non-linear optimization methods. Little attention has been paid to income, other than the average catch and income resulting overall seasonal trip. per studies These emphasis when performance are is adequate when considering on minimizing placed cost, not maximizing income. The average catch cannot be used to design hold sizes, since it will be exceeded approximately half the time. This will result in a vessel which is under capitalized, since there will be a lost opportunity to sell the fish which was caught but could not be fitted into the hold. However, if the hold size is increased arbitrarily, then it may result in a large vessel which is expensive to build and operate, which must pay for itself by catching more fish. Both of these conditions could lead to increased stock mortality, which is to detrimental the long health term of the industry. In addition, the deterministic methods do not allow for any assessment of financial risk. techniques engineering Systems can offer alternatives to deterministic approaches [4, 5, 6]. One of these methods which has the potential to allow for the random technique variation involves in economic the constructing a parameters computer is program simulation. to represent This the performance of a system as a function of time. The system is defined in terms of its components, and the overall system performance is evaluated by summation. Random variation of certain components can be accommodated by sampling from probability distributions, based on observed data. Multiple runs 3 of the simulation model are then made and the results interpreted using statistical theory, to understand their reliability. Model construction logical sequence predetermined of set simultaneously, requires events. of and breaking down Decisions rules. It is complicated made possible systems the can to can process be model be into the correct represented many represented by a sub-processes by relatively simple models, if specialized simulation languages are used. The disadvantage of the method is that the reliability of the final results are very dependent certain on processes, the tuning and the of the probability inter-relationships distributions of the sampled to times for generate the random events. Thus, the method relies on observed data to produce realistic results. It also depends on realistically modelling the decision processes involved. This may be relatively simple in an industrial production line, but becomes more complicated when dealing with individualistic highly fishing vessel skippers, and seasonal variation in the distribution of the fish. Simulation requires reliable measurements on the performance of the actual system, and then these have to be carefully interpreted in a manner which does not model. variables introduce This can which are any be unknown particularly based on a bias into important small any future when number applications considering of observations. of the stochastic The most obvious random variable in fishing is the catch obtained by the boat, which in turn may affect decisions made by the skipper. 4 If the mean catch per day varies with time and geographic location and the boats move between areas, then simulation should offer the most reliable It is also the best method of analyzing the performance of analysis method. two or more boats fishing together. In such cases the catches are not identical, independent Simulation distributions. modeling allows financial risk, which is also a random variable, to be analyzed. In this case, it is important to be able to base results on a large number of events. In reality, the fishing season for salmon is short, and decisions based on real life observations may be difficult to interpret, due to the small sample sizes. A successful simulation model will allow the analyst to investigate the effects of changing system parameters on vessel profitability. Factors which may be investigated are the technical factors affecting the boat such as size, fuel consumption and speed, or economic factors such as changes in catch rates, which can occur due to the natural variation in fish abundance. Other factors which can be investigated are operational factors, such as the number of boats fishing together. It is the intention of this thesis to demonstrate that simulation modelling can be developed into a useful analysis tool for predicting fishing vessel operating economics. variables distance Such a effecting between model the will realistically economics of allow fishing for boats, the such most as important catch rates, fishing grounds and the technical performance of the boat (hold size, speed and fuel consumption). It will also allow for the fact that skippers must choose between alternative locations, and the method of choosing may have some long term effect on the economic outcome. In order 5 to do this, it is necessary to investigate thoroughly the total fishing process, and create a model which can be programmed into a computer simulation. The model must then be validated by comparing its predictions against observations taken from the real system. The validation exercise is essential, since simulation is an empirical technique, and the accuracy of the model can be no better than the data used to develop the initial assumptions. Once the validation been carried has out, then changes can be made to the initial conditions of the simulation model and the results used to predict changes in the real system. The most important fishery, salmon seine fishery. in economic terms, in British Columbia is the The vessels used for this fishery are typically bigger than for any other type used for fishing in British Columbia, and so are most likely to be effected by changes in the economics of operations. They also have the technology for catching more fish than other methods, such as trolling or gill netting. For these reasons, it would be desirable to model these vessels since the overall benefits of any subsequent optimization are likely to be the highest. This work was carried out to support the development of an expert system for fishing vessel design, which required a method of analyzing a fishing vessel’s economic together performance. with A simulation information on model earnings, can potentially vessel mobility and give these data subsequent fuel consumption. The required fish hold size is the dominant factor affecting the capital and operating cost of the vessel. Also, the Department of Fisheries and Oceans (DFO) may be interested in being able to simulate vessel operations with 6 respect to predicting the impact of any future modifications to vessel replacement rules or quota assignments on vessel movement and productivity. 7 Chapter Salmon Seine Fishing 2 in British Columbia Before work on the simulation model could begin, it was necessary to establish the correct sequence features which were of events essential and identify technical the economic and for constructing an accurate representation of the fishing process. One source of observations on the salmon seine fishing process can be derived from a review of the literature published by other researchers. Another potentially valuable source is data collected by the Department of Fisheries and Oceans. 2.1 Development of Fishing Techniques Ledbetter [7] described the pacific salmon as a relatively predictable fish, due to its regular migration patterns. The fish move with the tide or current, and travel along the shore rather than in mid-strait. Underwater obstructions, such as changes in bottom contours or vegetation direct the fish into open water and so boats tend to congregate in these areas. Salmon often travel near the surface, and occasionally jump out of the water. These biological features make the salmon very easy to catch in shallow water and in entrances to spawning rivers. The five major salmon species in British Columbia are chinook, sockeye, coho, pink and chum. Of these, the seine vessels target primarily pink and chum, which are the varieties traditionally used for canning, but significant quantities of the other species are also caught. Seine caught fish tend to be of a lower quality relative to the other catching methods, since large volumes of 8 fish are caught and the fish can easily be damaged when the nets are being handled. In the traditional method of seine fishing, described in [8], one end of the net was held by a small boat, called a skiff, while the net was paid out from the fishing boat, as it steered round in a circle. Once the circle was complete, the net was drawn into a purse and hauled aboard using tackle suspended from a long boom. The bunt end of the net was then tripped, releasing the fish into the hold. The fish were packed in ice with no other processing carried out on board the boat. The net was then stowed on a rotating table, so that it could be re-set as quickly as possible. If the weight of the catch was more than the crew could haul by hand, then brailing nets were dipped into the purse to bring the fish aboard. The efficiency of the method was incrementally improved by holding the net open in a U-shape (with the mouth open to the current) for some time before it was drawn into a circle. The vessels used for this fishery [9] have traditionally had the engine and accommodation forward and a large deck area aft. The hold was in a central location, to avoid excessive trim when the fish were loaded. The rudder and propeller were fitted well under the counter stern to avoid fouling the net. Fuel tanks were located aft of the fish hold, and in the engine room. The net, the table and the skiff were all stowed relatively high on the deck, and so the designer had to ensure that the hull provided adequate stability. Technology has improved the performance of the fleet over the years [7, 8, 9, 10, 11, 12]. The first change was the introduction of the powered block on the end of the boom, which meant that the maximum catch that could be hauled 9 aboard was no longer limited by the strength of the crew. This also reduced the time between sets of the net. Further refinements saw the use of drum winches instead of the block and net table, and the the latest additions to the boats have been the running line, which eliminated the need for the skiff, and bow thrusters to improve the maneuverability of the boat during fishing. All these changes in technology have resulted in a reduction of the total time between sets from 55 minutes, with a power block on the end of the boom to 35 minutes for vessels with a seine drum. 2.2 Common Vessel Operating Practices Cove [10] discussed some aspects of fishing vessel operations. He noted that vessels often left port up to 2 days before an opening to investigate the fishing area and locate the fish. This was easy to do if there were jumpers’, fish which jumped out of the water, but it was noted that these observations were a relatively rare occurrence. Ledbetter [7] discussed some of the strategies used in salmon seine fishing in Johnstone Strait. This fishing area was characterized by strong tides, local reefs and protected waters, and at the time of writing was considered to be the dominant seine fishery in British Columbia. migration patterns, Since the salmon follow distinct in relatively shallow water, they are easiest to catch at specific locations. An efficient technique for this fishing area was to tie one end of the net to a fixed point on the bank, such as a tree, and hold the net open against the current, using the fishing boat. This method, referred to later as the point set, was efficient, since it minimized the amount of fuel used during the fishing process. 10 Since the salmon tend to be concentrated in specific locations and catch rates are easily observable from other boats, line-ups form at particularly productive spots. However, the optimum number of boats fishing at any one location is two, since one boat can be letting go while the other is pursing. By fishing in this way, very few fish can get past the nets. If the fishing area is restricted, then two or three boats can make it very difficult for other boats to fish at that location. An alternative strategy was to make open sets, a short distance away from the ‘best’ location. For this technique, the net is handled entirely from the water using the boat and the skiff. Ledbetter showed that the open set was only slightly less productive than the point set, with a mean catch rate of between 28 and 29 fish per set compared to a mean catch rate of between 32 and 36 fish per set, in a short line up (1-2 boats) for a point set. However, a high catch rate at a point set (40-45 fish per set) resulted in line-ups of up to 5 boats. The advantage of the open set was that the vessel could make more sets per hour, which potentially compensated for the lower catch rate per set. However, the technique may during be less profitable, due to the higher fuel consumption used fishing. Tidal activity was also observed to be important. Ledbetter [7] observed that although vessel activity level remained constant throughout the tidal cycle, the number of maximum catches with the ebb and flood were different (68 maximum catches were caught on the ebb, whilst 120 were obtained on the flood). This was important to the skipper, since typically 19 percent of total catch was taken in the maximum catch. 11 Figure 1. Statistical Area Map, Northern Half OEAO CAACFULLY I %*,t*ç &lA 10the 1011. 11 @ FM.,.. I’d 1**1.1 It It. 1.11.0,0* I’d I 0,1110,0*1111111.11*11.1 Z k*.oI. c.t .#10 hit 0.4.4.0,11 fl1 10,1.0,0, h*1b. V*g It. • • F*tene* Oceans PAches et Oceans Crnad 1*1’ —. oeht 11 3 fl.. 11*1*1*01 ariaS 1110*1 WI ItS 1*11 1111010 .101 F.. *0*0 0,0*1 0111.1.010*1010,10 10 0 *,4. 110*11.. F.Ve. 1 10110900.010 his • V.pt .1 FIt.... end 0*lW* 311.1. — 5101.1.10110*00 100 — 5*11100 hell All e,.WI *00*4 di,hi by FoA*y l9e5 .0410... STATIS11CAL AREA MAP SHOWING AREAS OF CATCH FOR BRITISH COLUMBIA WATERS NORTHERN HALF SIXTH EOITIeI Ft 985 12 Hilborn and Johnstone [12] Ledbetter fishing Strait as compared areas. and Juan de contrasted Fuca was Juan Fuca de and characterized by open water, high waves and less variation in geography. The fishing technique was slightly different in that the open set was the only one used. However, the fishing took place in a very confined area, defined by points on the map and line-ups of 100 boats waiting for 10 spots had been observed. Each boat waited (typically) 5 hours between setting nets. The boats also used larger ‘outside’ nets than the boats fishing in Johnstone Strait. The reason for this technique was not described by the authors, but after with DFO officials, experienced fishermen and industry watchers, discussions it was explained as follows. The migrating fish were in open water heading for their ‘home’ rivers. The ideal place to intercept them was on right the boundary of the fishing area, which had to be crossed by all the fish entering the area. A line of nets across the boundary formed a very effective barrier to the fish. Since the boundary was in the open ocean, it was purely a reference line on the map, and there were no places where point sets could be made. 2.3 It Constraints is Fishing on common practice Operations for governments to regulate their fisheries, and the Pacific salmon fishery is no exception. The constraints placed on the fishery by the government affect several factors of vessel operations and fishing activity, which are discussed in detail below. 2.3.1 Location & Openings The coast of British Columbia is divided into areas, as shown in Figures 1 and 2. In each statistical area the fleet is regulated by daily openings. Areas A0F0LLY 000I. CcItt. 1.00,1. mint Include II. mop 00.oni tutOr ot lleQQ#tinQOf Oil @000(0 totS DepI @1 F.ilt$(S. God e4* e..000.bkIy of It.. 11.0mon nod p00.00010.04 ho..t000.o.moI P numbr. .I.oc.ng II’. 0100 0 clOd. due feel. cc. couplet 3 TI. .t,flfllCOl 01o1 town ml lb.. omp 0.0100. u.ed 00 0 Quid. Only Foe moe. .00(1 infolmOhon .010, I. It. P.011.0 Fiolmey l0000p.m.pt 01.0 Regoloti000 2 I of F,toei.. Dm11.0. by ted 110.. mId 00.00$ 011i00 St0toIiCoI 0100101• divIded Dept Note All moo. .00.000 F.btoiny 906 — • I* 01 OCdonu SOUTHERN HALF SloTh EDITItN SHOWING AREAS OF CATCH FOR BRITISH COLUMBIA WATERS FF0 Canad STATISTICAL AREA MAP Fithetiotu Ocoaot. 00.3 Figure 2. Statistical Area Map, Southern Half 1903 Cj’I 14 generally open at 18:00 on Sunday, and are open between 2 and 4 days, in 12 hour increments, depending on the strength of the run. The policy of the Department of Fisheries and Oceans (DFO) is that fishing is closed until it is open. The openings, nature of this system enables boats move to easily between but potentially penalizes them for moving during an opening. Not all areas are open simultaneously. Northern areas tend to open early in the season and close first, and southern areas open later and close later. The fishing season for salmon is generally between early July and late November. These arrangements are discussed in [11, 12, 13]. 2.3.2 Fishing Gear The nature of salmon seine fishing means that it is extremely difficult to set the net in the dark, due to its size. This effectively limits the fishing to the hours of daylight. There are also regulatory restrictions on the gear. The dimensions of a salmon seine net are constrained by the ‘Pacific Commercial Salmon Fishery Regulations’ [14]. The Act limits the net to a length of between 150 and 220 (approximately fathoms 30 (274 metres). to The 402 metres) regulations and a depth are such of that 250 the meshes maximum allowable size can be carried by any seine boat, and so net size is effectively independent of vessel size. The regulations prohibit the use of a second, powered, vessel to assist in towing the net before it is pursed and the vessel can only carry one net at a time, with a limited amount of spare gear for making repairs. Also the maximum length of time that a net can be kept in the water before pursing is 20 minutes, and this is specified in the Act. Hilborn and Ledbetter [12] discussed the observation that the smaller, ‘inside’ net is used in Johnstone Strait, whereas the bigger ‘outside’ net is used in Juan de Fuca. 15 2.3.3 Vessel Dimensions Salmon fishing vessels have been licensed in British Columbia since 1969. At that time, any boat which had caught more than 10,000 lb of pink or chum salmon (or equivalent) in either of the two previous years was required to purchase a commercial salmon licence if it wished to continue fishing. At this time there was no restriction on the type of gear that could be used on the boat. In 1977, a separate category of salmon licence was introduced for salmon seiners. The licence was in the form of a seine privilege. Boats with this privilege could use seine gear and any other kind of gear, but other boats were prohibited from using seine gear. The number of seine privileges was fixed at the number of boats fishing at that time. Immediately after introduction the of the salmon licence, the vessel replacement rule was such that the total number of boats fishing must remain the same. A new boat could not be built without an old one being retired. The replacement approximated rules by were the modified net in tonnage 1971 and to take into account vessel overall length. Net tonnage size, is an approximation for the hold capacity of the vessel. Under the modified rule, the objective was to maintain a constant total tonnage. A larger boat could be introduced, but ft required the retirement of a sufficient number of smaller boats. This rule was not effective in controlling catching capability, since it took no account of the catching methods. For example two or three smaller gill netters could be replaced by a single seiner, with up to ten times the catching capacity. The current practice is to replace an old vessel with one of the same 16 Figure 3. Variation in Overall Length with Time, Salmon Seiners 40 y 0 a) I.1 a) = 36.122 9.6641e-3x - R2 0.006 = El 30 El E El 0 El El B E 0 • 20 El I’ ø0 El El B uuG El El 10 1900 4 rl rn I — 1920 I I — 1940 I — 1960 — 1980 2000 Year Figure 4. Variation in Brake Horsepower with Time, Salmon Seiners 800 4387.3 + 2.3722x R2 = 0.226 y = El 0 600 rn El o 0. a) § El 0 El 0,0 ELEPE!? 00 000 - 200 El 00 El 0 1900 1920 1940 1960 Year 1980 2000 17 overall length net tonnage. and Thus under the current vessel rules, the length and net tonnage are an integrated part of the constraints on the vessel design. The observations discussed above are taken from [15]. 2.4 Current Size Fleet and Vessel Dimensions In 1988, according to [16] there were 549 licenses for seine privileges, but later information [17] lists 522 vessels as having fished with seine nets for salmon. The total number of salmon licenses was 4413. In 1988, the value of seine caught salmon was $112M, compared to the total for the salmon fishery of $256M. These figures show how productive the seine fleet is relative to the other methods, when 44 per cent of the value of the catch was landed by 12 per cent of the licences. In 1989, there were 549 licences issued for salmon seining, of which approximately 60 per cent were licensed just for this fishery. The remaining boats held two or more licences, of which the most common combination was roe herring, with approximately 25 per cent of the total licences. A comparison of the average vessel dimensions for the salmon seine fleet with the roe herring fleet is given in Table I. These data were derived from DFO records released in support of this project. It can be seen from Table I that the combined salmon/herring vessels were bigger and newer, with more engine horsepower than the single license boats. It is interesting to note that the vessel parameters have changed with time. Length and horsepower are shown for each category of license in Figures 3 to 6. For the combined vessels, all the measures of vessel size have decreased with time, i. e. the newer boats are smaller than the older ones. 18 Figure 5. Variation in Length with Time, Combined Salmon/Herring Seiners 40 y 1930 — 181.96 1940 - 8.1627e-2x 1950 1960 R2 1970 0.245 1980 1990 Year Figure 6. Variation in Brake Horsepower with Time, Combined Salmon/Herring Seiners 1000• y 4035.2 + 2.2475x R2 = 0.060 9 800 9 U I- 1930 0 0 600 1940 1950 1960 0 1970 Year 1980 1990 19 However, the installed power has increased with time. For single licences, vessel sizes are static with time, but installed power has increased. Vessel Parameters Length, m. Gross tonnage, m 3 Horsepower, HP Age, years Number of boats All Salmon licenses Salmon/Herring licenses 17.0 115.8 244 21.4 264.7 405 21 124 35 507 Table I Comparison of Average Dimensions for Salmon Seine Vessel Fleets 2.5 Trends in Vessel Income It is interesting described to with Time speculate how much impact the changes in technology above have had on the economics of the fishery. This might be inferred from observations on past performance over a number of years. DFO publishes detailed annual summaries [16] of the total amount of fish caught. These data are summarized by species, type of gear and the geographic location of where the fish were caught. Information is also given on the total number of landings per year, the average weight and value of a landing, and the total payments to fishermen, which included bonus payments and direct delivery payments, in addition to the amount paid when the fish were landed. All of this data is given for the past 10 years. At the time of writing, the latest data available in this form was for the years between 1979 and 1988. Table II gives the annual summary data for salmon seining taken from [16]. It also 76296.0 29886.5 68681.0 30820.9 37289.6 13718.0 Mean Std. devn 3096.3 958.4 2059.75 2066.33 4099.40 2695.20 3929.55 1578.00 4191.14 3796.86 2946.50 3600.07 12 12 10 10 11 13 14 14 10 14 12.0 1.7 Ave. catch per landing, kg Landings 000’s Table II Summary of Annual Performance, Salmon Seine Fleet, 1979 to 1988 53010 49190 77220 62260 59710 41220 106010 110300 72900 131140 42522 41854 63864 51818 48443 38399 106902 101972 68117 122919 24717 24796 40994 26952 43225 20514 58676 53156 29465 50401 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 Total payments, $, 000’s Value, $, 000’s Total catch, tonnes Year 5646.8 2012.6 3543.5 3487.8 6386.4 5181.8 4403.9 2953.8 7635.9 7283.7 6811.7 8779.9 Ave. value per landing, $ 21 Figure 7. Regression of Total Catch by Salmon Seiners against Year, 1979 to 1988 100000- y - 4.7365e+6 + R2 2406.7x 0.282 80000 U) U) 60000 EI. 40000 , b 20000 0• . I • 1979 I • 1983 1981 I • 1985 1987 Year Figure 8. Regression of Number of Landings by Salmon Seiners Against Year, 1979 to 1988 15 y = - 444.81 + R2 0.23030x 14 P = 0.168 W p.IIl 1979 1981 1983 1985 Year 1987 22 gives the 10 year mean value for the total amount of fish caught and the average catch per delivery. Linear regression was used to identify possible trends in the data, as functions of time. Figure 7 shows that over the last 10 years the total catch by seine vessels has increased at an average rate of 2400 tonnes per year. It would appear over this period that there has been a steady increase in the amount of fish caught. However, when we make conventional the assumptions concerning a normal distribution of the residuals, determined after fitting the regression equation, we find that the probability of the slope being zero is 0.114. This means that at the 90 percent confidence level, we cannot reject the null hypothesis that the slope is zero. Given the small number of years used and the relatively large degree of variation between years, it is inconclusive to say that the total weight of fish is increasing. Another parameter to consider is the trend with number of landings against year, and the weight per landing. If the same amount of fish is caught with fewer landings, then the fishing operation may be more productive. However, if the total number of landings is increasing, then the operating costs may be increasing due to the cost of fuel and other consumables. The number of landings, in thousands, is regressed against year in Figure 8. Again the regression showed that there was a positive trend, and that deliveries were increasing on average at a rate of 230 per year. However, the probability that the slope is zero is 0.239, which means we cannot reject the null hypothesis that the number of deliveries was not increasing, at the 90 per cent confidence level. A similar regression of mean catch per delivery against 23 Figure 9. Regression of Average Catch per Landing against Year, Salmon Seine Vessels, 1979 to 1988 5000 y = 2.4518e+5 - + 125.17x R2 = 0.156 0. 4000 3000 (U 2000 (U 1000 1979 I 1981 • I I • 1983 1985 • I 1987 Year Figure 10. Regression of Normalized Dollars per Landing against Year, Salmon Seine Vessels, 1979 to 1988 10000• 6.9780e+5 + 354.78x R2 = 0.288 y = . 9000 8000 I 1979 1981 1983 Year 1985 1987 24 year is given in Figure 9. This showed that the mean catch per delivery was increasing slightly, at 123 kg per year, but again the probability of the slope being zero was high, at 0.258. Average catch per delivery, based on 10 years of data is 3096 kg. The price information was more difficult to interpret than the weight of fish being caught. This was due to the fact that the total amount of money earned from the fish was dependent on the average catch per delivery, the number of deliveries and the unit price of fish, all of which could vary independently. Dollar values were normalized by considering dollars per landing, in 1979 dollars. This was calculated by considering the ratio of dollars per kilogram, based on the total season values for each year, as a ratio to the dollars per kilogram in 1979. When the normalized data was regressed, it was found that although the slope was positive, showing on average an increase in the value of dollars per landing with time, this was not significant at the 90% confidence level. This is shown in Figure 10. It is also interesting to note that the total payments to the skipper were, on average, This 13.5% higher than the income due to the landed value of the fish. figure is clearly significant, and could make a big difference in the overall profitability of a fishing operation. It is apparent from these observations that there is a high degree of variation in the annual performance of the fleet. No conclusive trends can be made over a 10 year period. Although all trends show increased productivity over the 10 year period, they are not statistically significant, when the amount of scatter and number of samples is allowed for. It would be reasonable to interpret the 25 Figure 11. Average Number of Landings per Year, Salmon Seine, 1979 to 1988 26 / / 24 — I 0 22 0) I C P 20 / 18 1979 ¶1 • • . 1981 1983 1985 Year 1987 26 observations to show that the constraints have been working over the last ten years. If these data are to be interpreted in a more reliable manner, then longer periods of time are required. One interesting observation can be inferred from these data. If we assume that the number of seine licenses was fixed throughout this period (at the higher value of 549) we can estimate the average number of trips per year over the period. These data are shown plotted in Figure 11. It would seem that the average number of trips per year varies between 18 and 25. Thus the total number of trips is relatively small, but we have no information so far on the duration of these trips. Item Dollars License fishing income Other species fishing income Gross fishing income Operating Expenses Other income Fixed costs Net income Skipper payment Profit 232,000 117,000 349,000 -133,000 14,000 -63,000 167,000 -40,000 127,000 Income/trip (salmon) Estimates # trips/yr Estimated cost per trip Estimated profit per trip Table III Summary of Operating Economics, Salmon Seine Vessels, 1988 8,780 26.42 5,700 3,100 27 Income data for 1988 for all licence categories described above are given in [17]. Despite fact that the given on information is there the is only one variance or the year of data, number of boats and that no used in the analysis, it does give some useful information of vessel economics. These data are summarized in Table III definitions are given below. additional bonuses. for salmon seine fishing, and the Gross income includes fishing income, plus any Operating expenses include crew shares, fuel, lubrication oil and grease, food and provisions, bait, ice, salt and other expenses. Other income packing consists or income collecting, Unemployment fees, of charters, Insurance licence renewal from fee, benefits. other rebates, Fixed fishing lease costs gear maintenance, related or activities, rental include such as arrangements insurance, interest on debt, and accounting moorage and similar costs. These results give some very interesting information on the performance of the fleet. There was substantial income from sources other than the licence considered. For salmon seine boats, 33 percent of the gross fishing income came from other sources. The operating costs represented 38 percent of the gross fishing income. Fixed costs for salmon seining were 18 percent of gross fishing income. Average profit for salmon seining was $127K over the season. Estimates can also be made of some additional economic parameters from these data. Given the total income from salmon fishing from Table III, and dollars per trip from the annual summary data, Table II, we can estimate the mean number of trips per year to be 26.4. This compares very well with 25.5 28 estimated the from annual data, summary based on the total number of licences. The simplest assumption to make when calculating the expenses is that the total expenses are pro-rated in relation to earned income. Therefore estimated expenses for salmon fishing are $151K. Assuming 26.42 trips per year, the vessel needs an average income of at least $5.7K per trip to cover costs. 2.6 of Effect Vessel on Parameters Income So far only the average performance of the vessels has been considered. An important factor to determine is whether or not the vessel has an effect on its own overall performance. Hilborn and Ledbetter [12] discussed some of the aspects of vessel design on catching power, measured in dollars per week, in the British Columbia salmon seine fishery over five years, 1973 to 1977. They relationships explored the between attributes, vessel effect and geographic location and assessed the catching power, measured vessel importance of these factors in determining the total catch. They considered the Juan de Fuca and extremes, the in Johnstone terms Strait fisheries, of environment. From since a they linear represented regression the two of catching power against vessel parameters, length, gross tonnage, year built, listed value and horsepower, they concluded that vessel parameters alone could not account for variation in performance between boats. They noted that vessels which did well in Juan de Fuca and poorly in Johnstone Strait were longer (average length of 20.82 m) than those that did well in Johnstone Strait and poorly in Juan de Fuca (19.14 m). Boats that did poorly in both areas were the smallest of all (18.18 m). 29 They then important concluded in that determining factors other catching than power, vessel since parameters some boats must be consistently performed better than or worse than average (at least in one area). Effects that the authors considered were skipper skill, crew skill and design of the net. From analysis of the variance (ANOVA) of the vessels which fished both areas, they concluded that there was very little difference between the two areas in the contributions of the three elements (vessel attributes, gear design combined crew skill - - - It can and unexplained luck). The aggregate components were: 10% vessel 24% skipper/crew/net 66% luck be concluded from this study, that within a given area, vessel parameters had very little effect on the catching power, vessel and crew skill have some effect, but the biggest component of all was luck. The authors discussed the importance of area specialization to the performance of the boat. Some skippers preferred to fish in one area over another, for reasons such as proximity, length of season, typical weather conditions and size of boat. This area specialization can account for about 25% of the overall variation between boats, when boats that fish in both areas were considered. 2.7 Effect of Motivation and Mobility on Income One of the factors which must also be considered is skipper motivation and the number of fishing areas which are fished in a season. Hilborn and Ledbetter [11] discussed the general mobility of the fleet, within four years, 1973 to 1976. The fleet was divided into those boats which fished predominantly in one area 30 (stationary boats) and those which fished multiple areas (mobile boats). They concluded that the mobile boats distributed themselves between areas, in order to equalize the catch per unit effort (CPE), measured in dollars per week, for a given area relative to the overall average. They observed that some areas had consistently higher ratios of CPE than the average, and these areas tended to be more remote or subject to more extreme weather conditions. Areas which were consistently lower than average were more and accessible more sheltered. The authors did not address the mobility decision of an individual skipper, but gave some clues to the variation in attitudes. One category of skipper is someone who always fishes in one area. This could give the basis for one motivation or decision rule. For some years of their study, they noted that the number of mobile boats fishing in a given area was directly proportional to the CPE the previous week. Thus, if the area had been productive, more boats would fish there and if it had been less productive, the number of boats would reduce. It was found however, that this observation did not hold for all years. Despite this limitation, which may be due profitability, to this relative mobility merits of alternative pattern hypothesis areas could and form overall the seasonal basis for an alternative decision rule, such that the skipper directs the boat to the area which was the most productive area in the previous week. Cove [10] developed a model to account for the different levels of risk taken by skippers in between reward the fish gathering structure, process. technology and The the model specified environment relationships that influenced 31 the skipper’s indicated evaluation of a situation, and hence his decision. The model that understand a short situational term approach to production risk strategies. taking can be Unfortunately, used the to help paper does not give any information on the absolute differences in performance between the rates skippers. fished The skippers with the highest long term catch (and income) using a high number of low risk sets rather than a smaller number of high risk sets. A key factor in the decision process would appear to be whether sets were made on the basis of maximum values obtained or average values obtained. Some of the difference in performance between boats may be accounted for by the skipper’s attitude to risk, and his level of motivation. Hilborn [13] discussed some other aspects of motivation and the possible strategies that a skipper could adopt. He considered four possible successful strategies: - - - - specialize in one area specialize in moving between areas maximize catching power by using the best technology fish as many days as possible Another source of information on the fishing process was discussion with the fishermen. A crucial piece of information, which was not apparent from the reviews of the literature, was that a vessel rarely fished alone. usually part of a team with the biggest boat (the packer) Boats were used for the transportation of fish caught by all the vessels in the team. The other vessels would stay on the fishing grounds during the closed portion of the season 32 tracking the movement of the fish. The teams were often associated with a processing plant, and the fish were always brought to that port. Supplies for the boats left on the grounds would be brought out on the return trip by the packer. Obtaining intelligence on the fish movements was a sophisticated business. A sonar on the boat was used for detecting shoals of fish but greater range could be covered for less cost using the skiff when looking for fish on the surface (jumpers). Other methods used to locate fish included spotter aircraft and monitoring communications between other boats. Teams of boats would code information by using radio scramblers and cellular facsimile machines. Some skippers felt that there has been a general reduction in the level of skill required for fishing over the years. This was due mainly to the reduction in size of the areas where fishing could take place during an opening. This forced the boats to concentrate in that area, and so line-ups would become very long very quickly. The alternative strategy was to make open sets, away from the line-ups. Whilst the skippers accepted approximately half that of those in the line-up, more sets per unit time. This confirmed the that the catch rate was it was compensated for by observations of Hilborn and Ledbetter [11, 12] and Ledbetter [7]. The general strategy used by one skipper I talked to was to fish an area whenever there was an opening. This would mean a lot of movement during the season, but fuel cost was not a significant concern. When there were two or more openings simultaneously then a decision would have to be made to select an area. This was done using past records of catches for each area, based 33 on the time of the year. The vessels in the group would fish together, until catch rate fell below some (unspecified) catch rate, when the boats would split up and look for other locations individually. The boats would then regroup if necessary. 2.8 Important Factors to Include in a Simulation Model Based on the review of the fishing system for salmon seine vessels in British Columbia, we can reach the following conclusions on the factors affecting the performance of individual vessels, relative to the fleet in general. - The boat has little effect on catch rate within a given fishing area, probably due to the fact that there is little technological difference between boats. - - Boats transfer information, either deliberately or accidently The openings when fishing is permitted were highly regulated, in terms of time, and were a relatively short portion of the total time available. - Many boats move between areas, trying to obtain the best catch. This mobility may be based on comparisons of the value of fish caught in all the areas for the previous week, and moving to the area with the highest value. - - Fuel cost is not a prime factor in fishing strategy. Vessels do not fish independently. 34 - Average income per trip, in 1988, was estimated to be $8780, average cost per trip was estimated to be $5700, average profit per trip was estimated to be $3100. The number of trips per year was estimated to be between 18 and 25. 35 Chapter Operational Analysis of a 3 Salmon Catch and Seine Vessel Based on Voyage Data In order to be able to model the engineering aspects of a fishing vessel it is essential to know some technical details, such as the typical length of voyages, the fuel consumption of the vessel and other factors which will effect the design of a successful vessel. In this chapter, the operation of one particular vessel will be studied, in order to establish realistic technical specifications for a modern salmon seine fishing vessel. UBC researchers have developed a special relationship with one particular skipper of a salmon seine vessel. UBC staff and students have worked with him in modernizing his boat to improve fuel economy and reduce motions and accelerations induced by waves. As part of these studies, model data on the boat’s performance in calm water and head waves have been obtained, as well as full scale data [18, 19]. The hull had a registered length of 18.14 metres and was the largest of a group of three boats belonging to a small but integrated company which was involved in catching, processing and selling fish. The boat was built in 1987 and incorporated the latest technology in terms of gear handling, fish finding and information transfer. The skipper said that he had no particular preference for geographic areas when fishing for salmon. In addition to salmon and herring, the boat was also used to catch bait for sports fisheries and food for exhibits at the Vancouver Aquarium. These additional activities kept the vessel busy over a twelve month period. The boat had a crew of 5 or 6, depending on the type of fishing being carried out. 36 Since this vessel was the biggest in the team, it was used for the transportation of fish caught by all three vessels. The team was associated with a processing plant in Steveston, and the skipper always returned to this port after fishing. The other vessels would sometimes return to Steveston, but most likely would stay on the fishing grounds, tracking the movement of the fish, during the closed portion of the season. Supplies for the other two boats would be brought out on the return trip from Steveston to the fishing grounds. Sometimes a fourth vessel would operate with the group, but this one was based in Bella Bella. All four boats were operated by members of the same family. The three boats all processed their fish slightly differently from the established practice of salmon seiners. Typically, seine caught fish are of a lower quality than line caught fish or gill net caught fish. This is because the catching technique and the bulk storage on board the boat tend to bruise the fish, resulting in a lower quality product, which is suitable for canning but not for any other methods of processing. However, on these boats the fish were bled before being hand stowed in the hold. Also, the fish were kept in the hold for as short a time as possible. This gave a higher quality product which was suitable for processing and marketing as smoked salmon, with a considerably higher retail value than the canned product. Data on the actual performance for income and catch rates for the boat will be kept confidential, but some discussion can be made on the performance of the skipper relative to a sample from the overall fleet. The sample was a group of 121 seine boats for which UBC had a full description of the technical parameters. It seemed that this skipper caught consistently more fish than 37 average, over the course of a season. Based on the four years (1987 to 1990) for which data were available, the total catch of salmon was 31 percent higher than average, with the lowest value being 4 percent and the highest being 42 percent. The dollar value of the salmon was 24 percent higher than the mean. This difference between catch and income may have been due to catching more lower grade fish than was typical. The higher than average catch and income figures were due to a higher than average number of days fished. The 4-year mean for the number of days was 29 percent higher than average. The observations discussed above would tend to indicate that the skipper was motivated to earn more than average. The most likely sources for the increased motivation were his status as top performer within the ‘company’ fleet, the financing requirements for a new boat and an interest in the total production process, rather than just the fishing operations. A closer analysis of the data indicated that the catch rate per day for this skipper was close to the overall fleet average, which confirmed that the increased productivity was due directly to fishing more days per year. If we assume that this vessel represented average performance in terms of catch rate per unit time and we can determine an operational profile for this boat, it may give an indication of a typical operational profile for the rest of the fleet. 3.1 Data Collection for Voyage Profile Analysis As part of the UBC study, the vessel was instrumented to automatically measure and record fuel consumption, ship speed, engine revolutions, latitude, longitude and heading as functions of time. The voyage data available for this boat covered the period August to November, 1989. vessel was engaged in salmon seining. During this period the 38 When the data logging system was operational, it recorded data for every channel at a frequency of one point every five minutes. Data was retrieved from the system as a formatted text file. The standard sampling rate gave data that was too detailed for analysis of the overall voyage profile. It was decided that the average values of fuel consumption, speed and engine revolutions over a one hour period, together with the position and heading at the end of the period would be sufficient to identify major segments of activity. The methods by which the data were obtained are summarized in Table IV. Item Measurement Fuel consumption Engine rpm Latitude Longitude Speed Heading Time & date Flow meter in fuel line Shaft speed Loran navigation system Loran navigation system Differentiation of position data Position data or compass Internal clock on data acquisition computer Method Table IV Summary of Measurement Methods for Voyage Data A computer program was written to decode the logged data. Averages for the one hour period were calculated by checking the time and counting the number of data points. Gaps were identified by discontinuities in the sequence of the times. For incomplete records, averages were calculated on the basis of the number of observed points within the nominal one hour period. An additional variable was added, which was a counter from the beginning of the 39 data record. It was included so that sequential plotting of the data points could be carried out. The data acquisition system was started manually from on board the boat, and so data were missed when the equipment was not turned on. Data for latitude and longitude were occasionally missing when all other channels were working. This was presumed to be due to difficulties in receiving the LORAN-C position data. Another major problem was that data were overwritten when the memory buffer for the acquisition system was full, and potentially valuable data were lost. This was particularly frustrating when there were long periods of time when data were collected when the vessel was in port, without the engine running. Despite these limitations, these data proved to be extremely useful information for constructing a simplified voyage profile for salmon seining. 3.2 3.2.1 Voyage Overall Profile Analysis Operation During the period for which data was available, four distinct voyages were identified. The latitude and longitude data were used to determine the end points and the route for each voyage. The data was reduced, so that it only included the portions where the vessel was away from home port. An overview of the vessel movement during this period is shown in Figure 12. A summary of the duration of each trip is given in Table V. Some knowledge of the vessel operation was helpful when interpreting the data records to determine the voyage profile. When the boat was steaming to or from the grounds, it seemed as though the throttle was set, engine revolutions • : ‘a CM I q I -J j3. I j3. f.)u/•.•.•••.•.••co• 1’ iIThI ..v.v: L.v3Ev...:;.v:.v:.a.v. o 0 t3 m CM Oi ‘0 ‘D O •t• 0, i-I. 0 0 — Op ‘0 ‘P c < < c < c < c 0 +9 X° CD 0 . ...... .v..ov....;.v.v;:;. CD Cl) v.... El ©‘ D %z Øa. 3cD a tCD Ccf) CI) CD ‘ u2LZV:••••:•::• 01 cn ©c • ui ‘:v.•.•.•. /‘u/ A • — cn CCDCv....;’;.:C);....v.v..v;; . C) 0• • 0 cn -no.c.v:::.v:JIN’F.vz... SO a latitude C 41 were maintained at a steady level, and the vessel position was changing steadily. When fishing was taking place, the engine was running continuously, so that the net could be set and recovered, and the vessel could be maneuvered. However, we would not expect the engine activity or speed to be close to the expected maximum for long periods of time. Also, the vessel position would be static, or changing very slowly. Voyage # 1 2 3 4 Destination Juan de Fuca Discovery Johnstone/Bella Juan de Fuca Start date 04-09-89 09-09-89 Bella 22-09-89 01-10-89 Finish date Duration hrs. 06-09-89 13-09-89 29-09-89 03-10-89 43 81 177 39 Table V Summary of Voyage Times An activity which could not be distinguished from fishing, using the recorded data, was small local movement to change fishing locations. For this reason, both activities have been grouped together. The movement of the vessel during the presumed fishing activity is discussed in more detail below. A summary of the parameters used to determine the voyage profile is given in Table VI below. A typical record, taken for voyage #2 is shown in Figure 13. All the voyages for which data were available were characterized by the following sequence. The vessel left harbour, and sailed at a (relatively) high speed to the selected destination. There was always a period of zero engine activity after arriving at the fishing ground, presumably to give the skipper 42 Figure 13. Vessel Activity Profile, Ship Speed and Engine RPM against Time 15 2000 10 U, knots 4- 0 C 1000 a. .••-• 5 0 0 145 185 165 205 225 Hours Figure 14. Histogram of Vessel Speed, Sampled at Five Minute Intervals 100 80 60 4- C z a C.) 40 20 0 I 5.5 6.5 7.5 8.5 9.5 • 10.5 11.5 12.5 13.5 14.5 Speed, knots RPM 43 and crew a chance to get gear ready or search for signs of fish before fishing began. This period was as short as an hour, or as long as three days. The vessel then spent some time at medium engine activity, assumed to be fishing operations. On completion of fishing the vessel either ceased activity, changed areas or returned home at high speed. Engine none medium high rpm Ship Speed Position Most likely activity none low high static almost static changing inactive fishing/local transit searching Table VI Summary of Vessel Activity A summary of the voyage profiles, giving the percentage times spent in each activity is given in Table VII. Times were rounded to the nearest hour. Although all the profiles for the voyages followed a similar sequence, it was obvious that they differed in the distribution of the times. It was not possible to identify any consistent pattern between the voyages, but it is clear that the Juan de Fuca trips were different from the others. They were shorter, and the inactive period represented a much smaller portion of the total trip length. Only once did the boat change fishing areas in one trip, although on other occasions it did remain on the grounds overnight. In all voyages except one, fishing represented the shortest activity in the voyage profile. It is interesting to note that even in the relatively short time period observed, the vessel displayed a high degree of mobility. It covered a large portion of the British Columbia coast in a one month period. 44 Percent of Total Time Voyage 1 Voyage 2 Voyage 3 Process * Voyage 4 Sailing out Resting Fishing/local movement Moving areas Sailing back 30 21 *19 *0 *30 20 42 25 0 14 8 52 15 6 20 35 3 31 0 31 Total sailing Inactive Fishing *60 *21 *19 34 42 25 33 52 15 66 3 31 estimated from incomplete data Table VII Voyage Profiles for Seine Fishing Vessel 3.2.2 Detailed Analysis of Transit Portion of Voyage For this analysis, the raw data (logged every five minutes) for the steaming portion of the run was used. Histograms of speed for each voyage were plotted, and examined. A typical run, taken from voyage 2 is shown in Figure 14. A summary of the mean, standard deviations, kurtosis and skew for all the voyages is given in Table VIII. The duration was not necessarily the same as the sailing activity discussed above, since it only included the longest continuous record in each voyage segment. It is interesting to discuss these results, since they have an impact on the times to sail between fishing grounds, which will be required for the simulation. There was some degree of variation of the speed about the mean, and in some cases very high speeds were observed (greater than 15 knots, which may be possible with tide), but in general the standard deviation of the speed was of the order of 1.5 knots. The distributions generally had a pronounced peak, which was usually skewed to the right, but not consistently. 45 Figure 15. Ship Movement During Fishing Activity Latitude and Longitude, Juan de Fuca, 89-09-05 48.47 - 48.46U 48A-5 00 0 4844 0 0 0 0 hP 0 0 0 0 0 0 D 0EI 48.42.124.32 -124.31 -124.30 -124.29 -124.28 -124.27 -124.26 longitude . • • • • Figure 16. Ship Movement During Fishing Activity, Latitude and Longitude, Johnstone Strait, 89-09-12 50.4 00 503 \/ IoU Assumed fishing activity — . 50.2 50.1 -125.5 -125.4 longitude -125.3 46 Mean speed (knots) Voyage Stnd. devn. Duration (mins) RPM Kurtosis (approx. Skew constant) #1, #1, #2, #2, #3, #3, #3, #4, #4, Juan de Fuca, Out Juan de Fuca, home Discovery, out Discovery, home Johnstone, out Johnstone/B. Bella B. Bella to home Juan de Fuca, out Juan de Fuca, home 10.7 8.4 10.2 10.9 10.8 10.4 10.0 10.5 10.0 Mean Value 0.88 1.02 1.15 1.49 1.02 2.86 2.29 0.81 1.07 545 660 690 600 870 790 1680 660 730 1800 1600 1600 1800 1600 1600 1700 1600 1825 -0.161 -0.025 4.851 4.462 3.022 12.073 7.506 1.389 1.435 10.2 Table VIII Detailed Analysis of Transit Data The hull speed is the speed of a wave, which has a wavelength equal to the length of the ship. This is the practical maximum speed for a displacement hull, beyond which excessive power is required to obtain a higher speed. For this boat the hull speed was estimated to be 10.35 knots. This was very close to the overall mean value. It appeared that the skipper ran his boat at maximum speed when sailing to and from the fishing grounds. The amount of fish caught during the trip did not appear to affect vessel speed, but engine rpm was generally increased for the return journey. If this was the case for the whole fleet, then the variable having the most effect on speed difference between boats would be vessel length. 3.2.3 Fishing Portion of Voyage Another part of the process which had to be considered in detail was the fishing portion of the voyage. The two major areas of interest were the -0.201 0.218 2.149 1.99 1.632 2.263 -1.702 0.336 0.694 * sail home wait sail home wait move areas sail home sail home 10:40* 15:15 13:24 19:47 15:42 15:22 18:02 05:35 06:20 06:20 15:24 06:32 08:27 06:32 Juan de Fuca Discovery Pass. Discovery Pass. Johnstone Straight Johnstone Straight Bella Bella Juan de Fuca 89-09-05 89-09-11 89-09-12 89-09-25 89-09-26 89-09-27 89-10-02 Table IX Detailed Analysis of Fishing Portions of Voyages data missing after this time, until 19:00, when vessel is sailing wait wait wait wait wait sail out/wait sail out/wait Within 24 hour day Previous Subsequent activity activity Finish time Start time Approximate location Date Estimated number of fishing spots not clear not clear 2 3 4 3 not clear Estimated grid size, nautical miles 1.5*2.5 2.0*2.0 5.0* 10.0 5.5*1.0 6.5*4.0 2.5*1.5 45*3 48 number of sets (of the net) the vessel made in one day, and the total movement of the vessel during the period when fishing was possible. The data during the fishing/local searching portions were studied to try to identify these activities. Again the raw data were used. The position data were studied to investigate how much the ship moved during the fishing portion of the voyage. Fishing activity was characterized by relatively little vessel movement, with moderate engine activity. If the vessel was fishing one spot consistently, then the observed locations should cluster around a single value. Latitude and longitude were plotted for each identified fishing portion of the voyage, and the size of the grid that the vessel used during the fishing period was estimated from these data and any identifiable clusters were counted. This information is summarized in Table IX. However, there was not sufficient information available from the records to identify exactly how many sets were made. Some insight can be gained from this data. Again there appears to be a different pattern between the Juan de Fuca fishery, Figure 15 and the sheltered fishing of Johnstone Strait and Bella Bella, Figures 16 and 17. The Juan de Fuca fishery did not show consistent clustering, whereas most of the other fisheries did. This was consistent with differences in fishing techniques discussed by Hilborn and Ledbetter [11, 12]. For the Juan de Fuca fishery, the set was made in exposed sea conditions. The fishing took place on the seaward boundary to the grounds, and fish were intercepted as they crossed this line. The vessels were more likely to drift with wind and current in this condition, than in the sheltered fisheries, such as Discovery Passage and Johnstone Strait. 49 Figure 17. Ship Movement During Fishing Activity Latitude and Longitude, Bella Bella, 89-09-27 52.20 0 52.15• 52.10- -128.20 -128.15 -128.10 longitude Figure 18. Fuel Consumption against RPM, Based on One Hour Averages for All Voyages 100• y 0.22240 1.3521e-2x + 3.1726e-5x2 R2 = 0.985 - 80 0 0 60 iI , 0tm Oil o0 0,•.••• 0 •: I 1000 RPM 2000 50 It was clear that the vessel did not move large distances during the fishing activity, relative to the distances moved to get to the fishing spot. The largest estimated movement was approximately 8 nautical miles, and was made up of 3 smaller steps. It would appear that once a commitment has been made to a location the vessel remained there for a full fishing day. A movement of between 1 and 2 nautical miles would be expected when fishing in protected water, and was probably the result of fish movement or changes in tidal direction. Although there appeared to be no major clusters for the Juan de Fuca Strait, the area covered during this fishing period was relatively small. From a detailed study of the times for each activity it was noticed that the boat was usually in the selected location by the previous evening. Fishing usually began in the morning between 05:30 and 08:30. The only exception was the first fishing period in voyage #3 which began at 16:00. The time at which the fishing stopped was more varied, and could be between 13:00 and 20:00. No fishing seemed to take place after 21:00, but the boat did move between areas, or between the port and the fishing ground during darkness. Given the small time spent fishing, in relation to the time for the total voyage, it is difficult to see where absolute boat speed would give the vessel an economic advantage. It is possible that if the fishing takes place in specific locations, and all boats know where they are, then the first boat at that spot will have an advantage. However, given the amount of competition, and the diversity of the distances travelled by the boats, it is difficult to see how this advantage cannot be overcome by leaving earlier or leaving other members of the team at the best fishing spots to keep guard. Other advantages may be in 51 terms of increased fish quality, but again trade-offs could be made between power requirements for propulsion and fish processing equipment. It is also possible that larger installed power has benefits in the catching process, due to a higher speed increasing the swept volume of the net. 3.2.4 Fuel Consumption Fuel consumption during transit and fishing was expected to be a major factor influencing the economics of fishing vessels. Fuel consumption was highly correlated with engine revolutions, as can be seen in Figure 18, taken from voyage 3. Whilst the polynomial regression fitted to each voyage was slightly different, there was an insignificant loss of accuracy by using one equation for all the voyages. This is given in equation (1) below: Fuel consumption (l/hr) = 0.236 - 0.013*RPM + 2 3.152E5*RPM (1) It was apparent that there were four basic levels of engine activity typically used throughout a voyage. These were zero, while resting, 700 RPM for fishing/local searching, 1600 RPM for transit to the grounds (empty) and 1800 rpm for transit to the port (full). Very low levels of RPM were observed, which were less than the minimum RPM at which the engine would normally operate. These were obtained during the averaging process, where the engine was not running for all of the one hour period where data were logged. The recorded data gave a good indication of the movement of the vessel, and the amount of time spent in each activity during a voyage. Discussion with the skipper indicated that the records were reasonably typical of his operating style. The difficulty was that it was a very limited data set, and did not 52 represent a full season of operation. During the time that the data were being recorded the vessel was only active in one fishery. The data cannot be used for checking the simulation model for anything other than salmon seine fishing. Nevertheless, these are the only data we have on detailed movement patterns for a fishing boat. Although the number of voyages for which data were available was very small, it does generally agree with the observations recorded by other observers, and discussed in Chapter 2. The data acquisition could have been improved by expanding the memory, or storage capacity, so that potentially valuable data were not lost when the buffer was full. Alternatively, a regular series of visits could have be made to the boat to copy the data onto magnetic disks, before the buffer was full. It would also have been desirable to include some method of determining when the vessel was actually fishing. Perhaps an additional data channel to monitor the drum winch activity could have been incorporated into the system. It would also have been interesting to have catch data recorded for each set, in parallel with the vessel technical performance. 3.3 Summary of Observations on a Seine Vessel The data obtained from the voyage analysis can be used to give a good indication of vessel activity and fuel consumption on each part of the voyage. The vessel spent a relatively short period of time fishing, relative to other activities, and always returned to Steveston after each fishing trip. The vessel moved between port and the fishing grounds and back to port at its maximum speed. The speed did not vary between outward and return trips, but engine revolutions were increased for the return journey to maintain the speed. There was relatively little variation in speed over the course of the voyage. 53 Due to the length of the voyages and the observation that there was little variation in mean speed between voyages, accuracy would not be lost in a simulation model by assuming that the speed was constant during the transit portion of the voyage. The boat did not move much during the course of a fishing day, and for the purposes of simulation could be considered to be fishing in one spot. The fuel consumption during fishing was much lower than during transit portions of the voyage. The highest fuel consumption was when the vessel was returning to port. Fuel consumption during the return leg of the voyage was 31.5 percent higher than the outward leg. Fishing activity consumed fuel at a rate of 10 percent of the outward leg. Clearly fuel consumption during fishing was a small portion of the total fuel consumed, but distance to and from port may have an effect on the profitability of the vessel’s operations. Given the low rate of fuel consumption, the amount of vessel mobility during fishing is not critical, in relation to the transiting portions of the voyage profile. 54 Chapter Determination for of 4 Catch Salmon and Seine Income Fishing Data Boats This chapter will develop the background data for such important factors as the nature of the catch rate and how it can be translated into income for a fishing operation. The data that were available from the literature were not sufficient to develop a realistic simulation, where vessels had a choice of areas in which to fish. Most published data were based on the average catch, with little discussion on the nature of any random variability. The benefit of using simulation was being able to model the random variables, and so some preliminary work must be done in order to understand how the catch rate and its value vary with geographic location. These data will then be used within the simulation model. A simulation construct, simplify model due the to of the the system, full amount in fishing of order season would information required. to understand the be It complicated is dominant necessary to to mechanisms. However, any simplifications must be done in a realistic manner, such that the final model still represents decision of the skipper. the major components of the fishery and the After some consideration, it was decided that three geographic areas would represent an acceptable minimum number. This would mean that any decision would be more than a simple ‘heads’ or ‘tails’ and the selection process for three areas could easily be expanded to include more areas, if necessary. A preliminary review of the openings indicated that the instances when three or more areas were open together, if the areas were well 4748.7 3724 2415.6 1030.5 1291 819.8 49.4 205.1 114.4 Pink 916.7 247.9 529.6 712.4 290.1 13.4 206.1 41.4 47 Chum Table X Total Catch for DFO Geographic Areas, by Species 10 Year Averages, 1979 to 1988 (Thousands of fish) 201.9 241.3 202.1 1821.8 462.1 162.8 132.7 23 41.2 65.4 55.2 77.7 460.6 162.6 24.3 97.2 28.9 10.3 Butedale, Bella Bella, Bella Coola Nass, Skeena, etc Johnstone Strait West Coast Vancouver Island Queen Charlottes JuandeFucaStrait Georgia Strait Fraser River Rivers/Smiths Inlet 6, 7, 8 3, 4, 5 12, 13 21-27 1, 2E, 2W 20 14-18 28, 29 9, 10 267.2 1416.3 1627.3 1173.3 164.5 851 160 966.6 345.1 Chinook Sockeye Coho Name Area 5665.4 3971.9 2945.2 1742.9 1581.1 833.2 255.5 246.5 161.4 Total, Pink+Chum 91.38 69.87 60.70 33.53 66.70 44.53 39.59 19.49 28.92 % Total Ln 56 spaced, were relatively rare. This was because the fish tended to appear in the northern areas early in the season and the southern areas later in the year. Also, some areas would be rejected by individual skippers, based on historical records, personal preferences or intelligence on fish abundance. The next phase in the analysis was to select three representative areas to be included in the model. If vessel mobility was to be studied, then the areas should be well spaced. It would also be useful to include some areas studied by other researchers, and the areas should also be popular ones with fishermen. A summary of the 10 year data for all the aggregate fishing areas is given in Table X, taken from Bjerring [16]. These data showed that the most productive combined areas, in terms of the number of fish, were Butedale, Bella Bella and Bella Coola (Areas 6, 7, and 8 in Figure 1). This combined area would be interesting to include in the simulation, since we may expect high catch rates, which may have an effect on the size of the boat. Other areas which were documented as being popular, and productive, were Johnstone Strait (Area 12 and 13) and Juan de Fuca Strait (Area 20). The total catch per season, averaged over ten years, for these areas was approximately 30 percent and 80 percent lower than those from Areas 6, 7 and 8. This would indicate that the seasons were shorter for these areas, or that catch rates were lower. 4.1 Data Required for Simulation Model The ideal data for developing a simulation would have been catch per set for each area. However, only one set of published data was found at this level of detail, for Areas 12 and 13 [7]. These data gave mean catch per set for open sets, 57 point sets with short line-ups and point sets with long line-ups. An analysis of variance (ANOVA) on these data was carried out for set type, line-up and week. For the point set the mean catch was 32-36 fish and 28-29 for open set, but these differences were hardly significant at a practical level. The catch rates for different queue types for the point set were different however, with 27-28 fish per set for short line-ups (1-2 boats) and 40-45 fish per set for long lineups (3-5 boats). Ledbetter noted that there was little variation in the mean, implying that there was little difference due to ‘skill factor’ between skippers. Ledbetter also gave probability density functions for length of line-up. However, only one area was covered (Area 12-13), and the data may no longer be current. From discussions with the skipper, it seems that open sets are more common than they were at the time of Ledbetter’s observations, and fishing techniques differ between areas. It would be possible to use Ledbetter’s work for a simulation of Johnstone Strait by fitting probability distributions to lineups and catch rates, but it would give no information on the effects of mobility. It was not possible to obtain information at this level of detail for all the desired areas, and so data had to be found from other sources. 4.2 Summary of Data Available for All DFO Areas Another source of data was the records kept by DFO of landings for fish caught in a specific area, by boat and date. This was less detailed than the ideal data, but might give some information on the range of total catch per day, and the related income, which can be expected from a given area. Data were obtained 58 from DFO for all landings by salmon seine licences for four years (1987, 1988, 1989 and 1990). The data consisted of: - - - - - - - - - - date fish were landed, area fish were caught, vessel name, vessel identification number (CFV number), length of vessel, volume of vessel, age of vessel, quantity of fish (number, weight) for each species, dollar value of each species, length of trip, days. The first stage of the analysis was to reduce the data to total quantity of fish and dollar value per boat per trip. This was because data were collected for all types of salmon, classified by DFO, and it was important to know the total amount of fish caught by the boat. Some data were omitted, due to obvious errors or omissions. For example, a few vessels would have no length data, and were removed, and occasionally very high total catches, several million tonnes, would be obtained, which did not correlate with the number of fish or the dollar value. These were also omitted from the analysis. This accounted for only a few records, no more than 5 per area. From these data, the following parameters were derived for each day of the fishing season in each area: 59 Are a 6 6 6 6 Year # days (boats >= 6) 1987 1988 1989 1990 20 33 6 28 4419 7232 1143 5645 728 3025 322 3288 19.7 4265 2582 21 20 11 25 3095 4662 1951 3351 1792 3393 1289 2144 17.3 3236 1113 22 33 6 27 2327 4502 4166 3085 1235 2225 2825 676 20.3 3665 999 26 24 50 33 3353 2700 3971 4051 2011 1691 1741 2456 33.3 3341 629 18 17 34 24 3384 2248 3622 4114 2271 1625 1947 1897 23.0 3085 790 11 10 32 14 2584 1428 4575 7422 1130 1090 1298 3654 17.7 2862 2624 4 year mean 7 7 7 7 1987 1988 1989 1990 4 year mean 8 8 8 8 1987 1988 1989 1990 4 year mean 12 12 12 12 1987 1988 1989 1990 4 year mean 13 13 13 13 1987 1988 1989 1990 4 year mean 20 20 20 20 1987 1988 1989 1990 4 year mean Mean (kg/day) dev (kg/day) St. Table XI Summary of Annual Catch Data for Each Fishing Area, by Year 1987 to 1990 $/k g 1.90 1.76 1.17 1.06 mean $/day 8382 12729 1336 5995 7482 1.90 1.76 1.17 1.06 5872 8205 2281 3559 5453 1.90 1.76 1.17 1.06 4415 7923 4870 3276 5736 3.36 2.74 2.52 1.90 11250 7393 9998 7714 9547 3.36 2.74 2.52 1.90 11354 6154 9120 7834 8876 3.24 7.28 2.95 3.04 8360 10398 13496 22579 10751 60 - - - - number of boats reporting landing on given day. mean catch/day, kg. standard deviation of catch/day, kg. standard error of mean catch per day, kg. Day 1 was defined as July 1, and day 153 as November 30. No fishing was observed outside these periods. In order to ensure that reliable values of mean catch per day were obtained, only days where 6 or more boats reported a landing were used in the subsequent analysis. It was assumed that the date of the landing was the last day of fishing, i.e. for a one day trip the fish was caught that day. It is appreciated that this may be in error by the time it takes the boat to return to harbour, but no data were given for where the catch was landed. The sailing time may have had the effect of shifting the date by some constant. A refinement to the method would be to include the data on the dates of the openings and force the fish caught into the period of legal fishing activity. Unfortunately this was not available at the time the analysis was carried out. From these data we can produce a summary of the fishing activity in a given area. The important factors to consider were the number of boats which fished in each area, the duration of the season, the mean catch per day over the season, together with its standard deviation and the number of days when more than 6 boats reported a landing. These data are summarized for all the areas selected, by year, in Table XI. Since there was often a wide variation 61 Area Year First day Last day # days Total Mean Std. devn Boats >= 6 # boats boats/day boats/day Butedale [6, 7, 8] 1987 1988 1989 1990 12 9 17 14 92 89 88 107 21.00 28.67 7.67 26.67 410 505 89 499 35.32 59.45 16.39 49.88 13 94 21.00 375.75 40.26 33 29 17 37 85 114 117 116 22.00 20.50 42.00 57.00 460 471 502 508 48.60 49.00 59.50 63.40 4 year mean 29 108 35.38 485.25 55.13 Juan de Fuca 1987 [20] 1988 1989 1990 42 39 18 45 90 54 89 61 11 10 32 14 211 157 201 217 87.50 61.50 72.80 80.00 4 year mean 35.00 73.50 16.75 196.5 75.45 4 year mean Johnstone [12, 13] 1987 1988 1989 1990 Table XII Summary of Length of Season and Average Vessel Activity, by Fishing Area, 1987 to 1990 41.86 59.45 16.10 68.86 46.21 49.02 55.60 53.57 53.97 35.41 57.59 62.33 62 between years for a given area, the 4 year mean for the mean catchlday and the number of days is also given. Other data which could be derived from this analysis, for each area were: - - - - - earliest date of a landing latest date of a landing total number of days for each area total number of boats which fished that area number of boats per day (mean and standard deviation) These data are summarized in Table XII Table XIII gives, for each area; - - duration of trip (mean and standard deviation) total number of boats which used area one day trips - - % two day trips 4.3 Translation So far, only of Catch the weight Data to of salmon Income landed has been considered. This is important from the point of view of estimating the number of fish caught and its subsequent effect on the fish population. It is also important in relation to the design of the vessel, in terms of the size of the hold and the corresponding amount of ice required. However, the most important factor for voyage economics is the cash value of the fish. The conversion factor between the weight of fish and its dollar value needs to be determined. 63 Area Butedale [6, 7, 8] Year 1987 1988 1989 1990 4 year mean Johnstone [12, 13] 1987 1988 1989 1990 4 year mean Juan de Fuca [20] 4 year mean 1987 1988 1989 1990 Mean Length of trip, days 1.684 1.749 1.361 1.744 1.635 St. Devn. % 1 day trip % 2 day trip days 0.694 58 33.70 0.952 26.70 65.3 0.571 70.8 19.10 0.707 60.7 33.10 0.185 63.7 28.15 1.154 1.125 1.446 1.342 0.24 0.317 0.317 0.383 96.3 90.87 87.3 87.6 1.95 2.76 11.80 11.60 1.267 0.153 90.5175 7.03 1.734 1.699 2.203 2.173 0.547 0.508 0.488 0.433 64 54.1 17.4 15.2 28.90 43.90 76.10 79.30 1.952 0.273 37.675 57.05 Table XIII Summary of Length of Trip to Each Fishing Area, 1987 to 1990 64 Let us consider the expected range of income from different types of salmon species in terms of $/kg. The 1987 and 1988 averages for total landings in B.C. are given below, taken from [16]: Dollars per kilogram Year 1987 1988 Chinook Sockeye Coho Pink Chum 6.70 5.94 4.59 1.29 2.45 8.52 8.14 6.12 1.57 2.81 Table XIV Average Dollar Value for Salmon, by Species, 1987 and 1988 There is a quality factor implied in these figures, since expensive species are usually caught by troll, and frozen as individual fish. This results in a high quality product, which is sold as whole fish. For seine fishing, the large net and the bulk storage of fish in the hold generally results in a lower quality product. Seine vessels target mostly chum and pink salmon (Ledbetter), which are primarily sold for canning, and this is reflected in the price paid by the processor for the fish. From a review of the catch data, it seemed that there was a mix of species obtained from a single trip. Since this varied with geographic location, due to fish habitat, the simulation must include realistic values for each area. 65 Figure 19. Comparison of Regression Equations for Converting Catch to Income, Johnstone Strait, 1987 300000 * 200000 • E $, obs. — 0 U regression through origin linear regression 100000 -. - 0 0 20000 40000 60000 Fish, kg 80000 100000 - linear regression, log variables 66 A value of the mean dollars per kilogram was required for each area, and each year for which data were available. Very strong correlations were observed between total catch and total dollars for each area based on linear regression, (R > 2 =0.964), for the four years for which data were available. It was necessary to check which relationship was most the suitable procedure between the weight of fish and the for determining dollar value. The the analysis methods will be demonstrated with data taken from Areas 12/13 for 1987. The most obvious approach was a linear regression equation through the observed data for the total catch per year against total income. This is shown in Figure 19. At first sight the regression seems adequate. However, we note that the intercept with the y axis did not pass through the origin, which would give unreliable predictions of income for catch rates less than approximately 2500 kg. Another factor to consider was that the residuals were not randomly distributed, weight. since Weisberg transformation no [20] should large variances were observed at small values of fish suggested that in such cases, a variance stabilization be introduced by taking natural logarithms of the variables. Using this method, there was a much more random distribution of the residuals, and so the method was more rigorous. The regression line is also shown fitted to the data in Figure 19. A third alternative was to fit a least squares deviation equation to the observed data, forcing the equation through the origin. This was not unreasonable, since there should be zero income for zero fish. The regression equation was: y=13x+e (2) 67 where B was determined from 13= 2 Xiyi/Xj , with x as total weight of fish, in kilograms, y the total dollar value and e was the error between the actual and the predicted values. It was observed that the previous problem of non-random variance occurred. It is therefore accepted that this is strictly a least-squares deviation fit, and no statistical inferences can be made. From Figure 19, it can be seen that there was little practical difference between the three methods discussed above. The best method would have been to use the regression which included the variance stabilization, but this equation could not be programmed directly in the simulation language. It was decided that the best alternative equation was to use the linear regression through the origin. This analysis was carried out for all areas and all years and the results are also given in Table XI, along with the catch data. 4.4 Discussion of DFO Data From these data, it can be seen that actual income was always higher than the provincial average for pink salmon, and in most cases it was higher than the provincial average for chum salmon. Only in Areas 6/7/8 can we infer that most of the catch is made up of pink and chum, because the observed value of dollars per kilogram is between two provincial levels. Area 20 had a very high value of dollars per kilogram for 1988. This was up to 4 times higher than that observed for other areas. In this case the majority of the catch was made up of more expensive species such as chinook, coho and sockeye. In Table XI we see that Area 6 had the highest average catch per day, over the four years of data, at 4264 kilograms per day. Areas 7, 8, 12 and 13 all had catch rates between 3665 kilograms per day and 3084 kilograms per day, which were 68 close to the estimated 10 year average, described earlier. Area 20 had a slightly lower catch rate at 2862 kilograms per day. When studying the voyage economics, it is important to compare the different areas on the basis of dollars per trip, rather than kilograms per trip. Table XI also gives the average catch multiplied by the average dollars per kilogram for the areas and years described above. Area 20 had the highest dollars per day based on the four year average, at $10,700/day. The next highest was Area 12, which was $9547/day. These data showed that the areas identified in [11] were still the most economically productive, once allowance had been made for the dollar value of the fish. Areas 6, 7, and 8 had the lowest dollars per day, and therefore may be the least desirable, even though they were the most productive in terms of the total amount of fish caught. This analysis clearly illustrated the need to consider the dollar value of the fish, as well as the quantity caught. The mean number of boats per day, where there were 6 or more observations, over the full season is given in Table XII. It can be seen that Area 20 attracts the highest number of boats per day, when it is open, followed by Areas 12/13 and Areas 6/7/8. This follows the trend in dollars per day and would indicate that economics is a major motivation in fishing. Since the dollar value appears to be the driving factor in the movement of boat to a given area, then it would be possible just to consider the value of the fish, rather than the quantity and value. This was not desirable however, since the size of the catch affects the subsequent size of the vessel, and the value of the 69 fish may be affected by broader economic issues, outside the scope of this analysis. For these reasons it was decided to keep the two variables separate. A summary of the dates between which landings were recorded for each of the areas is also given in Table XII. Since areas within the same aggregate location seemed to follow similar patterns, I will consider only these larger areas, using averages over the four year period. The mean day for the first observation was day 13 in Area 6/7/8. The first observation in area 12/13 was day 29, and day 35 for area 20. The mean date for the last observation, for area 20 was day 73, followed by day 94 for Area 6/7/8 and day 109 for Area 12/13. It was interesting to note that based on the four years of observations, all four areas were open between days 35 and 73, out of a total season between day 13 and day 108. This period represented approximately 40% of the total time available, and the period where the most complex decisions were required of the skipper. If only one area was open, then the only decision required of the skipper was whether to fish or not. However, when there was a choice of areas, and if the objective was to maximize the total income for the season, it is important to know if there was a strategy which would meet this objective. Area 12 was open the most with a four year average of 33.3 fishing days. Most other areas had four year averages around 20 days. Despite the higher dollars per day value for Area 20, the fact that it was open fewer days, meant that a skipper could expect more total income for the season from fishing in Area 12/13, if only one area had to be chosen. The disadvantage of only fishing Area 12 would be that there would be a lost opportunity to make a higher income, on the days when Juan de Fuca was open. The maximum income would come from 70 Figure 20. Fishing Vessel Activity Profile 1987, All Areas 200 175 150 : 125 100 .J I 0 IIILILJ d ... 20 40 ... .... 60 80 100 I.. I 120 140 dag Figure 21. Fishing Vessel Activity Profile 1980, All Areas 300 250 200 1W a, a .a 150 p 100 50 U n 0 20 A1d i 40 . 60 dag i. 80 . 100 - 120 71 switching fishing areas at some time during the season, and this is something which must be included in the simulation. From the daily data we can also obtain an indication of the distribution of effort with time. This is shown as the maximum number of boats fishing as a function of date, for each year, in Figures 20 to 23. It can be seen that the effort was not uniformly distributed over the season, and there were periodic spikes within the data. These spikes were at approximately 7 day intervals, and reflected the nature of the openings described in [11, 12, 13]. The number of peaks for the total season was estimated to be between 11 and 13 over the four year period, which is less than the typical number of trips estimated from the annual summary data. This may be made up of boats making more than one trip per week, or by boats fishing in areas which were not studied. It is interesting to note that the effort for Area 6/7/8 was the highest when it was the only area open, at the beginning of the season. At the end of the season, the effort was much lower. This may represent the mobility described in [11], in that to maximize income, the skippers will pick the best area from those that are available. Another important factor which can be obtained from the data was the duration of each trip. This is summarized in Table XIII. It can be seen that the mean duration of the trip for all areas is between one and two days. Also it can be seen that the majority of trips for all areas were registered as one day trips, with the exception of Area 20, where most of the trips were two day trips. It can be seen from Table XII that almost all of the boats were recorded as having fished at least one day in Areas 6/7/8 and Areas 12/13. Only about half the fleet 72 Figure 22. Fishing Vessel ActiYitg Profile,1989, All Areus 225 200 175 150 125 ‘ 100 75 50 ,f .1 ij 25 20 — 40 — 60 80 100 120 dag Figure 23. Fishing Vessel ActivitU Profile,1990, All Areus 350 300 250 4’ , 0 .0 * 200 150 100 i 0 20 Ii i L 40 . 60 dag L •1 80 100 120 73 fished at all in Area 20. It does seem to be that the length of the trip is correlated to the catch rate, with the longer trips, for 1989 and 1990 being the years with the highest average income per trip. Hilborn and Ledbetter [12] noted that the mean length for boats fishing Area 20 was longer than those fishing Area 12/13. This was observed in these data also. The mean length of boat for each of the three areas is given in Table XV. Boat Length, m Area 6/7/8 Area 12/13 Area 20 Mean St. Devn. 18.238 18.499 20.372 3.919 3.097 2.972 Table XV Average Length of Vessels Fishing in Each Area, 1987 to 1990 It seems as though the bigger boats go more often to Area 20 for longer fishing trips than the exposed fishing smaller boats. location where This larger may be boats are a function of the more less influenced by the weather conditions. It may also be due to economics, in that the bigger boats have higher expenses, and so have to target the most lucrative fishing area, when it is available. It was discussed above that three areas, which were suitably spaced, were desirable from the point of view of developing the simulation. It would also be desirable to avoid areas which were adjacent, since fish may move between areas, and the catch rates would not be independent. It was noticed from a 74 preliminary study of the data that the catch rates and openings in adjacent areas were highly correlated, and including all the areas in the model would not add to its accuracy. For these reasons the areas selected for further study were Butedale, (Area 6), Johnstone Strait (Area 12 only) and Juan de Fuca (Area 20). 4.5 Nature of Distribution of Daily Catch So far only the mean daily catch over the season has been considered. Catch rate is discussed in the literature as a random variable, and the nature of the distribution of catch per day may have an effect on selection of an area to fish. In order to assess the risk associated with the fishing process, we need to know the nature of this random variable. In order to do this, the data for the landings from a single area, on a single date, must be studied. It was not possible to establish if all the fish was caught on that one day, since we only have the date of landing, but this is the best assumption that can be made. It must also be assumed that the boats were acting independently, and were only landing, or reporting landings, which were caught by that boat. It was also desirable to consider dates where a large number of boats reported landings. Exploratory histograms for several days from each area showed that there was a wide range of data, always with a minimum observed value close to zero. There was also a wide range of shapes of the histograms, between days within a region and between regions. Other researchers have looked at fitting statistical models to catch data. Ledbetter [7] discussed statistical models for salmon seine fishing, in Area 12. He considered the probability of observing a certain catch per boat, in terms 75 of number of fish, to be predicted by the negative binomial distribution, given in equation (3). P(x=k) =(k1)pr(ip)kr Curr [21] (3) considered the theoretical possibilities of fitting an Erlang model, equation (4), to catch per set of blue whiting in the North Sea. The model was derived for a fishery where fishing operations were not impeded by on-board processing requirements, so catch could be stowed in a very short time. This process was similar to salmon seine fishing, where fish were typically loaded straight into the hold. f(x) xk 1 expl- k xim) = (4) Curr argued that there was some theoretical basis for the use of the Erlang distribution, since it represented an activity which took place in stages, where each stage was exponentially distributed. (The sum of n independent exponential distributions is an Erlang distribution with k=n). It was argued that a single species fishery could be expected to fit such a process, with a haul being a single stage. However, the distribution for the catch per haul may not be exactly exponential, due to technological factors. The general case for the Erlang distribution (with non-integer k) is the gamma distribution, equation (5). 76 Figure 24. Gamma Distribution Fitted to Catch/Day August 10, Johnstone Strait, High Catch Rate 1.0• . 0.8 0.6 U- 0.4 . 0.2 — • 0.0.• 0 Max. likelihood estimate Fx(observed) I I • 10 20 Catchfday 30 (tonnes) Figure 25. Gamma Distribution Fitted to Catch/Day, August 24, Johnstone Strait, Medium Catch Rate 1.0• 0.8- 0.6x 0 LI 0.4- 0.2 - — • — 0 Max. likelihood estimate Fx(observed) I I 2 4 Catchiday (tonnes) 6 77 f(x) = 1 (xr aF(X) a -l exp(- -)a (5) Cuff fitted a gamma distribution to the data for a single haul for blue whiting. If this distribution was constant between hauls, then the additive property of the gamma distribution meant that the distribution for second and subsequent hauls could be calculated, but was also a gamma distribution. Thus using the same arguments as Curr, the distribution of the total catch per day for all boats fishing in the same area should also be a gamma distribution if all the boats have equal catching power and the variation in catch rate is due simply consistent to with sampling Ledbetter’s from the same observation underlying since the distribution. gamma This function is is the equivalent of the binomial function, for non-integer values of X. To test if the daily distribution of catch was represented by a gamma distribution, we can choose some days from the data, and test them to see if a gamma distribution fits the observed data. Area 12, for 1987, will be used, since it was used by Ledbetter, and was neither the year of minimum nor maximum total catch. Three days were chosen with high, medium and low catch rates. The days selected were: August 10 August 23 September 22 High catch rate Medium catch rate Low catch rate Estimates of the scale and shape parameters, a and ?, for these three days were determined from maximum likelihood methods [221. A summary of the 78 Figure 26. Gamma Distribution Fitted to Catch/Day, September 23, Johnstone Strait, Low Catch Rate 1.0• 0.8 I: I. 0.6 . I. • / I LI. I. 0.4 Max. likelihood estimate — 0.2 • Fx(observed) 0.0• I 0 2 Catchlday 4 (tonnes) Figure 27. Comparison of Probability Density Functions Fitted to Observed Data 1.5 August10 24 1.0•• -.-. -.- September23 ‘C 0.5 t. 4 0.0• 0 4% I I I 5 10 15 Catchlday (tonnes) 20 79 estimated parameters is given in Table XVI, and the fitted cumulative distributions are compared with the observed values in Figures 24 to 26. The comparison of the density functions, Figure 27 shows the wide variation which can be observed for total catch per day. Date Number of boats August 10 August 24 September 23 46 61 33 a 2.671 1.129 0.830 X mean catch (tonnes) 2.508 1.620 1.003 6.699 1.829 0.827 Table XVI Summary of Parameters for Probability Density Functions, Daily Catch Data Observed probability distributions were compared with the fitted ones, and a Kolmogoroff test used to test the level of fit. None of the distributions were rejected at a =0.05. This is strong evidence in favour of the gamma distribution as a family of two parameter distributions to represent the total catch per day for a given area and day. It can be concluded that the gamma distribution is good candidate for probabilistic modeling of the daily catch data. This is based on the observation that there is some theoretical justification for its choice and it is a very flexible shape. Provided that the gamma distribution is based on observations, it should give a realistic approximation to catch per day data. 80 4.6 Variation in Mean Catch per Day Over Full Season The discussion above suggested that there was a wide variation in the shape of the catch per day distribution, even for the same area and the same year. It was impractical to fit separate distributions to each day of the season, for each area, due to the amount of computation involved. It was clearly desirable to investigate methods of simplifying the process. Ledbetter [7] skipper/vessel suggested that effectiveness the may be distribution of average represented by a gamma or expected distribution (equation 5) of Poisson variables (x), where X uniquely describes the shape of the distribution and a is a scaling parameter reflecting the driving process of the system (salmon abundance). It would seem that the gamma distribution was a good model for the mean catch per day, when the whole season was considered. A program was written, using the methods given by Bury [22], for determining the maximum likelihood estimates of parameters for a two parameter gamma distribution fitted to the observed mean catch per day. A visual inspection of the data indicated that there was not sufficient evidence for three-parameter models. A comparison of the fitted distributions with the observed data is given in Figures 28 to 30, for each of the areas in the study. The estimated parameters for the distributions are given in Table XVII, together with the Kolmogoroff statistic determined from the observed data and the fitted distribution. It can be seen that in most cases the fitted distribution was not rejected at a =0.1 or a =0.05. There were some cases however, where the distributions were rejected, 1987 1988 1989 1990 1990 12 1987 1988 1989 1990 * 17.7 11 10 32 14 33.3 33 26 24 50 19.7 20 33 6 28 2862.37 2584.25 1428.10 4574.77 7422.36 3341.28 4051.47 3353.11 2700.18 3970.55 4264.57 4418.74 7232.40 1142.59 5644.63 Sigma 1264.68 981.54 901.38 4.97 3.18 10.53 3.22 2.77 2.65 2.75 4.M 35.60 6.31 14.59 1.86 Lamda 48699.45 43270.46 13112.27 790795.60 138018.0 133100.40 86138.27 34622.32 2529.09 81839.44 2660.58 734465.40 4.00 1.85 7.38 1.31 0.41 0.48 0.56 0.74 206.31 2.29 89.85 0.21 no yes no yes no no yes no no no no yes no * no no reject @ alpha = 0.1 no no no 0.065 0.133 0.150 0.237 0.114 0.289 no no no no * no no 0.080 0.077 0.158 0.129 0.158 0.125 Var. sigma Var. lamda Kolmogoroff reject @ statistic alpha = 0.05 Table XVII Summary of Fitted Distributions to Seasonal Catch Data, for Each Fishing Area, 1987 to 1990 1129.95 520.03 1090.31 449.25 1297.98 434.42 3654.15 2306.99 2456.05 1461.64 2010.96 1690.93 1741.18 124.12 727.85 3025.03 1145.92 321.61 78.33 3287.55 3030.21 # days Mean catch Std. devn (Boats >= 6) (kg/day ) (kg/day ) small number of openings, fit unreliable 4 year mean 20 20 20 20 4jar mean 1987 1988 1989 12 12 12 4_jar mean 6 6 6 6 Area Year I- 82 Figure 28. Comparison of Observed and Fitted Cumulative Distributions for Butedale o CDF, obs. 87 — • CDF, fitted 87 CDF, obs. 88 a CDF, fitted 88 x LI CDF, obs. 89 — — - CDF, fitted 89 CDF, obs. 90 CDF, fitted, 90 0 10000 20000 Mean catch per day (kg) Figure 29. Comparison of Observed and Fitted Cumulative Distributions for Juan de Fuca o — • a CDF,obs.87 CDF, fitted 87 COF, obs. 88 CDF,fitted88 x LI. o CDF, obs. 89 CDF, fitted 89 CDF,obs.90 CDF, fitted 90 0 10000 Mean catch per day (kg) 20000 83 Figure 30. Comparison of Observed and Fitted Cumulative Distributions for Johnstone Strait 1.0 o 0.8 CDF, obs. 87 — CDF, obs. 88 • 0.6 CDF,fitted87 x CDF,fitted88 U. o 0.4 CDF, obs. 89 — — - CDF, obs. 90 * 0.2 - - 0.0 0 2000 4000 6000 8000 Mean catch per day (kg) 10000 12000 CDF, fitted 89 CDF, fitted, 90 84 or where there were insufficient data. For example, Area 6 for 1989 had very few points. Area 20 in 1990 was the only fit which was rejected. These data seemed to show two almost constant catch rates, and perhaps two distributions ought to have been fitted. A detailed description of the methods used to fit the distributions and the tests of the fit is given in Appendix 1. 4.7 Simplification of Daily Catch Distributions We must also consider the relationship between the mean catch per day and the shape of the probability density function for catch per day. This is important since for one reason or another we do not expect one boat to obtain the mean catch for a given day. It will do better or worse than the mean based on a variety of factors such as the number of boats and other uncontrolled variables such as wind, weather and current. The mean catch per day was plotted against its standard deviation for all areas and all four years of data. It was noted that this relationship was reasonably constant for an area, but was different between areas. Figures 31 and 32 show this relationship for Area 12 and Area 20. Based on the single day data, if we assume a gamma distribution for daily catch distribution, then we can estimate the scale and shape parameters directly from the first and second moments, calculated for the area profile, rather than use maximum likelihood equations for each day. This relationship is given by: mean=aX variance = 2 a (6) (7) 85 Figure 31. Mean Catch per Day against Standard Deyiation Johnstone Strait, 1907 to 199o 9000 8000 - g = 646 2 = .744 r + 229.757 0 7000 0 0 6000 0 5000 0 0 0 000 4000 1000 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 mean catch/dag, kg Figure 32. Mean Catch per DayagainstStandard Deyiation Juan de Fuca, 1907 to 1990 ØLJUU 7000 .474x = .677 = 2 r + 127.358, 0 0 6000 d ‘ 0 5000 4000 3000 2000 0 0 0 1000 0 2000 4000 6000 8000 mean catch/dag, kg ioooo 12000 86 Area 6/7/8 Year Lamda Mean 1987 1988 1989 1990 All years 3.319 2.781 2.31 3.357 3.055 Std. devn. 1.636 1.776 4.573 3.673 Area 12/13 Year Lamda Mean 1987 1988 1989 1990 All years 2.587 1.744 2.405 1.906 2.195 Std. devn. 1.986 0.833 1.39 0.981 Area 20 Year Lamda Mean 1987 1988 1989 1990 All years 5.961 2.44 5.949 3.928 5.005 Std. devn. 2.975 1.191 2.877 2.504 95 percent Confidence Interval Lower 95 percent Confidence Interval Upper 2.907 2.4 0.332 2.539 3.731 3.162 4.288 4.174 95 percent Confidence Interval Lower 95 percent Confidence Interval Upper 1.983 1.481 2.103 1.646 3.191 2.007 2.707 2.167 95 percent Confidence Interval Lower 95 percent Confidence Interval Upper 3.962 1.588 4.912 2.482 7.959 3.291 6.986 5.374 Table XVIII Variation in Shape Parameter, Lamda, Between Years, for Three Fishing Areas, 1987 to 1990 87 Figure 33. Variation in Shape Parameter, A with Mean Catch per Day, Johnstone Strait 14 12 0 10 8 0 6 0 0 4 00 00 0 2 0 00 0 0 °P OooQ 000 0 o0n&Rfln?o. Q 0 J o ocbcb 0 1000 & 0 0 0 0 0000 0 00 0 gO 0 0 0 0 2000 3000 4000 5000 6000 7000 8000 9000 mean catch/day, kg Figure 34. Variation in Scale Parameter, a with Mean Catch per Day, Johnstone Strait LJUU I - 12000 I 0 10000 8000 a for 6000 mean A 0 0 D 0 1000 2000 3000 - 4000 - 5000 6000 mean catch/day, kg 7000 8000 9000 88 Figure 33 shows the shape parameter, X, plotted against mean catch per day and Figure 34 shows the scale parameter, a, plotted against mean catch per day, for Area 12. It would appear that the shape parameter shows no trend with mean catch per day, and so the simplest simplification would be to use the average value. relation to This can be rationalized on the basis of Curr’s discussion in the of effect technical factors, which should be reasonably constant for a given area. Once the value of A has been set, then the value of a was determined directly. Figures 33 and 34 show the fitted data in relation to the observations, reasonable for Area 12. Clearly to the observations. approximation the calculated values represent Although the results are a not shown here, the other areas were checked, and similar results were obtained. Table XVIII gives values of A, calculated for each year, rather than the mean for all four years. In all cases except one, Area 20 for 1988, the mean value of the annual data is inside the 95% confidence interval for the average value. It was observed that the mean catch per day for this area was much lower than the other three years for which data were available. Since the catch per day distribution is probably of secondary importance after the mean catch distribution, then this level of accuracy should be sufficient. There is also some doubt as to whether or not catch per day is a truly random variable. If the mean catch per day is plotted against day, there is often a significant trend. The data are shown in Figures 35 to 37 for Areas 6, 20 and 12 respectively, for 1987. It can be seen that the catch rate decreases as the season progresses, for Areas 12 and 20, but remains static for Area 6. The data are summarized for the other years in Table XIX. In only one case was the regression not significant at 90% confidence, for Areas 12 and 20. This may be 89 Figure 35. Variation in Mean Catch per Day with Day, Butedale, 1907 10000 9000 a y = 13.49x + 3993.129, r 2 = .02 8000 1 7000 0 00000 4’ E 000 0 0 0 4000 o0 3000 0 0 0 0 2000 1000 U I 15 20 25 30 35 40 day Figure 36. Variation in Mean Catch per Dog with Dog, Juan de Fuca, 1907 10000 9000 g = -50.41 lx + 5604.335, r 2 = .545 8000 4 7000 6000 o 5000 4000 0° to06b7b8b9b day 45 90 Year Number Slope, of days kg/day R2 Significant at 95% confidence Area 6 1987 1988 1989 1990 20 33 6 28 13.49 -64.847 16.513 196.072 -0.034 0.045 0.189 0.792 no no no yes Area 20 1987 1988 1989 1990 11 10 32 14 -50.411 -139.258 -34.17 -484 0.545 0.442 0.185 0.47 yes yes yes yes Area 12 1987 1988 1989 1990 44 41 84 57 -86.743 3.833 -44.209 -27.675 0.418 0.004 0.146 0.095 yes yes yes yes Table XIX Summary of Variation in Catch Rate with Time, 1987 to 1990 91 due to the fact that there is a finite fish population and that as the season progresses there are fewer fish to catch (due to the mortality caused by previous fishing within the same area). For Area 6 however, only one year showed a significant change with time, and this was an increase. In all cases, the trend included a large amount of scatter, and if performance for a single fishing day, at any point in the season, was required, then the assumption of a random variable should still be reasonable. 4.8 Summary of Catch and Income Data The mean catch per day over the whole season for a particular area can be modelled by a gamma distribution. Here the ‘mean catch per day’ means the total weight of fish caught by all the boats fishing in one area, in a twenty four hour period, divided by the number of boats. This distribution remains constant for the one year period. The catch per day for a particular boat fishing in that area can be modelled by a second gamma distribution. Here the ‘catch per day’ means the total amount of fish caught by a single boat fishing in that area in a single day. The catch per day distribution is related to the ‘mean catch per day’ by the four year average of the shape parameter, X. The two distributions were required to model the level of risk associated with an area, and a simulation which only included the mean catch per day would under-estimate the overall risk involved when a small number of boats were operating together. Within a given fishing area, there was considerable variation between the mean catch rates. One area could have a very high catch rate one year, and a very low one the next. When developing a simulation model, it will be 92 Figure 37. Variation in Mean Catch per Dog with Dog, Johnstone Strait, 1907 10000 9000 g = -86.1 39x + 7779 48, r 2 = .42 0 8000 C 7000 6000 0 0 4000 3000 2000 1000 30 40 50 60 dag 70 80 90 93 important to include these differences, since they could have an effect on the overall profitability of the vessel. The relationship between catch, in kilograms, and income in dollars, appeared to be constant, when averaged over the course of the season. In most years, there were factors of two observed in the value of the salmon caught in different areas and sometimes the factor was almost as high as four. These differences significant had effects on the income obtained from different fishing areas, and must be allowed for in the analysis. 4.9 Discussion of the Analysis in Relation to Simulation The analysis described above must be reviewed in terms of its usefulness for developing a simulation. The preliminary analysis indicated that there were no strong trends in catch per day with any vessel parameter which was logged by DFO. On this basis, the assumption implicit in the simulation, that catch is independent of the which did not vessel, show up seems reasonable. If however, there were trends in the preliminary analysis, then the result would represent the performance of a typical vessel, with parameters close to the mean values, and may not be realistic for vessels with extreme parameters. Fortunately, the salmon seine fleet is relatively homogeneous, and any bias that this simplification would introduce should be small. The alternative approach would have been to fit distributions to catch rates for each boat, as a function considerably more analysis. of area and time. This would have required In addition, the number of trips per year to a given area would have been small, would have been less reliable. and so the fitting distribution functions 94 The other major assumption implicit in the analysis was that the mean catch per day was not varying with time. This does not appear to be always true, since although there is considerable variation, the overall trend seems to be a reduction in catch rate with time, especially for Johnstone Strait and Juan de Fuca. Given these observations, a simulation developed using the analysis carried out in this chapter would be most representative of a ‘typical boat’, fishing on a ‘typical day’ in the season. The data could be used to model a single opening, taken at random from within the overall season. Multiple runs of the simulation would give mean values for catch and income data for a single trip, which would be representative of the long term seasonal values, but they would not necessarily simulate the overall performance of a boat over the season, opening by opening. This is reasonable, since the number of days each area is open varies between years, and a reliable economic parameter would be average income per trip. This could be multiplied by the number of trips in a given year to give an estimate of the total income. It is recognized that the data discussed above may not be ideal for the application being considered, but it appears that it is sufficient to allow a reasonable attempt at developing a simplified simulation model of a salmon seine fishing operation, which is also realistic. A portion of the fleet is highly mobile, as described by Hilborn and Ledbetter, and many boats do react on an opening by opening basis. Thus to model a single opening, and determine which strategy could have the best return in the long term, given a small amount of information would be a worthwhile objective. 95 Chapter Development for Having reviewed the Testing and Salmon of Simulation a Seine available data 5 Model Fishing on the operation and economic performance of salmon seine vessels in British Columbia, a simulation can now be developed which contains the essential features of the system and represents the behaviour of a ‘typical’ boat. The development of the simulation requires model collecting the together of the information discussed in the previous chapters and translating it into a series of rules that can be modelled by a computer performance of program. the boat, Information the catch required is and income on data, the the technical geographical locations of the fishing grounds relative to the home port for the vessel, and the way in which the skipper selects a place to fish. This chapter outlines the development of a working simulation model for salmon seine fishing in British Columbia. Special attention will be paid to developing a model which will obtain a higher than average income, since it is well known that successful strategies and technologies are copied by the rest of the fleet. Once the simulation model has been written, it must be verified against the observed data to check its accuracy. Once the accuracy of the initial model has been confirmed, then it can be used to test how different operating conditions will affect the economic performance of the boat. Since all the data described in the previous chapters were assumed to be for single boats, this was chosen as the starting point for the simulation process. 96 Once the simulation operation of a can expanded be single boat has been investigate to how successfully the validated profitability of the the operation varies when two or more boats fish together. The obvious candidate for the simulation was the vessel described in Chapter 3, for which the operational data were available. The simulation would model this vessel, operating within the three areas for which a detailed analysis of the catch data, described in Chapter 4, was carried out. These areas were Butedale (area 6), Juan de Fuca (area 20) and Johnstone Strait (area 12). Since the home port for the vessel was Steveston, this was used as the point where the fish was landed. This is quite reasonable, since it is the biggest fishing port in British Columbia, and many boats are based in there. The simulation must also address the rules for deciding which area to fish, since this was likely to have some effect on the average income and included the profitability. 5.1 5.1.1 For Information Vessel the minimum Required Technical sake of number for and Simulation Operational computational of economic efficiency, and technical Model Parameters the simulation parameters for the ship and gear. These were the values which were kept within the program, and used for data collection and analysis. This approach allowed for the fact that vessels operating simultaneously could have different technical parameters. In developing the simulation, it was also assumed that there was no correlation between vessel parameters and catch rate, but the maximum could be landed by a single boat depended on the hold size. catch which 97 After some consideration, it was decided that the following parameters covered the major technical and economic factors which effected the performance of the vessel. i. Ship speed, knots. This determined how much time it took the boat to move between locations. It was assumed that the speed of the vessel did not vary between the outward and return journeys. It is also assumed that the speed was constant. This was based on the observations on the vessel discussed in Chapter 3. ii. Total Hold Capacity 3 (m ) . This determined how much fish the boat could transport back to the port for processing. iii. Fuel Consumption and Fuel Cost Separate rates of fuel consumption, in litres per hour, were used for sailing out, fishing and sailing home. Total fuel cost per trip was used in the analysis, and this was obtained by summing the individual components. Fuel consumption rate was assumed to be constant for each leg of the voyage, based on the observations made on the vessel. Fuel cost per litre was assumed to be constant throughout the duration of the model. These were the factors used to determine the variable cost of operating the boat. iv. Location Code and Timer These were factors required for navigating the vessel between the port and the fishing areas, within the simulation, and logging the time spent in each activity. 98 v. Data Collection and Analysis 1. Fuel consumed this trip (litres). 2. Fish caught this trip (kg). 3. Income this trip ($). 4. Fuel expenses this trip ($). 5. Income-fuel expenses ($) These were the principle parameters which varied on a voyage by voyage basis. Notice that the model made no allowance for the fixed costs of operating the boat. This was difficult to determine unless more specific information on the cost of the vessel chosen for the simulation was known. The parameters used in the simulation model, based on observations on the vessel described in Chapter 3, are given below. Since the mean ship speed for all the voyages observed was close to 10 knots, this figure was used as a constant transit speed, loaded or light. The hold capacity was estimated to be 84.6 m . The fuel consumption was 59.4 litres per hour outward, 6.4 litres per 3 hour fishing and 78.1 litres per hour sailing home, loaded. Fuel cost was assumed to be 40 cents per litre. 5.1.2 Spatial Distribution of Fishing Grounds Once the vessel parameters were defined, the next important factor to consider in developing the model was the spatial distribution of the fishing areas. The three areas for which detailed analysis of the catch data was carried out were used in the simulation model. These appeared to be popular fishing areas, and were distributed such that there would be no possibility of the fish moving 99 between areas, during one particular opening. Thus the distributions used within the model would be independent. Also since the basis for the simulation was a single opening rather than a full season, we do not need to consider the overall fish population and the effect of last weeks catch on the total number of fish left. It was observed that the vessel moved relatively little during the course of fishing operations. Thus a reasonable simplification was to consider each fishing location as a single geographic point, at the approximate centre of the delineated fishing area. The distances between grid points used in the model are given in Table XX. 5.1.3 Openings and Other Constraints on Fishing The period of one week was used as the repeat period for the voyage profile. This was based on the observations [11, 12, 13], that the openings for a given area were typically seven days apart. This was confirmed by the area profile data, obtained from the analysis of the DFO data, given in Chapter 4. Using this time scale, the basic unit of one hour was adopted within the simulation model, since this waiting would give reasonably accurate voyage times, fishing times and times. It was assumed that openings lasted one day per week in a given area. This was based on the observations from the recorded length of the trips, taken from the DFO data, given in Chapter 4. Single day trips were the most probable for all areas, with the possible exception of Juan de Fuca, Area 20, for 1989 and 1990. It was also assumed that all areas were opened for fishing simultaneously within a single day, beginning at 06.00 and closing at 15.00. This was based on 100 Distance, nautical miles Location From Location Code To Steveston Butedale Johnstone St. Juan de Fuca Steveston Butedale Johnstone Juan de Fuca 1 2 3 4 0 290 100 75 0 190 365 0 175 0 Table XX Distances Between Port and Fishing Locations Used in Simulation Model the observation that most of the fishing periods from the monitored vessel were within this time period, and discussion in the literature which explained why the fishing took place in daylight. It was also assumed that notice of an opening was given for all areas simultaneously, 48 hours ahead of the opening. 5.1.4 Catch Data The simulation was Chapter 4. for Fishing Areas formulated to use the gamma distributions calculated in Mean catch per day for each area was sampled from a gamma distribution based on the seasonal values. The actual daily catch for the boat was sampled from another gamma distribution, based on the mean catch per day, taken from the seasonal distribution, and a shape parameter, , taken as the average of all the daily shape parameters for that area, over the four years for which data were available. Thus on any given day, the boat in the simulation could do considerably better or worse than the mean for the area. 101 Catch data were translated to income, based on the regression of total dollars earned for the season against total catch, also given in Chapter 4. 5.1.5 Operational Profile of Vessel The simplest case to consider was a stationary boat, described by Hilborn and Ledbetter, with the boat operating alone, since this corresponded to the catch data which was supplied by DFO. There was some evidence that this was a realistic situation, and this model could be useful in checking some of the assumptions made distributions of relationships are concerning catch rate the as a nature of function the of underlying geographic probability area. fundamental to the overall performance of the These simulation, and must be carefully verified. When the simulation was developed the following operational profile was assumed based on the literature review and the vessel operations data: i. At the start of the simulation, the vessel was in port. When the first opening was announced, the vessel left port and sailed to its selected area. In the case of the stationary boats discussed here, there was only one area which was fished within the simulation. The length of time to sail to the grounds was calculated from the distances in the location matrix, and the operating speed of the boat. ii. The vessel waited at the fishing grounds until the official opening, at 06.00 hours. The waiting time varied only as a function of the distance sailed, and so an area which was nearer to port had a longer waiting time than an area which was further away. Fuel consumed (quantity and dollars) during the voyage out was calculated. The waiting period reflected the observation that 102 the vessel always arrived at the ground before fishing, and the time there could be used to search for fish. The waiting time varied with the distance of the fishing waiting ground from the port, with shorter distances having longer times. iii. Once the area was open, the vessel fished for nine hours. The catch for the trip was determined from sampling a probability distribution, based on the mean daily catch for that day, and a shape parameter assumed constant for that area. The amount of fish caught was a random variable, and the value of the fish was a linear transformation of that variable. iv. On completion of fishing, the vessel returned to port. Fuel consumed on return trip was calculated. For the Stationary Model, the amount of fuel used when sailing to a particular area was constant, but different for each area. To analyze the results of the simulation, data was collected for: - - - - - Total quantity of fuel consumed during the voyage Total cost of fuel for the voyage. Amount of fish caught (as histogram) Value of fish caught. Profit, defined as income-fuel cost (as histogram). Profit was a random variable, but since the fuel cost for each component of the Stationary Model was constant and so was the value of dollars per kilogram, the distribution of profit in this case could be calculated by knowing the 103 distribution of fish caught. This will not be the case for other decision models, described below, where average fuel cost per trip will be a random variable. Another random variable to consider within the simulation was information on the maximum size of catch which might be expected during the season. This was required to determine the likelihood of the hold capacity being exceeded. In order to estimate the maximum catch from the simulation, it was necessary to set the number of trips in a typical season. Based on the observations on the fleet for the last ten years, 25 trips would seem to be a realistic number. An estimate of the distribution of this variable was obtained by determining the maximum catch simulation for within 2500 each sequence openings. Thus of we 25 can openings, obtain a and running distribution of the 100 maximum catches, and make some inferences on the probability of the hold capacity being exceeded. The financial risk involved in the operation of the boat was another random variable that was considered in the simulation model. In this case, risk was defined as the average number of trips per year which gave an income less than the operating costs for the boat. Based on analysis in Chapter 2, the average cost per trip was $5700, which included fuel cost. For the simulation model a value of $6000 per trip, after fuel costs had been deducted, was used as the level of income on which the risk was evaluated. This was based on the assumption that the skipper of the boat studied was fishing with a boat that was much newer than average, and would require a higher than average income to cover capital costs of the increased investment. Risk is also a random variable and its variation was calculated from the same openings, as was used for the distribution of maximum catches. sequence of 25 104 5.2 Development of Stationary Model The simulation described above was programmed as a network using SLAM II, [23], to represent 2500 parameters described above. openings for a single boat with the operating Details of the SLAM II program for the Stationary Model are given in Appendix 2. Maximum catch and risk were determined on the basis of a continuous sequence of 25 openings. This model was called the Stationary Model, since it represented boats which only fished in one area. The accuracy of the simulation model depends on the number of times for which data on individual openings are available. At 95 percent confidence for a sample of 2500 single openings, the mean of the observations simulation) will be within 0.la of the true value, where a (from the is the standard deviation of the sample mean. For 100 samples (for peak catch and risk), the mean of the assuming 95 Simulation observations from the simulation should be with 0.2a, again percent confidence. modelling relies heavily on comparing the results of the model with the equivalent observations from reality. If the agreement is good, then it can be inferred that the simulation is accurate. The only data that were available for making the comparison between the observations and the simulation were the same data that was used to develop the model. However, it was possible to re-orient the data to the performance of individual boats, which were fishing in any of the three areas, rather than the performance of all the boats fishing in one area on one day. 105 5.2.1 Data Available from Observations on the Fleet A detailed comparison between the simulation and the observed data must be carried out for at least one year for which data were available. After some consideration, it was decided to use 1988 as the test case, since this was a year where the average number of deliveries per boat, based on the total season, was close to 25. It was also a year with a high average number of boats per day in all three areas and so catch data should be reasonably reliable. It should be noted however that the catch rate and the income per trip for Butedale, Area 6, for that year were considerably higher than average. This may in fact be an advantage, when looking at mobility patterns, since highly motivated skippers may be willing to risk the longer journey for higher income rates. 510 vessels fished at least once in one of three areas during 1988. This was very close to the maximum number permitted, based on the number of licences issued. The amount of time when three areas were open together for 1988 was 16 days, based on sales slips for fish landed by 6 or more boats. This was approximately 15 per cent of the time for the total season available for any of the three areas, but represented 38 per cent of the amount of vessel activity, measured in boat-days. 452 boats fished at least once when all three areas were open simultaneously. Of these, 132 fished only in Butedale (Area 6), 88 only in Juan de Fuca (Area 20) and 138 only in Johnstone Strait (Area 12). 94 boats fished in two or more areas, and only 9 fished at least once in all three areas. 106 Area Name Observed data, short season Simulation data St. Devn. n Mean kg/day Mean kg/day St. Devn. 5220 1060 2500 2500 2650 2500 Observed data, short season Simulation data St. Devn. n Mean $/day Mean $/day St. Devn. n 9180 7750 7250 2500 2500 2500 6 Butedale 20 Juan de Fuca 12 Johnstone St. n = n 6736 1209.9 2037.6 3741 581.9 1719.7 132 88 138 7220 1410 2710 number of observations Table XXI Stationary Model, Comparison of Observed Daily Catch Rate with Simulation Results Area Name 10852 8650 6 Butedale 20 Juan de Fuca l2Johnstone St. n = 5699 5913 4324 3992 132 88 138 12700 10300 7430 number of observations Table XXII Stationary Model, Comparison of Observed Daily Income Rate with Simulation Results 107 Figure 38. Comparison of Mean Catch per Day, Observations for Each Area and Stationary Simulation 8000 >. a) 6ooo• . 4000 0 Mean kg/day, full season [I Mean kg/day, short season Mean kg/day, simulation C 2000 G 0• • Butedale I Juan de Fuca Area • Johnstone St. Figure 39. Comparison of Histogram of Observed Catch per Day with Simulated Values, Butedale, 1988 0.5 0.4 U C 0 0.3 I ..:. 0 10000 20000 30000 Catch per day, kg/day 40000 108 5.2.2 Validation of Stationary Model Against Observations There were several simplifying assumptions used to calculate the catch and dollar rates for the areas chosen. It was important to check how the final simulation predictions compared with the observed data. The easiest way to check this was to run the simulation model for the stationary case, and compare the calculated catch per trip and dollars per trip with observed values from vessels which fished those areas within the time period. A summary table of the mean catch per day is given in Table XXI and the mean income per day is given in Table XXII. A comparison of the mean values, with calculated error bars, based on a 95 per cent confidence interval for each of the three areas, is shown in Figure 38. We can see that for each area, the mean catch rate agrees well with the observed values. It is also interesting to compare the distribution of daily catch, for boats fishing in one area, over the course of the season. Inferences made on the results of the simulation will not be reliable if the distribution of catch rates is not realistic. From the data on individual boats we can compare the observed data with simulated catch per day. These comparisons are shown in Figures 39 to 41. It can be seen that the simulation gives a very good approximation to the catch per day distribution for a single boat over the full season for Butedale and Johnstone Strait. In these two cases, the statistical difference between the observed and the simulated distributions, based on a chi-square test, assuming 95 per cent confidence, is zero. For Juan de Fuca the fit was not as good, and the difference between the observations and the simulations is more than zero, assuming 95 per cent confidence. This can be explained by the data for that 109 Figure 40. Comparison of Histogram of Observed Catch per Day with Simulated Values, Juan de Fuca, 1988 0.5 0.4 >. U C 0 0.3 —D-—— 0.2 observation simulation .1 0 0.1• •.... 0.0 . 0 • 2000 • 4000 rn,. •iV-.,_ 6000 8000 . 10000 ... Catch per day, kglday Figure 41. Comparison of Histogram of Observed Catch per Day with Simulation, Johnstone Strait, 1988 0.3 0.2 C 0 0 . / —D-—— observation simulation 0 0.1• 0.0 - 0 2000 4000 6000 8000 Catch per day, kg/day 10000 110 area in 1988. It was pointed out previously that the actual shape parameter was significantly lower than the mean value for the four years of data. corresponding The observations difference between the consistent with this difference is simulated results and the between shape parameters. In such a case we would expect the observed results to have a more ‘peaky’ distribution than the simulated results and this is indeed the case. Thus the simulated catches model in this case between 500 and would 1500 kg, tend to under-predict the number of and over-predict the number of catches between 1500 and 4500 kg. Since the method worked in two out of three cases and the third still case gave reasonable results, it appears that the simplifications had little effect on the distribution of catch per day. Some interesting discussion points arise when one considers the comparison of income per day, derived from the simulation with the sales slip data from DFO. Figure 42 shows the mean income per day derived from the Stationary Model, compared with the observed values from the fleet. It can be seen that the results from the simulation are all higher than the observed values. It was noticed that the income per day for the short season used in the validation exercise was lower than the values calculated from the full season used in the simulation. This seemed to be due to a different mix of salmon species over the short season relative to the full season. It seems as though the income from the simulation is approximately 20 per cent higher than the observations in all areas. Since the simulation values were calculated from a linear transformation, and the catch rates agree well, it would be trivial to modify the results to the average dollars per kilogram for the short season. This Hi Figure 42. Comparison of Mean Income per Trip, Observations for Each Area with Stationary Simulation 1500O 0. 10000 A 0 $Itrip, short season $Itrip, simulation 500: • Butedale Juan de Fuca Johnstone St. Area Figure 43. Comparison of Average Catch per Trip and Average Income per Trip, Total Fleet with Random Simulation 10000 9000 8000 f 7000 6000 a Mean kgftrip ooo • Mean $Itrip 30130. cc Wa? 2000 1000. 0• I • Observations, all simulation, Random Category 112 modification would have no affect on the catch distribution, which is the parameter being compared, and so it was not done. The distributions used within the simulation model were based on a full season, whereas observed data were only for the time when all three areas were open simultaneously. The good comparison above described shows that the assumption that mean catch per day does not vary with day is valid, at least for the period when all areas are open. Figure 42 clearly shows the importance of including dollar value of fish, since although the catch rates for Juan de Fuca were low, compared to the other two areas, the high unit price of fish made it much more desirable than would initially have been thought. From this distributions within the discussion have had simulation. we may no substantial This conclude should that effect mean the simplifications on the catch that the underlying rates to the generated probability distribution functions for catch rate within each area will give realistic daily catch and subsequent income rates, when the other decision rules are modelled. 5.3 5.3.1 Development Random of Simulation for Mobile Boats Model We know that the Stationary Model does not represent all of the fleet, but we do not know how any particular skipper selects an area to fish. We can however analyze the DFO data for 1988 to examine the detailed mobility of individual boats. The fraction of the number of trips a boat made to each area, as a proportion of the total number of trips was calculated. A summary of the mean catch and income data, together with the average fraction of the trips to a 113 mean St. devn. kg/day 3454.48 3369.162 $/day 8376.34 5405.136 Fraction of trips to each area Area 6 0.339 0.448 Area 20 0.389 0.408 Area 12/13 0.272 0.453 11 st. error 95% lower 95% upper 452 452 158.472 254.236 3298.004 7867.865 3771.42 8884.809 452 452 452 0.021 0.019 0.021 0.280 0.335 0.212 0.398 0.443 0.332 Table XXIII Observed Catch and Income Data, All Fleet mean st. devn. n St. kg/day 3850 4290 2500 $/day 10200 8530 2500 Fraction of trips to each area Area 6 0.0812 100 0.3396 Area 20 0.3176 0.096 100 Area 12/13 0.3428 0.094 100 error 95% lower 95% upper 85.8 170.6 3766.2 9858.8 4021.6 10541.2 0.008 0.010 0.009 0.317 0.291 0.316 0.362 0.345 0.369 Table XXIV Simulated Catch and Income Data, Random Model mean st. devn. n St. kg/day 4330 4710 2500 $/day 11000 8760 2500 Fraction of trips to each area Area 6 0.472 0.0972 100 Area 20 0.1064 100 0.3672 Area 12/13 0.1612 0.0684 100 error 95% lower 95% upper 94.2 175.2 4141.6 10649.6 4518.4 11350.4 0.010 0.011 0.007 0.445 0.337 0.142 0.499 0.397 0.180 Table XXV Simulated Catch and Income Data, Forecast Model devn. fl kg/day 4311.4 3820.2 $/day 9728.8 5242.4 Fraction of trips to each area Area 6 0.475 0.563 Area 20 0.426 0.469 Area 12/13 0.011 0.047 257 257 238.3 327.0 4075.1 9074.8 4788.0 10382.8 257 257 257 0.030 0.029 0.003 0.504 0.367 0.005 0.622 0.485 0.017 mean St. St. error 95% lower 95% upper Table XXVI Observed Catch and Income Data, Boats Avoiding Area 12 114 given area, by the total fleet, are given in Table XXIII. It can be seen that the average mobility in 1988 was very close to an even distribution of boat entries to a given area. One possible scenario was that a vessel fished an equal number of times in each area. The simplest case of a mobile boat to simulate was a skipper which moved around between areas in a random manner, with each area having an equal probability of selection. The vessel would end up fishing an equal amount of time in each area. Average values of profit, income and catch could be obtained by combining the results of the three areas for the Stationary Model. However, some of the parameters which were discussed in the development of the model, such as risk, were obtained from the distribution of these variables. To obtain these parameters we must run a simulation since it is not possible to add the distributions from the separate areas together, as the scale parameters for the individual area distributions are different. The best approach modify the for obtaining the distributions of these variables was to simulation for the stationary boats by adding probabilistic selection of the fishing area, with each area having an equal probability of being selected. This model may not represent any particular mobility pattern, but will give a standard reference case to test the performance of alternative mobility strategies. If a selective mobility pattern did give not better performance than random mobility, it would not be beneficial to the operator. For this model, called the Random Model, the basic structure was the same as the Stationary Model. Three additional variables were added to count the number of times the vessel fished in each area within the 25 week season. 115 Figure 44. Comparison of Number of Trips to Each Area, 1988, Total Fleet with Random Simulation O.5 C 0• 0 0 Total fleet • Random simulation ) 0.2 0 I 0.1 1 I 0.0• • Butedale I • Juan de Fuca Johnstone St. Area Figure 45. Overall Fleet Performance, 1988, Comparison of Histogram of Observed Catch per Day with Random Simulation 0.5 0.4 (3 C 0 Q3 0 —0-—— I 0.2 random, sim. .1 0 0 0.1 o.o• 0 random, obs. 10000 —-fr 20000 Catch per day, kglday 30000 116 These data were collected as histograms, so that distributions could be fitted and hypotheses tested to ensure that the resulting represent an even allocation of entries to each area. mobility pattern did A detailed description of the SLAM II code for the Random Model is given in Appendix 3. The Random Model was run, for the same 1988 catch and income data as the Stationary Model, and the results were compared with the observed data on the fleet. The average catch per day and income per day are given in Table XXIV and shown plotted in Figure 43. The results show good agreement with the catch data, but less agreement with income. This was due to the same cause as the lack of agreement with the Stationary Model, in that the full seasonal values for dollars per kilogram were higher than for the comparison of the short season. A mobility data for the simulation and the observation is given in Figure 44. A comparison for the catch per day distributions for the simulation and the total fleet is shown in Figure 45. A chi-square test was used to compare the two distributions, and the hypothesis that the two distributions were the same was not rejected at 95 per cent confidence. 5.3.2 Forecast Model So far, none of the simulations have made use of any of the information which may be available to the skipper. The literature review indicated that the skipper’s ability to use information could be important to the profitability of the vessel. It would be reasonable for the skipper to have information on the average catch rate landing data, discussions for each geographic area, either with from other within skippers. the It based on intelligence on the company would be or from interesting observations to information could be used profitably, with a simple decision model. see if and this 117 A simplified version of the decision made by the mobile boats, described by Hilborn and Ledbetter [11], would be to assume that a boat will move to the area with the best return the previous opening. For the simulation, the decision could be made on the basis of the area with the best ‘profit’, defined as the mean income minus the cost of fuel to get to that area. For the simple model, the skipper would have no memory beyond the last opening, and so would make no long term inferences on the relative merits of the areas available. This represents the skipper giving more weight to the up to date information, rather than old information. The Random Model was modified to include extra code to route the vessel to the area with most profit the previous opening. If the boat had fished there the previous opening, then the profit was calculated on the basis of the mean catch for the ‘fleet’, rather than the performance of the boat. Another modification was to direct the vessel to Juan de Fuca for the first opening, when no information was available on any previous openings. This was based on the fact that this area had the highest number of boats per day over the four years of observations. This simulation was referred to as the Forecast Model, and it was run for the same catch, income and vessel data as for the Random Model and the Stationary Models described above. Details of the SLAM II code for the Forecast Model are given in Appendix 4. A summary of catch and income data for the Forecast Model is given in Table XXV. Figure 46 shows mean catch per day and mean income per day for the Random Model and the Forecast Model. From these data, we can see that the Forecast Model has a profit approximately 7 per cent better than the Random 118 Figure 46. Comparison of Mean Catch & Income per Trip, Random and Forecast Simulations, 1988 12000- 10000- 0. 8000- 0. C) 6000 0 Mean kgltrip • Mean $Itrip cc 2000- Random Forecast Category Figure 47. Comparison of Number of Trips to Each Area, Random and Forecast Simulations 0.5- >. 0.4- N. 0.2 ‘N C) * I I 0.0- • Butedale • I Juan de Fuca Area I Johnstone St. 0 Random • Forecast 119 Model. This difference is relatively small, but is significant at 95 per cent confidence. The best Stationary Model (Butedale) was approximately 19 per cent more profitable than the Random Model. The Random Model appeared to have no advantage, in terms of profitability, relative to the two best Stationary Models, or the Forecast Model. This would indicate that the simple act of moving around does nothing to improve the profitability of the vessel, based on a single year of observations. If we compare the performance of the Forecast Model with the Random Model, it can be seen that the biggest difference in the results was where the vessel fished, shown in Figure 47. The Forecast Model spent more time in Butedale and less time in Johnstone Strait than the Random Model. Thus the Forecast Model tended to fish more times in the area with the highest profit, and less times in the area with the lowest profit. However, the Forecast Model did not fish in Butedale a sufficient number of times to raise the average to the value of the Stationary Model for that area. The improvement in performance for the Forecast Model was due to the differences in mobility relative to the Random Model. 5.3.3 Validation It has of Forecast been demonstrated that Model the Forecast Model gave better performance than average, at least for one year of data. It remains to be seen if this represents a reasonable decision process, based on observations on the fleet. Again, there is no information on the individual skipper’s decision methods, but we can examine the mobility patterns of a sub-set of the fleet. The significant difference between the Forecast Model and the Random (average) Model was the difference in mobility patterns. The fleet data were examined 120 Figure 48. Comparison of Average Catch and Income per Trip, Sub-set Avoiding Johnstone Strait and Forecast model 12000 10000 8000 0. I.1 0) 6000 . C (0 (0 rn 4000 0 Mean kgItri p • Mean $Itnp 2000 0 Fleet, sub-set Forecast simulation Category Figure 49. Comparison of Number of Trips to Each Area, Sub-set Avoiding Johnstone Strait & Forecast Model >. 0 C 4) 0 4) I 4) > (U a) (0 0. I I- Butedale Juan de Fuca Area Johnstone St. 0 Fleet sub-set • Forecast 121 for boats which avoided Johnstone Strait, and their performance was compared to the overall performance. A sub-set of the data was developed, which entered Johnstone Strait, less than 7.45 out of 25 trips (the upper 95 percent confidence limit on the number of trips to that area, based on the simulation results). There were 257 boats which fell into this category. The summary statistics were calculated for this sub-set, and are summarized in Table XXVI. It can be seen that boats which fit this data set have a mean catch rate 25 per cent higher than the observed average for the total fleet and a mean income per trip 16 per cent higher than average. The mean catch per day and the mean income per day for this sub-set and the Forecast Model are compared in Figure 48. The observed data and the Forecast simulation match exactly for catch rate and are within 9 per cent for the income. The observed distribution of number of boats which fished in each area is compared with the values from the Forecast Model in Figure 49. It shows that more boats preferred Butedale than was predicted, and very few boats in this sub-set actually went to Johnstone Strait. A comparison was made of the distribution of the catch data from the Forecast Model and the 257 boats discussed above. This is shown in Figure 50. A chi square test was used to compare the distributions, and it was found that based on a 95 per cent confidence interval, the hypothesis that the two distributions were the same was not rejected. Another factor to consider, which has implications on the vessel design, is the hold size requirement for the vessel. The peak catch for the season should be 122 Figure 50. Comparison of Histogram of Observed Catch per Day, Sub-set of Fleet with Simulated Values, Forecast Model 0.5 0.4 > C 0.3 a. aj —a—— -- 0.2 4- 0 o.i 0.0• - 0 - - 10000 20000 30000 Catch per day, kglday 30 Figure 51. Comparison of Mean Peak Catch, 1988 Data, All Simulation Models 0 0 0 20 4- 4- 0 U : 0. io C 0 0 0 Model i • I . • I • I I Li • Fleet, Sub-set Forecast, simulation 123 checked to see if it is likely to be significantly larger for one decision rule over another. determined One measure of this parameter will be the mean peak catch, from the 100 samples of 25 continuous openings. Although the mean peak catch is not the most useful measure for design purposes, since there is a high probability of exceeding it, it is a stable parameter which can be estimated relatively reliably for the sample of 100 observations. Using the central limit theorem, the variance of the peak catch can be estimated to give confidence limits on the observed data from the simulation. These values are shown in Figure 51 and given in Table XVII, which give a summary of all five simulation models. From this data it can be seen that the largest hold size requirement was for the Stationary Model fishing Butedale. This required option a hold size approximately 32 per cent bigger than the Random Model. The hold size for the Forecast Model was approximately 8 per cent bigger than the Random Model. The other two models required hold sizes much smaller than the Random Model. The distribution of risk at $6000, in terms of the number of trips per 25 openings, for the three Stationary Models is shown in Figure 52 and for the Random and Forecast Models in Figure 53. From these data we can see that although the mean risk varies inversely with catch rate, the width of the distribution was similar for all the cases. The coefficient of variation for these distributions is quite high, and this is due to the relatively small number of openings in the course of a season. The mean taken from only 25 values will show a high degree of variation, but the seasonal mean, taken from 2500 observations, will be very accurate. A comparison of the number of trips made 124 Figure 52. Variation in Number of Trips Out of 25, where Income was < $6000, Stationary Models 30 20 U C —0--— 0 0 0 Juan de Fuca 0 I 10 Butedale - . - . --. Johnstone St. 4- 0 0 0 5 10 15 Number of trips/25 20 25 Figure 53. Variation in Number of Trips Out of 25, where Income was < $6000, Mobile Models 30 20 U Random C 0 —El-—— 0 I ‘I 0 10 4- 0 0 0 0 5 10 Number 15 of 20 trips/25 25 Foicast 125 to each area for the Random and the Forecast Models is shown in Figures 54 and 55. Again it can be seen that although the mean values are different, the variance of the mean is similar for both decision models. Based on the results of all the simulations, it can be seen that in each case the fuel cost is a relatively small portion of the income, with the highest proportion being 12 per cent, for the Stationary Model in Butedale. If this was the case, for 1988, we would not expect the cost of fuel to have had a significant effect on the decision where to fish. This was an observation that the skipper made, and this was discussed in Chapter 3. However, this may change if catch rates vary significantly between areas and years. 5.4 Summary In summary, it would appear that the Forecast Model does predict a significant improvement over the average income for the fleet, based on observations for the 1988 season. The improvement has occurred by making more trips to the most productive area and avoiding the least productive one. The mobility pattern predicted by the Forecast Model was observed in approximately 56 per cent of the fleet, and this portion of the fleet did produce incomes per trip which were significantly higher than the overall average for the fleet. This is strong evidence that the Forecast Model results give a realistic representation of a large proportion of the fleet, averaged over the total season. The best model of all for 1988 would have been to fish only in Butedale, and vessels following this decision process represented approximately 29 per cent of the fleet, which is still a significant portion. This would indicate that the Stationary Model was still a reasonable option to consider in any prediction methods. 126 Figure 54. Variation in Number of Trips Out of 25 to Each Area, Random Model 30 20 > C., —0-—— 0 4 0 JuandeFuca Q I ‘I 10 Butedale ----.-. Johnstone .1 0 0 0 0 5 10 Number 15 of 20 25 trips/25 Figure 55. Variation in Number of Trips Out of 25 to Each Area, Forecast Model 30 20 C) C 4) 0 I 0 > Butedale 0 10 •----D--- JuandeFuca - . - •-- Johnstone -. •1 4) 4) 0 0 5 10 Number 15 of tripsl25 20 25 127 Stationary Models Parameter Butedale Juan de fuca Johnstone Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit,$ Max. Catch, kg Risk, in 25 trips Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ Max. Catch, kg Risk, in 25 trips Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ Max. Catch, kg Risk, in 25 trips Mobile Models Parameter Forecast Model Random Model Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ Trip, Butedale Trip, Juan de Fuca Trip, Johnstone St. Max. Catch, kg Risk, in 25 trips Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ Trip, Butedale Trip, Juan de Fuca Trip, Johnstone St. Max. Catch, kg Risk, in 25 trips n mean 2500 2500 2500 2500 2500 100 100 2500 2500 2500 2500 2500 100 100 2500 2500 2500 2500 2500 100 100 4050 1620 7220 12700 11100 21800 7.99 1090 436 1410 10300 9830 4490 9.21 1430 573 2710 7430 6860 10300 14.8 n mean 2500 2500 2500 2500 2500 100 100 100 100 100 2500 2500 2500 2500 2500 100 100 100 100 100 2540 1020 4330 11000 9960 11.8 9.18 4.03 17800 9.93 2210 884 3850 10200 9330 8.49 7.94 8.57 16500 10.6 std. devn 95 percent CI 0 0.0 0 0.0 5220 204.6 9180 359.9 9180 359.9 7440 1473.1 2.34 0.5 0 0.0 0 0.0 1060 41.6 7750 303.8 303.8 7750 1450 287.1 2.24 0.4 0 0.0 0 0.0 2650 103.9 7250 284.2 7250 284.2 3560 704.9 2.39 0.5 std. devn 95 percent CI 1430 56.1 571 22.4 4710 184.6 8760 343.4 8690 340.6 2.43 0.5 2.66 0.5 1.71 0.3 6820 1350.4 2.28 0.5 1320 51.7 529 20.7 4290 168.2 8530 334.4 8440 330.8 2.03 0.4 2.4 0.5 2.35 0.5 6460 1279.1 2.65 0.5 Table XXVII Results of Simulation Models, 1988 Data 128 Chapter Sensitivity to of the Catch Rate 6 Forecast Model at Furthest Area The development of the simulation models was discussed in Chapter 5. The Forecast Model was successful in obtaining better than average performance, but this was for only one year of data. This chapter will investigate the sensitivity of the Forecast Model to changes in income, due to changes in the catch rate at the area furthest from the home port. It was shown in Chapter 5 that Butedale was the most profitable area, based on the Stationary Models for 1988. This area was also the one with the highest cost of travel. The profit for the Forecast Model was lower than the Stationary Model for Butedale, by approximately 11 percent. It is important to determine if the Forecast Model was unduly influenced into avoiding this area more than it should have done. To investigate this question, a sensitivity study was carried out to see how the results of the Forecast Model changed with catch rate at Butedale. For this study, only catch rate at Butedale was varied, since this was the area furthest away from port, and so was likely to have the most effect on mobility and the subsequent profitability of the operation. 6.1 Parameters for Study Since there was little difference in the cost of mobility between Johnstone Strait and Juan de Fuca Strait, the average catch rate over the season was fixed for these two areas at 3000 kilograms per day. This rate was picked since the overall provincial average of catch per day was calculated to be 3096 kilograms per day, based on the 10 year fleet performance data. Also, for the 129 four years of data analyzed in Chapter 4, the mean catch per day for Juan de Fuca was 2862 kilograms per day, and for Johnstone Strait was 3341 kilograms per day. The value of 3000 kilograms per day was obviously close to the long term value. For the sensitivity study, mean catch per day for the season at Butedale was varied between 2000 kilograms per day and 8000 kilograms per day, in increments of 1000 kilograms per day. These values were picked because they bracketed the observations for all areas and all years, and therefore were likely to cover the range of catch rates which might be expected. To simplify the interpretation of the results, the value of the fish was fixed at $2.50 per kilogram for all areas. This figure was close to the provincial average for all areas and all years studied. The mean catch for a given area on a given day is a random variable, with a range which is given by the shape of its probability density function. The seasonal shape parameter, A, described in Chapter 4, was kept constant for all areas, at a value of 4.25. Again this was close to the average value for all areas and all years in the study. Once the mean value and the shape parameter were fixed, then the scale parameter, sigma was determined. The resulting values are given in Table XXVIII. The Forecast simulation was run for each condition and the results are summarized in Table XXIX. The theoretical values for the Stationary Model were calculated in this instance, and are given in Table XXX. Similar calculations were made for the Random Model, assuming that the boats fished 130 an equal number of times in each area, and these results are given in Area mean catch kg/day Juan de Fuca 3000 4.25 705.9 Johnstone St. 3000 4.25 705.9 Butedale 2000 3000 4000 5000 6000 7000 8000 4.25 4.25 4.25 4.25 4.25 4.25 4.25 470.6 705.9 941.2 1176.5 1411.8 1647.1 1882.4 A Table a Table XXVIII Data Used in Sensitivity Study for Forecast Model 6.2 Results of Sensitivity Study A comparison of the profitability of Forecast Model with the Random Model is shown in Figure 56. This figure shows that the Forecast Model was generally more profitable than the average performance for the fleet, assuming that the average was calculated based on the boat fishing an equal number of times in all three areas. However, it can be seen that there was a range of catch rates, between 3500 and 5500 kg/day, when the Forecast Model was worse than the Random Model, by a factor of up to 16 percent. For the Stationary Model at Butedale, the profit was linearly proportional to the average catch rate. It was not necessary to run the simulation to obtain 131 Figure 56. Sensitivity of Forecast Model and Overall Average Performance to Catch Rate at Butedale 25000 20000- 15000 - ....‘...... Forecast model 0 0 all areas 100000 E 0 5000- 00 . I • • 4000 2000 Catch I rate, I • 6000 8000 Butedale, 10000 kg/day Figure 57. Sensitivity of Forecast and Stationary Models to Catch Rate at Butedale 25000 20000 • 15000 Forecast 0 0 II - 10000 1--- 0 E -. - 0 0 .E JuandeFuca — 5000 F. - 0 0• . 0 • 2000 Catch • • 4000 6000 rate, Butedale, I 8000 kglday 10000 Butedale 132 Forecast model Catch/day, Butedale, kg 2000 3000 4000 5000 6000 7000 8000 Mean catch/day kg Average fuel cost $ Average profit $ 2720 3070 3060 3170 4250 5750 7260 559 760 969 977 1160 1400 1440 6240 6910 6690 6940 9460 13000 16700 Table XXIX Sensitivity Study, Results of Forecast Model Stationary model Catch/day, kg Average fuel cost $ Average profit $ Butedale 2000 3000 4000 5000 6000 7000 8000 1620 1620 1620 1620 1620 1620 1620 3380 5880 8380 10880 13380 15880 18380 Juan de Fuca 3000 436 7064 Johnstone 3000 573 6927 Strait Table XXX Sensitivity Study, Results of Stationary Model 133 these data, since the only random variable was the catch data. The mean profit, p, (income-fuel) was obtained from the mean catch data, m, for each area by the simple linear transformations given below: Butedale m*2.50 1620 (8) p=m*2.50436 (9) p = - Juan de Fuca Johnstone Strait p=m*2.5O573 (10) Based on the mean profit data, it would have benefited the skipper to choose Juan de Fuca until the mean catch per day (for the season) at Butedale reached 3474 kilograms per day. Above this point, the been most profitable area would have Butedale. A comparison of the average profit per trip, for the Forecast Model and the three Stationary Models is given in Figure 57. This figure shows that for low catch rates at Butedale, the Forecast Model had a profit statistically the same as the best Stationary Model. However, the Forecast Model was not as profitable as the best Stationary Model, once the catch rates at Butedale exceeded 3474 kilograms per day. The Forecast Model profit was comparable to the boats which fished Juan de Fuca or Johnstone Strait, until the catch rate at Butedale reached 5000 kilograms per day. Above this point the Forecast Model was better than the second best Stationary Model, but the mean from the Butedale 134 Random model Catch/day, kg Mean Catch/day, Butedale 2000 3000 4000 5000 6000 7000 8000 2667 3000 3333 3667 4000 4333 4667 kg Average fuel cost $ Average profit $ 876 876 876 876 876 876 876 5791 6624 7457 8291 9124 9957 10791 Table XXXI Sensitivity Study, Results of Random Model 135 Figure 58. Number of trips to Butedale against Catch Rate at Butedale, Forecast Model 100’ y = R2 - — 17.714 + / 1.3143e-2x 0.972 80 a a 60 E x 0 40’ (0 a I .1 20 13 0’ . 0 I • 2000 • 4000 Catch rate, I 6000 I • 8000 Butedale, kg! day 10000 136 Stationary Model did not come within the 95 percent confidence interval of the Forecast Model, until the catch rates were higher than 7000 kilograms per day. 6.3 Discussion of Results There appears to be a lag in the profitability of the Forecast Model, relative to the area which was theoretically the most profitable. One factor which may have affected the profitability was the number of trips that the vessel made to Butedale. Figure 58 shows the percentage of trips to Butedale, per season, as a function of the catch rate at Butedale. It can be seen that the number of trips to Butedale, given by the Forecast Model was linearly proportional to catch rate in that area. Thus the mobility of the model is as expected, and the boat was making more trips to the area, as its profitability increased. To explain the lag, we must consider the probabilistic nature of the problem. Although the area with the best theoretical profitability can be easily identified by the analyst, the skipper (in the simulation) had to use incomplete information. The skipper’s decision, within the simulation, was based on selecting the area with the highest profitability the previous opening. When the mean profits per day for two areas are similar, then we might expect a high probability of the maximum profit the previous week being observed in the area which did not have the highest overall mean value for the season. The problem is compounded by the number of areas where the skipper may fish. Within the simulation, there was a choice of three areas. When there are two alternatives to the theoretically best area, then there is an even greater probability of the observed catch rate in the best area being lower than the 137 Figure 59. Histograms of Profit, Juan de Fuca, Johnstone Strait and Largest of Two Sampled Simultaneously 0.3 02 —a——— I o.i. 0.0 -10000 Juan de Fuca Johnstone / \ I. ----- Largest of two I 10000 20000 (Income-fuel cost)Iday, 0 30000 $ Figure 60. Histograms of Profit for Various Catch Rates at Butedale 0.3 >. U C 2000 kg/day —$—-- 5000 kg/day 8000 kg/day 0.1 . 4, i / 4, / , 0.0• -10000 —a-—— I 0 ft , ...I .E•• • .. . . . 10000 20000 (Income-fuel cost)/day, 30000 $ 138 catch rate in an alternative area. This factor was investigated by carrying out additional runs of the simulation and collecting data relevant to this particular study. A histogram of the largest profit from either Johnstone Strait or Juan de Fuca (for the same opening) was determined. This is shown in Figure 59. Three values of catch rate at Butedale were analyzed, 2000, 5000 and 8000 kg/day. These were sufficient to illustrate the point. The results are shown in Figure 60. Figure 59 shows the distribution of mean profit per day for vessels fishing Juan de Fuca and Johnstone Strait. This clearly illustrates, that for equal catch rate there was a negligible difference in profit between the two areas. Also shown in Figure 59 is the distribution of the largest value of profit, taken from two samples, one each from Juan de Fuca and Johnstone Strait. The modal value for this distribution was approximately the same as the modal value for the profit distribution at Butedale (Figure 60), when the mean catch per day for the season was 5000 kg/day. Thus, it is not until the catch rate at Butedale reaches this figure that the probability of obtaining the correct information on the best area is higher than the probability of obtaining the wrong information. This is reflected in the simulation, when after 5000 kg/day, the profit from the Forecast Model becomes higher than that from the Stationary Model fishing either Johnstone Strait or Juan de Fuca. From the sensitivity study, it can be concluded that the Forecast Model tended to correctly avoid Butedale when the catch rate was extremely low, and correctly prefer it when the catch rate was extremely high. However, there 139 was a range of catch rates where the Forecast Model’s performance was significantly lower than the best possible performance, in terms of average profit per trip. It is difficult to see a way around this deficiency, whilst only using the minimum amount of information. The reliability of the Forecast Model may be increased by basing the decision process on a longer memory than simply the last trip. This would be relatively simple to do in the simulation, by using a running mean, updated after each opening. However, in reality, the problem is compounded by possible variations in the price of fish over one season, and the fact that there is a very limited time to build a reliable database from which to determine the seasonal average. An alternative approach would be to design a boat which would be profitable on an income rate which was lower than the long term average value. Based on this analysis, a factor of 20 percent below the long term average value would seem to be reasonable. The minimum income required to cover the cost of operating the vessel should be set with this figure, rather than the average value. 6.4 Conclusions In general, the Forecast Model performs better than average. It performs particularly well when one area has either very high or very low profits. However, there is clearly a range of profits where the Forecast Model will perform worse than average. Although the illustration used here was chosen to highlight any potential problems, the results should be the same regardless of which geographic area was used as the variable. The difference due to the selection of the area will affect the absolute value at which the phase lag occurs. Since the decision for area selection was based on maximum profit, the 140 critical range, based on two areas with profits equal, and a third area between 1 and 1.5 times higher should exist regardless of which area was chosen for the variation. This may explain why some skippers are reluctant to move between areas, because there is a range of catch rates where there is a higher probability of making the wrong decision than making the right one. In such cases, it may be felt that avoiding this decision is a better alternative. This will probably mean that the skipper will pick the area for which he has the most reliable information and that is most likely to be the area where he fished last time. 141 Chapter Forecast of Sensitivity Model to 7 Number of Boats Operating Together So far only a single boat, fishing independently, has been simulated. This was the basis of the catch data available DFO, from and no information was available for teams of boats fishing together. However, we know that boats do fish together and we can assume that this is to the benefit of both skippers, or they would not do it. It would be interesting to investigate the possible benefits of two or more boats fishing together using the simulation model. This can be done by making some assumptions about the operating practices of the boats and modifying the simulation model. For this sensitivity study, only the Forecast Model will be used, since it was demonstrated in Chapter 6 that it performed as well or better than average in a wide range of catch distributions, which were likely to be observed in practice. In order to use the data on catches described in Chapter 4, we must assume that the catch rates between boats fishing together are not correlated. This may be an over-simplification, since it is quite likely that two boats fishing in close proximity will have catch rates that are highly correlated. However, without further data, or a much more detailed knowledge of vesseL location and catch rate, any other assumption cannot be justified from the observed data. 142 7.1 Modifications to Simulation Model The Forecast Model was modified to include two types of boats. The original boat was classed as a ‘packer’. It transported all the fish for the team back to the processing plant at the end of every opening. This model of operation was based on the skipper’s observations discussed in Chapter 3. The assumptions about sailing speed and fuel consumption were the same as those used in the earlier models. The packer was the boat that was active in the model when there was just a single boat. It was assumed that the decision of where to fish was based on the fuel cost of the packer only. The second class of boats were fishing boats, and it was assumed that these boats did not transport any fish. It was also assumed that these boats fished with the packer, and waited on the grounds during the closed season, rather than travel back to port. Both the packer and the fishing boats would move to the new area, if necessary, at the beginning of the simulation cycle, was 168 hours (one week) as in the single boat model. This which limited the minimum size of fishing boats within the model to be 9.25 metres, which is the hull length which could move the maximum distance (365 nautical miles) in 48 hours. This was not a problem in practice, since the minimum length of a registered salmon seine vessel was 10.3 metres. Some other simplifying assumptions were made in the development of the model. It was assumed that the fishing boats and the packer were identical. The reason for this assumption was to be able to use the observed vessel operations data, and also to minimize the number of variables for the sensitivity study. The fishing boats did not transport any fish, and so always moved in the light load condition. This represented a saving in fuel consumption of 24 percent, 143 relative to the same vessel moving in the loaded condition. Additional fuel savings would between result if the fishing vessel did not have to change areas, openings. The catch rate data used to investigate the effect of the number of boats was the same as for the 1988 model, used to validate the simulation. The price data was modified to reflect more realistic long term values. It was pointed out in Chapter 4, that the price per kilogram for Juan de Fuca in 1988 was much higher than was expected based on the other three years. For this reason the average price for this area for the three years, excluding 1988, was used within this model. For the other two areas, the average value for all four years was used. These values are given below; Area s/kg Butedale 1.472 Johnstone 2.629 Strait Juan de Fuca 7.2 7.2.1 Discussion Voyage of 3.076 Simulation Results Economics The simulation model was run for one packer and a packer plus a number of fishing vessels varying between one and three. The results are summarized in Table XXXII and shown plotted in Figures 61 to 63. The mean catch per boat, and income per boat, shown in Figure 61 did not change when the number of boats changed. This was to be expected, as the 144 Total Number of Boats 1 2 3 4 n 2500 2500 2500 2500 Fuel cost/boat, $ Standard devn. 1210 522 752 620 605 579 525 531 Mean total catch, kg Standard devn. CatchJboat, kg 5480 5070 5480 10700 8540 5350 16300 11900 5433 21500 15400 5375 Mean total income, $ Standard devn. Income/boat, $ 9200 7720 9200 17900 12500 8950 27200 17100 9067 36300 22100 9075 Mean profit, $ Standard devn. Profit/boat, $ 7990 7590 7990 16400 12300 8200 25400 17000 8467 34200 22100 8550 Mean risk 0.512 0.440 0.397 0.376 © $6000/boat n=number of observations Table XXXII Effect on Operating Economics of Number of Boats Fishing Together 145 catch per boat was independent of the number of boats, based on the assumptions made in developing the model. The average profit per boat, shown in Figure 62 did increase significantly, at 95 percent confidence, as shown. The value for 2 boats is 2.6 percent higher than for one boat, and for four boats it is 7 percent higher than for one boat. The increased profit came from reduced fuel consumption per boat, as can be seen in Figure 63. Since the fishing boats do not move as much as the packers, and when they do move their fuel consumption per voyage is lower. The overall effect was to lower the average fuel consumption per boat. It can also be seen from Figure 63 that the effect of the change was greatest from one to two boats but the change from three to four was still significant. If the number of boats in the team was increased to well above four, then the effect of the packer would be diminished and it is likely that some point would be reached where no further improvements would be expected. It appeared that the biggest change in the economic factors due to increasing the number of boats was the reduction of risk associated with ihe fishing operation. The risk was defined in Chapter 5 as the number of trips per season (25 openings) where the income including allowances for the with the number of boats was less than the cost of the voyage, fixed and variable costs. The variation in risk is also shown in Figure 63. From the values calculated by the simulation, the average risk associated with a single vessel was 51.2 percent. That is to say that 51.2 percent of the trips resulted in the vessel earning less than $6000 per trip which was the estimated cost per trip, averaged over the season, based on the data given in Chapter 2. However, when the number of boats was increased to two, the average risk per boat Figure 61. Variation of Catch and Income (per Boat) with Number of Boats Fishing Together 10-10000 146 .. 8000 8- 4- -6000 CU —rn-—— QU) U) 4• 4000 2 -2000 0 U) 0 — 0 I • 1 I I • 2 • 4 3 5 # boats Figure 62. Variation in ProfitlBoat with Number of Boats Fishing Together 9000 0. 1 4- single boat, mean value 8000 4- 0 .0 4-I 0 I 0. 7000 0 I I 1 2 — # boats I 3 — I 4 — 5 mean catch! boat 14 dropped to 44.0 percent. It dropped further for three and four boats to 39.7 percent and 37.6 percent respectively. After three boats it seems as though the risk was beginning to stabilize. The financial risk is an important factor for the skipper when deciding where to fish. Selecting a low risk decision may be important if the number of opportunities to make that decision are small, as is the case in a real fishing season. Clearly increasing the number of boats fishing together has a big effect on reducing the risk, even when all the other factors are unchanged. The reasons for reducing the risk are related to the fact that the profit per trip is a random variable. The basic distributions of catch per day are made up from a gamma distribution for mean catch per day for the season and then a second gamma distribution for actual catch rate for a boat that went to that area. Figure 64 shows a comparison of the histograms of average profit per boat obtained from the simulation, for one, two and three boats. It can be seen that the modal value of the profot per boat shifts very slightly to the right as the number of boats in the team is increased. This is due to the slight increase in mean profit per trip, due to the savings in fuel. However, the reduction in the probability of obtaining less than $6000 per trip is much larger than the shift of the modal value. This is because we are now taking multiple samples from one area on any given day. Thus if one boat has a particularly poor catch it is likely to be offset by a higher catch obtained from the other members within the team. The more boats per team fishing in a given area simultaneously the more likely that the mean catch for the team will approach the mean catch for the area on that day. This leads to the 148 Figure 63. Variation in Fuel Consumption and Risk at $6000 per Trip for Vessels Fishing Together 1400 0.6 1200 .1 0.5 0 1000 (U C 0 (0 * . . —a——— 800 * fuellboat risk @ $6Klboat 0.4 U U, —U) U, I 600 400 I 0 1 • I • 2 I 3 • -0.3 I 4 5 # boats Figure 64. Histograms of Profit per Boat, for One, Two and Three Boats Fishing Together 1 .OOe-4 8.000-5 4- C II 6.OOe-5 —a-—— ••• 4.OOe-5 -. - -+- -. 2.OOe-5 0.OOe+0 0 10000 profit, 20000 $Iboat 30000 one boat two boats three boats 149 reduction in risk since the chance of obtaining a very low total catch for the team is reduced. However, the chance of getting a profit which is significantly higher than the mean profit times the number of boats in the team is also reduced but this is more difficult to visualize since the tail of the distribution is very long. It can be seen that the probability determined from the simulation of a high profit per boat is lower for three boats than for a single boat fishing alone. 7.2.2 Capacity Transportation Another factor to consider besides the economics is the transportation capacity of the hulls. A larger boat will generally have a larger hold volume but if the hold is too large then the owner has invested too much in the capital cost of the boat. If the hold is too small then the result will be lost income opportunity several the because boats fish cannot be transported for processing. If we have fishing together and only one boat transporting the fish then transportation capacity must increase with the size of the team. The transportation capacity for two boats fishing together will be more than that required for one but not necessarily in a direct relationship to the number of boats. Since catch per trip is a random variable we must consider the required hold size in terms of probability of exceedence rather than absolute numbers. After some consideration it was decided that the parameter used for setting hold size would be the 99 percentile for the distribution of the maximum catch from 25 consecutive openings in a given season. In practical terms this would correspond to the largest catch of 100 boats fishing for 25 sequential openings using the ‘Forecast’ decision model. This was thought to be reasonable because 150 in practice 25 weeks was a long season and a shorter season would reduce the maximum expected catch. fishing boats could return to very if the catch rate was Steveston carrying some large then the of the catch, rather on grounds. If the fishing boats were radically different from than waiting the packer, Also, with no i.e. transportation capacity, the fish could probably be transported by other packers which were not filled to capacity. The results of the simulation, for a single vessel, gave a histogram for the maximum catch observed in a sequence of 25 openings. These data can be used to investigate trends in the However, exceedence. the catch rate, based on an assumed probability histogram was based on observations 100 of rather than the 2500 which were used for the comparison on daily catch rates. For this reason we might expect the results to be less reliable but they should still be sufficiently accurate to determine trends. The results would be more useful if we could postulate the form of the distribution for the maximum catch, since the hold rather capacity than the required observed could be histogram, interpolated from which be may a fitted irregular, distribution due to the reduced number of samples. If all the gamma distributions used in the simulation to model catch per day had had the same scale parameter, determine the distribution a, then it would have been possible to of catch per day for the fleet by adding the distributions together. This was not the case but since the statistical models for catch per day in each area used in the simulation were all gamma distributions, it was possible that the same type of distribution would give a good fit to the overall result. A gamma distribution was fitted to catch per trip for the 2500 trips and its scale and shape parameters are given in Table XXXIII. 151 Parameter Value Catch per day, kg Standard deviation n 5480 5070 2500 Gamma distribution, catch per day sigma lamda 4.69E-’-03 1.17E+00 19500 6900 100 Maximum catch, 25 trips, kg Standard deviation n Gumbel distribution, from gamma distribution Sigma Mu 99 percentile Gumbel distribution, 4.99E+03 1.68E+04 39.7 from simulation Sigma Mu 99 percentile n=number of observations Table XXXIII Fitted Distributions to Catch Data, Single Boat 5.38E+03 1.69E+04 41.7 152 The fitted distribution was tested against the simulated values with a chi squrare test and the fit was not rejected at 95 percent significance. If the overall distribution of catch per trip, for 2500 openings, can be fitted with a maximum gamma probability density catch out of 25 trips function then the distribution should be given by a for the Gumbel distribution (extreme value, type I), given in equation (11): f(x) = :i exp(- (x-i.t) with a modal value, - exp(- i, (x.t))) (11) which corresponded to the catch per day from the parent distribution which has a cumulative probability of 24/25 (0.96). The scale parameter, a, can also be estimated from the hazard function [22] for the parent distribution. The parameters for the Gumbel distribution were estimated from the fitted gamma distribution, and are given in Table XXXIII. Based on a chi-square test on the distribution of simulated maximum values and the values calculated from the Gumbel distribution, the difference between the two is insignificant at 95 percent signifcance. The simulated data and the calculated data for both the overall distribution of catch per trip and maximum catch for 25 trips are shown in Figure 65. It can be seen that calculated distributions fit the results from the simulation very well. There was another approach for fitting a distribution model to the observed maximum catch data, and that was to fit a Gumbel distribution directly to the observed data. This was done using moments and the results are also given in Table XXXIII. Again a chi-square test was used to compare the two distributions, 153 Figure 65. Comparison of Observed and Fitted Distributions for Daily Catch and Extreme Value from 25 Trips 2.OOe-4 daily value, simulation daily value, fitted extreme value, observation 1.00e4 extreme, from daily dist. ii extreme, fitted directly 0.OOe+0 - — 0 20000 40000 Catch per day, kg Figure 66. Variation in Scale and Shape Parameters for Fitted Distributions with Number of Boats 15- 10C C -D-- a, Gamma dist. x, Gamma dist. a, EV1 1” EV1 5. b 00 1 2 I I 3 4 # boats 5 154 and the difference was found to be at 95 percent confidence. insignificant, There was a slight difference between the two distributions, as can be seen in Figure 65, extreme which will have value distribution. some effect on estimating parameters It was found that the difference from the in the 99 percentile for the maximum catch for the single boat, calculated using the two methods discussed above, was less than 5 percent. When two or more boats were operating within the simulation, it was found that not all the parameters discussed above could be recorded, due to array size limitations on the version of SLAM being used. However, since it was shown above that the extreme values could be predicted from the fitted distribution to catch per day, the relevant information could be calculated. Chi-square tests were carried out on the differences between the simulated distributions and the fitted gamma distributions and none were rejected at 95 percent significance. The parameters for the gamma distributions and the extreme value distributions are given in Table XXXIV, together with the 99 percentile for maximum catch determined from the fitted distributions. The hold size may be determined from the catch size by assuming that it is also required to carry enough ice to preserve the fish during transportation. The industry standard is a ratio of approximately 2/3 fish to 1/3 ice. Table XXXIV also gives the estimated hold sizes, calculated using this ratio. Figure 66 shows the parameters from the catch per day and maximum catch for 25 trips plotted against the number of boats. These data show that there is an approximately linear trend with the number of boats. It is interesting to 155 Fitted distribution, catch/day gamma # boats sigma lamda 1 2 3 4 4.691 6.816 8.68 11.03 1.168 1.57 1.876 1.949 Fitted distribution, max. catch Gumbel (EV1) sigma mu 4.99E+03 7.72E+03 1.03E+04 1.32E+04 1.68E+04 2.92E+04 4.18E+04 5.44E+04 Max. catch size Required hold size 99 percentile, 99 percentile (tonnes, fish) (tonnes, fish + ice) 39.7 64.7 89.0 115.0 Table XXXIV Estimated Parameters for Fitted Distributions for Different Numbers of Boats 59.6 97.1 133.5 172.5 156 note that the catch per day distribution for two or more boats cannot be calculated from the catch per day distribution for one boat by assuming that multiple samples are taken from this distribution. This highlights the need for using simulation working to understand the operational aspects of multiple boats together. The 99 percentiles for required transportation capacity taken from the Gumbel distributions are shown plotted against the number of boats in Figure 67. It can be seen that the transportation capacity is not directly proportional to the number of boats. The maximum transportation capacity required for the catch from two boats fishing together was calculated to be 23 percent smaller than that required for two boats fishing independently. This ratio progressively decreased until it was 38 percent smaller for four boats. This reduction is due to the change is shape of the catch per day distribution as the number of boats is increased. It is interesting to note that the 99 percentile of the extreme value catch distribution is approximately 7.25 times larger than the mean catch per day and the corresponding hold size is approximately 10 times the mean catch, after allowance has been made for the ice. The transportation capacity of the fleet should be considered at this point. Figure 68 shows the distribution of hold volume calculated for a sample of 122 salmon seine vessels, together with the 99 percentile hold volumes based on the results of the simulation. This shows that approximately 48 percent of the fleet is suitable for fishing as a single boat/packer, 35 percent of the fleet is capable of acting as a packer for one boat and itself, 12 percent is capable of acting as a packer for two boats (and itsesif) and no vessels are capable of Figure 67. Estimated Peak Catch for 25 Openings, Based on 99 Percentile of Distribution of Maximum Catch 160 I 140• Boats fishing independently...,.., I I I I / 1 120 / ioo. / . —e—— # boats fishing together Figure 68. Observed Cumulative Distribution of Hold Volume for Salmon Seine Vessels 100• . . 80 0 0 157 .1 60 .1 C 0 U 0 0. 20 0• 0 50 100 150 hold volume, cubic metres 200 99 percentile, EV1 158 acting as a packer for three boats. Based on these data, it is clear that the majority of the fleet must fish alone or in pairs. 7.3 Conclusions In conclusion, there are direct benefits, in terms of increased profit per boat, when two or more boats fish together. This is provided that the fuel costs of the packer are absorbed by all the boats in the team. It would seem that the larger the number of boats in the team then the greater the benefit in terms of profit per trip. The biggest percentage change, however, is in the reduction of risk rather than increased income or reduced fuel costs. Based on 1988 data for catch rates, the practical limit for the size of a team would be three boats since the catch for this number of boats was within the transportation capacity of the packer in our simulation. If we consider the results in incremental terms, the biggest incremental benefit was in going from one boat to two, which may be another reason for the popularity of two boats fishing as a team. If resources were unlimited, then each boat will pay for itself, but practically the investment in constructing resources of many or purchasing independent another hull may be beyond the operators. The percentage change in profit was relatively small when the only variable was the number of boats. The maximum predicted difference was 7 percent for four boats fishing operating together together. this For the more difference was 2.6 likely condition of two percent. This difference, boats whilst statistically significant, was small in relation to the difference in profitability between and decision Stationary assumptions models, models, described observed described above that when in the investigating Chapter benefits 5. of It the Random, seems multiple that boats Forecast using the operating 159 together were changes in in fine tuning the profitability. These vessel management, improvements in rather than significant profitability could be enhanced by using fishing boats which consumed less fuel and had a lower minimum required income per trip, which could most easily be addressed by a smaller boat. 160 Chapter Performance It has Forecast of been demonstrated 8 Simulation, Based Observed Catch that the important on Four Years of Data factors in the overall earning power of a fishing boat, or teams of boats, within the simulations were the relative catch rates between areas, and the method of deciding which area to fish. The effect on profitability due to the number of boats in a team is statistically significant, but small in relation to these other two factors. Having investigated the basic parameters and sensitivity of the simulation models, the final question to addressed be was the performance of the Stationary and Forecast Models, for the four years for which catch data were available. There were two important questions to answer. One was to decide if the profitability of the Forecast method was higher than the Stationary decision method, at the end of a period of several years. The other was to determine if there were significant differences in the size of the boats required for the different decision methods. The Random Model was also run, to provide ‘baseline’ data on the average performance of the fleet. For simplicity, a single boat operating independently was simulated. The catch data used in the simulation were the gamma distributions for catch per day calculated for each area, and given in Table XVII for the four years for which data was available. The dollar values per kilogram were simplified to the modified average values, used in Chapter 7. The vessel parameters were the same as those used for the simulations described in Chapters 5, 6 and 7. Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ 25 Trips Max. Catch Risk Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ 25 Trips Max. Catch Risk Johnstone Fuel, litres Fuel cost, $ Fish, kg Fish,$ Profit, $ 25 Trips Max. Catch Risk Parameter Juan de fuca Year Butedale Model 3710 734.58 2.44 0.4831 100 12100 100 12.7 3560 2.39 0 0 2650 6960 6960 1450 1.89 704.9 0.5 0 0 3670 9650 9650 7000 2.63 14300 11 2770 1.84 0 0 2620 8050 8050 7420 0.2 0 0 730 1070 1070 stnd. devn. 1430 573 3920 10300 9740 11400 3.41 287.1 0.4 0.0 0.0 103.9 272.8 272.8 1090 436 4560 14000 13600 0.0 0.0 41.6 128.2 128.2 3050 25 7440 1473.1 2.51 0.5 0 0 1060 3270 3270 1989 4050 1620 1140 1680 61.5 95% CI mean 0.0 0.0 204.6 301.1 301.1 0 0 5220 7680 7680 stnd. devn. Table XXXV Summary of Simulation Results for Stationary Models Four Years, 1987 to 1990. 10300 15.3 1430 573 2710 7130 6560 0 0 0 0 3060 119.95 8050 315.56 8050 315.56 2500 2500 2500 2500 2500 1430 573 3330 8760 8180 1090 436 1410 4340 3900 4490 20 6910 12.1 100 100 0 0 0 0 1650 64.68 5080 199.14 5080 199.14 21800 10.6 1988 4050 1620 7220 10600 9000 1800 356.4 2.46 0.4870 1090 436 2530 7790 7350 2500 2500 2500 2500 2500 0 0 109.37 161.11 161.11 95% CI mean 3280 649.44 2.23 0.4415 mean stnd. devn. 1987 4050 0 1620 0 4520 2790 6650 4110 5030 4110 100 12000 100 16.9 2500 2500 2500 2500 2500 n 1386.0 16400 0.5 11.5 0.0 1430 0.0 573 143.9 4050 378.3 10600 378.3 10100 548.5 23400 0.4 2.8 0.0 1090 0.0 436 102.7 7320 315.6 22500 315.6 22100 6400 2.19 0 0 4060 10700 10700 8830 1.48 0 0 5790 17800 17800 9740 2.44 1267.2 0.4 0.0 0.0 159.2 419.4 419.4 1748.3 0.3 0.0 0.0 227.0 697.8 697.8 1928.5 0.5 mean stnd. 95% CI devn. 1990 4050 0 0.0 1620 0 0.0 5660 5700 223.4 8330 8390 328.9 6710 8390 328.9 1469.2 21300 0.0 15.4 0.0 0.0 28.6 41.9 41.9 95% CI ‘- Fuel, litres Fuel cost, $ Fish, kg Fish,$ Profit, $ 25 Trips # Butedale # Juan de Fuca # Johnstone Max. Catch Risk Fuel, litres Fuel cost, $ Fish, kg Fish, $ Profit, $ 25 Trips # Butedale # Juan de Fuca # Johnstone Max. Catch Risk Random Parameter Forecast Year Model 8.49 7.94 8.57 11600 13 0.40194 0.4752 0.4653 1528.56 0.48114 2.03 2.4 2.35 7720 2.43 8.49 0.4019 0.4752 7.94 0.4653 8.57 805.86 21300 9.91 0.4375 2.03 2.4 2.35 4070 2.21 0.4019 0.4752 0.4653 1279.1 0.5009 2.03 2.4 2.35 6460 2.53 Table XXXVI Summary of Simulation Results for Mobile Models Four Years, 1987 to 1990. 8.49 7.94 8.57 16500 15.2 0.4019 0.4752 0.4653 704.88 0.5385 2.03 2.4 2.35 3560 2.72 100 8.49 100 7.94 100 8.57 100 10900 100 14.1 51.744 20.7368 208.936 525.28 529.2 1320 529 5330 13400 13500 51.744 2210 884 20.737 114.86 5640 337.12 13500 349.66 12600 1320 529 2930 8600 8920 2210 884 3180 8540 7660 51.744 20.737 168.17 274.4 268.13 1320 529 4290 7000 6840 2210 884 3850 7490 6600 51.744 20.737 107.02 243.04 246.57 1320 529 2730 6200 6290 2210 884 3430 7620 6740 2500 2500 2500 2500 2500 0.25344 0.42966 0.38016 1467.18 0.41976 1.28 2.17 1.92 7410 2.12 29.8704 11.956 216.776 654.64 658.56 1.81 0 19.4 0.4455 0.4455 3.82 815.76 21800 0.3663 4.52 0 2.25 2.25 4120 1.85 0 18.2 6.8 12800 5.27 0.5068 0.2791 0.4692 1411.7 0.5524 2.56 1.41 2.37 7130 2.79 15.3 1.84 7.72 19300 12.6 0.2791 0.5108 0.4969 700.92 0.5563 100 2.39 100 10.7 100 11.9 100 10500 100 13.3 devn. 95% CI 762 305 5530 16700 16800 1990 95% CI mean std. 5.9976 1360 542 23.990 115.25 6820 341.04 20000 341.43 19500 153 612 2940 8700 8710 51.352 20.462 196 299.10 294.39 1310 522 5000 7630 7510 1.41 2.58 2.51 3540 2.81 832 333 2570 6600 6630 1540 614 3060 8030 7410 2500 2500 2500 2500 2500 1180 473 4370 13000 12500 std. 95% CI mean std. devn. devn. 1989 1988 95% CI mean 3010 1210 5440 9170 7970 mean std. devn. 1987 32.614 13.054 100.74 258.72 259.90 — n 0’ t’3 163 8.1 Results of Simulations for Four Years of Catch Data 8.1.1 Variation in Profitability The detailed results for all the parameters measured are summarized in Tables XXXV and XXXVI for each of the decision methods and each of the four years for which data were available. Mean profit per trip is plotted against year for the three Stationary Models and the Forecast Model in Figure 69. A summary of the results non-dimensionalized by the average catch for each year (from the Random Model) is given in Table XXXVII. When the Forecast Model was compared to individual Stationary Models over the four year period, its profitability was which was Juan de Fuca. Stationary area, 5 percent higher than the This difference was best insignificant, given the variation in the observations, but it is important to note that the Forecast Model was not worse than the best Stationary Model. The Forecast Model was 37 percent better than the second best Stationary Model, which was Johnstone Strait. The Forecast Model was the only model which performed better than the average. year Butedale Juan de Fuca Johnstone 1987 1988 1989 1990 0.746 1.364 0.008 0.533 1.091 0.591 1.775 1.754 1.214 0.994 1.272 0.802 1.099 1.208 1.632 1.548 0.663 1.303 1.070 1.372 4 year mean St. Forecast Table XXXVII Simulated Catch Data for Four Years, 1987 to 1990 Non-dimensionalized by Random Model always 164 Figure 69. Comparison of Forecast Model with Stationary Models, 4 Years of Data, Income - Fuel Cost, 1987 to 1990 30000’ 20000 / / —0—-— / —— 10000- Butedale 0 Juan de Fuca 4—— Johnstone /• Forecast 1987 1986 1988 1989 1990 1991 Year Figure 70. Comparison of Forecast Model with Stationary Model, Risk at $6000, 1987 to 1990 1.0- 0.8- / O.6’ —o-—— Juan de Fuca 0 — 0.4 Butedale — -— — Johnstone Forecast 0.2 0.0• 1986 . • 1987 I 1988 • I 1989 Year • I 1990 1991 165 Even though the Forecast Model was as good as the best Stationary Model, in the long term, it was not as good as the best possible performance. This is summarized in Table XXXVIII. Again the results were non-dimensionalized using the Random Model to represent the seasonal average. From these data it can be seen that over the four years, the Forecast Model would have averaged a profit 37 percent better than average, but 10 percent worse than the best possible performance. The area with the highest profit was not consistent throughout the four years of data. For 1987 it was Johnstone Strait, for 1988 it was Butedale and 1989 and 1990 it was Juan de Fuca. The magnitude of the difference in profit for the best area relative to the other areas was not consistent between years either, with 1987 being the smallest, and 1988 being the highest. The best possible performance over the four years would only have been obtained by moving between areas, but on a seasonal basis, rather than for individual openings. Year Forecast Best 1987 1988 1989 1990 1.096 1.208 1.632 1.548 1.210 1.364 1.775 1.754 Four year mean 1.371 1.526 Stationary Table XXXVIII Comparison of Forecast Model with Best Possible Area, 1987 to 1990 Non-dimensionalized by Random Model 166 It can be seen from Figure 69 that the Forecast Model was always more profitable than the second best Stationary area in any given year. This factor varied between 0.8 percent in 1987 to 93 percent in 1990. The second best area was Johnstone Strait, during 1988, 1989 and 1990. For 1987, Juan de Fuca was the second best area. It seems that the Forecast Model is never the best method in any one year, decision but it always had the second highest profitability of the rules. The best strategy would have been to identify the area with the highest mean profit per trip for a given year, then fish that area exclusively. The and difficulty in practice is identifying the area which has the highest catch rate be very protective of their information, and the only reliable record would be sales during the course of the fishing season. Skippers are likely to slip data, but this would have to be available to the fleet before the next opening. A further confusion would be the length of time for which the areas were actually open. Based on the observations on the fishing season, it was observed that the average number of openings, when these three areas were open simultaneously, varied between 5 and 6, and was generally governed by the length of the season at Juan de Fuca, which generally opened last and closed first. There is probably insufficient time to establish which area was actually the best, and the relatively small penalty for not requiring this information may be sufficient to justify the Forecast Model in practice. It was demonstrated in Chapter 6, that the Forecast Model could produce a profit which was worse than average. This did not occur for the simulations based on actual catch rates, but it is interesting to compare the relative performance of the Forecast Model for 1989 and 1990. In both years, the catch 167 rate at Juan de Fuca was the highest and in each case it was significantly higher than average. In 1989, however the catch rate at Johnstone Strait was also higher than average, but in 1990 it was lower than average. In 1989 the Forecast Model’s performance was better, relative to the average, than in 1990, even though the overall profit for Juan de Fuca was higher in 1990. It appears as though the problem for the Forecast Model, discussed in Chapter 6, where the model is misdirected could have occurred when using the real world data, even though it was never lower than average. 8.1.2 The Variation development in Risk of the risk parameter was discussed in Chapter 5. The variation of mean risk at $6000 per trip, for each of the decision models is shown in Figure 70 and Tables XXXV and XXXVI. From this it can be seen that the Forecast Model had the lowest risk, when averaged over the four years of data. The risk for the Forecast Model was approximately 7 percent lower than the best Stationary Model. The reduction in risk was slightly higher than the increased profitability, but more years of data would be required to confirm this observation. The risk was reduced for the Forecast Model, due to the skipper choosing to fish in the area of highest profitability from the previous opening. In any particular year, there tended to be one area which had catch rates much lower than the seasonal average. The Forecast Model tended to avoid these areas, and so the variations between seasons were smoothed out. It is interesting to variation note that Johnstone in risk between years. The Strait was level the area with the least of risk was determined by the required income per trip. The value of $6000 used in the simulations was set based on the data given in Table III, adjusted slightly for the fact that the boat 168 in the simulation was newer than average. If a particular boat was cheaper than average to operate, then the level of financial risk could be reduced. This may be a factor when picking Johnstone Strait as a stationary area, providing the long term profit of $8645 per trip covered the financial requirements for the vessel. This figure is the average of the Stationary Model for Johnstone Strait taken from Table XXXV. 8.1.3 Variation in Size of Vessel The other question to answer in this section was whether or not a different size of boat was required for a skipper using the Forecast Model instead of the Stationary Models. To investigate this the annual mean peak catch will be used. This is not the most useful parameter for estimating the size of the boat, but it should be a stable, unbiased parameter which can be estimated from the simulation, and where confidence intervals can be reliably fitted. The average peak values, together with 95% confidence intervals are plotted for the three Stationary Models and the Forecast Model in Figure 71. From this figure it can be seen that the most stable value of average peak catch was for approximately Johnstone Strait, with a four year average value of 13,000 kilograms. The other two areas had at least one year with an average peak catch much higher than this value, around 20,000 kilograms, but also had some values much lower. When the mean for the four years of data was considered, the ranking was Butedale, Johnstone Strait and Juan de Fuca. The average peak catch for higher than that for Juan de Fuca. Butedale was approximately 25 percent 169 Figure 71. Comparison of Average Peak Catch for Different Decision Methods, 1987 to 1990 30000 - 0’ 20000 a r —0—-— C., . > (U 4 .---- / .# aa -o- .-. , Butedale JuandeFuca Johnstone / —u——— / Forecast / a) 0 _ >Ig, 0• 1986 • i I • I • 1988 1987 I • 1989 1990 1991 Year 72. Comparison Simulation, 1987 Figure and 0.8 of to Mobility Between 1990, Butedale Observation 0.6 a) .! 0.4 •/., C .2 o — o o°. —0——- / - -. .0 0*0 • 0.2 0 • 0. — • 0.0• 1986 • . 1987 Simulation, Forecast • .0 I • 1988 Year •0 • 1989 • I 1990 1991 Observation 170 When the Forecast Model was considered, we can see that its highest mean peak catch was also approximately 20,000 kg. When the Forecast Model was averaged over four years of data, it had the highest average peak value, by approximately 10 percent, Stationary compared to the The Forecast Models. Model never obtained the highest average peak catch for any one year, but by between areas moving targeted the areas it tended to stabilize the long term value, However, with the highest profit. since it with the exception of Johnstone Strait, the maximum value, within the four years of data, was not noticeably different for the Forecast from Model the Stationary other two Models. It is difficult to draw any reliable conclusions from only four years of data, but is seems as though the Forecast Model significantly bigger than does Stationary the not require a boat which is Models, with the exception of Johnstone Strait. The lower catch rates for this area, in terms of quantity of fish, may be one of the influencing factors the size of boat fishing in Johnstone Strait, which was discussed in Chapter 4. Based on the simulations, it seems as though large boats fishing in Johnstone Strait will have transportation capacity, and a lower expected profit than could be other 8.2 surplus found in areas. Comparison of Results of A detailed comparison of the Simulation 1988 data was with Observations made with the results of the simulation in Chapter 5. This was extremely time-consuming to carry out, and would be unduly repetitive to carry out this procedure for all four years of data. However, some check on the overall performance of the simulations, relative to the actual fishing fleet would be desirable. It was easy to check the 171 first and second moments of catch per day distributions from the results in Tables XXXV and XXXVI and the observations in Table XVII. It can be seen that these are in good agreement. Income figures will not agree, since the modified average values of dollars per kilogram were used. One factor which can be the compared between Forecast and Models the observed data is a boat entry index to a given area. For the Forecast Model, this index was calculated from the fraction of the total number of trips that the boat made to a given area in a given year. For the observed data, the entry index was calculated from the average number of boats per day fishing in a given area, calculated over the full year. These values are compared for each area in Figures 72 to 74. From these figures, it can be seen that the entry index from the simulation generally matches the trends for the observed data for Butedale and Juan de Fuca. The Forecast Model predicted higher peaks and lower troughs than for the actual fleet performance. The Forecast Model exaggerated the trends in the fleet performance, profitable areas. due to the fact that the skipper was choosing the more In general, the fleet behaviour was distribution of effort than the Forecast Model predicted. an even These trends were closer to consistent with the observations made during the detailed comparison with the 1988 data in Chapter 5. Some of the differences can be explained by the assumptions made. For example, for Juan de Fuca in 1988, the Forecast Model had a lower number of entries than was observed from the fleet. This was possibly due to the fact that the simulations used a lower dollar value of the fish, which would 172 Figure 73. Comparison of Mobility Between Observation and Simulation,1987 to 1990, Juan de Fuca 0.8 0.6 (3 0.4 (0 444 0 / —I]-—— 4 -, - - -- Simulation Observation 0 h. 0.2 0.0• 1986 . p I • 1987 I • I • 1989 1988 1990 1991 year Figure 74. Comparison of Mobility Between Observation and Simulation, 1987 to 1990, Johnstone Strait 0.5 “4. 0.4 • . ,‘ 0 Cl) 00 0.3 —a-—— ..--. 0 .0 .I I_ 0 0_co 00. LI. 4 0.1• 1986 • • 1987 I 1988 • I 1989 year • I 1990 1991 Simulation Observation 173 significantly reduce the desirability of the area. Also for 1990, the actual entries at Butedale were much higher than would have been predicted by the Forecast Model. This is due to the fact that this area was the only one open in the early part of the season, and so the fleet did not need to determine which was the best area. However, the trends for Johnstone Strait were not matched well by the Forecast Model. It seems as though more boats prefer to fish in Johnstone Strait than the Forecast Model would indicate. The reason for this may be due to the fact that Johnstone Strait is open longer than the other areas (Table XII), and even though the income per trip was not the highest, when multiplied by the total number of days this was the area which produced the highest total income. 8.3 8.3.1 Vessel Fuel Design Features Consumption and from Derived the Simulations Mobility The Forecast Model had the second highest fuel consumption, averaged at $710 per trip. This was lower than the Stationary Model at Butedale, but higher than the other two increased Stationary Models. The higher cost of fuel was offset by earnings. Another factor to consider is the long term mobility of the vessel, in terms of determining if there is a preferred area, and how this may influence the vessel design. Table XXXIX gives the average proportion of trips to each area for the Forecast Model, over the four year study period. 174 year 1987 1988 1989 1990 4 year mean Butedale Juan de Fuca Johnstone 0.096 0.612 0.000 0.072 0.428 0.074 0.728 0.776 0.476 0.309 0.272 0.153 0.195 0.501 0.302 St. Table XXXIX Proportion of Total Trips to Each Area, Forecast Model From these data we can see that the boat fished approximately 50 percent of the time in Juan de Fuca, and 30 percent of the time in Johnstone Strait. Butedale was not a profitable area in the long term, despite its very high catch rates. Based on this information, it would appear that the boat should be optimized for Juan de Fuca, without compromising the operations in Johnstone Strait. The special features of Juan de Fuca would be the absence of places to make point sets, and so the vessel, deck arrangement and equipment should be sized for making open sets in exposed conditions. This may be the factor which influences the size of boats fishing in Juan de Fuca, relative to the other areas. These boats were bigger than the ones fishing in the other two areas, but based on the catch data there was no requirement for a larger transportation capacity than boats fishing at Butedale. 8.3.2 Empirical Relationships Between Mean Catch and Hold Size One measure of the size of the transportation capacity of the fleet is the average hold capacity, taken from Figure 68, which was calculated to be 65.7 175 Figure 75. Relationship Between Mean Catch per Day and 99 Percentile for 25 Consecutiye Trips C, — ‘C, C,U 6 N C, S 0 z 1 2 3 4 5 6 average catch, tonnes 7 8 176 tonnes. The largest average peak catch taken from the simulations discussed in Section 8.3.1 was approximately 20 tonnes, which when allowance was made for ice, would give a maximum required capacity of approximately 40 tonnes. Clearly the boats in the fleet are much bigger than would be predicted by the simulation. A more reliable estimate of the size of the boats would be to consider the extreme values in more detail. One obvious relationship is between the mean catch and the 99 percentile for the maximum catch in 25 openings. This would be helpful for designers in interpreting the required size of boat, when mean catch is the figure most commonly available. It was shown in Chapter 7 that the parameters for the extreme value distribution could be successfully estimated from the first and second moments of the observed histogram for maximum catch. These parameters for the fitted distributions, together with the calculated 99 percentile for each area and year are given in Table XXXX. Figure 75 shows a regression equation of mean catch per day against the 99 percentile for the maximum catch in 25 openings. It can be seen that the relationship is approximately linear. Based on this analysis, the 99 percentile is 7.1 times the mean catch. However, if one wanted to use the largest observed values, then using 9 times the mean catch would allow a small factor of safety. If it was required to include the volume of ice, then the relationship would be 10.6 for the regression equation, and 13.5 for the largest values. If we consider the largest mean catch observed within the simulation models (7300 kilograms for Juan de Fuca in 1989) the required hold size is 77.6 cubic metres. Based on the results of the simulation, 1 boat in 100 would require a Butedale Butedale Butedale Butedale Johnstone Johnstone Johnstone Johnstone Juan de Fuca Juan de Fuca Juan de Fuca Juan de Fuca Forecast Forecast Forecast Forecast Random Random Random Random Model 1987 1988 1989 1990 1987 1988 1989 1990 1987 1988 1989 1990 1987 1988 1989 1990 1987 1988 1989 1990 year 3280 7440 742 9740 3710 3560 7000 6400 1800 1450 2770 8830 3450 7130 4120 7410 3560 6460 4070 7720 Parameters from fitted 95 percent Distributions confidence mean peak catch sigma, EV1 mu, EV1 642.88 2557 1458.24 5801 145.43 579 1909.04 7594 727.16 2893 697.76 2776 1372 5458 1254.4 4990 352.8 1403 284.2 1131 542.92 2160 1730.68 6885 676.2 2690 1397.48 5559 807.52 3212 1452.36 5778 2776 697.76 1266.16 5037 797.72 3173 1513.12 6019 Table XXXX Parameters Fitted to Maximum Catch Distribution Assuming a Gumbel Distribution 12000 21800 3050 21300 12100 10300 14300 16400 6910 4490 11400 23400 10500 19300 12800 21800 10900 16500 11600 21300 mean peak std. devn. catch, kg 10524 18452 2716 16916 10430 8698 11150 13520 6100 3837 10153 19426 8947 16091 10946 18465 9298 13593 9768 17826 Maximum catch tonnes (99%, EV1) 22.29 45.14 5.38 51.85 23.74 21.47 36.26 36.47 12.56 9.04 20.09 51.1 21.32 41.66 25.72 45.04 22.07 36.76 24.37 45.52 I-. —I 178 hold bigger than this value. From observations on the fleet, we can see that approximately 30 boats 100 have holds bigger than this level. The 99 in percentile for the observations on the fleet is 150 tonnes. This would also indicate that the boats in the fleet are bigger (and more expensive) than the size required for the single day fishing trips predicted by the simulation, which was noted in Table XIII to be the most common scenario. It would appear that the boats are sized for multiple days fishing, between two and four days, or are sized for some fishery other than salmon seining. 8.4 Long Term Economic Predictions It is also interesting to compare the longer term economics of salmon seine fishing, based on the four years for which data were available. Let us consider an entrepreneur considering a $1M investment in a fishing boat. This is a ‘typical’ price for for a new boat. Then using the average cost per trip of $6000, the income from fishing and the cost of fuel consumed from the simulation, we can consider some measures of economic performance for a full fishing season. Since the overall economic performance will be sensitive to the number of trips per year, the effect of this variable was also studied. One crude measure of economic performance is the payback period. This is simply the time required to repay the initial investment based on the assumed annual costs and expenses and takes no account of interest rates or cash flows into the project after the payback period. The results of this analysis for the five decision rules are given in Table XXXXI. This crude analysis immediately shows that the Stationary Model at Butedale is a bad investment, and based on the average values predicted from the Mobile Model Stationary Mobile Model Stationary Forecast Random Butedale Juan de Fuca Johnstone St. Forecast Random Butedale Juan de Fuca Johnstone St. 12250 9287.5 11845 8400 5.70 13.89 8.55 20.83 Table XXXXI Calculation of Payback Period 1000000 -41.67 5.81 12.60 1000000 -62.50 8.71 18.90 Initial investment Payback period, yrs 175350 72000 116900 48000 -24000 172125 79350 30 5845 2400 6000 6000 Data Per trip, $ 20 trips/year Cost Profit/trip Profit/year Income (Inc.-fuel) 5200 -16000 6185 6000 -800 114750 12157 11737.5 6000 5737.5 52900 8645 2645 9197.5 6000 4.28 10.42 1000000 -31.25 4.36 9.45 233800 96000 -32000 229500 105800 40 3.42 8.33 1000000 -25.00 3.49 7.56 292250 120000 -40000 286875 132250 50 2.85 6.94 1000000 -20.83 2.90 6.30 350700 144000 -48000 344250 158700 60 ‘.0 180 simulation would never repay investment. the Payback period can be an effective measure of merit for short term investment (less than three years) and it is immediately clear from this analysis that even the descision rules with the highest income (Juan de Fuca and Forecast Models) require over 40 trips per year to bring the payback period less than 5 years. Based on the data in Table XII, we would expect that the average number of trips per year when both of these models were valid would be 16.75, although the maximum observed number was 32. These rate would give payback periods between 10 and 6 years. Since the lifetime of a fishing boat is relatively long, as can be seen in Table I, a more sophisticate financial analysis is required. Another method which is appropriate for this investment is to consider the internal rate of return for the project, based on an assumed 20 year life-span for the boat, with a resale value of $0.25M at the end of the 20 years. The internal rate of return is the equivalent interest rate generated by the project, assuming all investment is within retained the project. Again the sensitivity of the internal rate of return (IRR) to the number of trips per season was studied. This analysis is given in Table XXXXII for the Forecast Model and for the Stationary Model at Johnstone Strait. Based on 20 trips per year, the Forecast Model predicted an IRR of 10.445 percent, which is very low given the high level of risk associated with fishing operations. It is not until 50 trips per year that the IRR reaches 30 percent, which is probably more appropriate for high risk ventures. For Johnstone Strait, using the mean number of trips per year of 55 taken from Table XII, the IRR is approximately 13.7 percent. This is higher than the equivalent value 181 20 20 1000000 30 20 1000000 40 20 1000000 50 20 1000000 60 20 1000000 Annual income 116900 175350 233800 292250 350700 Resale value of boat 250000 250000 250000 250000 250000 10.445 16.955 23.105 29.092 35.005 Trips per year Number of years Investment in boat IRR Forecast Model Trips per year Number of years Investment in boat Annual income Resale value of boat IRR 20 20 1000000 30 20 1000000 40 20 1000000 50 20 1000000 60 20 1000000 52900 79350 105800 132250 158700 250000 250000 250000 250000 250000 2.292 5.867 9.136 12.209 15.151 Random Model Table XXXXII Calculation of Internal Rate of Return 182 for the Forecast Model, taken over the average length of time for which it is valid. For a vessel fishing in Johnstone Strait to obtain an IRR of around 30 percent, the investment in the boat should be reduced to approximately $0.44 M. This would correspond to the observation that boats fishing Johnstone Strait were, on average, smaller and older. In conclusion, when the same number of trips per year are considered then the Forecast model represents the best investment. However, this model is only valid for a short portion of the total season, and a better investment is to fish the Stationary Model at Johnstone Strait. For a full season, based on the four years of observed data, the best strategy would be to use the Forecast Model when all three areas were open, but then concentrate on fishing in Johnstone Strait. The higher rate of return for Johnstone Strait may be the reason why the Forecast Model under-predicts the number of boats fishing in Johnstone Strait. 8.5 Summary It was not possible to give definitive conclusions on the performance of the Forecast Model on the basis of only four years of data, but it does seem that it predicts (Random approximately Model) and 37 percent more profit per trip than the average 5 percent more than the best Stationary Model. The advantage comes from the skipper choosing the area with the best profit each year, which tends to stabilize the fluctuations which occur between years within a single area. The Forecast Model predicts about 10 percent less profit than the best possible choice of area each year. 183 The size of boat predicted by the Forecast Model was not significantly different from that for the Stationary Models, with the exception of Johnstone Strait. In this case, the predicted size of hold is approximately 30 percent smaller. However, in general the boat sizes predicted by the simulation model, for a single days fishing, are between 60 and 100 percent smaller than those observed in practice. The actual fleet is sized for making longer trips than a single day, although was the most common scenario. More boats prefer to fish in Johnstone Strait than is dictated by the short term catch rate, based on maximum profitability from a single opening. Factors which are probably influencing this decision are the fact that this area shows little variation in income and risk between years, and the fact that the season has more openings than the other areas, and so the total income over the season is the highest. 184 Chapter General 9.1 Discussion and 9 Further Work Summary Salmon seining was found to be a fishery particularly appropriate to modelling using simulation. In the period 1987 to 1990, the fishery was highly regulated, which limited the number of options available to a skipper in terms of selecting a place and time for fishing. This meant that the spatial distribution of suitable fishing locations and the times at which fishing was permitted were easily incorporated into a computer model when it was written in a simulation language. Observations on actual boat performance showed that there was little variation in vessel speed during the course of a voyage, and transit speeds could be considered as constant. The distances travelled by the boat when it was fishing were very small in relation to the distances travelled to the regulated fishing areas, which meant that fishing activity could be considered as taking place in a single location on a given day. The majority of trips were recorded as being a single day, which meant that the length of the voyage was not limited by the maximum range that the boats were capable of. It was also found that there was little variation in catch rate due to the technical parameters of the boat. This was thought to be due to the fact that all the boats carried nets which were the same size (although size would vary between fishing areas), and the fact that there was not a very large difference in the vessel dimensions. 185 Of all the input variables, the most influential random variable was found to be the daily catch rate at a given location, over the course of a season. It was found that other variables which affected the economic performance, such as vessel speed, fuel consumed during a trip and dollar value per kilogram of fish did not show sufficient variation to make it worthwhile considering them as random variables within the simulation. Output variables which were random, as a result of the catch data, were income per trip, maximum catch per season, the financial risk, the fuel consumption per trip and the number of trips to each area during a season (for mobile models). The data used for the statistical models of the catch rates were developed from landing data recorded by the Department of Fisheries and Oceans. It was found that gamma distributions gave very good models for catch rates. Some simplifications could be made to the distribution of catch per day about the mean, which were based on the geographic location and did not vary between years. Since vessel size appeared to have no effect on catch rate, in terms of catch (kilograms) per day, data from all boats fishing in one location could be used to develop statistical models of the catch data, with no observable distortion of the results due to the boat itself. The parameter which was used to judge the performance of the boats was average profit per trip, which included both the income earned from the catch and the cost of the fuel used to earn that income. It was assumed that other operating costs did not vary with the distance that the boat travelled. The analysis methods presented could have been improved by carrying out a detailed calculation to subtract these operating costs from the profit reported by the simulation model. Unfortunately no information was available for the 186 operating costs of the vessel used to check the simulation model. If these data were available, then they could easily be included in the calculations. The simulation was developed to model the performance of a vessel (or group of vessels fishing together) for a single opening, during the course of a fishing season, for three fishing areas open simultaneously. This represented the most complex portion of the fishing season, since it involved a choice of areas, with a high level of uncertainty as to which would be the best area. The simulation was not developed to model a complete season, opening by opening, since observations indicated that the number of occasions when three areas were open simultaneously was a relatively small percentage of the total number of openings in a season. Three decision rules were developed and programmed into the simulation, one based on Stationary boats (always fishing in the same spot), and two based on mobile boats. One mobile method assumed a random choice by the skipper to move between fishing areas, and the other (called the Forecast Model) fished in the area with the highest profit the previous opening. It was found that each model represented realistic, but different, views of the fishing operation. The Stationary Model represented a reasonably high proportion of the fleet, as did the Forecast Model. The Random Model gave a good approximation to the average performance of the whole fleet. It was found that in general, fishing in the area which had had the highest average profit the previous opening was a good strategy. This decision method tended to avoid the areas which had low catch rates, and tended to fish more times in areas which had high catch rates. Based on data for four years of 187 fishing operations, the Forecast Model gave a profit that was five per cent higher than the best Stationary Model and 37 percent better than the average. The Forecast Model was only 10 percent worse than the best possible performance over the period studied. It is important to be able to model better than average income since this will represent better than average skippers. These skippers catch the largest amounts of fish, which in turn will have the most effect on the stock. Other factors which were considered were the sensitivity of the profit earned by a single fishing vessel to variations in catch rate, using both real and synthesized data, to highlight any possible areas of weakness in the decision model. It was found that selecting the best area based on the previous opening was not a good strategy when the average profit from all three areas were approximately equal. For the fishing areas chosen, the income from the furthest area had to be at least twice the average value from the other two areas, in order for ft to be significantly more profitable. This was due to the fact that up to this point, there was a higher probability of selecting the wrong area as the area of highest catch. This gives some quantification to the observation that some skippers are relucant to move between fishing areas until catch rates are very high. Variations in the operating practice of the boats were investigated using simulation, and it was found that there was a slight increase in profit per boat, (approximately 2 per cent per boat) for each additional boat fishing as part of a team. In this study, only one boat was used to transport fish, while the other boats remained on the grounds. It was found however, that the biggest effect of boats fishing together was the reduction in financial risk. Risk was defined 188 as the probability of making a voyage, and not earning enough to cover the average cost per voyage. When two boats were fishing together, the risk was reduced to 44 per cent from 51 per cent. The risk continued to reduce for three and four boats fishing together, but at a lower rate. Thus, when the number of opportunities to make a decision were small, sending two boats to a given area, had a lower risk than just sending a single vessel. Another factor which was investigated with the simulation was the size of the fish hold required to transport the maximum catch which could be expected during the course of the season. The simulation was developed to model a single opening, and so it was necessary to fix the number of openings in a season, in order to estimate the distribution of maximum catch. From observations on the fleet performance, it was decided that 25 openings was a reasonable number. The maximum catch from 25 consecutive openings was simulated, and it was found that this could be approximated by a Gumbel distribution. The parameters for the Gumbel distribution could be estimated either from the estimated distribution of catch per trip, or from the distribution of maximum catch, recorded by the simulation. The simulation predicted vessel sizes which are smaller than the vessels observed in the current fishing fleet. Based on making a single fishing trip, the boats may be up to twice as big as they are required to be. This represents considerably more investment in the fleet than is required. Since many of the boats in the fleet are more than twenty years old, it is possible that the economic factors have changed with time, and catch rates no longer justify the investment in such large vessels. have become smaller with time. It was observed that vessel parameters 189 From the simulation, it was found that the biggest effect on profitability was the average income per trip for all three areas combined. If this was fixed, then the decision process was the next most important factor, followed by the number of boats fishing together as a team. The results of the simulations also showed that it was necessary to move between areas to obtain the highest profits. Movement between areas on an opening by opening basis, which was observed in the fleet behaviour, was probably the result of lack of information as to which was the best area for a given year. The simulation results predicted that on the basis of ‘profit per trip’, the Forecast Model offered highest mean profit per trip. However, when the expected number of trips per year were included, the best internal rate of return was offered by the Stationary Model at Butedale. This was the result of a higher average number of trips per year, which resulted in a larger income per season. Using the current value of a fishing vessel and the catch rates based on the four years of observed data, it is apparent that simply fishing for salmon is not a good investment, given the high levels of risk involved. It is essential for skippers and vessel owners to maximize the number of trips per year in order to make the investment profitable in the long term. The simulation model was developed to support the an expert system for fishing vessel design. The long term intention is to use the simulation to predict the transportation requirements of a vessel, or group of vessels. This would then be used to generate the basic design within the expert system. The simulation would then be used again to model the operating economics over a realistic range of catch rates and fishing locations. 190 9.2 Discussion on the Use of Simulation for Studying Fishing Boat Economics Simulation is a modelling technique which allows for a realistic representation of income and expenditure in fishing vessel operations. The biggest advantage of using simulation to model the economic performance of fishing vessels is that it allows many important parameters to be included as random variables. It was found that there was considerable variation in catch rate, and therefore income, between days, fishing areas and years, all of which had to be included if realistic results were required. The mobility of the fishing fleet meant that it would have been difficult to include this random variation in any other way. Other important variables, such as economic risk, maximum catch and the number of trips a vessel made to each area could also be analyzed as random variables. It also allowed for a model of the vessel mobility, and how fuel consumption would vary with different fishing scenarios. All these factors were important in taking a probabilistic approach to the analysis of the design and operating economics of fishing vessels. The probabilistic approach was essential when the level of financial risk was to be analyzed. When maximum catch was considered as a random variable, it meant that the hold size for a vessel could be determined based on the probability of obtaining a certain catch. It was clear from the analysis that the hold size required for vessels fishing Johnstone Strait was smaller than for any other area or decision rule. This may be one reason why it was observed that the smaller boats fished this area. The catch rate at Butedale was often higher, but the smaller vessels tended to fish this area also. 191 The major disadvantage of using simulation was that it required considerably more information than traditional deterministic design methods. For a fishery, such as salmon seine fishing in British Columbia, which has a relatively small number of boats and a well established operating practice, then this investment is worthwhile. The method used was essentially a ‘hindcasting’ technique which relied on past catch data to make inferences relative to the performance of a fishing vessel. For design purposes, it can be used to investigate a realistic range of catch rates, and distributions of parameters for given fishing areas. If this information were to be translated back into design parameters, it should result in fishing operations which are economically viable for the fishing fleet, but do not put the long term supply of fish in danger. The analysis developed for the simulation model may have included some factors which were inherent to the way the data was collected. For example, it was not possible to develop data on a catch per set basis, and so factors such as size of the net, weather conditions and other variables may be buried in the data. Thus, the catch rate data can only be strictly applied to salmon seine fishing gear and techniques used at the time the data were collected. 9.3 Future Uses of Simulation in Fishing Vessel Analysis All the analyses were carried out based on the technical performance of a single boat, for which data were available. It is recognized that other vessels will have different operating characteristics, and the simulation model could be adjusted to calculate the economic effect of the differences. The vessel used in the simulation had an installed power which was higher than average, 192 which may have effected fuel consumption. Other factors which may be considered for future simulation models are radically different hull form combinations, such as high speed planing hulls combined with packers. The Forecast decision method could be refined to keep longer term information, rather than just the data on the last opening. We can speculate that this would reduce the level of the performance deficiency identified in Chapter 6. However, the current model has the advantage of using the minimum amount of historical information. So far, only one fishery has been simulated. Another major fishery in British Columbia is the herring seine fishery, where most of the boats involved also fish for salmon. The herring season is different from salmon in that it is very short, but much higher catch rates are typically observed (50 tonnes per day for herring compared to 3 tonnes per day for salmon). It is reasonable that if the model can be applied to one seine fishery, it could be adjusted to another one, especially when the boats are the same. Two major fisheries which are different from seining are trawling and line fishing. It would be interesting to analyze these fisheries in order to develop a simulation model. However, data would be required on vessel operations and catch rates for different geographic areas in order to develop a successful model. The simulation models developed for this thesis could be used to consider the effect of external factors such as the cost of fuel and the price of fish on the profitability of a typical fishing operation. This would show at what point it would not pay for boats to remain in operation. Whilst this is clearly dependent on the tuning of the relationships within the model, it would be 193 easy to modify the computer programs for specific instances. However, since these are likely to be so specific, the best use of the simulation would be to answer specific questions on a specific operation. The application of simulation in this thesis has concentrated on the perspective of a skipper seeking to maximize the income obtained from a single fishing trip. It was assumed that if this can be successfully modelled, the seasonal catch can be maximized simply by fishing the maximum number of openings per year. However, the fishing scenario used in the simulations was a considerable simplification of reality. For example, not all areas are open simultaneously. In some cases the area which had the highest return may not be open the following week and in other cases areas may be open for different lengths of time. In such cases, it would be cheaper to stay on the grounds overnight, for a two day opening, than return to port each night. Therefore, the net profit per voyage may be higher, for a lower catch rate per day, if more days were available for fishing. These are fisheries management issues rather than direct engineering, but it would be possible to develop a simulation model with more emphasis on management issues. The long term objective would then be to balance the mortality rate required for a profitable industry with the required reproduction rate for a healthy stock. The biggest weakness in converting the simulations described in this thesis into fisheries management tools is that they take no account of the dynamic behaviour of the fish population. Clearly if the fish population is tied to a geographic area, the amount of fish at the end of the season is lower than at the beginning. development of the model. This is not allowed for within the 194 However, some aspects of fisheries management, such as vessel preferences for certain fishing locations, or changes in the number of trips permitted per year could be handled reasonably successfully by these relatively simple models. Again, due to the complex nature of some of these management issues, the best possible use of the model would be to use it to answer specific questions related to well defined structural changes to the fishing system. 195 References 1. Bower, T. C. ‘Fishing Vessel Optimization, A Design Tool’, M. A. Sc. Thesis, University of British Columbia, January 1985. 2. Sheshappa, D. S. ‘A Computer Design Model for Optimizing Fishing Vessel Designs Based on Techno-Economic Analysis’, Dr. Ing Thesis, Division of Marine System Design, Norwegian Institute of Technology, December, 1985. 3. Causal, S. M., McGreer, D. and Rohling, G. F. ‘A Fishing Vessel Energy Analysis Program’, Marine Technology, Vol. 26, No. 1, January 1989, pp 62-73. 4. Nickerson, T. B. ‘Systems Analysis in the Design and Operation of Fishing Systems’, Conference on Automation and Mechanization in the Fishing Industry, Montreal, 1970. 5. ‘Applied Operations Research in Fishing’, Proceedings, NATO Symposium on Applied Operaions Research in Fishing, Trondheim, 1979, Plenum Press, New York, 1981. 6. Hamlin, C. ‘Systems Engineering in the Fishing Industry’, Marine Technology, Vol. 23, No. 2, April 1986, pp 158-164. 7. Ledbetter, M. ‘Competition and Information Among British Columbia Salmon Purse Seiners’, Ph. D thesis, University of British Columbia, April 1986. 8. Schmidt, P. G. Jr. ‘Purse Seining: Deck Design and Equipment’, Fishing boats of the World 2, edited by Jan-Olaf Traung, FAO of UN, Rome, published by Fishing News Books, 1960. 9. Robert Allan, ‘British Columbia (Canada) Fishing Vessels’, Fishing Boats of the World 1, edited by Jan-Olaf Traung, FAO of UN, Rome, published by Fishing News Books, 1955. 10. Cove, J. J. ‘Hunters, Trappers and Gatherers of the Sea: A Comparative Study of Fishing Strategies’, Journal of the Fisheries Research Board of Canada, Vol. 30, No. 2, 1973. 11. Hilborn, R. and Ledbetter, M., ‘Analysis of the British Columbia Salmon Purse-Seine Fleet: Dynamics of Movement’, J. Fish. Res. Board Can. Vol. 36, 1979. 12. Hilborn, R. and Ledbetter, M., ‘Determinants of Catching Power in the British Columbia Salmon Purse Seine Fleet’, Can. J. Fish. Aquat. Sci. Vol 42, 1985. 13. Hilborn, R., ‘Fleet Dynamics and Individual Variation: Why Some People Catch More Fish than Others’, Can. J. Fish. Aquat. Sci. Vol 42, 1985. 14. Fisheries Act, Pacific Commercial Salmon Fishery Regulations, Queen’s Printer for Canada, Ottawa, 1978. 15. Pacific Coast Commercial Fishing Licensing Policy: Discussion Paper, Department of Fisheries and Oceans, September 1990. 196 16. Bjerring, J. H. and Chamut, P. S. ‘Annual Summary of British Columbia Commercial Catch Statistics, 1988’, Department of Fisheries and Oceans, Pacific Region, no date or report #. 17. ‘1990 Fact Sheet’, Department of Fisheries and Oceans, Pacific Region, no date or report #. 18. Causal, S. and McGreer, D. ‘Application of a Bulbous Bow to a Fishing Vessel’, International Fisheries Energy Optimization Workshop, University of British Columbia, Vancouver, B. C. August 28-30, 1989. 19. Avis, J., Dunwoody, B. and Molyneux, D. ‘Reducing Added Resistance of Fishing Boats Using a Bulbous Bow’, International Fisheries Energy Optimization Workshop, University of British Columbia, Vancouver, B. C. August 28-30, 1989. 20. Weisberg, S. ‘Applied Linear Regression’, 2nd Edition, John Wiley and Sons, 1985. 21. Curr, C. T. W. ‘A Mathematical Model Used for Pre-feasibility Studies of Fishing Operations’, NATO Symposium on Applied Operations Research in Fishing’, Trondheim, Norway, August 1979. 22. Bury, K. ‘Statistical Models in Applied Sciences’, Krieger Publishing Company, 1986. 23. Pritsker, A. A. B. ‘Introduction to Simulation and SLAM II’, 2nd Edition, John Wiley and Sons, 1984. 197 Appendix for Methods Fitting Gamma 1 Probability Density Functions to Observed Catch Data A random variable x is said to be Gamma distributed if its probability density function (PDF) is of the form: fg(x; a, x) = aIX) () exp (i), O<x,a,X (1) where u is a scale parameter and A is a shape parameter. The gamma function (X) is given by equation (2), r(x) = j e dx (2) and T(A) is equal to the factorial function (1-A)! where A is a positive integer. The maximum likelihood estimators for the parameters a and A are given by equations (3) and (4). (3) lno+w(X)=lnG where n II i=1 ’ 1 x (4) 198 Bury [1] gives methods of estimating the shape parameter, X, from either equation (5) or (6), depending on the value of g, where =(o.sooi for 0< g <= + O.1649g O.0544g2)g1 - (5) 0.577 or 8.899 + 17.80g .9775g 2 2 + g 11.97g 3 9.060g + + (6) for 0.577<=g <=17 where g () = in The variance of a and X were estimated from the variance-covariance matrix, given in equation 7. 1 n(xw’x-1) where ip’ a) -a -a x (7) is the trigamma function. Data were obtained from the Department of Fisheries and Oceans for each boat reporting a landing from each geographical area on a given date. The data were reduced to mean catch per day (and its standard deviation) for each day when there were six or more boats reporting a landing for a given area. Each year and area were analyzed seperately. Based on the fisheries biology literature, it was assumed that the gamma probability distribution was likely to 199 be a good model for the observed variation in mean catch per day for salmon seine fishing, over the course of a season. A computer program was written which read in the mean catch per day for each day, and then calculated the parameters required to solve equations (5) or (6) for A. This value was then used to solve equation (3). Estimates of the variance of the parameters, a and A, were made from the variance-covariance matrix, given in equation 7. The gamma probability function fitted to the data, using the methods described above, was compared against the observations (point by point) using a Kolmogoroff test, described in [2]. This test considers the maximum absolute deviation between the order statistic for the observed data (catch per day) and the predicted cumulative distribution function (CDF) at the same value of x. This deviation is refered to as the Kolmogoroff Statisitic. If this statistic is less than a critical value, which depends on the size of the sample and the assumed confidence level, a, then the fitted distribution is considered to be statistically the same as the observations. The observed deviations are less those accounted from simply by random sampling from that distribution. The tabulated values for the Kolmogoroff Statistic are given in [2]. In order to perform the Kolmogoroff Test on the observed data, it was necessary to write a program to calculate the CDF for the predicted distributions, since there is no analytical solution to the integration of the gamma PDF. This program was prepared using the methods given in [3]. The same program also calculated the Kolmogoroff Statisitic, using the methods described above. 200 Other data which were calculated were the number of boats reporting a landing on a given day and the number of days per year for which landings were reported. References 1. Bury, K. ‘Statistical Models in Applied Sciences’, Krieger Publishing Company, 1986, Chapter 9, pp 299 to 329. 2. Ibid, Chapter 6, pp 205 to 208. 3. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. ‘Numerical Recipes (Fortran version)’, Cambridge University Press, 1989, pp 156 to 157. 201 Appendix Description of SLAMII Stationary 2 Computer Program for Model The Stationary Model was programmed in SLAMII, using a network diagram. SLAMII was chosen since it was an established program, which was readily available at the University of British Columbia, and would run on a wide range of computer systems. There were three seperate networks used within the model. These were as foil ow s: - - - a vessel moving around between geographic areas fishing data generation for individual openings data collection on 25 consecutive openings The priciple features of each network will be described below. 1. Vessel Network The vessel network started by assigning the technical and economic parameters to the entity (vessel) entering the model. This was done by using the attributes, which can be assigned directly within SLAM II. In addition, one attribute was used within the model for timing, one for the location of the home port and one for the location of the fishing grounds. The entity was then held in a gate, which represented the vessel waiting in port. Once an opening was ‘announced’ the gate was opened from the ‘fishing data’ network and the vessel could take one of three branches within the network, each of which led to a different fishing area. The destination for a particular trip was 202 determined from the value of an attribute, which was initially assigned to the vessel, as it entered the model. This attribute was used to determine the distance of the fishing ground from the home port and when combined with the speed of the boat, was used to calculate the time the vessel took to reach the selected fishing grounds. The distances between the fishing grounds and the home port were stored as an array, and the attributes for the home port and the destination were used to locate elements within the array. Each of the three branches described above contained a gate, which held the vessel until the time when fishing could legally begin. This represented the vessel waiting on the fishing grounds and selecting a place to fish. The length of the wait was dependent on the distance from the port, with longer waits occuring at the closer areas. The gate was opened from the ‘fishing data’ network and the vessel fished for 8 hours, using fuel at the assumed rate of consumption during fishing activity. After 8 hours had passed the gate was closed again to prevent another vessel entering the area, and fishing illegally. The vessel’s catch was determined by sampling a random variable, which was modelled using a gamma distribution based on the mean catch per day, set within the ‘fishing data’ network. The parameters within the gamma distribution were set using SLAM!! global variables and so they could be transfered between networks very efficiently. One hour after the fishing area was closed the boat sailed home, using times calculated from the fishing location’s distance from the home port. Data was then collected on the simulated values of catch, income, fuel consumed, number of trips where the income was less than $6000 and the size 203 of the maximum catch. These data were collected as global variables, and transfered to the ‘25 consecutive openings’ network for tabulation. The vessel was then routed back to the gate representing its home port, after the destination code for the next trip had been changed. For the Stationary Model, since data was collected for each area seperately, the new destination was selected simply by rotation between each of the three branches, representing the three fishing areas. When the vessel arrived back at the port, the gate had already been closed, and so the vessel was held in port until the next opening. When the opening was ‘announced’ and the gate was opened, the model would begin again. 2. Opening Network This network was one line, which opened and closed the gates within the vessel network at the appropriate time and set the values of global variables used for the catch data. This network contained all the catch and income data, and was the one which was modified to study sensitivity of the results of the simulation to changes in catch rate between years. Input parameters were the price of fish and the scale and shape parameters for the mean catch per day (seasonal values) distribution for each area. The shape parameter for the daily catch distribution was assumed to be a constant, but its scale parameter was calculated based on the sampled value of mean catch per day. 204 This is best illustrated by an example. The parent distribution, for mean catch per day (for the season) would be set using numerical values derived from the observed catch data. ASSIGN XX(j)=GAMMA(a, b) XX(k)=c XX(l)= XX(j)/XX(k) mean catch per day (season) shape parameter, catch/day (vessel), constant scale parameter, catch/day (vessel) Then within the vessel network the catch is sampled using the following statement: ASSIGN XX(m)=GAMMA(XX(l),XX(k)) 3. Twenty Five Consecutive Openings Network This is another linear network, which is used to collect data on 25 consecutive openings. Data is transfered between the vessel network and this network using global variables. This network was added to be able to collect data on the long term statisitics, such as catch per trip, and the seasonal variables, such as maximum catch and risk, within the same model. It also serves as a timer for the overall model. This proved to be a simple and effective method of developing the model, which allowed sufficient flexibility for the model to be developed to include the alternative decision rules. It also allowed for data collection to be incorporated using the standard methods within the program language. A full listing of the SLAMII code for the Stationary Model is given below. 205 GEN,DAVID,STATIONARY MODEL,0 1/22/92,1; MODEL NAME: STAT88 FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY 3 MOST PRODUCTIVE AREAS, STATIONARY MODEL MODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMYITEE, DEC.1991 ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCH SHORTENED TO TRY TO FIT STUDENT VERSION ARRAYS ATRIBUTES FOR BOATS (1) SHIP SPEED (2) HOLD CAPACITY (3) LITRES/HOUR, OUTWARD (4) LITRES/HOUR, FISHING (5) LITRES/HOUR, RETURN (6) FUEL COST, $/L (7) HOME PORT (8) DESTINATION THIS TRIP (9) TIMER, START OF TRIP (10) FUEL USED THIS TRIP, LITRES (11) FISH CAUGHT THIS TRIP, KG (12) INCOME THIS TRIP, DOLLARS (13) EXPENSES THIS TRIP, DOLLARS (14) PROFIT THIS TRIP, DOLLARS ADDITIONAL ATTRIBUTES! USE GLOBAL VARIABLES INSTEAD XX(40) MAX. CATCH, AREA 1 XX(41) MAX. CATCH, AREA 2 XX(42) MAX. CATCH, AREA 3 XX(43) NO. OF TRIPS WHERE PROFIT <6000, AREA 1 XX(44) NO. OF TRIPS WHERE PROFIT <6000, AREA 2 XX(45) NO. OF TRIPS WHERE PROFIT <6000, AREA 3 LIMITS,6,14,15; ARRAY( 1 ,7)!0,20,75, 100,190,200,290; LOCATIONS NETWORK; GATE,HOME,CLOSED,4; GATE,AREA1 ,CLOSED, 1; GATE,AREA2,CLOSED,2; GATE,AREA3,CLOSED,3; CREATE,,,,1,1; DISTANCES BETWEEN PORT & CREATE BOAT BASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOC ASSIGN, ATRIB(1)=10.0; ASSIGN, ATRIB(2)=84.5; ASSIGN, ATRIB(3)=59.4; ASSIGN, ATRIB(4)=6.4; ASSIGN, ATRIB(5)=78.1; ASSIGN, ATRIB(6)=0.4; SPEED, KNOTS HOLD CAPACITY, M’3 FUEL CONS. LIHR, OUTWARD FUEL CONS. LJHR, FISHING FUEL CONS. L/HR, RETURN FUEL COST, $!L 206 ASSIGN, ATRIB(7)=1; ASSIGN, ATRIB(8)=7; LOCATION OF HOME PORT GO TO BUTEDALE, 1ST TRIP WAIT IN PORT FOR AN OPENING PORT AWAIT(4),HOME,; WAIT IN PORT SELECT DESTINATION THIS TRIP ACT,,ATRIB(8).EQ.7,BUTD; ACT,,ATRIB(8).EQ.3,JUAN; ACT,,ATRIB(8).EQ.4,JOHN; BUTDALE BUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT ACT,ATRIB(9),,; SAIL OUT TO FISH CALCULATE FUEL CONSUMED ASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); WAIT FOR OPENING, ON GROUNDS LOC1 AWAIT(1),AREA1,1; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(1 1)=GAMMA(XX(5),XX(6)); FISHING TIME, 9 HOURS ACT,9.O,,; ASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(4)*9.O; UPDATE FUEL CONSUMED SAIL HOME ACT, ATRIB(9),,; ASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMED DATA COLLECTION COLCT,ATRIB(1O),FUEL1,; RECORD FUEL THIS TRIP ASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COST OF FUEL THIS TRIP COLCT,ATRIB( 12),CFUEL1 ,,; COLCT,ATRIB(11),FISH1,20/O/500; RECORD CATCH THIS TRIP ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(7),; INCOME THIS TRIP COLCT, ATRIB(13),VFISH1,; ASSIGN, ATRIB(14)=ATRIB( 1 3)-ATRIB(12); SURPLUS, FISH-FUEL, DOLLARS COLCT, ATRIB(14),PROFIT1,20/O/1500,1; ACT,,ATRIB(1 1).LE.XX(40), SKP1; ACT,,ATRIB(11).GT.XX(40),; RECORD NEW MAXIMUM CATCH ASSIGN, XX(40)=ATRIB(1 1),; SKP1 GOON,1; COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000 207 ACT,,ATRIB(14).GE.6000,NX1; ACT,,ATRIB(14).LT.6000,; ASSIGN, XX(43)=XX(43)-’- 1,; NX1 GOON,1; ASSIGN, ATRIB(8)=3,; ACT,,,HOME; JUAN DE FUCA SET NEW DESTINATION STRAIT JUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT ACT,ATRIB(9),,; SAIL OUT TO FISH ASSIGN, ATRIB(lO)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMED WAlT FOR OPENING, ON GROUNDS LOC2 AWAIT(2),AREA2,l; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(11)=GAMMA(XX(15),XX(16)); FISHING TIME, 9 HOURS ACT,9.O,,; ASSIGN, ATRIB(lO)=ATRIB(1O)÷ATRIB(4)*9.O; UPDATE FUEL CONSUMED SAIL HOME ACT, ATRIB(9),,; ASSIGN, ATRIB(lO)=ATRIB(lO)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMED DATA COLLECTION RECORD FUEL THIS TRIP COLCT,ATRIB(lO),FUEL2,; COST OF FUEL THIS TRIP ASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COLCT,ATRIB(12),CFUEL2,,; RECORD CATCH THIS TRIP COLCT,ATRIB(l1),FISH2,20/O/500; ASSIGN, ATRIB(13)=ATRIB(l l)*XX(17),; INCOME THIS TRIP COLCT, ATRIB(13),VFISH2,; ASSIGN, ATRIB(14)=ATRIB(l 3)-ATRIB(1 2); SURPLUS, FISH-FUEL, DOLLARS COLCT, ATRIB(l 4),PROFIT2,20/O/1500, 1; ACT,,ATRIB(1 1).LE.XX(41), SKP2; ACT,,ATRIB(ll).GT.XX(41),; RECORD NEW MAXIMUM CATCH ASSIGN, XX(41)=ATRIB(l1),; SKP2 GOON,l; COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000 ACT,,ATRIB(14).GE.6000,NX2; ACT,,ATRIB(14).LT.6000,; ASSIGN, XX(44)=XX(44)+ 1,; NX2 000N,1; ASSIGN, ATRIB(8)=4,; ACT,,,HOME; SET NEW DESTINATION 208 JOHNSTONE STRAITJOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT SAIL OUT TO FISH ACT,ATRIB(9),,; CALCULATE FUEL CONSUMED ASSIGN, ATRIB(10)=ATRIB(3)*ATRIB(9); WAIT FOR OPENING, ON GROUNDS LOC3 AWAIT(3),AREA3,1; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(1 l)=GAMMA(XX(25),XX(26)); FISHING TIME, 9 HOURS ACT,9.0,,; UPDATE FUEL CONSUMED ASSIGN, ATRIB(10)=ATRIB(10)+ATRIB(4)*9.0; SAIL HOME ACT, ATRIB(9),,; ASSIGN, ATRIB(10)=ATRIB( 1O)÷ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMED DATA COLLECTION RECORD FUEL THIS TRIP COLCT,ATRIB(10),FUEL3,; COST OF FUEL THIS TRIP ASSIGN, ATRIB(12)=ATRIB(10)*ATRIB(6),; COLCT,ATRIB(12),CFUEL3,,; RECORD CATCH THIS TRIP COLCT,ATRIB(1 1),FISH3,20/0/500; INCOME THIS TRIP ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27),; COLCT, ATRIB(13),VFISH3,; SURPLUS, FISH-FUEL, ASSIGN, ATRIB(14)=ATRIB(13)-ATRIB(12); DOLLARS COLCT, ATRIB(1 4),PROFIT3,20/0/1 500,1; ACT,,ATRIB(1 1).LE.XX(42), SKP3; RECORD NEW MAXIMUM CATCH ACT,,ATRIB(11).GT.XX(42),; ASSIGN, XX(42)=ATRIB(11),; SKP3 GOON,1; COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000 ACT,,ATRIB(14).GE.6000,NX3; ACT,,ATRIB(14).LT.6000,; ASSIGN, XX(45)=XX(45)+1,; NX3 GOON,1; ASSIGN, ATRIB(8)=7,; ACT,,,HOME; HOME 000N,1; ACT,,,PORT; TERM; SET NEW DESTINATION **** ** * ** *** * ***** * *********** *** **** ******* ***** ****** ****** *** DATA GOES HERE ********************************************** 209 ;************************************************************* *** CATCH RATES AS SEEN BY BOAT, YEAR IS 1988, FROM CATCH DATA AVERAGE FISH PRICES OVER YEARS CREATE, 168,,,,; ASSIGN,XX(3)=48,; TIME TO OPENING CATCH RATES AND PRICES AVERAGE $/KG, BUTEDALE AVERAGE $/KG, JUAN DE FUCA AVERAGE $/KG, JOHNSTONE ASSIGN,XX(7)=1.472,; ASSIGN,XX(17)=3.076,; ASSIGN,XX(27)=2.629,; UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALE ASSIGN,XX(4)=GAMA( 1145.92,6.31),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCHJDAY ABOVE SHAPE PARAMETER SCALE PARAMETER ASSIGN,XX(6)=3.055,; ASSIGN,XX(5)=XX(4)/XX(6),; UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DE FUCA ASSIGN,XX(14)=GAMA(449.25,3. 18),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE SHAPE PARAMETER SCALE PARAMETER ASSIGN,XX(16)=5.005,; ASSIGN,XX(1 5)=XX(14)/XX(16),; UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JOHNSTONE ST. ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(26)=2. 195,; ASSIGN,XX(25)=XX(24)/XX(26),; SHAPE PARAMETER SCALE PARAMETER ************* OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICE ACT,XX(3),,; OPEN, AREA1,,; OPEN, AREA2,,; WAIT FOR OPENING OPEN AREA, BUTEDALE OPEN AREA, JUAN DE FUCA 210 OPEN AREA, JOHNSTONE OPEN, AREA3,,; DURATION OF OPENING ACT,8,,; CLOSE AREA CLOSE, AREA 1,,; CLOSE AREA CLOSE, AREA2,,; CLOSE AREA CLOSE, AREA3,,; ASSIGN,ATRIB(1)= 160-XX(3)-8 ACT,ATRIB(1),; ACT,8,,; TERM; OPENINGS & CLOSINGS, ONE WEEK INTERVALS MODIFY OPENINGS FOR SEASON, RATHER THAN FOR WEEK CREATE, 12600,,,,; REP GOON,1; OPEN, HOME,; ACT,56,,; CLOSE, HOME,1; ASSIGN, ATRIB(1)=ATRIB(1)+1,1; SEASON REPRESENTS 25 OPENINGS (168 SEASONS COUNT TRIPS * 25 = 4200 HRS), MODEL RUNS FOR 100 ACT, 1 12,ATRIB(1).LT.75,REP; ACT, 1 12,ATRIB(1).GE.75,; MAXIMUM CATCH THIS SEASON, COLCT, XX(40),MAX1,20/10000/1000; AREA 1 MAXIMUM CATCH THIS SEASON, COLCT, XX(41),MAX2,20/10000/1000; AREA 2 MAXIMUM CATCH THIS SEASON, COLCT, XX(42),MAX3,20/10000/1000; AREA 3 NUMBER OF TRIPS .LT. $6000, AREA 1 COLCT, XX(43),RISK1,26/0/1; NUMBER OF TRIPS .LT. $6000, AREA 2 COLCL, XX(44),RISK2,26/0/1; COLCL, XX(45),RISK3,26/0/1; NUMBER OF TRIPS .LT. $6000, AREA 3 ASSIGN, XX(40)=0,; ASSIGN, XX(41)=0,; ASSIGN, XX(42)=0,; ASSIGN, XX(43)=0,; ASSIGN, XX(44)=0,; ASSIGN, XX(45)=0,; REZERO SEASON VALUES TERM, 100; ENDNETWORK; FIN; 211 Appendix Description of SLAMII Random 3 Computer Program for Model The detailed development of the Stationary Model was described in Appendix 2. The random model was the same basic model, but with two small differences. These were: 1. Selection of Fishing Area For this model, the selection of the fishing area, after the first trip had been made was based on probabilistic branching at the node where the vessel was routed to a fishing area for a particular trip. Each area had an equal probability of selection. 2. Data Collection Data were collected, for this model, at the point just before the time when the vessel had reached the port. This modification was required since it was now no longer necessary to keep track of how much fish was caught in each area. Only one data collection point was required in the model and all entities (vessels) within this network passed through this point. Additional variables were added within the ‘vessel’ network to count the number of trips (out of 25) when the vessel made a trip to a particular area. These were collected as global variables for tabulation within the ‘25 Consecutive Openings’ module. A full listing of the SLAMII code for the Random Model is given below. 212 GEN,DAVID,RANDOM MODEL,O 1/22/92,1; MODEL NAME: RAND88 FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY 3 MOST PRODUCTIVE AREAS, RANDOM SELECTION OF AREA MODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMITI’EE, DEC.1991 ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCH SHORTENED TO TRY TO FIT STUDENT VERSION ARRAYS ATRIBUTES FOR BOATS (1) SHIP SPEED (2) HOLD CAPACITY (3) LITRES/HOUR, OUTWARD (4) LITRES/HOUR, FISHING (5) LITRES/HOUR, RETURN (6) FUEL COST, $/L (7) HOME PORT (8) DESTINATION THIS TRIP (9) TIMER, START OF TRIP (10) FUEL USED THIS TRIP, LITRES (11) FISH CAUGHT THIS TRIP, KG (12) INCOME THIS TRIP, DOLLARS (13) EXPENSES THIS TRIP, DOLLARS (14) PROFIT THIS TRIP, DOLLARS ADDITIONAL ATTRIBUTES! USE GLOBAL VARIABLES INSTEAD XX(40) NO. OF TRIPS TO AREA 1 XX(41) NO. OF TRIPS TO AREA 2 XX(42) NO. OF TRIPS TO AREA 3 XX(43) MAXIMUM CATCH THIS SEASON XX(44) NO. OF TRIPS WHERE PROFIT < 6000 LIMITS,6,14,15; ARRAY(1 ,7)/0,20,75, 100,190,200,290; LOCATIONS NETWORK; GATE,HOME,CLOSED,4; GATE,AREA1 ,CLOSED, 1; GATE,AREA2,CLOSED,2; GATE,AREA3,CLOSED,3; CREATE,,,,1,1; DISTANCES BETWEEN PORT & CREATE BOAT BASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOC ASSIGN, ATRIB(1)= 10.0; ASSIGN, ATRIB(2)= 150.0; ASSIGN, ATRIB(3)=59.4; ASSIGN, ATRIB(4)=6.4; ASSIGN, ATRIB(5)=78.1; ASSIGN, ATRIB(6)=0.4; ASSIGN, ATRIB(7)=1; SPEED, KNOTS HOLD CAPACITY, M3 FUEL CONS. LJHR, OUTWARD FUEL CONS. IJHR, FISHING FUEL CONS. L/HR, RETURN FUEL COST, $/L LOCATION OF HOME PORT 213 ASSIGN, ATRIB(8)=3; GO TO JUAN DE FUCA, 1ST TRIP WAIT IN PORT FOR ANY OPENING PORT AWAIT(4),HOME,; WAIT IN PORT SELECT DESTINATION THIS TRIP, RANDOM CHOICE FROM THREE AREAS ACT,,O.33333,BUTD; ACT,,O.33333,JUAN; ACT,,O.33334,JOHN; BUTDALE BUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT SAIL OUT TO FISH ACT,ATRIB(9),,; CALCULATE FUEL CONSUMED ASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); WAIT FOR OPENING, ON GROUNDS LOC1 AWAIT(1),AREA1,1; ASSIGN, ATRIB(11)=GAMMA(XX(5),XX(6)); SAMPLE DAILY CATCH DIST. CALCULATE VALUE OF FISH ASSIGN, ATRIB(13)=ATRIB(11)*XX(7); ACT/1,9.O,,; BUTEDALE, 9 HOURS ASSIGN, XX(40)=XX(40)+1; NO. TRIPS TO AREA 1 ACT,,,HOME; JUAN DE FUCA STRAIT JUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT ACT,ATRIB(9),,; SAIL OUT TO FISH ASSIGN, ATRIB( 1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMED WAIT FOR OPENING, ON GROUNDS LOC2 AWAIT(2),AREA2, 1; ASSIGN, ATRIB(11)=GAMMA(XX(15),XX(16)); SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(13)=ATRIB(11)*XX(17); CALCULATE VALUE OF FISH ACT/2,9.O,,; JUAN DE FIJCA, 9 HOURS ASSIGN, XX(41)=XX(41)+1; NO. TRIPS TO AREA 2 214 ACT,,,HOME; JOHNSTONE STRAIT JOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT SAIL OUT TO FISH ACT,ATRIB(9),,; CALCULATE FUEL CONSUMED ASSIGN, ATRIB(10)=ATRIB(3)*ATRIB(9); WAIT FOR OPENING, ON GROUNDS LOC3 AWAIT(3),AREA3, 1; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(1 1)=GAMMA(XX(25),XX(26)); CALCULATE VALUE OF FISH ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27); JOHNSTONE ST, 9 HOURS ACT/3,9.0,,; NO. TRIPS TO AREA 1 ASSIGN, XX(42)=XX(42)+1; ACT,,,HOME; HOME GOON,1; UPDATE FUEL CONSUMED, ASSIGN, ATRIB(10)=ATRIB(10)+ATRIB(4)*9.0; FISHING SAIL HOME ACT,ATRIB(9),,; ASSIGN, ATRIB( 10)=ATRIB(10)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMED, SAILING ACT,,ATRIB(1 1).LE.XX(43), SKIP; ACT,,ATRIB(11).GT.XX(43),; RECORD NEW MAXIMUM CATCH ASSIGN, XX(43)=ATRIB(1 1),; SKIP GOON,1; DATA COLLECTION, VESSEL INFORMATION FOR THIS TRIP RECORD FUEL THIS TRIP COLCT,ATRIB(1O),FUEL,; COST OF FUEL THIS TRIP ASSIGN, ATRIB(12)=ATRIB(10)*ATRIB(6),; COLCT,ATRIB(12),CFUEL,,; WT. OF FISH THIS TRIP COLCT,ATRIB(11),FISH,20/0/500; COLCT, ATRIB(13),VFISH,; VALUE OF FISH THIS TRIP SURPLUS, FISH-FUEL, ASSIGN, ATRIB(14)=ATRIB(1 3)-ATRIB(1 2); DOLLARS COLCT, ATRIB(14),PROFIT,20/0/1500,1; COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000 ACT,,ATRIB(14).GE.6000,NXT; ACT,,ATRIB(14).LT.6000,; ASSIGN, XX(44)=XX(44)+ 1,; NXT GOON,1; ACT,,,PORT; TERM; 215 *** DATA GOES HERE ********************************************** *** CATCH RATES AS SEEN BY BOAT, YEAR IS 1988, FROM CATCH DATA AVERAGE FISH PRICES OVER YEARS CREATE,168,,,,; ASSIGN,XX(3)=48,; TIME TO OPENING CATCH RATES AND PRICES ASSIGN,XX(7)=1.472,; ASSIGN,XX(17)=3.076,; ASSIGN,XX(27)=2.629,; AVERAGE $/KG, BUTEDALE AVERAGE $/KG, JUAN DE FUCA AVERAGE $/KG, JOHNSTONE UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALE ASSIGN,XX(4)=GAMA(1 145.92,6.31),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCHJDAY ABOVE ASSIGN,XX(6)=3.055,; ASSIGN,XX(5)=XX(4)/XX(6),; SHAPE PARAMETER SCALE PARAMETER UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DE FUCA ASSIGN,XX( 14)=GAMA(449.25,3. 18),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(16)=5.005,; ASSIGN,XX(15)=XX(14)/XX(16),; SHAPE PARAMETER SCALE PARAMETER UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JOHNSTONE ST. ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(26)=2. 195,; ASSIGN,XX(25)=XX(24)/XX(26),; SHAPE PARAMETER SCALE PARAMETER *** ** * ** * * *** OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICE 216 WAIT FOR OPENING ACT,XX(3),,; OPEN AREA, BUTEDALE OPEN, AREA1,,; OPEN AREA, JUAN DE FUCA OPEN, AREA2,,; OPEN AREA, JOHNSTONE OPEN, AREA3,,; DURATION OF OPEMNG ACT,8,,; CLOSE AREA CLOSE, AREA1,,; CLOSE AREA CLOSE, AREA2,,; CLOSE AREA CLOSE, AREA3,,; ASSIGN,ATRIB(1)= 160-XX(3)-8 ACT,ATRIB(1),; ACT,8,,; TERM; OPENINGS & CLOSINGS, ONE WEEK INTERVALS MODIFY OPENINGS FOR SEASON, RAThER THAN FOR WEEK CREATE,4200,,,,; REP GOON,l; OPEN, HOME,; ACT,56,,; CLOSE, HOME,1; ASSIGN, ATRIB(1)=ATRIB(l)+ 1,1; SEASON REPRESENTS 25 OPENINGS (168 SEASONS COUNT TRIPS * 25 = 4200 HRS), MODEL RUNS FOR 100 ACT, 1 12,ATRIB(1).LT.25,REP; ACT,1 12,ATRIB(1).GE.25,; TOTAL NO. TRIPS, AREA 1 COLCT, XX(40),TRIP1,26/0/1; TOTAL NO. TRIPS, AREA 2 COLCT, XX(41),TRIP2,26/O/1; TOTAL NO. TRIPS, AREA 3 COLCT, XX(42),TRIP3,26/0/1; MAXIMUM CATCH THIS SEASON COLCT, XX(43),MAXCAT,20/10000/1000; COLCT, XX(44),RISK,26/0/1; NUMBER OF TRIPS .LT. $6000 ASSIGN, XX(40)=0,; ASSIGN, XX(41)=0,; ASSIGN, XX(42)=0,; ASSIGN, XX(43)=0,; ASSIGN, XX(44)=0,; REZERO SEASON VALUES TERM,100; ENDNETWORK; FIN; 217 Appendix Description of SLAMII Forecast 4 Computer Program for Model The detailed development of the Stationary Model was described in Appendix 2, The modifications to this code to develop the Random Model were described in Appendix 3. There was only one difference between the Random Model and the Forecast Model. This is described below. 1. Selection of Fishing Area The selection of fishing areas for the Forecast Model was based on comparing the mean income, less fuel cost, for each of the three areas used within the simulation. The area with the highest value is selected for the trip the following week. This is done within the network by assigning the calculated value of income-fuel cost for each area to a global variable. One dummy variable is used, in order to keep track of the highest value, and one more global variable to record the location of the area with the highest profit. This variable is used to set the destination attribute for the next trip. By setting the dummy variable to be equal to the ‘profit’ at one location, and comparing it with another, it is straitforward to develop a network of comparative branches which results in the value and location of the fishing area with the highest profit the opening just past. The Forecast Model was moodified to include additional boats. For this modification, an additional attribute was added which identifed the entity (vessel) as a packer or a fishing boat. The packer always retained the destination at the end of an opening as the port, but a fishing boat waited at 218 the gate associated with the grounds until the opening was announced. At that point it would use the destination of the packer, calculated using the method above, to assign its next location. This was obtained from the global (dummy) variable included to track the location of the best area. The transfer of the fish between boats was assumed to take place within the hour between the end of the legal opening and the boats leaving the fishing grounds. A full listing of the Forecast Model, for one boat, together with a sample output file is given below. 219 GEN,DAVID,FORECAST MODEL,05/28/91, 1; MODEL NAME: FORE88 FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY 3 MOST PRODUCTIVE AREAS, MAXIMUM PROFIT LAST TRIP AS MOTIVATION MODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMITTEE, DEC.1991 ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCH SHORTENED TO TRY TO FIT STUDENT VERSION ARRAYS ATRIBUTES FOR BOATS (1) SHIP SPEED (2) HOLD CAPACITY (3) LITRES/HOUR, OUTWARD (4) LITRES/HOUR, FISHING (5) LITRES/HOUR, RETURN (6) FUEL COST, $/L (7) HOME PORT (8) DESTINATION THIS TRIP (9) TIMER, START OF TRIP (10) FUEL USED THIS TRIP, LITRES (11) FISH CAUGHT THIS TRIP, KG (12) INCOME THIS TRIP, DOLLARS (13) EXPENSES THIS TRIP, DOLLARS (14) PROFIT THIS TRIP, DOLLARS ADDITIONAL ATTRIBUTES/ USE GLOBAL VARIABLES INSTEAD XX(4O) NO. OF TRIPS TO AREA 1 XX(41) NO. OF TRIPS TO AREA 2 XX(42) NO. OF TRIPS TO AREA 3 XX(43) MAXIMUM CATCH THIS SEASON XX(44) NO. OF TRIPS WHERE PROFIT < 6000 LIMITS,6,14,15; ARRAY(1 ,7)/O,20,75, 100,190,200,290; LOCATIONS NETWORK; GATE,HOME,CLOSED,4; GATE,AREA1 ,CLOSED, 1; GATE,AREA2,CLOSED,2; GATE,AREA3,CLOSED,3; CREATE,,,,1,1; DISTANCES BETWEEN PORT & CREATE BOAT BASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOC ASSIGN, ATRIB(1)= 10.0; ASSIGN, ATRIB(2)= 150.0; ASSIGN, ATRIB(3)=59.4; ASSIGN, ATRIB(4)=6.4; ASSIGN, ATRIB(5)=78.1; ASSIGN, ATRIB(6)=O.4; ASSIGN, ATRIB(7)=1; SPEED, KNOTS HOLD CAPACITY, M3 FUEL CONS. L/HR, OUTWARD FUEL CONS. IJHR, FISHING FUEL CONS. IJHR, RETURN FUEL COST, $/L LOCATION OF HOME PORT 220 GO TO JUAN DE FUCA, 1ST TRIP ASSIGN, ATRIB(8)=3; WAIT IN PORT FOR ANY OPENING PORT AWAIT(4),HOME,; WAIT IN PORT SELECT DESTINATION THIS TRIP, BASED ON BEST RESULTS LAST OPENING ACT,,ATRIB(8).EQ.7,BUTD; ACT,,ATRIB(8).EQ.3,JUAN; ACT,,ATRIB(8).EQ.4,JOHN; ACT,,ATRIB(8).EQ. i,MISS; WAIT IN PORT THIS TRIP MISS GOON,i; ACT/i i,72,,SKIP; WAIT IN PORT BUTDALE BUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT ACT,ATRIB(9),,; SAIL OUT TO FISH CALCULATE FUEL CONSUMED ASSIGN, ATRIB(iO)=ATRIB(3)*ATRIB(9); WAiT FOR OPENING, ON GROUNDS LOC1 AWAIT(1),AREA1,i; ASSIGN, ATRIB(li)=GAMMA(XX(5),XX(6)); SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(13)=ATRIB(ii)*XX(7); CALCULATE VALUE OF FISH ACT/i,9.O,,; BUTEDALE, 9 HOURS ASSIGN, XX(40)=XX(40)i-1; NO. TRIPS TO AREA 1 ACT,,,HOME; JUAN DE FUCA STRAIT JUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT ACT,ATRIB(9),,; SAIL OUT TO FISH ASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMED WAIT FOR OPENING, ON GROUNDS 221 LOC2 AWAIT(2),AREA2,1; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(11)=GAMMA(XX(15),XX(16)); CALCULATE VALUE OF FISH ASSIGN, ATRIB(13)=ATRIB(11)*XX(17); JUAN DE FUCA, 9 HOURS ACTI2,9.O,,; NO. TRIPS TO AREA 2 ASSIGN, XX(41)=XX(41)+1; ACT,,,HOME; JOHNSTONE STRAIT JOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIP CALCULATE SAILING TIME ASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1); SAIL OUT SAIL OUT TO FISH ACT,ATRIB(9),,; CALCULATE FUEL CONSUMED ASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); WAIT FOR OPENING, ON GROUNDS LOC3 AWAIT(3),AREA3,1; SAMPLE DAILY CATCH DIST. ASSIGN, ATRIB(1 l)=GAMMA(XX(25),XX(26)); CALCULATE VALUE OF FISH ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27); ACT/3,9.O,,; JOHNSTONE ST, 9 HOURS NO. TRIPS TO AREA 1 ASSIGN, XX(42)=XX(42)i-1; ACT,,,HOME; HOME 000N,1; ASSIGN, ATRIB(1O)=ATRIB(lO)+ATRIB(4)*9.O; UPDATE FUEL CONSUMED, FISHING ACT,ATRIB(9),,; SAIL HOME ASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMED, SAILING ACT,,ATRIB(1 1).LE.XX(43), SKIP; RECORD NEW MAXIMUM CATCH ACT,,ATRIB(11).GT.XX(43),; ASSIGN, XX(43)=ATRIB(1 1),; SKIP 000N,1; DATA COLLECrION, VESSEL INFORMATION FOR THIS TRIP COLCT,ATRIB(1O),FUEL,; RECORD FUEL THIS TRIP ASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COST OF FUEL THIS TRIP COLCT,ATRIB(12),CFUEL,,; COLCT,ATRIB(11),FISH,20/O/500; WT. OF FISH THIS TRIP COLCT, ATRIB(13),VFISH,; VALUE OF FISH THIS TRIP ASSIGN, ATRIB(14)=ATRIB( 1 3)-ATRIB( 12); SURPLUS, FISH-FUEL, DOLLARS COLCT, ATRIB(14),PROFIT,20/O/1500, 1; COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000 ACT,,ATRIB(14).GE.6000,NXT; 222 ACT,,ATRIB(14).LT.6000,; ASSIGN, XX(44)=XX(44)+ 1,; NXT 000N,1; SELECT DESTINATION FOR NEXT WEEK, BASED ON HIGHEST MEAN PROFIT ASSUMES INFORMATION KNOWN FOR ALL THREE AREAS, AND SELECTS MAXIMUM PROFIT AREA, PROVIDED IT IS GREATER THAN REQUIRED DAILY MINIMUM XX(2), XX(12) AND XX(22) ARE PROFITS BASED ON AREA DATA THIS WEEK XX(8) IS DUMMY VARIABLE OF MAGNITUDE OF MAXIMUM PROFIT XX(9) IS DUMMY VARIABLE TO LOCATE AREA WITH MAXIMUM PROFIT GIVEN CHOICE BETWEEN EQUAL AREAS, THEN NEAREST IS TAKEN CALCULATE PROFIT FOR AREA 6, IF WE HAD FISHED THERE ASSIGN,XX(2)=XX(4)*XX(7)ARRAY( 1 ,7)*ATRIB(3)*ATRIB(6)/ATRIB(1 ),; ASSIGN,XX(2)=XX(2)-ARRAY(1 ,7)*ATRIB(5)*ATRIB(6)/ATRIB(1 ),; ASSIGN,XX(2)=XX(2)9*ATRIB(4)*ATRIB(6),; CALCULATE PROFIT FOR AREA 2, IF WE HAD FISHED THERE ASSIGN,XX(1 2)=XX(14)*XX(17)ARRAY(1 ,3)*ATRIB(3)*ATRIB(6)/ATRIB(1),; ASSIGN,XX(1 2)=XX(1 2)-ARRAY(1 ,3)*ATRIB(5)*ATRIB(6)/ATRIB(1 ),; ASSIGN,XX(1 2)=XX(1 2)9*ATRIB(4)*ATRIB(6),; CALCULATE PROFIT FOR AREA 3, IF WE HAD FISHED THERE ASSIGN,XX(22) =XX(24)*XX(27)ARRAY( 1 ,4)*ATRIB(3)*ATRIB(6)/ATRIB(1 ),; ASSIGN,XX(22)=XX(22)-ARRAY(1 ,4)*ATRIB(5) *ATPJB(6)/ATRIB(1 ),; ASSIGN,XX(22)=XX(22).9*ATRIB(4)*ATRIB(6),; FIND BEST AREA, BASED ON LARGEST PROFIT ASSIGN STARTING VALUES OF DUMMY VARIABLES ASSIGN,XX(8)=XX(12), XX(9)=3,; ACT,,XX(22).LE.XX(8),A3; ACT,,XX(22).GT.XX(8),; ASSIGN,XX(8)=XX(22),XX(9)=4,; A3 GOON,1; ACT,,XX(2).LE.XX(8),GOA; ACT,,XX(2).GT.XX(8),; ASSIGN,XX(8)=XX(2),XX(9)=7,; GOA GOON, 1; FISH NEXT TIME IF INCOME GT $3000 ACT,,XX(8).LE.3000,NOGO; ACT,,XX(8).GT.3000,; ASSIGN,ATRIB(8)=XX(9),; ACT,,,PORT 223 N000 000N,1; ASSIGN,ATRIB(8)= 1,; ACT,,,PORT; TERM; *** DATA GOES HERE *** CATCH RATES AS SEEN BY BOAT, YEAR IS 1988, FROM CATCH DATA AVERAGE FISH PRICES OVER YEARS CREATE,168,,,,; ASSIGN,XX(3)=48,; TIME TO OPENING CATCH RATES AND PRICES ASSIGN,XX(7)=1.472,; ASSIGN,XX(17)=3.076,; ASSIGN,XX(27)=2.629,; AVERAGE $/KG, BUTEDALE AVERAGE $/KG, JUAN DE FUCA AVERAGE $IKG, JOHNSTONE UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALE ASSIGN,XX(4)=GAMA(1 145.92,6.31),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(6)=3.055,; ASSIGN,XX(5)=XX(4)/XX(6),; SHAPE PARAMETER SCALE PARAMETER UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DE FUCA ASSIGN,XX(14)=GAMA(449.25,3. 18),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(16)=5.005,; ASSIGN,XX(1 5)=XX( 14)IXX(16),; SHAPE PARAMETER SCALE PARAMETER UNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JOUNSTONE ST. ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTION PARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAY ABOVE ASSIGN,XX(26)=2. 195,; ASSIGN,XX(25)=XX(24)/XX(26),; SHAPE PARAMETER SCALE PARAMETER 224 *** *** ** * * ** * OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICE WAIT FOR OPENING ACT,XX(3),,; OPEN AREA, BUTEDALE OPEN, AREA1,,; OPEN AREA, JUAN DE FUCA OPEN, AREA2,,; OPEN AREA, JOHNSTONE OPEN, AREA3,,; DURATION OF OPENING ACT,8,,; CLOSE, AREA1,,; CLOSE AREA CLOSE AREA CLOSE, AREA2,,; CLOSE, AREA3,,; CLOSE AREA ASSIGN,ATRIB(1)= 160-XX(3)-8 ACT,ATRIB(1),; ACT,8,,; TERM; OPENINGS & CLOSINGS, ONE WEEK INTERVALS MODIFY OPENINGS FOR SEASON, RATHER THAN FOR WEEK CREATE,4200,,,,; REP GOON,1; OPEN, HOME,; ACT,56,,; CLOSE, HOME,1; ASSIGN, ATRIB(1)=ATRIB(1)+1,1; SEASON REPRESENTS 25 OPENINGS (168 SEASONS COUNT TRIPS * 25 = 4200 HRS), MODEL RUNS FOR 100 ACT,1 12,ATRIB(1).LT.25,REP; ACT,1 12,ATRIB(1).GE.25,; COLCT, XX(40),TRIP1,2610/1; TOTAL NO. TRIPS, AREA 1 COLCT, XX(41),TRIP2,26/0/1; TOTAL NO. TRIPS, AREA 2 COLCT, XX(42),TRIP3,2610/1; TOTAL NO. TRIPS, AREA 3 COLCT, XX(43),MAXCAT,20/10000/1000; MAXIMUM CATCH THIS SEASON COLCT, XX(44),RISK,26/0/1; NUMBER OF TRIPS IT. $6000 ASSIGN, XX(40)=0,; ASSIGN, XX(41)=0,; ASSIGN, XX(42)=0,; ASSIGN, XX(43)=0,; ASSIGN, XX(44)=0,; REZERO SEASON VALUES TERM, 100; ENDNETWORK; FIN; 225 1 II SLAM SUMMARY SIMULATION PROJECT FORECAST MODEL BY DAVID 5/28/1991 DATE REPORT RUN NUMBER .4200E+06 CURRENT TIME STATISTICAL ARRAYS CLEARED AT TIME 1OF 1 0000E+OO **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE STANDARD COEFF. OF DEVIATION VARIATION .301E+04 .121E+04 .544E+04 .917E+04 .797E+04 .153E+02 .184E+01 .772E+01 .193E+05 .126E+02 FUEL CFUEL FISH VFISH PROFIT TRIP1 TRIP2 TRIP3 MAXCAT RISK .131E+04 .522E+03 .500E+04 .763E+04 .751E+04 .256E+01 .141E+01 .237E+01 .713E+04 .279E+01 .433E+00 .433E+00 .918E+O0 .832E+OO .942E+00 .167E+00 .764E+00 .306E+00 .370E+00 .221E+00 — MINIMUM VALUE MAXIMUM VALUE .109E+04 .436E+03 .264E+02 .812E+02 .135E+04 .800E+01 .000E+00 .200E+01 .905E+04 .500E+01 .405E+04 .162E+04 .440E+05 .648E+05 .634E+05 .220E+02 .600E+01 .160E+02 .440E+05 .200E+02 NO.OF OBS 2500 2500 2500 2500 2500 100 100 100 100 100 **FILE STATISTICS** FILE NUMBER 1 2 3 4 5 6 7 AVERAGE LENGTH LABEL/TYPE LOC1 LOC2 LOC3 PORT AWAIT AWAIT AWAIT AWAIT CALENDAR .069 .018 .070 .533 .000 .000 4.310 STANDARD DEVIATION .254 .132 .255 .499 .000 .000 .636 MAXIMUM LENGTH CURRENT AVERAGE LENGTH WAIT TIME 1 1 1 1 0 0 6 0 0 0 0 0 0 5 19.000 40.500 38.000 89.475 .000 .000 30.144 **REGULAR ACTIVITY STATISTICS** ACTIVITY INDEX/LABEL 1 2 3 11 BUTEDALE, JUAN DE FUCA JOHNSTONE ST WAIT IN PORT AVERAGE UTILIZATION .0329 .0039 .0165 .0019 STANDARD DEVIATION .1782 .0627 .1276 .0434 MAXIMUM CURRENT UTIL UTIL 1 1 1 1 0 0 0 0 ENTITY COUNT 1533 184 772 11 226 **GATE STATISTICS* * GATE LABEL GATE NUMBER CURRENT STATUS HOME AREA1 AREA2 AREA3 1 2 3 4 OPEN .3333 CLOSED .0476 .0476 CLOSED .0476 CLOSED **HISTOGP NUMBER 3** FISH 1 OBS RELA FREQ FREQ UPPER CELL LIM 0 + 0 108 182 207 194 157 136 127 136 112 105 88 98 79 66 74 76 47 44 48 42 374 ——— .000 .043 .073 .083 .078 .063 .054 .051 .054 .045 .042 .035 .039 .032 .026 .030 .030 .019 .018 .019 .017 .150 PCT. OF TIME OPEN .000E+00 .500E+03 .100E+04 .150E+04 .200E+04 .250E+04 .300E+04 .350E+04 .400E+04 .450E+04 .500E+04 .550E+04 .600E+04 .650E+04 .700E+04 .750E+04 .800E+04 .850E+04 .900E+04 .950E+04 .100E+05 INF 40 20 + + 60 + + + 80 + + 100 + + + + + **** C + C **** ÷**** + C + C + C *** + C *** + C ** + C + C + C + C + C + C * * + C + + C * + C + C + * + C + + C + ******* + 0 + + C + 20 + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE FISH .544E+04 STANDARD COEFF. OF DEVIATION VARIATION .500E+04 .918E+00 MINIMUM VALUE .264E+02 MAXIMUM VALUE .440E+05 NO.OF OBS 2500 227 * *HISGP 1 NUMBER 5** PROFIT OBS RELA FREQ FREQ UPPER CELL LIM 0 + 61 267 341 330 261 234 184 168 114 100 100 67 52 39 29 32 19 22 10 10 14 46 .024 .107 .136 .132 .104 .094 .074 .067 .046 .040 .040 .027 .021 .016 .012 .013 .008 .009 .004 .004 .006 .018 ——-. .000E+00 .150E+04 .300E+04 .450E+04 .600E+04 .750E+04 .900E+04 .105E+05 .120E+05 .135E+05 .150E+05 .165E+05 .180E+05 .195E+05 .210E+05 .225E+05 .240E+05 .255E+05 .270E+05 .285E+05 .300E+05 INF 20 + 40 + + 80 60 + + + + 100 + + + + + C + C + C ******* ***** + C + C + C + C *** + C ** + ** C + C +* + C + C C * + + + C * * + C C C + + + + + + + + +* + 0 C + + 20 + + + + 40 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE PROFIT .797E+04 STANDARD COEFF. OF DEVIATION VARIATION .751E+04 .942E+00 - MINIMUM VALUE MAXIMUM VALUE .135E+04 .634E+05 NO.OF OBS 2500 228 **HISTOGP NUMBER 6** TRI P1 1 OBS RELA FREQ FREQ UPPER CELL LIM 0 20 + 0 0 0 0 0 0 0 0 1 0 2 3 8 7 17 15 17 9 9 7 4 0 1 0 0 0 0 0 .000 .000 .000 .000 .000 .000 .000 .000 .010 .000 .020 .030 .080 .070 .170 .150 .170 .090 .090 .070 .040 .000 .010 .000 .000 .000 .000 .000 .000E+00 .100E+01 .200E+01 .300E+01 .400E+01 .500E+01 .600E+01 .700E+01 .800E+01 .900E+01 .100E+02 .11OE+02 .120E+02 .130E+02 .140E+02 .150E+02 .160E+02 .170E+02 .180E+02 .190E+02 .200E+02 .210E+02 .220E+02 .230E+02 .240E+02 .250E+02 .260E+02 INF + 40 + + 60 + + 80 + 100 + + + + + + + + + + + + + + + + + + + + + + +* + + + C + C **** + **** C + C + ******** C + ********* C + C + C + **** C + + C C C C C C + + + + + + + 100 + 0 + + 20 + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE TRIP1 .153E+02 STA11DARD COEFF. OF DEVIATION VARIATION .256E+01 .167E+00 MINIMUM VALUE MAXIMUM VALUE .800E+01 .220E+02 NO.OF OBS 100 229 **HISTOGPM NUMBER 7** TRIP2 1 OBS RELP FREQ FREQ UPPER CELL LIM 0 + 19 27 23 17 11 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .190 .270 .230 .170 .110 .020 .010 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000E+00 .100E+01 .200E+01 .300E+01 .400E+01 .500E+01 .600E+01 .700E+01 .800E+01 .900E+01 .100E+02 .11OE+02 .120E+02 .130E+02 .140E+02 .150E+02 .160E+02 .170E+02 .180E+02 .190E+02 .200E+02 .210E+02 .220E+02 .230E+02 .240E+02 .250E+02 .260E+02 INF 20 + + 60 40 + + + 80 + + 100 + + C +************** + C ************ + C ********* + C C C C C C C C C C C C C * + + + + + + + + + + + + c + C C C C C C C C C + + + + + + + + + ——— + 100 0 + + +********* + + 20 + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE TRIP2 .184E+01 STANUARD COEFF. OF DEVIATION VARIATION .141E+01 .764E+00 MINIMUM VALUE MAXIMUM VALUE .000E+00 .600E+01 NO.OF OBS 100 230 **HI5GP NUMBER 8** TRIP3 OBS RELA FREQ FREQ UPPER CELL LIM 0 + 0 0 2 1 4 8 14 18 20 12 13 2 3 1 1 0 1 0 0 0 0 0 .000 .000 .020 .010 .040 .080 .140 .180 .200 .120 .130 .020 .030 .010 .010 .000 .010 .000 .000 .000 .000 .000 0 0 0 0 0 .000 .000 .000 .000 .000 o .ooo 0 + 60 40 + .000E+00 + .100E+01 + .200E+01 + .300E+O1 +C .400E+01 C .500E+01 **** C .600E+01 ******* .700E+01 ********* .800E+01 ********** .900E+01 .100E+02 ****** .11OE+02 + .120E+02 * .130E+02 + .140E+02 + .150E+02 + .160E+02 + .170E+02 + .180E+02 + .190E+02 + .200E+02 + .210E+02 + .220E+02 + .230E+02 + .240E+02 + .250E+02 + .260E+02 + INF + + 100 20 + + + + 80 + + + 100 + + + + + + + + C + 20 + C + C + C + C + C + C + C+ C+ C C C C C C C C C C C C + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE TRIP3 .772E+01 STANDARD COEFF. OF DEVIATION VARIATION .237E+01 .306E+00 MINIMUM VALUE .200E+01 MAXIMUM VALUE .160E+02 NO.OF OBS 100 231 * *HISP 1 NUMBER 9** MAXCAT OBS RELA FREQ FREQ UPPER CELL LIM 0 20 + 4 3 3 8 7 5 8 4 6 10 5 4 5 4 5 4 1 2 0 2 0 10 .040 .030 .030 .080 .070 .050 .080 .040 .060 .100 .050 .040 .050 .040 .050 .040 .010 .020 .000 .020 .000 .100 .100E+05 .11OE+05 .120E+05 .130E+05 .140E+05 .150E-’-05 .160E+05 .170E+05 .180E+05 .190E+05 .200E+05 .210E+05 .220E+05 .230E+05 .240E+05 .250E+05 .260E+05 .270E+05 .280E+05 .290E+05 .300E+05 INF 60 40 + + + + + 80 + + 100 + + + + + C * + C + C + C **** + C *** + C + C + c + +***** C + +*** C + C +** + C +*** +** + C + c +** + +** c + + C + +* c + + C + + C C + + 100 0 + + C +***** ——— + + 20 + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE MAXCAT .193E+05 STANDARD COEFF. OF DEVIATION VARIATION .713E+04 .370E+00 MINIMUM VALUE .905E+04 MAXIMUM VALUE .440E+05 NO.OF OBS 100 232 **HIS NUNBER1O** RISK 1 OBS RELA FREQ FREQ UPPER CELL LIM 0 0 0 0 0 0 1 2 1 3 4 7 16 16 16 10 10 3 8 2 0 1 0 0 0 0 0 0 0 .000 .000 .000 .000 .000 .010 .020 .010 .030 .040 .070 .160 .160 .160 .100 .100 .030 .080 .020 .000 .010 .000 .000 .000 .000 .000 .000 .000 .000E+00 .100E+01 .200E+01 .300E+01 .400E+01 .500E+01 .600E+01 .700E+01 .800E+01 .900E+01 .100E+02 .11OE+02 .l2OEi-02 .130E+02 .140E+02 .150E+02 .160E+02 .170E+02 .180E+02 .190E+02 .200E+02 .210E+02 .220E+02 .230E+02 .240E+02 .250E+02 .260E+02 INF 40 20 + + + + + 80 60 + + 100 + + + + + + + + + + + + + + + + + + + C * + C ** + C + C + C + C + C + c +***** + +***** C + + C + + + + + + + + + + ——— + 100 0 + C+ C C C C C C C C C C + + 20 + + 40 + + 60 + + 80 + + 100 **STATISTICS FOR VARIABLES BASED ON OBSERVATION** MEAN VALUE RISK .126E+02 STANDARD COEFF. OF DEVIATION VARIATION .279E+01 .221E+00 MINIMUM VALUE MAXIMUM .500E+01 .200E+02 VALUE NO.OF OBS 100
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Simulation of voyage economics for salmon seine fishing boats in British Columbia Molyneux, William David 1992
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Title | Simulation of voyage economics for salmon seine fishing boats in British Columbia |
Creator |
Molyneux, William David |
Date Issued | 1992 |
Description | It is important to know the likely income to a fishing vessel, so that it can be operated as a profitable concern for its owner. Most work on fishing vessel design optimization has used average catch size and income as the measure of economic performance. Whilst this analysis is adequate when cost minimization is being considered, it is deficient for developing strategies for maximizing income. One analysis method which allows for the observed random variation in fishing operations is system simulation. It is the intention of this thesis to demonstrate that simulation modelling can be developed into a useful analysis tool for predicting fishing vessel operating economics. The same model can then be incorporated into expert system based design techniques. A simulation model for salmon seine fishing in British Columbia was developed which allowed for variation in catch rates with fishing locations, the distance between the locations and constraints on the fishing process. The vessel operational profile used in the simulation was based on a review of previous research, discussions with fishermen and industry representatives as well as previously unpublished data on vessel mobility and fuel consumption for a specific boat. The other data used in the simulation were developed from records of catches, kept by the Department of Fisheries and Oceans. These data were analyzed by each geographic area, to give the distribution of catch per day, income per day, length of voyage and number of trips per year for the four years 1987 to 1990. The model of the voyage economics was developed for three alternative decision rules. These were to always fish one geographic area (Stationary Model), to select the area which had the best performance during the last opening (Forecast Model) and to select the areas at random (Random Model). The simulation was run for each rule and the results were compared to observations derived from the performance of the actual fleet, for one year of observations. It was found that each simulated decision method was reflective of certain parts of the actual fleet. The results of additional simulations gave valuable insights into the most profitable methods of operating salmon seine fishing vessels. It was predicted that the Forecast Model provided an income 37 percent higher than average, based on four years of real catch data. However, a lower than average performance was predicted when the profit at each area was close to the mean value for all the areas in the model. The simulation quantifies the observed reluctance of skippers to change fishing locations. It was predicted that the vessels in the fleet had hold sizes which were between 60 and 100 percent bigger than was required, based on the most probable fishing trip. It was also predicted that the rate or return, based on the catch data and the investment in the boat, was much lower than would be expected for a high risk venture. When two or more boats operated together and pooled the operating expenses and income, the simulations showed that the risk of the income for the voyage being less than the expenses was considerable reduced. The biggest benefit was for two boats to be fishing together. This factor is important when the number of opportunities to fish are small, as observed in the British Columbia Salmon Season. |
Extent | 3950050 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-02-14 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0081020 |
URI | http://hdl.handle.net/2429/4604 |
Degree |
Master of Applied Science - MASc |
Program |
Mechanical Engineering |
Affiliation |
Applied Science, Faculty of Mechanical Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 1992-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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