Bioeconomic model of eastern baltic cod under the influence of nutrient enrichment

Average nitrogen 18 concentration in the spawning areas during the spawning season of cod stock is chosen to be an indicator of nutrient en- 19 richment.. The optimal cod stock is d

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nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1

NRM nrm˙137 Dispatch: 7-21-2012 CE: AFL Journal MSP No No of pages: 29 PE: Matthew

9

Department of Environmental and Business Economics

11 Centre for Fisheries & Aquaculture Management & Economics (FAME)

12 University of Southern Denmark and Faculty of Development Economics, Q1

15

Abstract The ob jective of this paper is to study the

16 economic management of Eastern Baltic cod (Gadus morhua )

17 under the inﬂuence of nutrient enrichment Average nitrogen

18 concentration in the spawning areas during the spawning sea-

son of cod stock is chosen to be an indicator of nutrient en-

19 richment The optimal cod stock is deﬁned using a dynamic

20 bioeconomic model for the cod ﬁsheries The results show that

21 the current stock level is about half of the estimated optimal

stock level and that the current total allowable catch (TAC)

22 is about one-fourth of the optimal equilibrium yield The

re-23 sults also indicate that the beneﬁt from a reduction in nitrogen

24 very much depends on the harvest policies If the TAC is set equal to the optimal equilibrium yield, the beneﬁt of a

nitro-25 gen reduction from the 2009 level to the optimal nitrogen level

26 would be about 604 million DKK over a 10-year time horizon,

27 given a discount rate of 4% per year However, if a recovery

management plan is chosen, the beneﬁt would only be about

28 49 million DKK over a 10-year time horizon.

29 Key Words: Bioeconomic model, Eastern Baltic cod,

31

32 1 Introduction The objective of this paper is to study the eco-

33 nomic management of Eastern Baltic cod (Gadus morhua ) under the

34 inﬂuence of nutrient enrichment This ﬁsh stock inhabits the regions

35 East of Bornholm in the ICES’ (The International Council for the

36 Exploitation of the Sea) subdivisions 25–32, and its spawning season

37 begins in early March and ends in September–October (Bagge and 38

39 ∗ Corresponding author Nguyen Viet Thanh, Department of Environmental and

40 Business Economics Centre for Fisheries & Aquaculture Management & Economics(FAME) University of Southern Denmark and Faculty of Development Economics, Q2

41 VNU University of Economics and Business e-mail: nvt@sam.sdu.dk

42 Received by the editors on 6t h july 2012 Accepted 4t h june 2012.

C o p y r i g h t c 2 0 1 2 W i l e y P e r i o d i c a l s , I n c

1

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4 Thurow [1994], Wieland et al [2000]) It is one of the most important

5 ﬁsh stocks in the Baltic Sea In Denmark, it accounts for over 33% of the

6 total cod landed and contributed about 14% to the total landing value

7 of Danish ﬁsheries in 2009 (Anon [2009]) In Sweden, it accounted for

8 4% of the total catch, but it contributed about 19% to the total land-

9 ing value of Swedish ﬁsheries in 2004 (Osterblom [2008]) Nine coun-

10 tries currently harvest Eastern Baltic cod: Germany, Finland, Russia,

11 Estonia, Latvia, Lithuania, Poland, Sweden, and Denmark Poland,

12 Sweden, and Denmark had the largest catch shares, which accounted

13 for 22%, 21%, and 17% of the total cod landing from the eastern Baltic

14 Sea in 2009, respectively (ICES [2010a]) The harvesting of eastern cod

15 mainly occurs at the beginning of the year For example, in Denmark,

16 landing from January to June accounted for about 73.2% of the total

17 Eastern Baltic cod landings in 2009 (Anon [2009]) There were about

18 13,900 ﬁshing vessels with a total 246,345 GT in the Baltic countries

19 (without Russia) in 2005 (Horbowy and Kuzebski [2006]) Trawls and

20 gillnets are the main ﬁshing gears for eastern Baltic cod ﬁsheries, which

21 contributed about 70% and 30% of the total landing in 2009, respec-

22 tively (ICES [2010b]) In 2010, the total landing of Eastern Baltic cod

23 was 50,277 tons, which was approximately equal to 12.8% of the high-

24 est landing of 391,952 tons in 1984 (ICES [2010a, 2011]) The ICES has

25 recommended that TACs should be calculated on the basis of ﬁshing

26 mortality and the stock spawning biomass (Radtke [2003]) The TACs

27 are annually allocated to the member states with the same percentages

28 annually (Nielsen and Christensen [2006]) The TAC for Eastern Baltic

29 cod has been separate from Western Baltic cod since 2004, and it was

30 set of 56,800 tons in 2010 (ICES [2009])

31 Eastern Baltic cod has been managed under a recovery program

32 since 2007 (EC [2007]) The main target of the recovery program is

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2

3

4 Rockmann et al [2007], HELCOM [2009]) When excess inputs of nu-

5 trients are introduced into ecosystems, which is called eutrophication,

6 the water becomes turbid from the dense populations of phytoplankton

7 Large aquatic plants are outcompeted and disappear along with their

8 associated invertebrate populations Moreover, decomposition of the

9 large biomass of phytoplankton cells may lead to low oxygen con-

10 centrations (hypoxia and anoxia), which kill ﬁsh and invertebrates

11 The outcome of eutrophication is a community with low biodiver-

12 sity and low esthetic appeal (Begon et al [2006]) In 1988, the

13 Helsinki Commission (HELCOM)1 decided to reduce nutrient inputs

14 by 50% because of the serious eutrophication problem in the Baltic

15 Sea.2

16 Insuﬃcient attention has been given to the eﬀect of nutrient enrich-

17

ment on the cod stock (Bagge and Thurow [1994], HELCOM [2009])

18 even though many papers have studied the eﬀects of temperature, salin-

Mackenzie et al [2007], Rockmann et al [2007], Heikinheimo [2008])

22 Nutrient enrichment can aﬀect both the growth and the reproduc-

23 tion of the exploited species, and these eﬀects depend on the nutri-

24

ent concentration level in the main habitat of the species (Breitburg

26 concentration on the recruits of the anchovy stocks in the Black Sea

27 Smith and Crowder [2005] ﬁnd the eﬀects of nitrogen loadings on the

28

growth of the blue crab ﬁshery in the Neuse River Estuary Finally,

29 Simonit and Perrings [2005] ﬁnd the eﬀects of nutrient enrichment on

investigates interdependence between pollution and ﬁsh resource har-

37 vest policies In this paper, a more realistic growth function is applied

38

by including both the growth and the recruitment of ﬁsh stock In

39

addition, the theoretical model is also applied to the cod stock and

40 nutrient pollution in the Baltic Sea The following speciﬁc questions

41 will be discussed:

42

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16 2 The bioeconomic model The bioeconomic model is tradi-

17 tionally based both on a biological model and an economic model of

18 the ﬁshery The social objective is to maximize the present value of the

19 proﬁt of the involved ﬁshermen over a certain time horizon subject to

20 the biological model of the ﬁsh stock We expand the model to include

21 the consequences of eutrophication We show how the optimal harvest

22 policy depends on the eutrophication level In the following section the

23 model is explained

24

25 2.1 Population dynamic In a basic form, changes in biomass

26 of an exploited ﬁsh population over time depend on the recruitment,

27 growth, capture, and natural death of individuals3 (Ricker [1987],

28 Beverton and Holt [1993]) The spawning stock is the mature part

29 of the population that spawns It is also assumed to be the part of the

30 population exposed to the ﬁshery Recruitment occurs when the ﬁsh

31 grow to maturity and enter the spawning stock It takes some time to

32 progress from spawning to recruitment; therefore we apply a delayed

33 discrete-time model (Clark [1976], Bjorndal [1988]):

34

35

(1) 36

37

38 where S t is the spawning biomass at the beginning of period t , and H t

39 is the harvest quantity in period t It is assumed that harvesting occurs

40 at the beginning of period t and that, S t − H t is the escapement The

41 escapement will grow by the function G t = G(S t ) The recruitment

42 is a function of the stock that need γ periods to grow into maturity

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2

3

4 R t = R(S t −γ ) To extend the model, we include the nutrient concen-

5 tration N t in both the growth and recruitment functions

13 2.2 The bioeconomic model It is assumed that the net beneﬁt

14 of the ﬁshery is a function of total harvest (H ) and spawning stock

15 biomass (SSB) (S ) with π t = π(H t , S t ) The function π is assumed to

16 be continuous, concave, and twice diﬀerentiable A general economic

17 objective is to maximize the net present value (NPV) of the net beneﬁts

18 from the ﬁshery subject to the dynamics of the ﬁsh stock:

27 where ρ = 1+ r is the discount factor, and r is the discount rate The

28 harvest has to be positive so H t ≥ 0 The maximization problem is

29 restricted by the present and previous γ years of stock levels However,

30 we are only interested in ﬁnding the optimal stock and harvest levels,

31 so the initial conditions are ignored

32 Problem (3) may be solved using the Method of Lagrange Multipli-

33 ers (see e.g., Conrad and Clark [1995]) We formulate the (current)

40 If the stock is considered a capital, the term4 (S t − H t )G t + R t − S t + 1

41 is the change in capital in period t + 1 Then λ t + 1 is the current value

42 shadow price of the resource in period 0 + 1 The partial deviates of

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13 where all the deviations with a prime are taken at time t The ﬁrst

14 order necessary condition for optimization requires that deviations (6)

15 and (7) be equal zero are:

22 In equilibrium, all variables are stationary over time, and the t sub-

23 script can therefore be dropped The restriction (4) implies

38 Equation (12) is called the discrete-time analog of the golden rule for

39 capital accumulation in natural resource economics (Clark and Munro [1975]) In the left hand side of this equation, the term ( π S

H

+ 1) is

41 called the marginal stock eﬀect (MSE), which represents the stock den-

42 sity inﬂuence on harvesting costs (Clark and Munro [1975], Bjorndal

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2

3

4 [1988]) The term (S −R ) G + ρ γ R in (12) is the marginal productiv-

5 ity It consists of t S the S part is related to the growth of

wo parts: ﬁrst

6 the escapement, and the second part is related to the recruitment The

7 second part is discounted with γ periods as a consequence of the delay

8 in maturity Given a discount rate of r , equation (12) can be solved

9 for the optimal stock level, S ∗, as a function of nutrient concentra-

10 tion (N ) Furthermore, the optimal harvest level, H ∗, can be derived

11 from (10) As the recruitment and growth functions are functions of

13 of N

14

15

16 3 An empirical analysis of Eastern Baltic cod The bioeco-

17 nomic model, as presented in the previous section, is now applied to

18 the Eastern Baltic cod ﬁsheries under the inﬂuence of nutrient enrich-

19 ment The TACs of the cod stock is expected to be relatively constant,

20 for example, it does not change by more than 15% between two subse-

21 quent years (EC [2007]) In this case and following Voss et al [2011],

22 the objective of the function is to maximize the NPV of utility function

37

38 Equations (10) and (12) can still be used to calculate the optimal

39 stock and optimal harvest for the Eastern Baltic cod ﬁsheries.5 We

40 use the Rsolnp package in the R software developed by Ghalanos

41 and Theussl (Ghalanos and Theussl [2011]) to solve the optimization

42 equation (13)

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4 3.1 Data Data on the annual cod landings, SSB, and recruit-

5 ments are available directly from ICES database (ICES [2010a])

6 The total nitrogen indicator (NTOT ) is derived from the HELCOM

7 database.6 To formulate a proper nitrogen indicator for the cod stock,

8 we use data collected from the stations that, are located in the ICES’

9 subdivisions 25, 26, and 28 with bottom depths greater than or equal

10 to 20 m In addition, we only use data collected during the spawning

11 season of the cod stock, which is from March to September The nitro-

12 gen concentration in the spawning areas during the spawning season is

18 where N t is the nitrogen indicator in year t , k is the number of obser-

19 vations, and N T OT i is the nitrogen concentration:

26 Table 1 shows the nitrogen index and the biological data of the East-

27 ern Baltic cod ﬁsheries from 1966 to 2009

28 Statistical data from the Ministry of Food, Agriculture and Fisheries

29 in Denmark are used to estimate the variable cost function In partic-

30 ular, a time series set of the annual cost and the annual catch of the

31 ﬁshing ﬁrms from 1995 to 2009 in Bornholm (Rønne) are used for the

32 estimation Most of the ﬁshing ﬁrms are individual persons, where one

33 person is the sole owner of a ﬁshing vessel with or without any company

34 structure Variable costs are the total variable costs of a ﬁshing ﬁrm

35 multiplied by the share of cod in the total harvest and deﬂated using

36 the consumer price index (2000 = 1).7 The data for the estimation are

37 described in Table 2

38

39

40 3.2 Recruitment function The stock–recruitment relationship

41 of the Eastern Baltic cod is assumed to follow a quadratic function, and

42 the nitrogen concentration is included as follows (Simonit and Perrings

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35 Juvenile cod is assumed to join in spawning stock at age 3, so the delay

36 period is γ = 2 The estimation of the recruitment functions for the

37 Eastern Baltic cod are described in Table 3

38

39 The model explains 53% the variance of the dependent variable, and

40 all the parameters are signiﬁcant at the 5% level or better Additionally,

41 the models indicate the autocorrelation in the residuals, which is often

42 noted in time series data derived from VPA (Knowler [2007]) The

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t − 2

2

3

4 TABLE 3 Estimation of the Eastern Baltic cod stock–recruitment function using

5 the quadratic model and the data for 1966–2009.

N ote: T he dep en de nt varia ble is Rt /St – 2 an d n = 39 T h e m o d els h ave b een

29 cod at age 2 from 1966 to 2009, w = 0.209 kg (ICES [2010b]), the ﬁnal

30 stock–recruitment function is determined

39 (1) Maximum recruitment: R∗ = 97 thousand tons (464 millions);

40 (2) Nitrogen concentration at R∗: N ∗ = 17.24 millimole/m3 ;

41

42 (3) SSB at R∗: SSB ∗ = 534 thousand tons

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28 FIGURE 1 Recruits as a function of SSB and nitrogen concentration.

29 3.3 The growth function We use a simple version of the

30 growth function (see e.g., Bjorndal [1988], Kronbak [2002]) Following

31 Ricker [1987], the growth function is assumed as follows

32

34

35 where δ t is called the net natural growth rate, which equals the instan-

36 taneous growth rate minus the instantaneous natural mortality rate

37 We assume that nitrogen enrichment has minimal eﬀects on the growth

38 of cod stock and it is ignored in the growth function.9 The relationship

39 between the net natural growth rate (δ) and the SSB (S ) is assumed

40 to follow a linear form10 :

41

42 (20) δ t = δ(S t ) = d + f S t

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t − 2

19 From (1) and (19), the net natural growth rate (δ) may also be cal-

20 culated according to the following formula

Table 4 shows the estimation of equation (20) using data for

27 1966–2009 The model has signiﬁcant parameters at the 1% level and

28 explains 33% of the variance of the dependent variable In addition,

29 δ∗(S ) < 0 for all stock levels, which implies that the net natural growth

30 rate reduces when the stock increases The net natural growth rate is

36 From (18) and (22), we have the model of the cod population dy-

37 namics under the inﬂuence of nitrogen:

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C

3

4 The main characteristics of this function are the following:

5

6 (1) Maximum sustainable yield: MSY = 269 thousand tons,

7 (2) Nitrogen concentration at MSY: Nmsy = 17.24 millimole/m3 ,

8 (3) SSB at MSY: SSBmsy = 564 thousand tons, and

9

10 (4) The carrying capacity: Smax = 974 thousand tons

11 The Eastern Baltic cod stock may have been closest to its carrying

12 capacity in late 1970s and early 1980s The current SSB level of 308.787

13 thousand tons (ICES [2011]) is about half of the stock level at the

14 maximum sustainable yield (SSB at MSY)

15

16 3.4 Variable cost function It is assumed that the total variable

17 cost of the ﬁsheries is a function of the total harvest (H ) and the SSB

18 (S ) (Clark [1990], Sandberg [2006], Rockmann et al [2009]) Since cod

19 is an internationally traded commodity, it is further assumed that cod

20 ﬁsheries have a perfectly elastic demand curve The net beneﬁt function

21 of the Eastern Baltic cod ﬁsheries in period t can be deﬁned as follows:

22

23

(24) 24

25

π(H t , S t ) = pH t − C t (S t , H t ),

26 where p is a constant price and, C t is the total variable cost of the

27 ﬁshery in period t The total variable cost of the Eastern Baltic cod

28 ﬁsheries is calculated as follows:

33 where C t is the total variable cost of the ﬁshery in period t , c ti is the

34 unit cost of harvest of ﬂeet i in period t, h t i is the harvest of ﬂeet i

35 in period t , and f is the number of ﬂeets The unit cost of harvest of

36 cod ﬁshing ﬁrms in the Bornholm region is assumed to be the unit cost

37 of harvest for the entire Eastern Baltic cod ﬁsheries (Kronbak [2002],

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2

3

4 TABLE 5 Estimation of the variable cost function for the Bornholm cod ﬁshery

a te d u sin g lin ea r regression

is the Bornholm average share of the cod landing The total

28 variable cost of Bornholm cod ﬁsheries is assumed to be the following

29 in a trans-log functional form (Clark [1990], Alaouze [1999], Sandberg

30 [2006], Rockmann et al [2007, 2009])

31

32 (27) C bt = α b S t β 1 h bt β 2 ,

33

34 where S t is the spawning stock in period t ; α b , β1 , β2 are the param-

35 eters that need to be estimated Substituting (27) into (26) yields

41 where α = αb m β 2 − 1 Using the data from the Bornholm cod ﬁsheries,

42 the estimation for the variable cost function is described in Table 5

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