Bioeconomic model of Eastern Baltic cod under the influence of nutrient enrichment

Bioeconomic model of Eastern Baltic cod under the influence of nutrient enrichment tài liệu, giáo án, bài giảng , luận v...

BIOECONOMIC MODEL OF EASTERN BALTIC COD UNDER THE INFLUENCE OF NUTRIENT ENRICHMENT

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

Department of Environmental and Business Economics, University of Southern Denmark, Denmark Faculty of Development Economics, VNU University of Economics and Business, Vietnam

E-mail:thanhmpa@gmail.com

Abstract The ob jective of this paper is to study the economic

man-agement of Eastern Baltic cod (Gadus morhua) under the influence of

nutri-ent enrichmnutri-ent Average nitrogen concnutri-entration in the spawning areas during

the spawning season of cod stock is chosen to be an indicator of nutrient

en-richment The optimal cod stock is defined using a dynamic bioeconomic

model for the cod fisheries The results show that the current stock level is

about half of the estimated optimal stock level and that the current total

allowable catch (TAC) is about one-fourth of the optimal equilibrium yield.

The results also indicate that the benefit from a reduction in nitrogen very

much depends on the harvest policies If the TAC is set equal to the optimal

equilibrium yield, the benefit of a nitrogen reduction from the 2009 level to

the optimal nitrogen level would be about 604 million DKK over a 10-year

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

management plan is chosen, the benefit would only be about 49 million DKK

over a 10-year time horizon.

Key Words: Bioeconomic model, Eastern Baltic cod, eutrophication.

1 Introduction. The objective of this paper is to study the economic

man-agement of Eastern Baltic cod (Gadus morhua) under the influence of nutrient

enrichment This fish stock inhabits the regions East of Bornholm in the ICES’(The International Council for the Exploitation of the Sea) subdivisions 25–32, andits spawning season begins in early March and ends in September–October (Bagge

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

in the Baltic Sea In Denmark, it accounts for over 33% of the total cod landed andcontributed about 14% to the total landing value of Danish fisheries in 2009 (Anon[2009]) In Sweden, it accounted for 4% of the total catch, but it contributed about19% to the total landing value of Swedish fisheries in 2004 (Osterblom [2008]).Nine countries currently harvest Eastern Baltic cod: Germany, Finland, Russia,Estonia, Latvia, Lithuania, Poland, Sweden, and Denmark Poland, Sweden, andDenmark had the largest catch shares, which accounted for 22%, 21%, and 17%

of the total cod landing from the eastern Baltic Sea in 2009, respectively (ICES

& Economics (FAME), Department of Environmental and Business Economics, University of

C o py rig ht c 2012 W iley Perio dicals, Inc.

259

[2010a]) The harvesting of eastern cod mainly occurs at the beginning of the year.For example, in Denmark, landing from January to June accounted for about 73.2%

of the total Eastern Baltic cod landings in 2009 (Anon [2009]) There were about13,900 fishing vessels with a total 246,345 GT in the Baltic countries (withoutRussia) in 2005 (Horbowy and Kuzebski [2006]) Trawls and gillnets are the mainfishing gears for eastern Baltic cod fisheries, which contributed about 70% and 30%

of the total landing in 2009, respectively (ICES [2010b]) In 2010, the total landing

of Eastern Baltic cod was 50,277 tons, which was approximately equal to 12.8% ofthe highest landing of 391,952 tons in 1984 (ICES [2010a, 2011]) The ICES hasrecommended that TACs should be calculated on the basis of fishing mortality andthe stock spawning biomass (Radtke [2003]) The TACs are annually allocated tothe member states with the same percentages annually (Nielsen and Christensen[2006]) The TAC for Eastern Baltic cod has been separate from Western Balticcod since 2004, and it was set of 56,800 tons in 2010 (ICES [2009])

Eastern Baltic cod has been managed under a recovery program since 2007 (EC[2007]) The main target of the recovery program is to ensure the sustainable ex-ploitation of the cod stocks by gradually reducing and maintaining the fishing mor-tality rates at certain levels (EC [2007]) The recovery program does not includechanges in nutrient loadings as a policy option However, the decline of the codstock in the early 1990s was considered a consequence of not only fishing pressurebut also environmental effects including temperature, salinity, and oxygen (K¨oster

et al [2009]) During this time, nutrient enrichment was also considered a serious

environmental problem for ecosystems in the Baltic Sea (MacKenzie et al [2002], Rockmann et al [2007], HELCOM [2009]) When excess inputs of nutrients are in-

troduced into ecosystems, which is called eutrophication, the water becomes turbidfrom the dense populations of phytoplankton Large aquatic plants are outcompetedand disappear along with their associated invertebrate populations Moreover, de-composition of the large biomass of phytoplankton cells may lead to low oxygenconcentrations (hypoxia and anoxia), which kill fish and invertebrates The outcome

of eutrophication is a community with low biodiversity and low esthetic appeal

(Be-gon et al [2006]) In 1988, the Helsinki Commission (HELCOM)1decided to reducenutrient inputs by 50% because of the serious eutrophication problem in the BalticSea.2

Insufficient attention has been given to the effect of nutrient enrichment on the codstock (Bagge and Thurow [1994], HELCOM [2009]) even though many papers havestudied the effects of temperature, salinity, oxygen, and inflows from the NorthSea (Westin and Nissling [1991], Gronkjer and Wieland [1997], Nissling [2004],

Koster et al [2005], Mackenzie et al [2007], Rockmann et al [2007], Heikinheimo

[2008]) Nutrient enrichment can affect both the growth and the reproduction of theexploited species, and these effects depend on the nutrient concentration level in

the main habitat of the species (Breitburg et al [2009]) Knowler [2001] empirically

finds the effects of phosphorus concentration on the recruits of the anchovy stocks

in the Black Sea Smith and Crowder [2005] find the effects of nitrogen loadings onthe growth of the blue crab fishery in the Neuse River Estuary Finally, Simonitand Perrings [2005] find the effects of nutrient enrichment on the growth of fishstocks in Lake Victoria Compared with these studies, this paper proposes a moregeneral approach that includes both the fisheries sector and the pollution sector

in a bioeconomic model With respect to this general approach, Tahvonen [1991]theoretically develops a model that combines optimal renewable resource harvestingand optimal pollution control Murillas-Maza [2003] also theoretically investigatesinterdependence between pollution and fish resource harvest policies In this paper,

a more realistic growth function is applied by including both the growth and therecruitment of fish stock In addition, the theoretical model is also applied to thecod stock and nutrient pollution in the Baltic Sea The following specific questionswill be discussed:

(1) How does nutrient enrichment affect the Eastern Baltic cod fisheries?

(2) What is the optimal harvest compared with the current level?

(3) How much would the cod fisheries benefit from nutrient reductions?

This paper proceeds as follows: The next section describes the model The ing section is an empirical analysis of the Eastern Baltic cod The paper concludeswith a summary derived from the empirical analysis

follow-2 The bioeconomic model. The bioeconomic model is traditionally basedboth on a biological model and an economic model of the fishery The social objec-tive is to maximize the present value of the profit of the involved fishermen over acertain time horizon subject to the biological model of the fish stock We expandthe model to include the consequences of eutrophication We show how the opti-mal harvest policy depends on the eutrophication level In the following section themodel is explained

2.1 Population dynamic. In a basic form, changes in biomass of an exploitedfish population over time depend on the recruitment, growth, capture, and naturaldeath of individuals3(Ricker [1987], Beverton and Holt [1993]) The spawning stock

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

of the population exposed to the fishery Recruitment occurs when the fish grow

to maturity and enter the spawning stock It takes some time to progress fromspawning to recruitment; therefore we apply a delayed discrete-time model (Clark[1976], Bjorndal [1988]):

S t+1 = (S t − H t ) G t + R t ,

(1)

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

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

of period t and that, S t − H t is the escapement The escapement will grow by the

function G t = G(S t ) The recruitment is a function of the stock that need γ periods

to grow into maturity R t = R(S t−γ ) To extend the model, we include the nutrient concentration N t in both the growth and recruitment functions

G t = G(S t , N t)

R t = R(S t−γ , N t−γ)(2)

Both functions are assumed to be continuous and differentiable

2.2 The bioeconomic model. It is assumed that the net benefit of the

fish-ery is a function of total harvest (H ) and spawning stock biomass (SSB) (S ) with

π t = π(H t , S t ) The function π is assumed to be continuous, concave, and twice

differentiable A general economic objective is to maximize the net present value(NPV) of the net benefits from the fishery subject to the dynamics of the fish stock:

1+ r is the discount factor, and r is the discount rate The harvest has

to be positive so H t ≥ 0 The maximization problem is restricted by the present

and previous γ years of stock levels However, we are only interested in finding the

optimal stock and harvest levels, so the initial conditions are ignored

Problem (3) may be solved using the Method of Lagrange Multipliers (see e.g.,Conrad and Clark [1995]) We formulate the (current) Lagrange expression as

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

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

of the resource in period 0 + 1 The partial deviates of the Lagrange model are:

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

condition for optimization requires that deviations (6) and (7) be equal zero are:

In equilibrium, all variables are stationary over time, and the t subscript can

therefore be dropped The restriction (4) implies

π H + 1) is called the marginal stock effect(MSE), which represents the stock density influence on harvesting costs (Clark andMunro [1975], Bjorndal [1988]) The term (S −R ) G G S + ρ γ R S in (12) is the marginalproductivity It consists of two parts: the first part is related to the growth of theescapement, and the second part is related to the recruitment The second part

is discounted with γ periods as a consequence of the delay in maturity Given a discount rate of r , equation (12) can be solved for the optimal stock level, S ∗, as a

function of nutrient concentration (N ) Furthermore, the optimal harvest level, H ∗,can be derived from (10) As the recruitment and growth functions are functions of

N , the NPV of the resource when it is optimized is also a function of N

3 An empirical analysis of Eastern Baltic cod. The bioeconomic model,

as presented in the previous section, is now applied to the Eastern Baltic codfisheries under the influence of nutrient enrichment The TACs of the cod stock isexpected to be relatively constant, for example, it does not change by more than15% between two subsequent years (EC [2007]) In this case and following Voss

et al [2011], the objective of the function is to maximize the NPV of utility function

π S

π H .

Equations (10) and (12) can still be used to calculate the optimal stock andoptimal harvest for the Eastern Baltic cod fisheries.5 We use the Rsolnp package inthe R software developed by Ghalanos and Theussl (Ghalanos and Theussl [2011])

to solve the optimization equation (13)

3.1 Data. Data on the annual cod landings, SSB, and recruitments are able directly from ICES database (ICES [2010a]) The total nitrogen indicator

avail-(NTOT ) is derived from the HELCOM database.6 To formulate a proper gen indicator for the cod stock, we use data collected from the stations that, arelocated in the ICES’ subdivisions 25, 26, and 28 with bottom depths greater than orequal to 20 m In addition, we only use data collected during the spawning season

nitro-of the cod stock, which is from March to September The nitrogen concentration inthe spawning areas during the spawning season is calculated as follows

where N t is the nitrogen indicator in year t, k is the number of observations, and

N T OT i is the nitrogen concentration:

⎧

⎪

⎪

in ICES 25, 26 and 28 from March to September of year t

in stations with bottom depth≥20 m.

Table 1 shows the nitrogen index and the biological data of the Eastern Balticcod fisheries from 1966 to 2009

Statistical data from the Ministry of Food, Agriculture and Fisheries in Denmarkare used to estimate the variable cost function In particular, a time series set of the

TABLE 1 Biological and environmental data: N has been estimated, SSB and Recruits are

from ICES [2011a].

3.2 Recruitment function. The stock–recruitment relationship of the ern Baltic cod is assumed to follow a quadratic function, and the nitrogen concen-tration is included as follows (Simonit and Perrings [2005]):

East-R t = aS t−γ N t−γ + bS t−γ2 + cN t−γ2 S t−γ

(15)

TABLE 2 Data for the Bornholm cod fisheries.

Year Total variable cost (million DKK) Total landing (1000 tons)

Source: IC ES, Fishkeriregnskabsstatistik, Fiskeristatistisk ˚ arb og and ow n calculations.

or the alternative form is

R t

S t−γ = aN t−γ + bS t−γ + cN t−γ2 .

(16)

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

γ = 2 The estimation of the recruitment functions for the Eastern Baltic cod are

described in Table 3

The model explains 53% the variance of the dependent variable, and all the rameters are significant at the 5% level or better Additionally, the models indicatethe autocorrelation in the residuals, which is often noted in time series data de-rived from VPA (Knowler [2007]) The estimated stock–recruitment function forthe Eastern Baltic cod is the following8

pa-R n t = 0.2015826S t−2 N t−2 −0.0016263S2

t−2 −0.0058455S t−2 N t−22 .

(17)

In this equation, R is measured in millions, S is measured in thousand tons, and

N is measured in millimole/m3 Given the average weight of cod at age 2 from

1966 to 2009, w = 0.209 kg (ICES [2010b]), the final stock–recruitment function is

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

model and the data for 1966–2009.

N ote: T he dep endent variable isR t/S t– 2 andn = 39 The models have b een estimated with first order

auto correlation, using the Prais–W insten transform ed regression estim ator.

In equation (18), R and S are measured in thousand tons, and N is measured in

millimole/m3 The graph of the stock–recruitment function is showed in Figure 1.The main characteristics of the stock–recruitment function are the following

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

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

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

3.3 The growth function. We use a simple version of the growth function(see e.g., Bjorndal [1988], Kronbak [2002]) Following Ricker [1987], the growthfunction is assumed as follows

G t = e δ t ,

(19)

where δ t is called the net natural growth rate, which equals the instantaneousgrowth rate minus the instantaneous natural mortality rate We assume that ni-trogen enrichment has minimal effects on the growth of cod stock and it is ignored

in the growth function.9 The relationship between the net natural growth rate (δ) and the SSB (S ) is assumed to follow a linear form10:

δ t = δ(S t ) = d + f S t

(20)

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

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

ac-cording to the following formula

of the dependent variable In addition, δ  (S ) < 0 for all stock levels, which implies

that the net natural growth rate reduces when the stock increases The net naturalgrowth rate is described as follows:

δ t = 1.140578 − 0.0012049S t

(22)

TABLE 4 Estimation of the natural growth for the Eastern Baltic cod using data for

The main characteristics of this function are the following:

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

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

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

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

The Eastern Baltic cod stock may have been closest to its carrying capacity inlate 1970s and early 1980s The current SSB level of 308.787 thousand tons (ICES[2011]) is about half of the stock level at the maximum sustainable yield (SSB atMSY)

3.4 Variable cost function. It is assumed that the total variable cost of

the fisheries is a function of the total harvest (H ) and the SSB (S ) (Clark [1990], Sandberg [2006], Rockmann et al [2009]) Since cod is an internationally traded

commodity, it is further assumed that cod fisheries have a perfectly elastic demand

curve The net benefit function of the Eastern Baltic cod fisheries in period t can

be defined as follows:

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

(24)