Reconciling Economic and Biological Modeling of Migratory Fish Stocks:Optimal Management of the...

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Reconciling economic and biological modeling of migratoryfish stocks: Optimal management of the Atlantic salmonfishery in the Baltic Sea

Soile Kulmalaa,b, Marita Laukkanenc,⁎, Catherine Michielsensb

aDepartment of Economics and Management, P.O. Box 27, 00014 University of Helsinki, FinlandbFinnish Game and Fisheries Research Institute, P.O. Box 2, 00791 Helsinki, FinlandcMTT Agrifood Research Finland, Luutnantintie 13, 00410 Helsinki, Finland

A R T I C L E I N F O

⁎ Corresponding author. Fax: +358 9 5608 6264E-mail address: [email protected] (

0921-8009/$ – see front matter © 2007 Elsevidoi:10.1016/j.ecolecon.2007.08.002

Please cite this article as: Kulmala, S. etmanagement of the Atlantic salmon fish

A B S T R A C T

Article history:Received 7 November 2006Received in revisedform 27 June 2007Accepted 4 August 2007

The paper puts forward a model of the Atlantic salmon fishery in the Baltic Sea thatintegrates the salient biological and economic characteristics of migratory fish stocks.Designed to be compatible with the framework used for actual stock assessments, themodelaccounts for age-structured population dynamics, the seasonal harvest and competingharvesting by commercial and recreational fishermen. It is parameterized for the SimojokiRiver stock. The socially optimal policy for maximizing discounted net benefits from thefishery within an uncertain environment is determined using a dynamic programmingapproach and numerical solution method. Our results indicate that substantial economicbenefits could be realized under optimal management without compromising stocksustainability.

© 2007 Elsevier B.V. All rights reserved.

Keywords:Bioeconomic modelingUncertaintyAge-structuredpopulation dynamicsOptimal resource managementIntegrated biological andeconomic modelingAtlantic salmon

1. Introduction

The management of salmon and other migratory species iscomplicated by the disparate interests of the fisheries thatharvest the fish at their different life stages and by thecomplexity of stock dynamics. Themanagement of the fisheryfor Atlantic salmon (Salmo salar) in the Baltic Sea hasemphasized biological objectives, and past managementefforts have drawn heated criticism from the fishing industry.Despite regulation based on stock conservation goals, wild

.M. Laukkanen).

er B.V. All rights reserved

al. Reconciling economery.... Ecological Econom

salmon stocks have declined over time (Karlsson and Karl-ström, 1994; Jutila et al., 2003; Romakkaniemi et al., 2003). Anactive policy debate has sprung up in the Nordic countries dueto the low profitability of commercial salmon fisheries and thehigh status of salmon for anglers. Scientists, fishermen,environmentalists and administrators alike have called forthe protection of wild salmon stocks. The Regional Council ofLapland has established a Salmon Fund, which aims atsettling the ongoing dispute over harvest allocation betweenprofessional and recreational fishermen. The International

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ic and biological modeling of migratory fish stocks: Optimalics (2007), doi:10.1016/j.ecolecon.2007.08.002

mailto:[email protected]

http://dx.doi.org/10.1016/j.ecolecon.2007.08.002


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Baltic Sea Fishery Commission has launched the “SalmonAction Plan 1997–2010”, a program designed to enhance wildsalmon populations and increase salmon catches.

Restoring salmon stocks and improving the profitability ofthe salmon harvest requires that both the ecological andeconomic characteristics of the fishery be taken into consid-eration. To be accurate, management prescriptions must ac-count for the conflicting interests of the different user groupsas well as the ecological complexity and uncertainty inherentin salmon stock dynamics. Although the European Commis-sion has emphasized the socio-economic aspects of fisheriesmanagement (European Commission, 2001), managementauthorities in the Baltic Sea region have primarily relied onmanagement advice from natural scientists (see e.g. ICES,2005). One reason why the economic point of view has re-mained underrepresented in management decisions may liein the highly simplified population models generally used ineconomic analyses. If the underlying biological model iselementary, management guidelines proposed by economistsare easily dismissed by natural scientists and managementauthorities (see e.g. Deacon et al., 1998).

The objective of this study is to develop tools for producingeconomically and biologically sound management guidelinesby constructing an economic optimization model that accom-modates the complexity of the biological modeling of resourcestock dynamics. To this end, we construct a bioeconomicmodel of the fishery for Atlantic salmon in the Baltic Sea. Themodel takes into account the migration patterns of salmon,age-structured stock dynamics and reproduction uncertainty,1

as well as the different economic and biological characteristicsof the several fisheries that target salmon. The bioeconomicmodel reconciles the economic modeling of salmon fisheriesin the Baltic Sea with the stock assessment models currentlyused as the basis for management advice (see, e.g., ICES, 2005).We apply the model to develop optimal policy prescriptionsfor managing the salmon fisheries in the Baltic Sea. In order tocontribute to the ongoing policy debate, the model is calib-rated with data for the Simojoki salmon stock, whose nativeriver is located in the northern Baltic Sea.

Dynamic optimization models addressing harvest alloca-tion between different user groups targeting a migratory spe-cies have generally collapsed the stock dynamics into simplebiomass models (Charles and Reed, 1985; Cook and McGaw,1996; Laukkanen, 2001). An exception is Pintassilgo and Duarte(2002) which uses a multi-gear and age-structured bioeco-nomic model to study optimal management of the NorthernAtlantic bluefin tuna, and produces an optimal open-loopsolution for a 25 year horizon. Bertignac et al. (2001) use anage-structured, multi-species and multi-fleet model to studythe Pacific Islands Nations tuna fisheries but reduce themaximization of resource rents into a static linear program-ming problem. Economic analyses accounting for uncertaintyhave also generally resorted to aggregated biomass models(Reed, 1974, 1978, 1979; Clark and Kirkwood, 1986; Sethi et al.,

1 Due to the M74-syndrome, a reproduction disorder of salmonthat causes close to 100 % mortality in the juvenile phase,recruitment uncertainty is the principal source of salmonpopulation fluctuations in the Baltic Sea (see, e.g., Karlsson andKarlström, 1994).

Please cite this article as: Kulmala, S. et al. Reconciling econommanagement of the Atlantic salmon fishery.... Ecological Econo

2005). Bjørndal et al. (2004) studied the Norwegian spring-spawning herring fishery using an age-structured model withrecruitment uncertainty but relied on simulations to comparealternativemanagement strategies. Thunberg et al. (1998) alsoaccounted for recruitment uncertainty in a model disaggre-gated by age and gear, but alsomerely compared the economicoutcome under three management scenarios.

The present paper extends the sequential harvest modelspresented by Charles and Reed (1985) and Laukkanen (2001,2003), and the multi-gear and age-structured model byPintassilgo and Duarte (2002). It combines an explicit analysisof sequential harvesting by competing user groups, an age-structured population model and an account of the uncer-tainty in the relationship between the stock size and thecorresponding recruitment. Both the gear mix and total effortare allowed vary from year to year in response the observedstock abundance. Dynamic programming and a numericalsolution method are used to derive optimal feedback man-agement prescriptions over an infinite time horizon.

The paper is structured as follows. The section to followpresents the biological, economic and institutional character-istics of the Baltic Salmon fishery. Section 3 describes thepopulation dynamic model and defines the economic benefitsof the salmon harvest. Section 4 formulates the decisionproblem that the fishery manager faces. In Section 5, wecalibrate the model. Section 6 discusses the optimal harvestpolicy and Section 7 concludes the paper with a summary ofthe insights gained in the study.

Fig. 1 –Migrationroutesof thesalmonstocks fromtheNorthernBaltic Sea.

ic and biological modeling of migratory fish stocks: Optimalmics (2007), doi:10.1016/j.ecolecon.2007.08.002


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2. The salmon fishery in the Baltic Sea

In the Baltic Sea region, juvenile salmon usually spend threeyears in rivers, after which they migrate into the Baltic MainBasin in the springtime. Adult salmon then spend 1 to 4 yearsfeeding at sea before they start the migration back to theirnatal rivers in the early summer to spawn (see e.g. Karlssonand Karlström, 1994). The focus of this study is the fisheryexploiting salmon whose native rivers are in the NorthernBaltic Sea area. The fishery operates in the Gulf of Bothnia andthe BalticMain Basin (Fig. 1). Characteristic of the fishery is thesequential harvesting of migrating fish. The sequentialfisheries differ in terms of gear, catchability, fishing costs,and the price obtained for their catch. The commercial off-shore fisheries use driftnets and longlines to harvest salmonfeeding in the main basin. Historically, most of the commer-cial salmon catch has been harvested by the coastal fisheriesin the Gulf of Bothnia, which takemature salmonmigrating totheir native rivers during the early summer (June and July)using driftnets and trapnets. In the rivers, the fish are har-vested by recreational fishermen, with angling being the onlyform of fishing permitted.

The value of commercial salmon landings in the regionreached 1.3 million euros in 2005 (FGFRI, 2006). Investments inriver restoration and smolt production indicate social valuenotably above the value of commercial catch: 9.3million euroswere used for habitat restoration in Finland during 1997–2005(Erkinaro et al., 2003), and the Finnish state budget includedapproximately 1.4 million euros for yearly salmon stockingprograms during 2000–2004 (Salminen et al., 2004). Salmonand sea trout are the most highly valued target species for

Fig. 2 –Structure of the salmon fishery in the Ba

Please cite this article as: Kulmala, S. et al. Reconciling econommanagement of the Atlantic salmon fishery.... Ecological Econom

recreational harvest in the Nordic countries (Toivonen et al.,2000). The current international salmon fishery regulationsare based on total allowable catch and technical managementmeasures such as minimum landing size, minimum driftnetmesh size, and minimum hook size. In addition, each BalticSea nation has its own regulatory measures. As of 2008, EUfishery regulations will ban the use of driftnets.

3. Bioeconomic model

Our bioeconomic model encompasses the five fisheries har-vesting the salmon stocks from the Northern Baltic Sea area:the coastal driftnet fishery (cdn), the coastal trapnet fishery(ctn), the river fishery (ri), the offshore driftnet fishery (odn)and the offshore longline fishery (oll). The control variablesare the levels of fishing effort for each fishery in each period.Fig. 2 illustrates the structure of the fishery. In our model, ayear begins in May, which is when smolts migrate from theirnatal river to the Baltic Main Basin and join the feeding adultpopulation. For the sake of tractability, the model assumesthat the different fisheries take place sequentially. The coastalharvest occurs in the early summer, when mature salmonstart their spawning migration north towards their natalrivers. The coastal driftnet fishery harvests the migrating sal-mon in June, and the coastal trapnet fishery the survivingsalmon once they arrive in the Gulf of Bothnia in July. Thesalmon surviving both coastal fisheries are harvested by therecreational river fishery in August, when they reach theirhome river. Salmon that survive the river fishery reproduce.The immature salmon that remain in the Baltic Main Basin inthe spring to feed are harvested by the offshore fishery in the

ltic Sea, following Michielsens et al. (2006).




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fall. The offshore driftnet fishery takes place in October, theoffshore longline fishery in December. In addition to naturalreproduction, the salmon stock is safeguarded throughstocking of juveniles. The population dynamics of rearedsalmon are similar to those of wild salmon except that thereared salmon enter the system through stocking. The naturalmortality during the first year that salmon spend at sea (post-smolt mortality) is also higher for reared salmon than for wildsalmon (Brown and Laland, 2001).

3.1. Population dynamics

We consider a discrete time and age-structured model ofpopulation dynamics that follows the life cycle of salmon. Ourmodel takes into account the following age groups: eggs, fry,parr, smolts, one-sea-winter and two-sea-winter salmon. Theone-sea-winter age group is further divided into two lifestages — immature salmon which remain in the Baltic MainBasin to feed and grilsewhichmature and start their spawningmigration. We assume here that all two-sea-winter salmonmature. The coastal driftnet, coastal trapnet and river fishe-ries harvest both grilse and two-sea-winter salmon while theoffshore driftnet and longline fisheries target immature one-sea-winter salmon. The population dynamics model for thesalmon stock is the same as the one proposed by Michielsenset al. (2006) and implementedwithin the International Councilfor the Exploration of the Sea (ICES) working group for theassessment of Atlantic salmon within the Baltic Sea (ICES,2005), with the exception that the model only accounts for thetwomost abundant types ofmature salmon i.e. grilse and 2SWsalmon.

The structure of the salmon population can be summarizedin a state vector, S, St≡ {s1,t,s2,t,…, s6,t}, which traces the size ofeach age group. The state of the salmon stock in period tdepends on the state of the stock and the fishing effort inperiod t−1. The fishing efforts of the five fisheries aresummarized in vector X, Xt≡ {Xt

cdn,Xtctn,Xt

ri,Xtodn,Xt

oll}. Thus,the state changes from one fishing season to the next followSt=G(St− 1,Xt−1), with the state transition functions definingsa,t=ga(St−1,Xt−1). Index a indicates the age group, a∈ {1,…,6},and G≡ {g1,g2,…, g6} is the vector of state transition equations.

The elements of the state vector S and the state transitionvector G{⋅} are described in Table 1. Appendix A describes thepopulation model in more detail. The notation in Table 1 andAppendix A is as follows: rs is sex ratio and fe average fecun-dity,m is the instantaneous naturalmortality rate, and q l

f is thecatchability coefficient of life stage l by fishery f. The harvestedlife stages— grilse, immature one-sea-winter salmonand two-sea-winter salmon — are subscripted by l={0,1,2}. Further, θtare independent and identically distributed random shocks onrecruitment, α and β are the recruitment parameters,mp-sm

w andmp-sm

r are the post-smolt mortalities for wild and rearedsalmon, I is the number of stocked smolts, and L is the matu-ration rate of one-sea-winter salmon.

3.2. Economic model

This section describes the catches and annual net economicbenefits to each of the five fisheries. Catch price, fishing costsand catchability vary between the fisheries, as they operate at


different times of the year, catch salmon of differing size anduse different equipment. The catch weight of salmon alsovaries according to life stage. Salmon caught in the studyregion are landed in Finland and in Denmark. According toSetälä et al. (2002), salmon prices in Finland are determinedmainly by the supply of Norwegian salmon. As the small-scalecatches of salmon native to Simojoki are also likely to havelittle effect on the market price of salmon in Denmark, weadopt the assumption of constant prices. The unit cost offishing effort is an aggregate measure that includes gearmaintenance, fuel and labor costs. As salmon fishery is a smallpart of the economy in the study region, the cost of fishingeffort is also constant by assumption. Throughout the model,Pf is the price of salmon in fishery f and cf the cost of fishingeffort.

The profits to each commercial fishery are calculated foreach time period as the difference between revenue and costs.The harvest by fishery f in period t takes the following func-tional form:

Hf ;t ¼X2

l¼0

Nfl;tð1� e�q f

l Xft ÞWl;

where Nl,tf is the number of life stage l fish available to

fishery f in period t, defined in the population modelpresented in Appendix A; (1− e−ql

fXft) the harvest rate of life

stage l by fishery f, with qlf the life stage specific catchabilitycoefficient and Xt

f the fishing effort; and Wl the catch weightof life stage l. The harvest rate is determined similarly toMichielsens et al. (2006). The revenue to fishery f is defined aspfHf,t and the cost as cfXt

f. Thus, profits to fishery f in period tare given by πf,t=pfHf,t− cfXt

f. The profit functions for thecommercial fisheries are written out below:

pcdn;t ¼ pcdne�m=12fLs5;tð1� e�qcdn0 Xcdnt ÞW0 þ s6;tð1� e�qcdn2 Xcdn

t ÞW2g� ccdnXcdn

t

ð1Þpctn;t ¼ pctne�m=6fLs5;te�qcdn0 Xcdn

t ð1� e�qctn0 Xctnt ÞW0 þ s6;te�qcdn2 Xcdn

t

�ð1� e�qctn2 Xctnt ÞW2g�cctnXctn

t

ð2Þ

podn;t ¼ podne�5=12mð1� e�qodn1 Xodnt Þð1� LÞs5;tW1 � codnXodn

t : ð3Þ

poll;t ¼ polle�7m=12e�qodn1 Xodnt ð1� e�qoll1 Xoll

t Þð1� LÞs5;tW1

� collXollt ð4Þ

The river harvest is taken by recreational anglers. Ouremphasis on allocating harvest between commercial andrecreational fisheries calls for a measure of marginal netbenefits for recreational fishing in terms of catch. We followthe approach used by Cook andMcGaw (1996) and assume thatthemarginal willingness to pay for recreational catch is linear,which gives rise to a quadratic net benefit function

NBri;t ¼ kHri;t � vðHri;tÞ2; ð5Þ

where Hri,t = e−m/4 [Ls5,t e− q0cdnXt

cdn

e− q0ctnXt

ctn

(1−e−q0riXt

ri

)W0+s6,t e−q2

cdnXtcdn

e−q2ctnXt

ctn

(1−e−q2riXt

ri

)W2], and k and v are parameters ofthe net benefit function. Empirical studies by Stevens (1966),



2 The Matlab code is available from the authors upon request.The CompEcon Toobox is a library of MATLAB functions fornumerically solving problems in economics and finance that wasdeveloped to accompany Miranda and Fackler (2002). The libraryis downloadable at http://www4.ncsu.edu/~pfackler/compecon/toolbox.html.

Table 1 – The elements of the state vector St and transition vector St=G(St−1,Xt−1)

Age group State variable State transition equation ga(St−1,Xt−1) for age group a asfunction of St−1 and Xt− 1

Egg s1,t g1(St−1, Xt−1)= rs ⋅ fe ⋅e−5m/12⋅s6,t− 1⋅e−q2cdnXcdn

e−q2ctnXctn

e−q2riX ri

Fry s2,t g2(St−1,Xt−1)=s1,t− 1

Parr s3,t g3(St−1,Xt−1)=s2,t− 1

Smolt s4,t g4(St− 1,Xt−1)=θts3,t−1 / (α+β⋅s3,t−1)One-sea-winter salmon s5,t g5(St−1, Xt−1)=e−mp-sm

ws 4,t− 1+e−mp-sm

rIt−1

Two-sea-winter salmon s6,t g6(St− 1, Xt− 1)= (1−L)e−m⋅s5,t−1 ⋅e−q1odnX odn

e−q1ollX oll


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Carson et al. (1989), Dalton et al. (1998), Parkkila (2005) andothers indicate that recreational fishing benefits are positivelyrelated to the number of fish caught per day. However, fish areonly one input into recreational fishing. The net benefitfunction in Eq. (5) is constructed for the purpose of commercialand recreational harvest allocations only and ignores therecreational benefits attributable to factors other than the fishresource.

The total annual net economic benefit πt for the NorthernBaltic salmon fishery is the sum of commercial profits andrecreational net benefits:

pt ¼ pcdn;t þ pctn;t þ podn;t þ poll;t þ NBri;t ð6Þ

4. The optimization problem

Eqs. (1)–(5) illustrate the interdependence of the sequentialfisheries. The harvest of each fishery affects the profits of thenext and reduces the future salmon stock. The optimal harveststrategy would balance the marginal profits of each fishery toequal the revenues foregone in the next fishery in the se-quence in the current seasonand in the future. The objective ofthe fisherymanager is tomaximize thediscountednet benefitsfrom the salmon fishery through the optimal choice of fishingeffort for the five sequential fisheries. In the beginning of everyseason, the manager observes the size of the salmon stock Stand then chooses the optimal vector of fishing effortsXt, whereXt≡ {Xt

cdn,Xtctn,Xt

ri,Xtodn,Xt

oll}. The net economic benefits for thefishery as a whole, πt(St, Xt), depend on state of the salmonstock St and the fishing efforts Xt.

The salmon stock evolves from one period to the nextaccording to the state transition equations St=G(St− 1, Xt−1)presented in Table 1. This is a controlled Markov process. Thenet benefits of the five fisheries targeting salmon are given byEqs. (1)–(5). The fishery manager seeks a sequence of fishingpolicies, X{⋅}, which prescribes the efforts Xt=Xt* (St) that in agiven state and period will maximize the expected net presentvalue of the current and future harvest over an infinite timehorizon T.

Bellman's (1957) principle of optimality implies that theoptimal policy must satisfy the functional equation

VðSÞ ¼ maxXaXðSÞ

fpðS;XÞ þ dEh½VðGðS;X; hÞÞ�g; ð7Þ

where V is the value function, δ is the discount factorcorresponding to discount rate i, and Eθ is the expectationoperator over the recruitment shocks θt. The reward functionπ(S, X) is bounded. Where the value of δ is less than one, the


mapping underlying the Bellman equation is a strongcontraction on the space of bounded continuous functionsand thus, by the Contraction Mapping Theorem, will possess aunique solution.

We solved the dynamic program numerically using thecollocation method. This technique involves writing the valuefunction approximant as a linear combination of n knownbasis functions φ1, φ2,…, φn whose coefficients c1, c2,…, cn aredetermined by the equation

VðSÞcXn

j¼1

cj/jðSÞ ð8Þ

The coefficients c1, c2,…, cn are defined by requiring the valuefunction approximant to satisfy the Bellman equation in Eq. (7)at a finite set of collocation nodes. The solution wasimplemented using the CompEcon Toolbox for Matlab.2 Thesolution produces policy functions for Xt⁎ (S) that provide amapping from the current state to the optimal harvest policy.

The solution to the problem can be characterized by thefirst-order equilibrium conditions known as Euler conditions.The relevant Euler conditions in the present case can bederived by applying the Karush–Kuhn–Tucker and EnvelopeTheorems to the optimization problem in Eq. (7). The effortlevels are bounded from below by zero. The Euler equationstake the form

pXðS;XÞ þ dEh½kðGðS;X; hÞÞdGX� ¼ s ð9Þ

and

pSðS;XÞ þ dEh½kðGðS;X; hÞÞdGS� ¼ kðSÞ; ð10Þ

where λ(S)≡V′(S) is the shadow value of the resource. Here, πX,πS,GX and GS denote the partial derivates. The efforts X and τmust satisfy the complementary condition

Xz0 and XiN0Z si ¼ 0: ð11Þ

Here, τ is a 1×dx vector whose ith element, τi, measures thecurrent and expected future reward from a marginal increasein the ith action variable Xi. If XiN0, τi must be zero; otherwiserewards could be increased by decreasing Xi.


http://www4.ncsu.edu/~pfackler/compecon/toolbox.html

http://www4.ncsu.edu/~pfackler/compecon/toolbox.html


Table 3 – Economic parameters

Abbreviation Definition Value Unit

ccdn Unit cost of coastal driftnetfishery

0.03 €/gearday

cctn Unit cost of coastal trapnetfishery

0.97 €/gearday

codn Unit cost of offshore driftnetfishery

0.05 €/gearday

coll Unit cost of offshore longlinefishery

0.03 €/gearday

pcdn Price for coastal driftnetfisherya

3.4 €/kg

pctn Price for coastal trapnetfisheryb

2.5 €/kg

podn Price for offshore driftnetfisheryc

3.6 €/kg

poll Price for offshore longlinefisheryc

3.6 €/kg

k Parameter of river net benefitfunction

39.3 €/kg

v Parameter of river net benefitfunction

0.00493 €/kgb

i Discount rate 0.05

a


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5. Model parameters

We parameterize the model by using estimates for the SimojokiRiver salmon stock. In keeping with the current salmonmanagement advice and the underlying parameter estimates,we measure fishing effort in terms of geardays (see, e.g., ICES,2005). A gearday is defined as units of gear times number offishingdays.Aseach fisheryusesdifferentgear, thedefinitionofagearday differs accordingly: for the offshore and coastal driftnetfisheries, a gearday is the number of nets times the number offishing days; for the coastal trapnet fishery it is the number oftrapnets times the number of fishing days; for the offshorelongline fishery it is the number of hooks times the number offishing days; and for the river fishery, a gearday is equal to anangling day.

Table 2 displays the biological parameters of the Simojokisalmon stock. The parameter estimates are based on theassessments currently used by the corresponding ICES workinggroup (ICES, 2005). Following Michielsens and McAllister (2004),the recruitment shocks θt are assumed to follow a lognormaldistribution. The recruitment errors are thus defined as θt=ezt,

Average price of salmon in the Åland Islands in June 2003 (FGFRI,2004).b Average producer price of salmon in the Bothnian Sea and theBothnian Bay in July 2003 (FGFRI, 2004).c Average producer price of salmon landed in Denmark in the year2003 (Danish Fisheries Directorate, 2004). Inwinter in particular, theFinnish offshore harvest is landed primarily in Denmark.

Table 2 – Biological parameters (from ICES, 2005)

Symbol Definition Value Unit

rs Sex ratio 0.5 Males andfemales

fe Fecundity 10,000 Eggs/female

m Instantaneous adult naturalmortality

0.18 year−1

q2cdn Catchability of two-sea-wintersalmon by cdn fishery

1.6e−7 geardays−1

q2ctn Catchability of two-sea-wintersalmon by ctn fishery


q2ri Catchability of two-sea-wintersalmon by ri fishery


q1odn Catchability of one-sea-wintersalmon by odn fishery


q1oll Catchability of one-sea-wintersalmon by oll fishery


q0cdn Catchability of grilse by cdnfishery


q0ctn Catchability of grilse by ctn fishery 1.9e−5 geardays−1

q0ri Catchability of grilse by ri fishery 2.0e−5 geardays−1

α Parameter of recruitment function 105β Parameter of recruitment function 8.515e−6

I Stockings 2000 number ofsmolts

mp-smw Post-smolt mortality of wild

salmon1.67 year−1

mp-smr Post-smolt mortality of reared

salmon2.2 year−1

L Maturation rate for one-sea-winter salmon

0.15

W0 Catch weight for grilse 0.97 kgW1 Catch weight for one-sea-winter

salmon3.95 kg

W2 Catch weight for two-sea-wintersalmon

8.65 kg

μ Mean of process error zt 0σ standard deviation of process

error Zt

0.48


where the process errors zt are normally distributed with meanμ and standard deviation σ.

Table 3 presents the economic parameters. Published costdata for the salmon fishery is almost nonexistent. Weobtained the fishing cost estimates by interviewing fishermenoperating in the fisheries considered in the study. The costestimates are averages of the values reported and account forthe variable costs: gear price, gear maintenance, vesselmaintenance, fuel and labor costs. The costs differ due tothe differences in the equipment and techniques used in thefive fisheries. The price parameter for fishery f is the averagewholesale price for the regionwhere the catch from fishery f islanded over the months that the fishery operates. The pricedata were obtained from official Finnish statistics (FGFRI,2004) and the statistics produced by the Danish FisheriesDirectorate (Danish Fisheries Directorate, 2004). The pricedifferences reflect seasonal variation in the volume andquality of the salmon harvest as a whole. A 5% rate ofdiscount was used. This value is in line with other appliedstudies on optimal resource management, such as Bjørndalet al. (2004), Pintassilgo and Duarte (2002), and Cook andMcGaw (1996).

The net benefits of the recreational harvest in the Simojokihave been estimated based on results of a contingentvaluation study (Parkkila, 2005) ascertaining the willingnessto pay (WTP) for stock improvements that would double theexpected catch per angling day in the river from its 2003 levelof 0.35 kg to 0.70 kg. The perceived benefits estimated in thecontingent valuation study give a measure of the consumer



Fig. 3 –Means and 90% probability intervals for fishing effortsin (a) the coastal trapnet and (b) river fisheries for a 50-yearsimulation period.

Fig. 4 –Means and 90% probability intervals for (a) the netbenefits to the coastal trapnet and (b) river fisheries for a50-year simulation period.


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surplus associated with the proposed increase in catch. Theestimated WTP among anglers for a stock improvement thatwould double the catch was 8.50 euros per angling day inaddition to the current expense of 12 euros a day.We assumeda linear marginal WTP for recreational harvest, fit the integralof the marginal WTP between the current and improved catchlevels to the estimated WTP values to estimate the individualnet benefit function, and then aggregated across the approx-imate angler population of 2900 anglers to obtain parametersof the social net benefit function in Eq. (5). The study byParkkila (2005) was constructed to assess the marginal netbenefits of recreationally caught salmon, which is the mea-sure needed for producing correct recreational-commercialharvest allocation decisions. Using the formulation in Eq. (5)focuses on the net benefits of angling attributable to catch andmay underestimate the overall value of the recreationalfishery, which should be borne in mind when comparing thelevels of commercial and recreational net benefits producedby the optimal solution.


6. Optimal policy

6.1. Baseline parameterization case

The dynamic behavior of themodelwas studied using aMonteCarlo simulation. The simulation generated 10,000 state andpolicy paths using as input the optimal effort levels Xt=Xt⁎ (St)defined as the solution to the dynamic program in Eq. (7). Thecurrent stock estimates were used as the initial state. Fig. 3presents the means and 90% probability intervals for optimalfishing effort in the coastal trapnet and river fisheries. Underthe optimal policy, only the coastal trapnet fishery and theriver fishery would remain active; the result holds for all stateconfigurations produced by the simulation. The fact that thecoastal trapnet fishery would continue to harvest under theoptimal harvest policy while the other commercial fisherieswould not — despite higher prices and lower unit costs — isexplained by the differences in the catchabilities. The catch-abilities of the targeted life stages by trapnet fishery aremarkedly higher than those by the other commercial fisheries,which suffices to compensate for the higher unit costs and



Fig. 5 –Mean and 90% probability interval for smolt-stagesalmon for a 50-year simulation period. The initial statecorresponds to the current stock estimates.


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lower price. Fig. 4 shows the means and 90% probabilityintervals for the net benefits to the two active fisheries. Thevariation in the coastal trapnet fishery's effort and net benefitsis considerable, whereas the river fishery's effort and netbenefits remain stable.When lowstock levels are observed, thecoastal trapnet fishery reduces its harvest to the benefit of theriver fishery, which is able to harvest from a relatively stablestockof salmon. The result follows from thedifferent characterof commercial and recreational fishing, which ismanifested inthe curvature of the net benefit functions: the marginal netbenefit of harvesting is constant in the trapnet fishery butdecreases in the river fishery. Fig. 5 presents themean and 90%probability interval for smolt-stage salmon under the optimalpolicy. The expected number of smolts converges to near75,000, some 20,000 more than the expectation if the fisherymaintained its current fleet configuration and effort levels.

6.2. Sensitivity analysis

We conducted a sensitivity analysis to study the effectchanges in the key economic and biological parameters onthe optimal policy. The parameters determining the relativeperformance of the commercial fisheries are the catch price,unit cost of fishing effort, and catch per unit of effort. Wherethe economic parameters were concerned, our sensitivityanalysis focused on the costs and net benefits of the riverfishery, for which data are sparse compared to price and catchper unit of effort data. We limited the analysis to the steadystate of the certainty-equivalent problem obtained by fixingthe recruitment shock at its mean.

Table 4 displays the certainty-equivalent steady state andthe results of the sensitivity analysis. The optimal effort levelsin the certainty-equivalent steady state computed at the basecase parameters are 50,408 geardays for the coastal trapnetfishery and 4093 angling days for the river fishery. The cor-responding harvest levels are approximately 43,000 kg and3700 kg. The coastal trapnet harvest in the certainty-equiva-lent steady state is slightly smaller than the current catch of


the coastal fisheries as a whole, which is 63,600 kg (personalcommunication, Marjaliisa Koljonen, Finnish Game andFisheries Research Institute). In contrast, the estimated recre-ational harvest is close to seven times the present harvest of560 kg (personal communication, Erkki Jokikokko, FinnishGame and Fisheries Research Institute). The cost savings fromclosing down the less efficient fisheries and the substantialincrease in the recreational harvest would produce social netbenefits substantially above those realized at present: in thecertainty-equivalent steady state, the annual net benefits ofthe Simojoki salmon stock are near 137,000 euros, as opposedto the current net benefits of approximately 80,000 euros.

Other things being equal, the unit cost of fishing effort inthe coastal trapnet fishery would have to be 80% higher thanthe current estimate for the coastal driftnet fishery to beincluded in the optimal policy (Table 4). Further increases incosts for the coastal trapnet fishery would only shift catchesbetween the coastal fisheries and the river fishery: at thecurrent estimates of offshore unit costs, the offshore fisheriesremain excluded from the harvest regardless of the coastalfisheries' unit costs. If instead the unit cost of the offshoredriftnet fishery were 89% below the current estimate, bothcoastal fisheries would be excluded from the optimal policyand replaced by the offshore driftnet fishery. Similarly, a unitcost 95% below the current estimate for the offshore longlinefishery would make that fishery the only active commercialone. On balance, the results appear robust to changes in thecost parameters. As fuel is the most important operating costin fishing, a decrease in fishing costs is unlikely. An increase inthe costs of trapnet fishing is a more likely scenario, since theincreasing seal population in the Baltic Sea may force salmonfishermen to switch to seal-safe nets.

Fig. 6 illustrates the effect of the fisheries' relative costs onthe optimal fishery configuration. The left-hand side showsthe case where the costs of the offshore driftnet and longlinefisheries and net benefits of the river fishery remain at theircurrent level while the costs of the coastal driftnet and trapnetfisheries vary. The coastal driftnet and trapnet fisheriesharvest together with the river fishery only for a narrowrange of costs. The right-hand side depicts the case where thecoastal fisheries' costs and the net benefits of the river fisheryremain at their current level while the offshore driftnet andlongline costs change. A significant decrease in fishing costswould be required in both offshore fisheries for them to beincluded in the optimal harvest policy. Again, the two offshorefisheries coexist only for a narrow cost range. The effect ofcosts on the optimal fishery configuration is tied to thecatchabilities by the fisheries. The costs of offshore longlinefishing would have to fall roughly one order of magnitudebelow those of offshore driftnet fishing to compensate for thedifference in the catchabilities by the fisheries and allow bothto continue harvesting. The effect is similar in the case of thecoastal fisheries.

Changes in the marginal WTP for recreational harvest andin the biological parameters resulted only in a shift of harvestbetween the coastal trapnet fishery and the river fishery; theoptimal fishery configuration remained unchanged (Table 4).Shifts in themarginal WTP of up to 20% upward or downward,aswell as similar relative changes in the slope,maintained theoptimal fishery configuration of coastal trapnets and river



Table 4 – Optimal policy and sensitivity analysis

Fishery Base case 80 % increase CTN costs 89 % decrease in ODN costs 95 % decrease in OLL costs

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

CDN 0 0 0 78517 1168 1616 0 0 0 0 0 0CTN 50408 43073 58787 41179 38911 41355 0 0 0 0 0 0RI 4093 3725 78040 3469 3755 78112 4737 3716 78017 5208 3698 77965ODN 0 0 0 0 0 0 4748680 22599 55238 0 0 0OLL 0 0 0 0 0 0 0 0 0 11640400 21991 60660

0

Fishery 20% increase in the intercept ofmarginal WTP for recreational harvest

20% decrease in the intercept ofmarginal WTP for recreational harvest

20% increase in the slope of marginalWTP for recreational harvest

20% decrease in the slope of marginalWTP for recreational harvest

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

Effort(geardays)

Catch(kg)

Net benefits(EUR)

CDN 0 0 0 0 0 0 0 0 0 0 0 0CTN 49594 42419 57941 51214 43721 59624 49413 42273 57753 51065 43601 59469RI 4939 4487 112428 3250 2964 49910 5126 4655 97546 3406 3105 65035ODN 0 0 0 0 0 0 0 0 0 0 0 0OLL 0 0 0 0 0 0 0 0 0 0 0 0

Fishery 80000 stocked smolts Increased post-smolt mortalities: mp-smw =2.2, mp-sm

r =2.8 Lower maturation rate: L=0.1

Effort (geardays) Catch (kg) Net benefits (EUR) Effort (geardays) Catch (kg) Net benefits (EUR) Effort (geardays) Catch (kg) Net benefits (EUR)

CDN 0 0 0 0 0 0 0 0 0CTN 82693 95101 157541 15751 7756 4111 53249 47421 66899RI 3851 3717 78018 5757 3783 78173 3981 3723 78032ODN 0 0 0 0 0 0 0 0 0OLL 0 0 0 0 0 0 0 0 0

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3 In models with both recruitment uncertainty and uncertaintydriving from stock measurements or policy implementation, theharvest policy produced by the stochastic model is moreconservative than that produced by the corresponding determi-nistic model. See, e.g., Clark and Kirkwood (1986) and Sethi et al.(2005).

Fig. 6 –Optimal fishery configuration as a function of fisheries' unit costs.


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fishery only. As one would expect, an upward shift in themarginal WTP allocates more harvest to the recreational riverfishery and decreases the profits of the coastal trapnet fishery.

The optimal fishery configuration also remains unalteredirrespective of changes in the stockings, the post-smoltmortality and the maturation rate (Table 4). In the period1996–2002, the average number of stocked smolts in theSimojoki was approximately 80,000 (Erkinaro et al., 2003),which is significantly higher than the current number of 2000.Increasing the number of reared smolts did not affect theoptimal policy in terms of active fisheries. The effect on effortsand catches is the opposite of that brought about by anincrease in post-smolt mortalities: the optimal efforts, catchesand profits of the coastal trapnet fishery now increasesomewhat while those of the river fishery remain virtuallyconstant. At issue here again are the different catchabilitiesand decreasing versus constant marginal benefits of harvest-ing in the river and coastal trapnet fisheries. Higher effort andcatches are now required in the coastal trapnet fishery tobalance the marginal net benefits to equal those in the riverfishery.

Kallio-Nyberg et al. (2004) propose higher post-smoltmortality rates for wild and reared salmon than those usedin the ICES stock assessments. Although post-smolt mortalityis the principal biological parameter affecting salmon stocksizes after reproduction, an increase in post-smolt mortalityrates did not affect the optimal policy with regard to thenumber of active fisheries. It did, however, result in asignificant decrease in the effort, catch and profits in thecoastal trapnet fishery. The higher post-smolt mortalitiesresult in an over 80% decrease in the optimal harvest to thetrapnet fishery while the river harvest remains practicallyunaltered. At low stock levels the marginal benefit ofadditional effort falls more rapidly in the coastal trapnetfishery than in the river fishery, where the catchability of two-sea-winter salmon is markedly higher than in the coastaltrapnet fishery, and where the marginal benefit of additionalharvest is relatively high at low harvest levels.

Decreasing the maturation rate to 0.1 from the currentestimate of 0.15 did not affect the number of active fisheries.The effort, catch and profits of the trapnet fishery all increasedslightly while the outcome for the river fishery remainedessentially unchanged.Without offshore fisheries, the smalleravailability of grilsewould be compensated for by an increasednumber of two-sea-winter salmon available to the trapnet andriver fisheries. The trapnet fishery, which is the first to harvesthoming fish, would reap the benefits of an increased number


of the larger two-sea-winter salmon. As a decrease in thematuration rate increases the number of salmon that areavailable to the offshore fisheries (Eqs. (4) and (5)), theassumption that the offshore fisheries harvest only one-sea-winter salmon while the other three fisheries harvest bothone- and two-sea-winter salmon cannot be considered crucialfor the exclusion of the offshore fisheries in the optimal policy.

7. Summary and discussion

This paper provides a bioeconomic model of the fishery forAtlantic salmon in the Baltic Sea that is compatible with thestock assessment models currently used to produce manage-ment advice. It thus bridges the gap between economic andbiological models. The study extends the bioeconomic litera-ture on the optimal management of salmon by considering anage-structured model of population dynamics and sequentialharvest by multiple fisheries with different economic char-acteristics and impacts on the stock. The paper outlines adynamic optimization framework for numerically determin-ing the optimal harvest policy for each fishery. Using datacalibrated for the Simojoki salmon stock, the model has beenapplied to solve for the optimal harvesting policy and theoptimal allocation of harvest between the five fisheriesharvesting salmon from the Northern Baltic Sea area.

Uncertainty was included in the model in the form ofrecruitment fluctuations, which are the principal source ofsalmon population uncertainty in the Baltic Sea. In the case ofa risk-neutral fishery manager, the optimal policy dependsexclusively on the mean of the recruitment shock. When themean shock is one, the optimal policy for each state producedby the stochastic model coincides with the optimal policyproduced by the deterministic model, in which the recruit-ment shock is fixed at its mean.3 While the optimal policy ineach state is similar to that indicated by the deterministicmodel, accounting for recruitment uncertainty yields insightinto the volatility that the processmay exhibit and its effect onthe optimal fishery configuration.




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The result that the coastal and offshore driftnet fisheriesand the offshore longline fishery should be excluded fromharvesting is robust to variation in the population size: thefisheries were excluded everywhere along the simulatedstate paths, even when very large shocks were realized andthe harvestable population was abundant. The result is alsorobust to changes in the key economic and biologicalparameters. Our findings are in line with the forthcomingchanges in the EU Common Fisheries Policy, which willprohibit driftnet harvesting. However, the empirical analysispresented in this paper is confined to the Simojoki salmonstock, and the result that some fisheries should be excludedfrom harvest cannot be directly generalized to other Balticsalmon fisheries. Nevertheless, the Baltic Sea offshorefisheries' relatively low profitability is also present in indus-try statistics, which show that vessels have already beenexiting — in 1999, 316 vessels participated in offshoreharvest, while in 2005 the number had fallen to 175, andonly 33 vessels received more than 50% of their annualincome from the salmon fishery. (ICES, 2006). In Finland, only8% of the salmon catch in 2005 was caught by longlines.(FGFRI, 2006).

Our results indicate that the total social net benefits fromthe salmon fishery could increase by up to 70% throughreallocation of the salmon harvest. A possible consequence ofrestructuring the fishery would be that part of the labor andcapital currently engaged in the driftnet and longline fisherieswould move to the coastal trapnet fishery. Furthermore, thesubstantial increase in the recreational catch would likelycreate new employment opportunities in providing servicesfor recreational fishermen, such as boat rental and organizedfishing trips (see e.g. Parkkila, 2005). Through shifts in laborforce part of the increased social net benefits generated by theoptimal policy could be directed to those currently participat-ing in the driftnet and longline fisheries. The fisheries are asmall part of the economy in the study region and notphysically isolated from it. In light of the arguments presentedabove, one would expect the social costs associated withbanning driftnets and longlines from harvesting Simojokisalmon to be relatively small.

To obtain economically optimal management advice forthe Baltic as a whole, the framework provided here should beextended to consider multiple coexisting stocks, and thedata needed for empirical analysis should be gathered for allBaltic salmon fisheries. The current guidelines for managingBaltic salmon ignore the economic aspects of the fishery(ICES, 2005). The sensitivity analysis carried out here under-lines the importance of economic information for fisheriesmanagement. In the sequential fishery model, relativechanges in the fishing costs affect the optimal fisheryconfiguration, whereas changes in the biological parametersonly alter the allocation of the harvest between the activefisheries. Collecting representative fishing cost data for allthe Baltic salmon fisheries is essential for producingmanagement recommendations that account for economicconsiderations. Further research on the value of recreationalfisheries in the Baltic salmon rivers is also needed. Finally,our focus here has been on optimal harvest policy under theassumption that the Baltic salmon fishery is managed by asingle authority. A worthwhile extension would be trans-


boundary cooperation to sustain the optimal policy, for thereare a number of countries that harvest salmon in the BalticMain Basin.

Acknowledgements

This researchwas a part of the Academy of Finland's Baltic SeaResearch Program and funded by the Finish Ministry ofAgriculture and Forestry (project number 310921). We wouldlike to thank the project partners for their collaboration. Wealso thank Marko Lindroos, Jon Olaf Olaussen and RagnarArnason for their insightful comments on an earlier version ofthis paper.

Appendix A Population dynamics

The appendix describes the population dynamics by agegroup. The eggs hatch in the spring. After hatching, it takesa salmon approximately three and a half years to sequentiallydevelop into fry (s2), parr (s3) and finally reach the smolt stage(s4). The relationship between the number of eggs and thenumber of smolts can be summarized by a Beverton–Holtstock-recruitment function (see, e.g., Michielsens and McAll-ister, 2004). Fry (s2) and parr (s3) are used as accountingvariables in the our model: s3,t=s1,t−2. The number of wildsmolts in May of year t is therefore given by

s4;t ¼ s3;t�1

aþ bs3;t�1ht: ðA1Þ

We assume that the reproduction function and associat-ed parameters are the same for wild and reared salmon. Thenumber of one-sea-winter salmon in May of year t is givenby

s5;t ¼ s4;t�1e�mwp−sm þ It�1e�mr

p−sm : ðA2Þ

The mature one-sea-winter salmon, grilse, start theirspawning migration. The number of grilse available to thecoastal driftnet fishery in June of year t is given by

Ncdn0;t ¼ Ls5;te�m=12: ðA3Þ

The number of grilse that are available to coastal trapnetsin July of year t is defined by

Nctn0;t ¼ Ncdn

0;t e�qcdn0 Xcdnt e�m=12: ðA4Þ

The number of grilse that reach the river fishery in Augustof year t is given by

Nri0;t ¼ Nctn

0;t e�qctn0 Xctn

t e�m=12: ðA5Þ

We assume that grilse, which are predominantly males(Jokikokko et al., 2004), die naturally if they are not caught inthe river fishery. Thus, they do not reproduce in our model.




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The number of immature one-sea-winter salmon availableto the offshore driftnet fishery in October of year t is given by

Nodn1;t ¼ ð1� LÞs5;te�5m=12: ðA6Þ

The number of one-sea-winter salmon reaching theoffshore longline fishery in December of year is given by theequation

Noll1;t ¼ Nodn

1;t e�qodn1 Xodnt e�m=6: ðA7Þ

The number of two-sea-winter salmon in May equals thenumber of one-sea-winter salmon surviving the offshorelongline fishery, minus natural mortality:

s6;t ¼ ð1� LÞe�ms5;te�qodn1 Xodnt e�qoll1 Xoll

t ðA8Þ

The number of two-sea-winter salmon available to thecoastal driftnet fishery in June of year t is given by equation

Ncdn2;t ¼ e�m=12s6;t: ðA9Þ

The number of two-sea-winter salmon available to thecoastal trapnet fishery is given by

Nctn2;t ¼ Ncdn

2;t e�qcdn2 Xcdnt e�m=12: ðA10Þ

The number of two-sea-winter salmon reaching the riverfishery is

Nri2;t ¼ Nctn

2;t e�qctn2 Xctn

t e�m=12: ðA11Þ

Finally, the number of spawning salmon (SSN) is given by

SSNt ¼ Nri2;te

�qri2Xrie�m=6: ðA12Þ

By assumption all salmon die spawning. The number ofeggs produced is given by

Nweg;t ¼ SSNtd rsd fe: ðA13Þ

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