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Optimal harvest policies in salmon gauntlet fisheries : terminal versus mixed stock fishery harvest Luedke, Wilfred Harold 1990

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OPTIMALHARVESTPOLICEES IN SALMON GAUNTLETFISHERIES: TERMINAL VERSUS MIXED STOCK FISHERY HARVEST By WILFRED HAROLD LUEDKE B.Sc., The University cf British Columbia, 1980 A THE SIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR THE DEGREE OF MASTER O F SCIENCE in TOE FACULTY O F GRADUATE STUDIES (Department of Zoology) We accept this thesis as conforming to the required standard THE UNIVERSITY O F BRITISH COLUMBIA October 1990 © Wilfred Harold Luedke, 1990 In presenting this thesis in partial fulfilment cf the requiremenis for an a d v a n c e d degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that p s rmi s s ion for extensive c o p y i n g cf this thesis for scholarly purposes may be granted by t h e head cf my department or by his or her representatives. It is understood that copying or publication cf this thesis for financial gain shall not be allowed without my wr i t t en permission. (Signature) Department of ^ g o I The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT Acase study cf the chum salmon (Oiicorhynchus keta) gauntlet fisheriesin SouthernBrit-ish Columbiais described. Acrimony betwsenindustry and governmentmanagers has been commonplace in the management of thus fishery. In a n attempt to alleviate this acrimony, a management system call the "clockwork" has been implemented, which provides all fishermen an opportunity for greater understanding of the management rationale and greater input into the decision-makingprocess. The clockwork has been generally successful; the stocks ^re rebuilding and the fishermen are involvedin the management cf the fishery. However, two problems aie identifiedin the clockwork. First, the successcf the clock-work in alleviatingthe aaimony associated with the chumfishery depends on the ability of fishery managers to provide sound and scientifically defensible in-seasonstock assessments. If the assessments have no better track record than the intuition of managers and fishermen then the clockwork will not be successful. Second, there is a nagging problem of allocation of harvestsbetween the mixed stcx^, fishery in Johnstone Strait and the terminal fishery in the Fraser River. The main factor is the difference in price behveen the two fisheries; the price in the terminal fishery is only about one-third cf the price paid in the mixed stock fishery, Dynamic programming techniques are used to determine the optimal harvest strategiesfor this gauntlet fishery. Generally, the opti-mal strategy is similar to a fixed escapementstrategy when both stocks are equally abundant. But when one stock is much more abundant the optimal strategy is to harvest harder in the mixed stockfishery. With the current difference in value per fish between the two fisheries, the optimalexploitationTates i n the terminal area are zero, all the catch i s taken in the mixed stock fishery. The minimum price at which terminal fisheries provide long term economic benefit is the threshold price. For the parameters used to describe the current fishery, the threshold price is approximately 40^ 'A the mixed stock fishery price. Furthermore, the threshold price differs with stock recruitment parameters, especially stock productivity and recruitment variability. Generally the more similarthe stocksare, with respect to stock and recruitment characteristics, the lower the threshold value for fishing in the terminal areas. The results provide a basis for discussioncf the utility cf terminal fisheries, and by adjustingthe relative value of the terminal fishery in relation to the mixed stock fishery can incorporate additional social and aesthetic values, as well as costs such as harvesting costs and fisheries management costs. ' '- ii ACKNOWLEDGEMENTS Reflecting on the several years since beginning thiswork, lrealizehow many people have helped me along to where I am today. T h ^ start and end withmy supervisor, CJ, Walt-ers, who provided the initial inspirationand incentive for my work in fisheries, provided sub-stantia\training and insight over the years, then provided me with the dirs±im required whenl needed it most I an also indebtedto R. Hilbom for his inspiration and direction; NJ. Wilimovsky for the unforgettable training in fisheriesmanagement and insight on my own abilities; andD. Ludwig and M.C.Healey for their helpful criticism- Outside the University cf R C , I would like to thank the 19S3-&5 members of the Johnstone Strait - Fraser River Advisory Committee, especially Ed Safartk Jr., for the insightand background they provided. Within the Department of Fisheries and Oceans I would like to thankAD. Anderson and AP. Gould for the opportunities and advice they have provided, andL Hopworor his help. Finally I would like to thank my wife Val and my mother for the support and encouragement. Table of Contents 1. INTRODUCTION 1 l.lExistin^ theory 1 . 12 Definition of tne problem 4 2 CASE STUD'Y 7 2 1 Overview t of the stocks and the fishery 7 22 The Clockwork Management System 9 2 3 In-seasunAssessnamfMethodoiogies - 15 24 The Terminal Fishery Issue 20 2 5 Data Sources 22 2.6 Stock and Recruitment Analysis 23 2.7 Recruitment Variability and Stock Correlation 28 2.8 Fishery Parameter Estimates 31 2,8,1 Discount Pate 31 2.82 Value per Fish 32 29 Overview of the case study 33 3. METHODS 35 3.1 Stochastic Dynamic Programming •• 35 3 2 The Ingredients 36 3.3Program structure 39 3.4 Conventions for presenting optimization results 40 35 Potential limitations in the methodology 40^ 4. RESULTS 42 4.1 The Optimal Strategy 42 4 2 Deciding where to fish; the long term value of several management philo-sophies. 45 4.3 Sensitivity to fevahiecf fifhin the terminal fisheries 51 4.4 Sensitivity to the Ricker parameters 56 4 5 Sensitivity to stochastic processes 60 4.6 Numerical problems with the computational procedwe 68 5. DISCUSSION 70 6. SUMMARY 73 7. LITERATURE CITED 76 8. APPENDICES 82 S.I Appendix A Clockwork in-season information bulletin and stock assessment methodology published for distribution to fishermen 83 8 2 Appendix B Optimal solutions for scenarios with varied Ricker avalues. I l l Table cf Figures 2J_ The major chum salmon fisheries dnsouthernB.G 10 22. Alternative harvest strategiesforthe chumfisheiy 13 2.3. Stock-recruit data for Fraser and non-Fraserdnm. 26 2A Ln (R/S)vsSforFraser andnon-Fraserchum. 27 2 5 . Distributioncf Ricker a values 29 2.6. Timeseries of annual deviations f rom average R/S 30 4.1. Optimal strategy curves for theJohnstone St fishery 44 4.3. NPV in relation to terminal price ^ ' ' --t-. 54 4 j . optimal strategy tor the non-traser terminal nshery 4.6. Fishing regimeboundaries when Ricker B's differ 4.7. Fishing regime boundaries when Ricker B's are the same 60 4.8. NPV m relation recruitment variability of 0% and 50% 64 4.9. NPV in relation recruitment variability of 90% 65 4.10. Relation between NPV and recruitment variability 4.11. Optimal strategy for three levels of variability 67 n n n n u u u u n n u u i? Table of Tables 21. The clockwork harvest strategy, 1987-1990 12 22. 'weekly test fishery cpue calculations 17 . 2J3. In-season assessments using tetfisheiycpue. - 19 24. In-seasonassassnaibsusirg commercial fishery cpue 19 I S . Clockwork in-season ct±fcaaw=tii accuracy. 19 2 6. Three scenarios for correlation cf variability 31 41. NPV far various fishery combinations, obiective-MEY 47 4 2 . NPV forvarious fisheries combinatiosis, objective=<MSY 48 OPTIMAL HARVEST POLICIES UN SALMON GAUNTLET FISHERIES: TERMINAL VERSUS MIXED STOCK FISHERY HARVEST 1. INTRODUCTION The salmonfisheries inBritish Columbiarepreseiit a complex management systemwith multiple stocks, multiple species, multiple fisheries,and multiple user groups d l looking for a substantial share of the catch. This complexity often results in management decisions which arebased on simple intuitionrather than scientific principles. Thishas, in the past, leadto distrust and aaimony between the fisheries managers and the user groups. In this thesis I will describe a management system which attemptsto alleviate the management conflicts, and report on its success. This thesis will also address two other aspects of British Columbia salmon fisheries, multiple stocks and multiple fisheries. Many British Columbia salmon fisheries are gauntlets consisting cf a seriescf fisheries initially harvesting a mixture of steaks and subsequently harvesting the same stocks separately in terminal areas. This thesis will investigate the optimalharvest strategies for a gauntlettype fishery based on the southern British Columbia chum salmon (Oncorhynchus keta) fisheries. 11 Existing theory While the theory of exploiting fish stocks had received considerable attentionprior to 1954, it was not until Ricker (1954)that stock and recruitment theory was used to predict a Maximum Sustainable Yield (MSY) for semelparous speaes such as the Pacific Salmon. His initial analysis was for a single stock in an e quilibriumstate. In 1958 Ricker identified the fixed escapement policy re quired for MSY. But he also identified some complicating factors: 1 ^ harvesting a mixture of stocks in a common fishery, 2) the variability in recruitment arising fromrandom environmentalfliictuations, and 3) conflicting management objectives. These factors became the basis for much subsequent work on the theory of optimal management for salmon fisheries. The followingparagraphs leview that work. Ricker (1953)first identified the pipblem of harvesting several stocks in a common fishery. He showed that achievingthe MSY in a mixed stock fishery potentially results in the extinction of one or more of the less productive stocks. Paulik et al. '(I967)reteated these results by calculating the optimal equilibriumharvest strategy for a mixture ofstocks ina common fishery. In this case the optimum harvest was higher than the harvest from a fixed escapement policy based on the sum of the individual escapement goals (i.e. the method used in many mixed stock salmon fisheries). Ricker (1973) simulatedthe exploitationcf a mixture of five stocks. The simulations suggestedlikely sequencescf catch in determining and achiev-ing MSY. In "this work Ricker warned that harvestingthe stocks in common might reduce the overall recruitment. HDbcm (1976) showed that the fixed escapement policy for managing mixed stock fisheries is optimal only under a limitedrange of stock sizes. When the ratio cf the stocksdifferssignificandy &oml:l then a higher exploitationrate shouldbe applied. Oth-ers including Clark (1976), Anderson (1977), Huppert (1979), and Hilbom (1984) compared harvest policies in a single mixed Steele salmon fishery. Ricker (1973) and Hilbom (1985) identified additional concerns with mixed stockfisheries, namely the incorrect estimation of stock recruitment parameters when data fromstrv.k mixtures are analyzed as a singleunit stock. * Someof these same authors (Ricker 1958, Paulik et al. 1967)noted that harvestingthe stocks separately in terminal areas would produce the maximum yield. Ricker (1958) even suggested that any adjustments of gear, area, or time which would promote the individual exploitationcf the separate stocks would increase the yield. But salmon fisheries in British Columbia are generally gauntlets, consistingof both a mixed stock fishery and separate terminal single stock fisheries. Consequently it is necessary to determine harvest strategies which include both types of fisheries, inis thesis will address this problem through a case study of a British Columbia salmon gauntlet fishery. Since the existing literature on mixed stock fisheriesharvesting was based largely on equilibriumconditions, I consideredit important to determinethe implications cf environ-mentally based variability in stock and recruitment on the determination cf optimal strategies. Several authors have examined the effects cf variability on optimal harvest policies for a single stock. Ricker (1958).mdLarkin and Ricker (1964) showed that environmentally caused vari-ability in recruitment can significantly improve the long term average harvest if the manager is able to adjusthawesi; rates in relation to the variability. Moreover high variability resulted in a higher incidence cf ywrs withno fishingand ahigher potential for over-exploiting less productive stocks. Tautzet al. (1969)reiterated these conclusionsfor long term environmental trends. Reed (1979)used stochasticdynamic programmingto show that fixed escapement policies are indeedoptimal for single stock systems, under a wide variety of assumptions about variation; subsequent research has elaborated on his theoretical findings (reviewin Mangel 1985). Walters' (1975a,b) work on Skeena River sockeye and pink incorporated his-toric variation in the Ricker productionparameter into the determination cf an optimal liar-vest strategy. The effect of environmental variability on stock and recruitment and optimal harvest strategieswas als> addressedby May efc al (1978), Mendelssohn (1980), Reed (1981), Charles (1983), Walters (1934), Walters and Hilbom (1976,1978), Ludwig (1982)and Ludwig and Walters (1982). Clark (1985) reviewed several of these papers and suggested that random events would have very little quantitative effect onthe outcome of aioplimization analysis. With respect to mixed stocks, Ricker (1973) suggested that random processes affecting each stock separately would be moder ited over a mixture of stocks, thereby resulting in only mod-est increasesinyields from mixf es of stocks, Further to this paper there has been little^/ork on the effects of random processe on harvesting mixtures of stocks. Early in the evolution of researchon salmon fisheriespolicy it was recognized that the choice of the management objective can be an important determinant of the optimum harvest strategy. But once again the work has dealt mainly with single stocks and usually under equi-librium conditions. Ricker (1954,1958) and Larkin and Ricker (1964) compared alternative strategiesin order to achieve Nfeximxn Sustained Yield (MSY), They found that a constant escapement policy was optimal under the MSY objective. But they also provided a warning. Managing toward MSY resulted in a highinter-annualvariability of catchcs, with the potential that fishing be stopped altogether in many years, Regardless of these concerns, the resulting concept of M5Y became the guiding objective for salmon fisheries management. And the con-stant escapement strategy became the primary means to achieve MSY. Econorrtic and social considerations were not directly consideredby fisheriesmanagersinthe implementation of the MSY objective and constant escapement. Instead, as Healey (1984) suggested, "if this (MSY) could be implemented with minimum interference to the industry it was assumed that the otherthings (economicand social considerations) would work out for the best", By 1975it became clear that MSY and the constant escapement strategy were not meeting social and eco-nomic goals. a result the objective cf Optimum Sustained Yield (OSY) was developed to n n n n-j n n ~i i ujj o u y u. u.-io meet these concerns (Roedel 1975, Larkin 1977), However, the incorporationof nonbiological concerns into management objectives was a slow process. Economic considerations, which already had been the focus of study by Gordon (1953,1954), were most readily incorporated into the objective called Maximum Economic Yield (or MEY, see Crutchfield 1961,1975, Reed (1974), Clark andMunro 1975, dark 1976,1985, Anderson 1977, for overviews). Through the following decade a wider range of economic, social, and resource considerations were addressedand often incorporated into fisheriesmanagementobjectives. Allen (1973), Walters (1975), Clark (1976), Walters and Hilbom (1976), Hilbom and Walters (1976), Keeney (1977), Crutchfield (1979), Mendelssohn (1980b), Hilbom (1984), Deriso (1984), Walters (1986), and others explored the relationship between alternative objectives for management and various harvest strategies. Mendelssohn (1980c), Healey (1984) and others examined methods for determiningand evaluating multiple objectives in fisheries. Onthe operations level, salmon fisheries managers have incorporatedthe OSY mandateby settingup industry advisory com-mittees where it is hoped that concensus can be reached on the best balance of conservation and economic objectives through a process of debate and collaborationbehveen the government managers and representatives of the fishing industry. One of the f i st such com-mittees on the Pacific Coast was the "Johnstone Strait • Fraser River Chum Advisory Commit-tee" which was setup in 1976and includeda aoss-sectionof the user groups and areas involved in the chun salmon fishery (Hilborn and Luedke 1987). 12 Definition of the problem The literature on mixed stock fisheries has focused on a single fishery which harvests a mixture of stocks under equilibrium conditions. Someauthorshave consideredterminal lisheries in isolation, indicating a terminal only approach to harvest would provide the M5Y, However, this assumption does not reflect the gauntlet structure of most salmon fisheriesin British Columbia, That is, the salmonmust pass through severalfisheriesduringthe migra-tion to their natal stream. Generally this gauntlet consists of both types of fisheries; first the f i i imust face at least one "outside"mixed stock fishery (at the initial approach of the salmon to the continent),then several "terminal" single stock fisheries in or near the river mouths. In "this thesis I will address the gauntlet nature of the fisheries by determining the optimal exploitation rates for a fisheiy consisting of both outside and terminal harvest areas. Thehypothesisfor this thesis is that the terminal only approach is not the optimal pol-icy in a gauntlet fishery when objectives other than AiSY are included. In particular, the opti-mal allocation <f effort (Le.. harvest rate) betiueen mixed stock and single stock areas within a gauntlet fishery may depend on the relative values (prices) for fish in tlte various areas. Consequently the sensitivity of theresults to the differential value cf catch from each fishery ivill be addressed. The main objective functionused in this thesis w i 11 be the total discounted value, how-ever, results from thisobjectivewillbe comparedto other objectives such as MSY. In addition to this extensionof mixed stock fisheries theory, I wi 11 also address the complicatingfactors cf environmentallyinducedrecruitment variability, correlationin variability between stocks, and conflicting management objectives. Due to the analytical intractability of the problem, no one has addressed all these factors together. For examplemost previous work has addressed the MSV objective for a single stock with a deterministic recruitment process. Other works focusedon the effect of environmental variation on a single stock. Consequently it has been up to the fisheries managers to incorporate the various generalities into a workablemanage-ment regime (e.g. objectiveand strategy). Hopefully the numerical modellingmethods used in this thesis, which allow all these factors to be incorporated, wi 11 provide genuine insight into the optimal policies for the specific fishery consideredand for other salmon gauntlet fisheries on the Pacific Coast The following section wi 11 provide some background to this definition of the problem. But first allow me to explain the nature of this thesis. The originalintenv of this thesis was to address two aspects of the problem, long term strategies in gauntlet fisheries and short term (in-season) methodologies for implementation cf management strategies. My researchtm the in-seasoximethodologies has centered on the developmentcf a "clockwork" management sys-tem for attaining strategicobjectivesthrough an open, objective, and scientifically based pro-cess of in-season decision making. But this thesis does not concentrate on the complete description and analy sis of the clockwork management sy stem developed for chum salmon fisheries in the Johnstone Strait to Fraser River area. The reasons for this are two-fold. First the Clockwork is well establishednow with documentationin the literature (Hilborn and Luedke 1987,Luedke 1988) and numerous reviews by Department cf Fisheries and Oceans sci-entists and fidiingindustry representatives. The basic structure has been accepted and applied to other salmon fLSadss (e.g. Barkl^' Soundsockeye). Furthermore the Clockwork has fit into political initiatives for co-managementof the Pacific fisheries resources. There are still someproblems, however, as will be discussedin the following chapter. This leads to the second reason for not focusing on the workings of the Clockwork. Rather than reiterating much of the existing work I a n taking this opportunity to focus on a nagging problem affect-ing the Clockwork, namely the utility of terminal fisheries. 2. CA'iE STUDY 21 Overview of the stocks and the fishery The impetus for this study comes from concerns regarding the harvest strategy for southernBritish Columbia chum salmon (Oiicorfiyiichus keta) stocks. The fishery harvests two major stocks, the Fraser River stock which consists of genetically similar sub-stocks that spawn within th e Fraser River watershed, and the non-Fraser stock which consists mainly of chum from mid-Vancouver Island enhancementfacilitiesbut also includes other genetically similar stocks around Georgia Strait (Beachamdt al. 1985). These stocks have been the focus of bio-logical study for over 20 years (Wickett 1958;Palmer 1972; Anderson 1977; Beacham and Starr 1982; Anderson and Beacham 1983;Beachametal. 1985;LuedkeetaL 1988). Severalbiological characteristicscf chum sahnonhave particular significance ^management. Theseare described in the following paragraphs. Chum salmon are generally the least productive salmon in British Columbia. The aveF» age ratio of adult returns per spawner is only 1.81, lower than pink salmon (O.gorbusclia) which typically return at a rate of about21, coho(0,kisutch) at 31,andsockeye (O.nerkn) and chinook (O.tshmoytscha) at 4 l(Wong 1982). A result cf tbis generally low rate of return and the large natural variation associated with it is that returns are ofbenno greater than the paren-tal brood stock. Consequent ly ears with no fishing are more likely than when harvesting other salmon species, when the stocks are managed with a fixed escapementpolicy. After an oceanic migration of 3-5 years, these chum salmon stocks return, mainly through the Johnstone Strait, to spawn in the lower reaches cf rivers flowing into the John-stone and Georgia Straits. The spawning migration begins in mid September after the pink and sockeye ru ns have passed, and continues into November. ' I lie runs are available in each fil l ing area for only 6-7weeks. The unique late timingrelalive to other salmon species allevi-atesmuchofthemixedspeciesproblemsfoundinmany other salmon fisheries. For this thesis a stock is defined as the smallest component identifiable with current stock compositionestimation techniques. Genetic stock identification (GS1) techniques are the most commonly used methods of stock identificationin southern B.C. chum salmon. In this technique, elecrophoretic characteristics of the chum salmon are used to determine maximum likelihood estimatesof stock contributions using the Mixture Model developed by Fournier et: al (1984), This technique delineates fishery samples into individual sub-stocks, and then pools these sub-stocks into genetically similar stock groups. Unfortunately the pooling criteria are sometimesadjusted to reflect political boundaries rather than genetic similarities. For exam-ple, the Nooksack and Skagit rivers in Washington State are genetically similar to the Fraser River stock group, yet due to politicalfdifferences these stocks are pooled with the Puget Soundstockgroup. There are sigmficantgeneticdifferencesbetwaen thiBemajor stock groups, namely the Fraser River, Georgia Strait (non-Fraser), and Puget Sound. Stock compo-sition samples are taken weekly from a tes: fishery in Johnstone Strait and subsequently from any commercial fisheries. These data are used for in-season assessment and post-season determination of catch per stock for domestic stock assessments and international treaty obligations. The southernB.C. chum electrophoreticanaly seshave been conducted since 1982. As the chum salmon approach their natal streams there is a general degradationcf body tissue (IgarashiandZawa, 1953)andbody fat(Zawa andlgarashi, 1954) as metabolic enejgy reserves are diverted to migration requirements and reproductive tissues. The result is a decrease in market value and grade from "silver bright" in Johnstone Strait to "semi-bright" and "dark" grades in the terminal fisheries. These gradings generate as much as a two thirds drop in landed price between the outside mixed stock fishery and the terminal fishery. The degradation is more rapid in chum and pink salmon than in other species such as sockeye or chinook salmon. The chum are harvested in three major Canadian fisheries (Fig. 2,1), which comprise a gauntlet fishery consisting cf one mixed stock fishery and two major terminal fisheries. The first and largest fishery in "this gauntlet is the Johnstone Strait fishery. About two-thirds of the total chum catch in the Johnstone Strait to Fraser River area has historically been taken in this fishery.-Both gillnet and purse-seine boats fish there, but in recent years seine catches have predominated. The purse seine fleet traditionally consisted of vessels out cf local communi-ties such as Port Hardy, Alert Bay, Sointula, and Campbell River, but in the past few years almost every seine boat in British Columbia has fished for chum salmon in Johnstone Strait. This trend of increasingmobililv parallels increasing efficiency in the seine fleet and reflects the fishermen's need to extend their individual fishing seasons as capital investment increases and fishing time at each fishery decreases. The two major terminal fisheries include a gillnet fishery in the Fraser River andafishery atQualicum. The Fraser River fishery has also tradi-tionally consisted cf vessels fromlocal communities along the river. The Qualicum fishery on the other hand is a relatively recent fishery created to harvest surplus stock to local enhancement facilities. 2.2 The C l o c k w o r k M a n a g e m e n t System Prior to 1983 the managementof the chum salmon fisheries was based on MSY and a constant escapement strategy. However, during the fishingseason this systemoftencrumbled under intense lobbyingpressure by fishermen's groups, especially duringyears of low stock size. Management decisions were often politically'motivated, leaving distrust between user groups and the managers in the Department of Fisheries and Oceans (D FO), and ultimately resulting in an over-exploitationof the chum stocks. For instance, Wong (1982)showedthat the Fraser d i m escapement level shouldbe at least twice the level achieved in the mid 1970's. Bi 1963, in response to increasing dissatisfaction with the way the chum fishery was being managed, industry representatives approachedDr. Ray Hilbom at the University of British Columbia (UBC) and asked for a review cf the current management system. At that time I became involved and undertookthe review and implementation cf a new management system as a thesis topic. Our hypothesis was that a simplification of the management system, with involvement cf the users in the long-term management (e.g. formulation cf objectives) and the short-termmanagement (e.g, in-seasondecision-making), would result in greater understanding and cooperation of the fishermen in the management process and thereby allowmore successful management and avoid poor decisions based on political lobbying. Our hypothesis suggested full involvement of the fishermen in the management cf the resource. This placed us squarely in the midst cf a debate on the role cf user groups in resource man-agement; Walker (1973), Shabman (1974), and Odum and Skjei (1974) have debated the ques-tion for the case of Chesapeake Bay, while Cushing (1974), Miller (1976), and Pringle (1985) also made comments for other fisheries. The new management system, called the "clockwork", included 1) a set of objectives for the fishery, 2) a program of data collection and analysis to provide information for in-season estimation of stock abundance and composition, and 3) a set of rules collectively formulated by DFO managers and fishermen's representatives by which the fishery would be managed. These rules governed the in-season week-to-week decision making based on the weekly stock assessments (e.g. why, when, wher e,, and how commercial fisheries would be conducted). The clockwork would have to be set up prior to each fishing season. The in-season decision-making process would then run like a wound dock; fisheries would open and dose according to the predefined rules. We also felt iit was important to publish the assessments and rules in such a way that any commerdal fisherman would be able to calculate the size of the chum run, the allowable catch, and the number of days fishing that could be expired. The purpose of codifying the process would be to eliminate the in-season wrangling between fishermen and DFO, when an extra day of fishing; could mean thousands of dollars to eadi fisherman. The clockwork would be formulated when more objective thinking prevailed, before the sea-son. If both sides could abide by the rules during the season, a new sense of cooperation might be attained. The groundwork for the clockwork already existed; the Johnstone Strait - Fraser Riv^r Chum Advisory Committee met regularly with DFO and was generally accepted within the fishing industry as a useful form of interaction with DFO. In addition the in-season estimation methods of rim size were well developed and were simple enough to be formalized into stan-dard calculations that everyone co A understand. With DFO and industry support for the dockwork concept, Ray Hilborn and I were invited to become technical advisors to industry and agreed to hdp formulate the clockwork,. For a detailed description of background to the dockwork, the people involved, and the events during the implementation in 1983 through 1985, see Hilborn and Luedke (1987). A brief description of the history of my involvement in the dockwork follows. This description focuses on the main components of the clockwork: objectives for the fishery, a harvest strat-egy, an agreed upon in-season assessment methodology, decision making rules, 'and a pub-lished in-season guide to management. The implementation of the dockwork occurred over the period 1983 to 1985. In the first year, 1983, our efforts were limited to a review of the in-season management methods. We found them acceptable, but thought they could be simplified to permit greater understanding by the fishermen. These methods and some basic rules were accepted by the fishermen at a UBC workshop in June 1983. Di 1984we held several workshop withDFO and the fishermen, Objectives cf the chum fishery were established ard some alternative fishing strategies to meet the objectives were introducedand analysed. The objectivesin order cf the fishermen's priority were: 1)to acliieve the itHxinum potential cf the resource and the maximum long-termbenefitstothe fishermen, 2) define the optimum escapement goal as 2,500,000 wild chum for the Johnstone Strait to Fraser River area, including a goal of 700,000 for the Fraser River, 3) reach this escapement goal within three cycles (12-15 yrs), 4) learn as much as possible about the productivity of the stocks, 5) allow limited fishing at low stock sizes, and 6) stabilize the annual catch. In consideration^ fishermens' concerns, the escapement goal of 25 million would not be implemented u-fcil 1995; instead intermediate goalswouldbe used, startingat 1.8millionand increasingin phases until 1995. With these objectivesinmind, alternative harvesting strate-gies were discussed and compared, includinga constant harvest rate, fixed escapement, an4,a variable harvest rate strategy (Figure 22) . The variable harvest rate strategy was chosen by the fishermen as the most likely to achieve the stated objectives. The current phase (1987-1990)uses the followingharvest rate schedule shown in Table 2.1. Table 2.1. The Advisors' variable harvest rate strategy for John-stone Strait chum fisheries, 1987-1990. Total stock size Allowable harvest rate " 0-3,000,000* ~~ <10%b 3,000,000 - 3,600,000 20% 3,600,000-4,500,000 30% 4,500,000up 40% * total stock size of 3,000,000 million includes escapement goal of - • 2,000,000 wild chum and a predicted return of 900,000 enhanced chum plus 100,000USA bound chum. Enhanced and USA com-ponents assumed constant. b 3-10% tf the total run is caught in assessment fisheries, native fisheries, and incidentally in pink and sockeye fisheries. Figure 22. Alternative harvest strategiescomparedfortheJohnstoneStrait chum salmon fisheries. For each strategy, (he desired catch for any year dsexpressedas afunctionof the total runsize for that year. Advisors Stepped Harvest Rates Sbn»d Km?* R* Stock Size (millions) 13. The final major step in the implementationof the clockwork was to distribute a pub-lished form of the rules and the in-seasonassessment methods to all fishermen, so that anyone would be able to calculate the chum runs/ze. The package which was distributedto the fishing industry in 1985 is presented in Appendix A. During this initial phase,theclockworkproved to be a useful management tool. At its most superfiaal level, the clockwork ensured that management decisionsactually taken were consistentwith o f e s developedby industry and government. The clockwork process also provided a foram in which management policies and in-season fLSiirgplans were discussed and implemented, with DFO benefitting from fishermens' experience and vice versa. Unfortunately the clockworkwas only partially successfulin alleviating the acrimony associated with the in-season management of the Johnstone Strait to Fraser River chum fishery. Our initial assessment in 1985(Hilborn andLuedke 1987)wasthat acrimony would always exist, especially sincewe were dealing with fishermen's livelihoods, and when ^ adversely affectedby management decisions they will fight. However, since then I have con-cluded that the in-season acrimony is directly related to the managers' scientific ability to manage the stocks. If there is any doubt in the managers' ability to determine stock size, then the management system is opened to conflict. Many fishermen are able to use local knowl-edge and experience to determine quite accurately the abundance cf s a l n c n This is reflected in the fact that inmany test fisheries(e,g, mainland inlet pinks, Barkley Soundsockeye, West Coast Vancouver Island chums) DFO hires a fisherman to go fishing and provide advice on stock abundance, often without any rigorous samplingmethodology. Consequently, when these same fishermen suggest that the clockwork in-season assessments are not providing a true indication cf the chum abundance in JohnstoneStrait, conflict begins. Ari example cf this problem occurred in 1985. The clockwork in-season assessments were based on two sources, a commercial assessment fishery in the th!?,4 week of September, and a test fishery from mid Septemberthrough October, conducted for almost twenty years by the same knowledgeable local fisherman. The commercial assessmentfishery suggesteda run sizejust above that required for a fishery ;in keeping with the clockwork tUe-S a commercial fishery was scheduled for mid-October. Test fishing during the first part of the season did not change the in-season estimate of run size (recall that the in-season assessment methodology and rules were published in 1985, so anyone could calculate run size). Consequently, when the commercial fishery turned out to be successful, many fishermen suggested the clockwork assessments were wrong and demanded another fishery. Well, the dockworkprevailed and no other fishery was conducted. But the fishermen were right; the runinto the southern part of Georgia Strait was very large, in factthe escapement into the Fraser River exceeded the his-toric maximum by 50% (unfortunately the winter cf 1985-86 included severe freezing in November and record flooding in December, so only average fry production resulted from the large spawningrun). In retrospect, the clockwork management system attemptedto attain cooperation of the use r groups simply by involving them in all aspects of the management cf the chum salmon fishery in Johnstone Strait. It is now my view that this was a flawed approach. Certainly the fishermen shouldplay anintegralroleinthe long-termmanagement, including determining objectives, harvest strategies,and a frameworkfor decision making d e s (especially detail^on allocation between gears, and when and where to fid}. But the in-seasonmanagement cf the British Columbia salmon fisherie s is a complex system, which must be managed by proper scientific methods. Consequently I suggestthat cooperation from the user groups will follow proper scientific management, which requires the manager to have the resource as his primary client so that he will not be unduly influenced by lobbying from user groups. Despite these problems, in a 1986review, fishermenand managers alike expresseda general belief that the basis for the clockwork system was sound, worthwhile, and should con-tinue. However, the exampleof the 1985season identified two issues: first, a i inadequate in-season assessment methodology in Johnstone Strait, «nd second, the rationale for fishing in the terminal areas, especially the Fraser River. The first problem became my focus of attention €or the next two years, as I was hired by DFO to improve the clockwork assessment" rnethodOlogy, This work will be briefly described in the next section. The second issue has been addressed several times since the implementationof the clockwork, and still is actively debated among the user groups. This issue forms the basis for subsequent chapters of this thesis. 2.3 In-seasqn Assessment Methodologies Historically, the methodology for in-season assessment of the chum salmon run through Johnstone Strait consisted of two components: a single commercial assessment fishery in the 15 third week of September, and second, a seine test fishery in upper JohnstoneStrait (Double Bay area) during September and October. In 1985,the September assessmentwas based on a regressionbetween total commercial catch in the third week cf September and total stock size (r*-.64), with data available since 1972. Catch per unit effort (cpue) data for this fishery pro-vided no significantrelationship. The second assessmenttechnique was a relationship between cumulativetest fLshingcatchper effort and total stock size (r 2~.95) using c ata since 1979(datawere available back to 1965 but because they were collected under different objec-tives, the effort was sporadic and so could not be used to determine cumulative catch per unit effort). SeeAppendixB for a "workbook* type of descriptionofthe methods in 1985, In reaction to dissatisfactionfromthe industry representatives, the fisheries managers identified two problems in the in-season assessments, First, commercial fishery data for other fisheries in September and October did not provide a significantpredictiverelationship. Could a predictive relationship be determined? Second, test fishingeffort (e.g. sample sii£ selection)was based on the experience and irrbuLtimof the test fishing skipper and could not be quantified(recall that the same knowledgeable, and respected, local fisherman conducted the test fishery for twenty years). Could a more systematic approach, independent of the experiencecf the current test fisherman, be implementedwithout loss of predictivevalue? I investigated these questions; the methods and results are briefly described in the following paragraphs; for more a detailed descriptionsee Luedke et al (1988), Luedke (1985), Luedke (1987). I first analysed the existingtest fishery data, using stepwise regression methods, to determinethe value of each sample site in predicting total run size (Luedke 1985). At a subse-quent workshop, with local JohnstoneStrait fishermenand DFO managers, it was decided that the existing test fishery should be modified; effort was increased to five to six day s per week (fromthree to five days), the number cf sample sites was reduced from24 to 12, and some basic rules were implemented to control effort allocation to the sample sites yet provide suffi • cient flexibility to the existing test fisherman (e,g, at least 2 sets at each site per week, 6 sets per day, no more than 'wo sets per day at any site). The predictive relationship of cumulative mean weekly catch per unit effort versus total stock size would still be used. In addition a second seine test fishery was implemented, in Johnstone Strait proper adjacent to the original test fishery, but with only eight sample sites and d f e s similar to those described above. The data from thisnewtest fishery would not be used in the existing predictive relationship, rather a new data set would be started for future use. A n example of the resulting assessment procedure is now described. The mean weekly catch per set (cpue) from the test fishery is recorded as shown in the first row in Table 2.2 (the example year is 1987, the actual run size was 1,973 million). The secondrow shows the two week cumulative cpue, or simply the current week cpue plus the previous week cpue. The subsequentrows are calculated the same way for more weeks (e.g. 3 week cumulative cpue for week 1014 equals the s u m of the cpue in weeks 1011+1012+1013). The value in each cell is used to predict stock size based on linear regressions betjreen test f i l i n g cpue and total stock (note that weekly cpue cells are not used because cf high variation in the weekly relation-ships). Table 2.2. Weekly test fishery catchper unit effort calculations. Fishing season week (month/ week) Data format 9 /4 10/1 10/2 10/3 10/4 Weekly cpue 180 122 682 200 95 2 week cumulative 302 804 882 297 3 week cumulative 983 1004 979 4 week cumulative 1280 1100 5 week cumulative 1280 The regression statistics and stock size estimatesare shown in Table 2.3. The averagecf the available estimates in each week is used as the weekly estimate fein the test fishery (sepa-rate from any commericialfishery estimate). Inl 9861 was hired to analyse the Johnstone Strait commercial chum fishery data,, including d l catch and effort data since 1970. In order to use any catch and effort data it is important to first verify that the effort data are standardized for vessel characteristics and tem-poral trends in fishingpower. This was accomplished through discussionswith numerous fishermenand fisheries officers and biologists. It was evidentthat fishing vesselshave undergone .significant changes since 1970, which have increased their catching power consid-erably. My standardization of the catch and effort data is detailed in Luedke (1986). Summa-rizing: for each data point, catch was standardized to represent a 24 h seine fishery and a 36 h 17 gill net fishery; to reflect reduced abundance due to fisheries in the preceding week; and to reflectchangesin efficiency of the gear. Furthermore gillnet catch aiid effort were converted to the equivalent of seinenet catch and effort based on the ratio cf their cpue's. The resulting "total catchper seine equivalent unit" was then used ina linear regression with total stock size. Only data points within three days (e.g. total data range is 7 days) of the Julian date of the current fishery are utilized. The resulting relationships were generally all significantand provided favourableestimates (comparedto known total stock size) when used with inputs from previous years. As an example of the methodology, the regression statisticsforthe 1987 third week of Septemberfishery are shownin Table 24. The clockwork estimate is the aver-age cf the commercial fishery and test fishery estimates, v i th commercial fishery data and test fishery data given equal weight The current clockwork assessmentmethodologies appear to be working quite well; in the last fiveyears the errors in the in-seasonestimatehave generally been small (Table Even when the relative errors were large in 1987and 1989, the absolute error was small enough so as not to move the harvest rate to a different harvest level in the stepped strategy (Table 2.1). Consequently, inyears cf small stock size below the thresholdfor moving to a 20%harvest rate, no fishery was conducted. In two of the three years where fishable sur-pluses were present, escapement goals were achieved andharvest rates were considerably reduced from similary ears in the past. With the basic in-season assessment methodology in place, the clockworkmust now be allowed to prove itself to the fishermen. Certainly this will take time, and involve some mis-takes. For example, rememberingthat in 1985 the fishermen were right in their call for further fishing, a similarset of events unfolded in 1988; although there was a record catch in a mid-October commercial fishery, it wasnot enough to cause the Clockwork assessment equa-tions to increase the estimated run size to the point that another commercial fishery could be conducted. This time the fishermenprevailed, the clockwork broke down, and another large catch was taken within six days of the previous fishery. Unfortunately this time the clock-work methodology was right and the stock was subjected to a 40% exploitation rate. It is apparent that for the fishermen to accept the clockwork completely, the assessment Table 2.3. ^feddy test fishery estimatescf chum run throujhJohnstone Strait. Mon Independent Variable Regression $tat5 Point Standard Tfe^dY /Wk data format Yrs rz Estimate Error Estimate -10/1 2 week cumulative 7 .93 i ,ao,ooo 17% i,ao,oco 1012 2 week cumulative 7 .90 2,420,000 13% 3 week cumulative 7 .92 2,190,000 1396 2,305,000 1013 2 week cumulative 7 .94 2,880,000 9% 3 week cumulative 7 .97 2,370,000 7% 4 week cumulative 7 .96 2,190,000 9% 2,480,000 1014 2 week cumulative 7 .55 not used 3 week cumulative 7 ,7L 2,363,941 23% 4 week cumulative 7 .80 2,164,000 21% 5 week cumulative 7 .83 2,074,000 21% 2,201,000 Table 2.4. Commercial fishery estimates for 1987 (actual stock 1.97 million). Mon Independent Variable Regression Stats Point Standard Weekly /Wk data format Yrs r2 Estimate Error Estimate 913 Area 12 cpue 14 .75 1,934,000 32% Area 12+13 cpue 14 .76 1,990.,000 28% 1,962,000 Johnstone Strait = statistical areas 12 plus 13. cpue » catch per seine boat Table 2.5. Clockwork in-season assessment accuracy Stock size Estimate (millions) hindcast 1985 1986 1987 1988 1989 Week 1013in-season (% error to post-season) 3.4 -10% 3.37 -13.2% 2.1 5.9% 3.4 10.0% • 2.86 73% Find In-season (% error to post-season) 3.45 -8.T& 3.81 -2.0% 2.3 16.2% 3.45 11.6% 2.6 57"o Post season actual 3.78 3.88 1.97 3.09 1.65 . . ^ . 19 . n n n n n n 3 j , U. U. U U U'LLD • methodology must continueto provide accurate in-season assessments. The assessmentshave to have a better track record than the intuition cf the fisheries managers and fishermen if the clockwork is to be successful. 2.4 The Terminal Fisheiy Issue Recall that folio wingthe 1985season, two issues were identified by fishermen and fisheries managers alike as requiring attention. The first was the in-seasonassessmentmeth-odology and the second was the rationale for fidiingin the terminal areas, especially the Fraser River. This issue, tfiidi k a m e the impetus for the remainder of this thesis, is described in this section. There is always intense lobby ingby fishermen to get a larger share of the catch for their gear type and to conduct fisheries in their preferred areas. On one side of the debaie are the large seiners, with crews of five or six, and the local Johnstone Strait fishermen, including many native M i a i s , who lobby for more fishing time in Johnstone Strait. They cite the high value of the outside catch relative to the terminal areas. The processors agree. The Johnstone Strait fishermen and the processors have also been vocal about the terminal fisheries. For example, at one advisory meeting, some fishermen and processors complained about the extent of the terminal fisheries, claiming that more catch should be taken in Johnstone Strait. To make their point the processor openedup two tins of chum salmon meat, one from the ter-minal fishery and one from the Johnstone Strait fishery. The terminal fish definitely produced a less visually pleasing and less aromaticproduct. In contrast, with smaller vessel size and lower efficiency, gill net fishermen tend to live near the terminal areas and often do not like to travel far away from their area to fish. This is especially true in the Fraser River. These fishermen cite social values as well as economic val-ues (e.g. reduced harvesting costs) as they lobby for their traditional rights to fish in their areas. They also recall large catches in the Fraser River in the 1940's and 50's. And they ; v suggest that the Fraser River stock, the largest in the collection of stocks between Johnstone Strait and the I JSA. should be harvested more exclusively in the Fraser River (i.e. the resource could be managed better from terminal areas, in keeping with early principles from Ricker 1958). 20 These requests have been addressed in the clockwork. The initial clockworkhad a rule by which the Fraser River was guaranteedan opening for every two commercial fisheries held in Johnstone Strait, Rasallthe 1985exampleagain;withamissed opportunity for a commer-a a 1 fishery in Johnstone Strait, the terminal run into the Fraser River was considerable (e.g. estimated in-season at over one million). But because only one fishery had occurredin Johnstone Strait, no fishery was allowed in the Eraser River. This caused considerablegrief to local fishermen. However, buoyed by this unexpected escapement and the potential benefit? future, the Fraser River fishermen, together with fisheries managers, developed separate strategy based only on the terminal run size, and independent of the Johnstone Strait fishery. This new harvest strategy divided all surpluses over the escapement goal between escapemen and commercial fisheries accordingto a predefined plan. Thereby the local fishermen could reap part of the benefits cf the expectedbonanza. Unfortunately, the bonanzahas not yet developed. Fraser River returns have been mod-erate in the past few years, but less than required for a commercial fishery under the current clockwork. Consequently, the Fraser River fishermen are again disgruntled. The remainder of this thesis will attempt to provide some insight into the issue of the strategic utility of terminal fisheries. I will focus on the main objective defined by the fisher-men, that is, to maximize the long term benefit of the chum salmon resource to the fishermen. I will attempt to provide only one perspective, based on economic value, and will not attempt to quantify the social values of the traditional terminal fisheries. However, I believe that the 7 methodology and results are robust enough that these social values can be incorporated easily into the final results. The remainder of mis chapter presents the stock-recruitment analyses and fishery value analyses needed for the analysis of optimal harvest strategies in the chum fishery. The param-eters which are required include the stock-recruit parameters, with an estimate of the random variation of the recruitment and the joint probability of occurence for variation among the two stocks. In addition the discount rate and price per fish in the terminal area relative to the mixed stock*area are required. . 2.5 Data Sources Since this work is based on the case study of Johnstone Strait" Fraser River chum salmon, the requiredparameters are estimated f rom the data available for these stocks. These data include catches from sales slips, Fishery Officer escapement estimates, and biological data from test and commercial fisheries. The escapement data were taken directly from Fishery Officerestimatesof escapement. A common problem with thes<? data is error in the measurement of the spawners. Walters and Ludwig (1981) andLudwigandWalters(1981)showedtheeffectsof such error on stock recruitment analyses, including completely masking the S-R relationship. For chuxisaimon in the Johnstone Strait to Fraser River area, these measurement errors have not been determined, but are thoughtto be in the order of 10 to 40 % (pers comm with FSheries Officers). However, this error is low relative to other salmon species such as coho, because the large body size and behaviour of chum on the spawninggrounds make them easy to see and count (pers comm wiBn Fishieries Officers). Also, Wong (1982) showed that southern B.C. chum stock-recruit assessments are not changed significantly by using statistical methods that do account for errors in spawningescapement. Consequently the escapement data are used as provided. Recruitment data are derived from escapement, catch, and biological data. In contrast to the spawner data, the catch data are relatively accurate because of the requirement to submit sales slips in the British Columbia commercial fishing industry. These catch data were appor-tioned to stocks using run reconstruction methods (Starr and Hilbom 1988) which allocate the catch to the stocks in proportion to escapements. After 1985, stock composition estimates, based on electrophoretic analyses were used to allocate catches to stocks. The two methods provide similar estimates of stock composition (i.e. within 10%) in the major mixed stock fishery (Luedke et al. 1988). The annual returns were then allocated into brood year returns (e.g. recruitment) using age composition data from the Johnstone Strait test fishery weighted by an index of weekly catch per unit effort in the test fishery (Luedke et al. 1988). Personal communications with industry representatives and government managers were used to make estimates of other parameters such as landed values in the mixed stock and ter-minal fisheries. 2.6 Stock and Recruitment Analy ids Prediction of the long term effects of harvest choices, and optimizationmethods suchas dynamic programming, require a transition function to predict stock size from one period to the next, as a function of the harvest removed and the spawning sbockleft behind in each period. I assume that the transitioncan be adequately describedby the stock-recruitment function of Ricker (1954). It will be discussed in this section. Also re quired in the transition are a stochastic function with an associated joint probability distribution for variation cf the two stocks around the average stock-recruit relation, and the discountrate. These will be described in the following sections. The spawner - recruit data are presentedin Figure 2.3. Also presented is the spawner -recruit relationship based on the model developed by Ricker (1954) .The form cf the Ricker model which will be used here and which has the most biologically meaningful parameters is (1) R ~Seall~SIB)+v ^ where R is recruitment, S is the number cf spawnersgivingrise to the recruitment, a is an index of the productivity of the stock when there are few spawners and compensatory effects are not present, B is the unfished equilibriumstock size(Ricker's P r), and v is anormally dis-tributed (mean cf 0) random envjianmeiital variably JepiessJlting the combined effect cf environmental factors on survival. Walters and Hilborn (1976), and Walters (1986) provide a theoretical justification for "this tochastic variable by noting that e" can be viewed as random survival resulting from several independent and multiplicative environmental factors operat-ing in series. Thus v represents a s um cf several random factors and should be normally dis-tributed by the central limit theorem. Allen (1973) provides empirical evidence for the assumptionof normality, usingSkeena sockeve. Peterman (1981) provides further empirical evidence. Equation ( l ) )an be rewrittenas (2) 1 n(RIS)~a+(alB)S+v which assumes additiye and normally distributed errors and allows the parameters to be esti-mated using least squaresmethods. The data used to determine the relationship from equa-tion (2) 816 presented in Figure 2A, The scale for the axes in this figure are based on indepen-dent evidence lhal lite stocks have twen generally over-exploited through the years used here, Evidence includes actions by managers in the 1960's who closed the fishery for several years 23 in response to very low escapements and perceptions of 'over-exploitation(e,g. reduced aver-age catches). Furthermore Beacham (1984) calculated the optimal harvest rate at 32%, yet his-toric harvest rateshave averagednearer 45-504. In 24 of the 34years since 1955 this esti-mated optimumharvest rate was exceeded. In 1982 even the fishingindustry expressed concern over the chronic over-exploitationwhich they recognized was due in part to their own political lobbying for more f i l i n g time, Assuming that the stocks have been over-exploitedand the axes in Figure 2.4 are indica-tive of a potential range of spawners, then it is apparent that the data in Figure2.4 lack good contrast in spawning stock sizes. This lack of contrast in the spawner data leads to problems in the estimation cf the Ricker parameters using least squareslinear regression as per equation (2) and Figure 2.4. The Ricker a value is determined as the y-intercept cf the regression line and the Ricker B value is the x-intercept. The grouping of the spawner data at the low end results in a relatively precise estimation of the Ricker a value, but much less confidence in Jj^ e Ricker B value, Since it is meaninglessto fit a single regression line through these highly variable data, the best estimateof the Ricker a parameter is taken to be the mean y-value, or about 0.7 for both the Fraser River and non-Fraser chun stocks. Since ary stock - recruit analysis will provide a wide range of Ricker B values, it is nec-essary to utilize some independentestimates and general conclusions by others. For example, one estimate of the Ricker B value can be based on independent estimates of the optimum number cf spawners. The first reported attempt to develop an estimate of the optimum for the stocks in question was in 1962 (Anon 1963). The estimate of 2,400,000 for all stocks and 500,000 for the Fraser River alone was based on an average of the highest observed escape-ments in the period 1940 to 1960 which produced a greater recruitment. Since that time there have been modifications to the targets for individual systems but the total remains near 2,500,000 including 700,000 for the Fraser River (Palmer 1972, Anderson 1977). The rationales for these modificationshave generally not been well documented. Most estimates are based on the average cf escapements which produced maximum recruits per spawner, or habitat uti-lization surveys, or the judgement of people familiar with the spawning areas. Since then Bea-cham (1984)estimatedthe total optimum escapement for all stacks at 2,900,000 from stock and recruitment analysis. AndPease (1982) suggested an. Tent goal of 1,000,000 for the Fraser River, with a wide range of600,000 to 3,000,000. If we assumefromthese reports that the optimumforthe non-Fraser stocks is at ibout 2,000,000 and for the Fraser stock at about 1,000,000 and back Ci culate using the approxima»: tion fromHilborn (1985), Sopt-(0.5-0.07fl)B, estimatescf Ricker B for the non-Fraser and Fraser stocks are 4,500,000 and 2,200,000 respectively. Or we can base our expansion of the optimum spawning stock on a more well defined stock - recruit relationship such at Skeena sockeye, where the equilibrium stock size is approximately two and a half times the «*jrtimum escape-ment (Walters 1975). Using the previous ^Dtimum of 3.000.000 would sueeest a Ricker value of about 7,500,1000 for all sf r v~ t o 1"1 e Johnstone Strait to Fraser River area.-The parameter estimates which will be used in S i s study are a ftaKr=0.7, a^.f^^O.7, Brras. 500,000, B^.pn^S^OO^OO. In general then these parameter estimates suggest stocks which have a low productivity and a large equilibrium stock size. The result is a nearly linear Ricker stock - recruitment curve over a range of stock sizes near the optimum, with not much difference in the yield for escapements well above and below the optimum escapement. The optimal exploitation rates based on these parameter estimates are approximately 32% for each stock. Given the difficulty in fitting the Ricker model because of the lack of contrast in the data it is not hard to see why fisheries managers have resorted to using an average RIS with some environmental component in most predictions. It is probably as good as any other recruit-ment model. Certainly it will be important to determine how sensitive any results are to the Ricker parameters. Figure 2.3. Stock and recrui tment data for Fraser and non-Fraser chum stocks, Two Ricker curves based on the data are also presented. The lower curve does not incorporate uncer-tainty, while the upper curve does using the average value of the stochasticvariable v in Equa-tion l(i.e. oJ/2 - 0.2 for non-Fraser and 0.1 for Fraser). FHASER RIVER CHUM SPAWNER-RECRUITS TOTAL SPAWNERS; WLO+ENHANCEO: 1 9 6 0 - 8 3 , R=>Se*p(.85( l - S / 2 . 6 4 ) + 82 + > < •. > .R -Se«p ( . 75 (1 -S /2 .M) ) + 8 1 > / - 1:1 + 72 / / + 6 6 / / + l / A + 7 7 / + 6 5 / / > / 9 + 78 / / J ^ l S 0 0 .2 0 .4 0 . 6 0 . 8 1 1.2 1.4 1.6 1.8 2 NON-FRASER CHUM SPAWNER-RECRUiT WILD+ENHA.NCED; 1 9 6 0 - 8 3 Figure 2.4. Natural log of recruits per spawner (R IS) in relation to spawners (S), for Fraser and non-Fraser chum. LN (R/S) vs SPAWNERS FRASER RIVER: TOTAL SPAWNERS: 6 0 - 8 3 "N 2.6 2.4 -2.2 2 1.6 1.6 -1.4 1.2 -1 0.8 0.6 -0.4 0.2 -0 • 82 • 65 D 64 • 74 •i%i , 6 * 7 3 III • 75 - C • 8 3 • 63 • 68 I 77 0.2 0.4 0 . 6 0 .8 "i 1 1 1 r—I 1 1 1 r ' 1-2 1.4 1.6 1.8 2 Spawners (mi l l ions) LN (R/S) vs SPAWNERS NON-FRASER; WLD+ENHANCED; 1 9 6 0 - 8 3 1 2 Spawners (mi l l ions) •27 2.7 Recruitment Variability and Stock Correlation Stochastic variation can be incorporated into equation (l)either by treatinga as a con-stant and havingnonzero variance foru, or by omittingu and treatinga as a random variable. Either way, high variability aroundihe mean value is expected, since the early life history stages of chum salmon are particularly susceptible to random environmental fluctuations (e.g. spawning occurs in late November/ December which increases the likelihood cf freezing, while the passive downstreammigration soon after hatching increases the risk to predation and flooding). Walters (1975)used a distributioncf calculatedRicker a values to simulatevariability for astudy of optimum harvesting cf Skeenasockeye. Hie distributioncf Ricker a values he used was essentiallynormal. The distributionscf calculated Ricker a values for the chum stocks in this case study (i.e. treating y=0) as per Walters (1975)are showninFigure25. Notethatfor the non-Fraser stock the frequency of low Ricker a values isvery high, indicatingsusceptibjjity to environmental fluctuations and intrinsic poor productivity. Also note that since the distrib-utions of Ricker a values for these chum stocks (Figure 2.5)appear almost uniform, the Ricker a value will be held constantin this study. Instead variability wi I Ibe incorporatedinto the Ricker transition function by adding the stochastic variable v, defined by three Outcomes: good, normal, and poor (e.g. v= +0.5,0.0, -0.5). This defines the stochastic variable v shown previously in the Ricker equation. The magnitude of the variation represented in this vector is based on the apparentdeviations from average recruit per spawner as shown in Figure 2.6, where the standard deviation is approximately 0.5. The form of this vector permits an analy-sis cf the sensitivity of the results to the magnitude of the recruitment variability, as will be presentedin a subsequent chapter. A second component of the stochastic representation concerns how equally the two ,. recruitments are affected by, or subjected to, random environmental fluctuations. The degree to which the two stocks are similarly iiffected by random environmental fluctuations is repre-sentedby a "joint probability of occurrence" of the stochastic values for v. It is expected that the optimal harvest policy will be sensitive to the joint probability. Consequently three scenarios are developed arbitrarily in Table 2.6 representing low, medium, and high joint Figure 25. Distribution of Ricker a values for Fraser and non-Fraser chum, Ricker a values calculated as Ln(R/S)/ (,1-Sl HJ assumingBFmt,-2/500,000, B^.^-S,000,000. non-Fraser wild S lock 1S60-84, t=5000 Fraser wild s t o c k , 1 9 6 0 - 8 4 , b = 2 5 0 0 probabilities cf bad, aveiage, and good iscimtnHits. For example, a probability cf Fraser --0.5 and non-Fraser - (3.5in the high correlationscenario is .02, and the probability of Fraser « -0.5 and non-Fraser - 0.5 in the low correlationscenario is ,11. For the case study presented here a hi^icorrelat ionin iecxuitnB± deviations between the two stocks is assumed. This is based on the observationin Figure 2.6 that in most years the variation in recruitment is in the same direction for both stocks. In 17 of 23 years the devi-ation from average return per spawner is in the same direction. Figure 2.6. Time series of annual deviation from average RIS for Fraser and non-Fraser chum stocks, wild component only, for years 1960-84. \ Annual deviat ion f r o m average r / s Wild churn brood returns, 1 9 6 0 - 8 4 30 Table2.6. Threescenariosfor low,medium,and high probabilitiesofjointoccurrence (correlation) of bad, average, and good productivity (-.5,0, +5) for Fraser and non-Fraser stocks. Variation in the Fraser stock across top and variation in the non-Fraser stock down first column. For example, a probability of Fraser- -0.5 and non-Fraser - 0.5 in the high correlationscenario i s ,02, and the probability of Fraser - 0.5 and non-Fraser- -0.5 in the low correlationscenario i s .11. Low correlation Medium correlation High correlation -.5 0.0 +.5 -.5 0.0 +.5 -5 0.0 +5 -.5 .11 .11 .11 -.5 JE7 .10 .045 -5 ,23 .07 .02 0.0 .11 .12 .11 0.0 .10 .17 .10 ' 0.0 .CD7 .23 .07 +.5 .11 .11 .11 +.5 .045 .10 .17 +5 .032 .07 .23 2.8 Fishery Parameter Estimates The methodology used in this thesis produces optimal harvest strategies and the result-ing optimal catch and escapement as a functionof stock size. Consequently we assume com-plete accuracy in the annual clockwork system for estimation of most fishery variables, that is, we assume that stock abundance, stock composition, catch, escapement, and exploitation rates are known each year and / or applied without error. Certainly this is a brave assumption, but it does reflect the increasing ability of fisheries w orkers to collect such information during the fishing season. But there are a few parameters over which the manager has no control, and which may affect the solution. Consequently these are identified and considered in the model. 2.8.1 Discount Rate Clark (1976)emphasizedthat economic and social considerations are crucial in fisheries management. He used the "total discounted net economic revenue" as an objective for man-agement, which is a function of the discount rate and the net revenue per fish over time. The process of discounting the value of future revenue is defined as the reverse process of compounding the interest on present revenues. Clark emphasizes the need to incorporate the discount rate, since if the maximum per capita growth rate of a population is less than the dis-count rate and the cost of harvesting is neglected, then the optimal economic policy is to drive the stock to extinction Walters andHilborn (1976) indicate the critical nature of the discount rate to adaptive control problems. Without a discount rate, they suggest, all management emphasis would be put on getting better informationno matter what the cost in terms of lost yields. Clark (1985) goes so far as suggestingthat the biologist/ manager often adopts a low discountrate since he tends to adopt a long-term point of view. In contrast, industry is more concerned, with the sho rt term benefits, and hence implicitly uses a higher discount rate. Clark suggests that any suppressioncf this dimension of the analysismay provide misleading results. However, Clark (1985) identified a controversy over the use cf economic and social dis-count rates. He suggested that there is a general belief by many that discountingis related to anticonservation. While some authors suggest the use cf zero discount rate in public conservationdecisions (Pagel976), others have recommendedrates cf 2-3% per annumas appropriatevalues based on longtermyields from government bonds. But Clark points out that most large firms use discount rates of approximately 10% per annum. The discount rate used in this study is arbitrarily set at ten percent per stage (i.e. time step) in the dynamic programming model, which works out to an effective annual discount rate of 2.5% over the four year life cycle of the chum salmon. 2.8.2 Value per Fish For the following analysis, the value per fish caught in the mixed stock fisher}' of John-stone Strait is assumed to be the recent average price per pound of two dollars times the recent average weight of chum salmon (approximately ten pounds) or twenty dollars per fish in total. Terminal values are determined as a fraction of the mixed stock value, generally aver-aging about one-third of the mixed stock fishery price. These values have remained relatively stable through recent years despite increased marketing of the roe from terminally caught chum salmon. Moreover, these are ex-vessel prices and do not include harvesting costs, man-agement costs, or any value attached to social and aesthetic concerns. -The soaal and aesthetic values are open to wide interpretation, and so are not included in this analysis. Similarly, the cost of harvesting may be open to interpretation. If the cost is ! based only on annual operating costs, including fuel, wages, maintenance, etc., as well as man-agement and enforcement costs, then I suggest there may be little differencein costs between the mixed stock fishery in JohnstoneStrait and the terminal fisheries. For example, compare the cost of harvesting 1,000,000 chum salmon in the Johnstone Strait fishery versus several ter-minal fisheries. The direct cost in Johnstone Strait would be based on a two or three day fishery, with about 400 seiners and 700 gill netters, travel cosis for local and non-local vessels, packing costs, processing costs, as well as management and enforcementcosts. Thecostof harvesting 1,000,000 fish in the terminal area would require operation of several fisheries over a much longer time frame of several weeks, with associatedcosts of harvesting, travel, pro-cessing, and management and enforcement. The cost of the current capitalizationin the industry may also be open to interpretation. The industry is set up to harvest and process, large amountscf fishin a short period, with large seiners and efficient processing plants. I Thus the cost cf this capitalizationmay include not only interest payments, depreciation, etc. but should also include a cost of disrupting "this framework. Regardless, because the costs and values are open to interpretation, this analysis will focus on the relative ex-vessel prices paid to fishermen in the mixed stock and terminal fisheries. However, the sensitivity of the optimal solution to the relative values of the fish (termi-nal fishery relative to outside fishery) should provide insight into the overall value of terminal fisheries even f all the differential costs and values in the two fisheries are not explicitly includedin the calculations. 2.9 Overview c£ the case study I In this chapter a case study cf the Johnstone Straitto Fraser River chum salmon fishery., , I has been described. The components of the case study comprise the base case. These include: ; • Ricker parameters cf ano„.Frmcr=0.7, aFrilTCr=0.7, Bnon.Frm(r=5000, BFt>KT~25Q0. wilii the Ricker B parameters presented in thousands; three outcomes for the stochastic variable u, defined by good, norma}.. s»nd pejr n« +, -0.5); a high correlation in recruitment deviations between the two stocks (e.g. correlation factor •= 3 for high); a discount rate of 10% (applied to the value matrix as 1-discount rate, or the "discount factor"=.9); a price per fish in the John-. : / ' '33 stone Strait mixed stock fishery of 20 dollars and a terminal price (tv) relative to the mixed stock fishery price (e.g. tv=0.3). These parameters will form the basis for much of the analysis in this thesis, and so are called the "case study scenario". Note that these parameters are referenced throughout the text, especially the "case study" set of parameters. In figures the parameters used in the analysis are presented in the following form: a , ^ . ^ , a ^ , B ^ . ^ , R w Johnstone Strait price, terminal price, discount factor, correlation factor (or .7,.7,5000,250(,20„3,.9,3 for the case study scenario). Variations from the "case study scenario" parameters are indentified through this parameter list. 3. METHODS Numerical optimization methods are used in this thesis. Why use numerical methods ~" versus more generalanalyticalmethods? Taha (1976)suggests that the best solutionis mea-sured by a model's representation of the system, that is, all the necessary variables are defined, the parameters are accurate, and the objectives are reasonable. In this regard, analytical methods generally are not able to incorporate a large number of variables. Numer-ical methods provide greater flexibility when dealingwith several variables. But evenmost numerical techniques (e.g. forward looking simulation) are not useful with a large number of variables. One technique which can incorporate several variables and maintainutility is dynamic programming. This technique will provide the basis for determiningoptimal solu-tions in this thesis. The technique, the ingredients required, and the computer programs used will be described in this chapter. 31 Stochastic Dynajnic Programming * The case study described in this thesis includes two chum salmon stocks, three fisheries, and basic stock and recruitment processes, stochastic processes, and. differential value between fisheries. It would be an almost impossible task to find the optimal feedbackharvest policies for this case study if it were not for a relatively simple method of optimizationcalled dynamic programming. This method, developedby Bellman (1961) and Bellman and Dreyfus (1962) and later adapted for use in fisheries by Reed (1974), Walters (1975), Clark ( B76,1985), Walt-ers and Hilbom (1976), Hilborn (1976), Mendelssohn (1980)has greatly reduced the computa-tional constraintsof many optimization problems. What is dynamic programming? Walters (1975,1986) provide a good introduction to the technique. Summarizing: Dynamic programming has some basic elements, including state variables (e.g, fish stocks), decision or control variables (e.g. exploitation rates), stages (e.g. year), a dynamic model to predict the state from one stage to the next (e.g. Ricker stock recruit model),and an objectivefunction(e.g. MSY) to specify the value of the decision made in each stage. If stochastic outcomes are importantthe dynamic model must specify not a single . future state, but instead must specify probabilities for each of a set of possible new states. The technique works backwards from a known endpoint (e.g. value of the fishery is zero) then finds an optimum control to use at every alternative combination of state variables that may v 3,5 n n n n < n n u o LI, U, U, U.. i. u LI, I O occur at that stage. The optimal solution for each stage is a functionof the value obtained at that stage, plus the long term value resulting from the state(s) in future stages; at any stage this long term value has been precomputed due to the technique of working backward through time. The overall solution will be optimal across stages. In harvesting problems where the transition model and short term value calculation are the same at every stage, the overall solution will be a stationary optimal policy, Walters (1986) defines a stationary policy as one where the best choice depends on the state in a year, but not on the particular year. However, even this technique is limitedto three to five variables, depending on the computing power available. But thanksto rapidly increasingcomputingpower this "Curse of Dimensionality11 has been reduced significantly as is evidencedby the resurgence of research using dynamic programming (C.W. Clark pers coram). Consequently, dynamic programming techniques will be used to determine optimal harvesting strategies for this case study. 3.2The Ingredients The main ingredients in the dynamic programming are the state and control variables, the transition function, and the objective function. The use of these ingredients in the pro-grams written for this thesis are presentedbelow. Two state variables representing the Fraser andnon-l'raser chum stocks are used. The state variables range between 0 and 5100 (note that all slates are presented as actual stock size divided by 1000), and were discretizedin40 increments of 150. These increments were deter-mined by trial and error and reflect a requirement for all possible recruitments in the trans-ition between stages. These increments are also large enough to be meaningful to fisheries managers managing stocks during the fishing season (e.g. smallest possible level to which managers would attempt to implement management measures). Finer state increments did not change the solutions. Three control variables represent the three fisheries, Johnstone Strait (JST), all non-Fraser terminal fisheries (MVI, for the main non-Fraser terminal fishery at Qualicum in the. mid-Vancouver Island region), and the Fraser River (FR). Each control variable consists of a har-vest rate between 0 and 1.0, discretized in increments of 0.05. Since the objective of this paper is to determine the utility of the terminal fisheries, some computer runs of the model will eliminate one or both of the terminal fisheries (i.e. control variables). Each variation repre-sents a "management philosophy". Comparison of the results across management philosoph-ies should provide insight into the utility of the terminal fisheries, satisfying the adage 'you don't know what it's worth 'till it's gone'. Five management approaches are considered in this analysis: 1)eliminate the mixed stock fishery and use only the two terminal fisher-ies, one in the Fraser River and the other in the mid Vancouver I sland area (MVI+FR). This is the only approach where catch must be taken in the terminal area. In the following approaches with terminal fisheries included, the utilization of the terminal fisheries is determinedby the optimal control strategy; 2) use only the one mixed stock fishery in Johnstone Strait and eliminate all terminal fisheries (JST); 3) eliminate the terminal fishery in the Fraser River and use only the mixed stock fishery in Johnstone Strait plus one terminal fishery for the non-Fraser stock (JST+MVI); 4) eliminate the terminal fishery for the non-Fraser stock and use only the mixed stock fishery plus one terminal fishery in the Fraser River OST+FR); and finally 5) a completely flexible approach with a mixed stock fishery in JohnstoiB Strait plus the two terminal fisheries (JST+MV1+FR). ,Each stage in the dynamic program represents a cycle in the d u n salmon life history. Assuming that all recruitment occurs at age four (infact 60-80% return at age four), then each stage in the dynamic program represents a four year cycle. Consequently, the transition between stages can be predicted using the Ricker model as outlined in the previous chapter. Recruitment i s predicted for a range of stochastic outcomes (e.g. poor, average, and good) and a range of joint probabilities (see Table 2.6). All alternative combinations of these components (e.g. annual harvest and subsequent recruitment) are assessedto find the best possible balance between the short term value in har-vesting v, at each time step and the long term value in allowing the stocks to spawn .V,tl. The objective function which determines the best trade-off is the discounted total value, and (faUowiijgthe basic structure in Walters 1.986) is defined as where 5 is the discount factor (1-discount rate) and T is an arbitrary end time (e.g. 20 years). The annual value is a function of the system state (e.g. stock sizes) x and the control variables (e.g. harvest rates) u such that 37 (4) V, = v,(xu,x2l,ull,u2t„u3l) Since the controls used vaU. in general affect the next state . r , , a n d this wIL in tumaffect the next value increment i, then the long term value V is a functionof i : i^ + i I(*I., + i>xi,i +1) If Vf,, is the highest possible long term value for every state combination that might arise, and pOti.Mi.*c2.i»i|-ti,i>*2,i>"i.f>"2,!>u3.i) is the probability assigned to each possible next state through the transition function, then the objective function which satisfies the "principle of optimality" fsom time t forward is the one that maximizes (6) VC^pX,,, 11 ,.„ H, „«3,,) + I,(41 p(xu t! | xu,x2t„ U,,„ H2,,.U,.X+,(*ii, + i.*2.rM) over choices Note that ;c,n is a function of u, through the stock - recruit relation. The maximum value V?C*i,n*2.i) is found by searching across all combinations cf harvest rSfes and calculatingthe value cf each choiceusing equation (6), then saving the highest value as v;. The immediate value v, is taken to the total landed value across all fisheries, where the value from each fishery is catch times the price per In the case study presented here the price per fish is changed to reflect two possible objectives; maximize the catch when the price is equal in all fisheries, or maximize the economic value when the price in the terminal fisher-ies is lower than in the mixed stock fisheries. In the transition fern one stage to the next, the value of the predicted recruitment is cal-culated from the value matrix Unfortunately, the next states (recruitments) do not always match the discrete states defined in the long term value matrix. To determine the' value of such states, interpolation is required. By trial and error testing of several methods, a simple bi-linear interpolation routine (from Press et al. 1986) was found to work well. The requirement for interpolation presents a significant computational overhead, but can only be avoided by very fine discretization (Mendelssohn 1980), which is computationally costly in itself. . . . . •••• 38 3.3 Program structure The dynamic program algorithm used in "this analysis includes the two state variables-(e.g. stocks) and three possible control variables (e.g. harvest rates for each fishery). A sto-chastic vector cf joint probability cf occurence i s initialized for cither low, medium, or high correlationcf the recruitment variability between stocks, Alternative basic management philosophies (e.g. combinationscf fisheries) are definedinthe initializationof the model ty reducing harvest rate choices in unwanted fisheries to a single choice of zero harvest rate. To increase efficiency all possible catches and resultingrecruitments are precomputed in the in t tializationsection, over all state and control combinations. Parameter inputs to the Ricker model for each stock, and choices for discountrate, fish prices, and the joint stochastic probabilities are all input through a separate data file. The key to optimization using dynamic programming is to work backwards starting from an arbitrary endpoint far enough into the future to ensure that the optimal control policy converges to a stable "stationary feedback policy" (Walters 1986) that is independent of time and of the endpoint value choice. In "this analysis the endpoint in time is 20 stages (chum salmon life cycles cf four years each), providing sufficienttime for all control policies to con-verge. For each stage, beginning at the endpoint, the program loops over all combinations of stock sizes and possible harvest rates from the various fisheries. Within each loop the average value over a range of stochastic probabilities is determined. The maximum value for the har-vest in each stageplus all future stages i s saved, in the value matrix, which is the link between the stages. At the end of each stage the discount rate is applied to the value matrix. The computations were made on a variety of available VAX computers. On the fastest, a model 8530, finding an optimum policy for the full complement of variables required approxi-mately 24 hours of cpu time, By eliminating a single fishery this cpu requirement was reduced to about 2 hours. The efficiency of the current program was achieved by pre-calculating all possible catch, spawning stock, and recruitment transitions outside the main model loops. The first version of the program, which included these processes inside the main loops, required almost 150 hours of cpu time. It became clear during this work that effi-cient programming was a necessity when using dynamic programming techniques. 39 34 Conventions for presenting optimization results The optimal solution is presented in two parts, the controlpolicy (i.e. harvest rates as a function of the stock sizes) and the resulting value matrix (i.e. Net Present Value). These are determined for every combination cf non-Fraser and Fraser stock sizes. In the output, the non-Fraser stock is represented on the vertical axis and the Fraser stock is represented on the horizontal axis. The NPV represents the long term value of the resource in millions of dollars. Only stationary policy results (e.g. after 20 backward stages) are presentedhere. A n interestingfeature cf dynamic programming is that the controlpolicy quickly con-verges to the optimal stationary policy, usually with i n 2-15 time steps depending on the num-ber of variables involved and the choice of endpointvalues. The value matrix also converges to the Net Present Value but over a much longer time frame depending on the number cf variables and the discount rate. Using two stocks and two fisheries I found this convergence to occur in about 60 time steps. However, noticingthat the annual rate cf increase in the^alue matrix converged almost as quickly as the controlpolicy, the Net Present Value was calculated as the increase in the value matrix at each time step divided by the discount rate for the time step. This produced the same result as allowingthe value matrix to converge after 60 time steps. Finally, recall that each time step (or stage) represents a four year cycle in the life history of the chum salmon (assumingonly one age class of age 4). Thus the results are based on a single cycle; which means the NPV reported in flisanaly sis constitutes only one quarter of the NPV forthe total resource fcllfour cycles). 3.5 Potential limitations in the methodology The implementation cf the methodology presentedhere has some potential limitations. The limitations apparent to me are described in this section. Several aspects of the chum salmon fisheries cause uncertainty. The first uncertainty is in the in-season stock assessments and consequent ability to harvest to desired levels; In the actual fishery the in-season stock assessments have genefally been reasonably accurate; within ten percent of the actual run size. The accuracy of the in-season assessments is critical if the correct exploitation rates are to be applied. Furthermore, when fisheries are conducted to try 40 and achieve a specificexploitationrate, inability to control the fishing fleet may result in the harvest being under or over the desired rate. In the dynamic programming model, there is-assumed to be no uncertainty in the application cf the exploitationrate. In addition there are some apparentproblems with the determination of stock composi-tion using current electrophoretictechniques (Luedke and Anderson f 989). First, small com-ponents appear to be biased upwards. Second, the variation between replicate samples is great (Luedke and Anderson 1989); two samples taken at the same time and from the same sites in Johnstone Strait may produce very different results (e.g. size of the Fraser River com-ponenthas differedby 50% in such replicated samples). Consequently, the uncertainty in the stock composition(e.g, size cf each stock) makes applicationof optimalexploitationrates, which are based on kncming the stock composition, very difficult. The dynamic programming model is necessarily limited in scope to reduce the computa-tional constraints. For example, the Ricker transition function assumes a single age class tasthe chum salmon life history. Another example, is the use of only two stocks, when the non-Fraser stock consists of several geographically distinct stocks harvested by several differ-ent terminal fisheries. Another example, is the singular view of the differential value between mixed stock and terminal fisheries, based only on the ex-vessel price paid to fishermen, and not incorporating other social values or costs of harvesting. Such simplifications may make the results problematic with regard to a definitive solution for the Johnstone Strait to Fraser River chum salmon fishery. However, the results presented in this thesis should provide a general understanding of the optimal exploitation in this type of gauntlet fishery, and robust enough to become the basis lor further discussion and allow incorporation of subjective fac-tors such as social values. Some numerical aspects of the methodology as implemented may also limit the breadth of the results. For example, a wider range of stochastic outcomes with a finer discretization could have been used. They were not addressed because of the computational burden and the anticipated small effect (Clark 1985). 4. RESULTS In Chapter 2, the case study for the current chum fishery in the Johnstone Strait to Fraser River area was described. In this chapterthe optimal harvest strategy for this case study will be presented for several management philosophies, that is, combinations of fishery locations. The differentmanagement phiolosophies ais: 1 ^ harvest only in the mixed stock area where market value per fidiis greatest and cost of harvesting is loweredby using only one fisher}', 2) eliminate the mixed stock fishery and use only terminal fisheries to maximize catch, or 3) allow any combinationof mixed stock plus terminal fisheries. The following analysis will show the differences in the long term value of these management philosophies for the case study scenario. Subsequently the analysis will attempt to determine the optimal utilization of the terminal fisheries in the case study. It i s suspected that the current difference in value per fish between the mixed stock and terminal fisheries will be an important variable in this analy-sis. -sk Further to the case study solution, more general results are presented by examining the sensitivity of the optimal solution to the various parameters and variables used. Here the focus will be on the sensitivity of the optimal strategy to the relative price paid per fish in the terminal fisher)'. Other considerations include the sensitivity of the results to the Ricker parameters used. Systematic sets of dynamic programming solutions are presented to show how the optimal utilization of terminal fisheries is related to the Ricker parameters and the value of the fish in the terminal area. These results are more generally applicable to other fisheries. 4.1 The Optimal Strategy The optimal harvest strategy determined by the dynamic programming techniques used in this thesis provides the basis for the subsequent comparison of management philosophies and determination of the utility of terminal fisheries. Consequently this section will focus on a general description of the optimal strategy, using a simple example to show how the strategy is affected by changes in the basic Ricker parameters, the stochastic function, and the discount rate. . The optimal harvest strategy consists of the best harvest rates for d l stock size combina-tions in the form of a multi-dimensional control law (Allen\973, and Walters 1975have referred to these controllaws as "optimal strategy curves", but they have also been called harvest rate isoclinesby Hilbom 1976, and simply, optimal exploitation rate curves ty Walters and Hilbom 1976). The optimalharvest strategy for the most basic case of the Johnstone Strait mixed stock fishery is pre sented i n Figure 4.1. This result is based on the case study scenario developed earlier, with Ricker parameters for the Fraser and non-Fraser stocks at a n=.7, a,mnt=.7, 8n,=»2500, B,„mn,=5000, but no stochasticity, andzero discount rate. The two stocksare presented in increments of 150,000with Fraser across the top and non-Fraser along the side. At each stock combination an optimalharvest rate has been determined, in this case using a dynamic program model with 2 state (Fraser and non-Fraser stocks) and lcontrol variable (mixed stockfishery in JohnstoneStrait-JST), The 10%, 30%, and50% harvest rate isoclines are shown in Figure 4.1 a-d. ^ Fixed escapementlines, representingthe 10% and 30%surpluses above the combined fixed escapement, are also shown (as per Hilbom 1976). These lines are based on the combined optimum escapement of the Fraser and non-Fraser stocks and are calculated as ,, Combined escapement _ rraser stock " ; - nonrraser stock (I -harvest rate) These lines provide a basis for comparing the classical fixed escapement theory with the opti-mal harvest strategy. Note that the optimal strategy and the fixed escapement strategy are the same only in the middle section of Figure 4.1a, when both stocks are similar in size (relative to their Ricker B values). But as the ratio of the stocks changes from 1:1 (one stock low abun-dance and the other stock high abundance), the optimal strategy shows an increase in the har-vest rate (i.e. harvest harder) by departing from the fixed escapement isoclines (see also Hil-born 1976). It is under these circumstances that the classical fixed escapement theory has been of limited utility in a mixed stock fishery. For example, current management practices often decrease the harvest to protect weak stocks (i.e. manage to the weakest stock). The comparison of the classical fixed escapement strategy with the optimal strategy is concluded'by showing the limited circumstances under which the two strategies are most equal. As Hilborn (1976) showed, the optimal strategy and the fixed escapement strategy are most similar when the Ricker parameters are the same between stocks; in this case (a fR=.7, V) O O o o anmFR"-7, BfJ!=-5000, B„mFR"5000). This finding is reiteratedin Figure 4.1 .b; the optimal strategy nearly parallels the fixed escapement strategy with still someminor increase in harvest rates when one stock is much more abundant relative to the other. The effect cf adding a discount rate of 10%(Figure4.1c) to the base case (Figure4,la) is to become less conservative (harvest harder), since the future value of the resource is lessened. The effect is most pronounced when the ratio of the stocks differs from 1:1, The optimal strategy curves derivedby including the stochastic function from the case study scenario, which includes three stochastic outcomes (bad-0.5, average-l,good-1.5) and ahighjoint probability of the stocks having the same outcome (seeTable2,6), are presented shown in Figure 4,Id. Generally, there is a small difference in the optimal strategy under the stochastic variationin recruitment. The difference, which is generally less than five percent change in exploitationrates, occurs mainly at the extremes when one stock is weak and the other is strong. The result is a slightlymore conservative harvest strategy in the face of va4; ability in recruitment. Note that Clark (1985) suggested that changing from a deterministic model to a stochastic model is likely to have very little quantitativeeffecton the outcome of the optimization analysis. This was generally confirmed here, especially when both stocks are a similar size, The next section will utilize these outputs in a comparison of the basic differences between the management philosophies of fishing in terminal areas, mixed stock areas, or a combination of the two areas. 4.2 Deciding where to fish; the long term value of severalmanagement philosophies. In the previous example, only one single control variable, representing the mixed stock fishery in Johnstone Strait, was used in the dynamic programming model. In this section two more control variables (representing the terminal fisheries) will be included in the model. Model runs will consequently incorporate one, two, or three fisheries, representing the three possible fisheries identified in the case study scenario; the mixed stock fishery in Johnstone Btiait, a terminal fishery in the Fraser River, and a terminal fishery for the non-Fraser stock (mainly at mid Vancouver Island). The way in which these fisheries are combined defines a management philosophy, such as: use only the outside mixed stock fishery to maximize the quality of the catch, use only the terminal fisheries to maximize catch and eliminate mixed stock fishery problems, or any combination of the mixed stock plus terminal fisheries. The optimal harvest strategies for these management philosophies will be determined and com-pared in this section. The strategies will be calculated for the case study scenario formulated in Chapter 2. Itesl l that the cose study scenario consists of two stocks, Fraser and non-Fraser, with equal productivity <J„,„ra=.7) but with different Ricker B values (Bra'=2500, B„,„,fR=5000); The recruitment is subjected to a stochastic function with three outcomes (bad, average, good) and a high joint probability of the stocks having the same outcome (see Table 2.1). The ex-vessel value of the fish in the terminal fisheries is generally only one third of the value in the mixed stock fishery in JohnstoneStrait. To simplify the comparisonl will report a single expected value which represents an average of the Net Present Value (NPV) for all stock combinations in a range around the opti-mum recruitment (R'fr -1127, R'„mnt =2255). The range is arbitrarily chosen as m (RpH - 25%, R^w - 25%)to(RfR + 25%, R^„fr + 25%) - (2550,1200)fo(4200,2100) Other ranges were considered, including the complete range of 0 to the Ricker B value, but the conclusions were not sensitive to the range. The "average" (NPV) for each combination of fisheries is presented in Table 4.1. For the case study scenario the NPV is 309.1 million dollars for most management philosophies (this NPV is for the single cycle used in this analysis; the total NPV of the resource for four differ-ent cycles would be four times thisamount or approximately 1.2billion dollars). However, the NPV for the philosophy which uses only terminal fisheries is considerably less at 95.3 million dollars. It is apparent that, given the current price for the terminally caught chum salmon, moving to a management philosophy which uses only terminal fisheries significantly reduces the NPV of the resource. In contrast all other fishery combinations provide the same NPV; a result which becomes apparent by looking at the distribution of the catch under each management philosophy. Under the actual parameters and prices, and assuming the objective is to maximize the value of the resource, no terminal fisheries are utilized in the optimal solu-tion; all the catch is taken in the Johnstone Strait mixed stock fishery. With only one fishery being utilized it is not surprising that the optimal harvest rate strategy curves in Figure 4.1d are the same for all philosophies. Table 4.1. Net Present Value and annual catch from various fishery combinations, using the case study scenario. NPV is presented as an average over a probable range cf stock combinations, betweenR"-25% and R'+25%, Fishery Combination MVI Fraser JSt only JSt MVI JSt Fraser JSt MVI Fraser NPV (millicns$) 95.3 309.1 309.1 309.1 309.1 Annual Catch 1981 2005 2005 2005 2005 (xlOOO) outsidecatch ' 0 2005 2005 2005 2005 terminal catch 1981 0 0 0 0 Since the objective in this optimizelion was to maximize the NPV over the two stockSf the differential value of the fish bet ween llie mixed slcx:k and terminal fisheries is probably an important factor in the optimal solution. In the following paragraphs this factor is addressed bv making the value of the terminally caught fish equal to the value of the fish caught in the mixed stock fishery. Otherwise the scenario remains the same. And since the differential value is no longer a factor, the results are equivalent to using the MSY objective. The res-ilts for this scenario are presented in Table 42. Several points can be made. First, the NPV is greatest when bcth terminal fisheries are used. Second, the lowest NPV is producedby fishingonly in the mixed stock fisher)' in Johnstone Strait. These results reflect conclusions drawn by previous workers. For example, Ricker (1958) suggested that stock be harvested much as possible, while Paulik et al. (1967) showed that the terminal fisheries will maximize the catch. However, Paulik et al. (1967) compared only the extreme cases, a mixed stock fishery against terminal fisheries, but not both together. In this analysis, a combination of the two fisheries is considered. As shown in Table 4.2, combining the mixed stock fishery with the terminal fisheries produces the same NPV as using only terminal fisher-ies, but with a significant harvest in the mixed stock fishery. This result suggests it is not nec-essary to go to the extreme of harvesting only in terminal fisheries; MSY can still be achieved with some mixed stockharvest. Furthermore, note that both terminal fisheries are required to achieve the maximum values; when only one terminal fishery is used with the mixed stock fishery in JohnstoneStrait, an intermediateNPV is produced. Table 4.2. Net Present Value and catch fem various fishery combinations, using case study scenario except NO DIFFERENCE in value between mixed stock and terminal area; NPV is an average over a probable range of stock combinations, between R'-25% and R*+25%. Fishery Combination MVI Fraser JSt only JSt MVI JSt Fraser JSt MVI Fraser NPV (millions $) 317.4 309.1 312.0 312.7 317.4 Annual Catch 1981 2005 1979 1981 1958 (xlOOO) outside catch 0 2005 1833 1924 934 terminal catch 1981 0 145 57 1023 This simplified comparison, using average values, masks the changes in NPV as stock sizes change. Consequently, three cross-sections of NPV from the optimal solution are shown in Figure 4.2a-c for three non-Fraser stock sizes (e.g. small, medium, and large) and a complete range of the Fraser stock sizes. Note that the same scenario as above is used here, with fish prices equal between fisheries (making it equivalent to an MSY objective). In figures 4.2a-c the upper unmarked line represents the two philosophies, terminal fishing only (MVI+FR) and mixed plus terminal fisheries (JST+MVI+FR), both of which provide the maximum NPV. The lower unmarked line, which provides the least NPV, represents the philosophy which uses only the mixed stock fishery in Johnstone Strait (JST). Between these extremes are the two fishery combinations which include the mixed stock fishery but only a single terminal fishery in either mid-Vancouver Island (marked by an opt n square) or the Fraser River (marked by a closed diamond). In general, there is a precipitous decline in NPV when one stock goes extinct (e.g. stock size reaches Q), Furthermore the slope of the lines in each figure indicate the value in rebuild-ing the Fraser stock; there is approximate? a20% increase in totalNPV fromlow to high Fraser stock size. The differences in the NPV axis between graphs provide an indication of the value in rebuilding the non-Fraser stock. The differencebetween the low non-Fraser stock and high non-Fraser stock size (ag. Figure 'a' bends sharply at NPV of about 200 while Figure 'c' bends sharply at NPV of about 300) suggests an increase cf approximately 50% in totalNPV. Finally, note that the differences between the lines (i.e. management philosophies) is least when the ratio of the stocks is not significantly different from 1:1 (e.g. spacing between groups cf lines in left side of Figure 'a', most of Figure 'b', and the right side of Figure 'c'). Conversely, note that the largest differences between the lines (i.e. management philosophies) occurs when the ratio of the stocks is substantially different from 1:1 (e.g. spacing between groups of lines in Figure 'a' right side when Fraser high and non-Fraser low, and in Figure left side whe.i Fraser low and non-Fraser high). This again reflects the cla?oical problem with harvest management theory: all the management philosophies work equally well only when both stocks are about the same size. It is when the ratio of the stocks is significantly different firmlil that the classical management theory breaks down, and there is a need to adjust the management strategy to reflect this difference in abundance between the stocks. In summary, there is little choice in the management philosophy for the case study sce-nario when the objective is to rnsoriiniaa the long term value of the stocks. The optimal solu-tion suggests there is little economic benefit to be derived from a terminal fishery. The fish should either be harvested harder in the mixed stock fishery or allowed to spawn. The trade-off is based on the value of the fish in the terminal fisheries, since when the differential val ue of the lisli between the fishing areas is disregarded (e.g. use MSY as an objective), the terminal fisheries become a rt integral component of the overall management strategy, espe- ; cially when the ratio of the stocks differs significantly from 1:1. This raises the question of the relationship between the use of terminal fisheries and the terminal price paid for the fish. This question will be addressed in the following section. 4.3 Sensitivity to the value of f ishin the terminal fisheries. The optimal solution appears to be sensitive to the differentialvalue of the fish between the mixed stock and terminal fishing areas. Consequently, in this section, the relationship between the terminal fishery price per fish and the utility of terminal fisheries in the optimal solution will be determined. The basis for the analysis remains the case study scenario, except that the terminal price per fish wi 11 be varied between 0 and 1.0 (relativeto the price per fish in the mixed stock fishery in Johnstone Strait). There exists a relationshipbetween NPV of the two stocks and the terminal price per fish. Each point inFigure 4.3 repres ents a i average value over a range of stock sizes around the combinedoptimumrecruifff-ent for the two stocks (+'/" 25% as explained in the previous section). Three fishery combinations are compared, each with a choice of harvest in the out-side fishery plus one or both of the terminal fisheries. The three combinations are: the mixed stock fishery (JST) villi either the licn-Fraser terminal fishery generally at mid-Vancouver ^ Island (MVI) or the Fraser River terminal fishery (FR) or both (MVI+FR). It is apparentthat a threshold terminal price exists for each stock (Figure 4.3). Below this threshold the optimalsolution sets the terminal exploitation rate to 0.0 (i.e. terminal fisheries are not utilized) and the NPV of the resource remains constant. Above this threshold, terminal fisheries are utilized and the NPV increases geometrically. Overall, the NPV of the three fishery combination (JST+MVI+FR) is the sum of the two fishery combinations (JST+MVI and JST+FR), The threshold price is different for the different terminal fisheries (Figure 4.3). The threshold price for the Fraser River terminal fishery (the smaller stock) is about 0.4 of the mixed stock fishery price, while in the non-Fraser terminal fishery (the larger stock) the thresholdprice is approximately 0.8 of the mixed stock fishery price. This result likely reflects stock and secruit differeneesbetween Uw stocks and will be explored in the next section. But first it is important to determine the behaviour of the optimal strategy at different stock sizes. Recall that the values in Figure 4.3 were based on an average over a probable range of stock sizes around the combined optimum recruitment. Using an average value over a limited range of stock sizes may mask the behaviour of the optimal harvest strategy, espe-cially where it has proven to be most different from classical strategies (such as fixed escape-Figure 4.3. The NPV cf three fishery combinat ionsi l relation to terminal price |Kir fish; using a i average va lce over a range of stock sizes+1 -25% around the combined optimum recruit-ment. Ihe lowergraphshowstheaverageannuala i t chover the same range. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Terminal value relative to the mixed fishery value .JST+MVI ...JST+FR . JST+MVI+FR ^ 2030 <3 2020 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Terminal value relative to the mixed fishery value . . . JST+MVI _«_JST+FR JST+MVI+FR 52-ment),that is, when there is a large difference in stock size (one stock low find the other high). To show the behaviour of the optimal harvest strategy at different stock sizes and/under varying terminal fiAprices, a seriescf optimal harvest strategy curves are presented in Fig-ures 44 and 4 5. Figure 4.4 is based on the two fishery combination, Johnstone Strait plus Fraser River, and is used to show how the optimal strategy reacts when the non-Fraser stock is low and the Fraser stock is high. Figure 4 5 is based on the combination of the Johnstone Strait and Qualicum fisheries, and shows what happens under that philosophy for the condi-tion of low Iraser River stock and high non-Fraser stock. Generally, terminal price is important in determining the utility of the terminal fishery in the optimal solution (Figure 4.4 and 4.5). When the terminal price per fish is below the threshold price, terminal fisheries are not utilized (i.e. the optimal strategy sets the harvest rate to zero in the terminal area). Even in extreme situations, where one stock is very small com-pared to the other, terminal fisheries are not utilized if the terminal price per fish is low. ^ The optimal solution is to harvest harder in the mixed stock fishery. For example, as shown in Figure 4.4, as the terminal price in the Fraser River ilshery is decreased there is a gradual decline in the terminal harvest rates, until there is essentially no terminal fishery when the ter-minal price of 0.3 is reached, When using the non-Fraser terminal fishery (Figure 4.5), the decrease in terminal harvest rates is much more rapid as the price is lowered. When the Fraser stock is low, the mixed stock harvest rates are reduced and terminal harvest is used only as long as the terminal price stays above 0.7 relative to the mixed stock fishery. Below this terminal price, the optimum economic solution is to harvest harder in the mi;:ed stock fishery. This strategy may be due to the variability of recruitment; since low stocks may take longer to rebuild in a highly variable environment. The economic value of waiting for the stock to rebuild is low, and more value is gained by not foregoing catch of the other stock. Figure 4.4. Optimal harvest strategy curves (10%, 30%, and 50% harvest rate) for the John-stone Strait and Fraser River fisheries, over a range of terminal fishery prices, using the case study scenario with 2 controls (JST+FR). F R A S E R S T O C K S I Z E Johnstone Strait fishery 3600 6 ° Fraser terminal fishery g'jj 0 3600 p, : : : : : : : : : : : : : : : : ; ; i i i i i T r f p ^ i i i i i i i i f ? ! ! ! ! ! ! ! ! ; ; ; ! ! • ! i i i i ! ! ! ! ! ! i • ! ! ! i i Nil!!: : : : : : : : : : : : : i i i i i i ; ; ; i i i i i i ! ; ; . ! • ! ! ; ; ; i i i ; ; ; ; ; ; ! ! ! i i i i i i i i i i i ; ; ; ; ; ; ; ; ! ; : : : : : : : : : :•: . :•:: : :•: ! ! ! ! ! ! ! ! ! ! ! ! ; ! ! ! ! : • • : t ; : : : t : ; ' > • • 0.3 - 54 n n n n ri nT< nf uuuu i uuo r Figure 45, Optimal harvest strategy curves (10%, 30%, and 50% harvest rate) tiir the John-stone Strait and non-Fraser terminal fisheries, over a range of terminal fishery prices, using th6 case study scenario with 2 controls (JST+MVI). F R A S E R S T O C K S I Z E Johnstone Strait fishery o : : p^ r*:::::::::: I Non-Fraser terminal fishery, o 11I I I1 I i i 1: I I 1 : 1 I I i : : i 1 ! ! ! ! ! . ! ! !•! i i i i i i i i : : : p s ^ i i i i i i i i i i i . . ^ S - i S j s S A i . i . S i . i i i i i ; Mi : : : i fflliffflMNn : ; : .1 i 1 i M l m i f & i i i i 1 : : : : : : : i i I :I : i fT : i i i i i i i i : : I I i : I : I i i : I i I : I i I i l l i i iiiiiiii-iii-iiiii-ii; i i i i i i i i i i • 55 In summary, there appears to be a threshold price below which terminal fisheries are not utilized in the optimal solution. Under the terminal fishery prices provided in the current case study (e,g, 0.3 relative to the outside fishery price) no terminal fisheries should be utilized. Greater long term economic benefit is derived from allowing the chum salmon to spawn. The threshold price for includingterminal fisheries is different between the Fraser andnon-Fraser stocks. This difference may be a result of a dependence of the threshold price on the stock parameters including the Ricker parameters and the probability of stochasticevents affecting each stock in the same way. These relationships will be explored in the following sectionby varying the stock and recruit parameters cf the case study. 4.4 Sensitivity to the Ricker parameters, The objective cf His section is to determine the relationship between the threshold price in the terminal area and the Ricker stock and recruitment parameters, especially the Ricker a productivity parameter. The iritialhypo thesis is that the utility cf the terminal fishery increases as the differences in the stock and recruitment characteristics increase, that is, one stock becomes more productive than the other. However, in reality, just the opposite occurred: the greater the difference in productivity between stocks, the lower the utility of the terminal fishery. This analysis should make the previous results applicable to wore general situations as well as address situations such as changes in the relative productivity cf stocks through enhancement. The case study scenario is used as the basis for this analysis. Recall that the Ricker B values are in the ratio of 2:1. Seven venations on the case study scenario will be formulated by varying the ratio of the Ricker a parameters from 3:1,2:1,1.4:1,1:1,1:1.4,1:2, to 1:3. Hie size of the increments was determined by trial and error to show change in the.threshold val-ues. For each variation the value in the terminal area will be varied between 0 and 1 in 0.1 increments. For each variation, optimal solutions are determined for three management , philosophies, all of which include the mixed stock fishery in Johnstone Strait and one or more terminal fisheries (e.g. JST+MVI+FR, JST+MVI, and JST+FR). As in the previous sections/ the . average NPV over a probable range around the optimum recmitmcnt (R '±25%) is used as the basis for comparison. Thus Figure 4.3 is recreated for a range of Ricker a parameter combina-tions for the two stocks (see Appendix B, left-top figure on each page). In addition to calculating the average N P V over a probable range of stock sizes around the optimum recruitment(R'±2S°/o), two additional ranges are used and presentedin Appen-dix B for comparison. To provide greater indication cf behaviour at extreme differences in stock sizes, the average NPV over a broader range cf stock sizes, from zero to the Ricker B value (0,0 to B„m.FI!| Bfs), is used. Second, the simple case of the value at the optimumrecruit-ment R'is used. A comparison of the different results suggests that the threshold value is gen-erally insensitive to the range cf stocks used. The general form of the results <m Ap pendix B) parallels Figure 4.3. That is, a threshold value exists for each management philosophy below which the NPV is constant end either no terminal fisheries are utilized or any utilization cf the terminal fisheries does not increase the totalNPVof theresource. Above thisthresholdtheNP V increases geometric-ally, For each variation, the threshold values for the Fraser River terminal fisheiry and the non-Fraser terminal fishery, as determined visually from the figures in Appendix B, are pres-ented m Figure 4.6. The threshold values for eachvariation of Rickw parameters forma boundary signifyinga change in management philosophy (i.e. the use of terminal fisheries). Above the boundary terminal exploitation rates are held at zero and only mixed stock fisheries are used, while below the boundary both the mixed stock, and terminal area fisheries are uti-lized, In Figure4.6 tfiree regions are defined in this mannei', In the upper region no terminal fisheries are utilized. Between the two lines the terminal fishery for the smaller stock (i.e. Fraser) is utilized. And below all the lines, both terminal fisheries are utilized, Generally, Figure 4.6 indicates that terminal fisheries much more applicable to the smaller stock, that is, the Fraser stock. This result suggests th?l when the non-Praser s t o i ic low that the fishery manager should be more conservative in the mixed stock fishery, and h? . much more willing to harvest the Fraser stock terminally. In, contrast, when the Prssi-r stock is low, there is no benefit to the NPV of the resource to adopt a uw-"er^ti w strategy ist '.he mixed stock fishery, as evidenced by the high threshold values iox 'orsniw.'] harvest o' 'he rvrm-Fraser stock. The shape of the boundary lines suggests that the lowest th^' ic ld value occ irs lvhen the stocks have similar productivity (although there is some ske wr.i•<»;> toward the nits e pro-ductive stock). As the stocks become less similar the terminal fa:-her ( threshold value Figure 4.6. Regions cf fishing regimes (e.g. mixed stock fishery only, or mixed stock plus ter-minal) as definedby the threshold value in the terminal fishery in relation to the Ricker a pro-duction parameters (two stocks with different Ricker B values in ratio 2:1; B - 5,000,000, BftKtr-2,500,000). Ratio of Hicker 'a' Values a1 = 1.5 1.0 1.0 0.7 0.7 0,5 0.5 a2 = 0.5 0.5 0.7 0.7 1.0 1.0 1,5 ratio = 3:1 2:1 1.4:1 1:1 1:1.4 1:2 1:3 Price per Fish in Terminal Fishery Relative to Outside Fishery 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mixed Stock Fishery Oniy X Mixed stock plus Fraser Terminal Mixed plus Both Terminal Fisheries increases,. The rate of increase in the threshold value is proportional to die rate at which the stocks become dissimilar. For example, in the left side of Figure 4.6 the productivity of the larger stock is increasing, which increases the dissimilarity cf the stocks, rt suiting in increas-ing threshold values in the Fraser River fisher)' boundary line. But on the right side of Figure 4.6 the small stock is becoming more productive, so the dissimilarity with respect to both parameters is not as gre?t, as reflected by the less rapid increase in the squired threshold val-ues for the Fraser River terminal fisher)'. The shape of the boundary .line for the non-Fraser •58 stock (e.g. the larger stock with respect to Ricker B values) suggests that terminal fisheries for this stock are less beneficial for future value than allowing the fish to spawn and provide future catch. The same analysis was conducted, except with the two stocks having the same Ricker B value, to produce Figure47. Underthis scenario both stocks have the same threshold values for terminal fisheries. The uniform shape cf the boundary line also reflects the similarity of the stocks. It is interesting to note that the 'threshold value is lowestnot when the stocks are exactly the same, but when the productivities are slightly different. Similarities to Figure 4.6 are evident, the threshold value increases proportionately as the difference in the ratio of the Ricker a values increases. In summary, the analyses in this sectionhave shown that the threshold value for fish ing in terminal areas decreases as the stocks become more similar. That is, given two stocks of snriJa? productivity, the fishery manager should be more willing to forego fishing opportuni-tie s in the mixed stock fishery if one stock is much more abundant than the other, than he would if the stockswere markedly differentin productivity. The value of fishingthe abundant stock in the terminal area is increased (e,g, the threshold value is low). In contrast, when one stock is more productive than the other the fishery manager should be less willing to forego a fishery in the mixed stock area (e.g. the terminal threshold value is high). When the terminal price is low, there is more economic benefit to maintaining harvest in the mixed stock fishery tbancurtailingthe fishery for the benefit of the weak stock. Above the threshold terminal price, there is more economic benefit to fishing the abundant stock in the terminal area and reducing the exploitationrate on the weak stock. Terminal price is therefore a major considerationin determining the utility of the terminal fishery in achieving maximum eco-nomic value. — • Note the difference from results obtained under the MSY objective, where terminal price is implicitly not a factor, and terminal fisheries are much more readily utilized to protect the weaker stock in the mixed stock fishery. The difference in the optimal solutions for these two objectives leads me to wonder why the economic objective puts so little weight on the weak stock. Certainty it is not apparent that the optimal solution should lead to the extinction of a Figure 47. Regions of fishing regimes (e.g. mixed stock fishery orJy, or mixed stock s teJ-. minal) as definedby the threshold value in the terming] fishery in relation to the Ricker q pro-duct ion parameters ( two stocks w i t h the same Ricker B values; B ^.pr-o- - 2,500,000, „ 2,500,000). Ratio of Bicker'a' Values a1 = 1.5 a 2 = 0.5 ratio = 3:1 O.r-^ — 1.0 1.0 0.7 0.7 0.5 0 5 0.5 0.7 0.7 1.0 1.0 1.5 2:1 ii 1.41 1:1 1:1.4 U 1:2 t. 1:8 Price per .F.i§ti.iP Terminal Fishery Relative to Outside Fishery 0.1 0. 0.: P,4 0.5 0.6 0.7 0.8 0.9 1.0 Mixed Stock Fishery Only IVll^ ed pigs Both Terminal Fisheries stock. In fact, when a stock gets veiy weak, the exploitation rate is reduced considerably, noted in Figure 4.5. Ccu'd it be a result cf the recruitment variability in each stock? The s e n' sitivity of the optimal solution to this variability will be deteriiuried in the following 4.5 Sensitivity to stochasticprocesses, In addition to the Ricker model, the transition between stock and recruitment to tt\e dynamic program includes stochastic variation in ^ e recruitment for each stock, with at\ a5sO ciated joint probability that can include shared variation between stocks (see Chap'er 2). The -60 j..--'.'.- •:—r. —* • " ,, - -n& -'•-'---.-_-jar.-*- T. " '-''-.-.. -I - - •""--'-. ^ "J-J- ^  ~ Z'S* sensitivity cf the optimal solutionto the pattern cf recmitmentTariability will be determined in tiiis section. It is important to note tha' this analysis deals with fluctuations in recruitment rather than uncertainty about the average recruitment relationship; that broader uncertainty may have significantconsequences on the management strategy (Ludwig and Walters 1982). Recall in section 4.1, that it was determined that moving from a deterministic to a sto-chastic model had a marginal effect on the optimal solution for the one fishery case (JST). As Clark (1985) suggested, simply passing from a deterministicmodel to a stochastic one has minor effects on the optimal solution. Could these seemingly minor changes in the optimal strategy be enough to make the threshold values lor the terminal fisheriesso high? I would expect at least pari of the reason €orhigh threshold values for terminal fishing to be t h r : ari-ability in recruitment, This variability may affect the long term value of the fishery more than it affects the optimal exploitationrates. Consequently, a potential reason for high threshold values is that benefits accruedby variable recruitment are greater tbanbenefitsfrom fishiqg into escapement in the terminal area at reduced prices. If this were so, then modelling the deterministic base case scenario over a range of terminal values should result in a lower thresholdvalue. In this analysis, deterministic refers to application cf the stochasticvector with a magni-tude of 0% variationin recruitment, Consequently, the stochastic variable v in the Ricker model is still being defined by the recruitment variation vector. In contrast, the classical definition of deterministic suggests that the stochastic variable v is not definedexternally, which requires that the Ricker parameters be corrected for the observed variation in the "Ln(R/S) vsS* relationship. These corrections, based on the residual error variance, produce a differentstock - recrui: curve (Figure 2,3), and consequently, a differentoptimalharvest strat-egy. By assuming that the stochasticvector is being maintained, even at a magnitude of'zero, the sensitivity cf the results to this magnitudecan be addressed. A deterministic and stochastic version of the case study scenario are compared in Figure 4.8, usingthe average NPV (over the range of stocks sizes R "±25%, and only for the fishery combination JST+FR) in relation to the terminal fishery price. For the deterministic case, there is veiy little change in the NPV over the full range of terminal prices. Consequently it is not 61 i ^ / dear whether the threshold value is reduced. In addition, there is a smal I differencein the NPV between the two cases. The averageNPV is reduced by 35 percent when switching from the deterministiccase to the 50% stochastic case. To explore this further, the opposite approach is taken, and the recruitment variability is increased to 90% (in the formcf the vector bad=.l, average=l, good-1.9). InFigure4.9, the average NPV (overthe range cf stocks sizesR*±25%, and only for the fishery combination JST+FR) in relation to the terminal fishery price, is presented. It is evident from figures 4.8 and 4.9 that the NPV cf the resource decreases with increased variability. Furthermore, the decrease between the 502 and 90% variability cases is much greater than the decrease between the 0% and 50% variability cases. There appears to be a non-linear relationship betweenNPV and the variability cf recruitment. In contrast, the threshold value for the Fraser River fishery (FR) is similarto the scenario with 50% variability. To determine the relationship between the magnitude cf the recruitment variability a^d the effect on the optimal solution and especially the NPV, the stochasticvector is varied in the base case scenario for a single mixed stock fishery (JST). The resulting average NPV and catch are presented in Figure 4.10, using the same range of stocks as in previous examples. Recall that catch is de f ie d a s the annual catchinyearonecf the dynamic program solution (i.e. the last year when working backward from year 20). There is no significant change in the results from the deterministic case (e.g. magnitude=0) i r t i l the magnitude cf the variability exceeds about 0.5 (withrespect to the NPV). When the magnitude of the variability exceeds this level the NPV decreases significantly. The line cf average catchremains stable initially from the deterministiccase to magnitude of variability cf 0.3. It then decreases, indicating a more con-servativeapproach as variability increases. But when the magnitude of the variability reaches the level where the NPV begins to decrease significantly, then catches r ie quickly , suggesting the policy that managers should not be conservative and take the available catch while they can. Continuing with the comparison, the effect of the stochastic variability on the form of the optimal harvest strategy curves is considered next. The analysis is again based on the base case scenario with two possible fisheries (JST+FR). Three levels of recruitment-variability will be used, the base case 50%, and two extremes of 0% (deterministic) and 90% (applied through the vector .9,1,19). In each case a high joint probability of each stock being affectedin the same way is assumed Also recall the terminal price in the base case is 0.3 relative to the mixed stock fishery price. Figure 4,11 contains the optimalharvest strategy curves for each case. The top row of figures represents the harves t strategy curves for both fisheries combined (total exploitation). Belowthis the strategy curves for each component fishery are presented, first the mixed stock fishery in Johnstone Strait and then the terminal Fraser River fishery. Two aspects of the utilization of the Fraser terminal fishery are evident. First, reiteratingpre-vious results, this terminal fishery is utilized only when the non-Fraser stock is low and the Fraser stock is high, Secund, it is evident that the utilizationcf the terminal fishery decreases withincreasedvariability. In the Johnstone Strait fishery the harvest becomes slightly more conservative as the variability increasesfrom 0% to 50%; similar to previous results such as section4.1 and Figure 4.8(singlefishery case scenario). Note however, that as the variability increases to 90%the form of the harvest rate isocline changes considerably. The change seems to focus or. the non-Fraser stock. There is a significant increase in the mixed stock fishery (JST) harvest whether the Fraser stock is weak or even moderately strong. In this case the optimal strategy very nearly approximates the fixed escapement strategy for the non-Fraser stock alone, the harvest strategy curves are not influencedby the Eraser stock. This seems to coincide with the increase in the average first year catch in Figure 4.10, when the magnitude of the variability increases above 0.7. Note that there is nu increase in the utilization of the non-Fraser terminal fishery under these circumstances, all the increase is placed in Johnstone Strait. At this magnitudeof Variability the optimal solutionfrom this dynamic program suggests it is prudent to take a signifrcantharvest while it is available. mm •••SCfrrfr i 'lS^ r t jsiCw Figure 4.8. Average NPV (over range R"±25%) for cafe study scenario with deviations fixin the averagerecruitmentequal to 0%(upper)and50% (lower). recruitmentvariability = 0% (deterministic) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fish value in terminal area relativeto mixed stock area _ * J S t + F R — JSt+MVI recruitment variation = 50% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fish value in terminal area relative to mixed stock . . . JST+FR .JST+MVI . J S T + M V I + F R 64 4.9. Average NPV (over range R"±25%) f o r case s t u d y scenario w i t h deviat ions i n the a v e r a g e recruitment q u a i to 90%. recruitment variation = 90% Fish value in terminal area relative to mixed stock , _ J S T + F R ^ . J S T + M V I 65 Figure4.10. Average (overrangeR ±25%)NPV andyear onecatchforbasecasescenariowith only one possible fishery (JST, recall previous resultsshowed not terminal fishery at complete base case) and recruitment variability ranging betweenO% and 90%. 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 Magnitude of recruitment variabilitY(l-x,l,l+x) NPV Catch i n vca r 1 BagwtftfnaBiaawiafidaa&Bfi^  H h WlfcllHIt I j-JL^. -»•- a-..' .t.J.. f--,. ' •, Figure 4.31. Harvest strategy curves for the case study scenario, under three magnitudes cf recruitment variability 0%, 50%, and 90%. Harvest rate curves for all fisheries combined is sho^vn first, then the component fisheries, Johnstone Strait and then Fraser River. The non-Fraser terminal fishery is not shown because terminalharvest rates are zero using this base scenario (i.e. terminal price is 0.3). 67" n n n n • n n n n u u 0 u u u u u rAannfaT • i TOiT^^ftirnif Afnrrwrit nwmia»Vl In summary, the optimal harvest strategy curves are only marginally affectedby moder-ate recruitment Variability; the form of fee solution is not much differentbetween the deter-ministic and stochastic base case (magnitude cf variability equals 50%) scenarios. As the mag-nitude of the variability increases the harvest becomes more conservativeintil. a point is reached under extreme annual variation, where the optimal solution suggests a much more aggressive approach to harvesting. At this point it is prudent to take the catch while it is available. The harvest rate isocline appears to reflect a fixed escapement strategy for only the large stock. The NPV of the resource also is only marginally affectedby moderate recruitment variability. But when the magnitude of the annual variation increase beyond the moderate level (in this case study 508) the NP V decreases quickly and substantially. 4.6 Numerical problems with the computational procedure. This section will identify and describe some of the numerical difficultiesencountered in the dynamic programming calculations, While these difficulties precluded a more fully devel-oped generalizationcf the results, there was no apparent impact on the general conclusions formulated. The most apparent problem was the instability of the optimal control strategy deter-mined by the stochastic dynamic program with 2 state and 3 control variables. The optimal exploitationrates determined by the program appeared to "flip" back and forthbetween high and low rates in each of the three differentfisheries. For example, within a smallrangeof stock sizes (e.g, nonFR,FR = 3600,2550 to 3900,2700)the optimal exploitationrates in each fishery vary widely, between 0 percent and 40-60 percent. There may be several explanations for this apparent instability. First, a arall part cf the instability (i.e. changesof 5%)may be due to the discretizationin the control variable. Since it is discretizedin5 percent intervals (e.g. the minimum increment fisheries managers could hope to attain), the dynamic program may be flippingbetween incrementalrates when anintermediaterate is optimal. Second, since there are three control variables, the dynamic program may be finding more than one solution to the optimization. In other words, the values in the region of the optimal solution may be flatwith one control choice providingvery little difference from a very different choice. ' 68 " „ - . . . - n n n n n n n i \ \ . u u u u • u, U^O ' I Fortunately, this instability did not affect the conclusions. 7fhe 'total" outputs in the optimal solution,namely the 'Net Present Valse' and 'total exploitationrate', showedno insta-bility for the case of three control variables 0ST+ MVI+FR), That is, the instability was limited to within a fishery, and when the fishery specific exploitationrates were combined, the overall exploitationrate appeared stable. Furthermore, the instability was evident only for the case with threecontrol variables (JST+MVI+FR). It was not evident for the case using two control variables (e.g. JST+MVI and JST+FR). Consequently, the results from these cases were used to determine patterns of exploitation in the specific fisheries. Had it been critical to examine the fLsheryspecific exploitationrates for the case with three control variables, the instability couldhave been eliminated. One potential method for eliminatingthe instability may be the inclusion of a secondary objective in the optimization. If several solutionssatisfy the first objective, then a secondary objective, such as maximizing sodal values in eachfishery-or simply maximizing the mixed stock fishery harvest, or even maximizing the overall yield, coul d have provided the necessary measure to find a unique solution. Theuse of any these additional objectives was not attempted '69 5. DISCUSSION Price is an important factor in determiningthe optimal allocation cf harvest between sequential fisheries. When the difference in price between the fisheriesis large, exploitationin the terminal fisheries should decrease, and, the remaining stock should be harvested in the mixed stockfishery or permitted to spawn. When the price differenceis relatively low, or when the objective is to maximize the yield, terminal fisheries should be utilized to a greater extent, especially in cases where stock abundances differ markedly from each other. The results also show that the harvest strategy is dominatedby the most productive and I or largest stock. The optimal strategy is less concerned with protecting the smaller or less productive rtock in the mixedstoclc fishery, whichis a different view frommany strategics for chum, Chi-nook, and coho fisheries in B.C. and Washington State. The results and conclusions presented in this thesis are based on a case study involving the Johnstone Strait to Fraser River chum salmon fishery. Because this case study is only a representation of the actual fishery, not all stock and management variables could be included. Some important factors which may affect the applicability cf the results to the actual fishery are noted here. First, the non-Fraser stock used in the case study actually consists cf genetically similar but geographically distinct stocks, which are managed independently in separate terminal areas. Sinceno single terminal fishery can be conductedforthe entire non-Fraser stock,the direct applicability cf the results for the non-Fraser terminal fisheries are limited. However, insight can be gained on the interactionbetween the non-Fraser and Fraser componentsof the chum run. Furthermore, this complication should not affect the applicability of the results to the Fraser terminal fishery and the generalizationsthat canbe made about management of gauntlet fisheries. Secondly, the present analysis focuses on the economic value of terminal fisheries. I have not attemptedto incorporate the social values associated with the Fraser River fishery because cf the difficulty in quantifying these values. Consequently, while the results suggest that the Fraser River terminal fishery provides no economic benefit to the overall long term value ot the resource, there ivuty be some benefit £ social values are included. Considering •7 0 that the price in the Fraser River terminal fishery is already near the thresholdprice for termi-nal fisheries, the inclusion of social values should increase the actual price above the threshold value required for terminal fishing. Theresultsof this thesis provide a framework for the inclusionof social values and subsequentevaluation. In addition to social values, geneticand aesthetic values, andharvestingcosts and management costs may be considered. Third, the case study assumes knowledge 9f the Ricker stock and recruitment parame-ters, as well as in-season stock compositionand stock sizes. Walters and Hilborn (1976) and Ludwig and Walters (1981,1982) suggestmeans of dealingwith uncertainty in the stock and recruitment furctdm, and Fried and Hilbom (1988)usedBayesianmethodsto deal with uncer-tainty in in-season stock assessment. The clockwork harvest strategy recognizes the implica-tions and solutionsnotedby these authors (e.g. learning fromhigh spawning stocks is a stated objective which is achieved by limiting the exploitationrate to 40% for very large htb) . While the results presentedhere ignore these uncertainds;, they should be addressed in future research on management strategies. For example, it might be found that terminal fisheries are more valuable in situationswhere stock size or composition cannot be accurately estimated u±i l the fish are past the mixed f ih ing area; it mightbe best in such cases to reduce the mixed stock fishery catch (useconservativeexploitationrates) and use the resulting stock size estimates, and subsequentterminal area estimates, to operate the terminal fisheries to reach e scapement goals more precisely. In c> 'der to maximize the information from the mixed stock fishery, the nature of the fishery may have to be changed to reduce impact on the run and yet provide information on stock size. it How can the results in this thesis be implemented? The clockwork management system developed for this fishery already provides a useful forum to catalyze discussionamongthe user groups and managers. Through this forum, the overall objective cf the fishery should be more clearly defined. There is a need to identify and explain the implications of different objectiveson the optimumexploitationin the mixedstock and terminal chum fisheries. Part cf this discussion should define economic, social, and other values associated with each fishery. It will be difficult to gain a consensus on the priority cf objectives (economic versus socid) since traditional fishingnatterns have undergone rapid changes in some gear types but not others (e.g. high capitalization cf the seine vessels with new and larger vessels, increased fishing efficiency, mobility, etc.). Given some consensus about thevalue of eachfishery, the results in thisthesiscan provide insight into potential rules for using terminal fisheries. For example, basic rules on when terminal fisheries should be used could be developed using the optimal harvest strategies, and then modified to addressuncertainty in the stock a id recruit-ment estimates and uncertainties in in-season stock assessments and stock composition. In addition, harvest strategies in the Fraser River might reflect not only the social and economic value to local fishermen, but also the value of additional spawners to the total economic value cf the resource (note this is already reflectedin the Fraser harvest strategy to some extent, as surpluses above the escapementgoal are shared between catch and escapement, to provide more information on the stock and recruitment relationship). The dynamic programming techniques used in this thesis can provide further utility by comparing and describingthe implications of different objectives such as MSY, MEY, minimiz-ing the variance of catches, or combinations of these. For example, the fishermen's Union has proposed that a minimum harvest rate be applied within the Fraser River, to provide chum fisheries for local fishermen. Dynamic programming could be used to show the implications of this strategy for the long term value of the fishery, and allow comparisons to other objec-tives and strategies. For example, by using a minimum harvest rate of 15% in the control vari-able for the Fraser PJver terminal fishery, the dynamic programming method indicates that the overall catch in all fisheries would be increased by only 11% (e.g. a reduction in the mixed stock fishery harvest would be used to compensate for the Fraser River harvest) while the Net Present Value of the resource would decrease by 8%. 6. SUMMARY One cf the most contentiously managed salmon, fisheries inBritish Columbia is the John-stone Strait chum salmon fishery. In the past, management actions have oftenresulted from political lobbying by fishermen. It is appacrent that acrimony and the resulting lack cf cooperationhave been a major hindrance to the success cf management in this fishery. A "clockwork" management system was developed for the Johnstone Straitfishery in an attempt to rationalize management methods and improvethe relationship 'between fishermen and DFO fishery managers. Through the clockwork, strategicobjectives are developed and attained using a steppedharvest rate strategy and an objective process of in-season decision makiig'. The clockwork also provides a forum through which accountability ior managment actionsis determined. The clockwork generally has been successful in conservation terms; harvest rates have been reduced .(from pre-clockwork levels and escapementshave increased considerably. However, two problems art identified. First, there is continuing debate between knowl-edgeable fishermen and DPO managers over the stock assessments made by DFO biologists arid used as a basis for decisionmaking in the clockwork. Hie solution to this problem lies in the ability of managers to replace simple intuition with defensible so 1 enti 11 cmethods for esti-mating abundance from in-seasonindicatctrs. Consequently, a methodology cf in-seasonstock assessment has been developed which incorporates test fishing and commercial catch data. While this methodology has proven reasonably precise, the resulting stock assessmentswill always be open to criticism (due to the high degree cf variability in the stock assessment infor-mation), Consequently, it wi 11 take time to build the trust and cooperation of the fishermen, which wEL be required for the clockwork to succeed in the long term. The second problem became the focus for this thesis. Two aspects of the fishery, namely its gauntlet nature mid the decrease in value of the fish as they reach freshwater in the termi-nal area, have led to vigorous debate among fishermenover the utility of the Fraser River ter-minal fishery. Tlhis thesis uses dynamic programming methods to determine optimal harvest strategies for a cast; study based on the Johnstone Strait to Fraser River chum salmon gauntlet fishery. The case study variables include two stocks representing the Fraser and non-Fraser stocks, three possible fisheries (including one mixed stock and two terminal fisheries), recruit-ment variability (based onhistoric data), a Johnstone Strait price per fish of $20, a terminal price per fish of 0.3 cf the mixed stock fishery price, and a discountrate of 1 Opercent. The main objective is to maximize the long term value of the resource. The ability of the different combinations of fisheries (e.g. mixed stock only, two terminal fisheries, a mixed stock plus one or two terminal fisheries) to maximize the long term value of the resource is compared. The results indicate that the Fraser River terminal fishery provides no net economic benefit at currentfish prices, exceptwhenthe non-Fraser stockisvery low relative to the Fraser stock. In fact, a managementphilosophy based only on terminal fisheries would significantly reduce the long term value of the resource. The mixed stock fishery is required to maximize longterm value. However, when the objective is to maximize yield, ter-minal fisheries become an essentialcomponent. Although Paulik et al. (1967) concluded that using only terminal fisheries produced the MSY, the analysis in this thesis showsthat MSY can be achieved using a combination of mixed stock and terminal fisheries. The differencjnn utility of the terminal fisheriesunder the MEY and MSY objectives showsthe importance of defining the overall objective for the fishery. The utility of the terminal fishery depends on two factors: the relative size of the stocks, and the price paid for the fish in the terminal area. With the current decrease in price & m the JohnstoneStrait to the terminal fisheries(i.e. terminal price is about 30%of the mixed stock fishery price), the Fraser River terminal fishery does not provide any benefit to the long term value (NPV)of the resource. The threshold price (i.e. the price at which an increase in the overall value of the resource is realized) for the Fraser River terminal fishery is about 40% of the mixed stock fishery price. TheNPV is constant below the threshold price and increases geometrically above the threshold price. The price per fish in the terminal area is obviously an important consideration in the management of ti ischum fishery. Generally, the optimal harvest strategy for the Johnstone Strait mixed stock fishery par-allels a fixed escapementstrategy when the stocks are in the ratio of 1:1. When the ratio dif-fers substantially feml:l (one stockhigh and the other low) the optimal strategy is to harvest harder than the fixed escapement strategy. It is under such conditions that terminal fisheries are utilized in the optimal harvest strategy, v . . The threshold price for initiatingterminal fisheries is dependent on the Ricker stock and recruitment parameters. As the productivity of the stocks becomes more similar, the threshold price for initiating terminal fisheries decreases. That is, given tv/0 stocks of similar productiv-ity, the fishery manager shouldbe more willing to forego fishing opportunities in the mixed stock fishery when the stocks differ substantially in abundance (onestock is low and the other high),tbanhe would if the stocks were markedly different in productivity, Thevalue of fish-ing the abundant stock in the terminal area isincreased, Incontrast, when one stock is more productive tbanthe other the fishery manager shouldbe less willing to forego a fishery in the mixed stock area (e.g. the terminal threshold value is high) in order to conduct a terminal fishery on a large terminal run. There is greater value in allowing terminal runs to spawn and contribute to a futuremixed stock fishery. The threshold price is also sensitive to the Ricker B parameter. As the difference between the Ricker B values of the stocks increases, the differences between threshold prices for the terminal fisheries increase as well. The threshold price of the terminal fishery for the larger stock (higher Ricker B) increases. The result is that the fishery manager should be less willing to harvest the large stock in the terminal area, unless the price per fish in the terminal fishery is high. Recruitment variability affected the results only when the magnitude of the variability was high, above 50% (standard deviation). Below this level there was little effect on the value of the resource or the harvest strategy. Above this level, the NPV of the resource decreased quickly as it became less worthwhileto reduce the immediatecatch and value from the mixed stock fishery (in order to protect against over-exploitation) while providing a hedge against under-exploitation in the form of a terminal fishery. 7. LITERATURE CITED Allen, K.R. 1973. T)te influence of random fluctuations in the stock recruitment relation on the economic return from salmonfisheries. Cons. Int. Explor. Mer. Rapp. 164:351-359." Anon. 1963. Annual Report to the Salmon Management Committee on the status of the chum salmonstoc/(s of the Johnstone Strait Study Area and on prospects for 1963. Department of Fisheries and Oceans, Vancouver, B.C, Cirmlar-, August 1963. Anderson,AD. 1977. The1976returnofchumsalmonstoctetotheJohnstoneStrait-Fraser River Study Area, and prospects for 1977. Can Dep. Fish. Pac. Reg. Tech Rep. Pac / T 77-12. Anderson, AD. and TD. Beacham. 1983. The migration and exploitation of chum salmon stocks cf the Johnstone Strait - Frase River Study Area, 1962-1970. Can. Tech. Rep E d c AquatSci. 1166:125pp. Anderson, L.G. 1977. The economics cf fisheries management. Baltimore: Johns Hopkins Press. Beacham, TD. 1984. Catch, escapement, andexploitationof chumsalmon inBritish Colum-bia, 1951 -1981. Can. Tech. Rep. Fish. Aquat. Sci. 1270:201p. Beacham, TD, RE. Withler, and AP. Gould. 1985. Biochemical genetic stock identificationof chumsalmonin southern British Columbia. Can. J. Fish. Aquat. Sci. 42:437-448. Beacham, TD. andP. Starr. 1982. Population biology of chum salmon, Oncoihyiichus keta, from the Fraser River, British Columbia. Fish. Bull. U.S. 80:813-825, Bellman, R, and S. Dreyfus. 1962. Applied dynamic programming, Princeton Univ. Press, Princeton, N.J. Bellman, R. 1961. Adaptive control processes: a guided tour. PrincetonUniv. Press, Prince-ton, N.J. Charles, AT. 1983. Optimal fisheriesinvestmentunder uncertainty. Can. J. Fish. Aquat. Sci, 40:2080-2091. Charles, A.T., andW.J. Reed. 1985. A bioeconomic analysis of sequentialfisheries: competi-tion, co-existence, and optimal harvest allocationbetween inshore and offshore fleets. Can. J. Fish. Aquat. Sci, 42:952-962. Clark, C.W, and G. Munro. 1975. The economics cf fishing and modern capital theory: a sim-plified approach. J. of Environmental Economics and Management. 2:92-106. Clark, C.W. 1976. MathematicalBioeconomics: the optimal management of renewable resources. A Wiley Interscience Publication, John-Wiley and Sons. 352 p, Clark, C.W. .1985. Bioeconomicmodellingandfisheriesmanagement. A Wiley Interscience Publication. John-Wiley and Sans. 291 p, • v Crutchfleld, J. A. 1961. An economic evaluation of alternative methods of fishery regulation., J. of Law and Econ. 4131-143. Crutchfield, J.A 1975. An economicview of optimum sustainedyield. inP.M. Roedel [ed.] Optimum sustainableyield as a concept in fisheries management. Am. Fish. Soc Spec. Publ. 9, Washington, D.C. Crutchfield, J. A 1979. Economic and social implications of the main policy alternatives for controllingfishingeffort. J. Fish. Res. Board Can. 36(7);742-752, Cushing, D.H. 1974. Alink between science and management in fisheries. Fi.4i.Hull. U.S. 72:859-864. Deriso, Richard. 1984. Risk adverse har vesting strategies, in Resource Management, Proceed-ings of a Workshop in Ashland, Oregon, 1984. M Mangel (editor). Lecture Notes in Biomathematics61. Springer-Verlag. 138p. Fournier, D.A, T.D.Beacham, B,E,Riddell, and C.A.Busack. 1984. Estimating stock composi-tion in mixed stock fisheries using morphometric, meristic, and electrophoreticcharac-teristics. Can. J. Fish. Aquat. Sd. 41:400-408. Fried, S JXL ^nd R Hilbom. 1988. In-season forecasting cf Bristol Bay, Alaska, sockeye salmon abundance using Bay esian probability theory. Can J, Fish. Aquat. Sci. 45:850-855. _ Gordon, H. Scott. 1953. An economic approach to the optimum utilization cf fishery resources. J. Fish. Res. Board Can. 10:442-457, Gordon, H Scott. 1954, The economic theory of a common properly resource: the fishery. J. Political Economy 62124142. Gulland, J.A. 1972. Can a study of stock and recruitment aid management decisions? Rapp. P.-v. Reun. Ccns. perm. int. Explor. Mer, 162368-372. Healey, MC. 1984. Multiattribute analysis and the concept cf Optimum Yield. Can. J. Fish. Aquat. Sci. 41:1393-1406. Hilbom, R. 1976. Optimal exploitationof multiple stocks by a common fishery: a new meth-odology, J. Fish. Res. Board Can, 33:1-5. Hilbom, R. 1984. A comparison cf harvest policies f c mixed stock fisheries, in Resource Management, Proceedings of a Workshop in Ashland, Oregon, 1984. M. Mangel (edi-tor). -Lecture Notes inBiomathematics 61. Springer-Verlag. 138p. Hilbom, R. 1985. Apparent stock recruitment relationships immixed stock fisheries. Can. J. Fish. Aquat. Sci, 42:718-723. Hilbom, R. 1985. Simplifiedcalculationof optimum spawning stock size from Ricker's stock recruitment curve. Can. J. Fish. Aquat. Sci. 42:1833-1834,. Hilborn, Ray. 1975. Expected changes in stock recruitment parameters when exploiting mixed stocks of salmon. IIASA report. , Hilbom, Ray. 1978. Stepping through dynamic programming Abeginners guide to stochas-tic dynamicprogramm'tng for resource management. Unpublished manuscript from IARE. Huppert, DD. 1979. Implications of multipurpose flestsnnd mixed stocksfor controlpoli-aes. J. Fish Res. Board Can. 36:845-854. Igarashi, H, andK. Zama. 1953. Biochemicalstudiescf the salmon, Oncotiiynchus kcta: I. The changes in the chemical components of the body tissues during the spawning migration. Bull. Jap. Soc. Sd. Fish. 18(11):6-10. Keeney, R 1977 . A utility function for examining policy affezting salmonin the Skeena River. J. Fish. Res. Board Can 34:49-63. Larkin, PA, and WE. Ricker. 1964. Further information on sustained yields from fluctuating environments. J. Fish. Res. Bd Can. 21(l):l-7. Larkin, RA 1977. An epitaph for the concept of maximum sustainedyield. Trans. Am. E d c Soc. 1061-11. Lord, Gary E. 1973. Characterizationcf the optimum data acquisition and management cf a salmonfishery as a stochastic dynamic program. Fish. Bull. U.S. 71(4);1029-1037, Lovejoy, William S. 1988. Effect cf stochasticity on optimal harvesting strategies in some lumped parameter fishery models. Can. J. Fish. Aquat. Sd. 45:1789-1800. Ludwig, D. 1982. Harvesting strategies for a randomly fluctuatingpopulation. J. Ctns. int. Explor, Mer. 39(2):168-174. Ludwig, D., andC.JWalters, 1981. Measurementerrors and uncertainty inparameier esti-mates for stock and recruitment, Can. J. Fish. Aquat. Sd, 38:711-720. Ludwig, D. ,and C.J.Walters. 1982. Optimal harvesting with imprecise parameter estimates. Ecol. Modelling, 14:273-292. Luedke, W.H 1985. Analysis cf the upper Johnstone Strait test fishirigdata. Unpublished report prepared for the Department of Fisheries and Oceans, 3225 StephensonPoint Road, Nanaiiro,B.C. V9TlK3;49p. Luedke, W.H, 1986. A standardizationof the catch and effort data from the commercial chum salmon fisheries in Johnstone Strait, 1972-1985. Unpublished report, Department of Fisheries and Oceans, 3225 StephensonPoint Road, Nanairro,B.C. V9T 1K3; 5p. Luedke, WH, AP. Gould, andMK. Farwell. 1988. A review and analysis cf the 1986 Chum salmon season in the Johnstone Strait-Fraser River Study Area. Can.Tech. Rep. Fish. Aquat. Sd. 1604:56p, Luedke, WH. and AD. Anderson. 1989. A review and analysis of the chum genetic stock identification program in southernBritish Columbia Unpublished working paper of the Pacific Stock AssessmentReviewCommitteeS89-14, April 1989. Mendelssohn, R. 1980. Asystematicapproachto determining mean-variance tradeoffs when managing randomly varying populations. Math Biosci. 50:75-84. Mendelssohn, R 1980b. Discount factors and risk aversion in managing random fish popula-tions. Can. J. Fish. Aquat. Sci. 39:1252-1257. Mendelssohn, R. 1980c. Using Markov decisionmodels and related techniques for purposes other than simple optimization: analyzingthe consequencesof policy alternatives on the management cf salmon runs. Fishery Bull. 78:35-50, M11a-; R T 1976. North Americancrabfisheriesregulations and their rationales. Fish. Bull. U.S. 74:623-633. Odum, WE. and S.S. SkjeL 1974. The issue of wetlands preservation and management: a sec-ond view. Coastal Zone Manage. J. 1:151-163. Palmer, RN. 1972. Fraser River chumsalmon. Can. Fish. Serv. Pac. Reg. Rep. 1972-l:284p. Paulik, G. J.A.S. Hourston, and P.A.Larkin, 1967. Exploitationof multiple stocks by a com-mon fishery. J. Fish Res. Bd Can. 24:2527-2537. "O Pearse, P.H, 1982. Turning the tide: anewpolicy for Canada's Pacific fisheries. Commission on Pacific Fisheries, Policy Report. 292p. Peterman, RM 1981. Form of randomvariation in salmon smolt-to-adult relations and its influence on production estimates. Can. J. Fish. Aquat. Sci. 38:1113-1119. Press, W.H., BP. Flannery,S.A.Teukolsky/and W.T. Vetterling, 1986. Numerical Recipes; The Art of Scientific Computing. Cambridge University Press. Pringle, JD. 1985. The human factor in fishery resource management. Can. J. Fish. Aquat. Sd. 42:389-392. Reed, W.J. 1974. A stochastic model for the economic management of a renewable animal resource. Math. Biosci. 22:313-337, Reed, W.J. 1979. Optimalescapementlevels in stochastic and deterministic harvesting mod-els. J. Environ Econ Manag, 6350-353. Reed, W.J. 1981. Effects cf environmental variability as they pertain to lisheriesxnanagement, inK.B. Haley (Ed), Applied Operations Research in Fishing. NATO Conference Series 11-Systems Science, Vol, 10, Plenum, New York, pp. 69-80. Ricker, W.E. 1954. Stock and recruitment. J. Fish. Res. Board Can. 11559-623. Ricker, WE. 1958. Maximum sustainedyields from fluctuating environments and mixed stocks. J. Fish. Res. Bd Canadal5:991-1006. . '' ; ' ' Ricker, W.E. 1973. Two mechanisms that make it impossible to maintain peak period yields from stocks of Pacific salmon and other fishes. J. Fish. Res. Board Can. 30:1275-1286. Roedel, P.M. (ed.) 1975. Optimum sustainedyield as a concept in fisheries management. Am. Fish. Soc. Sjpec.Publ. 9:89p. Shahman,L.A 1974. Toward effectivepublic participation in coastalzone management. Coastal Zone Manage. J. 1:197-207. Spivey, W Allen. 1973. Optimizationin complex management systems. Trans. Amer. Fish. Soc. 102(2):492-499. Starr, P., and RHilbom. 1988. Reconstruction of harvest rates and stock contribution in gauntlet salmon fisheries: applicationto British Columbia and Washington sockeye (Oii-cotiiynchus nerkn). Can. J. Fish. Aquat. Sd. 45:2216-2229, Tautz, Arthur, and P A Larkin. 1969. Some effects of simulated long term environmental fluctuationsonmaximum sustainedyield. J. Fish Res. Bd. Can. 262715-2726. Walker, RA. 1973. Wetlands preservation and management on Chesapeake Bay: the role cf science innatural resource polity. CoastalZone Manage. J. 1:75-101. Walters, C.J. 1975a. Optimal harvest strategiesfor salmonin relation to environmental vari-ability and uncertainly about production parameters. J. Fish. Res. Board Can. 32:1777-1784. Walters, C.J. 1975b. Optimalharvest strategies for Pink Salmonin the SkeenaRiver: Acom-pressedanalysis. Proceedings of a workshop of saLronrnanagernent..IIASA. Austria. Feb 1975. Walters, C.J. 1978. Some dynamic programming applicationin fisheries management, in Dynamic Programming and its applications, ML. Puterman (ed.). Academic Press. Walters, C.J. 1984. Methods of managing fisheries under uncertainly, in R.M. May (Ed.), Exploitation cf Marine Communities. Dahlem Konferenzen, Springer-Verlag.Berlin, 263-274, Walters, C.J. 1985. Bias in the estimation of functional relationships from time series data. Can. J. Fisk Aquat. Sci, 42147-149. Walters, C.J. 1986. Adaptive Management cf Renewable Resources, MacMillan Publishing, New York. 3'/4p, Walters, C.J.andR. Hilborn, 1976. Adaptive control cf fishingsystems. J, Fish. Res. Board Can. 33145-159. Walters, C.J. and R. Hilborn, 1978. Ecological optimizationand adaptive management. Ann. Rev. Ecol. Syst. 9:157-188. Walters. C..T. andD. Ludwig. 1981. Effects of measurement errors on the assessment of stock-recruitmentrelationships. Can. J. Fisk Aquat. Sci, 38:704-10. Wickett, W.P. 1958. Review of certain environmental factors affecting the production of pink and chum salmon. J. Fish. Res. Bd Can. 15.LLQ3-1126. "80 Wong,F.Y.C. 1982. Analysis of stock-recruitment dynamics cf British Columbia salmon. MSc thesis, University cf B.C. 221pp. Zama, K,andH.lgarashi, 1954. Biochemicalstudiescf the salmon, Oncorliynclms keta: II. The changes in the components cf the depot fats during the spawning migration. Bull. Jap. Soc. Sci. Fish 19(11):1087-1091. '81 8. APPENDICES 82 Oil Appendix A Clockworkin-seasoninformation bulletin and stock assessment methodology pub-lished for distribution to fishermen _ • • n n n n vrrn o iv ^ u u u u (i ru Li" i a THE 1985 CLOCKWORK FOR MANAGING THE JOHNSTONE STRAIT-FRASER RIVER CHUM FISHERIES by The Johnstone Strait-Fraser River Chum Advisors September 1985 84 THE 1985 CLOCKWORK MANAGING THE JOHNSTONE STRAIT-FRASER RIVER CHUM FISHERY The clockwork approach describes a system of managing the fishery by a predetermined and clearly stated management plan formulated by all the user groups. During the season "the clockwork" determines the management decisions; decisions like how much fishing will be allowed. This booklet presents a short explanation of the clockwork formulated to manage the Johnstone Strait and Fraser River chum fisheries. The clockwork will bs described, both in terms of what it is and ' how it works. Included in this description are the rules by which the chum fisheries will be managed. In addition this booklet presents a week by week guide to the inf,eason management of the chum fisheries. WHY tO WE NEED THE CLOCKWORK? The clockwork helps solve a basic fisheries problem ~ the lack of communication and cooperation between fishermen and DFO. Fishermen often complain they don't know how or why decisions are made iir»the management of a fishery. On the other side, DFO spends a lot of time and money defending and explaining management actions taken during the season, Many actions have not been properly doeument-.pd and as a consequence it has often been difficult to learn from past experiences. A more rational way of managing is using the clockwork approach. The clockwork requires fishermen, processors, and DFO to carefully decide on a set of rules to manage the fishery by, before the season begins. Then as the season progresses the rules will dictate how and when management decisons will be made; whether commercial fishing is allowed or conservation measures should be implemented. The clockwork is a written agreement, between all user groups and the Department, that must include the following elements: 1. A clear set of objectives, most importantly the escapement 'goal, • 2. A program of data collection that will provide information necessary for inseason estimates of run size and stock composition. ... . 3. An accurate, reliable set of methods to estimate run size and stock composition. 4. A set of rules stating how the objectives will be achieved; how ,estimates of run size will be used to determine openings; when and how catches will be allocated to the different fishing areas; in general, everything necessary to make decisions and manage the fishery will be written in the rules., What can we gain from using the clockwork? We .can gain more rational, well managed fisheries. Fishermen will become-more involved in the management, decision making process. This will lead to greater 85 awareness cf problems in managing the fishery and the stocks, and as the people closest to the resource be able to offer useful advice.-In addition, fishermen will be able to use the clockwork, to determine potential fishing patterns and so plan their season accordingly. DFO also can benefit from the clockwork, Documentation of the data collection and analysis methods will provide DFO more feedback and help to identify weaknesses that require further study. In short, the clockwork will provide an opportunity to rebuild the salmon stocks and improve inseason management. HOW TO GET INVOLVED? The clockwork emphasizes that everyone using the resource should have a say in its future. All user groups are involved in formulating the clockwork through representatives on the Johnstone Strait-Fraser River Chum Salmon Advisory Committee. The committee is responsible for the formulation of the clockwork before the fishing season begins and it's evaluation when the season is over. Membership is presently not fixed, but includes seiners and gillnetters representing the major fishing areas in the south coast, and a processor. The committee also includes DFO representatives. THE OBJECTIVES OF THE CLOCKWORK If the clockwork is to succeed, a clear set of objectives must be agreed to by the advisory committee. The overall objective expressed by the Johnstone Strait —Fraser River Advisors at a 1962 UBC workshop was "to achieve the maximum potential of the resource and maximum long term benefits to the fishermen." Subsequently, the following objectives were established by the Johnstone Strait-Fraser River Advisoi'5 for chum salmon in what DFO calls the Study Area, which includes Johnstone Strait, the Strait of Georgia, the Fraser River and all other tributaries„ 1. Define the optimum escapement goal as 2,500,000 wild chums. 2. Reach this escapement goal within three cycles .(12-15 years). 3. Learn as much as possible about, the productivity of the stocks. 4. Allow limited fishing at low stock sizes. 5. Stabilize the annual catch. The first and most important objective is the escapement goal (or how many fish do you let spawn?). Since it was unlikely that objective 1 could be achieved in the near future without undue hardship oft the fishermen, a lesser goal was establi.shed for the years 1.984 to 1986. The committee agreed, that an escapement of at least 1,800,000 wild chums must be achieved in the Study Area, to ensure an escapement greater than the current average. More over., the advisors agreed that a minimum escapement of 500,000 wild chums is required in the Fraser River. This means no fishing until we have - a wild run size of 1,800,000 chums. But "enhanced" or "hatchery" chums are .mixed in with the wild ones; in 1985 about 700,000 "enhanced" chums are expected to 86 return. In addition it' « e*'r>»r»-i that about 100,000 "American» chums will pass through Johnstone Strait. Consequently, to achieve the current escapement goal a total run through Johnstone Strait of 2,600,000 chums is necessary before commercial fisheries can be opened. The time required to achieve objective 1 varies between 5 and '30 years depending on the harvesting strategy (eg. constant 30% harvest rate, fixed escapement, etc.). After reviewing each strategy the advisors agreed that a reasonable time frame to achieve objective I would be three cycles or about 12 to 15 years. Furthermore, the advisors established objective 3 to determine the maximum potential and productivity of the resource; that is, how big could the run and the annual catch become? This would be achieved by allowing greater escapements when the stock size is very large., A major concern of the advisors was the benefit the fishermen could derive from the resource. Although the long term benefits should be maximized, the short term needs should not be overlooked. Objectives 4 and 5 address these concerns. From these objectives the advisors formulated the following rules to manage the Johnstone Strait chum fisheries. Rules were al&p determined for the Qualicum and Fraser River fisheries (Appendix 2). MANAGEMENT RULES FOR JOHNSTONE STRAIT The following rules have been collectively agreed to by the Johnstone Strait ~ Fraser River Chum Salmon Advisory Committee and so become the guidelines by which the chum salmon fishery will b4 managed. At the end of the season the performance and suitability of these rules will be evaluated by the committee and the necessary1 changes made. RULE l. The desired minimum wild stock escapement is 1,800,000, Including expected stocks of enhanced and American chums a total run of 2,600,000 .chums through Johnstone Strait is required before fishing is allowed. RULE 2. The catch of chum salmon will be determined by the South Coast Harvest Plan, which gives the desired harvest rates and probable number of openings after the third week of September. South Coast Harvest Plan Total stock size Allowable total harvest rate Probable number of openings 0 - 2.6 million 10%* 0 2.6 - 3.3 20% 1-2 openings 3.3 - 4,8 30% 2-3 openings 4.8 up 40% 4 or more * 3 to 10% of each years total run is caught in test fisheries, native fisheries, and early commercial fisheries. RULE 3. DFO presently estimates that the greatest production of wild chum salmon in the Fraser River would result from about 700,000 spawners. This is called the optimum escapement. It has been a difficult goal to achieve, only once in the past 20 years have 700,000 chums spawned in the Fraser River. To ensure that the present stock abundance is protected while permitting some harvest in mixed stock areas, the minimum escapement is initially set at 500,000. To achieve this goal and still provide commercial fisheries the following-rules are used. A) No commercial openings in Johnstone Strait or the Fraser River are possible unless the total size of the Fraser River "escapement is greater than 500,000. B) The Fraser River chum fishery will ope:i only if Johnstone Strait opens after the 3rd week of September. The timing of these openings is determined by the clockwork, but in the Fraser River only after the International Pacific Salmon Fisheries Commission relinquishes control in midOctober. The Cottonwood test fishing information will determine , the Fraser River fishing pattern to target on the strongest Fraser stocks. 88 RULE 4. Chum salmon abundance in Johnstone Strait will be assessed during the season by the following methods: A) A preseason forecast will be presented to the Advisors before July 31,1985. This preseason forecast will be used until the end of the third week of September. B) The stock estimate will ba revised at the end of the third week of September. The nev estimate will be based on commercial chum catch during the 3rd week of September. C) The next inseason update of stock size will be at the end of the first week of October, and will be based on test fishing results. D) At the end of the 2nd week of October, test fishing results will again be used to revise the stock estimate. Each new stock size estimate is an average of the most current and past estimates. RULE 5. The protection of weak stocks will be accomplished by closing specific terminal areas and adjusting the timing of Johnstone Strait openings to minimize the impact on the weak stocks. The harvest of strong stocks not fully exploited in Johnstone Strait may be accomplished by terminal fisheries. RULE 6. The Johnstone Strait openings will be conducted under the following guidelines. A) Openings are minimum 24 hours, for gillnets and seines. B) An opening in the third week of September is necessary to provide information for the first inseason update of run size. Openings during the first three weeks of September are a result of pink abundance in odd years or sockeye abundance during the high cycle of the Adams River run. C) Openings under the South Coast Harvest Plan start following the third week of September. D) The following areas in Johnstone Strait will be opened under the plan. Area 12: full openings with no'ribbon boundaries. Area 13: full openings with no ribbon boundaries, RULE 7. The following test fishing program will be conducted in Johnstone Strait in 1985. A) Test fishing in Area 12 will operate 3 days per week during the first three weeks of September: from the 3rd week of September through the 4th week of October test fisheries will operate 5 days per week. B) Test fisheries will operate simultaneously in Areas-12 and 13. Two seine boats will be used in the Area 12 test fishery, and one seine vessel in the Area 13 test fishery. Johnstone Strait seine boats will be used. C) The sites to be fished in each area are: Area 12: Double Bay/Blackfish Sound area (see the attached map). Area 13: Camp Pt. To Deep Water Bay arD) Each site must be fished a minimum of 2 times per week, the time and tide at which each is fished is left to the skipper to decide. E) If disrupted by weather, mechanical failure, etc. as many locations as possible will be fished in the remaining time. F) Test catches are estimated by a DFO representative and the skipper; if there is substantial disagreement between the two The Area 12 (Upper Johnstone Strait) test fishing sites. 1 Big 3«y 2 T h a B l u f f 3 B l o w H O I * 4 B l u a l l n a 5 B o l d P o i n t « C h i n a t o w n 7 C r a c r o l t Po in t 8 O o u b l o B a y 8 K a l p P o i n t 1 0 M« r r y Q o Round 1 1 P a r s o n B a y 1 2 S l w a i h R o c k 1 3 T h a B a n k W h l t a R o c k s I S V ' h l t a B a a c h 1 8 B l ' n k h o r n P a n l n a u l a 1 7 R e t u r n Po in t I B F r a ^ h w a t a r B a y 1 0 Izuml R o c k 2 0 B a u x a C o v * ' - ' « ; T ' l a g r a p h C o v a 2 2 B t l v i * C o v a 2 3 N l m p k U l R l » a r 3 * B l a c k l i s t ! S o u n d i estimates the catch will be hauled on board and counted. G) At the eud o£ each week the average catch per set for that week will be calculated and released to industry by Friday 3pm. DFO revised stock estimates will also be released at this time. RULE 6. Stock composition in Johnstone Strait will be determined at the end of the season, from weekly samples taken from the testfishery, and analyzed elactrophoretically at the Pacific Biological Station. Each week 150 fish will be taken for the analysis. This information will be used at the end of the season to determine relative stock strengths and run timing on a weekly basis. THE COMPONENTS OF THE CLOCKWORK The clockwork for the Johnstone Strait chum fisheries consists of two components. On the'one hand are the tools used by DFO; the catch and effort from past years, current catch and effort, and test fishing results are used to estimate stock size, while electrophoresis is used to determine stock composition. The other component of the clockwork consists of the objectives and rules produced by industry and government, combining their varied perspectives, concerns, and knowledge to produce a mangement plan acceptable to all. The components of the clockwork are determined before the fishing season begins. Once the season starts the management and structure of the fishery are determined by the clockwork, not by D?0, fishermen lobby groups, or anyone else. DFO has a specific job to do as outlined by the clockwork. They collect information from the commercial and test fisheries to produce estimates of stock size and stock composition. The results are fed through the rules to determine how much fishing is allowed. This happens each week, like clockwork, as pictured in Figure 1. Figure 1. The clockwork, as it runs each week. Finally, after the season is over, fishermen and DFO must evaluate the success of the clockwork that year, Were the stated rules sufficient to achieve the desired objectives? Were the escapement goals reached? Did anything unexpected happen during the past season that requires change or amendment to the rules? Perhaps a group of independent technical experts could produce the evaluation, based on input from the concerned groups. The Advisory Committee could then, respond to their conclusions by modifying the clockwork accordingly. Past data f Run s i z e es t imate Commercial . ca t ch I 92 HOW DOES THE CLOCKWORK RUN? The clockwork starts at the beginning of September with a preseason forecast, which gives us an idea of what will happen durincf the coming season. During the first three weeks of September, wd usually expect pink or sockeye fisheries in Johnstone Strait. At thS end of the third week of September, the incidental chum catch during the last three weeks is used to calculate tbe first inseason estimate of stock size. This "3rd week of September" estimate is applied to th6 South Coast Harvest Plan (Rule 2) to determine the allowable catch remaining and the number of openings we can expect. In addition to the commercial catch, a test fishing progranf operating during September and October provides information used to estimate stock site after the first week of October. A revised estimate can be determined each week from this information and fed through the South Coast Harvest Plan to see if any fish are left to be caught. Appendix 1 shows a simplified version of the stock assessment methods that dictate how the fishery is managed. With a minimum of effort anyone can make a rough estimate of the stock size. The estimate will give you an idea of the status of the chum stocks as^a whole and how much fishing will be allowed in Johnstone Strait. Work through each section only at the proper time, following the timetable shown below. DATE SECTION OF CLOCKWORK TO USE SEPT. 1-t4 SEPT. 20-28 OCT. 4-6 SECTION 1 SECTION 2 SECTION 3 OCT. 11-13 OCT. 18-20 SECTION 4 AND 5 SECTION 5' APPENDIX 1 A FISHERMEN'S GUIDE TO ESTIMATING CHUM SALMON STOCK SIZE AND PROBABLE FISHING PATTERNS One of the benefits of the clockwork is the opportunity for fishermen to determine stock size and probable fishing patterns on their own. This is accomplished by using the calculation sheets provided in the following sections, and the rules written above. The only information needed that is not provided are the weekly commercial or test fishing catches, and these are available through any DFO office. Once the catch is known, just fill in the blanks to calculate a rough estimate of stock size; then using the rules determine what the allowable catch is for the year. If we haven't taken all the allowable catch, an opening is likely. The methods described here have proven to be the most reliable methods each week. They produce an estimate of the size cf stock and whether or not an opening can be expected. The following sections -4,re specific to the 1985 version of the clockwork. At the end of the season new data is used to update and refine these methods. No changes can be made during the season. SECTION 1...Using the preseason forecast. The preseason forecast of run size is determined by DFO, before the season begins. Using this forecast, fishermen can determine the general fishing pattern for the year. Use the South Coast Harvest Plan in Rule 2 to determine the harvest rate in item 2, the number of openings we can expect on item 3, and the allowable catch for this year on item 4. < The next step is to calculate how much of this allowable catch will be taken during the season in non commmercial fisheries. Each year 2-5% of the total run is taken in testfisheries and native food fisheries; an average 3% is used to determine the catch on item 5. The allowable catch remaining is then calculated on item 6. If there is some allowable catch remaining a fishery can be expected. 94' ESTIMATING CHUM SALMON STOCK SIZE and PROBABLE FISHING PATTERNS IN JOHNSTONE STRAIT Section l...Using the preseason forecast. REQUIRED STOCK SIZE 2 ,t>00,ooo STOCK ESTIMATE IOO 1. Preseason forecast. — — APPLYING THE RULES , , „ . 2. Desired harvest rate from the South Coast ^ q o ^ Harvest Plan (see Rule 2 ) . . . . . . . . . . . . . . 3. Probable number of openings this year TOD Di iiiuei yi - • 7 OS (after 3rd week of September; see Rule 2).. - j , 'otal allowable catch (item 1 x 2) . . . i o l < DETERMINING THE CATCH . . , 'i. Expected season-long catch in test fisheries and native food fisheries. 7 4 ^ 0 0 0 (average 3% o£ total stock size).. 2-5. Remaining allowable catch I7Z 300 (item 4 - 5) 2— SECTION 2...Using the third week of September catch. At the end of the 3rd week of September (9/3) a second estimate is made. This estimate is based on the chum catch during the 3rd veek. First, the actual catch is standardized to the equivalent of a 2 day opening. This allows us to compare this years catch with catches of past years, Enter the duration of the opening on line 1 and the adjustment factors from the following table on lines 2 and 3. Two methods are used to determine the stock size, one uses only Area 12 catch, the other Area 12 and 13 catch. Each method proceeds in the same manner. First enter the actual catches. Then the catches must be standardized to a 2 day opening. The adjustment to a 2 day fishery is easily done Erom th{' following table and equation. The adjustment factors €or converting September catches to a 2-day opening. Actua) number Adjustment Gear type days fished factor SEINE 1 day 1.53 2 days no adjustment 3 days 0.79 GILLNET 1.5 days no adjustment 2.5 days 0.67 3.5 days 0.50 Standardized = Actual x Adjustment factor catch catch for actual number days fished Once the standardized total commercial catch is determined the stock size can be estimated from the proper graph. Starting from the catch on the bottom axis, move straight up to the best fit line from past years data ooints, then left to determine the new stock size estimate. This estimate is usually accurate to within 20% o£ the actual stock size. The two estimates are then averaged in the following manner and the average entered on line 16. Average = Area 12 estimate + Area 12+13 estimate estimate 2 Now its just a matter of determining the allowable catch from the rules (see South Coast Harvest Plan'in Rule 2 ) , calculating how much of it is left to be caught, and seeing whether an opening is likely. The second to third weeks of October are the most desirable time for a fishery because of the reduced significance of the Fraser River component in Johnstone Strait in the presence of large numbers of enhanced chum. 96 Section 2-..Estimate at end of 3rd week in September. ESTIMATING THE STOCK SIZE 1. Duration of week 9/3 fishery (in days) . . . » 2. ^factor for seine 3. factor for gillnet METHOD 1 ' Commercial„catch in Area 12 during week 9/3! f. Area 12 seirie eaten . 5. Area 12 gillnet catch • Standardizing the catch: 6. S^t^ndajdiz|^ Area 12 seine catch 7. Standardized Area 12 gillnet catch (item 3 x 5) r 8. TOTAL standardized area 12 catch (item 6 + 7) Art* 13 aelria«flUlnat eaten, weak 9/3. ttan tftauaandtl Relationship used to predict total stock size from Area 12 catch. 9 . Estimated total stock size from Area 12 graph (using total in item 8)... . . . . . . . . . . _ _ METHOD 2 Commercial catch from Area 12+13 during 9/3: 10. Area 12 + 13 seine catch 11. Area 12 + 13 gillnet catch Standardizing the catch: 12. S^ tandajjdiz^ jJjArea 12+13 seine catch 13. Standardized Area 12+13 gillnet catch (item 3 x 11) 14. TOTAL standardized area 12+13 catch jfitem 12 + 13) Araa 12*13, aalna.glUnat eaten, xaalc 1/3. (ten ttiouaaflda) R e l a t i o n s h i p used to p r e d i c t t o t a l s tock s i z e from area 12+13 c a t c h . 15. Es t imated t o t a l stock s i z e from Area 12+13 graph (us ing t o t a l in item 14) . . . . . . . . . . 16. TOTAL STOCK SIZE e s t i m a t e (average of e s t imate in item 9 and 15) , APPLYING THE RULES 17. Desired harvest rate for t o t a l stock s i z e n t e m , if iK ,frqm the South Coast Harvest Plan ( s ee Rule 2 ) 18. Total a l lowable catch ( i tem 16 * 17) ASSESSING CATCH SO I1'A It..., in areas 12,13, and 29. 19. Catch from previous Sect ion ( s e c t i o n I, item 5) 20. Week 9/1 chum c a t c h . . 21. Week 9/2 chum catch 22. Week 9/3 chum catch . 2 3 ' T f t ' e ' i J . f U S M Y ^ f ? . . . . DETERMINING ALLOWABLE CATCH REMAINING 24. AlLawahle catch remaining, (item 18 - 2 3 ) . . If item 24 greater than zero then f i s h i n g i s a l lowed. If item 24 l e s s than zero no f i s h i n g a l l o w e d , wait for next stock update. SECTION 3. ..Using tes catches through the first week of Octobgf. Since commercial catch data are not a l w a y s available in October a more reliable source of information must be used to estimate stock size. The Area 12 test fishery has p r o v i d e d an accurate estimate in recent y e a r s , on average to within about 10% of the actual stock size. This estimate uses the average catch per set from the testfishery from the 4th week of September (9/4) through the 1st week of October (10/1). The average catch per set for the two week period is required on line 1. Then use the relationship shown in the graph to estimate this years stock size. For example, a 2 week total catch per set of 600 chums p r e d i c t s a total stock size of about 2.4 million. A more reliable estimate is d e t e r m i n e d by averaging this estimate with the previous estimate (ie. 9/3 c o m m e r c i a l catch estimate). Add the two estimates together and divide by 2 to get the working estimate; enter it on line 3. Using the stock estimate on line 3 , turn to the rules (ie. Rule 2, South Coast Harvest Plan) to d e t e r m i n e the desired harvest rate. Then calculate the allowable catch on line 5 . Next determine how many chums have already been caught on lines 6 through 9, and how many are left to catch o n _ l i n e 10. If we haven't c a u g h t a l l the allowable catch then an opening is likely. "" IOC •ai&yS: Section 3...Using test fishing catch at end of 1st week in Oct. DETERMINING THE STOCK ESTIMATE 1. Average test catch/set for 9/4-10/1. 300 400 800 BOO 700 Avbfiga Lit UiMnl e«tsh 174-10/1 Relationship between test fishing catch and total stock size. 2. Estimated total istock size from above graph (using item 1) 3 TOTAL STOCK SIZE (average of v-.wo estimates made so far, item 1 6 in section 2; and item 2 above). . . . . . . . . • • • APPLYING THE RULES . 4. Desired harvest rate for total stock size (item 3; see Ruls 2). ... . . •••••• • • • 5. Total allowable catch (item 3 x 4)......-ASSESSING CATCH SO FAR in areas 12,13, and 29. 6. Total catch to date from previous section (item 23; section 2 ) . . . 7. Week 9/4 chum catch. . . . . . • • • • 8. Week 10/1 chum catch 9. Total catch to date (items 6+7+8) DETERMINING THE ALLOWABLE CATCH REMAINING 10. Allowable catch remaining (item 5 - 9). • • • If item 10 greater than zero then a fishery can b^expected. If item 10 less than zero then no fishery allowed. 101 n n n n „ n u u u u d • SECTION 4...Using test fishing catches through the 2nd week of October. -So far there have beer; 3 d i f f e r e n t ways of estimating stock size; the preseason forecast, commercial catch during week 9 / 3 , and test fishing catches during w e e k s 9 / 4 - r 0 / 1 . This week test fishing is used in the same way as last week except that 3 weeks of test fishing c a t c h e s are used. The average catch per set for the 3 week period is entered on line 1, then the relationship shown in the graph is used to estimate the stock s i z e . Once again this estimate is averaged with previous estimates (eg. 9/3 catch estimate and 9/4-10/1 test fishing e s t i m a t e ) . Apply the rules (ie. South Coast Harvest Plan) to determine the allowable catch on l i n e 5. Then its just a matter of adding up the c a t c h so far and determining how much of the allowable catch is remaining on line 9, Section 4...Using test fishing catch at end of 2nd week in O c t . Avang* tilt fUMnp catcA f/4-lQrt Relationship between test fishing catch and s 2. Estimated total stock size from graph (using item 1) . . . . . . . . . . 3. TOTAL STOCK SIZE (avera9e. , ? f three estimates made so far, itfem.16 l n section 2; item 2 in section 3, and item.2 a b o v e ) . . APPLYING THE RULES 4. Desired harvest rate for total stock size (use item 3; see Rule 2)...... . 5. Total allowable catch (item 3 x 4) ASSESSING THE CATCH SO FAR in areas 12,13, and 29. 6 . Total catch to date from previous section (item 9; section 3). . . 7 . Week 10/2 chum catch. .•....• 8 . Total catch to date (items 6+7). ALLOWABLE CATCH REMAINING 9 . Allowable catch remaining (item S - 8 ) . . . . . I £ item 9 greater than zero then a fishery can be expected. If item 9 less than zero then no fishery allowed. 103 n n n rr- > u u u u v i b SECTION 5...The average testcatch past the middle of October. By the middle of October we should have a pretty g o o d i d | a °£ £ h e stock size; from the preseason forecast, the earl*. September commercial catch, and finally No new estimates are made, So catch is determined each week see if further fishing can be allowe two estimates :!rom test f i s O i n g f? v, in this section, the r e m a i n 1 1 ^ '"lloyable from the.last, estimate, o f . S 1 2 e , to allowed in J o h n s t o n e S t r a i t . Section 5...Third week in October. STOCK ESTIMATE 1, Same estimate as in 2nd week of October •(.section 4; item 3) APPLYING THE RULES 2. Desired harvest rate from South Coast Harvest Plan (see Rule 2; use item I) 3. Total allowable catch (item 1 x 2 ) . CATCH SO FAR 4. Total catch to date from previous S e c t i o n (item 6; section i) 5. Week 10/3 chum catch 6. Total catch to date (items 4+5). ....... ALLOWABLE CATCH REMAINING 7. Allowable catch remaining (item 3 " fil- . . . : If item 7 greater than zero then a fishery can be expected. If item 7 less than zero then no fishery allowed. APPENDIX 2 MANAGEMENT RULES FOR THE QUALICUM (AREA 14) FISHERY Enhanced stocks from the _ Qualicum area will be harvested terminally if not fully exploited in the Johnstone Strait fishery. At full production this area will produce just less than one million "hatchery" chums that will require harvesting at a much higher rate than wild stocks could withstand. Consequently, passing wild stocks must be protected from the high terminal harvest rates. Of special concern are the Fraser River chums passing through Area 14 and other species moving into Big Qualicum area streams, particularly Chinooks. On the other hand , it is important 'that the "hatchery" fish be harvested early, while they are still in good condition and highly marketable. Accordingly, the following objectives are used to determine the rules by which the fishery will be managed. Objectives of the Qualicum Fishery: 1985 1. Harvest bright fish. 2. Attain required escapements of 90,000 to the Big Qualicum River, 80,000 to the Little Qualicum channel and river, and* 50,000 to the Puntledge River. 3. Harvest less than 10% Fraser River chums. 4. Harvest the maximum number of coho. 5. Harvest the minimum number of chinook. 6. Provide an equal opportunity for gillnets and seines. RULE 1, In order to achieve the highest quality product as possible, as many chums as p o s u M e will be harvested as silver brights. Openings in Johnstone Strait will attempt to harvest as many Qualicum area chums as possible. Furthermore, approximately 60% of the total allowable catch of Qualicum area chums will be harvested as the fish reach the terminal area, before any escapements or estimates of run size are available. RULE 2. A cleanup fishery will be conducted in late November after required escapements have been reached. RULE 3. October openings in the Qualicum area will be scheduled and located-to minimize the catch of chinook salmon and maximize the catch of coho salmon. . "" ' RULE 4. Possible fishing areas include 14-4,5,7,9,10,11. The actual areas opened for the Qualicum fishery are determined by the abundance of Fraser River chums in the area. Areas will be opened only if there are less than 10% Fraser River chums in the test fishing catches in each area. The sub-areas may be partitioned to meet this requirement and provide passage for Fraser River chums. Under current legislation sub-areas can now be legally partitioned. RULE 5. The abundance of Fraser River chums will be determined by e l e c t r o p h o r e s e s . The following sampling program will be used t o collect fish for analysis. A ) The sampling w i l i b e conducted by a local gillnet and seine vessel from the second week through the fourth week of October. B) Chums will be c o l l e c t e d from areas 14-5,7,9,10. In Area 14-5 samples will be collected inside and outside of the Sisters to Flora light line. In Area 14-S a single sample will be taken from the northwest end of the boundary common with Area 14-C) The sample size required is 150 fish from each area. Locations fished within the area are determined by the skipper and the local DFO b i o l o g i s t , but should be as widespread as possible. D ) Samples should b e taken by W e d n e s d a y , the samples analyzed in two days, and the results distributed to local offices and industry by Friday afternoon. RULE 6. New legislation p e r m i t s the subdivision of statistical a r e a s . Non-compliance with a n n o u n c e d boundaries will result'in ( legal action against individuals responsible, or complete closure for widespread disregard of boundary. Probable Fishing Pattern in the Qualicum fishery: Mid October: Next week: Next week: Late November:. December: 24h g i l l n e t s , 48h r e c o v e r y , 24h seines 24h s e i n e s , 48h recovery, 24h gillnets repeat if required. 24h g i l l n e t s , 24h s e i n e s , repeat until maximum catch is r e a c h e d . Pack fishery to clean up small surpluses. 108 - - n n n n • n <1 11 , u u u u u ri c I MANAGEMENT RULES FOR THE FRASER RIVER FISHERY. The optimum' escapement of wild Fraser River chum salmon is presently considered to be about 700,000. This level of escapement has been achieve6 only once in the past 20 years. Consequently the advisors established an interim level of 500,000 to b e used through 1986. After 1986 the minimum required escapement increases to 700,000 wild chums. As stocks continue to rebuild harvest strategies will allow even greater levels of escapement, providing u s e f u l information on the productivity and maximum potential of the F r a s e r River stocks. To meet the escapement requirements and p r o v i d e m a x i m u m benefits to the fishermen, the following objectives and rules have been determined. Objectives of the Fraser River chum fishery. 1. H a r v e s t , the maximum amount under the S o u t h Coast Harvest Plan. 2. Provide fishing time in Fraser River equal to Johnstone Strait if there is only 1 opening a l l o w e d in Johnstone Strait. ^ 3. Provide a Fraser River opening for every two in Johnstone Strait if more than t opening allowed in J o h n s t o n e Strait. 4. Provide opportunities to both up-river a n d lower river fishermen. 5. M i n i m i z e the harvest of coho and steelhead. 6. Minimize the harvest of non Fraser chum. RULE l. Inseason estimates of escapement are determined by subtracting catch of Fraser chum from estimates of the total run. T h e total run of Fraser chum is based on a preseason expected proportion of the total run in the Study Area; and is updated as new estimates of total run in the S t u d y 1 Area are determined. Catch is d e t e r m i n e d from native, commercial, and test fisheries in the Fraser River and Johnstone Strait, RULE 2, Required minimum escapement of Fraser c h u m is 5 0 0 , 0 0 0 . RULE 3. Allowable catch of Fraser chums is determined by overall harvest rate on Study Area chum under South Coast H a r v e s t Plan. RULE 4. In order to achieve equality of opportunity for harvesting' of Fraser chum the Johnstone Strait and Fraser River areas should receive an equal number of fisheries. Timing of openings in Johnstone Strait will attempt to minimize catch of Fraser River c h u m . RULE 5. Fraser River openings will be scheduled on the basis of: 1. C a t c h must not exceed limits under South Coast Harvest Plan. 2 . Target on strongest Fraser River s t o c k s , preferably enhanced stffd&r.. 3. Openings only after October 15 to avoid the p e a k s of coho or steelhead runs. . ' RULE 6. Areas o p e n e d will be 2 9 - 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 . Areas 2 9 T ' through 29-10 w i l l remain closed to directed chum fisheries to a v o r d harvesting non-Fraser chum, RULE 7. Openings w i l l be not less than 12 hours. • - v, ' » * . [ t - >T B i i • ' * jr . • 8.2 Appendix B Optimal solutions for scenarios with varied Ricker a values. Each page represents a single variation of the base case scenario. The results from these varia-tions were used to build figures 4.6 and 4.7. Top graphs represent average NPV and bottom graphs represent average annual catch. Three different stock size ranges are used to determine the average values and show sensitivity in result to range used. The average values are calculated first over range of R"-25% to R"+25%; second over range 0,0 to Ricker B FR/ Ricker BmmFR; and third at R". Within each graph, generally results for control combinations (JST+FR) and (JST+MVI), are shown completely while control combination (JST+MVI+FR) is repre-sented by only selected results. lit venation 7: -5,1.5,5000£500j0,tv,.9,3 variation 7: variation 7: . ^ . 5 fDO£500^0,tv,.9,3 ; 0 0.1 0.2 03 0.4 OS 0.6 0.7 0.8 0.9 1 " Value in terminal area relative to mixed stock area __JSt+MVI+FR _*_JSt+FR _ J S t + M V I 0 0.1 0.2 0 J 0.4 0 3 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area .JSt+MVI+FR _«_JSt+FR ^ . JS t+MVI 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR ^ . JS t+FR ^ .JSt+MVI variation 7: .5,1.5,5000^500,20^,.9,3 variation 7: -5,l-5,5000^50cu0,tv,.9,3 5 2700 6 : 2600 _JSt 0 0.1 0 2 0 3 0 4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area +MVI+FR ^ . J S t + F R ^ .JSt+MVI 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR _ J S t + F R ^ . JS t+MVI 0 0.1 0.2 0 3 0.4 03 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mfced stock area JSt+FR ^.JSt+MVI JSt+MVI+FR . i-v NJ i bale caw: .7^000^500^0,tv,.9 r3 bate cats: .7r.7^OQ0^S00,20ytvr9i3 base case: .7,.7^0002500^0,tv,.9,3 0 0.1 1 2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 ' Value in terminal area relative to mixed stock area _ JSt+MVI+FR _^_JSt+FR ^ .JSt+MVI 0 0.1 0.2 03 0.4 OJ 0.6 0.7 0.8 0.9 1 Value in terminal ares relative to mixed stock area ^ JSt+MVI+FR _^JSt+FR ^ . JS t+MVI 0 0.1 0J2 03 OA OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area __ JSt+MVI+FR JSt+FR ^ J S t + M V I 2030 2020 2010 2000 1990 1980 >1970 1960 1950 1940 bale case: ,71.7^000>250(W01tvr9^ base case: .7I.7r500Q£500,2G,tv,.9,3 base case: .7r7,5000£500^0,tv,.9t3 a 0 0.1 0 2 0 3 0.4 0-5 0.6 0.7 0.8 0l9 1 0 Value in terminal area relative to mixed stock area __ JSt+MVI+FR JSt+FR _ J S t + M V I 0 0.1 0.2 0 3 0.4 0 J 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _ J S t + F R ^ J S t + M V I 0 0.1 0 2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _*_JSt+FR ^ .JSt+MVI variation 3: 1,.7,5C:.^ >0£0,tv,.9,3 variation 3:1^7^000^50cu0,tv,.9^ variation 3: l,.7,5000,2500,20,tv,.9,3 . 415 0 0.1 02 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR JSt+FR _ J S t + M V I o 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JS t+MVI+FR _^JSt+FR ^ J S t + M V I variation 3:1,.7,5000,2500,20,tv,.93 o 0 1 0.2 0 3 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _JS t+MVI+FR _^JSt+FR - . JS t+MVI variation 3: lr7,5000£,.93 2440 2430 as 2420 ca •s 2410 a 2400 d 2390 2380 2370 0 0.1 -03. 0 3 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _JSt+MVIvFR ^ . JS t+FR ^.JSt+MVI 0 0.1 0.2 0 3 0.4 OS 0.6 0.7 0.8 0.? 1 Value in terminal area relative to mixed stock area JSt+MVI+FR -»-JSt+FR ^.JSt+MVI 0 0.1 0.2 0 3 0.4 0 3 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _JSt+MVI+FR _»_JSt+FR _JSt+MVI i > variation 5: .7,1,5000,2500^0, tv,.9;3 variation 5: •7,l,5000,2500,20>tv,.9,3 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR __JSt+FR ^ .JSt+MVI variation 5: .7,1,5000,2500,20,tv,.9,3 0 0.1 0.2 0 3 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _»_JSt+FR ^ . JS t+MVl variation 5: -7,l,5000£500£0,tv,.9,3 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 OS 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _^JSt+ER ^ .JSt+MVI 3150 0 0.1 02 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in tenninal area relative to mixed stock area .JSt+MVI+FR _»_JSt+FR ^ .JSt+MVI i-1' CJV variation & U,.505000l2500,20ptv1.9,3 variation & 1.5r5,5000,2s00,20>tv,.9r> variation 8:1.5,.5,5000,2500,20,tv,.9,3 0 0.1 0.2 0 3 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR _ J S t + F R ^.JSt+MVI 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR JSt+FR ^.JSt+MVI variation i 1J,3^OO0,250O,2O^V,. 0 0.1 0.2 0 3 0.« 0£ 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR JSt+FR ^.JSt+MVI variation 8:13^000250000,*, .9,3 i 0 0.1 0.2 0 3 0.4 OS OA 0.7 0.8 0.9 1 3 Value in terminal area relative to mixed stock area _JS l+MVI+FR ^ . JS t+FR _ J S t + M V I 0 0.1 0.2 0 3 0.4 0 5 0.6 0.7 0.8 0.9 1 Value til terminal area relative to mixed stock a n a _ JSt+MVI+FR ^.JSt+FR ^.JSt+MVI 0 0.1 0.2 0 3 0.4 05 0.6 0.7 0.8 0.9 1 Value ia terminal area relative to mixed stock area JSt+MVI+FR JSt+FR ^.JSt+MVI i-1 • . -J' i variation: 1,.7,2500^ 500^ 0,tv,.93 variation: 1,.7,2500,2500,20, tv,.9,3 variation: 1,-7,2500,2500,20, tv,.93 0 0.1 02. 03 0.4 05 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mi i -d stock area _^JSt+MVI+FR _ J S t + rR ^.JSt+MVI 0 0.1 0.2 0.3 0.4 0J 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area ^.JSt+MVI+FR _ J S t + F R ^.JSt+MVI 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area ^.JSt+MVI+FR _^_JSt+FR ^.JSt+MVI 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 i Value in terminal area relative to npxed stock area JSt+MVI+FR JSt+FR ^.JSt+MVI 0 0.1 0.2 03 0.4 03 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR JSt+FR ^.JSt+MVI : 0 0.1 0.2 0 3 0.4 0 3 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR _^JSt+FR ^.JSt-rMVI variation: 1,-5,2500,2500,20,tvr9,3 variation: 1.,.5,2500,25OO^rv,^ variation: 1,-5,2500,2500,20,tv,.9,3 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _^_JSt+FR ^JSt+MVI 0 0.1 0.2 0.3 0.4 05 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _^JSt+MVI+FR _ J S t + F R JSt+MVI 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area .^.JSt+MVI+FR _*_JSt+FR _^_JSt+MVI 0 0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _JSt+MVI+FR _^JSt+FR ^.JSt+MVI 0 0.1 0.2 0.3 0.4 0-5 0.6 C.7 0.8 0.9 1 Value in terminal area relative to mixed stock area .JSt+MVI+FR _^JSt+FR ^.JSt+MVI 0 0.1 0.2 0.3 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area .JSt+MVI+FR _ J S t + F R _ JSt+MVI variation: .5,1,2500,2500,20, tv,.9,3 variation: .5,1,2500,2500,20,tv,.9,3 variation: .5,1 ,2S00^5C0,20,tv,.9,3 0 0.1 0.2 03 OA 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock arcs .JSt+MVI+FR ^.JSt+FR ___JSt+MVI 0 0.1 0 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area -JSt+MVI+FR _*.J5t+FR _»_JSt+MVI 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _»_JSt+FR ,_JSt+MVI variation: .5,1,2500,2500,20,tv,.3,3 0 0.1 0 2 03 OA 0J 0.6 0.7 0.8 0.9 1 5 Value in terminal area relative to mixed stock area ^.JSt+MVI+FR _ J S t + F R _^JSt+MVI 0 0.1 0 2 03 0.4 OS 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _^JSt+FR ^.JSt+MVI 1500 k 1000 3 500 variation: .5,1,2500,2500,20,tv,.9,3 0 0.1 0.2 0.3 0.4 0-5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area .JSt+MVI+FR JSt+FR JSt+MVI so.. M, i variation: 5,15,2500,2500^0,tv,.9,3 variation: 5,15,2500,2500,20,tv,.9,3 variation: 5,15,2500£5c0^0,tv,.93 0 0.1 0.2 0 3 0.4 05 0.6 0.7 0.8 0.9 1 " Value in terminal area relative to mixed stock area ^.JSt+MVI+FR _ J 3 t + F R _JSt+MVI variation: 5,15,2500^500,20,tv,.9,3 0 O.i 0.2 0 3 0.4 0 5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR ^.JSt+FR ^.JSt+MVI variation: 5,15,25QO>2500,20,tv,.9,3 0 0.1 0O. 0 3 0.4 0 5 0.6 0.7 0.8 0.9 Value in terminal area relative to mixed stock ai JSt+MVI+FR ^.JSt+FR ^_JSt+MVI variation: .5,15,2500^500,20,!^.9,3 3 0 0.1 0 2 0 3 0.4 05 0.6 0.7 0.8 0.9 1 5 Value in terminal area relative to mixed stock area ^JSt+MVI+FR ^.JSt+FR ^JSt+MVI « O 1040 j-1020 u 1000 CG 1 980 s> • c e o 6 960 940 920 900 u 6 880 860 0 0.1 0.2 0 3 0.4 05 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area JSt+MVI+FR _»_JSt+FR ^.JSt+MVI 0 0.1 03. 0 3 0.4 0 5 0.6 0.7 0.8 0.9 Value in terminal area relative to mnxd stock a: JSt+MVI+FR ^.JSt+FR ^.JSt+MVI to tO' variation:.?,1.^0,2500,20,w,.9,3 variation: .7,1,2500,2500^0,tv,.9,3 variation: .7,1,2500,2500,20,tv,.9,3 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 " Value in terminal area relative to mixed stock area __JSt+MVI+FR _ J S t + F R ^.JSv+MVI variation: ,7,l,2500,2500^0,tv,.9,3 0 0.1 0.2 0.3 0.4 0J aS 0.7 0.8 0.9 1 Value in terminal area relative to mixsd stock area _ JSt+MVI+FR _^JSt+FR ^.JSt+MVI variation: .7,l,2500,2500^0,tvr93 0 0.1 02 03 0.4 OS 0.6 0.7 0.8 0.9 1 J , Value-in terminal area relative to mixed stock area ^.JSt+MVI+FR _^JSt+FR ^_J§t+MVI 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR _^JSt+FR ^.JSt+MVI 2000 1500 1000 variation: .7,1,2500^500,20,tv,.9,3 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed rtock area JSt+MVI+FR __JSt+FR ^.JSt+MVI 500 • 0 0.1 03. 0.3 0.4 05 0.6 0.7 0.8 0.9 1 Value in terminal area relative to mixed stock area _ JSt+MVI+FR _JSt+FR _JSt+MVI i 1 i r i. ri'O n n n n 'L L I' U ! U U IJ U VZT Catch over rangeK*-25% to R* K S g tj K B 3 g 8 g S o NPV over range R*-25% to R*+25% cn + <e> i? B-S S £ + 5 3 § S Annual catch over range O-Riclcer B § i 1 1 1 1 i 1 1 i NPV over range O-Ricker B Catch at R* ! fci B g ! g 8 8 NPV at R* W U W I/) V) w w w Ku «*> & u u & O M VA o Vt O 


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