Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Simulation of voyage economics for salmon seine fishing boats in British Columbia Molyneux, William David 1992

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1992_fall_molyneux_william.pdf [ 3.77MB ]
Metadata
JSON: 831-1.0081020.json
JSON-LD: 831-1.0081020-ld.json
RDF/XML (Pretty): 831-1.0081020-rdf.xml
RDF/JSON: 831-1.0081020-rdf.json
Turtle: 831-1.0081020-turtle.txt
N-Triples: 831-1.0081020-rdf-ntriples.txt
Original Record: 831-1.0081020-source.json
Full Text
831-1.0081020-fulltext.txt
Citation
831-1.0081020.ris

Full Text

SIMULATION OF VOYAGE ECONOMICS FORSALMON SEINE FISHING BOATS IN BRiTISH COLUMBIAbyWILLIAM DAVID MOLYNEUXB. Sc. (Hons.) The University of Newcastle-Upon-Tyne, 1977A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinFACULTY OF GRADUATE STUDIES(Department of Mechanical Engineering)We accept this thesis as conformingto the required standardTHE UNWERSITY OF BRITISH COLUMBIASeptember 1992© William David Molyneux, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Jc’c IThe University of British ColumbiaVancouver, CanadaDate 5 CcLl>-.4 CD)DE.6 (2/88)11AbstractIt is important to know the likely income to a fishing vessel, so that it can beoperated as a profitable concern for its owner. Most work on fishing vesseldesign optimization has used average catch size and income as the measure ofeconomic performance. Whilst this analysis is adequate when costminimization is being considered, it is deficient for developing strategies formaximizing income. One analysis method which allows for the observedrandom variation in fishing operations is system simulation. It is the intentionof this thesis to demonstrate that simulation modelling can be developed into auseful analysis tool for predicting fishing vessel operating economics. Thesame model can then be incorporated into expert system based designtechniques.A simulation model for salmon seine fishing in British Columbia was developedwhich allowed for variation in catch rates with fishing locations, the distancebetween the locations and constraints on the fishing process. The vesseloperational profile used in the simulation was based on a review of previousresearch, discussions with fishermen and industry representatives as well aspreviously unpublished data on vessel mobility and fuel consumption for aspecific 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 byeach geographic area, to give the distribution of catch per day, income perday, length of voyage and number of trips per year for the four years 1987 to1990.111The model of the voyage economics was developed for three alternativedecision rules. These were to always fish one geographic area (StationaryModel), to select the area which had the best performance during the lastopening (Forecast Model) and to select the areas at random (Random Model).The simulation was run for each rule and the results were compared toobservations derived from the performance of the actual fleet, for one year ofobservations. It was found that each simulated decision method was reflectiveof certain parts of the actual fleet.The results of additional simulations gave valuable insights into the mostprofitable methods of operating salmon seine fishing vessels. It was predictedthat the Forecast Model provided an income 37 percent higher than average,based on four years of real catch data. However, a lower than averageperformance was predicted when the profit at each area was close to the meanvalue for all the areas in the model. The simulation quantifies the observedreluctance of skippers to change fishing locations. It was predicted that thevessels in the fleet had hold sizes which were between 60 and 100 percentbigger than was required, based on the most probable fishing trip. It was alsopredicted that the rate or return, based on the catch data and the investmentin 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 expensesand income, the simulations showed that the risk of the income for the voyagebeing less than the expenses was considerable reduced. The biggest benefitwas for two boats to be fishing together. This factor is important when thenumber of opportunities to fish are small, as observed in the British ColumbiaSalmon Season.ivTABLE OF CONTENTSAbstract iiList of Tables viiiList of Figures xiAcknowledgements xviChapter 1. Introduction 1Chapter 2. Salmon Seine Fishing in British Columbia 72.1 Development of Fishing Techniques 72.2 Common Vessel Operating Practices 92.3 Constraints on Fishing Operations 122.3.1 Location & Openings 122.3.2 Fishing Gear 142.3.3 Vessel Dimensions 152.4 Current Fleet Size and Vessel Dimensions 172.5 Trends in Vessel Income with Time 192.6 Effect of Vessel Parameters on Income 282.7 Effect of Motivation and Mobility on Income 292.8 Important Factors to Include in a Simulation Model 33Chapter 3. Operational Analysis of a Salmon Seine VesselBased on Catch and Voyage Data 353.1 Data Collection for Voyage Profile Analysis 373.2 Voyage Profile Analysis 383.2.1 Overall Operation 393.2.2 Detailed Analysis of Transit Portion of Voyage 443.2.3 Fishing Portion of Voyage 463.2.4 Fuel Consumption 513.3 Summary of Observations on a Seine Vessel 52VChapter 4. Determination of Catch and Income Datafor Salmon Seine Fishing Boats 544.1 Data Required for Simulation Model 564.2 Summary of Data Available for All DFO Areas 574.3 Translation of Catch Data to Income 624.4 Discussion of DFO Data 674.5 Nature of Distribution of Daily Catch 744.6 Variation in Mean Catch per Day Over Full Season 804.7 Simplification of Daily Catch Distributions 844.8 Summary of Catch and Income Data 914.9 Discussion of Analysis in Relation to Simulation 93Chapter 5. Development and Testing of a Simulation Modelfor Salmon Seine Fishing 955.1 Information Required for Simulation Model 965.1.1 Vessel Technical and Operational Parameters 955.1.2 Spatial Distribution of Fishing Grounds 985.1.3 Openings and Other Constraints on Fishing 995.1.4 Catch Data for Fishing Areas 1005.1.5 Operational Profile of Vessel 1015.2 Development of Stationary Model 1045.2.1 Data Available from Observations on the Fleet 1055.2.2 Validation of Stationary Model against Observations 1085.3 Development of Simulation of Mobile Boats 1125.3.1 Random Model 1125.3.2 Forecast Model 1165.3.3 Validation of Forecast Model 1195.4 Summary 125viChapter 6. Sensitivity of Forecast Model to Catch Rate at Furthest Area 1286.1 Parameters for Study 1286.2 Results of Sensitivity Study 1306.3 Discussion of Results 1366.4 Conclusions 139Chapter 7. Sensitivity of Forecast Model to Number ofBoats Operating Together 1417.1 Modifications to Simulation Model 1427.2 Discussion of Simulation Results 1437.2.1 Voyage Economics 1437.2.2 Transportation Capacity 1497.3 Conclusions 158Chapter 8. Performance of Forecast SimulationBased on Four Years of Observed Catch Data 1608.1 Results of Simulations for Four Years of Catch Data 1628.1.1 Variation in Profitability 1638.1.2 Variation in Risk 1678.1.3 Variation in Size of Vessel 1688.2 Comparison of Results of Simulation with Observations 1708.3 Vessel Design Features Derived from the Simulations 1738.3.1 Fuel Consumption and Mobility 1738.3.2 Empirical Relationships Between Mean Catch and Hold Size 1748.4 Long Term Economic Predictions 1788.4 Summary 182Chapter 9. General Discussion and Further Work 1849.1 Summary 1849.2 Discussion on the Use of Simulationfor Studying Fishing Boat Economics 1909.3 Future Uses of Simulation in Fishing Vessel Analysis 191viiReferences 195Appendix 1. Methods for Fitting Probability Density Functions toObserved Catch Data 197Appendix 2. Description of SLAM II Computer Program forStationary Model 201Appendix 3. Description of SLAM II Computer Program forRandom Model 211Appendix 4. Description of SLAM II Computer Program forForecast Model 217viiiLIST OF TABLESTable I Comparison of Average Dimensions forSalmon Seine Vessel Fleets 19Table II Summary of Annual Performance, Salmon Seine Fleet,1979 to 1988 20Table III Summary of Operating Economics, Salmon Seine Vessels, 1988 26Table IV Summary of Measurement Methods for Voyage Data 38Table V Summary of Voyage Times 41Table VI Summary of Vessel Activity 43Table VII Voyage Profiles for Seine Fishing Vessel 44Table VIII Detailed Analysis of Transit Data 46Table IX Detailed Analysis of Fishing Portion of Voyages, 1989 47Table X Total Catch for DFO Geographic Areas, by Species, 10 Year Averages,1979 to 1988 55Table XI Summary of Annual Catch Data for Each Fishing Area,by Year 1987 to 1990 59Table XII Summary of Length of Season and Average Vessel Activity,by Fishing Area, 1987 to 1990 61Table XIII Summary of Length of Trip for Each Fishing Area, 1987 to 1990 63Table XIV Average Dollar Value for Salmon by Species, 1987 and 1988 64Table XV Average Length of Vessels Fishing in Each Area, 1987 to 1990 73Table XVI Summary of Parameters for Probability Density Functions,Daily Catch Data 79Table XVII Summary of Fitted Distributions to Seasonal Catch Data, for EachFishing Area, 1987 to 1990 81ixTable XVIII Variation in Shape Parameter, X, Between Years, for Three FishingAreas, 1987 to 1990 86Table XIX Summary of Variation in Catch Rate with Time, 1987 to 1990 90Table XX Distance Between Port and Fishing LocationsUsed in Simulation Model 100Table XXI Stationary Model, Comparison of Observed Daily Catch Rate withSimulated Results 106Table XXII Stationary Model, Comparison of Observed Daily Income Rate withSimulated Results 106Table XXIII Observed Catch and Income Data, All Fleet 113Table XXIV Simulated Catch and Income Data, Random Model 113Table XXV Simulated Catch and Income Data, Forecast Model 113Table XXVI Observed Catch and Income Data, Boats Avoiding Area 12 113Table XXVII Results of Simulation Models, 1988 Data 127Table XXVIII Data Used in Sensitivity Study for Forecast Model 130Table XXIX Sensitivity Study, Results of Forecast Model 132Table XXX Sensitivity Study, Results of Stationary Model 132Table XXXI Sensitivity Study, Results of Random Model 134Table XXXII Effect of Number of Boats Fishing Togetheron Operating Economics 144Table XXXIII Fitted Probability Density Functions to Catch Data, Single Boat 151Table XXXIV Estimated Parameters for Fitted Distributions for DifferentNumbers of Boats 155Table XXXV Summary of Simulation Results for Stationary Models,Four Years, 1987 to 1990 161Table XXXVI Summary of Simulation Results for Mobile Models,Four Years, 1987 to 1990 162xTable XXXVII Simulated Catch Data for Four Years, 1987 to 1990Non-dimensionalized by Random Model 163Table XXXVIII Comparison of forecast Model with Best Possible Area,1987 to 1990, Non-dimensionalized by Random Model 165Table XXXIX Proportion of Total Trips to Each Area, Forecast Model 174Table XXXX Parameters Fitted to Maximum Catch Distribution,Assuming a Gumbel Distribution 177Table XXXXJ Calculation of Payback Period 179Table XXXXII Calculation of Internal Rate of Return 181xiLIST OF FIGURESFigure 1 Statistical Area Map, Northern British Columbia 11Figure 2 Statistical Area Map, Southern British Columbia 13Figure 3 Variation in Overall Length with Time, Salmon Seiners 16Figure 4 Variation in Brake Horsepower with Time, Salmon Seiners 16Figure 5 Variation in Overall Length with Time, Salmon/HerringSeiners 18Figure 6 Variation in Brake Horsepower with Time, Salmon/HerringSeiners 18Figure 7 Regression of Total Catch by Salmon Seiners against Year,1979 to 1988 21Figure 8 Regression of Number of Deliveries by Salmon Seiners againstYear, 1979 to 1988 21Figure 9 Regression of Average Catch per Delivery against Year, SalmonSeine Vessels, 1979 to 1988 23Figure 10 Regression of Normalized Dollars per Delivery against Year,Salmon Seine Vessels, 1979 to 1988 23Figure 11 Average Number of Deliveries per Year, Salmon Seine, 1979 to1988 25Figure 12 Seine Fishing Boat Voyages, September/October 1989 40Figure 13 Vessel Activity Profile, Ship Speed and Engine RPM againstTime 42Figure 14 Histogram of Vessel Speed, Sampled at Five Minute Intervals 42Figure 15 Ship Movement During Fishing Activity, Latitude andLongitude, Juan de Fuca, 89-09-05 45Figure 16 Ship Movement During Fishing Activity, Latitude andLongitude, Johnstone Strait, 89-09-05 45xiiFigure 17 Ship Movement During Fishing Activity, Latitude andLongitude, Bella Bella, 89-09-05 49Figure 18 Fuel Consumption against RPM, Based on One Hour Averages forAll Voyages 49Figure 19 Comparison of Regression Equations for Converting Catch toIncome, Johnstone Strait, 1987 65Figure 20 Fishing Vessel Activity Profile, 1987, All Areas 70Figure 21 Fishing Vessel Activity Profile, 1988, All Areas 70Figure 22 Fishing Vessel Activity Profile, 1989, All Areas 72Figure 23 Fishing Vessel Activity Profile, 1990, All Areas 72Figure 24 Gamma Distribution Fitted to Catch/Day, August 10, JohnstoneStrait, High Catch Rate 76Figure 25 Gamma Distribution Fitted to CatchJDay, August 24, JohnstoneStrait, Medium Catch Rate 76Figure 26 Gamma Distribution Fitted to Catch/Day, September 23,Johnstone Strait, Low Catch Rate 78Figure 27 Comparison of Probability Density Functions Fitted toObserved Data 78Figure 28 Comparison of Observed and Fitted Cumulative Distributionsfor Butedale 82Figure 29 Comparison of Observed and Fitted Cumulative Distributions forJuan de Fuca 82Figure 30 Comparison of Observed and Fitted Cumulative Distributions forJohnstone Strait 83Figure 31 Mean Catch per Day against Standard Deviation, JohnstoneStrait, 1987 to 1990 85xiiiFigure 32 Mean Catch per Day against Standard Deviation, Juan de Fuca,1987 to 1990 85Figure 33 Variation in Shape Parameter, X, with Mean Catch per Day,Johnstone Strait 87Figure 34 Variation in Shape Parameter, a, with Mean Catch per Day,Johnstone Strait 87Figure 35 Variation in Mean Catch per Day with Day, Butedale 1987 89Figure 36 Variation in Mean Catch per Day with Day, Juan de Fuca 1987 89Figure 37 Variation in Mean Catch per Day with Day, Johnstone St 1987 92Figure 38 Comparison of Mean Catch per Day, Observations for Each Areaand Stationary Simulation 107Figure 39 Comparison of Distribution of Observed Catch per Day withSimulated Values, Butedale, 1988 107Figure 40 Comparison of Distribution of Observed Catch per Day withSimulated Values, Juan de Fuca, 1988 109Figure 41 Comparison of Distribution of Observed Catch per Day withSimulated Values, Johnstone Strait, 1988 109Figure 42 Comparison of Mean Income per Day, Observations for EachArea with Stationary Simulation 111Figure 43 Comparison of Average Catch per Day and Average Income perDay, Total Fleet with Random Simulation 111Figure 44 Comparison of Number of Trips to Each Area, 1988, Total Fleetwith Random Simulation 115Figure 45 Overall Fleet Performance, 1988, Comparison of Distribution ofObserved Catch per Day with Random Simulation 115Figure 46 Comparison of Mean Catch & Income per Day, Random andForecast Simulations, 1988 118xivFigure 47 Comparison of Number of Trips to Each Area, Random andForecast Simulations 118Figure 48 Comparison of Average Catch and Income per Day, SubsetAvoiding Johnstone Strait and Forecast Model 120Figure 49 Comparison of Number of Trips to Each Area, Subset AvoidingJohnstone Strait and Forecast Model 120Figure 50 Comparison of Distribution of Observed Catch per Day, Subset ofFleet with Simulated Values, Forecast Model 122Figure 51 Comparison of Mean Peak Catch, 1988 Data,All Simulation Models 122Figure 52 Variation in Number of Trips/25 where Income was < $6000,Stationary Models 124Figure 53 Variation in Number of Trips/25 where Income was < $6000,Mobile Models 124Figure 54 Variation in Number of Trips/25 to Each Area, Random Model 126Figure 55 Variation in Number of Trips/25 to Each Area, Forecast Model 126Figure 56 Sensitivity of Forecast Model and Overall Average Performanceto Catch Rate at Butedale 131Figure 57 Sensitivity of Forecast Model and Stationary Models to CatchRate at Butedale 131Figure 58 Number of Trips to Butedale against Catch Rate at Butedale,Forecast Model 135Figure 59 Histograms of Profit, Juan de Fuca, Johnstone Strait and Largestof Two Sampled Simultaneously 137Figure 60 Histograms of Profit for Various Catch Rates at Butedale 137Figure 61 Variation of Catch and Income (per Boat) with Number of BoatsFishing Together 146xvFigure 62 Variation in Profit/Boat with Number of Boats Fishing Together 146Figure 63 Variation in Fuel Consumption and Risk at $6000 per Trip forVessels Fishing Together 148Figure 64 Histograms of Profit per Boat for One, Two and Three BoatsFishing Together 148Figure 65 Comparison of Observed and Fitted Distributions for Daily Catchand Extreme Value for 25 Trips 153Figure 66 Variation in Scale and Shape Parameters for Fitted Distributionswith Number of Boats 153Figure 67 Estimated Peak Catch for 25 Openings, Based on 99 Percentile ofDistribution of Maximum Catch 157Figure 68 Observed Cumulative Distribution of Hold Volume for SalmonSeine Vessels 157Figure 69 Comparison of Forecast Model with Stationary Models, 4 Years ofData, Income - Fuel Cost, 1987 to 1990 164Figure 70 Comparison of Forecast Model with Stationary Models, 4 Years ofData, Risk at $6000, 1987 to 1990 164Figure 71 Comparison of Average Peak Catch for Different DecisionMethods, 1987 to 1990 169Figure 72 Comparison of Mobility Between Observation and Simulation,1987 to 1990, Butedale 169Figure 73 Comparison of Mobility Between Observation and Simulation,1987 to 1990, Juan de Fuca 172Figure 74 Comparison of Mobility Between Observation and Simulation,1987 to 1990, Johnstone Strait 172Figure 75 Relationship Between Mean Catch per Day and 99 Percentile for25 Consecutive Trips 175xviAcknowledgementsI would like to thank Dr. S. Calisal, Dr. F. Sassani and Ms. N. Hofmann for theiracademic guidance and advice and the staff of the Pacific Region of theDepartment of Fisheries and Oceans who provided the catch data. The membersof the Technical Advisory Committee on Replacement Rules providedextremely helpful commentary on this work at several stages in itsdevelopment and many of their suggestions have been included. Finally Iwould like to thank my family for their eternal patience and moral supportthroughout this project. The National Research Council (Institute for MarineDynamics) provided the financial support for this work, through anAgreement for Collaboration with the University of British Columbia.1Chapter 1IntroductionIndustrial fisheries are economic activities, and are subject to the sameeconomic principles as other businesses. However, constraints in the form ofinput controls are placed on fishing operations in order to preserve the fishstock for sustainable fisheries development. If these constraints aresuccessful, then there is a limit to the growth of the industry, since there is amaximum total amount of fish which can be caught. It is therefore importantfor fishing vessel owners, designers and regulators to be able to predict theeconomic performance of alternative fishing vessel designs within a widerange of possible operating scenarios and constraints.A full understanding of the expected catching power of a fishing vessel isrequired before it is built, to ensure it is not severely under or overcapitalized. In order to obtain this understanding, the analysis methods usedmust include estimates of the expected income to the vessel from the value ofthe fish caught, together with the cost of owning and operating the vessel. Theexpenses associated with the vessel are the capital cost of the hull and fishinggear, together with the variable costs (such as fuel and other consumablesupplies) and the share of the income paid to the skipper and crew. Fixed costsinclude the cost of the fishing licence, harbour fees and other incidentalexpenses. A well constructed model will allow the vessel designer to optimizethe initial design for a new boat, or an owner to optimize the operation of oneor more existing boats fishing together.2There have been many deterministic studies of methods for reducingoperating costs of fishing vessels. A lot of emphasis has been given tooptimizing design for minimum fuel cost or minimum overall operating costbased on combined capital cost and operating cost [1, 2, 3]. These methods giveresults which are amenable to linear and non-linear optimization methods.Little attention has been paid to income, other than the average catch andresulting income per trip. These studies are adequate when consideringoverall seasonal performance when emphasis is placed on minimizing 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 avessel which is under capitalized, since there will be a lost opportunity to sellthe fish which was caught but could not be fitted into the hold. However, if thehold size is increased arbitrarily, then it may result in a large vessel which isexpensive to build and operate, which must pay for itself by catching morefish. Both of these conditions could lead to increased stock mortality, which isdetrimental to the long term health of the industry. In addition, thedeterministic methods do not allow for any assessment of financial risk.Systems engineering techniques can offer alternatives to deterministicapproaches [4, 5, 6]. One of these methods which has the potential to allow forthe random variation in the economic parameters is simulation. Thistechnique involves constructing a computer program to represent theperformance of a system as a function of time. The system is defined in termsof its components, and the overall system performance is evaluated bysummation. Random variation of certain components can be accommodated bysampling from probability distributions, based on observed data. Multiple runs3of the simulation model are then made and the results interpreted usingstatistical theory, to understand their reliability.Model construction requires breaking down the process into the correctlogical sequence of events. Decisions made can be represented by apredetermined set of rules. It is possible to model many sub-processessimultaneously, and complicated systems can be represented by relativelysimple models, if specialized simulation languages are used.The disadvantage of the method is that the reliability of the final results arevery dependent on the tuning of the inter-relationships of the times forcertain processes, and the probability distributions sampled to generate therandom events. Thus, the method relies on observed data to produce realisticresults. It also depends on realistically modelling the decision processesinvolved. This may be relatively simple in an industrial production line, butbecomes more complicated when dealing with highly individualistic fishingvessel skippers, and seasonal variation in the distribution of the fish.Simulation requires reliable measurements on the performance of the actualsystem, and then these have to be carefully interpreted in a manner whichdoes not introduce any unknown bias into any future applications of themodel. This can be particularly important when considering stochasticvariables which are based on a small number of observations. The mostobvious random variable in fishing is the catch obtained by the boat, which inturn may affect decisions made by the skipper.4If the mean catch per day varies with time and geographic location and theboats move between areas, then simulation should offer the most reliableanalysis method. It is also the best method of analyzing the performance oftwo or more boats fishing together. In such cases the catches are not identical,independent distributions. Simulation modeling allows financial risk, whichis also a random variable, to be analyzed. In this case, it is important to be ableto base results on a large number of events. In reality, the fishing season forsalmon is short, and decisions based on real life observations may be difficultto interpret, due to the small sample sizes.A successful simulation model will allow the analyst to investigate the effectsof changing system parameters on vessel profitability. Factors which may beinvestigated are the technical factors affecting the boat such as size, fuelconsumption and speed, or economic factors such as changes in catch rates,which can occur due to the natural variation in fish abundance. Other factorswhich can be investigated are operational factors, such as the number of boatsfishing together.It is the intention of this thesis to demonstrate that simulation modelling canbe developed into a useful analysis tool for predicting fishing vessel operatingeconomics. Such a model will realistically allow for the most importantvariables effecting the economics of fishing boats, such as catch rates,distance between fishing grounds and the technical performance of the boat(hold size, speed and fuel consumption). It will also allow for the fact thatskippers must choose between alternative locations, and the method ofchoosing may have some long term effect on the economic outcome. In order5to 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 againstobservations taken from the real system. The validation exercise is essential,since simulation is an empirical technique, and the accuracy of the model canbe no better than the data used to develop the initial assumptions. Once thevalidation has been carried out, then changes can be made to the initialconditions of the simulation model and the results used to predict changes inthe real system.The most important fishery, in economic terms, in British Columbia is thesalmon seine fishery. The vessels used for this fishery are typically biggerthan for any other type used for fishing in British Columbia, and so are mostlikely to be effected by changes in the economics of operations. They also havethe technology for catching more fish than other methods, such as trolling orgill netting. For these reasons, it would be desirable to model these vesselssince the overall benefits of any subsequent optimization are likely to be thehighest.This work was carried out to support the development of an expert system forfishing vessel design, which required a method of analyzing a fishing vessel’seconomic performance. A simulation model can potentially give these datatogether with information on earnings, vessel mobility and subsequent fuelconsumption. The required fish hold size is the dominant factor affecting thecapital and operating cost of the vessel. Also, the Department of Fisheries andOceans (DFO) may be interested in being able to simulate vessel operations with6respect to predicting the impact of any future modifications to vesselreplacement rules or quota assignments on vessel movement and productivity.7Chapter 2Salmon Seine Fishing in British ColumbiaBefore work on the simulation model could begin, it was necessary to establishthe correct sequence of events and identify the technical and economicfeatures which were essential for constructing an accurate representation ofthe fishing process. One source of observations on the salmon seine fishingprocess can be derived from a review of the literature published by otherresearchers. Another potentially valuable source is data collected by theDepartment of Fisheries and Oceans.2.1 Development of Fishing TechniquesLedbetter [7] described the pacific salmon as a relatively predictable fish, dueto its regular migration patterns. The fish move with the tide or current, andtravel along the shore rather than in mid-strait. Underwater obstructions,such as changes in bottom contours or vegetation direct the fish into openwater and so boats tend to congregate in these areas. Salmon often travel nearthe surface, and occasionally jump out of the water. These biological featuresmake the salmon very easy to catch in shallow water and in entrances tospawning 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 significantquantities of the other species are also caught. Seine caught fish tend to be of alower quality relative to the other catching methods, since large volumes of8fish are caught and the fish can easily be damaged when the nets are beinghandled.In the traditional method of seine fishing, described in [8], one end of the netwas held by a small boat, called a skiff, while the net was paid out from thefishing boat, as it steered round in a circle. Once the circle was complete, thenet was drawn into a purse and hauled aboard using tackle suspended from along boom. The bunt end of the net was then tripped, releasing the fish intothe hold. The fish were packed in ice with no other processing carried out onboard the boat. The net was then stowed on a rotating table, so that it could bere-set as quickly as possible. If the weight of the catch was more than the crewcould haul by hand, then brailing nets were dipped into the purse to bring thefish aboard. The efficiency of the method was incrementally improved byholding the net open in a U-shape (with the mouth open to the current) forsome time before it was drawn into a circle.The vessels used for this fishery [9] have traditionally had the engine andaccommodation forward and a large deck area aft. The hold was in a centrallocation, to avoid excessive trim when the fish were loaded. The rudder andpropeller 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 thedesigner 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 theend of the boom, which meant that the maximum catch that could be hauled9aboard was no longer limited by the strength of the crew. This also reduced thetime between sets of the net. Further refinements saw the use of drum winchesinstead of the block and net table, and the the latest additions to the boats havebeen the running line, which eliminated the need for the skiff, and bowthrusters to improve the maneuverability of the boat during fishing. All thesechanges in technology have resulted in a reduction of the total time betweensets from 55 minutes, with a power block on the end of the boom to 35 minutesfor vessels with a seine drum.2.2 Common Vessel Operating PracticesCove [10] discussed some aspects of fishing vessel operations. He noted thatvessels often left port up to 2 days before an opening to investigate the fishingarea and locate the fish. This was easy to do if there were jumpers’, fish whichjumped out of the water, but it was noted that these observations were arelatively rare occurrence.Ledbetter [7] discussed some of the strategies used in salmon seine fishing inJohnstone Strait. This fishing area was characterized by strong tides, localreefs and protected waters, and at the time of writing was considered to be thedominant seine fishery in British Columbia. Since the salmon follow distinctmigration patterns, in relatively shallow water, they are easiest to catch atspecific locations. An efficient technique for this fishing area was to tie oneend of the net to a fixed point on the bank, such as a tree, and hold the netopen against the current, using the fishing boat. This method, referred to lateras the point set, was efficient, since it minimized the amount of fuel usedduring the fishing process.10Since the salmon tend to be concentrated in specific locations and catch ratesare easily observable from other boats, line-ups form at particularlyproductive spots. However, the optimum number of boats fishing at any onelocation is two, since one boat can be letting go while the other is pursing. Byfishing in this way, very few fish can get past the nets. If the fishing area isrestricted, then two or three boats can make it very difficult for other boats tofish 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 waterusing the boat and the skiff. Ledbetter showed that the open set was onlyslightly less productive than the point set, with a mean catch rate of between28 and 29 fish per set compared to a mean catch rate of between 32 and 36 fishper set, in a short line up (1-2 boats) for a point set. However, a high catch rateat a point set (40-45 fish per set) resulted in line-ups of up to 5 boats. Theadvantage 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, thetechnique may be less profitable, due to the higher fuel consumption usedduring fishing.Tidal activity was also observed to be important. Ledbetter [7] observed thatalthough vessel activity level remained constant throughout the tidal cycle,the number of maximum catches with the ebb and flood were different (68maximum catches were caught on the ebb, whilst 120 were obtained on theflood). This was important to the skipper, since typically 19 percent of totalcatch was taken in the maximum catch.11Figure 1. Statistical Area Map, Northern HalfOEAO CAACFULLYI %*,t*ç &lA 10the 1011. 11 @ FM.,.. I’d 1**1.1It It. 1.11.0,0* I’d I 0,1110,0*1111111.11*11.1Z k*.oI. c.t .#10 hit 0.4.4.0,11 fl1 10,1.0,0,h*1b. V*g It. 11 1*1’ —. oeht3 fl.. 11*1*1*01 ariaS 1110*1 WI ItS 1*11 1111010 .1010 *,4. F.. *0*0 0,0*1 0111.1.010*1010,10 10110*11.. F.Ve.1 10110900.010 his• V.pt .1 FIt.... end 0*lW* 311.1.— 5101.1.10110*00 100 di,hi by .0410...— 5*11100hell All e,.WI *00*4 FoA*y l9e5• F*tene* PAches• Oceans et Oceans CrnadSTATIS11CAL AREA MAPSHOWING AREAS OF CATCH FORBRITISH COLUMBIA WATERSNORTHERN HALFSIXTH EOITIeI Ft 98512Hilborn and Ledbetter [12] compared and contrasted Juan de Fuca andJohnstone Strait as fishing areas. Juan de Fuca was characterized by openwater, high waves and less variation in geography. The fishing technique wasslightly different in that the open set was the only one used. However, thefishing took place in a very confined area, defined by points on the map andline-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 afterdiscussions with DFO officials, experienced fishermen and industry watchers,it was explained as follows. The migrating fish were in open water heading fortheir ‘home’ rivers. The ideal place to intercept them was right on theboundary of the fishing area, which had to be crossed by all the fish enteringthe area. A line of nets across the boundary formed a very effective barrier tothe fish. Since the boundary was in the open ocean, it was purely a referenceline on the map, and there were no places where point sets could be made.2.3 Constraints on Fishing OperationsIt is common practice for governments to regulate their fisheries, and thePacific salmon fishery is no exception. The constraints placed on the fisheryby the government affect several factors of vessel operations and fishingactivity, which are discussed in detail below.2.3.1 Location & OpeningsThe 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. AreasFigure2.StatisticalAreaMap, SouthernHalfCj’IPA0F0LLYIlleQQ#tinQOfOil @000(0totSDepI@1F.ilt$(S.God00.onie4*e..000.bkIyofIt..11.0monnodp00.00010.04ho..t000.o.moI2000I.CcItt.1.00,1.mintIncludeII.moptutOrotnumbr..I.oc.ngII’.01000clOd.duefeel.cc.couplet3TI..t,flfllCOl01o1townmllb..omp0.0100.u.ed000Quid.OnlyFoemoe..00(1infolmOhon.010,I.It.P.011.0Fiolmeyl0000p.m.pt01.0Regoloti000•DeptofF,toei..mId00.00$011i00St0toIiCoI0100101•divIdedbyted110..—Dm11.0.NoteAll moo..00.000F.btoiny906I*Fithetiotu00.3Ocoaot.01OCdonuCanadSTATISTICALAREAMAPSHOWINGAREASOFCATCHFORBRITISHCOLUMBIAWATERSSOUTHERNHALFSloThEDITItNFF0190314generally open at 18:00 on Sunday, and are open between 2 and 4 days, in 12hour increments, depending on the strength of the run. The policy of theDepartment of Fisheries and Oceans (DFO) is that fishing is closed until it isopen. The nature of this system enables boats to move easily betweenopenings, but potentially penalizes them for moving during an opening. Notall areas are open simultaneously. Northern areas tend to open early in theseason and close first, and southern areas open later and close later. Thefishing season for salmon is generally between early July and late November.These arrangements are discussed in [11, 12, 13].2.3.2 Fishing GearThe nature of salmon seine fishing means that it is extremely difficult to setthe net in the dark, due to its size. This effectively limits the fishing to thehours of daylight. There are also regulatory restrictions on the gear. Thedimensions of a salmon seine net are constrained by the ‘Pacific CommercialSalmon Fishery Regulations’ [14]. The Act limits the net to a length of between150 and 220 fathoms (274 to 402 metres) and a depth of 250 meshes(approximately 30 metres). The regulations are such that the maximumallowable size can be carried by any seine boat, and so net size is effectivelyindependent 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 vesselcan only carry one net at a time, with a limited amount of spare gear formaking repairs. Also the maximum length of time that a net can be kept in thewater before pursing is 20 minutes, and this is specified in the Act. Hilbornand Ledbetter [12] discussed the observation that the smaller, ‘inside’ net isused in Johnstone Strait, whereas the bigger ‘outside’ net is used in Juan deFuca.152.3.3 Vessel DimensionsSalmon fishing vessels have been licensed in British Columbia since 1969. Atthat time, any boat which had caught more than 10,000 lb of pink or chumsalmon (or equivalent) in either of the two previous years was required topurchase a commercial salmon licence if it wished to continue fishing. At thistime there was no restriction on the type of gear that could be used on theboat. In 1977, a separate category of salmon licence was introduced for salmonseiners. The licence was in the form of a seine privilege. Boats with thisprivilege could use seine gear and any other kind of gear, but other boats wereprohibited from using seine gear. The number of seine privileges was fixed atthe number of boats fishing at that time.Immediately after the introduction of the salmon licence, the vesselreplacement rule was such that the total number of boats fishing must remainthe same. A new boat could not be built without an old one being retired. Thereplacement rules were modified in 1971 to take into account vessel size,approximated by the net tonnage and overall length. Net tonnage is anapproximation for the hold capacity of the vessel. Under the modified rule, theobjective was to maintain a constant total tonnage. A larger boat could beintroduced, but ft required the retirement of a sufficient number of smallerboats.This rule was not effective in controlling catching capability, since it took noaccount of the catching methods. For example two or three smaller gill netterscould be replaced by a single seiner, with up to ten times the catchingcapacity. The current practice is to replace an old vessel with one of the same16400 30a)I-.1a)E020101900Figure 4. Variation in Brake Horsepower with Time,Salmon Seiners800y = 4387.3 + 2.3722x R2 = 0.226El0600rnElo §0. Ela)El 00,0 ELEPE!?00- 000200El00El01900Figure 3. Variation in Overall LengthSalmon Seinerswith Time,y = 36.122 - 9.6641e-3x R2 = 0.006ElEl El0ElEl4rlEl BuuGEl ElEl B I’ ElE•ø0rnI — I — I — I —1920 1940 1960 1980 2000Year1920 1940 1960 1980 2000Year17overall length and net tonnage. Thus under the current vessel rules, thelength and net tonnage are an integrated part of the constraints on the vesseldesign. The observations discussed above are taken from [15].2.4 Current Fleet Size and Vessel DimensionsIn 1988, according to [16] there were 549 licenses for seine privileges, but laterinformation [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 seinecaught salmon was $112M, compared to the total for the salmon fishery of$256M. These figures show how productive the seine fleet is relative to theother methods, when 44 per cent of the value of the catch was landed by 12 percent of the licences.In 1989, there were 549 licences issued for salmon seining, of whichapproximately 60 per cent were licensed just for this fishery. The remainingboats held two or more licences, of which the most common combination wasroe herring, with approximately 25 per cent of the total licences. Acomparison of the average vessel dimensions for the salmon seine fleet withthe roe herring fleet is given in Table I. These data were derived from DFOrecords released in support of this project.It can be seen from Table I that the combined salmon/herring vessels werebigger and newer, with more engine horsepower than the single licenseboats. It is interesting to note that the vessel parameters have changed withtime. Length and horsepower are shown for each category of license inFigures 3 to 6. For the combined vessels, all the measures of vessel size havedecreased with time, i. e. the newer boats are smaller than the older ones.18Figure 5. Variation in Length with Time,Combined Salmon/Herring Seiners40y — 181.96 - 8.1627e-2x R2 0.2451930 1940 1950 1960 1970 1980 1990YearFigure 6. Variation in Brake Horsepower with Time,Combined Salmon/Herring Seiners1000•y 4035.2 + 2.2475x R2 = 0.06098009 0I- U600 0 01930 1940 1950 1960 1970 1980 1990Year19However, the installed power has increased with time. For single licences,vessel sizes are static with time, but installed power has increased.Vessel Parameters All Salmon Salmon/Herringlicenses licensesLength, m. 17.0 21.4Gross tonnage, m3 115.8 264.7Horsepower, HP 244 405Age, years 35 21Number of boats 507 124Table IComparison of Average Dimensions forSalmon Seine Vessel Fleets2.5 Trends in Vessel Income with TimeIt is interesting to speculate how much impact the changes in technologydescribed above have had on the economics of the fishery. This might beinferred from observations on past performance over a number of years. DFOpublishes detailed annual summaries [16] of the total amount of fish caught.These data are summarized by species, type of gear and the geographiclocation of where the fish were caught. Information is also given on the totalnumber of landings per year, the average weight and value of a landing, andthe total payments to fishermen, which included bonus payments and directdelivery 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 latestdata available in this form was for the years between 1979 and 1988. Table IIgives the annual summary data for salmon seining taken from [16]. It alsoYearTotalcatch,Value, $,Totalpayments,LandingsAve.catchperAve.valuepertonnes000’s$,000’s000’slanding,kglanding,$1979247174252253010122059.753543.51980247964185449190122066.333487.81981409946386477220104099.406386.41982269525181862260102695.205181.81983432254844359710113929.554403.91984205143839941220131578.002953.8198558676106902106010144191.147635.9198653156101972110300143796.867283.71987294656811772900102946.506811.7198850401122919131140143600.078779.9Mean37289.668681.076296.012.03096.35646.8Std.devn13718.030820.929886.51.7958.42012.6TableIISummaryofAnnualPerformance,SalmonSeineFleet,1979to198821Figure 7. Regression of Total Catch bySalmon Seiners against Year, 1979 to 1988100000-y - 4.7365e+6 + 2406.7x R2 0.28280000U)U)60000 EI.40000,20000 b0•. • I • I • I1979 1981 1983 1985 1987YearFigure 8. Regression of Number of Landings bySalmon Seiners Against Year, 1979 to 198815y = - 444.81 + 0.23030x R2 = 0.16814 P Wp.IIl1979 1981 1983 1985 1987Year22gives the 10 year mean value for the total amount of fish caught and theaverage catch per delivery.Linear regression was used to identify possible trends in the data, as functionsof time. Figure 7 shows that over the last 10 years the total catch by seinevessels has increased at an average rate of 2400 tonnes per year. It wouldappear over this period that there has been a steady increase in the amount offish caught. However, when we make the conventional assumptionsconcerning a normal distribution of the residuals, determined after fitting theregression equation, we find that the probability of the slope being zero is0.114. This means that at the 90 percent confidence level, we cannot reject thenull hypothesis that the slope is zero. Given the small number of years usedand the relatively large degree of variation between years, it is inconclusiveto say that the total weight of fish is increasing.Another parameter to consider is the trend with number of landings againstyear, and the weight per landing. If the same amount of fish is caught withfewer landings, then the fishing operation may be more productive. However,if the total number of landings is increasing, then the operating costs may beincreasing 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 thatdeliveries were increasing on average at a rate of 230 per year. However, theprobability that the slope is zero is 0.239, which means we cannot reject thenull hypothesis that the number of deliveries was not increasing, at the 90 percent confidence level. A similar regression of mean catch per delivery against23Figure 9. Regression of Average Catch per Landingagainst Year, Salmon Seine Vessels, 1979 to 19885000y = - 2.4518e+5 + 125.17x R2 = 0.1560.400030002000(U(U1000 I • I • I • I1979 1981 1983 1985 1987YearFigure 10. Regression of Normalized Dollars per Landingagainst Year, Salmon Seine Vessels, 1979 to 198810000•y = . 6.9780e+5 + 354.78x R2 = 0.28890008000I1979 1981 1983 1985 1987Year24year is given in Figure 9. This showed that the mean catch per delivery wasincreasing slightly, at 123 kg per year, but again the probability of the slopebeing zero was high, at 0.258. Average catch per delivery, based on 10 years ofdata is 3096 kg.The price information was more difficult to interpret than the weight of fishbeing caught. This was due to the fact that the total amount of money earnedfrom the fish was dependent on the average catch per delivery, the number ofdeliveries and the unit price of fish, all of which could vary independently.Dollar values were normalized by considering dollars per landing, in 1979dollars. 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 perkilogram in 1979. When the normalized data was regressed, it was found thatalthough the slope was positive, showing on average an increase in the valueof dollars per landing with time, this was not significant at the 90% confidencelevel. This is shown in Figure 10.It is also interesting to note that the total payments to the skipper were, onaverage, 13.5% higher than the income due to the landed value of the fish.This figure is clearly significant, and could make a big difference in theoverall profitability of a fishing operation.It is apparent from these observations that there is a high degree of variationin the annual performance of the fleet. No conclusive trends can be made overa 10 year period. Although all trends show increased productivity over the 10year period, they are not statistically significant, when the amount of scatterand number of samples is allowed for. It would be reasonable to interpret the25Figure 11. Average Number of Landings per Year,Salmon Seine, 1979 to 198826/24 /— I0220)C I20 P/18 . ¶1 • •1979 1981 1983 1985 1987Year26observations to show that the constraints have been working over the last tenyears. If these data are to be interpreted in a more reliable manner, thenlonger periods of time are required.One interesting observation can be inferred from these data. If we assume thatthe number of seine licenses was fixed throughout this period (at the highervalue of 549) we can estimate the average number of trips per year over theperiod. These data are shown plotted in Figure 11. It would seem that theaverage number of trips per year varies between 18 and 25. Thus the totalnumber of trips is relatively small, but we have no information so far on theduration of these trips.Item DollarsLicense fishing income 232,000Other species fishing income 117,000Gross fishing income 349,000Operating Expenses-133,000Other income 14,000Fixed costs-63,000Net income 167,000Skipper payment-40,000Profit 127,000Income/trip (salmon) 8,780Estimates# trips/yr 26.42Estimated cost per trip 5,700Estimated profit per trip 3,100Table IIISummary of Operating Economics,Salmon Seine Vessels, 198827Income data for 1988 for all licence categories described above are given in[17]. Despite the fact that there is only one year of data, and that noinformation is given on the variance or the number of boats used in theanalysis, it does give some useful information of vessel economics.These data are summarized in Table III for salmon seine fishing, and thedefinitions are given below. Gross income includes fishing income, plus anyadditional bonuses. Operating expenses include crew shares, fuel, lubricationoil and grease, food and provisions, bait, ice, salt and other expenses. Otherincome consists of income from other fishing related activities, such aspacking or collecting, charters, rebates, lease or rental arrangements andUnemployment Insurance benefits. Fixed costs include insurance, accountingfees, licence renewal fee, gear maintenance, interest on debt, moorage andsimilar costs.These results give some very interesting information on the performance ofthe fleet. There was substantial income from sources other than the licenceconsidered. For salmon seine boats, 33 percent of the gross fishing incomecame from other sources. The operating costs represented 38 percent of thegross fishing income. Fixed costs for salmon seining were 18 percent of grossfishing income. Average profit for salmon seining was $127K over the season.Estimates can also be made of some additional economic parameters from thesedata. Given the total income from salmon fishing from Table III, and dollarsper trip from the annual summary data, Table II, we can estimate the meannumber of trips per year to be 26.4. This compares very well with 25.528estimated from the annual summary data, based on the total number oflicences.The simplest assumption to make when calculating the expenses is that thetotal expenses are pro-rated in relation to earned income. Therefore estimatedexpenses for salmon fishing are $151K. Assuming 26.42 trips per year, thevessel needs an average income of at least $5.7K per trip to cover costs.2.6 Effect of Vessel Parameters on IncomeSo far only the average performance of the vessels has been considered. Animportant factor to determine is whether or not the vessel has an effect on itsown overall performance. Hilborn and Ledbetter [12] discussed some of theaspects of vessel design on catching power, measured in dollars per week, inthe British Columbia salmon seine fishery over five years, 1973 to 1977. Theyexplored the relationships between catching power, measured vesselattributes, vessel effect and geographic location and assessed the importanceof these factors in determining the total catch. They considered the Juan deFuca and the Johnstone Strait fisheries, since they represented the twoextremes, in terms of environment. From a linear regression of catchingpower against vessel parameters, length, gross tonnage, year built, listed valueand horsepower, they concluded that vessel parameters alone could notaccount for variation in performance between boats. They noted that vesselswhich 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 andpoorly in Juan de Fuca (19.14 m). Boats that did poorly in both areas were thesmallest of all (18.18 m).29They then concluded that factors other than vessel parameters must beimportant in determining catching power, since some boats consistentlyperformed better than or worse than average (at least in one area). Effectsthat the authors considered were skipper skill, crew skill and design of thenet. From analysis of the variance (ANOVA) of the vessels which fished bothareas, they concluded that there was very little difference between the twoareas in the contributions of the three elements (vessel attributes, gear designcombined crew skill and unexplained luck). The aggregate components were:- 10% vessel- 24% skipper/crew/net- 66% luckIt can be concluded from this study, that within a given area, vesselparameters had very little effect on the catching power, vessel and crew skillhave some effect, but the biggest component of all was luck. The authorsdiscussed the importance of area specialization to the performance of the boat.Some skippers preferred to fish in one area over another, for reasons such asproximity, length of season, typical weather conditions and size of boat. Thisarea specialization can account for about 25% of the overall variation betweenboats, when boats that fish in both areas were considered.2.7 Effect of Motivation and Mobility on IncomeOne of the factors which must also be considered is skipper motivation and thenumber 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 area30(stationary boats) and those which fished multiple areas (mobile boats). Theyconcluded that the mobile boats distributed themselves between areas, in orderto equalize the catch per unit effort (CPE), measured in dollars per week, for agiven area relative to the overall average. They observed that some areas hadconsistently higher ratios of CPE than the average, and these areas tended tobe more remote or subject to more extreme weather conditions. Areas whichwere consistently lower than average were more accessible and moresheltered.The authors did not address the mobility decision of an individual skipper, butgave some clues to the variation in attitudes. One category of skipper issomeone who always fishes in one area. This could give the basis for onemotivation or decision rule.For some years of their study, they noted that the number of mobile boatsfishing 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 hadbeen less productive, the number of boats would reduce. It was found however,that this observation did not hold for all years. Despite this limitation, whichmay be due to relative merits of alternative areas and overall seasonalprofitability, this mobility pattern hypothesis could form the basis for analternative decision rule, such that the skipper directs the boat to the areawhich was the most productive area in the previous week.Cove [10] developed a model to account for the different levels of risk taken byskippers in the fish gathering process. The model specified relationshipsbetween reward structure, technology and the environment that influenced31the skipper’s evaluation of a situation, and hence his decision. The modelindicated that a situational approach to risk taking can be used to helpunderstand short term production strategies. Unfortunately, the paper doesnot give any information on the absolute differences in performance betweenthe skippers. The skippers with the highest long term catch (and income)rates fished using a high number of low risk sets rather than a smallernumber of high risk sets. A key factor in the decision process would appear tobe whether sets were made on the basis of maximum values obtained oraverage values obtained. Some of the difference in performance between boatsmay be accounted for by the skipper’s attitude to risk, and his level ofmotivation.Hilborn [13] discussed some other aspects of motivation and the possiblestrategies that a skipper could adopt. He considered four possible successfulstrategies:- specialize in one area- specialize in moving between areas- maximize catching power by using the best technology- fish as many days as possibleAnother source of information on the fishing process was discussion with thefishermen. A crucial piece of information, which was not apparent from thereviews of the literature, was that a vessel rarely fished alone. Boats wereusually part of a team with the biggest boat (the packer) used for thetransportation of fish caught by all the vessels in the team. The other vesselswould stay on the fishing grounds during the closed portion of the season32tracking the movement of the fish. The teams were often associated with aprocessing plant, and the fish were always brought to that port. Supplies forthe boats left on the grounds would be brought out on the return trip by thepacker.Obtaining intelligence on the fish movements was a sophisticated business. Asonar on the boat was used for detecting shoals of fish but greater range couldbe covered for less cost using the skiff when looking for fish on the surface(jumpers). Other methods used to locate fish included spotter aircraft andmonitoring communications between other boats. Teams of boats would codeinformation by using radio scramblers and cellular facsimile machines.Some skippers felt that there has been a general reduction in the level of skillrequired for fishing over the years. This was due mainly to the reduction insize of the areas where fishing could take place during an opening. Thisforced the boats to concentrate in that area, and so line-ups would becomevery long very quickly. The alternative strategy was to make open sets, awayfrom the line-ups. Whilst the skippers accepted that the catch rate wasapproximately half that of those in the line-up, it was compensated for bymore sets per unit time. This confirmed the observations of Hilborn andLedbetter [11, 12] and Ledbetter [7].The general strategy used by one skipper I talked to was to fish an areawhenever there was an opening. This would mean a lot of movement duringthe season, but fuel cost was not a significant concern. When there were twoor more openings simultaneously then a decision would have to be made toselect an area. This was done using past records of catches for each area, based33on the time of the year. The vessels in the group would fish together, untilcatch rate fell below some (unspecified) catch rate, when the boats would splitup and look for other locations individually. The boats would then regroup ifnecessary.2.8 Important Factors to Include in a Simulation ModelBased on the review of the fishing system for salmon seine vessels in BritishColumbia, we can reach the following conclusions on the factors affecting theperformance of individual vessels, relative to the fleet in general.- The boat has little effect on catch rate within a given fishing area, probablydue 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 oftime, and were a relatively short portion of the total time available.- Many boats move between areas, trying to obtain the best catch. Thismobility may be based on comparisons of the value of fish caught in all theareas 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 pertrip 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 25.35Chapter 3Operational Analysis of a Salmon Seine Vessel Based onCatch and Voyage DataIn order to be able to model the engineering aspects of a fishing vessel it isessential to know some technical details, such as the typical length of voyages,the fuel consumption of the vessel and other factors which will effect thedesign of a successful vessel. In this chapter, the operation of one particularvessel will be studied, in order to establish realistic technical specifications fora modern salmon seine fishing vessel.UBC researchers have developed a special relationship with one particularskipper of a salmon seine vessel. UBC staff and students have worked with himin modernizing his boat to improve fuel economy and reduce motions andaccelerations induced by waves. As part of these studies, model data on theboat’s performance in calm water and head waves have been obtained, as wellas full scale data [18, 19]. The hull had a registered length of 18.14 metres andwas the largest of a group of three boats belonging to a small but integratedcompany which was involved in catching, processing and selling fish. Theboat was built in 1987 and incorporated the latest technology in terms of gearhandling, fish finding and information transfer. The skipper said that he hadno particular preference for geographic areas when fishing for salmon. Inaddition to salmon and herring, the boat was also used to catch bait for sportsfisheries and food for exhibits at the Vancouver Aquarium. These additionalactivities kept the vessel busy over a twelve month period. The boat had a crewof 5 or 6, depending on the type of fishing being carried out.36Since this vessel was the biggest in the team, it was used for the transportationof fish caught by all three vessels. The team was associated with a processingplant in Steveston, and the skipper always returned to this port after fishing.The other vessels would sometimes return to Steveston, but most likely wouldstay on the fishing grounds, tracking the movement of the fish, during theclosed portion of the season. Supplies for the other two boats would be broughtout on the return trip from Steveston to the fishing grounds. Sometimes afourth vessel would operate with the group, but this one was based in BellaBella. All four boats were operated by members of the same family.The three boats all processed their fish slightly differently from theestablished practice of salmon seiners. Typically, seine caught fish are of alower quality than line caught fish or gill net caught fish. This is because thecatching technique and the bulk storage on board the boat tend to bruise thefish, resulting in a lower quality product, which is suitable for canning butnot for any other methods of processing. However, on these boats the fishwere bled before being hand stowed in the hold. Also, the fish were kept in thehold for as short a time as possible. This gave a higher quality product whichwas suitable for processing and marketing as smoked salmon, with aconsiderably higher retail value than the canned product.Data on the actual performance for income and catch rates for the boat will bekept confidential, but some discussion can be made on the performance of theskipper relative to a sample from the overall fleet. The sample was a group of121 seine boats for which UBC had a full description of the technicalparameters. It seemed that this skipper caught consistently more fish than37average, over the course of a season. Based on the four years (1987 to 1990) forwhich data were available, the total catch of salmon was 31 percent higherthan average, with the lowest value being 4 percent and the highest being 42percent. The dollar value of the salmon was 24 percent higher than the mean.This difference between catch and income may have been due to catchingmore lower grade fish than was typical. The higher than average catch andincome figures were due to a higher than average number of days fished. The4-year mean for the number of days was 29 percent higher than average.The observations discussed above would tend to indicate that the skipper wasmotivated to earn more than average. The most likely sources for the increasedmotivation were his status as top performer within the ‘company’ fleet, thefinancing requirements for a new boat and an interest in the total productionprocess, rather than just the fishing operations. A closer analysis of the dataindicated that the catch rate per day for this skipper was close to the overallfleet average, which confirmed that the increased productivity was duedirectly to fishing more days per year. If we assume that this vesselrepresented average performance in terms of catch rate per unit time and wecan determine an operational profile for this boat, it may give an indication ofa typical operational profile for the rest of the fleet.3.1 Data Collection for Voyage Profile AnalysisAs part of the UBC study, the vessel was instrumented to automatically measureand record fuel consumption, ship speed, engine revolutions, latitude,longitude and heading as functions of time. The voyage data available for thisboat covered the period August to November, 1989. During this period thevessel was engaged in salmon seining.38When the data logging system was operational, it recorded data for everychannel at a frequency of one point every five minutes. Data was retrievedfrom the system as a formatted text file. The standard sampling rate gave datathat was too detailed for analysis of the overall voyage profile. It was decidedthat the average values of fuel consumption, speed and engine revolutionsover a one hour period, together with the position and heading at the end ofthe period would be sufficient to identify major segments of activity. Themethods by which the data were obtained are summarized in Table IV.Item Measurement MethodFuel consumption Flow meter in fuel lineEngine rpm Shaft speedLatitude Loran navigation systemLongitude Loran navigation systemSpeed Differentiation of position dataHeading Position data or compassTime & date Internal clock on data acquisition computerTable IVSummary of Measurement Methodsfor Voyage DataA computer program was written to decode the logged data. Averages for theone hour period were calculated by checking the time and counting thenumber of data points. Gaps were identified by discontinuities in the sequenceof the times. For incomplete records, averages were calculated on the basis ofthe number of observed points within the nominal one hour period. Anadditional variable was added, which was a counter from the beginning of the39data record. It was included so that sequential plotting of the data points couldbe carried out.The data acquisition system was started manually from on board the boat, andso data were missed when the equipment was not turned on. Data for latitudeand longitude were occasionally missing when all other channels wereworking. This was presumed to be due to difficulties in receiving the LORAN-Cposition data. Another major problem was that data were overwritten when thememory buffer for the acquisition system was full, and potentially valuabledata were lost. This was particularly frustrating when there were long periodsof time when data were collected when the vessel was in port, without theengine running. Despite these limitations, these data proved to be extremelyuseful information for constructing a simplified voyage profile for salmonseining.3.2 Voyage Profile Analysis3.2.1 Overall OperationDuring the period for which data was available, four distinct voyages wereidentified. The latitude and longitude data were used to determine the endpoints and the route for each voyage. The data was reduced, so that it onlyincluded the portions where the vessel was away from home port. An overviewof the vessel movement during this period is shown in Figure 12. A summaryof the duration of each trip is given in Table V.Some knowledge of the vessel operation was helpful when interpreting thedata records to determine the voyage profile. When the boat was steaming to orfrom the grounds, it seemed as though the throttle was set, engine revolutionslatitudeacncnuicnSO0—01j3.•••‘:v.•.•.•.©cAu2LZV:••••:•::•‘CD/‘u/If.)u/•.•.•••.•.••co•CI)j3.L.v3Ev...:;.v:.v:.a.v.Ccf)-JtCD1’iIThIa3cD‘aIIN’:-no.c.v:::.v:JF.vz.....v.v:qCCDCv....;’;.:C);....v.v..v;;Øa.C)0•.•ov.....v..ov....;.v.v;:;.%z......©‘I.CDD ElCMX°+9CD<<<<0000Cl)cccci-I.0,OiOp0O‘0‘0m•t•‘D‘PCMt3—C41were maintained at a steady level, and the vessel position was changingsteadily. When fishing was taking place, the engine was runningcontinuously, so that the net could be set and recovered, and the vessel couldbe maneuvered. However, we would not expect the engine activity or speed tobe close to the expected maximum for long periods of time. Also, the vesselposition would be static, or changing very slowly.Voyage # Destination Start Finish Durationdate date hrs.1 Juan de Fuca 04-09-89 06-09-89 432 Discovery 09-09-89 13-09-89 813 Johnstone/Bella Bella 22-09-89 29-09-89 1774 Juan de Fuca 01-10-89 03-10-89 39Table VSummary of Voyage TimesAn activity which could not be distinguished from fishing, using the recordeddata, was small local movement to change fishing locations. For this reason,both activities have been grouped together. The movement of the vesselduring the presumed fishing activity is discussed in more detail below. Asummary of the parameters used to determine the voyage profile is given inTable 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 thefollowing sequence. The vessel left harbour, and sailed at a (relatively) highspeed to the selected destination. There was always a period of zero engineactivity after arriving at the fishing ground, presumably to give the skipper424-CzaC.)100806040200Figure 13. Vessel Activity Profile,Ship Speed and Engine RPM against TimeFigure 14. Histogram of Vessel Speed,Sampled at Five Minute Intervals9.5 10.5 11.5 12.5 13.5 14.5U,4-0C151050145200010000a.knots.••-• RPM165 185 205 225Hours5.5 6.5 7.5 8.5I •Speed, knots43and crew a chance to get gear ready or search for signs of fish before fishingbegan. This period was as short as an hour, or as long as three days. The vesselthen spent some time at medium engine activity, assumed to be fishingoperations. On completion of fishing the vessel either ceased activity, changedareas or returned home at high speed.Engine rpm Ship Speed Position Most likely activitynone none static inactivemedium low almost static fishing/local searchinghigh high changing transitTable VISummary of Vessel ActivityA summary of the voyage profiles, giving the percentage times spent in eachactivity is given in Table VII. Times were rounded to the nearest hour.Although all the profiles for the voyages followed a similar sequence, it wasobvious that they differed in the distribution of the times. It was not possible toidentify any consistent pattern between the voyages, but it is clear that theJuan de Fuca trips were different from the others. They were shorter, and theinactive period represented a much smaller portion of the total trip length.Only once did the boat change fishing areas in one trip, although on otheroccasions 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 theBritish Columbia coast in a one month period.44Percent of Total TimeProcess Voyage 1 Voyage 2 Voyage 3 Voyage 4Sailing out 30 20 8 35Resting 21 42 52 3Fishing/local movement *19 25 15 31Moving areas *0 0 6 0Sailing back *30 14 20 31Total sailing *60 34 33 66Inactive *21 42 52 3Fishing *19 25 15 31* estimated from incomplete dataTable VIIVoyage Profiles for Seine Fishing Vessel3.2.2 Detailed Analysis of Transit Portion of VoyageFor this analysis, the raw data (logged every five minutes) for the steamingportion 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. Asummary of the mean, standard deviations, kurtosis and skew for all thevoyages is given in Table VIII. The duration was not necessarily the same asthe sailing activity discussed above, since it only included the longestcontinuous record in each voyage segment.It is interesting to discuss these results, since they have an impact on the timesto 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 somecases very high speeds were observed (greater than 15 knots, which may bepossible with tide), but in general the standard deviation of the speed was ofthe order of 1.5 knots. The distributions generally had a pronounced peak,which was usually skewed to the right, but not consistently.45Figure 15. Ship Movement During Fishing ActivityLatitude and Longitude, Juan de Fuca, 89-09-0548.47 -48.46-U48A-5004844 00 0 hP 00 0 0 0 D00 0 0EI48.42-. • • • •.124.32 -124.31 -124.30 -124.29 -124.28 -124.27 -124.26longitudeFigure 16. Ship Movement During Fishing Activity,Latitude and Longitude, Johnstone Strait, 89-09-1250.400503\/ IoU— Assumed fishingactivity .50.250.1-125.5 -125.4 -125.3longitude46Voyage Mean speed Stnd. Duration RPM Kurtosis Skew(knots) devn. (mins) (approx.constant)#1, Juan de Fuca, Out 10.7 0.88 545 1800 -0.161 -0.201#1, Juan de Fuca, home 8.4 1.02 660 1600 -0.025 0.218#2, Discovery, out 10.2 1.15 690 1600 4.851 2.149#2, Discovery, home 10.9 1.49 600 1800 4.462 1.99#3, Johnstone, out 10.8 1.02 870 1600 3.022 1.632#3, Johnstone/B. Bella 10.4 2.86 790 1600 12.073 2.263#3, B. Bella to home 10.0 2.29 1680 1700 7.506 -1.702#4, Juan de Fuca, out 10.5 0.81 660 1600 1.389 0.336#4, Juan de Fuca, home 10.0 1.07 730 1825 1.435 0.694Mean Value 10.2Table VIIIDetailed Analysis of Transit DataThe hull speed is the speed of a wave, which has a wavelength equal to thelength of the ship. This is the practical maximum speed for a displacementhull, beyond which excessive power is required to obtain a higher speed. Forthis boat the hull speed was estimated to be 10.35 knots. This was very close tothe overall mean value. It appeared that the skipper ran his boat at maximumspeed when sailing to and from the fishing grounds. The amount of fishcaught during the trip did not appear to affect vessel speed, but engine rpmwas generally increased for the return journey. If this was the case for thewhole fleet, then the variable having the most effect on speed differencebetween boats would be vessel length.3.2.3 Fishing Portion of VoyageAnother part of the process which had to be considered in detail was thefishing portion of the voyage. The two major areas of interest were theWithin24hourdayEstimatedEstimatedDateApproximateStartFinishPreviousSubsequentgridsize,numberoflocationtimetimeactivityactivitynauticalmilesfishingspots89-09-05JuandeFuca05:3510:40*waitsailhome1.5*2.5notclear89-09-11DiscoveryPass.06:2015:15waitwait2.0*2.0notclear89-09-12DiscoveryPass.06:2013:24waitsailhome5.0*10.0289-09-25JohnstoneStraight15:2419:47waitwait5.5*1.0389-09-26JohnstoneStraight06:3215:42waitmoveareas6.5*4.0489-09-27BellaBella08:2715:22sailout/waitsailhome2.5*1.5389-10-02JuandeFuca06:3218:02sailout/waitsailhome45*3notclear*datamissingafterthistime,until19:00,whenvesselissailingTableIXDetailedAnalysisofFishingPortionsofVoyages48number of sets (of the net) the vessel made in one day, and the total movementof the vessel during the period when fishing was possible. The data during thefishing/local searching portions were studied to try to identify theseactivities. Again the raw data were used.The position data were studied to investigate how much the ship moved duringthe fishing portion of the voyage. Fishing activity was characterized byrelatively little vessel movement, with moderate engine activity. If the vesselwas fishing one spot consistently, then the observed locations should clusteraround a single value. Latitude and longitude were plotted for each identifiedfishing portion of the voyage, and the size of the grid that the vessel usedduring the fishing period was estimated from these data and any identifiableclusters were counted. This information is summarized in Table IX. However,there was not sufficient information available from the records to identifyexactly how many sets were made.Some insight can be gained from this data. Again there appears to be adifferent pattern between the Juan de Fuca fishery, Figure 15 and thesheltered fishing of Johnstone Strait and Bella Bella, Figures 16 and 17. TheJuan de Fuca fishery did not show consistent clustering, whereas most of theother fisheries did. This was consistent with differences in fishing techniquesdiscussed by Hilborn and Ledbetter [11, 12]. For the Juan de Fuca fishery, theset was made in exposed sea conditions. The fishing took place on the seawardboundary 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 JohnstoneStrait.49Figure 17. Ship Movement During Fishing ActivityLatitude and Longitude, Bella Bella, 89-09-2752.20052.15•52.10--128.20 -128.15 -128.10longitudeFigure 18. Fuel Consumption against RPM,Based on One Hour Averages for All Voyages100•y 0.22240 - 1.3521e-2x + 3.1726e-5x2R2 = 0.985800060iI Oil0tm,o0 •:0,•.••• I0 1000 2000RPM50It was clear that the vessel did not move large distances during the fishingactivity, relative to the distances moved to get to the fishing spot. The largestestimated movement was approximately 8 nautical miles, and was made up of 3smaller steps. It would appear that once a commitment has been made to alocation the vessel remained there for a full fishing day. A movement ofbetween 1 and 2 nautical miles would be expected when fishing in protectedwater, and was probably the result of fish movement or changes in tidaldirection. Although there appeared to be no major clusters for the Juan deFuca 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 boatwas usually in the selected location by the previous evening. Fishing usuallybegan in the morning between 05:30 and 08:30. The only exception was thefirst fishing period in voyage #3 which began at 16:00. The time at which thefishing stopped was more varied, and could be between 13:00 and 20:00. Nofishing 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 aneconomic advantage. It is possible that if the fishing takes place in specificlocations, and all boats know where they are, then the first boat at that spotwill have an advantage. However, given the amount of competition, and thediversity of the distances travelled by the boats, it is difficult to see how thisadvantage cannot be overcome by leaving earlier or leaving other members ofthe team at the best fishing spots to keep guard. Other advantages may be in51terms of increased fish quality, but again trade-offs could be made betweenpower requirements for propulsion and fish processing equipment. It is alsopossible that larger installed power has benefits in the catching process, dueto a higher speed increasing the swept volume of the net.3.2.4 Fuel ConsumptionFuel consumption during transit and fishing was expected to be a major factorinfluencing the economics of fishing vessels. Fuel consumption was highlycorrelated with engine revolutions, as can be seen in Figure 18, taken fromvoyage 3. Whilst the polynomial regression fitted to each voyage was slightlydifferent, there was an insignificant loss of accuracy by using one equationfor all the voyages. This is given in equation (1) below:Fuel consumption (l/hr) = 0.236 - 0.013*RPM + 3.152E5*RPM (1)It was apparent that there were four basic levels of engine activity typicallyused throughout a voyage. These were zero, while resting, 700 RPM forfishing/local searching, 1600 RPM for transit to the grounds (empty) and 1800rpm for transit to the port (full). Very low levels of RPM were observed, whichwere less than the minimum RPM at which the engine would normallyoperate. These were obtained during the averaging process, where the enginewas 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, andthe amount of time spent in each activity during a voyage. Discussion with theskipper indicated that the records were reasonably typical of his operatingstyle. The difficulty was that it was a very limited data set, and did not52represent a full season of operation. During the time that the data were beingrecorded the vessel was only active in one fishery. The data cannot be used forchecking the simulation model for anything other than salmon seine fishing.Nevertheless, these are the only data we have on detailed movement patternsfor a fishing boat. Although the number of voyages for which data wereavailable was very small, it does generally agree with the observationsrecorded by other observers, and discussed in Chapter 2.The data acquisition could have been improved by expanding the memory, orstorage capacity, so that potentially valuable data were not lost when thebuffer was full. Alternatively, a regular series of visits could have be made tothe boat to copy the data onto magnetic disks, before the buffer was full. Itwould also have been desirable to include some method of determining whenthe vessel was actually fishing. Perhaps an additional data channel to monitorthe drum winch activity could have been incorporated into the system. Itwould also have been interesting to have catch data recorded for each set, inparallel with the vessel technical performance.3.3 Summary of Observations on a Seine VesselThe data obtained from the voyage analysis can be used to give a goodindication of vessel activity and fuel consumption on each part of the voyage.The vessel spent a relatively short period of time fishing, relative to otheractivities, and always returned to Steveston after each fishing trip. The vesselmoved between port and the fishing grounds and back to port at its maximumspeed. The speed did not vary between outward and return trips, but enginerevolutions were increased for the return journey to maintain the speed.There was relatively little variation in speed over the course of the voyage.53Due to the length of the voyages and the observation that there was littlevariation in mean speed between voyages, accuracy would not be lost in asimulation model by assuming that the speed was constant during the transitportion of the voyage. The boat did not move much during the course of afishing day, and for the purposes of simulation could be considered to befishing in one spot.The fuel consumption during fishing was much lower than during transitportions of the voyage. The highest fuel consumption was when the vessel wasreturning to port. Fuel consumption during the return leg of the voyage was31.5 percent higher than the outward leg. Fishing activity consumed fuel at arate of 10 percent of the outward leg. Clearly fuel consumption during fishingwas a small portion of the total fuel consumed, but distance to and from portmay have an effect on the profitability of the vessel’s operations. Given thelow rate of fuel consumption, the amount of vessel mobility during fishing isnot critical, in relation to the transiting portions of the voyage profile.54Chapter 4Determination of Catch and Income Datafor Salmon Seine Fishing BoatsThis chapter will develop the background data for such important factors asthe nature of the catch rate and how it can be translated into income for afishing operation. The data that were available from the literature were notsufficient to develop a realistic simulation, where vessels had a choice of areasin which to fish. Most published data were based on the average catch, withlittle discussion on the nature of any random variability. The benefit of usingsimulation was being able to model the random variables, and so somepreliminary work must be done in order to understand how the catch rate andits value vary with geographic location. These data will then be used withinthe simulation model.A simulation model of the full fishing season would be complicated toconstruct, due to the amount of information required. It is necessary tosimplify the system, in order to understand the dominant mechanisms.However, any simplifications must be done in a realistic manner, such that thefinal model still represents the major components of the fishery and thedecision of the skipper. After some consideration, it was decided that threegeographic areas would represent an acceptable minimum number. This wouldmean that any decision would be more than a simple ‘heads’ or ‘tails’ and theselection process for three areas could easily be expanded to include moreareas, if necessary. A preliminary review of the openings indicated that theinstances when three or more areas were open together, if the areas were wellTotal,%TotalAreaNameChinookSockeyeCohoPinkChumPink+Chum6,7,8Butedale,BellaBella,BellaCoola65.4267.2201.94748.7916.75665.491.383,4,5Nass,Skeena,etc55.21416.3241.33724247.93971.969.8712,13JohnstoneStrait77.71627.3202.12415.6529.62945.260.7021-27WestCoastVancouverIsland460.61173.31821.81030.5712.41742.933.531,2E, 2WQueenCharlottes162.6164.5462.11291290.11581.166.7020JuandeFucaStrait24.3851162.8819.813.4833.244.5314-18GeorgiaStrait97.2160132.749.4206.1255.539.5928, 29FraserRiver28.9966.623205.141.4246.519.499,10Rivers/SmithsInlet10.3345.141.2114.447161.428.92TableXTotalCatchforDFOGeographicAreas, bySpecies10YearAverages,1979to1988(Thousandsoffish)Ln56spaced, were relatively rare. This was because the fish tended to appear in thenorthern areas early in the season and the southern areas later in the year.Also, some areas would be rejected by individual skippers, based on historicalrecords, personal preferences or intelligence on fish abundance.The next phase in the analysis was to select three representative areas to beincluded in the model. If vessel mobility was to be studied, then the areasshould be well spaced. It would also be useful to include some areas studied byother 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 inTable X, taken from Bjerring [16]. These data showed that the most productivecombined areas, in terms of the number of fish, were Butedale, Bella Bella andBella Coola (Areas 6, 7, and 8 in Figure 1). This combined area would beinteresting 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, wereJohnstone Strait (Area 12 and 13) and Juan de Fuca Strait (Area 20). The totalcatch per season, averaged over ten years, for these areas was approximately30 percent and 80 percent lower than those from Areas 6, 7 and 8. This wouldindicate that the seasons were shorter for these areas, or that catch rates werelower.4.1 Data Required for Simulation ModelThe ideal data for developing a simulation would have been catch per set foreach area. However, only one set of published data was found at this level ofdetail, for Areas 12 and 13 [7]. These data gave mean catch per set for open sets,57point sets with short line-ups and point sets with long line-ups. An analysis ofvariance (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, butthese differences were hardly significant at a practical level. The catch ratesfor different queue types for the point set were different however, with 27-28fish per set for short line-ups (1-2 boats) and 40-45 fish per set for long line-ups (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 longerbe current. From discussions with the skipper, it seems that open sets are morecommon than they were at the time of Ledbetter’s observations, and fishingtechniques differ between areas. It would be possible to use Ledbetter’s workfor a simulation of Johnstone Strait by fitting probability distributions to line-ups and catch rates, but it would give no information on the effects ofmobility.It was not possible to obtain information at this level of detail for all thedesired areas, and so data had to be found from other sources.4.2 Summary of Data Available for All DFO AreasAnother source of data was the records kept by DFO of landings for fish caughtin 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 therelated income, which can be expected from a given area. Data were obtained58from 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 fishand dollar value per boat per trip. This was because data were collected for alltypes of salmon, classified by DFO, and it was important to know the totalamount of fish caught by the boat. Some data were omitted, due to obviouserrors or omissions. For example, a few vessels would have no length data, andwere removed, and occasionally very high total catches, several milliontonnes, would be obtained, which did not correlate with the number of fish orthe dollar value. These were also omitted from the analysis. This accounted foronly a few records, no more than 5 per area.From these data, the following parameters were derived for each day of thefishing season in each area:59Are a Year # days Mean St. dev $/k g mean(boats >= 6) (kg/day) (kg/day) $/day6 1987 20 4419 728 1.90 83826 1988 33 7232 3025 1.76 127296 1989 6 1143 322 1.17 13366 1990 28 5645 3288 1.06 59954 year mean 19.7 4265 2582 74827 1987 21 3095 1792 1.90 58727 1988 20 4662 3393 1.76 82057 1989 11 1951 1289 1.17 22817 1990 25 3351 2144 1.06 35594 year mean 17.3 3236 1113 54538 1987 22 2327 1235 1.90 44158 1988 33 4502 2225 1.76 79238 1989 6 4166 2825 1.17 48708 1990 27 3085 676 1.06 32764 year mean 20.3 3665 999 573612 1987 26 3353 2011 3.36 1125012 1988 24 2700 1691 2.74 739312 1989 50 3971 1741 2.52 999812 1990 33 4051 2456 1.90 77144 year mean 33.3 3341 629 954713 1987 18 3384 2271 3.36 1135413 1988 17 2248 1625 2.74 615413 1989 34 3622 1947 2.52 912013 1990 24 4114 1897 1.90 78344 year mean 23.0 3085 790 887620 1987 11 2584 1130 3.24 836020 1988 10 1428 1090 7.28 1039820 1989 32 4575 1298 2.95 1349620 1990 14 7422 3654 3.04 225794 year mean 17.7 2862 2624 10751Table XISummary of Annual Catch Datafor Each Fishing Area, by Year1987 to 199060- 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 wasobserved outside these periods. In order to ensure that reliable values of meancatch per day were obtained, only days where 6 or more boats reported alanding were used in the subsequent analysis.It was assumed that the date of the landing was the last day of fishing, i.e. for aone day trip the fish was caught that day. It is appreciated that this may be inerror by the time it takes the boat to return to harbour, but no data were givenfor where the catch was landed. The sailing time may have had the effect ofshifting the date by some constant. A refinement to the method would be toinclude the data on the dates of the openings and force the fish caught into theperiod of legal fishing activity. Unfortunately this was not available at thetime the analysis was carried out.From these data we can produce a summary of the fishing activity in a givenarea. The important factors to consider were the number of boats which fishedin each area, the duration of the season, the mean catch per day over theseason, together with its standard deviation and the number of days whenmore than 6 boats reported a landing. These data are summarized for all theareas selected, by year, in Table XI. Since there was often a wide variation61Area Year First day Last day # days Total Mean Std. devnBoats >= 6 # boats boats/day boats/dayButedale 1987 12 92 21.00 410 35.32 41.86[6, 7, 8] 1988 9 89 28.67 505 59.45 59.451989 17 88 7.67 89 16.39 16.101990 14 107 26.67 499 49.88 68.864 year mean 13 94 21.00 375.75 40.26Johnstone 1987 33 85 22.00 460 48.60 46.21[12, 13] 1988 29 114 20.50 471 49.00 49.021989 17 117 42.00 502 59.50 55.601990 37 116 57.00 508 63.40 53.574 year mean 29 108 35.38 485.25 55.13Juan de Fuca 1987 42 90 11 211 87.50 53.97[20] 1988 39 54 10 157 61.50 35.411989 18 89 32 201 72.80 57.591990 45 61 14 217 80.00 62.334 year mean 35.00 73.50 16.75 196.5 75.45Table XIISummary of Length of Season and AverageVessel Activity, by Fishing Area,1987 to 199062between years for a given area, the 4 year mean for the mean catchlday andthe 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 XIITable XIII gives, for each area;- duration of trip (mean and standard deviation)- total number of boats which used area- one day trips- % two day trips4.3 Translation of Catch Data to IncomeSo far, only the weight of salmon landed has been considered. This isimportant from the point of view of estimating the number of fish caught andits subsequent effect on the fish population. It is also important in relation tothe design of the vessel, in terms of the size of the hold and the correspondingamount of ice required. However, the most important factor for voyageeconomics is the cash value of the fish. The conversion factor between theweight of fish and its dollar value needs to be determined.63Area Year Mean Length St. Devn. % 1 day trip % 2 day tripof trip, days daysButedale 1987 1.684 0.694 58 33.70[6, 7, 8] 1988 1.749 0.952 65.3 26.701989 1.361 0.571 70.8 19.101990 1.744 0.707 60.7 33.104 year mean 1.635 0.185 63.7 28.15Johnstone 1987 1.154 0.24 96.3 1.95[12, 13] 1988 1.125 0.317 90.87 2.761989 1.446 0.317 87.3 11.801990 1.342 0.383 87.6 11.604 year mean 1.267 0.153 90.5175 7.03Juan de Fuca 1987 1.734 0.547 64 28.90[20] 1988 1.699 0.508 54.1 43.901989 2.203 0.488 17.4 76.101990 2.173 0.433 15.2 79.304 year mean 1.952 0.273 37.675 57.05Table XIIISummary of Length of Tripto Each Fishing Area,1987 to 199064Let us consider the expected range of income from different types of salmonspecies in terms of $/kg. The 1987 and 1988 averages for total landings in B.C.are given below, taken from [16]:Dollars per kilogramYear 1987 1988Chinook 6.70 8.52Sockeye 5.94 8.14Coho 4.59 6.12Pink 1.29 1.57Chum 2.45 2.81Table XIVAverage Dollar Value for Salmon,by Species, 1987 and 1988There is a quality factor implied in these figures, since expensive species areusually caught by troll, and frozen as individual fish. This results in a highquality product, which is sold as whole fish. For seine fishing, the large netand the bulk storage of fish in the hold generally results in a lower qualityproduct. Seine vessels target mostly chum and pink salmon (Ledbetter), whichare primarily sold for canning, and this is reflected in the price paid by theprocessor for the fish. From a review of the catch data, it seemed that therewas a mix of species obtained from a single trip. Since this varied withgeographic location, due to fish habitat, the simulation must include realisticvalues for each area.65• $, obs.— regression through originlinear regression-. -- linear regression, log variablesFigure 19. Comparison of Regression Equations forConverting Catch to Income, Johnstone Strait, 1987*E0U30000020000010000000 20000 40000 60000 80000 100000Fish, kg66A value of the mean dollars per kilogram was required for each area, and eachyear for which data were available. Very strong correlations were observedbetween total catch and total dollars for each area based on linear regression,(R2>=0.964), for the four years for which data were available. It was necessaryto check which was the most suitable procedure for determining therelationship between the weight of fish and the dollar value. The analysismethods will be demonstrated with data taken from Areas 12/13 for 1987.The most obvious approach was a linear regression equation through theobserved data for the total catch per year against total income. This is shownin Figure 19. At first sight the regression seems adequate. However, we notethat the intercept with the y axis did not pass through the origin, which wouldgive unreliable predictions of income for catch rates less than approximately2500 kg. Another factor to consider was that the residuals were not randomlydistributed, since no large variances were observed at small values of fishweight. Weisberg [20] suggested that in such cases, a variance stabilizationtransformation should be introduced by taking natural logarithms of thevariables. Using this method, there was a much more random distribution ofthe residuals, and so the method was more rigorous. The regression line is alsoshown fitted to the data in Figure 19.A third alternative was to fit a least squares deviation equation to the observeddata, 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)67where B was determined from 13= Xiyi/Xj2 , with x as total weight of fish, inkilograms, y the total dollar value and e was the error between the actual andthe predicted values. It was observed that the previous problem of non-randomvariance occurred. It is therefore accepted that this is strictly a least-squaresdeviation fit, and no statistical inferences can be made.From Figure 19, it can be seen that there was little practical differencebetween the three methods discussed above. The best method would have beento use the regression which included the variance stabilization, but thisequation could not be programmed directly in the simulation language. It wasdecided that the best alternative equation was to use the linear regressionthrough the origin. This analysis was carried out for all areas and all yearsand the results are also given in Table XI, along with the catch data.4.4 Discussion of DFO DataFrom these data, it can be seen that actual income was always higher than theprovincial average for pink salmon, and in most cases it was higher than theprovincial average for chum salmon. Only in Areas 6/7/8 can we infer thatmost of the catch is made up of pink and chum, because the observed value ofdollars per kilogram is between two provincial levels. Area 20 had a very highvalue of dollars per kilogram for 1988. This was up to 4 times higher than thatobserved for other areas. In this case the majority of the catch was made up ofmore expensive species such as chinook, coho and sockeye.In Table XI we see that Area 6 had the highest average catch per day, over thefour years of data, at 4264 kilograms per day. Areas 7, 8, 12 and 13 all had catchrates between 3665 kilograms per day and 3084 kilograms per day, which were68close to the estimated 10 year average, described earlier. Area 20 had a slightlylower catch rate at 2862 kilograms per day.When studying the voyage economics, it is important to compare the differentareas on the basis of dollars per trip, rather than kilograms per trip. Table XIalso gives the average catch multiplied by the average dollars per kilogramfor the areas and years described above. Area 20 had the highest dollars perday based on the four year average, at $10,700/day. The next highest was Area12, which was $9547/day. These data showed that the areas identified in [11]were still the most economically productive, once allowance had been made forthe dollar value of the fish. Areas 6, 7, and 8 had the lowest dollars per day, andtherefore may be the least desirable, even though they were the mostproductive in terms of the total amount of fish caught. This analysis clearlyillustrated the need to consider the dollar value of the fish, as well as thequantity 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 attractsthe highest number of boats per day, when it is open, followed by Areas 12/13and Areas 6/7/8. This follows the trend in dollars per day and would indicatethat economics is a major motivation in fishing.Since the dollar value appears to be the driving factor in the movement of boatto 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 thesize of the catch affects the subsequent size of the vessel, and the value of the69fish may be affected by broader economic issues, outside the scope of thisanalysis. 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 theareas is also given in Table XII. Since areas within the same aggregate locationseemed to follow similar patterns, I will consider only these larger areas, usingaverages over the four year period. The mean day for the first observation wasday 13 in Area 6/7/8. The first observation in area 12/13 was day 29, and day 35for 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 wasinteresting to note that based on the four years of observations, all four areaswere open between days 35 and 73, out of a total season between day 13 and day108. This period represented approximately 40% of the total time available, andthe period where the most complex decisions were required of the skipper. Ifonly one area was open, then the only decision required of the skipper waswhether to fish or not. However, when there was a choice of areas, and if theobjective was to maximize the total income for the season, it is important toknow 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. Mostother areas had four year averages around 20 days. Despite the higher dollarsper day value for Area 20, the fact that it was open fewer days, meant that askipper could expect more total income for the season from fishing in Area12/13, if only one area had to be chosen. The disadvantage of only fishing Area12 would be that there would be a lost opportunity to make a higher income, onthe days when Juan de Fuca was open. The maximum income would come from70Figure 20. Fishing Vessel ActivityProfile 1987, All Areas200175150125: 100IIILILJ d.J I... ....... I.. I0 20 40 60 80 100 120 140dagFigure 21. Fishing Vessel ActivityProfile 1980, All Areas3002502001Wa,a.a 150p10050n U 1Ad i. i..-0 20 40 60 80 100 120dag71switching fishing areas at some time during the season, and this is somethingwhich must be included in the simulation.From the daily data we can also obtain an indication of the distribution ofeffort with time. This is shown as the maximum number of boats fishing as afunction of date, for each year, in Figures 20 to 23. It can be seen that theeffort was not uniformly distributed over the season, and there were periodicspikes within the data. These spikes were at approximately 7 day intervals, andreflected the nature of the openings described in [11, 12, 13]. The number ofpeaks for the total season was estimated to be between 11 and 13 over the fouryear period, which is less than the typical number of trips estimated from theannual summary data. This may be made up of boats making more than onetrip 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 itwas the only area open, at the beginning of the season. At the end of theseason, the effort was much lower. This may represent the mobility describedin [11], in that to maximize income, the skippers will pick the best area fromthose that are available.Another important factor which can be obtained from the data was theduration of each trip. This is summarized in Table XIII. It can be seen that themean duration of the trip for all areas is between one and two days. Also it canbe 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. Itcan be seen from Table XII that almost all of the boats were recorded as havingfished at least one day in Areas 6/7/8 and Areas 12/13. Only about half the fleet72Figure 22. Fishing Vessel ActiYitgProfile,1989, All Areus225200175150125‘ 100755025,f .1 ij — —______________________________________20 40 60 80 100 120dagFigure 23. Fishing Vessel ActivitUProfile,1990, All Areus3503002504’, 2000.0* 150100__.ILIi Ii i L . L •10 20 40 60 80 100 120dag73fished at all in Area 20. It does seem to be that the length of the trip iscorrelated to the catch rate, with the longer trips, for 1989 and 1990 being theyears with the highest average income per trip.Hilborn and Ledbetter [12] noted that the mean length for boats fishing Area20 was longer than those fishing Area 12/13. This was observed in these dataalso. The mean length of boat for each of the three areas is given in Table XV.Boat Length, mMean St. Devn.Area 6/7/8 18.238 3.919Area 12/13 18.499 3.097Area 20 20.372 2.972Table XVAverage Length of VesselsFishing in Each Area, 1987 to 1990It seems as though the bigger boats go more often to Area 20 for longerfishing trips than the smaller boats. This may be a function of the moreexposed fishing location where larger boats are less influenced by theweather conditions. It may also be due to economics, in that the bigger boatshave 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, weredesirable from the point of view of developing the simulation. It would also bedesirable to avoid areas which were adjacent, since fish may move betweenareas, and the catch rates would not be independent. It was noticed from a74preliminary study of the data that the catch rates and openings in adjacentareas were highly correlated, and including all the areas in the model wouldnot add to its accuracy. For these reasons the areas selected for further studywere Butedale, (Area 6), Johnstone Strait (Area 12 only) and Juan de Fuca(Area 20).4.5 Nature of Distribution of Daily CatchSo far only the mean daily catch over the season has been considered. Catchrate is discussed in the literature as a random variable, and the nature of thedistribution 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 knowthe nature of this random variable.In order to do this, the data for the landings from a single area, on a singledate, must be studied. It was not possible to establish if all the fish was caughton that one day, since we only have the date of landing, but this is the bestassumption that can be made. It must also be assumed that the boats wereacting independently, and were only landing, or reporting landings, whichwere caught by that boat. It was also desirable to consider dates where a largenumber of boats reported landings. Exploratory histograms for several daysfrom each area showed that there was a wide range of data, always with aminimum observed value close to zero. There was also a wide range of shapesof 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 terms75of number of fish, to be predicted by the negative binomial distribution, givenin equation (3).P(x=k) =(k1)pr(ip)kr (3)Curr [21] considered the theoretical possibilities of fitting an Erlang model,equation (4), to catch per set of blue whiting in the North Sea. The model wasderived for a fishery where fishing operations were not impeded by on-boardprocessing requirements, so catch could be stowed in a very short time. Thisprocess was similar to salmon seine fishing, where fish were typically loadedstraight into the hold.f(x)=______xk 1 expl- k xim) (4)Curr argued that there was some theoretical basis for the use of the Erlangdistribution, since it represented an activity which took place in stages, whereeach stage was exponentially distributed. (The sum of n independentexponential distributions is an Erlang distribution with k=n). It was arguedthat a single species fishery could be expected to fit such a process, with a haulbeing a single stage. However, the distribution for the catch per haul may notbe exactly exponential, due to technological factors. The general case for theErlang distribution (with non-integer k) is the gamma distribution, equation(5).76Figure 24. Gamma Distribution Fitted to Catch/DayAugust 10, Johnstone Strait, High Catch Rate1.0•.0.80.6U-0.4.0.2 — Max. likelihood estimate• Fx(observed)0.0.• I • I0 10 20 30Catchfday (tonnes)Figure 25. Gamma Distribution Fitted to Catch/Day,August 24, Johnstone Strait, Medium Catch Rate1.0•0.8-0.6-x0LI0.4-0.2 -— Max. likelihood estimate• Fx(observed)—I I0 2 4 6Catchiday (tonnes)77f(x) = 1 (xr - l exp(--) (5)aF(X) a aCuff 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 ofthe gamma distribution meant that the distribution for second and subsequenthauls could be calculated, but was also a gamma distribution.Thus using the same arguments as Curr, the distribution of the total catch perday for all boats fishing in the same area should also be a gamma distributionif all the boats have equal catching power and the variation in catch rate isdue simply to sampling from the same underlying distribution. This isconsistent with Ledbetter’s observation since the gamma function is theequivalent of the binomial function, for non-integer values of X.To test if the daily distribution of catch was represented by a gammadistribution, we can choose some days from the data, and test them to see if agamma distribution fits the observed data. Area 12, for 1987, will be used, sinceit was used by Ledbetter, and was neither the year of minimum nor maximumtotal catch. Three days were chosen with high, medium and low catch rates.The days selected were:August 10 High catch rateAugust 23 Medium catch rateSeptember 22 Low catch rateEstimates of the scale and shape parameters, a and ?, for these three days weredetermined from maximum likelihood methods [221. A summary of the78Figure 26. Gamma Distribution Fitted to Catch/Day,September 23, Johnstone Strait, Low Catch Rate1.0•________0.8I:I.0.6/ ._I.I •LI.I.0.4— Max. likelihood estimate0.2• Fx(observed)0.0• I0 2 4Catchlday (tonnes)Figure 27. Comparison of Probability DensityFunctions Fitted to Observed Data1.5August10August241.0••-.--.-. September23‘C0.5t.4 4%0.0• I I I0 5 10 15 20Catchlday (tonnes)79estimated parameters is given in Table XVI, and the fitted cumulativedistributions are compared with the observed values in Figures 24 to 26. Thecomparison of the density functions, Figure 27 shows the wide variation whichcan be observed for total catch per day.Date Number a X mean catchof boats (tonnes)August 10 46 2.671 2.508 6.699August 24 61 1.129 1.620 1.829September 23 33 0.830 1.003 0.827Table XVISummary of Parameters forProbability Density Functions, Daily Catch DataObserved probability distributions were compared with the fitted ones, and aKolmogoroff test used to test the level of fit. None of the distributions wererejected at a =0.05. This is strong evidence in favour of the gamma distributionas a family of two parameter distributions to represent the total catch per dayfor a given area and day.It can be concluded that the gamma distribution is good candidate forprobabilistic modeling of the daily catch data. This is based on the observationthat there is some theoretical justification for its choice and it is a veryflexible shape. Provided that the gamma distribution is based on observations,it should give a realistic approximation to catch per day data.804.6 Variation in Mean Catch per Day Over Full SeasonThe discussion above suggested that there was a wide variation in the shape ofthe catch per day distribution, even for the same area and the same year. Itwas impractical to fit separate distributions to each day of the season, for eacharea, due to the amount of computation involved. It was clearly desirable toinvestigate methods of simplifying the process.Ledbetter [7] suggested that the distribution of average or expectedskipper/vessel effectiveness may be represented by a gamma distribution(equation 5) of Poisson variables (x), where X uniquely describes the shape ofthe distribution and a is a scaling parameter reflecting the driving process ofthe system (salmon abundance). It would seem that the gamma distribution wasa good model for the mean catch per day, when the whole season wasconsidered.A program was written, using the methods given by Bury [22], for determiningthe maximum likelihood estimates of parameters for a two parameter gammadistribution fitted to the observed mean catch per day. A visual inspection ofthe data indicated that there was not sufficient evidence for three-parametermodels.A comparison of the fitted distributions with the observed data is given inFigures 28 to 30, for each of the areas in the study. The estimated parametersfor the distributions are given in Table XVII, together with the Kolmogoroffstatistic determined from the observed data and the fitted distribution. It canbe seen that in most cases the fitted distribution was not rejected at a =0.1 ora =0.05. There were some cases however, where the distributions were rejected,AreaYear#daysMeancatchStd.devnSigmaLamdaVar.sigmaVar.lamdaKolmogoroffreject@reject@(Boats>=6)(kg/day)(kg/day)statisticalpha=0.05alpha=0.161987204418.74727.85124.1235.602529.09206.310.158noyes61988337232.403025.031145.926.3181839.442.290.129no*no*6198961142.59321.6178.3314.592660.5889.850.158nono61990285644.633287.553030.211.86734465.400.210.125nono4_jarmean19.74264.57121987263353.112010.961264.682.65133100.400.480.080nono121988242700.181690.93981.542.7586138.270.560.077nono121989503970.551741.18901.384.M34622.320.740.065nono121990334051.472456.051461.642.77138018.00.410.133nono4jarmean33.33341.28201987112584.251129.95520.034.9748699.454.000.150nono201988101428.101090.31449.253.1843270.461.850.237noyes201989324574.771297.98434.4210.5313112.277.380.114nono201990147422.363654.152306.993.22790795.601.310.289yesyes4yearmean17.72862.37*smallnumberofopenings,fitunreliableTableXVIISummaryofFittedDistributionstoSeasonalCatchData,forEachFishingArea,1987to1990I-82Mean catch per day (kg)o CDF, obs. 87— CDF, fitted 87• CDF, obs. 88CDF, fitted 88CDF, obs. 89— —- CDF, fitted 89CDF, obs. 90CDF, fitted, 90o CDF,obs.87— CDF, fitted 87• COF, obs. 88CDF,fitted88o CDF, obs. 89CDF, fitted 89CDF,obs.90CDF, fitted 90Figure 28. Comparison of Observed and FittedCumulative Distributions for Butedale0 10000axLIaxLI.20000Figure 29. Comparison of Observed and FittedCumulative Distributions for Juan de Fuca0 10000 20000Mean catch per day (kg)830.00 2000 4000 6000 8000 10000 12000o CDF, obs. 87— CDF,fitted87• CDF, obs. 88CDF,fitted88o CDF, obs. 89— —- CDF, fitted 89* CDF, obs. 90- -- CDF, fitted, 90Figure 30. Comparison of Observed and FittedCumulative Distributions for Johnstone Strait1.00.80.60.40.2xU.Mean catch per day (kg)84or where there were insufficient data. For example, Area 6 for 1989 had veryfew points. Area 20 in 1990 was the only fit which was rejected. These dataseemed to show two almost constant catch rates, and perhaps two distributionsought to have been fitted.A detailed description of the methods used to fit the distributions and the testsof the fit is given in Appendix 1.4.7 Simplification of Daily Catch DistributionsWe must also consider the relationship between the mean catch per day andthe shape of the probability density function for catch per day. This isimportant since for one reason or another we do not expect one boat to obtainthe mean catch for a given day. It will do better or worse than the mean basedon a variety of factors such as the number of boats and other uncontrolledvariables such as wind, weather and current.The mean catch per day was plotted against its standard deviation for all areasand all four years of data. It was noted that this relationship was reasonablyconstant for an area, but was different between areas. Figures 31 and 32 showthis relationship for Area 12 and Area 20. Based on the single day data, if weassume a gamma distribution for daily catch distribution, then we can estimatethe scale and shape parameters directly from the first and second moments,calculated for the area profile, rather than use maximum likelihood equationsfor each day. This relationship is given by:mean=aX (6)variance = a2 (7)85Figure 31. Mean Catch per Day against StandardDeyiation Johnstone Strait, 1907 to 199o9000-8000 g = 646 + 229.757 0r2 = .7447000 0 006000 0 0500000004000100000 1000 2000 3000 4000 5000 6000 7000 8000 9000mean catch/dag, kgFigure 32. Mean Catch per DayagainstStandardDeyiation Juan de Fuca, 1907 to 1990ØLJUU= .474x + 127.358, 07000r2 = .6770 06000d 5000‘ 400030002000001000 00 2000 4000 6000 8000 ioooo 12000mean catch/dag, kg86Area 6/7/8 95 percent 95 percentLamda Confidence ConfidenceYear Mean Std. devn. Interval IntervalLower Upper1987 3.319 1.636 2.907 3.7311988 2.781 1.776 2.4 3.1621989 2.31 4.573 0.332 4.2881990 3.357 3.673 2.539 4.174All years 3.055Area 12/13 95 percent 95 percentLamda Confidence ConfidenceYear Mean Std. devn. Interval IntervalLower Upper1987 2.587 1.986 1.983 3.1911988 1.744 0.833 1.481 2.0071989 2.405 1.39 2.103 2.7071990 1.906 0.981 1.646 2.167All years 2.195Area 20 95 percent 95 percentLamda Confidence ConfidenceYear Mean Std. devn. Interval IntervalLower Upper1987 5.961 2.975 3.962 7.9591988 2.44 1.191 1.588 3.2911989 5.949 2.877 4.912 6.9861990 3.928 2.504 2.482 5.374All years 5.005Table XVIIIVariation in Shape Parameter, Lamda,Between Years, for Three Fishing Areas,1987 to 199087Figure 33. Variation in Shape Parameter, Awith Mean Catch per Day, Johnstone Strait1412 010806 00 004 00 0 0 0 0 0 000 OooQ °P 0000 0 00 o0n&Rfln?o.oJ 0 02ocbcb & 0 0000 0000 gO0 1000 2000 3000 4000 5000 6000 7000 8000 9000mean catch/day, kgFigure 34. Variation in Scale Parameter, awith Mean Catch per Day, Johnstone StraitLJUU - I I12000 0100008000a for mean A60000D0 1000 2000 3000 - 4000 - 5000 6000 7000 8000 9000mean catch/day, kg88Figure 33 shows the shape parameter, X, plotted against mean catch per dayand 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 withmean catch per day, and so the simplest simplification would be to use theaverage value. This can be rationalized on the basis of Curr’s discussion inrelation to the effect of technical factors, which should be reasonablyconstant for a given area. Once the value of A has been set, then the value of awas determined directly. Figures 33 and 34 show the fitted data in relation tothe observations, for Area 12. Clearly the calculated values represent areasonable approximation to the observations. Although the results are notshown here, the other areas were checked, and similar results were obtained.Table XVIII gives values of A, calculated for each year, rather than the meanfor all four years. In all cases except one, Area 20 for 1988, the mean value ofthe annual data is inside the 95% confidence interval for the average value. Itwas observed that the mean catch per day for this area was much lower thanthe other three years for which data were available. Since the catch per daydistribution is probably of secondary importance after the mean catchdistribution, then this level of accuracy should be sufficient.There is also some doubt as to whether or not catch per day is a truly randomvariable. If the mean catch per day is plotted against day, there is often asignificant trend. The data are shown in Figures 35 to 37 for Areas 6, 20 and 12respectively, for 1987. It can be seen that the catch rate decreases as theseason progresses, for Areas 12 and 20, but remains static for Area 6. The dataare summarized for the other years in Table XIX. In only one case was theregression not significant at 90% confidence, for Areas 12 and 20. This may be89Figure 35. Variation in Mean Catch perDay with Day, Butedale, 190710000 a9000 y = 13.49x + 3993.129, r2 = .0280001 700000000 0 000 04’ 4000 0 0E o0 0 03000 0 020001000U I15 20 25 30 35 40 45dayFigure 36. Variation in Mean Catch perDog with Dog, Juan de Fuca, 1907100009000 g = -50.41 lx + 5604.335, r2 = .54580004 70006000o 50004000 0°to06b7b8b9bday90Year Number Slope, R2 Significantat 95%of days kg/day confidenceArea 61987 20 13.49 -0.034 no1988 33 -64.847 0.045 no1989 6 16.513 0.189 no1990 28 196.072 0.792 yesArea 201987 11 -50.411 0.545 yes1988 10 -139.258 0.442 yes1989 32 -34.17 0.185 yes1990 14 -484 0.47 yesArea 121987 44 -86.743 0.418 yes1988 41 3.833 0.004 yes1989 84 -44.209 0.146 yes1990 57 -27.675 0.095 yesTable XIXSummary of Variation inCatch Rate with Time,1987 to 199091due to the fact that there is a finite fish population and that as the seasonprogresses there are fewer fish to catch (due to the mortality caused byprevious fishing within the same area). For Area 6 however, only one yearshowed 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 singlefishing day, at any point in the season, was required, then the assumption of arandom variable should still be reasonable.4.8 Summary of Catch and Income DataThe mean catch per day over the whole season for a particular area can bemodelled by a gamma distribution. Here the ‘mean catch per day’ means thetotal weight of fish caught by all the boats fishing in one area, in a twentyfour hour period, divided by the number of boats. This distribution remainsconstant for the one year period. The catch per day for a particular boatfishing 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 fishingin 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. Thetwo distributions were required to model the level of risk associated with anarea, and a simulation which only included the mean catch per day wouldunder-estimate the overall risk involved when a small number of boats wereoperating together.Within a given fishing area, there was considerable variation between themean catch rates. One area could have a very high catch rate one year, and avery low one the next. When developing a simulation model, it will be92Figure 37. Variation in Mean Catch perDog with Dog, Johnstone Strait, 1907100009000 g = -86.1 39x + 7779 48, r2 = .4208000C70006000 00400030002000100030 40 50 60 70 80 90dag93important to include these differences, since they could have an effect on theoverall profitability of the vessel.The relationship between catch, in kilograms, and income in dollars, appearedto 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 indifferent areas and sometimes the factor was almost as high as four. Thesedifferences had significant effects on the income obtained from differentfishing areas, and must be allowed for in the analysis.4.9 Discussion of the Analysis in Relation to SimulationThe analysis described above must be reviewed in terms of its usefulness fordeveloping a simulation. The preliminary analysis indicated that there wereno strong trends in catch per day with any vessel parameter which was loggedby DFO. On this basis, the assumption implicit in the simulation, that catch isindependent of the vessel, seems reasonable. If however, there were trendswhich did not show up in the preliminary analysis, then the result wouldrepresent the performance of a typical vessel, with parameters close to themean values, and may not be realistic for vessels with extreme parameters.Fortunately, the salmon seine fleet is relatively homogeneous, and any biasthat this simplification would introduce should be small.The alternative approach would have been to fit distributions to catch rates foreach boat, as a function of area and time. This would have requiredconsiderably more analysis. In addition, the number of trips per year to agiven area would have been small, and so the fitting distribution functionswould have been less reliable.94The other major assumption implicit in the analysis was that the mean catchper 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 areduction in catch rate with time, especially for Johnstone Strait and Juan deFuca.Given these observations, a simulation developed using the analysis carriedout in this chapter would be most representative of a ‘typical boat’, fishing ona ‘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 thesimulation would give mean values for catch and income data for a single trip,which would be representative of the long term seasonal values, but theywould not necessarily simulate the overall performance of a boat over theseason, opening by opening. This is reasonable, since the number of days eacharea is open varies between years, and a reliable economic parameter would beaverage income per trip. This could be multiplied by the number of trips in agiven year to give an estimate of the total income.It is recognized that the data discussed above may not be ideal for theapplication being considered, but it appears that it is sufficient to allow areasonable attempt at developing a simplified simulation model of a salmonseine fishing operation, which is also realistic. A portion of the fleet is highlymobile, as described by Hilborn and Ledbetter, and many boats do react on anopening by opening basis. Thus to model a single opening, and determinewhich strategy could have the best return in the long term, given a smallamount of information would be a worthwhile objective.95Chapter 5Development and Testing of a Simulation Modelfor Salmon Seine FishingHaving reviewed the data available on the operation and economicperformance of salmon seine vessels in British Columbia, a simulation can nowbe developed which contains the essential features of the system andrepresents the behaviour of a ‘typical’ boat. The development of the simulationmodel requires the collecting together of the information discussed in theprevious chapters and translating it into a series of rules that can be modelledby a computer program. Information is required on the technicalperformance of the boat, the catch and income data, the geographicallocations of the fishing grounds relative to the home port for the vessel, andthe way in which the skipper selects a place to fish. This chapter outlines thedevelopment of a working simulation model for salmon seine fishing inBritish Columbia. Special attention will be paid to developing a model whichwill obtain a higher than average income, since it is well known thatsuccessful strategies and technologies are copied by the rest of the fleet.Once the simulation model has been written, it must be verified against theobserved data to check its accuracy. Once the accuracy of the initial model hasbeen confirmed, then it can be used to test how different operating conditionswill affect the economic performance of the boat.Since all the data described in the previous chapters were assumed to be forsingle boats, this was chosen as the starting point for the simulation process.96Once the operation of a single boat has been successfully validated thesimulation can be expanded to investigate how the profitability of theoperation varies when two or more boats fish together. The obvious candidatefor the simulation was the vessel described in Chapter 3, for which theoperational data were available.The simulation would model this vessel, operating within the three areas forwhich a detailed analysis of the catch data, described in Chapter 4, was carriedout. These areas were Butedale (area 6), Juan de Fuca (area 20) and JohnstoneStrait (area 12). Since the home port for the vessel was Steveston, this was usedas the point where the fish was landed. This is quite reasonable, since it is thebiggest 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 andprofitability.5.1 Information Required for Simulation Model5.1.1 Vessel Technical and Operational ParametersFor the sake of computational efficiency, the simulation included theminimum number of economic and technical parameters for the ship andgear. These were the values which were kept within the program, and used fordata collection and analysis. This approach allowed for the fact that vesselsoperating simultaneously could have different technical parameters. Indeveloping the simulation, it was also assumed that there was no correlationbetween vessel parameters and catch rate, but the maximum catch whichcould be landed by a single boat depended on the hold size.97After some consideration, it was decided that the following parameters coveredthe major technical and economic factors which effected the performance ofthe vessel.i. Ship speed, knots.This determined how much time it took the boat to move between locations. Itwas assumed that the speed of the vessel did not vary between the outward andreturn journeys. It is also assumed that the speed was constant. This was basedon the observations on the vessel discussed in Chapter 3.ii. Total Hold Capacity (m3).This determined how much fish the boat could transport back to the port forprocessing.iii. Fuel Consumption and Fuel CostSeparate rates of fuel consumption, in litres per hour, were used for sailingout, fishing and sailing home. Total fuel cost per trip was used in the analysis,and this was obtained by summing the individual components. Fuelconsumption rate was assumed to be constant for each leg of the voyage, basedon the observations made on the vessel. Fuel cost per litre was assumed to beconstant throughout the duration of the model. These were the factors used todetermine the variable cost of operating the boat.iv. Location Code and TimerThese were factors required for navigating the vessel between the port andthe fishing areas, within the simulation, and logging the time spent in eachactivity.98v. Data Collection and Analysis1. 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 voyagebasis. Notice that the model made no allowance for the fixed costs of operatingthe boat. This was difficult to determine unless more specific information onthe cost of the vessel chosen for the simulation was known.The parameters used in the simulation model, based on observations on thevessel described in Chapter 3, are given below. Since the mean ship speed forall the voyages observed was close to 10 knots, this figure was used as aconstant transit speed, loaded or light. The hold capacity was estimated to be84.6 m3. The fuel consumption was 59.4 litres per hour outward, 6.4 litres perhour fishing and 78.1 litres per hour sailing home, loaded. Fuel cost wasassumed to be 40 cents per litre.5.1.2 Spatial Distribution of Fishing GroundsOnce the vessel parameters were defined, the next important factor to considerin developing the model was the spatial distribution of the fishing areas. Thethree areas for which detailed analysis of the catch data was carried out wereused in the simulation model. These appeared to be popular fishing areas, andwere distributed such that there would be no possibility of the fish moving99between areas, during one particular opening. Thus the distributions usedwithin the model would be independent. Also since the basis for the simulationwas a single opening rather than a full season, we do not need to consider theoverall fish population and the effect of last weeks catch on the total numberof fish left.It was observed that the vessel moved relatively little during the course offishing operations. Thus a reasonable simplification was to consider eachfishing location as a single geographic point, at the approximate centre of thedelineated fishing area. The distances between grid points used in the modelare given in Table XX.5.1.3 Openings and Other Constraints on FishingThe 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 givenarea were typically seven days apart. This was confirmed by the area profiledata, obtained from the analysis of the DFO data, given in Chapter 4. Using thistime scale, the basic unit of one hour was adopted within the simulation model,since this would give reasonably accurate voyage times, fishing times andwaiting times.It was assumed that openings lasted one day per week in a given area. This wasbased on the observations from the recorded length of the trips, taken fromthe DFO data, given in Chapter 4. Single day trips were the most probable forall areas, with the possible exception of Juan de Fuca, Area 20, for 1989 and1990. It was also assumed that all areas were opened for fishing simultaneouslywithin a single day, beginning at 06.00 and closing at 15.00. This was based on100Distance, nautical milesLocationFrom Steveston Butedale Johnstone Juan de FucaLocationCode 1 2 3 4ToSteveston 0Butedale 290 0Johnstone St. 100 190 0Juan de Fuca 75 365 175 0Table XXDistances Between Port and Fishing LocationsUsed in Simulation Modelthe observation that most of the fishing periods from the monitored vesselwere within this time period, and discussion in the literature which explainedwhy the fishing took place in daylight. It was also assumed that notice of anopening was given for all areas simultaneously, 48 hours ahead of theopening.5.1.4 Catch Data for Fishing AreasThe simulation was formulated to use the gamma distributions calculated inChapter 4. Mean catch per day for each area was sampled from a gammadistribution based on the seasonal values. The actual daily catch for the boatwas sampled from another gamma distribution, based on the mean catch perday, taken from the seasonal distribution, and a shape parameter, , taken asthe average of all the daily shape parameters for that area, over the four yearsfor which data were available. Thus on any given day, the boat in thesimulation could do considerably better or worse than the mean for the area.101Catch data were translated to income, based on the regression of total dollarsearned for the season against total catch, also given in Chapter 4.5.1.5 Operational Profile of VesselThe simplest case to consider was a stationary boat, described by Hilborn andLedbetter, with the boat operating alone, since this corresponded to the catchdata which was supplied by DFO. There was some evidence that this was arealistic situation, and this model could be useful in checking some of theassumptions made concerning the nature of the underlying probabilitydistributions of catch rate as a function of geographic area. Theserelationships are fundamental to the overall performance of the simulation,and must be carefully verified.When the simulation was developed the following operational profile wasassumed 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 openingwas announced, the vessel left port and sailed to its selected area. In the case ofthe stationary boats discussed here, there was only one area which was fishedwithin the simulation. The length of time to sail to the grounds was calculatedfrom 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 06.00hours. The waiting time varied only as a function of the distance sailed, and soan area which was nearer to port had a longer waiting time than an areawhich was further away. Fuel consumed (quantity and dollars) during thevoyage out was calculated. The waiting period reflected the observation that102the vessel always arrived at the ground before fishing, and the time therecould be used to search for fish. The waiting time varied with the distance ofthe fishing ground from the port, with shorter distances having longerwaiting times.iii. Once the area was open, the vessel fished for nine hours. The catch for thetrip was determined from sampling a probability distribution, based on themean daily catch for that day, and a shape parameter assumed constant forthat area. The amount of fish caught was a random variable, and the value ofthe fish was a linear transformation of that variable.iv. On completion of fishing, the vessel returned to port. Fuel consumed onreturn trip was calculated. For the Stationary Model, the amount of fuel usedwhen 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 theStationary Model was constant and so was the value of dollars per kilogram, thedistribution of profit in this case could be calculated by knowing the103distribution 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 informationon the maximum size of catch which might be expected during the season. Thiswas required to determine the likelihood of the hold capacity being exceeded.In order to estimate the maximum catch from the simulation, it was necessaryto set the number of trips in a typical season. Based on the observations on thefleet for the last ten years, 25 trips would seem to be a realistic number. Anestimate of the distribution of this variable was obtained by determining themaximum catch within each sequence of 25 openings, and running thesimulation for 2500 openings. Thus we can obtain a distribution of 100maximum catches, and make some inferences on the probability of the holdcapacity being exceeded.The financial risk involved in the operation of the boat was another randomvariable that was considered in the simulation model. In this case, risk wasdefined as the average number of trips per year which gave an income lessthan the operating costs for the boat. Based on analysis in Chapter 2, theaverage cost per trip was $5700, which included fuel cost. For the simulationmodel a value of $6000 per trip, after fuel costs had been deducted, was used asthe level of income on which the risk was evaluated. This was based on theassumption that the skipper of the boat studied was fishing with a boat thatwas much newer than average, and would require a higher than averageincome to cover capital costs of the increased investment. Risk is also a randomvariable and its variation was calculated from the same sequence of 25openings, as was used for the distribution of maximum catches.1045.2 Development of Stationary ModelThe simulation described above was programmed as a network using SLAM II,[23], to represent 2500 openings for a single boat with the operatingparameters described above. Details of the SLAM II program for the StationaryModel are given in Appendix 2. Maximum catch and risk were determined onthe basis of a continuous sequence of 25 openings. This model was called theStationary Model, since it represented boats which only fished in one area.The accuracy of the simulation model depends on the number of times forwhich data on individual openings are available. At 95 percent confidence fora sample of 2500 single openings, the mean of the observations (from thesimulation) will be within 0.la of the true value, where a is the standarddeviation of the sample mean. For 100 samples (for peak catch and risk), themean of the observations from the simulation should be with 0.2a, againassuming 95 percent confidence.Simulation modelling relies heavily on comparing the results of the modelwith the equivalent observations from reality. If the agreement is good, thenit can be inferred that the simulation is accurate. The only data that wereavailable for making the comparison between the observations and thesimulation were the same data that was used to develop the model. However, itwas 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 ofall the boats fishing in one area on one day.1055.2.1 Data Available from Observations on the FleetA detailed comparison between the simulation and the observed data must becarried out for at least one year for which data were available. After someconsideration, it was decided to use 1988 as the test case, since this was a yearwhere 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 dayin all three areas and so catch data should be reasonably reliable. It should benoted 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 anadvantage, when looking at mobility patterns, since highly motivated skippersmay 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 veryclose to the maximum number permitted, based on the number of licencesissued. The amount of time when three areas were open together for 1988 was16 days, based on sales slips for fish landed by 6 or more boats. This wasapproximately 15 per cent of the time for the total season available for any ofthe 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 moreareas, and only 9 fished at least once in all three areas.106Observed data, short season Simulation dataArea Name Mean kg/day St. Devn. n Mean kg/day St. Devn. n6 Butedale 6736 3741 132 7220 5220 250020 Juan de Fuca 1209.9 581.9 88 1410 1060 250012 Johnstone St. 2037.6 1719.7 138 2710 2650 2500n = number of observationsTable XXIStationary Model, Comparison of ObservedDaily Catch Rate with Simulation ResultsObserved data, short season Simulation dataArea Name Mean $/day St. Devn. n Mean $/day St. Devn. n6 Butedale 10852 5913 132 12700 9180 250020 Juan de Fuca 8650 4324 88 10300 7750 2500l2Johnstone St. 5699 3992 138 7430 7250 2500n = number of observationsTable XXIIStationary Model, Comparison of ObservedDaily Income Rate with Simulation Results107Figure 38. Comparison of Mean Catch per Day,Observations for Each Area and Stationary Simulation8000>.6ooo•a).0 Mean kg/day, full season4000 [I Mean kg/day, short seasonMean kg/day, simulationC2000G0•• I •Butedale Juan de Fuca Johnstone St.AreaFigure 39. Comparison of Histogram of ObservedCatch per Day with Simulated Values, Butedale, 19880.50.4UC0 0.3I ..:.0 10000 20000 30000 40000Catch per day, kg/day1085.2.2 Validation of Stationary Model Against ObservationsThere were several simplifying assumptions used to calculate the catch anddollar rates for the areas chosen. It was important to check how the finalsimulation predictions compared with the observed data. The easiest way tocheck this was to run the simulation model for the stationary case, andcompare the calculated catch per trip and dollars per trip with observed valuesfrom vessels which fished those areas within the time period. A summary tableof the mean catch per day is given in Table XXI and the mean income per day isgiven in Table XXII.A comparison of the mean values, with calculated error bars, based on a 95 percent confidence interval for each of the three areas, is shown in Figure 38. Wecan see that for each area, the mean catch rate agrees well with the observedvalues. It is also interesting to compare the distribution of daily catch, forboats fishing in one area, over the course of the season. Inferences made onthe results of the simulation will not be reliable if the distribution of catchrates is not realistic. From the data on individual boats we can compare theobserved data with simulated catch per day. These comparisons are shown inFigures 39 to 41.It can be seen that the simulation gives a very good approximation to the catchper day distribution for a single boat over the full season for Butedale andJohnstone Strait. In these two cases, the statistical difference between theobserved and the simulated distributions, based on a chi-square test, assuming95 per cent confidence, is zero. For Juan de Fuca the fit was not as good, and thedifference between the observations and the simulations is more than zero,assuming 95 per cent confidence. This can be explained by the data for that109Figure 40. Comparison of Histogram of ObservedCatch per Day with Simulated Values, Juan de Fuca, 19880.50.4>.UC0 0.3—D-—— observation0.2 simulation.100.1••....0.0 .• •rn,. •iV-.,_ ... .0 2000 4000 6000 8000 10000Catch per day, kgldayFigure 41. Comparison of Histogram of ObservedCatch per Day with Simulation, Johnstone Strait, 19880.30.2C00./ —D-—— observation0 simulation0.1•0.0 -0 2000 4000 6000 8000 10000Catch per day, kg/day110area in 1988. It was pointed out previously that the actual shape parameter wassignificantly lower than the mean value for the four years of data.The corresponding difference between the simulated results and theobservations is consistent with this difference between shape parameters. Insuch 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 thesimulated model in this case would tend to under-predict the number ofcatches between 500 and 1500 kg, and over-predict the number of catchesbetween 1500 and 4500 kg. Since the method worked in two out of three casesand the third case still gave reasonable results, it appears that thesimplifications had little effect on the distribution of catch per day.Some interesting discussion points arise when one considers the comparisonof income per day, derived from the simulation with the sales slip data fromDFO. Figure 42 shows the mean income per day derived from the StationaryModel, compared with the observed values from the fleet. It can be seen thatthe results from the simulation are all higher than the observed values. It wasnoticed that the income per day for the short season used in the validationexercise was lower than the values calculated from the full season used in thesimulation. This seemed to be due to a different mix of salmon species over theshort season relative to the full season. It seems as though the income from thesimulation is approximately 20 per cent higher than the observations in allareas. Since the simulation values were calculated from a lineartransformation, and the catch rates agree well, it would be trivial to modify theresults to the average dollars per kilogram for the short season. ThisHiFigure 42. Comparison of Mean Income per Trip,Observations for Each Area with Stationary Simulation1500O0.10000A 0 $Itrip, short season500:•$Itrip, simulationButedale Juan de Fuca Johnstone St.AreaFigure 43. Comparison of Average Catch per Trip and AverageIncome per Trip, Total Fleet with Random Simulation1000090008000 f70006000 a Mean kgftripooo • Mean $Itrip30130.2000ccWa? 1000.0• • IObservations, all simulation, RandomCategory112modification would have no affect on the catch distribution, which is theparameter being compared, and so it was not done.The distributions used within the simulation model were based on a full season,whereas observed data were only for the time when all three areas were opensimultaneously. The good comparison described above shows that theassumption that mean catch per day does not vary with day is valid, at least forthe period when all areas are open. Figure 42 clearly shows the importance ofincluding dollar value of fish, since although the catch rates for Juan de Fucawere low, compared to the other two areas, the high unit price of fish made itmuch more desirable than would initially have been thought.From this discussion we may conclude that the simplifications to thedistributions have had no substantial effect on the catch rates generatedwithin the simulation. This should mean that the underlying probabilitydistribution functions for catch rate within each area will give realistic dailycatch and subsequent income rates, when the other decision rules aremodelled.5.3 Development of Simulation for Mobile Boats5.3.1 Random ModelWe know that the Stationary Model does not represent all of the fleet, but we donot know how any particular skipper selects an area to fish. We can howeveranalyze the DFO data for 1988 to examine the detailed mobility of individualboats. The fraction of the number of trips a boat made to each area, as aproportion of the total number of trips was calculated. A summary of the meancatch and income data, together with the average fraction of the trips to a113mean St. devn. 11 st. error 95% lower 95% upperkg/day 3454.48 3369.162 452 158.472 3298.004 3771.42$/day 8376.34 5405.136 452 254.236 7867.865 8884.809Fraction of trips to each areaArea 6 0.339 0.448 452 0.021 0.280 0.398Area 20 0.389 0.408 452 0.019 0.335 0.443Area 12/13 0.272 0.453 452 0.021 0.212 0.332Table XXIIIObserved Catch and Income Data, All Fleetmean st. devn. n St. error 95% lower 95% upperkg/day 3850 4290 2500 85.8 3766.2 4021.6$/day 10200 8530 2500 170.6 9858.8 10541.2Fraction of trips to each areaArea 6 0.3396 0.0812 100 0.008 0.317 0.362Area 20 0.3176 0.096 100 0.010 0.291 0.345Area 12/13 0.3428 0.094 100 0.009 0.316 0.369Table XXIVSimulated Catch and Income Data, Random Modelmean st. devn. n St. error 95% lower 95% upperkg/day 4330 4710 2500 94.2 4141.6 4518.4$/day 11000 8760 2500 175.2 10649.6 11350.4Fraction of trips to each areaArea 6 0.472 0.0972 100 0.010 0.445 0.499Area 20 0.3672 0.1064 100 0.011 0.337 0.397Area 12/13 0.1612 0.0684 100 0.007 0.142 0.180Table XXVSimulated Catch and Income Data, Forecast Modelmean St. devn. fl St. error 95% lower 95% upperkg/day 4311.4 3820.2 257 238.3 4075.1 4788.0$/day 9728.8 5242.4 257 327.0 9074.8 10382.8Fraction of trips to each areaArea 6 0.563 0.475 257 0.030 0.504 0.622Area 20 0.426 0.469 257 0.029 0.367 0.485Area 12/13 0.011 0.047 257 0.003 0.005 0.017Table XXVIObserved Catch and Income Data, Boats Avoiding Area 12114given area, by the total fleet, are given in Table XXIII. It can be seen that theaverage mobility in 1988 was very close to an even distribution of boat entriesto a given area. One possible scenario was that a vessel fished an equal numberof times in each area.The simplest case of a mobile boat to simulate was a skipper which movedaround between areas in a random manner, with each area having an equalprobability of selection. The vessel would end up fishing an equal amount oftime in each area. Average values of profit, income and catch could beobtained by combining the results of the three areas for the Stationary Model.However, some of the parameters which were discussed in the development ofthe 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 toadd the distributions from the separate areas together, as the scale parametersfor the individual area distributions are different.The best approach for obtaining the distributions of these variables was tomodify the simulation for the stationary boats by adding probabilisticselection of the fishing area, with each area having an equal probability ofbeing selected. This model may not represent any particular mobility pattern,but will give a standard reference case to test the performance of alternativemobility strategies. If a selective mobility pattern did not give betterperformance than random mobility, it would not be beneficial to the operator.For this model, called the Random Model, the basic structure was the same asthe Stationary Model. Three additional variables were added to count thenumber of times the vessel fished in each area within the 25 week season.115Figure 44. Comparison of Number of Trips to EachArea, 1988, Total Fleet with Random SimulationO.5C0•00 Total fleet)0.2• Random simulation0I0.11I0.0• • • IButedale Juan de Fuca Johnstone St.AreaFigure 45. Overall Fleet Performance, 1988, Comparison ofHistogram of Observed Catch per Day with Random Simulation0.50.4(3C0 Q30I—0-—— random, obs.0.2 random, sim..1000.1o.o• —-fr0 10000 20000 30000Catch per day, kglday116These data were collected as histograms, so that distributions could be fittedand hypotheses tested to ensure that the resulting mobility pattern didrepresent an even allocation of entries to each area. A detailed description ofthe 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 theStationary Model, and the results were compared with the observed data on thefleet. The average catch per day and income per day are given in Table XXIVand shown plotted in Figure 43. The results show good agreement with thecatch data, but less agreement with income. This was due to the same cause asthe lack of agreement with the Stationary Model, in that the full seasonalvalues for dollars per kilogram were higher than for the short season. Acomparison of the mobility data for the simulation and the observation isgiven in Figure 44. A comparison for the catch per day distributions for thesimulation and the total fleet is shown in Figure 45. A chi-square test was usedto compare the two distributions, and the hypothesis that the two distributionswere the same was not rejected at 95 per cent confidence.5.3.2 Forecast ModelSo far, none of the simulations have made use of any of the information whichmay be available to the skipper. The literature review indicated that theskipper’s ability to use information could be important to the profitability ofthe vessel. It would be reasonable for the skipper to have information on theaverage catch rate for each geographic area, based on intelligence on thelanding data, either from within the company or from observations anddiscussions with other skippers. It would be interesting to see if thisinformation could be used profitably, with a simple decision model.117A simplified version of the decision made by the mobile boats, described byHilborn and Ledbetter [11], would be to assume that a boat will move to the areawith the best return the previous opening. For the simulation, the decisioncould be made on the basis of the area with the best ‘profit’, defined as themean 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 wouldmake 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 thearea with most profit the previous opening. If the boat had fished there theprevious opening, then the profit was calculated on the basis of the meancatch for the ‘fleet’, rather than the performance of the boat. Anothermodification was to direct the vessel to Juan de Fuca for the first opening,when no information was available on any previous openings. This was basedon the fact that this area had the highest number of boats per day over thefour years of observations. This simulation was referred to as the ForecastModel, and it was run for the same catch, income and vessel data as for theRandom Model and the Stationary Models described above. Details of the SLAMII code for the Forecast Model are given in Appendix 4.A summary of catch and income data for the Forecast Model is given in TableXXV. Figure 46 shows mean catch per day and mean income per day for theRandom Model and the Forecast Model. From these data, we can see that theForecast Model has a profit approximately 7 per cent better than the Random118Figure 46. Comparison of Mean Catch & Incomeper Trip, Random and Forecast Simulations, 198812000-10000-8000-0.0. 0 Mean kgltripC)6000• Mean $Itripcc2000-Random ForecastCategoryFigure 47. Comparison of Number of Tripsto Each Area, Random and Forecast Simulations0.5-0.4->.N. 0 Random0.2‘N • ForecastC) *II0.0- • I • IButedale Juan de Fuca Johnstone St.Area119Model. This difference is relatively small, but is significant at 95 per centconfidence. The best Stationary Model (Butedale) was approximately 19 percent more profitable than the Random Model. The Random Model appeared tohave no advantage, in terms of profitability, relative to the two best StationaryModels, or the Forecast Model. This would indicate that the simple act ofmoving around does nothing to improve the profitability of the vessel, basedon 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 vesselfished, shown in Figure 47. The Forecast Model spent more time in Butedale andless time in Johnstone Strait than the Random Model. Thus the Forecast Modeltended to fish more times in the area with the highest profit, and less times inthe area with the lowest profit. However, the Forecast Model did not fish inButedale a sufficient number of times to raise the average to the value of theStationary Model for that area. The improvement in performance for theForecast Model was due to the differences in mobility relative to the RandomModel.5.3.3 Validation of Forecast ModelIt has been demonstrated that the Forecast Model gave better performancethan average, at least for one year of data. It remains to be seen if thisrepresents 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. Thesignificant difference between the Forecast Model and the Random (average)Model was the difference in mobility patterns. The fleet data were examined0Fleet, sub-set Forecast simulationCategoryFigure 49. Comparison of Number of Trips to Each Area,Sub-set Avoiding Johnstone Strait & Forecast Model120Figure 48. Comparison of Average Catch and Income per Trip,Sub-set Avoiding Johnstone Strait and Forecast model120001000080006000 0 Mean kgItrip• Mean $Itnp40002000rn0.I-.10).C(0(0>.0C4)04)I4)>(Ua)(00.II-0 Fleet sub-set• ForecastButedale Juan de Fuca Johnstone St.Area121for boats which avoided Johnstone Strait, and their performance wascompared 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 95percent confidence limit on the number of trips to that area, based on thesimulation results).There were 257 boats which fell into this category. The summary statisticswere calculated for this sub-set, and are summarized in Table XXVI. It can beseen that boats which fit this data set have a mean catch rate 25 per centhigher than the observed average for the total fleet and a mean income pertrip 16 per cent higher than average. The mean catch per day and the meanincome per day for this sub-set and the Forecast Model are compared in Figure48. The observed data and the Forecast simulation match exactly for catch rateand are within 9 per cent for the income. The observed distribution of numberof boats which fished in each area is compared with the values from theForecast Model in Figure 49. It shows that more boats preferred Butedale thanwas predicted, and very few boats in this sub-set actually went to JohnstoneStrait.A comparison was made of the distribution of the catch data from the ForecastModel and the 257 boats discussed above. This is shown in Figure 50. A chisquare test was used to compare the distributions, and it was found that basedon a 95 per cent confidence interval, the hypothesis that the two distributionswere the same was not rejected.Another factor to consider, which has implications on the vessel design, is thehold size requirement for the vessel. The peak catch for the season should be122Figure 50. Comparison of Histogram of Observed Catch per Day,Sub-set of Fleet with Simulated Values, Forecast Model0.50.4>C0.3a.—a—— Fleet, Sub-set-- Forecast, simulationaj 0.24-0o.i0.0•-- -0 10000 20000 30000Catch per day, kgldayFigure 51. Comparison of Mean Peak Catch,1988 Data, All Simulation Models30002004-4-0U: io0.C000 i • I • I • I •IModel.Li123checked to see if it is likely to be significantly larger for one decision ruleover another. One measure of this parameter will be the mean peak catch,determined from the 100 samples of 25 continuous openings. Although themean peak catch is not the most useful measure for design purposes, sincethere is a high probability of exceeding it, it is a stable parameter which canbe estimated relatively reliably for the sample of 100 observations. Using thecentral limit theorem, the variance of the peak catch can be estimated to giveconfidence limits on the observed data from the simulation. These values areshown in Figure 51 and given in Table XVII, which give a summary of all fivesimulation models.From this data it can be seen that the largest hold size requirement was for theStationary Model fishing Butedale. This option required a hold sizeapproximately 32 per cent bigger than the Random Model. The hold size for theForecast Model was approximately 8 per cent bigger than the Random Model.The other two models required hold sizes much smaller than the RandomModel.The distribution of risk at $6000, in terms of the number of trips per 25openings, for the three Stationary Models is shown in Figure 52 and for theRandom and Forecast Models in Figure 53. From these data we can see thatalthough the mean risk varies inversely with catch rate, the width of thedistribution was similar for all the cases. The coefficient of variation for thesedistributions is quite high, and this is due to the relatively small number ofopenings in the course of a season. The mean taken from only 25 values willshow a high degree of variation, but the seasonal mean, taken from 2500observations, will be very accurate. A comparison of the number of trips madeFigure 52. Variation in Number of Trips Out of 25,where Income was < $6000, Stationary Models30Figure 53. Variation in Number of Trips Out of 25,where Income was < $6000, Mobile Models25Random—El-—— Foicast124UC00I04-020100—0--— Butedale0 Juan de Fuca- . - . ---. Johnstone St.0 5 10 15Number of trips/2520 253020UC00I‘I0 104-0000 5 10 15 20Number of trips/25125to each area for the Random and the Forecast Models is shown in Figures 54and 55. Again it can be seen that although the mean values are different, thevariance 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 thefuel cost is a relatively small portion of the income, with the highestproportion being 12 per cent, for the Stationary Model in Butedale. If this wasthe case, for 1988, we would not expect the cost of fuel to have had a significanteffect on the decision where to fish. This was an observation that the skippermade, and this was discussed in Chapter 3. However, this may change if catchrates vary significantly between areas and years.5.4 SummaryIn summary, it would appear that the Forecast Model does predict a significantimprovement over the average income for the fleet, based on observations forthe 1988 season. The improvement has occurred by making more trips to themost productive area and avoiding the least productive one. The mobilitypattern predicted by the Forecast Model was observed in approximately 56 percent of the fleet, and this portion of the fleet did produce incomes per tripwhich were significantly higher than the overall average for the fleet. This isstrong evidence that the Forecast Model results give a realistic representationof a large proportion of the fleet, averaged over the total season. The bestmodel of all for 1988 would have been to fish only in Butedale, and vesselsfollowing this decision process represented approximately 29 per cent of thefleet, which is still a significant portion. This would indicate that theStationary Model was still a reasonable option to consider in any predictionmethods.Figure 54. Variation in Number of Trips Out of 25to Each Area, Random Model300 Butedale•----D--- JuandeFuca- . - •---. Johnstone0 5 10 15 20 25>C.,04I‘I0.100C)C4)0I0>•14)4)12620—0-—— ButedaleQ JuandeFuca10 ----.-. Johnstone0Number of trips/25Figure 55. Variation in Number of Trips Out of 25to Each Area, Forecast Model30201000 5 10 15 20 25Number of tripsl25127Stationary ModelsParameter n mean std. devn 95 percentCIButedale Fuel, litres 2500 4050 0 0.0Fuel cost, $ 2500 1620 0 0.0Fish, kg 2500 7220 5220 204.6Fish, $ 2500 12700 9180 359.9Profit,$ 2500 11100 9180 359.9Max. Catch, kg 100 21800 7440 1473.1Risk, in 25 trips 100 7.99 2.34 0.5Juan de fuca Fuel, litres 2500 1090 0 0.0Fuel cost, $ 2500 436 0 0.0Fish, kg 2500 1410 1060 41.6Fish, $ 2500 10300 7750 303.8Profit, $ 2500 9830 7750 303.8Max. Catch, kg 100 4490 1450 287.1Risk, in 25 trips 100 9.21 2.24 0.4Johnstone Fuel, litres 2500 1430 0 0.0Fuel cost, $ 2500 573 0 0.0Fish, kg 2500 2710 2650 103.9Fish, $ 2500 7430 7250 284.2Profit, $ 2500 6860 7250 284.2Max. Catch, kg 100 10300 3560 704.9Risk, in 25 trips 100 14.8 2.39 0.5Mobile ModelsParameter n mean std. devn 95 percentCIForecast Fuel, litres 2500 2540 1430 56.1Model Fuel cost, $ 2500 1020 571 22.4Fish, kg 2500 4330 4710 184.6Fish, $ 2500 11000 8760 343.4Profit, $ 2500 9960 8690 340.6Trip, Butedale 100 11.8 2.43 0.5Trip, Juan de Fuca 100 9.18 2.66 0.5Trip, Johnstone St. 100 4.03 1.71 0.3Max. Catch, kg 100 17800 6820 1350.4Risk, in 25 trips 100 9.93 2.28 0.5Random Fuel, litres 2500 2210 1320 51.7Model Fuel cost, $ 2500 884 529 20.7Fish, kg 2500 3850 4290 168.2Fish, $ 2500 10200 8530 334.4Profit, $ 2500 9330 8440 330.8Trip, Butedale 100 8.49 2.03 0.4Trip, Juan de Fuca 100 7.94 2.4 0.5Trip, Johnstone St. 100 8.57 2.35 0.5Max. Catch, kg 100 16500 6460 1279.1Risk, in 25 trips 100 10.6 2.65 0.5Table XXVIIResults of Simulation Models, 1988 Data128Chapter 6Sensitivity of the Forecast Modelto Catch Rate at Furthest AreaThe development of the simulation models was discussed in Chapter 5. TheForecast Model was successful in obtaining better than average performance,but this was for only one year of data. This chapter will investigate thesensitivity of the Forecast Model to changes in income, due to changes in thecatch rate at the area furthest from the home port.It was shown in Chapter 5 that Butedale was the most profitable area, based onthe Stationary Models for 1988. This area was also the one with the highest costof travel. The profit for the Forecast Model was lower than the StationaryModel for Butedale, by approximately 11 percent. It is important to determineif the Forecast Model was unduly influenced into avoiding this area more thanit should have done. To investigate this question, a sensitivity study wascarried out to see how the results of the Forecast Model changed with catchrate at Butedale. For this study, only catch rate at Butedale was varied, sincethis was the area furthest away from port, and so was likely to have the mosteffect on mobility and the subsequent profitability of the operation.6.1 Parameters for StudySince there was little difference in the cost of mobility between JohnstoneStrait and Juan de Fuca Strait, the average catch rate over the season was fixedfor these two areas at 3000 kilograms per day. This rate was picked since theoverall provincial average of catch per day was calculated to be 3096kilograms per day, based on the 10 year fleet performance data. Also, for the129four years of data analyzed in Chapter 4, the mean catch per day for Juan deFuca was 2862 kilograms per day, and for Johnstone Strait was 3341 kilogramsper day. The value of 3000 kilograms per day was obviously close to the longterm value.For the sensitivity study, mean catch per day for the season at Butedale wasvaried between 2000 kilograms per day and 8000 kilograms per day, inincrements of 1000 kilograms per day. These values were picked because theybracketed the observations for all areas and all years, and therefore werelikely to cover the range of catch rates which might be expected. To simplifythe interpretation of the results, the value of the fish was fixed at $2.50 perkilogram for all areas. This figure was close to the provincial average for allareas and all years studied.The mean catch for a given area on a given day is a random variable, with arange which is given by the shape of its probability density function. Theseasonal shape parameter, A, described in Chapter 4, was kept constant for allareas, at a value of 4.25. Again this was close to the average value for all areasand all years in the study. Once the mean value and the shape parameter werefixed, then the scale parameter, sigma was determined. The resulting valuesare given in Table XXVIII.The Forecast simulation was run for each condition and the results aresummarized in Table XXIX. The theoretical values for the Stationary Modelwere calculated in this instance, and are given in Table XXX. Similarcalculations were made for the Random Model, assuming that the boats fished130an equal number of times in each area, and these results are given in TableArea mean catch A akg/dayJuan de Fuca 3000 4.25 705.9Johnstone St. 3000 4.25 705.9Butedale 2000 4.25 470.63000 4.25 705.94000 4.25 941.25000 4.25 1176.56000 4.25 1411.87000 4.25 1647.18000 4.25 1882.4Table XXVIIIData Used in Sensitivity Study forForecast Model6.2 Results of Sensitivity StudyA comparison of the profitability of Forecast Model with the Random Model isshown in Figure 56. This figure shows that the Forecast Model was generallymore profitable than the average performance for the fleet, assuming that theaverage was calculated based on the boat fishing an equal number of times inall 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 theRandom Model, by a factor of up to 16 percent.For the Stationary Model at Butedale, the profit was linearly proportional tothe average catch rate. It was not necessary to run the simulation to obtain131Figure 56. Sensitivity of Forecast Model and OverallAverage Performance to Catch Rate at Butedale2500020000-0015000 - ....‘......Forecast modelAverage,all areas10000-0E05000-0-. • I • I • I0 2000 4000 6000 8000 10000Catch rate, Butedale, kg/dayFigure 57. Sensitivity of Forecast and StationaryModels to Catch Rate at Butedale2500020000• 15000010000-Forecast0Johnstone1--- JuandeFucaII0 —E -. - Butedale00.E 5000 -F.00•. • • • I0 2000 4000 6000 8000 10000Catch rate, Butedale, kglday132Forecast model Mean Average AverageCatch/day, catch/day fuel cost profitkg $ $Butedale, kg2000 2720 559 62403000 3070 760 69104000 3060 969 66905000 3170 977 69406000 4250 1160 94607000 5750 1400 130008000 7260 1440 16700Table XXIXSensitivity Study, Results of Forecast ModelStationary model Average AverageCatch/day, kg fuel cost profit$ $Butedale2000 1620 33803000 1620 58804000 1620 83805000 1620 108806000 1620 133807000 1620 158808000 1620 18380Juan de Fuca3000 436 7064Johnstone Strait3000 573 6927Table XXXSensitivity Study, Results of Stationary Model133these data, since the only random variable was the catch data. The mean profit,p, (income-fuel) was obtained from the mean catch data, m, for each area bythe simple linear transformations given below:Butedalep = m*2.50 - 1620 (8)Juan de Fucap=m*2.50436 (9)Johnstone Straitp=m*2.5O573 (10)Based on the mean profit data, it would have benefited the skipper to chooseJuan de Fuca until the mean catch per day (for the season) at Butedale reached3474 kilograms per day. Above this point, the most profitable area would havebeen Butedale.A comparison of the average profit per trip, for the Forecast Model and thethree Stationary Models is given in Figure 57. This figure shows that for lowcatch rates at Butedale, the Forecast Model had a profit statistically the same asthe best Stationary Model. However, the Forecast Model was not as profitable asthe best Stationary Model, once the catch rates at Butedale exceeded 3474kilograms per day. The Forecast Model profit was comparable to the boatswhich fished Juan de Fuca or Johnstone Strait, until the catch rate at Butedalereached 5000 kilograms per day. Above this point the Forecast Model was betterthan the second best Stationary Model, but the mean from the Butedale134Random model Mean Average AverageCatch/day, kg Catch/day, kg fuel cost profit$ $Butedale2000 2667 876 57913000 3000 876 66244000 3333 876 74575000 3667 876 82916000 4000 876 91247000 4333 876 99578000 4667 876 10791Table XXXISensitivity Study, Results of Random Model135Figure 58. Number of trips to Butedale againstCatch Rate at Butedale, Forecast Model100’y = - 17.714 + 1.3143e-2x /R2 — 0.97280aa60Ex40’ 0(0aI.120130’. • I • I • I0 2000 4000 6000 8000 10000Catch rate, Butedale, kg!day136Stationary Model did not come within the 95 percent confidence interval of theForecast Model, until the catch rates were higher than 7000 kilograms per day.6.3 Discussion of ResultsThere appears to be a lag in the profitability of the Forecast Model, relative tothe area which was theoretically the most profitable. One factor which mayhave affected the profitability was the number of trips that the vessel made toButedale. Figure 58 shows the percentage of trips to Butedale, per season, as afunction of the catch rate at Butedale. It can be seen that the number of tripsto Butedale, given by the Forecast Model was linearly proportional to catchrate in that area. Thus the mobility of the model is as expected, and the boatwas 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 easilyidentified by the analyst, the skipper (in the simulation) had to use incompleteinformation. The skipper’s decision, within the simulation, was based onselecting the area with the highest profitability the previous opening.When the mean profits per day for two areas are similar, then we might expecta high probability of the maximum profit the previous week being observed inthe 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 mayfish. Within the simulation, there was a choice of three areas. When there aretwo alternatives to the theoretically best area, then there is an even greaterprobability of the observed catch rate in the best area being lower than the137Figure 59. Histograms of Profit, Juan de Fuca, JohnstoneStrait and Largest of Two Sampled Simultaneously0.302—a——— Juan de FucaI Johnstoneo.i. / \ ----- Largest of two0.0 I. I-10000 0 10000 20000 30000(Income-fuel cost)Iday, $Figure 60. Histograms of Profit for VariousCatch Rates at Butedale0.3>.UC—a-—— 2000 kg/day—$—-- 5000 kg/day8000 kg/day0.1.4, ft4, i .E•• •// , ..., ...II . .0.0•-10000 0 10000 20000 30000(Income-fuel cost)/day, $138catch rate in an alternative area. This factor was investigated by carrying outadditional runs of the simulation and collecting data relevant to this particularstudy.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. Threevalues 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 Figure60.Figure 59 shows the distribution of mean profit per day for vessels fishingJuan de Fuca and Johnstone Strait. This clearly illustrates, that for equal catchrate there was a negligible difference in profit between the two areas. Alsoshown in Figure 59 is the distribution of the largest value of profit, takenfrom two samples, one each from Juan de Fuca and Johnstone Strait. The modalvalue for this distribution was approximately the same as the modal value forthe profit distribution at Butedale (Figure 60), when the mean catch per dayfor the season was 5000 kg/day. Thus, it is not until the catch rate at Butedalereaches this figure that the probability of obtaining the correct informationon the best area is higher than the probability of obtaining the wronginformation. This is reflected in the simulation, when after 5000 kg/day, theprofit from the Forecast Model becomes higher than that from the StationaryModel fishing either Johnstone Strait or Juan de Fuca.From the sensitivity study, it can be concluded that the Forecast Model tendedto correctly avoid Butedale when the catch rate was extremely low, andcorrectly prefer it when the catch rate was extremely high. However, there139was a range of catch rates where the Forecast Model’s performance wassignificantly lower than the best possible performance, in terms of averageprofit per trip. It is difficult to see a way around this deficiency, whilst onlyusing the minimum amount of information. The reliability of the ForecastModel may be increased by basing the decision process on a longer memorythan simply the last trip. This would be relatively simple to do in thesimulation, by using a running mean, updated after each opening. However,in reality, the problem is compounded by possible variations in the price offish over one season, and the fact that there is a very limited time to build areliable database from which to determine the seasonal average.An alternative approach would be to design a boat which would be profitableon an income rate which was lower than the long term average value. Basedon this analysis, a factor of 20 percent below the long term average valuewould seem to be reasonable. The minimum income required to cover the costof operating the vessel should be set with this figure, rather than the averagevalue.6.4 ConclusionsIn general, the Forecast Model performs better than average. It performsparticularly well when one area has either very high or very low profits.However, there is clearly a range of profits where the Forecast Model willperform worse than average. Although the illustration used here was chosento highlight any potential problems, the results should be the same regardlessof which geographic area was used as the variable. The difference due to theselection of the area will affect the absolute value at which the phase lagoccurs. Since the decision for area selection was based on maximum profit, the140critical range, based on two areas with profits equal, and a third area between1 and 1.5 times higher should exist regardless of which area was chosen forthe variation. This may explain why some skippers are reluctant to movebetween areas, because there is a range of catch rates where there is a higherprobability of making the wrong decision than making the right one. In suchcases, it may be felt that avoiding this decision is a better alternative. This willprobably mean that the skipper will pick the area for which he has the mostreliable information and that is most likely to be the area where he fished lasttime.141Chapter 7Sensitivity of Forecast Model to Number of Boats OperatingTogetherSo far only a single boat, fishing independently, has been simulated. This wasthe basis of the catch data available from DFO, and no information wasavailable for teams of boats fishing together. However, we know that boats dofish together and we can assume that this is to the benefit of both skippers, orthey would not do it. It would be interesting to investigate the possible benefitsof two or more boats fishing together using the simulation model. This can bedone by making some assumptions about the operating practices of the boatsand modifying the simulation model. For this sensitivity study, only theForecast Model will be used, since it was demonstrated in Chapter 6 that itperformed as well or better than average in a wide range of catchdistributions, which were likely to be observed in practice.In order to use the data on catches described in Chapter 4, we must assume thatthe catch rates between boats fishing together are not correlated. This may bean over-simplification, since it is quite likely that two boats fishing in closeproximity will have catch rates that are highly correlated. However, withoutfurther data, or a much more detailed knowledge of vesseL location and catchrate, any other assumption cannot be justified from the observed data.1427.1 Modifications to Simulation ModelThe Forecast Model was modified to include two types of boats. The original boatwas classed as a ‘packer’. It transported all the fish for the team back to theprocessing plant at the end of every opening. This model of operation wasbased on the skipper’s observations discussed in Chapter 3. The assumptionsabout sailing speed and fuel consumption were the same as those used in theearlier models. The packer was the boat that was active in the model whenthere was just a single boat. It was assumed that the decision of where to fishwas based on the fuel cost of the packer only.The second class of boats were fishing boats, and it was assumed that theseboats did not transport any fish. It was also assumed that these boats fishedwith the packer, and waited on the grounds during the closed season, ratherthan travel back to port. Both the packer and the fishing boats would move tothe new area, if necessary, at the beginning of the simulation cycle, whichwas 168 hours (one week) as in the single boat model. This limited theminimum size of fishing boats within the model to be 9.25 metres, which is thehull length which could move the maximum distance (365 nautical miles) in 48hours. This was not a problem in practice, since the minimum length of aregistered salmon seine vessel was 10.3 metres.Some other simplifying assumptions were made in the development of themodel. It was assumed that the fishing boats and the packer were identical. Thereason for this assumption was to be able to use the observed vessel operationsdata, 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 lightload condition. This represented a saving in fuel consumption of 24 percent,143relative to the same vessel moving in the loaded condition. Additional fuelsavings would result if the fishing vessel did not have to change areas,between openings.The catch rate data used to investigate the effect of the number of boats wasthe same as for the 1988 model, used to validate the simulation. The price datawas modified to reflect more realistic long term values. It was pointed out inChapter 4, that the price per kilogram for Juan de Fuca in 1988 was muchhigher than was expected based on the other three years. For this reason theaverage price for this area for the three years, excluding 1988, was usedwithin this model. For the other two areas, the average value for all four yearswas used. These values are given below;Area s/kgButedale 1.472Johnstone Strait 2.629Juan de Fuca 3.0767.2 Discussion of Simulation Results7.2.1 Voyage EconomicsThe simulation model was run for one packer and a packer plus a number offishing vessels varying between one and three. The results are summarized inTable XXXII and shown plotted in Figures 61 to 63.The mean catch per boat, and income per boat, shown in Figure 61 did notchange when the number of boats changed. This was to be expected, as the144TotalNumber of Boats 1 2 3 4n 2500 2500 2500 2500Fuel cost/boat, $ 1210 752 605 525Standard devn. 522 620 579 531Mean total catch, kg 5480 10700 16300 21500Standard devn. 5070 8540 11900 15400CatchJboat, kg 5480 5350 5433 5375Mean total income, $ 9200 17900 27200 36300Standard devn. 7720 12500 17100 22100Income/boat, $ 9200 8950 9067 9075Mean profit, $ 7990 16400 25400 34200Standard devn. 7590 12300 17000 22100Profit/boat, $ 7990 8200 8467 8550Mean risk 0.512 0.440 0.397 0.376© $6000/boat________ ________ ________ _______n=number of observationsTable XXXIIEffect on Operating Economicsof Number of Boats Fishing Together145catch per boat was independent of the number of boats, based on theassumptions made in developing the model. The average profit per boat, shownin 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 fourboats it is 7 percent higher than for one boat.The increased profit came from reduced fuel consumption per boat, as can beseen 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. Theoverall effect was to lower the average fuel consumption per boat. It can alsobe seen from Figure 63 that the effect of the change was greatest from one totwo boats but the change from three to four was still significant. If thenumber of boats in the team was increased to well above four, then the effectof the packer would be diminished and it is likely that some point would bereached where no further improvements would be expected.It appeared that the biggest change in the economic factors due to increasingthe number of boats was the reduction of risk associated with ihe fishingoperation. The risk was defined in Chapter 5 as the number of trips per season(25 openings) where the income was less than the cost of the voyage,including allowances for the fixed and variable costs. The variation in riskwith the number of boats is also shown in Figure 63. From the valuescalculated by the simulation, the average risk associated with a single vesselwas 51.2 percent. That is to say that 51.2 percent of the trips resulted in thevessel 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 boatFigure 62. Variation in ProfitlBoat withNumber of Boats Fishing Together90000.14-80004-0.04--I0I0.70000Figure 61. Variation of Catch and Income (per Boat)with Number of Boats Fishing Together10- -10000..8- 80004-CU -60004• 4000QU)U)U)02 -20000146—rn-—— mean catch!boatincomelboat— I • I • I •0 1 2 3 4# boats5____________single boat,mean valueI I — I — I —1 2 3 4 5# boats14dropped to 44.0 percent. It dropped further for three and four boats to 39.7percent and 37.6 percent respectively. After three boats it seems as though therisk was beginning to stabilize.The financial risk is an important factor for the skipper when deciding whereto fish. Selecting a low risk decision may be important if the number ofopportunities to make that decision are small, as is the case in a real fishingseason. Clearly increasing the number of boats fishing together has a bigeffect 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 tripis a random variable. The basic distributions of catch per day are made up froma gamma distribution for mean catch per day for the season and then a secondgamma 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 boatobtained 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 tothe right as the number of boats in the team is increased. This is due to theslight 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 muchlarger than the shift of the modal value. This is because we are now takingmultiple samples from one area on any given day. Thus if one boat has aparticularly poor catch it is likely to be offset by a higher catch obtained fromthe other members within the team. The more boats per team fishing in agiven area simultaneously the more likely that the mean catch for the teamwill approach the mean catch for the area on that day. This leads to the—a-—— one boat••• two boats-. - -+--. three boats148—a——— fuellboat* risk @ $6KlboatI • I • I • I1 2 3 4.10C0. .UU,—U)4-CIIFigure 63. Variation in Fuel Consumption andRisk at $6000 per Trip for Vessels Fishing Together1400 0.612000.5_(U1000(0*8000.4U,I600400 -0.30 5# boatsFigure 64. Histograms of Profit per Boat,for One, Two and Three Boats Fishing Together1 .OOe-48.000-56.OOe-54.OOe-52.OOe-50.OOe+00 10000 20000 30000profit, $Iboat149reduction in risk since the chance of obtaining a very low total catch for theteam is reduced. However, the chance of getting a profit which is significantlyhigher than the mean profit times the number of boats in the team is alsoreduced but this is more difficult to visualize since the tail of the distribution isvery long. It can be seen that the probability determined from the simulationof a high profit per boat is lower for three boats than for a single boat fishingalone.7.2.2 Transportation CapacityAnother factor to consider besides the economics is the transportationcapacity of the hulls. A larger boat will generally have a larger hold volumebut if the hold is too large then the owner has invested too much in the capitalcost of the boat. If the hold is too small then the result will be lost incomeopportunity because fish cannot be transported for processing. If we haveseveral boats fishing together and only one boat transporting the fish thenthe transportation capacity must increase with the size of the team. Thetransportation capacity for two boats fishing together will be more than thatrequired for one but not necessarily in a direct relationship to the number ofboats.Since catch per trip is a random variable we must consider the required holdsize in terms of probability of exceedence rather than absolute numbers. Aftersome consideration it was decided that the parameter used for setting hold sizewould be the 99 percentile for the distribution of the maximum catch from 25consecutive openings in a given season. In practical terms this wouldcorrespond to the largest catch of 100 boats fishing for 25 sequential openingsusing the ‘Forecast’ decision model. This was thought to be reasonable because150in practice 25 weeks was a long season and a shorter season would reduce themaximum expected catch. Also, if the catch rate was very large then thefishing boats could return to Steveston carrying some of the catch, ratherthan waiting on grounds. If the fishing boats were radically different fromthe packer, i.e. with no transportation capacity, the fish could probably betransported by other packers which were not filled to capacity.The results of the simulation, for a single vessel, gave a histogram for themaximum catch observed in a sequence of 25 openings. These data can be usedto investigate trends in the catch rate, based on an assumed probability ofexceedence. However, the histogram was based on 100 observations ratherthan the 2500 which were used for the comparison on daily catch rates. Forthis reason we might expect the results to be less reliable but they should stillbe sufficiently accurate to determine trends. The results would be more usefulif we could postulate the form of the distribution for the maximum catch, sincethe hold capacity required could be interpolated from a fitted distributionrather than the observed histogram, which may be irregular, due to thereduced number of samples.If all the gamma distributions used in the simulation to model catch per dayhad had the same scale parameter, a, then it would have been possible todetermine the distribution of catch per day for the fleet by adding thedistributions together. This was not the case but since the statistical models forcatch per day in each area used in the simulation were all gammadistributions, it was possible that the same type of distribution would give agood fit to the overall result. A gamma distribution was fitted to catch per tripfor the 2500 trips and its scale and shape parameters are given in Table XXXIII.151Parameter ValueCatch per day, kg 5480Standard deviation 5070n 2500Gamma distribution, catch per daysigma 4.69E-’-03lamda 1.17E+00Maximum catch, 25 trips, kg 19500Standard deviation 6900n 100Gumbel distribution, from gamma distributionSigma 4.99E+03Mu 1.68E+0499 percentile 39.7Gumbel distribution, from simulationSigma 5.38E+03Mu 1.69E+0499 percentile 41.7n=number of observationsTable XXXIIIFitted Distributions to Catch Data,Single Boat152The fitted distribution was tested against the simulated values with a chisqurare test and the fit was not rejected at 95 percent significance.If the overall distribution of catch per trip, for 2500 openings, can be fittedwith a gamma probability density function then the distribution for themaximum catch out of 25 trips should be given by a Gumbel distribution(extreme value, type I), given in equation (11):f(x) = :i exp(- (x-i.t) - exp(- (x.t))) (11)with a modal value, i, which corresponded to the catch per day from theparent distribution which has a cumulative probability of 24/25 (0.96). Thescale parameter, a, can also be estimated from the hazard function [22] for theparent distribution. The parameters for the Gumbel distribution wereestimated from the fitted gamma distribution, and are given in Table XXXIII.Based on a chi-square test on the distribution of simulated maximum valuesand the values calculated from the Gumbel distribution, the differencebetween the two is insignificant at 95 percent signifcance. The simulated dataand the calculated data for both the overall distribution of catch per trip andmaximum catch for 25 trips are shown in Figure 65. It can be seen thatcalculated distributions fit the results from the simulation very well.There was another approach for fitting a distribution model to the observedmaximum catch data, and that was to fit a Gumbel distribution directly to theobserved data. This was done using moments and the results are also given inTable XXXIII. Again a chi-square test was used to compare the two distributions,Figure 65. Comparison of Observed and Fitted Distributionsfor Daily Catch and Extreme Value from 25 Trips2.OOe-41.00e4ii0.OOe+0 - —0 20000 40000Catch per day, kgFigure 66. Variation in Scale and Shape Parametersfor Fitted Distributions with Number of Boats15-153daily value, simulationdaily value, fittedextreme value, observationextreme, from daily dist.extreme, fitted directlya, Gamma dist.x, Gamma dist.a, EV11” EV1CCb10-5.0--D--I I0 1 2 3 4 5# boats154and the difference was found to be insignificant, at 95 percent confidence.There was a slight difference between the two distributions, as can be seen inFigure 65, which will have some effect on estimating parameters from theextreme value distribution. It was found that the difference in the 99percentile for the maximum catch for the single boat, calculated using the twomethods discussed above, was less than 5 percent.When two or more boats were operating within the simulation, it was foundthat not all the parameters discussed above could be recorded, due to array sizelimitations on the version of SLAM being used. However, since it was shownabove that the extreme values could be predicted from the fitted distribution tocatch per day, the relevant information could be calculated. Chi-square testswere carried out on the differences between the simulated distributions andthe fitted gamma distributions and none were rejected at 95 percentsignificance.The parameters for the gamma distributions and the extreme valuedistributions are given in Table XXXIV, together with the 99 percentile formaximum catch determined from the fitted distributions. The hold size may bedetermined from the catch size by assuming that it is also required to carryenough ice to preserve the fish during transportation. The industry standardis a ratio of approximately 2/3 fish to 1/3 ice. Table XXXIV also gives theestimated hold sizes, calculated using this ratio.Figure 66 shows the parameters from the catch per day and maximum catchfor 25 trips plotted against the number of boats. These data show that there isan approximately linear trend with the number of boats. It is interesting to155Fitted distribution, Fitted distribution, Max. catch Required holdcatch/day max. catch size sizegamma Gumbel (EV1)# boats sigma lamda sigma mu 99 percentile, 99 percentile(tonnes, fish) (tonnes, fish + ice)1 4.691 1.168 4.99E+03 1.68E+04 39.7 59.62 6.816 1.57 7.72E+03 2.92E+04 64.7 97.13 8.68 1.876 1.03E+04 4.18E+04 89.0 133.54 11.03 1.949 1.32E+04 5.44E+04 115.0 172.5Table XXXIVEstimated Parameters for Fitted Distributionsfor Different Numbers of Boats156note that the catch per day distribution for two or more boats cannot becalculated from the catch per day distribution for one boat by assuming thatmultiple samples are taken from this distribution. This highlights the need forusing simulation to understand the operational aspects of multiple boatsworking together.The 99 percentiles for required transportation capacity taken from the Gumbeldistributions are shown plotted against the number of boats in Figure 67. Itcan be seen that the transportation capacity is not directly proportional to thenumber of boats. The maximum transportation capacity required for the catchfrom two boats fishing together was calculated to be 23 percent smaller thanthat required for two boats fishing independently. This ratio progressivelydecreased until it was 38 percent smaller for four boats. This reduction is due tothe change is shape of the catch per day distribution as the number of boats isincreased. It is interesting to note that the 99 percentile of the extreme valuecatch distribution is approximately 7.25 times larger than the mean catch perday 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 122salmon seine vessels, together with the 99 percentile hold volumes based onthe results of the simulation. This shows that approximately 48 percent of thefleet is suitable for fishing as a single boat/packer, 35 percent of the fleet iscapable of acting as a packer for one boat and itself, 12 percent is capable ofacting as a packer for two boats (and itsesif) and no vessels are capable of157Figure 67. Estimated Peak Catch for 25 Openings,Based on 99 Percentile of Distribution of Maximum Catch160IIIII140• Boats fishing /independently...,..,1120ioo. //.—e—— 99 percentile, EV1# boats fishing togetherFigure 68. Observed Cumulative Distribution ofHold Volume for Salmon Seine Vessels100• . .800.1060.1C0U00.200•0 50 100 150 200hold volume, cubic metres158acting as a packer for three boats. Based on these data, it is clear that themajority of the fleet must fish alone or in pairs.7.3 ConclusionsIn 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 thepacker are absorbed by all the boats in the team. It would seem that the largerthe number of boats in the team then the greater the benefit in terms of profitper trip. The biggest percentage change, however, is in the reduction of riskrather than increased income or reduced fuel costs. Based on 1988 data forcatch rates, the practical limit for the size of a team would be three boats sincethe catch for this number of boats was within the transportation capacity ofthe 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 maybe another reason for the popularity of two boats fishing as a team. Ifresources were unlimited, then each boat will pay for itself, but practically theinvestment in constructing or purchasing another hull may be beyond theresources of many independent operators.The percentage change in profit was relatively small when the only variablewas the number of boats. The maximum predicted difference was 7 percent forfour boats operating together. For the more likely condition of two boatsfishing together this difference was 2.6 percent. This difference, whilststatistically significant, was small in relation to the difference in profitabilitybetween decision models, observed when investigating the Random, Forecastand Stationary models, described in Chapter 5. It seems that using theassumptions described above that the benefits of multiple boats operating159together were in fine tuning the vessel management, rather than significantchanges in profitability. These improvements in profitability could beenhanced by using fishing boats which consumed less fuel and had a lowerminimum required income per trip, which could most easily be addressed by asmaller boat.160Chapter 8Performance of Forecast Simulation, Based on Four Years ofObserved Catch DataIt has been demonstrated that the important factors in the overall earningpower of a fishing boat, or teams of boats, within the simulations were therelative catch rates between areas, and the method of deciding which area tofish. The effect on profitability due to the number of boats in a team isstatistically significant, but small in relation to these other two factors. Havinginvestigated the basic parameters and sensitivity of the simulation models, thefinal question to be addressed was the performance of the Stationary andForecast Models, for the four years for which catch data were available. Therewere two important questions to answer. One was to decide if the profitabilityof the Forecast method was higher than the Stationary decision method, at theend of a period of several years. The other was to determine if there weresignificant differences in the size of the boats required for the differentdecision methods. The Random Model was also run, to provide ‘baseline’ data onthe average performance of the fleet.For simplicity, a single boat operating independently was simulated. The catchdata used in the simulation were the gamma distributions for catch per daycalculated for each area, and given in Table XVII for the four years for whichdata was available. The dollar values per kilogram were simplified to themodified average values, used in Chapter 7. The vessel parameters were thesame as those used for the simulations described in Chapters 5, 6 and 7.ModelParameternmeanstnd.95%CImeanstnd.95%CImeanstnd.95%CImeanstnd.95%CIdevn.devn.devn.devn.Year1987198819891990ButedaleFuel,litres2500405000405000.0405000.0405000.0Fuelcost,$2500162000162000.0162000.0162000.0Fish,kg250045202790109.3772205220204.6114073028.656605700223.4Fish,$250066504110161.11106007680301.11680107041.983308390328.9Profit,$250050304110161.1190007680301.161.5107041.967108390328.925TripsMax.Catch100120003280649.442180074401473.1305074201469.22130097401928.5Risk10016.92.230.441510.62.510.5250.20.015.42.440.5JuanFuel,litres2500109000109000.0109000.0109000.0defucaFuelcost,$25004360043600.043600.043600.0Fish,kg25002530165064.681410106041.645602620102.773205790227.0Fish, $250077905080199.1443403270128.2140008050315.62250017800697.8Profit,$250073505080199.1439003270128.2136008050315.62210017800697.825TripsMax.Catch10069101800356.444901450287.1114002770548.52340088301748.3Risk10012.12.460.4870201.890.43.411.840.42.81.480.3JohnstoneFuel,litres2500143000143000.0143000.0143000.0Fuelcost,$25005730057300.057300.057300.0Fish,kg250033303060119.9527102650103.939203670143.940504060159.2Fish, $250087608050315.5671306960272.8103009650378.31060010700419.4Profit,$250081808050315.5665606960272.897409650378.31010010700419.425TripsMax.Catch100121003710734.58103003560704.91430070001386.01640064001267.2Risk10012.72.440.483115.32.390.5112.630.511.52.190.4TableXXXVSummaryofSimulationResultsforStationaryModelsFourYears,1987to1990.‘-ModelParameternmeanstd.95%CImeanstd.95%CImeanstd.95%CImeanstd.95%CIdevn.devn.devn.devn.Year—1987198819891990ForecastFuel,litres2500154083232.6143010131051.35211801535.9976136076229.8704Fuelcost,$250061433313.054121052220.46247361223.99054230511.956Fish,kg250030602570100.745440500019643702940115.2568205530216.776Fish,$250080306600258.7291707630299.10130008700341.042000016700654.64Profit,$250074106630259.9079707510294.39125008710341.431950016800658.5625Trips#Butedale1002.391.410.279115.32.560.50680001.811.280.25344#JuandeFuca10010.72.580.51081.841.410.279118.22.250.445519.42.170.42966#Johnstone10011.92.510.49697.722.370.46926.82.250.44553.821.920.38016Max.Catch100105003540700.921930071301411.7128004120815.762180074101467.18Risk10013.32.810.556312.62.790.55245.271.850.36634.522.120.41976RandomFuel,litres25002210132051.7442210132051.7442210132051.7442210132051.744Fuelcost,$250088452920.73788452920.73788452920.73788452920.7368Fish,kg250034302730107.0238504290168.1731802930114.8656405330208.936Fish, $250076206200243.0474907000274.485408600337.121350013400525.28Profit,$250067406290246.5766006840268.1376608920349.661260013500529.225Trips#Butedale1008.492.030.40198.492.030.40198.492.030.40198.492.030.40194#JuandeFuca1007.942.40.47527.942.40.47527.942.40.47527.942.40.4752#Johnstone1008.572.350.46538.572.350.46538.572.350.46538.572.350.4653Max.Catch100109003560704.881650064601279.1116004070805.862130077201528.56Risk10014.12.720.538515.22.530.5009132.210.43759.912.430.48114TableXXXVISummaryofSimulationResultsforMobileModelsFourYears,1987to1990.0’t’31638.1 Results of Simulations for Four Years of Catch Data8.1.1 Variation in ProfitabilityThe detailed results for all the parameters measured are summarized in TablesXXXV and XXXVI for each of the decision methods and each of the four years forwhich data were available. Mean profit per trip is plotted against year for thethree Stationary Models and the Forecast Model in Figure 69. A summary of theresults non-dimensionalized by the average catch for each year (from theRandom Model) is given in Table XXXVII.When the Forecast Model was compared to individual Stationary Models overthe four year period, its profitability was 5 percent higher than the bestStationary area, which was Juan de Fuca. This difference was insignificant,given the variation in the observations, but it is important to note that theForecast Model was not worse than the best Stationary Model. The ForecastModel was 37 percent better than the second best Stationary Model, which wasJohnstone Strait. The Forecast Model was the only model which alwaysperformed better than the average.year Butedale Juan de Fuca Johnstone St. Forecast1987 0.746 1.091 1.214 1.0991988 1.364 0.591 0.994 1.2081989 0.008 1.775 1.272 1.6321990 0.533 1.754 0.802 1.5484 year mean 0.663 1.303 1.070 1.372Table XXXVIISimulated Catch Data for Four Years, 1987 to 1990Non-dimensionalized by Random Model164Figure 69. Comparison of Forecast Model with Stationary Models,4 Years of Data, Income - Fuel Cost, 1987 to 199030000’20000 // —0—-— Butedale/ 0 Juan de Fuca— — 4—— Johnstone10000- /•Forecast1986 1987 1988 1989 1990 1991YearFigure 70. Comparison of Forecast Model withStationary Model, Risk at $6000, 1987 to 19901.0-0.8-O.6’ / —o-—— Butedale0 Juan de Fuca0.4 — — -—— JohnstoneForecast0.20.0•. • I • I • I1986 1987 1988 1989 1990 1991Year165Even though the Forecast Model was as good as the best Stationary Model, inthe long term, it was not as good as the best possible performance. This issummarized in Table XXXVIII. Again the results were non-dimensionalizedusing the Random Model to represent the seasonal average.From these data it can be seen that over the four years, the Forecast Modelwould have averaged a profit 37 percent better than average, but 10 percentworse than the best possible performance. The area with the highest profitwas not consistent throughout the four years of data. For 1987 it was JohnstoneStrait, for 1988 it was Butedale and 1989 and 1990 it was Juan de Fuca. Themagnitude of the difference in profit for the best area relative to the otherareas was not consistent between years either, with 1987 being the smallest,and 1988 being the highest. The best possible performance over the four yearswould only have been obtained by moving between areas, but on a seasonalbasis, rather than for individual openings.Year Forecast Best Stationary1987 1.096 1.2101988 1.208 1.3641989 1.632 1.7751990 1.548 1.754Four year mean 1.371 1.526Table XXXVIIIComparison of Forecast Model with Best Possible Area, 1987 to 1990Non-dimensionalized by Random Model166It can be seen from Figure 69 that the Forecast Model was always moreprofitable than the second best Stationary area in any given year. This factorvaried between 0.8 percent in 1987 to 93 percent in 1990. The second best areawas Johnstone Strait, during 1988, 1989 and 1990. For 1987, Juan de Fuca wasthe second best area. It seems that the Forecast Model is never the best methodin any one year, but it always had the second highest profitability of thedecision rules.The best strategy would have been to identify the area with the highest meanprofit per trip for a given year, and then fish that area exclusively. Thedifficulty in practice is identifying the area which has the highest catch rateduring the course of the fishing season. Skippers are likely to be veryprotective of their information, and the only reliable record would be salesslip data, but this would have to be available to the fleet before the nextopening. A further confusion would be the length of time for which the areaswere actually open. Based on the observations on the fishing season, it wasobserved that the average number of openings, when these three areas wereopen simultaneously, varied between 5 and 6, and was generally governed bythe length of the season at Juan de Fuca, which generally opened last andclosed first. There is probably insufficient time to establish which area wasactually the best, and the relatively small penalty for not requiring thisinformation may be sufficient to justify the Forecast Model in practice.It was demonstrated in Chapter 6, that the Forecast Model could produce aprofit which was worse than average. This did not occur for the simulationsbased on actual catch rates, but it is interesting to compare the relativeperformance of the Forecast Model for 1989 and 1990. In both years, the catch167rate at Juan de Fuca was the highest and in each case it was significantlyhigher than average. In 1989, however the catch rate at Johnstone Strait wasalso higher than average, but in 1990 it was lower than average. In 1989 theForecast 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 appearsas though the problem for the Forecast Model, discussed in Chapter 6, wherethe model is misdirected could have occurred when using the real world data,even though it was never lower than average.8.1.2 Variation in RiskThe development of the risk parameter was discussed in Chapter 5. Thevariation of mean risk at $6000 per trip, for each of the decision models isshown in Figure 70 and Tables XXXV and XXXVI. From this it can be seen thatthe Forecast Model had the lowest risk, when averaged over the four years ofdata. The risk for the Forecast Model was approximately 7 percent lower thanthe best Stationary Model. The reduction in risk was slightly higher than theincreased profitability, but more years of data would be required to confirmthis observation. The risk was reduced for the Forecast Model, due to theskipper choosing to fish in the area of highest profitability from the previousopening. In any particular year, there tended to be one area which had catchrates much lower than the seasonal average. The Forecast Model tended toavoid these areas, and so the variations between seasons were smoothed out.It is interesting to note that Johnstone Strait was the area with the leastvariation in risk between years. The level of risk was determined by therequired income per trip. The value of $6000 used in the simulations was setbased on the data given in Table III, adjusted slightly for the fact that the boat168in the simulation was newer than average. If a particular boat was cheaperthan average to operate, then the level of financial risk could be reduced. Thismay be a factor when picking Johnstone Strait as a stationary area, providingthe long term profit of $8645 per trip covered the financial requirements forthe vessel. This figure is the average of the Stationary Model for JohnstoneStrait taken from Table XXXV.8.1.3 Variation in Size of VesselThe other question to answer in this section was whether or not a differentsize of boat was required for a skipper using the Forecast Model instead of theStationary 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 itshould be a stable, unbiased parameter which can be estimated from thesimulation, and where confidence intervals can be reliably fitted. The averagepeak values, together with 95% confidence intervals are plotted for the threeStationary Models and the Forecast Model in Figure 71.From this figure it can be seen that the most stable value of average peakcatch was for Johnstone Strait, with a four year average value ofapproximately 13,000 kilograms. The other two areas had at least one year withan 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 ofdata was considered, the ranking was Butedale, Johnstone Strait and Juan deFuca. The average peak catch for Butedale was approximately 25 percenthigher than that for Juan de Fuca.169Figure 71. Comparison of Average Peak Catch forDifferent Decision Methods, 1987 to 199030000 -__________________________________________0’20000a r —0—-— ButedaleC.,.---- JuandeFuca. > .# /(U 4a , - .-. -o- Johnstonea // —u——— Forecast/a)_0>Ig,0•• i • I • I • I1986 1987 1988 1989 1990 1991YearFigure 72. Comparison of Mobility Between Observationand Simulation, 1987 to 1990, Butedale0.80.6a).! 0.4•/., —0——- Simulation, ForecastC.0 •.2 o / - -. Observation— .0 0*0o•o°. 0.2•00. — • •00.0• . • I • • • I1986 1987 1988 1989 1990 1991Year170When the Forecast Model was considered, we can see that its highest meanpeak catch was also approximately 20,000 kg. When the Forecast Model wasaveraged over four years of data, it had the highest average peak value, byapproximately 10 percent, compared to the Stationary Models. The ForecastModel never obtained the highest average peak catch for any one year, but bymoving between areas it tended to stabilize the long term value, since ittargeted the areas with the highest profit. However, with the exception ofJohnstone Strait, the maximum value, within the four years of data, was notnoticeably different for the Forecast Model from the other two StationaryModels.It is difficult to draw any reliable conclusions from only four years of data, butis seems as though the Forecast Model does not require a boat which issignificantly bigger than the Stationary Models, with the exception ofJohnstone Strait. The lower catch rates for this area, in terms of quantity offish, may be one of the factors influencing the size of boat fishing inJohnstone Strait, which was discussed in Chapter 4. Based on the simulations, itseems as though large boats fishing in Johnstone Strait will have surplustransportation capacity, and a lower expected profit than could be found inother areas.8.2 Comparison of Results of Simulation with ObservationsA detailed comparison of the 1988 data was made with the results of thesimulation in Chapter 5. This was extremely time-consuming to carry out, andwould be unduly repetitive to carry out this procedure for all four years ofdata. However, some check on the overall performance of the simulations,relative to the actual fishing fleet would be desirable. It was easy to check the171first and second moments of catch per day distributions from the results inTables XXXV and XXXVI and the observations in Table XVII. It can be seen thatthese are in good agreement. Income figures will not agree, since the modifiedaverage values of dollars per kilogram were used.One factor which can be compared between the Forecast Models and theobserved data is a boat entry index to a given area. For the Forecast Model, thisindex was calculated from the fraction of the total number of trips that theboat made to a given area in a given year. For the observed data, the entryindex was calculated from the average number of boats per day fishing in agiven area, calculated over the full year. These values are compared for eacharea in Figures 72 to 74.From these figures, it can be seen that the entry index from the simulationgenerally matches the trends for the observed data for Butedale and Juan deFuca. The Forecast Model predicted higher peaks and lower troughs than forthe actual fleet performance. The Forecast Model exaggerated the trends in thefleet performance, due to the fact that the skipper was choosing the moreprofitable areas. In general, the fleet behaviour was closer to an evendistribution of effort than the Forecast Model predicted. These trends wereconsistent with the observations made during the detailed comparison with the1988 data in Chapter 5.Some of the differences can be explained by the assumptions made. Forexample, for Juan de Fuca in 1988, the Forecast Model had a lower number ofentries than was observed from the fleet. This was possibly due to the fact thatthe simulations used a lower dollar value of the fish, which would172Figure 73. Comparison of Mobility Between Observationand Simulation,1987 to 1990, Juan de Fuca0.80.6(30.4 / —I]-—— Simulation(0 444 04-, - - -- Observation0h._0.20.0•. p • I • I • I1986 1987 1988 1989 1990 1991yearFigure 74. Comparison of Mobility Between Observationand Simulation, 1987 to 1990, Johnstone Strait0.5“4.0.4. ,‘•0Cl)000.3—a-—— Simulation..--. Observation0.0I_ .I00_co00.LI. 40.1•• • I • I • I1986 1987 1988 1989 1990 1991year173significantly reduce the desirability of the area. Also for 1990, the actualentries at Butedale were much higher than would have been predicted by theForecast Model. This is due to the fact that this area was the only one open inthe early part of the season, and so the fleet did not need to determine whichwas the best area.However, the trends for Johnstone Strait were not matched well by theForecast Model. It seems as though more boats prefer to fish in JohnstoneStrait than the Forecast Model would indicate. The reason for this may be due tothe 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 bythe total number of days this was the area which produced the highest totalincome.8.3 Vessel Design Features Derived from the Simulations8.3.1 Fuel Consumption and MobilityThe Forecast Model had the second highest fuel consumption, averaged at $710per trip. This was lower than the Stationary Model at Butedale, but higher thanthe other two Stationary Models. The higher cost of fuel was offset byincreased earnings.Another factor to consider is the long term mobility of the vessel, in terms ofdetermining if there is a preferred area, and how this may influence thevessel design. Table XXXIX gives the average proportion of trips to each areafor the Forecast Model, over the four year study period.174year Butedale Juan de Fuca Johnstone St.1987 0.096 0.428 0.4761988 0.612 0.074 0.3091989 0.000 0.728 0.2721990 0.072 0.776 0.1534 year mean 0.195 0.501 0.302Table XXXIXProportion of Total Trips to Each Area,Forecast ModelFrom these data we can see that the boat fished approximately 50 percent ofthe 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 catchrates. Based on this information, it would appear that the boat should beoptimized for Juan de Fuca, without compromising the operations in JohnstoneStrait.The special features of Juan de Fuca would be the absence of places to makepoint sets, and so the vessel, deck arrangement and equipment should be sizedfor making open sets in exposed conditions. This may be the factor whichinfluences 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, butbased on the catch data there was no requirement for a larger transportationcapacity than boats fishing at Butedale.8.3.2 Empirical Relationships Between Mean Catchand Hold SizeOne measure of the size of the transportation capacity of the fleet is theaverage hold capacity, taken from Figure 68, which was calculated to be 65.7175C,—‘C,C,UN6C,S0zFigure 75. Relationship Between Mean Catch perDay and 99 Percentile for 25 Consecutiye Trips1 2 3 4 5 6 7 8average catch, tonnes176tonnes. The largest average peak catch taken from the simulations discussed inSection 8.3.1 was approximately 20 tonnes, which when allowance was madefor 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 thesimulation.A more reliable estimate of the size of the boats would be to consider theextreme values in more detail. One obvious relationship is between the meancatch and the 99 percentile for the maximum catch in 25 openings. This wouldbe helpful for designers in interpreting the required size of boat, when meancatch is the figure most commonly available. It was shown in Chapter 7 thatthe parameters for the extreme value distribution could be successfullyestimated from the first and second moments of the observed histogram formaximum catch. These parameters for the fitted distributions, together withthe 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 99percentile for the maximum catch in 25 openings. It can be seen that therelationship is approximately linear. Based on this analysis, the 99 percentileis 7.1 times the mean catch. However, if one wanted to use the largest observedvalues, 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 be10.6 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 cubicmetres. Based on the results of the simulation, 1 boat in 100 would require aModelyearmeanpeakstd.devn.95percentParametersfromfittedMaximumcatchcatch,kgconfidenceDistributionstonnesmeanpeakcatchsigma,EV1mu,EV1(99%,EV1)Butedale1987120003280642.8825571052422.29Butedale19882180074401458.2458011845245.14Butedale19893050742145.4357927165.38Butedale19902130097401909.0475941691651.85Johnstone1987121003710727.1628931043023.74Johnstone1988103003560697.762776869821.47Johnstone1989143007000137254581115036.26Johnstone19901640064001254.449901352036.47JuandeFuca198769101800352.81403610012.56JuandeFuca198844901450284.2113138379.04JuandeFuca1989114002770542.9221601015320.09JuandeFuca19902340088301730.6868851942651.1Forecast1987105003450676.22690894721.32Forecast19881930071301397.4855591609141.66Forecast1989128004120807.5232121094625.72Forecast19902180074101452.3657781846545.04Random1987109003560697.762776929822.07Random19881650064601266.1650371359336.76Random1989116004070797.723173976824.37Random19902130077201513.1260191782645.52TableXXXXParametersFittedtoMaximumCatchDistributionAssumingaGumbelDistributionI-.—I178hold bigger than this value. From observations on the fleet, we can see thatapproximately 30 boats in 100 have holds bigger than this level. The 99percentile for the observations on the fleet is 150 tonnes. This would alsoindicate that the boats in the fleet are bigger (and more expensive) than thesize required for the single day fishing trips predicted by the simulation,which was noted in Table XIII to be the most common scenario. It wouldappear that the boats are sized for multiple days fishing, between two and fourdays, or are sized for some fishery other than salmon seining.8.4 Long Term Economic PredictionsIt is also interesting to compare the longer term economics of salmon seinefishing, based on the four years for which data were available. Let us consideran 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$6000, the income from fishing and the cost of fuel consumed from thesimulation, we can consider some measures of economic performance for a fullfishing season. Since the overall economic performance will be sensitive tothe number of trips per year, the effect of this variable was also studied.One crude measure of economic performance is the payback period. This issimply the time required to repay the initial investment based on the assumedannual costs and expenses and takes no account of interest rates or cash flowsinto the project after the payback period.The results of this analysis for the five decision rules are given in Table XXXXI.This crude analysis immediately shows that the Stationary Model at Butedale isa bad investment, and based on the average values predicted from theDataPertrip,$trips/year2030405060ModelIncome(Inc.-fuel)CostProfit/tripProfit/yearStationaryButedale618552006000-800-16000-24000-32000-40000-48000JuandeFuca1215711737.560005737.5114750172125229500286875344250JohnstoneSt.9197.58645600026455290079350105800132250158700MobileForecast122501184560005845116900175350233800292250350700Random9287.5840060002400480007200096000120000144000ModelInitialinvestment10000001000000100000010000001000000StationaryButedalePaybackperiod,-62.50-41.67-31.25-25.00-20.83JuandeFucayrs8.715.814.363.492.90JohnstoneSt.18.9012.609.457.566.30MobileForecast8.555.704.283.422.85Random20.8313.8910.428.336.94TableXXXXICalculationofPaybackPeriod‘.0180simulation would never repay the investment. Payback period can be aneffective measure of merit for short term investment (less than three years)and it is immediately clear from this analysis that even the descision ruleswith the highest income (Juan de Fuca and Forecast Models) require over 40trips per year to bring the payback period less than 5 years. Based on the datain Table XII, we would expect that the average number of trips per year whenboth of these models were valid would be 16.75, although the maximumobserved number was 32. These rate would give payback periods between 10and 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 isappropriate for this investment is to consider the internal rate of return forthe project, based on an assumed 20 year life-span for the boat, with a resalevalue of $0.25M at the end of the 20 years. The internal rate of return is theequivalent interest rate generated by the project, assuming all investment isretained within the project. Again the sensitivity of the internal rate ofreturn (IRR) to the number of trips per season was studied. This analysis isgiven in Table XXXXII for the Forecast Model and for the Stationary Model atJohnstone Strait.Based on 20 trips per year, the Forecast Model predicted an IRR of 10.445percent, which is very low given the high level of risk associated with fishingoperations. It is not until 50 trips per year that the IRR reaches 30 percent,which is probably more appropriate for high risk ventures. For JohnstoneStrait, using the mean number of trips per year of 55 taken from Table XII, theIRR is approximately 13.7 percent. This is higher than the equivalent value181Trips per year 20 30 40 50 60Number of years 20 20 20 20 20Investment in boat 1000000 1000000 1000000 1000000 1000000Annual income 116900 175350 233800 292250 350700Resale value of boat 250000 250000 250000 250000 250000IRR 10.445 16.955 23.105 29.092 35.005Forecast ModelTrips per year 20 30 40 50 60Number of years 20 20 20 20 20Investment in boat 1000000 1000000 1000000 1000000 1000000Annual income 52900 79350 105800 132250 158700Resale value of boat 250000 250000 250000 250000 250000IRR 2.292 5.867 9.136 12.209 15.151Random ModelTable XXXXIICalculation of Internal Rate of Return182for the Forecast Model, taken over the average length of time for which it isvalid. For a vessel fishing in Johnstone Strait to obtain an IRR of around 30percent, the investment in the boat should be reduced to approximately $0.44M. This would correspond to the observation that boats fishing JohnstoneStrait were, on average, smaller and older.In conclusion, when the same number of trips per year are considered thenthe Forecast model represents the best investment. However, this model is onlyvalid for a short portion of the total season, and a better investment is to fishthe Stationary Model at Johnstone Strait. For a full season, based on the fouryears of observed data, the best strategy would be to use the Forecast Modelwhen all three areas were open, but then concentrate on fishing in JohnstoneStrait. The higher rate of return for Johnstone Strait may be the reason whythe Forecast Model under-predicts the number of boats fishing in JohnstoneStrait.8.5 SummaryIt was not possible to give definitive conclusions on the performance of theForecast Model on the basis of only four years of data, but it does seem that itpredicts approximately 37 percent more profit per trip than the average(Random Model) and 5 percent more than the best Stationary Model. Theadvantage comes from the skipper choosing the area with the best profit eachyear, which tends to stabilize the fluctuations which occur between yearswithin a single area. The Forecast Model predicts about 10 percent less profitthan the best possible choice of area each year.183The size of boat predicted by the Forecast Model was not significantly differentfrom that for the Stationary Models, with the exception of Johnstone Strait. Inthis case, the predicted size of hold is approximately 30 percent smaller.However, in general the boat sizes predicted by the simulation model, for asingle days fishing, are between 60 and 100 percent smaller than thoseobserved in practice. The actual fleet is sized for making longer trips than asingle day, although was the most common scenario.More boats prefer to fish in Johnstone Strait than is dictated by the short termcatch rate, based on maximum profitability from a single opening. Factorswhich are probably influencing this decision are the fact that this area showslittle variation in income and risk between years, and the fact that the seasonhas more openings than the other areas, and so the total income over theseason is the highest.184Chapter 9General Discussion and Further Work9.1 SummarySalmon seining was found to be a fishery particularly appropriate tomodelling using simulation. In the period 1987 to 1990, the fishery was highlyregulated, which limited the number of options available to a skipper in termsof selecting a place and time for fishing. This meant that the spatialdistribution of suitable fishing locations and the times at which fishing waspermitted were easily incorporated into a computer model when it was writtenin a simulation language.Observations on actual boat performance showed that there was little variationin vessel speed during the course of a voyage, and transit speeds could beconsidered as constant. The distances travelled by the boat when it was fishingwere very small in relation to the distances travelled to the regulated fishingareas, which meant that fishing activity could be considered as taking place ina single location on a given day. The majority of trips were recorded as being asingle day, which meant that the length of the voyage was not limited by themaximum range that the boats were capable of. It was also found that therewas 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 whichwere the same size (although size would vary between fishing areas), and thefact that there was not a very large difference in the vessel dimensions.185Of all the input variables, the most influential random variable was found to bethe daily catch rate at a given location, over the course of a season. It wasfound that other variables which affected the economic performance, such asvessel speed, fuel consumed during a trip and dollar value per kilogram of fishdid not show sufficient variation to make it worthwhile considering them asrandom 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 toeach area during a season (for mobile models).The data used for the statistical models of the catch rates were developed fromlanding data recorded by the Department of Fisheries and Oceans. It was foundthat gamma distributions gave very good models for catch rates. Somesimplifications could be made to the distribution of catch per day about themean, which were based on the geographic location and did not vary betweenyears. Since vessel size appeared to have no effect on catch rate, in terms ofcatch (kilograms) per day, data from all boats fishing in one location could beused to develop statistical models of the catch data, with no observabledistortion of the results due to the boat itself.The parameter which was used to judge the performance of the boats wasaverage profit per trip, which included both the income earned from thecatch and the cost of the fuel used to earn that income. It was assumed thatother operating costs did not vary with the distance that the boat travelled. Theanalysis methods presented could have been improved by carrying out adetailed calculation to subtract these operating costs from the profit reportedby the simulation model. Unfortunately no information was available for the186operating costs of the vessel used to check the simulation model. If these datawere available, then they could easily be included in the calculations.The simulation was developed to model the performance of a vessel (or groupof vessels fishing together) for a single opening, during the course of afishing season, for three fishing areas open simultaneously. This representedthe most complex portion of the fishing season, since it involved a choice ofareas, with a high level of uncertainty as to which would be the best area. Thesimulation was not developed to model a complete season, opening by opening,since observations indicated that the number of occasions when three areaswere open simultaneously was a relatively small percentage of the totalnumber of openings in a season.Three decision rules were developed and programmed into the simulation, onebased on Stationary boats (always fishing in the same spot), and two based onmobile boats. One mobile method assumed a random choice by the skipper tomove between fishing areas, and the other (called the Forecast Model) fishedin the area with the highest profit the previous opening. It was found thateach model represented realistic, but different, views of the fishing operation.The Stationary Model represented a reasonably high proportion of the fleet, asdid the Forecast Model. The Random Model gave a good approximation to theaverage performance of the whole fleet.It was found that in general, fishing in the area which had had the highestaverage profit the previous opening was a good strategy. This decision methodtended to avoid the areas which had low catch rates, and tended to fish moretimes in areas which had high catch rates. Based on data for four years of187fishing operations, the Forecast Model gave a profit that was five per centhigher than the best Stationary Model and 37 percent better than the average.The Forecast Model was only 10 percent worse than the best possibleperformance over the period studied. It is important to be able to model betterthan average income since this will represent better than average skippers.These skippers catch the largest amounts of fish, which in turn will have themost effect on the stock.Other factors which were considered were the sensitivity of the profit earnedby a single fishing vessel to variations in catch rate, using both real andsynthesized data, to highlight any possible areas of weakness in the decisionmodel. It was found that selecting the best area based on the previous openingwas not a good strategy when the average profit from all three areas wereapproximately equal. For the fishing areas chosen, the income from thefurthest area had to be at least twice the average value from the other twoareas, in order for ft to be significantly more profitable. This was due to thefact that up to this point, there was a higher probability of selecting thewrong area as the area of highest catch. This gives some quantification to theobservation that some skippers are relucant to move between fishing areasuntil catch rates are very high.Variations in the operating practice of the boats were investigated usingsimulation, 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 ofa team. In this study, only one boat was used to transport fish, while the otherboats remained on the grounds. It was found however, that the biggest effectof boats fishing together was the reduction in financial risk. Risk was defined188as the probability of making a voyage, and not earning enough to cover theaverage cost per voyage. When two boats were fishing together, the risk wasreduced to 44 per cent from 51 per cent. The risk continued to reduce for threeand four boats fishing together, but at a lower rate. Thus, when the number ofopportunities 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 thefish hold required to transport the maximum catch which could be expectedduring the course of the season. The simulation was developed to model asingle opening, and so it was necessary to fix the number of openings in aseason, in order to estimate the distribution of maximum catch. Fromobservations on the fleet performance, it was decided that 25 openings was areasonable number. The maximum catch from 25 consecutive openings wassimulated, and it was found that this could be approximated by a Gumbeldistribution. The parameters for the Gumbel distribution could be estimatedeither from the estimated distribution of catch per trip, or from thedistribution of maximum catch, recorded by the simulation.The simulation predicted vessel sizes which are smaller than the vesselsobserved 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 representsconsiderably more investment in the fleet than is required. Since many of theboats in the fleet are more than twenty years old, it is possible that theeconomic factors have changed with time, and catch rates no longer justifythe investment in such large vessels. It was observed that vessel parametershave become smaller with time.189From the simulation, it was found that the biggest effect on profitability wasthe 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 thenumber of boats fishing together as a team. The results of the simulations alsoshowed that it was necessary to move between areas to obtain the highestprofits. Movement between areas on an opening by opening basis, which wasobserved in the fleet behaviour, was probably the result of lack of informationas to which was the best area for a given year.The simulation results predicted that on the basis of ‘profit per trip’, theForecast Model offered highest mean profit per trip. However, when theexpected number of trips per year were included, the best internal rate ofreturn was offered by the Stationary Model at Butedale. This was the result of ahigher average number of trips per year, which resulted in a larger incomeper season. Using the current value of a fishing vessel and the catch ratesbased on the four years of observed data, it is apparent that simply fishing forsalmon is not a good investment, given the high levels of risk involved. It isessential for skippers and vessel owners to maximize the number of trips peryear in order to make the investment profitable in the long term.The simulation model was developed to support the an expert system forfishing vessel design. The long term intention is to use the simulation topredict the transportation requirements of a vessel, or group of vessels. Thiswould then be used to generate the basic design within the expert system. Thesimulation would then be used again to model the operating economics over arealistic range of catch rates and fishing locations.1909.2 Discussion on the Use of Simulation for Studying Fishing BoatEconomicsSimulation is a modelling technique which allows for a realisticrepresentation of income and expenditure in fishing vessel operations. Thebiggest advantage of using simulation to model the economic performance offishing vessels is that it allows many important parameters to be included asrandom variables. It was found that there was considerable variation in catchrate, and therefore income, between days, fishing areas and years, all ofwhich had to be included if realistic results were required. The mobility of thefishing fleet meant that it would have been difficult to include this randomvariation 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 alsobe analyzed as random variables. It also allowed for a model of the vesselmobility, and how fuel consumption would vary with different fishingscenarios. All these factors were important in taking a probabilistic approachto the analysis of the design and operating economics of fishing vessels. Theprobabilistic approach was essential when the level of financial risk was to beanalyzed.When maximum catch was considered as a random variable, it meant that thehold size for a vessel could be determined based on the probability of obtaininga certain catch. It was clear from the analysis that the hold size required forvessels fishing Johnstone Strait was smaller than for any other area ordecision rule. This may be one reason why it was observed that the smallerboats fished this area. The catch rate at Butedale was often higher, but thesmaller vessels tended to fish this area also.191The major disadvantage of using simulation was that it required considerablymore information than traditional deterministic design methods. For a fishery,such as salmon seine fishing in British Columbia, which has a relatively smallnumber of boats and a well established operating practice, then thisinvestment is worthwhile. The method used was essentially a ‘hindcasting’technique which relied on past catch data to make inferences relative to theperformance of a fishing vessel. For design purposes, it can be used toinvestigate a realistic range of catch rates, and distributions of parameters forgiven fishing areas. If this information were to be translated back into designparameters, it should result in fishing operations which are economicallyviable for the fishing fleet, but do not put the long term supply of fish indanger.The analysis developed for the simulation model may have included somefactors which were inherent to the way the data was collected. For example, itwas not possible to develop data on a catch per set basis, and so factors such assize of the net, weather conditions and other variables may be buried in thedata. Thus, the catch rate data can only be strictly applied to salmon seinefishing gear and techniques used at the time the data were collected.9.3 Future Uses of Simulation in Fishing Vessel AnalysisAll the analyses were carried out based on the technical performance of asingle boat, for which data were available. It is recognized that other vesselswill have different operating characteristics, and the simulation model couldbe adjusted to calculate the economic effect of the differences. The vessel usedin the simulation had an installed power which was higher than average,192which may have effected fuel consumption. Other factors which may beconsidered for future simulation models are radically different hull formcombinations, such as high speed planing hulls combined with packers.The Forecast decision method could be refined to keep longer terminformation, rather than just the data on the last opening. We can speculatethat this would reduce the level of the performance deficiency identified inChapter 6. However, the current model has the advantage of using theminimum amount of historical information.So far, only one fishery has been simulated. Another major fishery in BritishColumbia is the herring seine fishery, where most of the boats involved alsofish for salmon. The herring season is different from salmon in that it is veryshort, but much higher catch rates are typically observed (50 tonnes per dayfor herring compared to 3 tonnes per day for salmon). It is reasonable that ifthe model can be applied to one seine fishery, it could be adjusted to anotherone, especially when the boats are the same. Two major fisheries which aredifferent from seining are trawling and line fishing. It would be interestingto analyze these fisheries in order to develop a simulation model. However, datawould be required on vessel operations and catch rates for differentgeographic areas in order to develop a successful model.The simulation models developed for this thesis could be used to consider theeffect of external factors such as the cost of fuel and the price of fish on theprofitability of a typical fishing operation. This would show at what point itwould not pay for boats to remain in operation. Whilst this is clearlydependent on the tuning of the relationships within the model, it would be193easy to modify the computer programs for specific instances. However, sincethese are likely to be so specific, the best use of the simulation would be toanswer specific questions on a specific operation.The application of simulation in this thesis has concentrated on theperspective of a skipper seeking to maximize the income obtained from asingle fishing trip. It was assumed that if this can be successfully modelled,the seasonal catch can be maximized simply by fishing the maximum numberof openings per year. However, the fishing scenario used in the simulationswas a considerable simplification of reality. For example, not all areas are opensimultaneously. In some cases the area which had the highest return may notbe open the following week and in other cases areas may be open for differentlengths of time. In such cases, it would be cheaper to stay on the groundsovernight, 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, ifmore days were available for fishing.These are fisheries management issues rather than direct engineering, but itwould be possible to develop a simulation model with more emphasis onmanagement issues. The long term objective would then be to balance themortality rate required for a profitable industry with the requiredreproduction rate for a healthy stock. The biggest weakness in converting thesimulations described in this thesis into fisheries management tools is thatthey take no account of the dynamic behaviour of the fish population. Clearlyif the fish population is tied to a geographic area, the amount of fish at the endof the season is lower than at the beginning. This is not allowed for within thedevelopment of the model.194However, some aspects of fisheries management, such as vessel preferencesfor certain fishing locations, or changes in the number of trips permitted peryear could be handled reasonably successfully by these relatively simplemodels. 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 specificquestions related to well defined structural changes to the fishing system.195References1. 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 VesselDesigns Based on Techno-Economic Analysis’, Dr. Ing Thesis, Division ofMarine System Design, Norwegian Institute of Technology, December, 1985.3. Causal, S. M., McGreer, D. and Rohling, G. F. ‘A Fishing Vessel EnergyAnalysis Program’, Marine Technology, Vol. 26, No. 1, January 1989, pp 62-73.4. Nickerson, T. B. ‘Systems Analysis in the Design and Operation of FishingSystems’, Conference on Automation and Mechanization in the FishingIndustry, Montreal, 1970.5. ‘Applied Operations Research in Fishing’, Proceedings, NATO Symposium onApplied Operaions Research in Fishing, Trondheim, 1979, Plenum Press, NewYork, 1981.6. Hamlin, C. ‘Systems Engineering in the Fishing Industry’, MarineTechnology, Vol. 23, No. 2, April 1986, pp 158-164.7. Ledbetter, M. ‘Competition and Information Among British Columbia SalmonPurse Seiners’, Ph. D thesis, University of British Columbia, April 1986.8. Schmidt, P. G. Jr. ‘Purse Seining: Deck Design and Equipment’, Fishing boatsof the World 2, edited by Jan-Olaf Traung, FAO of UN, Rome, published byFishing News Books, 1960.9. Robert Allan, ‘British Columbia (Canada) Fishing Vessels’, Fishing Boats ofthe World 1, edited by Jan-Olaf Traung, FAO of UN, Rome, published by FishingNews Books, 1955.10. Cove, J. J. ‘Hunters, Trappers and Gatherers of the Sea: A Comparative Studyof 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 SalmonPurse-Seine Fleet: Dynamics of Movement’, J. Fish. Res. Board Can. Vol. 36, 1979.12. Hilborn, R. and Ledbetter, M., ‘Determinants of Catching Power in theBritish Columbia Salmon Purse Seine Fleet’, Can. J. Fish. Aquat. Sci. Vol 42, 1985.13. Hilborn, R., ‘Fleet Dynamics and Individual Variation: Why Some PeopleCatch More Fish than Others’, Can. J. Fish. Aquat. Sci. Vol 42, 1985.14. Fisheries Act, Pacific Commercial Salmon Fishery Regulations, Queen’sPrinter for Canada, Ottawa, 1978.15. Pacific Coast Commercial Fishing Licensing Policy: Discussion Paper,Department of Fisheries and Oceans, September 1990.19616. Bjerring, J. H. and Chamut, P. S. ‘Annual Summary of British ColumbiaCommercial Catch Statistics, 1988’, Department of Fisheries and Oceans, PacificRegion, no date or report #.17. ‘1990 Fact Sheet’, Department of Fisheries and Oceans, Pacific Region, nodate or report #.18. Causal, S. and McGreer, D. ‘Application of a Bulbous Bow to a Fishing Vessel’,International Fisheries Energy Optimization Workshop, University of BritishColumbia, Vancouver, B. C. August 28-30, 1989.19. Avis, J., Dunwoody, B. and Molyneux, D. ‘Reducing Added Resistance ofFishing Boats Using a Bulbous Bow’, International Fisheries EnergyOptimization 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 ofFishing Operations’, NATO Symposium on Applied Operations Research inFishing’, Trondheim, Norway, August 1979.22. Bury, K. ‘Statistical Models in Applied Sciences’, Krieger PublishingCompany, 1986.23. Pritsker, A. A. B. ‘Introduction to Simulation and SLAM II’, 2nd Edition, JohnWiley and Sons, 1984.197Appendix 1Methods for Fitting Gamma Probability Density Functionsto Observed Catch DataA random variable x is said to be Gamma distributed if its probability densityfunction (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 byequations (3) and (4).(3)lno+w(X)=lnG (4)wherenII x1’i=1198Bury [1] gives methods of estimating the shape parameter, X, from eitherequation (5) or (6), depending on the value of g, where=(o.sooi + O.1649g - O.0544g2)g1 (5)for 0< g <= 0.577 or8.899 + 9.060g + .9775g2 (6)17.80g + 11.97g2 + g3for 0.577<=g <=17where g = in ()The variance of a and X were estimated from the variance-covariance matrix,given in equation 7.a) -a1 (7)n(xw’x-1) -a xwhere ip’ is the trigamma function.Data were obtained from the Department of Fisheries and Oceans for each boatreporting a landing from each geographical area on a given date. The datawere reduced to mean catch per day (and its standard deviation) for each daywhen there were six or more boats reporting a landing for a given area. Eachyear and area were analyzed seperately. Based on the fisheries biologyliterature, it was assumed that the gamma probability distribution was likely to199be a good model for the observed variation in mean catch per day for salmonseine fishing, over the course of a season. A computer program was writtenwhich read in the mean catch per day for each day, and then calculated theparameters required to solve equations (5) or (6) for A. This value was thenused to solve equation (3).Estimates of the variance of the parameters, a and A, were made from thevariance-covariance matrix, given in equation 7.The gamma probability function fitted to the data, using the methods describedabove, was compared against the observations (point by point) using aKolmogoroff test, described in [2]. This test considers the maximum absolutedeviation between the order statistic for the observed data (catch per day) andthe predicted cumulative distribution function (CDF) at the same value of x.This deviation is refered to as the Kolmogoroff Statisitic. If this statistic is lessthan a critical value, which depends on the size of the sample and the assumedconfidence level, a, then the fitted distribution is considered to be statisticallythe same as the observations. The observed deviations are less those accountedfrom simply by random sampling from that distribution. The tabulated valuesfor the Kolmogoroff Statistic are given in [2].In order to perform the Kolmogoroff Test on the observed data, it wasnecessary to write a program to calculate the CDF for the predicteddistributions, since there is no analytical solution to the integration of thegamma PDF. This program was prepared using the methods given in [3]. Thesame program also calculated the Kolmogoroff Statisitic, using the methodsdescribed above.200Other data which were calculated were the number of boats reporting alanding on a given day and the number of days per year for which landingswere reported.References1. Bury, K. ‘Statistical Models in Applied Sciences’, Krieger PublishingCompany, 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. ‘NumericalRecipes (Fortran version)’, Cambridge University Press, 1989, pp 156 to 157.201Appendix 2Description of SLAMII Computer Program forStationary ModelThe Stationary Model was programmed in SLAMII, using a network diagram.SLAMII was chosen since it was an established program, which was readilyavailable at the University of British Columbia, and would run on a wide rangeof computer systems.There were three seperate networks used within the model. These were asfoil ow s:- a vessel moving around between geographic areas- fishing data generation for individual openings- data collection on 25 consecutive openingsThe priciple features of each network will be described below.1. Vessel NetworkThe vessel network started by assigning the technical and economicparameters to the entity (vessel) entering the model. This was done by usingthe attributes, which can be assigned directly within SLAM II. In addition, oneattribute was used within the model for timing, one for the location of thehome port and one for the location of the fishing grounds. The entity was thenheld in a gate, which represented the vessel waiting in port. Once an openingwas ‘announced’ the gate was opened from the ‘fishing data’ network and thevessel could take one of three branches within the network, each of which ledto a different fishing area. The destination for a particular trip was202determined from the value of an attribute, which was initially assigned to thevessel, as it entered the model. This attribute was used to determine thedistance of the fishing ground from the home port and when combined withthe speed of the boat, was used to calculate the time the vessel took to reach theselected fishing grounds. The distances between the fishing grounds and thehome port were stored as an array, and the attributes for the home port andthe destination were used to locate elements within the array.Each of the three branches described above contained a gate, which held thevessel until the time when fishing could legally begin. This represented thevessel waiting on the fishing grounds and selecting a place to fish. The lengthof the wait was dependent on the distance from the port, with longer waitsoccuring 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 ofconsumption during fishing activity. After 8 hours had passed the gate wasclosed again to prevent another vessel entering the area, and fishing illegally.The vessel’s catch was determined by sampling a random variable, which wasmodelled using a gamma distribution based on the mean catch per day, setwithin the ‘fishing data’ network. The parameters within the gammadistribution were set using SLAM!! global variables and so they could betransfered between networks very efficiently. One hour after the fishing areawas closed the boat sailed home, using times calculated from the fishinglocation’s distance from the home port.Data was then collected on the simulated values of catch, income, fuelconsumed, number of trips where the income was less than $6000 and the size203of the maximum catch. These data were collected as global variables, andtransfered to the ‘25 consecutive openings’ network for tabulation.The vessel was then routed back to the gate representing its home port, afterthe destination code for the next trip had been changed. For the StationaryModel, since data was collected for each area seperately, the new destinationwas selected simply by rotation between each of the three branches,representing the three fishing areas. When the vessel arrived back at theport, the gate had already been closed, and so the vessel was held in port untilthe next opening. When the opening was ‘announced’ and the gate wasopened, the model would begin again.2. Opening NetworkThis network was one line, which opened and closed the gates within thevessel network at the appropriate time and set the values of global variablesused 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 thesimulation to changes in catch rate between years.Input parameters were the price of fish and the scale and shape parametersfor the mean catch per day (seasonal values) distribution for each area. Theshape parameter for the daily catch distribution was assumed to be a constant,but its scale parameter was calculated based on the sampled value of meancatch per day.204This is best illustrated by an example. The parent distribution, for mean catchper day (for the season) would be set using numerical values derived from theobserved catch data.ASSIGN XX(j)=GAMMA(a, b) mean catch per day (season)XX(k)=c shape parameter, catch/day (vessel), constantXX(l)= XX(j)/XX(k) scale parameter, catch/day (vessel)Then within the vessel network the catch is sampled using the followingstatement:ASSIGN XX(m)=GAMMA(XX(l),XX(k))3. Twenty Five Consecutive Openings NetworkThis is another linear network, which is used to collect data on 25 consecutiveopenings. Data is transfered between the vessel network and this networkusing global variables. This network was added to be able to collect data on thelong term statisitics, such as catch per trip, and the seasonal variables, such asmaximum catch and risk, within the same model. It also serves as a timer forthe 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 includethe alternative decision rules. It also allowed for data collection to beincorporated using the standard methods within the program language. A fulllisting of the SLAMII code for the Stationary Model is given below.205GEN,DAVID,STATIONARY MODEL,0 1/22/92,1;MODEL NAME: STAT88FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY3 MOST PRODUCTIVE AREAS, STATIONARY MODELMODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMYITEE, DEC.1991ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCHSHORTENED TO TRY TO FIT STUDENT VERSION ARRAYSATRIBUTES 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, DOLLARSADDITIONAL ATTRIBUTES! USE GLOBAL VARIABLES INSTEADXX(40) MAX. CATCH, AREA 1XX(41) MAX. CATCH, AREA 2XX(42) MAX. CATCH, AREA 3XX(43) NO. OF TRIPS WHERE PROFIT <6000, AREA 1XX(44) NO. OF TRIPS WHERE PROFIT <6000, AREA 2XX(45) NO. OF TRIPS WHERE PROFIT <6000, AREA 3LIMITS,6,14,15;ARRAY( 1 ,7)!0,20,75, 100,190,200,290; DISTANCES BETWEEN PORT &LOCATIONSNETWORK;GATE,HOME,CLOSED,4;GATE,AREA1 ,CLOSED, 1;GATE,AREA2,CLOSED,2;GATE,AREA3,CLOSED,3;CREATE,,,,1,1; CREATE BOATBASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOCASSIGN, ATRIB(1)=10.0; SPEED, KNOTSASSIGN, ATRIB(2)=84.5; HOLD CAPACITY, M’3ASSIGN, ATRIB(3)=59.4; FUEL CONS. LIHR, OUTWARDASSIGN, ATRIB(4)=6.4; FUEL CONS. LJHR, FISHINGASSIGN, ATRIB(5)=78.1; FUEL CONS. L/HR, RETURNASSIGN, ATRIB(6)=0.4; FUEL COST, $!L206ASSIGN, ATRIB(7)=1; LOCATION OF HOME PORTASSIGN, ATRIB(8)=7; GO TO BUTEDALE, 1ST TRIPWAIT IN PORT FOR AN OPENINGPORT AWAIT(4),HOME,; WAIT IN PORTSELECT DESTINATION THIS TRIPACT,,ATRIB(8).EQ.7,BUTD;ACT,,ATRIB(8).EQ.3,JUAN;ACT,,ATRIB(8).EQ.4,JOHN;BUTDALEBUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC1 AWAIT(1),AREA1,1;ASSIGN, ATRIB(1 1)=GAMMA(XX(5),XX(6)); SAMPLE DAILY CATCH DIST.ACT,9.O,,; FISHING TIME, 9 HOURSASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(4)*9.O; UPDATE FUEL CONSUMEDACT, ATRIB(9),,; SAIL HOMEASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMEDDATA COLLECTIONCOLCT,ATRIB(1O),FUEL1,; RECORD FUEL THIS TRIPASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COST OF FUEL THIS TRIPCOLCT,ATRIB(12),CFUEL1 ,,;COLCT,ATRIB(11),FISH1,20/O/500; RECORD CATCH THIS TRIPASSIGN, ATRIB(13)=ATRIB(1 1)*XX(7),; INCOME THIS TRIPCOLCT, ATRIB(13),VFISH1,;ASSIGN, ATRIB(14)=ATRIB( 1 3)-ATRIB(12); SURPLUS, FISH-FUEL,DOLLARSCOLCT, ATRIB(14),PROFIT1,20/O/1500,1;ACT,,ATRIB(1 1).LE.XX(40), SKP1;ACT,,ATRIB(11).GT.XX(40),; RECORD NEW MAXIMUM CATCHASSIGN, XX(40)=ATRIB(1 1),;SKP1 GOON,1;COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000207ACT,,ATRIB(14).GE.6000,NX1;ACT,,ATRIB(14).LT.6000,;ASSIGN, XX(43)=XX(43)-’- 1,;NX1 GOON,1;ASSIGN, ATRIB(8)=3,; SET NEW DESTINATIONACT,,,HOME;JUAN DE FUCA STRAITJUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(lO)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAlT FOR OPENING, ON GROUNDSLOC2 AWAIT(2),AREA2,l;ASSIGN, ATRIB(11)=GAMMA(XX(15),XX(16)); SAMPLE DAILY CATCH DIST.ACT,9.O,,; FISHING TIME, 9 HOURSASSIGN, ATRIB(lO)=ATRIB(1O)÷ATRIB(4)*9.O; UPDATE FUEL CONSUMEDACT, ATRIB(9),,; SAIL HOMEASSIGN, ATRIB(lO)=ATRIB(lO)+ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMEDDATA COLLECTIONCOLCT,ATRIB(lO),FUEL2,; RECORD FUEL THIS TRIPASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COST OF FUEL THIS TRIPCOLCT,ATRIB(12),CFUEL2,,;COLCT,ATRIB(l1),FISH2,20/O/500; RECORD CATCH THIS TRIPASSIGN, ATRIB(13)=ATRIB(l l)*XX(17),; INCOME THIS TRIPCOLCT, ATRIB(13),VFISH2,;ASSIGN, ATRIB(14)=ATRIB(l3)-ATRIB(1 2); SURPLUS, FISH-FUEL,DOLLARSCOLCT, ATRIB(l4),PROFIT2,20/O/1500, 1;ACT,,ATRIB(1 1).LE.XX(41), SKP2;ACT,,ATRIB(ll).GT.XX(41),; RECORD NEW MAXIMUM CATCHASSIGN, XX(41)=ATRIB(l1),;SKP2 GOON,l;COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000ACT,,ATRIB(14).GE.6000,NX2;ACT,,ATRIB(14).LT.6000,;ASSIGN, XX(44)=XX(44)+ 1,;NX2 000N,1;ASSIGN, ATRIB(8)=4,; SET NEW DESTINATIONACT,,,HOME;208JOHNSTONE STRAIT-JOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(10)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC3 AWAIT(3),AREA3,1;ASSIGN, ATRIB(1 l)=GAMMA(XX(25),XX(26)); SAMPLE DAILY CATCH DIST.ACT,9.0,,; FISHING TIME, 9 HOURSASSIGN, ATRIB(10)=ATRIB(10)+ATRIB(4)*9.0; UPDATE FUEL CONSUMEDACT, ATRIB(9),,; SAIL HOMEASSIGN, ATRIB(10)=ATRIB( 1O)÷ATRIB(5)*ATRIB(9); UPDATE FUEL CONSUMEDDATA COLLECTIONCOLCT,ATRIB(10),FUEL3,; RECORD FUEL THIS TRIPASSIGN, ATRIB(12)=ATRIB(10)*ATRIB(6),; COST OF FUEL THIS TRIPCOLCT,ATRIB(12),CFUEL3,,;COLCT,ATRIB(1 1),FISH3,20/0/500; RECORD CATCH THIS TRIPASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27),; INCOME THIS TRIPCOLCT, ATRIB(13),VFISH3,;ASSIGN, ATRIB(14)=ATRIB(13)-ATRIB(12); SURPLUS, FISH-FUEL,DOLLARSCOLCT, ATRIB(1 4),PROFIT3,20/0/1 500,1;ACT,,ATRIB(1 1).LE.XX(42), SKP3;ACT,,ATRIB(11).GT.XX(42),; RECORD NEW MAXIMUM CATCHASSIGN, XX(42)=ATRIB(11),;SKP3 GOON,1;COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000ACT,,ATRIB(14).GE.6000,NX3;ACT,,ATRIB(14).LT.6000,;ASSIGN, XX(45)=XX(45)+1,;NX3 GOON,1;ASSIGN, ATRIB(8)=7,; SET NEW DESTINATIONACT,,,HOME;HOME 000N,1;ACT,,,PORT;TERM;**** ** * ** *** * ***** * *********** *** **** ******* ***** ****** *********DATA GOES HERE **********************************************209;****************************************************************CATCH RATES AS SEEN BY BOAT, YEAR IS 1988, FROM CATCH DATAAVERAGE FISH PRICES OVER YEARSCREATE, 168,,,,;ASSIGN,XX(3)=48,; TIME TO OPENINGCATCH RATES AND PRICESASSIGN,XX(7)=1.472,; AVERAGE $/KG, BUTEDALEASSIGN,XX(17)=3.076,; AVERAGE $/KG, JUAN DE FUCAASSIGN,XX(27)=2.629,; AVERAGE $/KG, JOHNSTONEUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALEASSIGN,XX(4)=GAMA(1145.92,6.31),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCHJDAYABOVEASSIGN,XX(6)=3.055,; SHAPE PARAMETERASSIGN,XX(5)=XX(4)/XX(6),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DEFUCAASSIGN,XX(14)=GAMA(449.25,3.18),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(16)=5.005,; SHAPE PARAMETERASSIGN,XX(1 5)=XX(14)/XX(16),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY,JOHNSTONE ST.ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(26)=2. 195,; SHAPE PARAMETERASSIGN,XX(25)=XX(24)/XX(26),; SCALE PARAMETER*************OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICEACT,XX(3),,; WAIT FOR OPENINGOPEN, AREA1,,; OPEN AREA, BUTEDALEOPEN, AREA2,,; OPEN AREA, JUAN DE FUCA210OPEN, AREA3,,; OPEN AREA, JOHNSTONEACT,8,,; DURATION OF OPENINGCLOSE, AREA 1,,; CLOSE AREACLOSE, AREA2,,; CLOSE AREACLOSE, AREA3,,; CLOSE AREAASSIGN,ATRIB(1)= 160-XX(3)-8ACT,ATRIB(1),;ACT,8,,;TERM;OPENINGS & CLOSINGS, ONE WEEK INTERVALSMODIFY OPENINGS FOR SEASON, RATHER THAN FOR WEEKCREATE, 12600,,,,;REP GOON,1;OPEN, HOME,;ACT,56,,;CLOSE, HOME,1;ASSIGN, ATRIB(1)=ATRIB(1)+1,1; COUNT TRIPSSEASON REPRESENTS 25 OPENINGS (168 * 25 = 4200 HRS), MODEL RUNS FOR 100SEASONSACT, 1 12,ATRIB(1).LT.75,REP;ACT, 1 12,ATRIB(1).GE.75,;COLCT, XX(40),MAX1,20/10000/1000; MAXIMUM CATCH THIS SEASON,AREA 1COLCT, XX(41),MAX2,20/10000/1000; MAXIMUM CATCH THIS SEASON,AREA 2COLCT, XX(42),MAX3,20/10000/1000; MAXIMUM CATCH THIS SEASON,AREA 3COLCT, XX(43),RISK1,26/0/1; NUMBER OF TRIPS .LT. $6000, AREA 1COLCL, XX(44),RISK2,26/0/1; NUMBER OF TRIPS .LT. $6000, AREA 2COLCL, XX(45),RISK3,26/0/1; NUMBER OF TRIPS .LT. $6000, AREA 3ASSIGN, 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 VALUESTERM, 100;ENDNETWORK;FIN;211Appendix 3Description of SLAMII Computer Program forRandom ModelThe 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 AreaFor this model, the selection of the fishing area, after the first trip had beenmade was based on probabilistic branching at the node where the vessel wasrouted to a fishing area for a particular trip. Each area had an equalprobability of selection.2. Data CollectionData were collected, for this model, at the point just before the time when thevessel had reached the port. This modification was required since it was nowno 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 variableswere 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 globalvariables for tabulation within the ‘25 Consecutive Openings’ module.A full listing of the SLAMII code for the Random Model is given below.212GEN,DAVID,RANDOM MODEL,O 1/22/92,1;MODEL NAME: RAND88FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY3 MOST PRODUCTIVE AREAS, RANDOM SELECTION OF AREAMODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMITI’EE, DEC.1991ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCHSHORTENED TO TRY TO FIT STUDENT VERSION ARRAYSATRIBUTES 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, DOLLARSADDITIONAL ATTRIBUTES! USE GLOBAL VARIABLES INSTEADXX(40) NO. OF TRIPS TO AREA 1XX(41) NO. OF TRIPS TO AREA 2XX(42) NO. OF TRIPS TO AREA 3XX(43) MAXIMUM CATCH THIS SEASONXX(44) NO. OF TRIPS WHERE PROFIT < 6000LIMITS,6,14,15;ARRAY(1 ,7)/0,20,75, 100,190,200,290; DISTANCES BETWEEN PORT &LOCATIONSNETWORK;GATE,HOME,CLOSED,4;GATE,AREA1 ,CLOSED, 1;GATE,AREA2,CLOSED,2;GATE,AREA3,CLOSED,3;CREATE,,,,1,1; CREATE BOATBASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOCASSIGN, ATRIB(1)= 10.0; SPEED, KNOTSASSIGN, ATRIB(2)= 150.0; HOLD CAPACITY, M3ASSIGN, ATRIB(3)=59.4; FUEL CONS. LJHR, OUTWARDASSIGN, ATRIB(4)=6.4; FUEL CONS. IJHR, FISHINGASSIGN, ATRIB(5)=78.1; FUEL CONS. L/HR, RETURNASSIGN, ATRIB(6)=0.4; FUEL COST, $/LASSIGN, ATRIB(7)=1; LOCATION OF HOME PORT213ASSIGN, ATRIB(8)=3; GO TO JUAN DE FUCA, 1ST TRIPWAIT IN PORT FOR ANY OPENINGPORT AWAIT(4),HOME,; WAIT IN PORTSELECT DESTINATION THIS TRIP, RANDOM CHOICE FROM THREE AREASACT,,O.33333,BUTD;ACT,,O.33333,JUAN;ACT,,O.33334,JOHN;BUTDALEBUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC1 AWAIT(1),AREA1,1;ASSIGN, ATRIB(11)=GAMMA(XX(5),XX(6)); SAMPLE DAILY CATCH DIST.ASSIGN, ATRIB(13)=ATRIB(11)*XX(7); CALCULATE VALUE OF FISHACT/1,9.O,,; BUTEDALE, 9 HOURSASSIGN, XX(40)=XX(40)+1; NO. TRIPS TO AREA 1ACT,,,HOME;JUAN DE FUCA STRAITJUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB( 1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC2 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 FISHACT/2,9.O,,; JUAN DE FIJCA, 9 HOURSASSIGN, XX(41)=XX(41)+1; NO. TRIPS TO AREA 2214ACT,,,HOME;JOHNSTONE STRAITJOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(10)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC3 AWAIT(3),AREA3, 1;ASSIGN, ATRIB(1 1)=GAMMA(XX(25),XX(26)); SAMPLE DAILY CATCH DIST.ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27); CALCULATE VALUE OF FISHACT/3,9.0,,; JOHNSTONE ST, 9 HOURSASSIGN, XX(42)=XX(42)+1; NO. TRIPS TO AREA 1ACT,,,HOME;HOME GOON,1;ASSIGN, ATRIB(10)=ATRIB(10)+ATRIB(4)*9.0; UPDATE FUEL CONSUMED,FISHINGACT,ATRIB(9),,; SAIL HOMEASSIGN, ATRIB( 10)=ATRIB(10)+ATRIB(5)*ATRIB(9); UPDATE FUELCONSUMED, SAILINGACT,,ATRIB(1 1).LE.XX(43), SKIP;ACT,,ATRIB(11).GT.XX(43),; RECORD NEW MAXIMUM CATCHASSIGN, XX(43)=ATRIB(1 1),;SKIP GOON,1;DATA COLLECTION, VESSEL INFORMATION FOR THIS TRIPCOLCT,ATRIB(1O),FUEL,; RECORD FUEL THIS TRIPASSIGN, ATRIB(12)=ATRIB(10)*ATRIB(6),; COST OF FUEL THIS TRIPCOLCT,ATRIB(12),CFUEL,,;COLCT,ATRIB(11),FISH,20/0/500; WT. OF FISH THIS TRIPCOLCT, ATRIB(13),VFISH,; VALUE OF FISH THIS TRIPASSIGN, ATRIB(14)=ATRIB(13)-ATRIB(1 2); SURPLUS, FISH-FUEL,DOLLARSCOLCT, ATRIB(14),PROFIT,20/0/1500,1;COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000ACT,,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 DATAAVERAGE FISH PRICES OVER YEARSCREATE,168,,,,;ASSIGN,XX(3)=48,; TIME TO OPENINGCATCH RATES AND PRICESASSIGN,XX(7)=1.472,; AVERAGE $/KG, BUTEDALEASSIGN,XX(17)=3.076,; AVERAGE $/KG, JUAN DE FUCAASSIGN,XX(27)=2.629,; AVERAGE $/KG, JOHNSTONEUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALEASSIGN,XX(4)=GAMA(1 145.92,6.31),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCHJDAYABOVEASSIGN,XX(6)=3.055,; SHAPE PARAMETERASSIGN,XX(5)=XX(4)/XX(6),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DEFUCAASSIGN,XX( 14)=GAMA(449.25,3. 18),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(16)=5.005,; SHAPE PARAMETERASSIGN,XX(15)=XX(14)/XX(16),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY,JOHNSTONE ST.ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(26)=2. 195,; SHAPE PARAMETERASSIGN,XX(25)=XX(24)/XX(26),; SCALE PARAMETER*** ** * ** * * ***OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICE216ACT,XX(3),,; WAIT FOR OPENINGOPEN, AREA1,,; OPEN AREA, BUTEDALEOPEN, AREA2,,; OPEN AREA, JUAN DE FUCAOPEN, AREA3,,; OPEN AREA, JOHNSTONEACT,8,,; DURATION OF OPEMNGCLOSE, AREA1,,; CLOSE AREACLOSE, AREA2,,; CLOSE AREACLOSE, AREA3,,; CLOSE AREAASSIGN,ATRIB(1)= 160-XX(3)-8ACT,ATRIB(1),;ACT,8,,;TERM;OPENINGS & CLOSINGS, ONE WEEK INTERVALSMODIFY OPENINGS FOR SEASON, RAThER THAN FOR WEEKCREATE,4200,,,,;REP GOON,l;OPEN, HOME,;ACT,56,,;CLOSE, HOME,1;ASSIGN, ATRIB(1)=ATRIB(l)+ 1,1; COUNT TRIPSSEASON REPRESENTS 25 OPENINGS (168 * 25 = 4200 HRS), MODEL RUNS FOR 100SEASONSACT, 1 12,ATRIB(1).LT.25,REP;ACT,1 12,ATRIB(1).GE.25,;COLCT, XX(40),TRIP1,26/0/1; TOTAL NO. TRIPS, AREA 1COLCT, XX(41),TRIP2,26/O/1; TOTAL NO. TRIPS, AREA 2COLCT, XX(42),TRIP3,26/0/1; TOTAL NO. TRIPS, AREA 3COLCT, XX(43),MAXCAT,20/10000/1000; MAXIMUM CATCH THIS SEASONCOLCT, XX(44),RISK,26/0/1; NUMBER OF TRIPS .LT. $6000ASSIGN, XX(40)=0,;ASSIGN, XX(41)=0,;ASSIGN, XX(42)=0,;ASSIGN, XX(43)=0,;ASSIGN, XX(44)=0,; REZERO SEASON VALUESTERM,100;ENDNETWORK;FIN;217Appendix 4Description of SLAMII Computer Program forForecast ModelThe detailed development of the Stationary Model was described in Appendix 2,The modifications to this code to develop the Random Model were described inAppendix 3. There was only one difference between the Random Model and theForecast Model. This is described below.1. Selection of Fishing AreaThe selection of fishing areas for the Forecast Model was based on comparingthe mean income, less fuel cost, for each of the three areas used within thesimulation. The area with the highest value is selected for the trip thefollowing week. This is done within the network by assigning the calculatedvalue of income-fuel cost for each area to a global variable. One dummyvariable is used, in order to keep track of the highest value, and one moreglobal variable to record the location of the area with the highest profit. Thisvariable is used to set the destination attribute for the next trip. By setting thedummy variable to be equal to the ‘profit’ at one location, and comparing itwith another, it is straitforward to develop a network of comparative brancheswhich results in the value and location of the fishing area with the highestprofit the opening just past.The Forecast Model was moodified to include additional boats. For thismodification, an additional attribute was added which identifed the entity(vessel) as a packer or a fishing boat. The packer always retained thedestination at the end of an opening as the port, but a fishing boat waited at218the gate associated with the grounds until the opening was announced. At thatpoint it would use the destination of the packer, calculated using the methodabove, 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 fishbetween boats was assumed to take place within the hour between the end ofthe legal opening and the boats leaving the fishing grounds.A full listing of the Forecast Model, for one boat, together with a sample outputfile is given below.219GEN,DAVID,FORECAST MODEL,05/28/91, 1;MODEL NAME: FORE88FIRST ATTEMPT AT REAL DATA, 3 AREAS SIMULTANEOUSLY3 MOST PRODUCTIVE AREAS, MAXIMUM PROFIT LAST TRIP AS MOTIVATIONMODIFIED TO INCORPORATE SUGGESTIONS OF THESIS COMMITTEE, DEC.1991ADDITIONS: VARIATION OF RISK, PROFIT AND MAXIMUM CATCHSHORTENED TO TRY TO FIT STUDENT VERSION ARRAYSATRIBUTES 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, DOLLARSADDITIONAL ATTRIBUTES/ USE GLOBAL VARIABLES INSTEADXX(4O) NO. OF TRIPS TO AREA 1XX(41) NO. OF TRIPS TO AREA 2XX(42) NO. OF TRIPS TO AREA 3XX(43) MAXIMUM CATCH THIS SEASONXX(44) NO. OF TRIPS WHERE PROFIT < 6000LIMITS,6,14,15;ARRAY(1 ,7)/O,20,75, 100,190,200,290; DISTANCES BETWEEN PORT &LOCATIONSNETWORK;GATE,HOME,CLOSED,4;GATE,AREA1 ,CLOSED, 1;GATE,AREA2,CLOSED,2;GATE,AREA3,CLOSED,3;CREATE,,,,1,1; CREATE BOATBASIC DATA ON BOAT, CURRENT VESSEL IS NOMINALLY KYNOCASSIGN, ATRIB(1)= 10.0; SPEED, KNOTSASSIGN, ATRIB(2)= 150.0; HOLD CAPACITY, M3ASSIGN, ATRIB(3)=59.4; FUEL CONS. L/HR, OUTWARDASSIGN, ATRIB(4)=6.4; FUEL CONS. IJHR, FISHINGASSIGN, ATRIB(5)=78.1; FUEL CONS. IJHR, RETURNASSIGN, ATRIB(6)=O.4; FUEL COST, $/LASSIGN, ATRIB(7)=1; LOCATION OF HOME PORT220ASSIGN, ATRIB(8)=3; GO TO JUAN DE FUCA, 1ST TRIPWAIT IN PORT FOR ANY OPENINGPORT AWAIT(4),HOME,; WAIT IN PORTSELECT DESTINATION THIS TRIP, BASED ON BEST RESULTS LAST OPENINGACT,,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 TRIPMISS GOON,i;ACT/i i,72,,SKIP; WAIT IN PORTBUTDALEBUTD ASSIGN, ATRIB(8)=7; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(iO)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAiT FOR OPENING, ON GROUNDSLOC1 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 FISHACT/i,9.O,,; BUTEDALE, 9 HOURSASSIGN, XX(40)=XX(40)i-1; NO. TRIPS TO AREA 1ACT,,,HOME;JUAN DE FUCA STRAITJUAN ASSIGN, ATRIB(8)=3; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDS221LOC2 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 FISHACTI2,9.O,,; JUAN DE FUCA, 9 HOURSASSIGN, XX(41)=XX(41)+1; NO. TRIPS TO AREA 2ACT,,,HOME;JOHNSTONE STRAITJOHN ASSIGN, ATRIB(8)=4; DESTINATION THIS TRIPCALCULATE SAILING TIMEASSIGN, ATRIB(9)=ARRAY(ATRIB(7),ATRIB(8))/ATRIB(1);SAIL OUTACT,ATRIB(9),,; SAIL OUT TO FISHASSIGN, ATRIB(1O)=ATRIB(3)*ATRIB(9); CALCULATE FUEL CONSUMEDWAIT FOR OPENING, ON GROUNDSLOC3 AWAIT(3),AREA3,1;ASSIGN, ATRIB(1 l)=GAMMA(XX(25),XX(26)); SAMPLE DAILY CATCH DIST.ASSIGN, ATRIB(13)=ATRIB(1 1)*XX(27); CALCULATE VALUE OF FISHACT/3,9.O,,; JOHNSTONE ST, 9 HOURSASSIGN, XX(42)=XX(42)i-1; NO. TRIPS TO AREA 1ACT,,,HOME;HOME 000N,1;ASSIGN, ATRIB(1O)=ATRIB(lO)+ATRIB(4)*9.O; UPDATE FUEL CONSUMED,FISHINGACT,ATRIB(9),,; SAIL HOMEASSIGN, ATRIB(1O)=ATRIB(1O)+ATRIB(5)*ATRIB(9); UPDATE FUELCONSUMED, SAILINGACT,,ATRIB(1 1).LE.XX(43), SKIP;ACT,,ATRIB(11).GT.XX(43),; RECORD NEW MAXIMUM CATCHASSIGN, XX(43)=ATRIB(1 1),;SKIP 000N,1;DATA COLLECrION, VESSEL INFORMATION FOR THIS TRIPCOLCT,ATRIB(1O),FUEL,; RECORD FUEL THIS TRIPASSIGN, ATRIB(12)=ATRIB(1O)*ATRIB(6),; COST OF FUEL THIS TRIPCOLCT,ATRIB(12),CFUEL,,;COLCT,ATRIB(11),FISH,20/O/500; WT. OF FISH THIS TRIPCOLCT, ATRIB(13),VFISH,; VALUE OF FISH THIS TRIPASSIGN, ATRIB(14)=ATRIB( 1 3)-ATRIB( 12); SURPLUS, FISH-FUEL,DOLLARSCOLCT, ATRIB(14),PROFIT,20/O/1500,1;COUNT TRIPS WHERE PROFIT WAS LESS THAN $6000ACT,,ATRIB(14).GE.6000,NXT;222ACT,,ATRIB(14).LT.6000,;ASSIGN, XX(44)=XX(44)+ 1,;NXT 000N,1;SELECT DESTINATION FOR NEXT WEEK, BASED ON HIGHEST MEAN PROFITASSUMES INFORMATION KNOWN FOR ALL THREE AREAS, AND SELECTSMAXIMUMPROFIT AREA, PROVIDED IT IS GREATER THAN REQUIRED DAILY MINIMUMXX(2), XX(12) AND XX(22) ARE PROFITS BASED ON AREA DATA THIS WEEKXX(8) IS DUMMY VARIABLE OF MAGNITUDE OF MAXIMUM PROFITXX(9) IS DUMMY VARIABLE TO LOCATE AREA WITH MAXIMUM PROFITGIVEN CHOICE BETWEEN EQUAL AREAS, THEN NEAREST IS TAKENCALCULATE PROFIT FOR AREA 6, IF WE HAD FISHED THEREASSIGN,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 THEREASSIGN,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 THEREASSIGN,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 PROFITASSIGN STARTING VALUES OF DUMMY VARIABLESASSIGN,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 $3000ACT,,XX(8).LE.3000,NOGO;ACT,,XX(8).GT.3000,;ASSIGN,ATRIB(8)=XX(9),;ACT,,,PORT223N000 000N,1;ASSIGN,ATRIB(8)= 1,;ACT,,,PORT;TERM;***DATA GOES HERE***CATCH RATES AS SEEN BY BOAT, YEAR IS 1988, FROM CATCH DATAAVERAGE FISH PRICES OVER YEARSCREATE,168,,,,;ASSIGN,XX(3)=48,; TIME TO OPENINGCATCH RATES AND PRICESASSIGN,XX(7)=1.472,; AVERAGE $/KG, BUTEDALEASSIGN,XX(17)=3.076,; AVERAGE $/KG, JUAN DE FUCAASSIGN,XX(27)=2.629,; AVERAGE $IKG, JOHNSTONEUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, BUTEDALEASSIGN,XX(4)=GAMA(1 145.92,6.31),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(6)=3.055,; SHAPE PARAMETERASSIGN,XX(5)=XX(4)/XX(6),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY, JUAN DEFUCAASSIGN,XX(14)=GAMA(449.25,3.18),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(16)=5.005,; SHAPE PARAMETERASSIGN,XX(1 5)=XX( 14)IXX(16),; SCALE PARAMETERUNDERLYING ANNUAL CATCH DISTRIBUTION, MEAN CATCH PER DAY,JOUNSTONE ST.ASSIGN,XX(24)=GAMA(98 1.54,2.75),; SEASONAL CATCH DISTRIBUTIONPARAMETERS FOR CATCH PER DAY DISTRIBUTION, GIVEN MEAN CATCH/DAYABOVEASSIGN,XX(26)=2. 195,; SHAPE PARAMETERASSIGN,XX(25)=XX(24)/XX(26),; SCALE PARAMETER224*** *** ** * * ** *OPEN AND CLOSE AREA, ONE DAY OPENING PER WEEK, 48 HOURS NOTICEACT,XX(3),,; WAIT FOR OPENINGOPEN, AREA1,,; OPEN AREA, BUTEDALEOPEN, AREA2,,; OPEN AREA, JUAN DE FUCAOPEN, AREA3,,; OPEN AREA, JOHNSTONEACT,8,,; DURATION OF OPENINGCLOSE, AREA1,,; CLOSE AREACLOSE, AREA2,,; CLOSE AREACLOSE, AREA3,,; CLOSE AREAASSIGN,ATRIB(1)= 160-XX(3)-8ACT,ATRIB(1),;ACT,8,,;TERM;OPENINGS & CLOSINGS, ONE WEEK INTERVALSMODIFY OPENINGS FOR SEASON, RATHER THAN FOR WEEKCREATE,4200,,,,;REP GOON,1;OPEN, HOME,;ACT,56,,;CLOSE, HOME,1;ASSIGN, ATRIB(1)=ATRIB(1)+1,1; COUNT TRIPSSEASON REPRESENTS 25 OPENINGS (168 * 25 = 4200 HRS), MODEL RUNS FOR 100SEASONSACT,1 12,ATRIB(1).LT.25,REP;ACT,1 12,ATRIB(1).GE.25,;COLCT, XX(40),TRIP1,2610/1; TOTAL NO. TRIPS, AREA 1COLCT, XX(41),TRIP2,26/0/1; TOTAL NO. TRIPS, AREA 2COLCT, XX(42),TRIP3,2610/1; TOTAL NO. TRIPS, AREA 3COLCT, XX(43),MAXCAT,20/10000/1000; MAXIMUM CATCH THIS SEASONCOLCT, XX(44),RISK,26/0/1; NUMBER OF TRIPS IT. $6000ASSIGN, XX(40)=0,;ASSIGN, XX(41)=0,;ASSIGN, XX(42)=0,;ASSIGN, XX(43)=0,;ASSIGN, XX(44)=0,; REZERO SEASON VALUESTERM, 100;ENDNETWORK;FIN;2251SLAM II SUMMARY REPORTSIMULATION PROJECT FORECAST MODEL BY DAVIDDATE 5/28/1991 RUN NUMBER 1OF 1CURRENT TIME .4200E+06STATISTICAL ARRAYS CLEARED AT TIME 0000E+OO**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OFVALUE DEVIATION VARIATIONMINIMUM MAXIMUM NO.OFVALUE VALUE OBSFILENUMBER LABEL/TYPEAVERAGE STANDARDLENGTH DEVIATIONMAXIMUM CURRENT AVERAGELENGTH LENGTH WAIT TIMEFUEL .301E+04 .131E+04 .433E+00 .109E+04 .405E+04 2500CFUEL .121E+04 .522E+03 .433E+00 .436E+03 .162E+04 2500FISH .544E+04 .500E+04 .918E+O0 .264E+02 .440E+05 2500VFISH .917E+04 .763E+04 .832E+OO .812E+02 .648E+05 2500PROFIT .797E+04 .751E+04 .942E+00 — .135E+04 .634E+05 2500TRIP1 .153E+02 .256E+01 .167E+00 .800E+01 .220E+02 100TRIP2 .184E+01 .141E+01 .764E+00 .000E+00 .600E+01 100TRIP3 .772E+01 .237E+01 .306E+00 .200E+01 .160E+02 100MAXCAT .193E+05 .713E+04 .370E+00 .905E+04 .440E+05 100RISK .126E+02 .279E+01 .221E+00 .500E+01 .200E+02 100**FILE STATISTICS**1 LOC1 AWAIT .069 .254 1 0 19.0002 LOC2 AWAIT .018 .132 1 0 40.5003 LOC3 AWAIT .070 .255 1 0 38.0004 PORT AWAIT .533 .499 1 0 89.4755 .000 .000 0 0 .0006 .000 .000 0 0 .0007 CALENDAR 4.310 .636 6 5 30.144**REGULAR ACTIVITY STATISTICS**ACTIVITY AVERAGE STANDARD MAXIMUM CURRENT ENTITYINDEX/LABEL UTILIZATION DEVIATION UTIL UTIL COUNT1 BUTEDALE, .0329 .1782 1 0 15332 JUAN DE FUCA .0039 .0627 1 0 1843 JOHNSTONE ST .0165 .1276 1 0 77211 WAIT IN PORT .0019 .0434 1 0 11**GATE STATISTICS* *226GATE GATENUMBER LABEL11 HOME2 AREA13 AREA24 AREA3CURRENT PCT. OFSTATUS TIME OPENOPEN .3333CLOSED .0476CLOSED .0476CLOSED .0476**HISTOGP NUMBER 3**FISH**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OF MINIMUMVALUE DEVIATION VARIATION VALUEMAXIMUM NO.OFVALUE OBSOBS RELA UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +0 .000 .000E+00 + +108 .043 .500E+03 +182 .073 .100E+04 **** C +207 .083 .150E+04 **** C +194 .078 .200E+04 ÷**** C +157 .063 .250E+04 C +136 .054 .300E+04 C +127 .051 .350E+04 *** C +136 .054 .400E+04 *** C +112 .045 .450E+04 ** C +105 .042 .500E+04 C +88 .035 .550E+04 C +98 .039 .600E+04 C +79 .032 .650E+04 C +66 .026 .700E+04 * C +74 .030 .750E+04 * C +76 .030 .800E+04 + C +47 .019 .850E+04 * C +44 .018 .900E+04 + C +48 .019 .950E+04 * C +42 .017 .100E+05 + C +374 .150 INF ******* C——— + + + + + + + + + + +0 20 40 60 80 100FISH .544E+04 .500E+04 .918E+00 .264E+02 .440E+05 25002271 * *HISGPPROFITNUMBER 5****STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OF MINIMUMVALUE DEVIATION VARIATION VALUEMAXIMUM NO.OFVALUE OBSOBS RELA UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +61 .024 .000E+00 + +267 .107 .150E+04 C +341 .136 .300E+04 C +330 .132 .450E+04 ******* C +261 .104 .600E+04 ***** C +234 .094 .750E+04 C +184 .074 .900E+04 C +168 .067 .105E+05 *** C +114 .046 .120E+05 ** C +100 .040 .135E+05 ** C +100 .040 .150E+05 C +67 .027 .165E+05 +* C +52 .021 .180E+05 * C +39 .016 .195E+05 + C +29 .012 .210E+05 * C +32 .013 .225E+05 * C +19 .008 .240E+05 + C +22 .009 .255E+05 + C +10 .004 .270E+05 +10 .004 .285E+05 +14 .006 .300E+05 +46 .018 INF +* C——-. + + + + + + + + + + +0 20 40 60 80 100PROFIT .797E+04 .751E+04 .942E+00 - .135E+04 .634E+05 25002281 **HISTOGPTRI P1NUMBER 6**+ + + + + + + + + + ++ + + + + + + + + + +**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STA11DARD COEFF. OF MINIMUMVALUE DEVIATION VARIATION VALUEMAXIMUM NO.OFVALUE OBS20 40 60 80 100OBS RELA UPPERFREQ FREQ CELL LIM 00 .000 .000E+00 + +0 .000 .100E+01 + +0 .000 .200E+01 + +0 .000 .300E+01 + +0 .000 .400E+01 + +0 .000 .500E+01 + +0 .000 .600E+01 + +0 .000 .700E+01 + +1 .010 .800E+01 + +0 .000 .900E+01 + +2 .020 .100E+02 +* +3 .030 .11OE+02 + C +8 .080 .120E+02 **** C +7 .070 .130E+02 **** C +17 .170 .140E+02 C +15 .150 .150E+02 ******** C +17 .170 .160E+02 ********* C +9 .090 .170E+02 C +9 .090 .180E+02 C +7 .070 .190E+02 **** C +4 .040 .200E+020 .000 .210E+02 +1 .010 .220E+02 + C0 .000 .230E+02 + C0 .000 .240E+02 + C0 .000 .250E+02 + C0 .000 .260E+02 + C0 .000 INF + C100 0 20 40 60 80 100TRIP1 .153E+02 .256E+01 .167E+00 .800E+01 .220E+02 1001 **HISTOGPMTRIP2NUMBER 7**229**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANUARD COEFF. OF MINIMUMVALUE DEVIATION VARIATION VALUEMAXIMUM NO.OFVALUE OBSOBS RELP UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +19 .190 .000E+00 +********* +27 .270 .100E+01 +************** C +23 .230 .200E+01 ************ C +17 .170 .300E+01 ********* C +11 .110 .400E+012 .020 .500E+01 * C1 .010 .600E+01 + C0 .000 .700E+01 + C0 .000 .800E+01 + C0 .000 .900E+01 + C0 .000 .100E+02 + C0 .000 .11OE+02 + C0 .000 .120E+02 + C0 .000 .130E+02 + C0 .000 .140E+02 + C0 .000 .150E+02 + C0 .000 .160E+02 + C0 .000 .170E+02 + C0 .000 .180E+02 + c0 .000 .190E+02 + C0 .000 .200E+02 + C0 .000 .210E+02 + C0 .000 .220E+02 + C0 .000 .230E+02 + C0 .000 .240E+02 + C0 .000 .250E+02 + C0 .000 .260E+02 + C0 .000 INF + C——— + + + + + + + + + + +100 0 20 40 60 80 100TRIP2 .184E+01 .141E+01 .764E+00 .000E+00 .600E+01 100230**HI5GP NUMBER 8**TRIP3OBS RELA UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +0 .000 .000E+00 + +0 .000 .100E+01 + +2 .020 .200E+01 + +1 .010 .300E+O1 +C +4 .040 .400E+01 C +8 .080 .500E+01 **** C +14 .140 .600E+01 ******* C +18 .180 .700E+01 ********* C +20 .200 .800E+01 ********** C +12 .120 .900E+01 C +13 .130 .100E+02 ****** C +2 .020 .11OE+02 + C +3 .030 .120E+02 * C +1 .010 .130E+02 + C+1 .010 .140E+02 +0 .000 .150E+02 + C+1 .010 .160E+02 + C0 .000 .170E+02 + C0 .000 .180E+02 + C0 .000 .190E+02 + C0 .000 .200E+02 + C0 .000 .210E+02 + Co .ooo .220E+02 + C0 .000 .230E+02 + C0 .000 .240E+02 + C0 .000 .250E+02 + C0 .000 .260E+02 + C0 .000 INF + C+ + + + + + + + + + +100 0 20 40 60 80 100**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OF MINIMUM MAXIMUM NO.OFVALUE DEVIATION VARIATION VALUE VALUE OBSTRIP3 .772E+01 .237E+01 .306E+00 .200E+01 .160E+02 1001 **HISPMAXCATNUMBER 9**231OBS RELA UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +4 .040 .100E+05 +3 .030 .11OE+05 + C +3 .030 .120E+05 * C +8 .080 .130E+05 C +7 .070 .140E+05 **** C +5 .050 .150E-’-05 *** C +8 .080 .160E+05 C +4 .040 .170E+05 C +6 .060 .180E+05 c +10 .100 .190E+05 +***** C +5 .050 .200E+05 +*** C +4 .040 .210E+05 +** C +5 .050 .220E+05 +*** C +4 .040 .230E+05 +** C +5 .050 .240E+05 +** c +4 .040 .250E+05 +** c +1 .010 .260E+05 + C +2 .020 .270E+05 +* c +0 .000 .280E+05 + C +2 .020 .290E+05 + C +0 .000 .300E+05 + C +10 .100 INF +***** C——— + + + + + + + + + + +100 0 20 40 60 80 100**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OF MINIMUM MAXIMUM NO.OFVALUE DEVIATION VARIATION VALUE VALUE OBSMAXCAT .193E+05 .713E+04 .370E+00 .905E+04 .440E+05 1001 **HISRISKNUNBER1O**232**STATISTICS FOR VARIABLES BASED ON OBSERVATION**MEAN STANDARD COEFF. OF MINIMUMVALUE DEVIATION VARIATION VALUEMAXIMUM NO.OFVALUE OBSOBS RELA UPPERFREQ FREQ CELL LIM 0 20 40 60 80 100+ + + + + + + + + + +0 .000 .000E+00 + +0 .000 .100E+01 + +0 .000 .200E+01 + +0 .000 .300E+01 + +0 .000 .400E+01 + +1 .010 .500E+01 + +2 .020 .600E+01 + +1 .010 .700E+01 + C +3 .030 .800E+01 * C +4 .040 .900E+01 ** C +7 .070 .100E+02 C +16 .160 .11OE+02 C +16 .160 .l2OEi-02 C +16 .160 .130E+02 C +10 .100 .140E+02 +***** c +10 .100 .150E+02 +***** C +3 .030 .160E+02 + C +8 .080 .170E+02 C+2 .020 .180E+02 + C0 .000 .190E+02 + C1 .010 .200E+02 + C0 .000 .210E+02 + C0 .000 .220E+02 + C0 .000 .230E+02 + C0 .000 .240E+02 + C0 .000 .250E+02 + C0 .000 .260E+02 + C0 .000 INF + C——— + + + + + + + + + + +100 0 20 40 60 80 100RISK .126E+02 .279E+01 .221E+00 .500E+01 .200E+02 100

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0081020/manifest

Comment

Related Items