Emmi Nieminen
Marko Lindroos &
Outi Heikinheimo
Optimal bioeconomic multispecies
fisheries management: A Baltic Sea
case study
University of Helsinki
Department of Economics and Management
Discussion Papers n:o 53
Helsinki 2011
Optimal bioeconomic multispecies fisheries management: A Baltic Sea case
study
Nieminen, E.1, Lindroos, M.1 & Heikinheimo, O.2.
1
University of Helsinki, Department of Economics and Management, Finland.
2
Finnish Game and Fisheries Institute, Helsinki, Finland.
Abstract
The aim of the paper is to assess the Baltic cod, herring and sprat fisheries by a
bioeconomic model. We compare the current fishing policies to optimal policies under two
different environmental conditions. According to the results the fishing mortalities of Baltic
cod, herring and sprat are not at the most profitable level, and they should be lower in order
to maximize the profits. The lower fishing mortality of cod would result in a cod stock
recovery. If the environmental conditions in the Baltic Sea improved, cod stock would recover
even without a decrease in the fishing mortality. In addition, the increased cod stock would
restrict herring and sprat stocks remarkably, and harvesting of these species would not be as
profitable anymore.
Keywords: Bioeconomic modelling; fisheries management; multispecies modeling
Funding from the Academy of Finland is gratefully acknowledged.
1
1 Introduction
Baltic cod (Gadus morhua callarias), Baltic herring (Clupea harengus membras (L.)) and
sprat (Sprattus sprattus) are the most commercially exploited fish species in the Baltic Sea.
They constitute about 95 % of the total catches in the Baltic Sea (ICES 2009). Especially the
cod fishery has been managed from a biological perspective and the economic performance
has been more or less ignored. However, the conservation policy has not been that successful,
the cod stocks have decreased, and the economic profits have been poor. Since 1985 the cod
catches decreased rapidly and at the same time the catches of sprat, a prey species of cod,
increased (Fig. 1). The herring catches slightly decreased, but in the recent years they have
been increasing again.
Fig. 1. Development of the catch sizes of cod, herring and sprat in the Baltic Sea (modified
from ICES 2010a).
These three species have special interactions. Baltic cod is the main predator in the Baltic Sea
and it feeds on herring and sprat. In addition, adult cod feed on young cod, and both cod and
sprat feed on cod eggs. Cod cannibalism has been suggested to have a strong self-regulatory
2
effect on cod stock. (Sparholt 1994.) These kinds of interactions have strong effects on the
fish stock development in the Baltic Sea, and also important influences on both biological and
economic performances. Similarly, economic factors can have biological effects. When some
species is heavily harvested, the price may decrease due to the increased supply. In
consequence of this the fishers may start harvesting some other species which have higher
price. Thus, the amounts of the stocks can vary due to price fluctuations.
We develop a deterministic, discrete multispecies bioeconomic model for Baltic cod, Baltic
herring and sprat concerning the Baltic Sea fishery. The aim is to find the economically
optimal fishing mortalities for these species. This is done by constructing a numerical
biological model including economic components. The optimizing is conducted by a
viewpoint of one fisheries management planner, and the aim is to maximize the social welfare
of the entire fisheries industry. If the optimization was conducted by an individual fisher’s
point of view, the catches would be higher and furthermore the stocks lower. After
constructing the model, we compare four different scenarios. The first two scenarios are
conducted under prevailing environmental conditions with current and optimal fishing
mortalities, and the next two scenarios are conducted under more favourable environmental
conditions for cod recruitment.
Bioeconomic fishery models have often been applied for only one species, and species
interactions have been neglected. These kinds of single-species models have been applied for
cod fishery (Armstrong & Sumaila 2000; Röckmann 2006; Kronbak & Lindroos 2007; Kar &
Chattopadhyay 2009), as well as for herring fishery (Björndal et al. 2004; Kulmala et al.
2007). Bioeconomic models including several species have been applied to some extent, but
the case studies have focused on some other regions than the Baltic Sea (Placenti et al. 1992;
3
Ulrich et al. 2002). In addition, more general multispecies bioeconomic studies omitting
numeric analysis have been conducted (Chaudhuri 1986; Agar & Sutinen 2004). Multispecies
modelling have often been conducted by using complicated models, such as multispecies
virtual population analysis, MSVPA (Sparre 1991; Magnusson 1995). These models consider
only biological aspects, and the economics are fully ignored.
The main extension to earlier bioeconomic models concerning the Baltic Sea is that now we
take into account the interactions of different species. The study region is the whole Baltic
Sea while most of the earlier studies have been applied to some specific part of the sea, for
example the Central Baltic. In addition, we include the environmental conditions affecting
cod recruitment into the model, and show how much these different salinity levels can have
effects on the stock dynamics of all of the three species.
Section 2 shortly presents the species included in our model and their fisheries. Sections 3 and
4 include the biological and economic components of the bioeconomic analysis, and section 5
constructs the bioeconomic optimization problem and collects all the parameters and model
values. Section 6 presents the results of each scenario and a sensitivity analysis conducted,
and finally section 7 concludes the study.
2 Fishery of the species
Baltic cod
Cod is the most important and valuable fish species in the Baltic Sea. The stocks have instead
been declining and the economic performance has been very poor (ICES 2009; AER 2009).
The abundance of cod is low at present, and the current level of cod fishery is not sustainable
4
(HELCOM 2008a). Still, recently stocks have been increasing again due to a lower fishing
mortality, but the catches are still very low because of fishing regulations (ICES 2010a).
There are three management stocks for cod: Subdivision 21 (Kattegat), subdivisions 22-24
(Western Baltic cod) and subdivisions 25-32 (Eastern Baltic cod) (Fig. 2). Western and
Eastern cod stocks have separate spawning areas, but some mixing happens regularly between
the stocks (FGFRI 2009a). A successful spawning is highly dependent on favourable
environmental conditions. Cod eggs can survive only in quite saline and oxygen-rich water,
and thus it can be mainly found from the southern parts of the Baltic Sea (HELCOM 2008a).
Nowadays too low salinity and oxygen levels are the main reasons constraining the growth of
the cod stocks (Köster et al. 2005).
Fig. 2. ICES subdivisions in the Baltic Sea (HELCOM 2010).
Baltic herring
Herring is used for human consumption or animal fodder, depending on its size. The usage is
usually driven by market conditions. (ICES 2009.) Cod predation and competition with sprat
5
affect negatively the herring stock. Because herring and sprat are harvested as a mixture, their
reported catches are somewhat uncertain. (ICES 2010b.)
Herring is divided into four separate stocks. Herring in subdivisions 25-29 and 32 (excluding
Gulf of Riga) is the so called Central Baltic herring (Fig. 2), and it is the most abundant
herring stock in the Baltic Sea. The stock had a high biomass level in the early 1970s but it
has decreased since then. The spawning stock biomass and the recruitment are at present
below the long-term average. The stocks of Gulf of Riga herring (subdivision 28.2) and
Bothnian Sea herring (subdivision 30) are at high levels, but the state of Bothnian Bay herring
(subdivision 31) is much poorer. (ICES 2009.)
Baltic sprat
Sprat is a quite similar species to herring, and it is mainly used for canned food or animal
fodder (FGFRI 2009c). Sprat can be found in most parts of the Baltic Sea (HELCOM 2008b),
and at present it is commercially the most abundance exploited fish species in the Baltic Sea
(ICES 2010a). The sprat stock is heavily dependent on the abundance of the cod stock
through predation mortality. This can be seen from the historical statistics: when the cod stock
has been at a high level, the sprat stock has been lower. When the cod biomass decreased in
1990s, the sprat stock recorded a high level. (Möllmann et al. 2003.)
Sprat is managed by one TAC concerning the whole Baltic Sea (ICES 2009). There are large
fluctuations between years in the sprat catches and in the stock sizes. The catches started
growing in the latter half of the 20th century due to increased trawling, but started decreasing
in the 1980s because of increased cod stock. Since the year 1990 the sprat catches have
increased again and become five times larger. (FGFRI 2009c.)
6
3 Population dynamics model
We simulate the population dynamics for each species in age groups 2-81 as
N a (t )
N a 1 (t 1)e
Z a 1 ( t 1)
(1)
where Na-1(t-1) is the number of individuals in age group a-1 at time t-1, and Za-1(t-1) is the
total mortality of the cohort (Hilborn & Walters 1992). The total age-specific mortality
Za-1(t-1) consists of fishing mortality F(t-1), which we assume to be the same for each age
group that is harvested, and natural mortality Ma-1(t-1):
Z a 1 (t 1)
F (t 1) M a 1 (t 1)
(2)
The number of individuals in the first age group is derived from a recruitment function that is
based on a spawning stock biomass (SSB), which is the sum of the biomass of mature fish
over all age groups:
SSB (t )
N a (t )e
F (t ) M a (t )
MOaWAa
(3)
a
where N a (t )e
F (t ) M a (t )
is the stock size of age group a at the time of spawning, MOa is the
proportion of mature individuals in age group a, and WAa is the age-specific mean weight of
an individual (Kulmala et al. 2007).
1
Age group 2 consist of individuals aged 1-2 years, age group 3 consist of individuals aged 2-3 years and so on.
7
The recruitment function for herring and sprat is modelled by using Ricker’s formation as in
ICES (2005) and Heikinheimo (2010):
R(t )
SSB(t )e
SSB (t )
(4)
where R(t) is the amount of recruits in time period t, SSB(t) is the spawning stock biomass,
and
and
are the recruitment parameters. Instead, the recruitment of cod is modelled using
a function according to Hilborn and Walters (1992) that has been applied also in Heikinheimo
(2010):
R (t )
where ,
and
SSB (t )e
SSB ( t )
(E E)
are recruitment parameters. The difference E
(5)
E is the deviation from the
average salinity level, and we denote it as parameter . This environmental parameter affects
cod recruitment, and we define it according to ICES (2005). The deviation from the mean
salinity level was about 0.8 in 1974-1986, and we use this value for the case of good
environmental conditions. Based on a bad salinity period in 1987-2004, we use a value of
-0.05 for bad environmental conditions. (Heikinheimo 2010.) We assume that at present bad
environmental conditions are predominant. We make comparison between low and high
salinities in order to observe consequences the good environmental conditions could have.
Salinity level has a direct link to the climate change. Some scenario simulations confirm that
average salinity would decrease due to climate change. This occurs partly because
precipitation would increase in general, and at the same time the runoff of river flows would
8
increase. These kinds of major changes would have impacts on species distribution and food
webs in the Baltic Sea. (HELCOM 2007.)
The annual harvest for each age group is given by the equation
H a (t )
F (t )
* N a (t ) *(1 e
F (t ) M a (t )
F ( t ) M a (t )
)
(6)
and the annual total harvest in biomass
H (t )
WAa H a (t )
a
(7)
(Hilborn & Walters 1992; Kulmala et al. 2007). We assume that only cod in age groups 3-8
are harvested, and herring and sprat harvesting considers age groups 2-8. These fishing
mortalities are constant for each harvested age group.
Predation mortalities
The main interactions we take into consideration are cod predation on herring, sprat and on
young cod (Fig. 3). In addition, the fishing fleet affects the population dynamics of each
species.
9
Fig. 3. The main interactions taken into account in the model.
We use predation mortality M2, which is part of natural mortality M, for illustrating the
predation effect towards herring and sprat, and we estimate it by using the predation function
according to Heikinheimo (2010). The number of herring and sprat eaten by one cod in age
group a in one year t, or the functional response, is
Pa (t )
Ca ( N h s (t )) n
( N h s (t )) n ( Dh s ) n
(8)
where Ca 2 is the maximum herring and sprat consumption in numbers by cod in age group a.
In other words, Ca is the number of prey individuals eaten in one year when the abundance of
the clupeids was at a maximum level. The values for Ca are derived according to the results of
SGMAB (Study Group on Multispecies Assessment in the Baltic) key run. Dh+s3 represents
the size of the herring and sprat stocks when the consumption was half of the maximum.
Heikinheimo (2010) used a value of 260,000 million for Dh+s, but it considered only the cod
stock in ICES subdivisions 25-32. We use a value of 325,000 million for the whole Baltic Sea.
2
Ca=[30 100 135 135 135 135 135 135]. Cod in the first age group consumes sprat and herring together 30
individuals in one year, and cod in the second age group consumes 100 individuals and so on.
3
Subscripts c, h, and s refer to cod, herring and sprat respectively throughout the study.
10
Nh+s(t) is the size of the herring and sprat stocks in numbers, a is age group of cod, and n is a
constant that determines the type of the functional response. We use type III functional
response, and thus n=2. (Heikinheimo 2010.)
The functional responses for herring and sprat separately are
Ph , a (t )
N h (t ) Pa (t )
N h (t ) wN s (t )
(9)
Ps ,a (t )
wN s (t ) Pa (t )
N s (t ) wN s (t )
(10)
where Ph,a (t) is the number of herring eaten by one cod in age group a in one year t, and Ps,a(t)
is the number of sprat eaten by one cod in age group a in one year t. Nh(t) and Ns(t) are the
numbers of herring and sprat individuals in the stocks. Cod prefers sprat to herring possibly
due to the bigger size of herring or its behavior (ICES 2005). Thus, we use a preference
coefficient w=2 for sprat. The total predation mortalities M2 for herring and sprat caused by
cod in one year are
8
Nc,a (t ) Ph,a (t )
a 1
N h (t )
M2h (t )
8
N c ,a (t ) Ps ,a (t )
a 1
N s (t )
M2s (t )
(11)
(12)
where Nc,a(t) is the number of cod in one age group a. Since younger and smaller individuals
are more preferred as food, the predation mortality of herring in the first age group is 3*M2h.
11
Sprat seems to be quite equally preferred as food within different age groups, and thus age
differentiation has not been made. (Heikinheimo 2010.)
Other interactions
There also exist other interactions that we take into account. Herring benefits from a low
abundance of sprat stock, and the mean weight in the herring spawning stock increases under
these conditions. The sprat stock is low when the abundance of cod is high due to the high
cod predation mortality on sprat. Thus, the mean weight in the herring spawning stock is
modelled to be dependent on the size of the cod stock. When the cod stock size increases, the
sprat stock decreases and furthermore, the mean weight in the herring spawning stock
increases. Herring benefits from a lower sprat stock due to increased abundance of food and
space. (Heikinheimo 2010.)
Cod cannibalism is not directly included into the model, but it has been taken into
consideration by higher natural mortality. Cannibalism increases along with the growing
density of individuals since alternative food is more difficult to find. We model the
cannibalism simply by using higher natural mortality rate for young age groups when cod is
abundant. We assume that the natural mortality is higher for two or three first age groups
depending on the different cod stock sizes. (Heikinheimo 2010.)
4 Economic model
Cost function
Our cost function structure for cod harvesting follows Arnason et al. (2000):
12
H (t ) 2
Cc (t ) cc
B(t )
(13)
where Cc(t) are the total costs of cod harvesting in one year t, cc is a cost parameter for cod
harvesting, H(t) is the total yield of cod, and B(t) is the total biomass of cod. Costs are total
costs except for depreciation and interest payments. (Arnason et al. 2000.) We use the cost
parameter according to Kronbak and Lindroos (2007), where cc is estimated for the Baltic Sea
cod fishery (Kronbak & Lindroos 2007).
For herring and sprat the costs are defined following Gordon (1954). The cost function is
C (t ) cE (t )
(14)
where C(t) are the total costs for harvesting, c is harvesting cost per effort day, and E(t) is the
amount of the effort days (Gordon 1954). This can be furthermore rewritten, and the total
costs in one year are estimated as the sum of the costs of sprat, fodder herring, and human
consumption herring harvesting as follows:
Ch s (t )
Xc f
Fh (t ) Fs (t )
F (t )
(1 X )cd h
qf
qd
(15)
The cost parameter c is different for these two harvesting categories, as well as is the
catchability coefficient q. We assume based on Kulmala et al. (2007) that harvesting cost
parameter cf is 644 €/effort day for fodder herring and sprat, and cd is 3,227 €/effort day for
herring that goes for human consumption. We use different fishing costs for food and fodder
herring because food herring vessels are bigger and have more crew than fodder vessels, and
13
they also have higher fuel costs. In addition, food vessels have higher quality demands related
to hygienic requirements. (Kulmala et al. 2007.) Catchability coefficient q is divided in
Kulmala (2004) into several classes between different vessel segments, and we combine these
coefficients so that q is 0.00004338 for human consumption herring and 0.0000047115 for
sprat and fodder herring (Kulmala 2004).
We assume that age groups 2-4 (the first age group is not harvested at all) refer to fodder
herring and age groups 5-8 to herring that go for human consumption. Parameter X is the
herring catch in the age groups 2-4 plus the total sprat catch divided by the total catches of
these two species in one year:
4
8
H h, a (t )
X
a 2
8
H s , a (t )
a 2
8
H h, a (t )
a 2
(16)
H s , a (t )
a 2
When we use this kind of parameter X, the costs are formed accurately. A particular
proportion of the harvesting faces lower harvesting costs (fodder herring and sprat) and the
rest face higher harvesting costs (human consumption herring).
Price function
There exist many different variables that affect the fish price, and the amount of harvests
cannot explain the price alone. Thus, we assume that the price is constant for each species,
and it does not vary within the amount of harvested fish or for any other reason. We make a
price differentiation only within different sizes of herring. Herring goes for two purposes: for
animal fodder and human food. Animal fodder herring faces lower price at the markets than
14
larger human consumption herring. We use prices 0.13 €/kg for fodder herring and 0.2 €/kg
for human consumption herring. Cod price used is 1.35 €/kg and sprat 0.13 €/kg. The prices
are calculated from AER (2009) reports for a several year averages of Baltic Sea coastal
countries.
5 Bioeconomic optimization and model parameters
The aim of the bioeconomic analysis is to solve the optimal fishing mortality path F (our
choice variable) over the time period. We construct a deterministic, discrete fishery model,
and use a simulation period of 50 years with a one year time step. Starting values are the
averages of years 2006-2008 from ICES (2009) and the simulation period is 2008-2057.
For solving the economically optimal fishing mortality paths we first form an objective
function, and then maximize the net present value (NPV, the discounted difference between
revenues and costs) over the simulation period under biological constraints. Maximizing is
conducted by optimizing the fishing mortality paths of each species.
We conduct the modelling by using MATLAB software, and use its fmincon optimization
toolbox for maximization. This toolbox finds the minimum or maximum of constrained
nonlinear multivariable function. The maximization follows Gordon’s (1954) approach. The
objective function to be maximized in order to maximize the social welfare is the discounted
net present value of the profits over simulation period from harvesting, i.e. the total flow of
the discounted future profits:
50
max
t=1
Pc (t ) Ph (t ) Ps (t ) Cc (t ) Ch s (t )
(1 r )t 1
(17)
15
This objective function consists of revenues and costs of harvesting. Pc(t), Ph(t) and Ps(t) refer
to the revenues of harvesting of cod, herring and sprat respectively, and the revenues are
species specific price p (€/kg) times each species catch in biomass H(t). Cc and Ch+s are the
costs of cod and herring-sprat harvesting. Parameter r is the discount rate and t is time, in our
model a year. We maximize this objective function (17) under biological harvesting constraint
(equation 6) by controlling the fishing mortality. A population dynamics equation (equation 1)
constraints the harvesting.
The MATLAB code includes all needed starting values for cod, herring and sprat that are
based on ICES (2009). All parameters and initial values are collected in Tables 1-4.
Table 1. Summary table of parameter values.
a
cc, cf, cd
q f , qd
p
Age range
Recruitment function parameter
Recruitment function parameter
Recruitment function parameter
Recruitment function parameter
Cost parameter
Catchability coefficient
Price of fish (€/kg)
Cod
1-8
7.58
0.001
1.55
1)
0.8/-0.05
1.26
1.35
Herring
1-8
42
-7
4.6*10
2)
644/3227
-6
-5 2)
4.7*10 /4.3*10
0.13/0.2
2)
1)
Cod recruitment parameter under good/bad environmental conditions.
2)
Cost parameter, catchability coefficient and price of fodder herring/human consumption herring.
Sprat
1-8
5
e
-6
5.0*10
644
-6
4.7*10
0.13
16
Table 2. Initial values of population dynamics of cod.
Age
group
a
1
2
3
4
5
6
7
8
1)
Population
size ('000)
Nc,a(1)
207 503
242 543
156 618
68 048
25 498
72 460
2 095
929
Mean
weight (kg)
WAc,a
0.06
0.19
0.42
0.90
1.35
1.81
2.56
4.30
Maturity
proportion
MOc,a
0
0.12
0.39
0.78
0.88
0.87
0.84
0.86
Natural
mortality
Mc,a 1)
0.2/0.7/2.2
0.2/0.3/0.65
0.2/0.2/0.3
0.2/0.2/0.21
0.2/0.2/0.2
0.2/0.2/0.2
0.2/0.2/0.2
0.2/0.2/0.2
Natural mortalities of cod with stock sizes of <500 million / 500-1,500 million / >1,500 million individuals.
Table 3. Initial values of population dynamics of herring.
Age
group
a
Population
size ('000)
Nh,a(1)
Mean
weight (kg)
WAh,a2)
Maturity
proportion
MOh,a
Natural
mortality
M1h,a
1
26 900 628
0.016
0
0.21
2
13 999 278
0.025/0.04/0.05
0.64
0.21
3
9 841 531
0.025/0.04/0.05
0.94
0.20
4
9 215 972
0.025/0.04/0.05
0.99
0.22
5
6 724 475
0.025/0.04/0.05
0.98
0.22
6
4 431 361
0.025/0.04/0.05
1
0.20
7
1 917 298
0.025/0.04/0.05
1
0.20
8
1 500 210
0.025/0.04/0.05
1
0.22
1)
Mean weight in the herring spawning stock (age groups 2-8) with cod stock sizes of < 1,000 million / 1,0001,500 million / > 1,500 million individuals
Table 4. Initial values of population dynamics of sprat.
Age
group
a
Population
size ('000)
Ns,a(1)
Mean
weight (kg)
WAs,a
Maturity
proportion
MOs,a
Natural
mortality
M1s,a
1
83 387 000
0.006
0.17
0.26
2
46 331 667
0.008
0.93
0.26
3
37 532 333
0.009
1
0.24
4
22 769 000
0.01
1
0.23
5
11 522 667
0.01
1
0.23
6
3 034 333
0.011
1
0.23
7
1 069 000
0.011
1
0.23
8
1 483 333
0.012
1
0.24
17
6 Results
We simulate the model under four different scenarios. The first scenario is the current
situation with the current fishing mortalities under bad environmental conditions (Table 5).
Scenario 2 is also conducted under bad environmental conditions, but now we optimize the
fishing mortalities. Scenarios 3 and 4 consider situations under good environmental
conditions with current and optimal fishing mortalities.
Table 5. The four different scenarios.
Fishing mortalities
Environmental conditions
Scenario 1
Current
Bad
Scenario 2
Optimal
Bad
Scenario 3
Current
Good
Scenario 4
Optimal
Good
The net present values are positive in each scenario (Fig. 4), i.e. the fisheries are profitable in
each case. Still, NPV is higher in other scenarios compared to the first scenario. In Scenario 2
NPV is almost three times higher than in Scenario 1 (Table 6) due to reduced fishing
mortality that leaves more cod into the sea for future harvests. Under good environmental
conditions NPV is also higher with the optimal fishing mortalities (Scenario 4) than with the
current mortalities (Scenario 3). Thus, the Baltic Sea fishery of these three species seems to
be profitable in all scenarios, but by fishing mortality optimizing the net present value can be
significantly higher. In Scenario 3 NPV is almost seven times higher than in Scenario 1, and
in Scenario 4 ever higher. An interesting point is that in Scenario 2 NPV becomes almost
three times higher compared to Scenario 1, but the proportional increase is much less in
Scenario 4 compared to Scenario 3. According to this, the fishing regulations are relatively
more important under bad environmental conditions.
18
’
Fig. 4. The net present values under different scenarios with 2 % discount rate4.
All the main results of each scenario are compiled in Table 6, and next we take a closer look
of each of them; first under bad environmental conditions and then under improved
environmental conditions.
Table 6. Average steady states of the four scenarios.
Nc
Nh
Ns
SSBc
SSBh
SSBs
Fc
Fh
Fs
Hc
Hh
Hs
NPV
Scenario 1
0.7
66
190
0.2
0.9
0.9
0.59
0.24
0.47
88
200
300
1.8
Scenario 2
1.5
75
240
0.5
1.6
1.3
0.28
0.21
0.05
160
310
57
5.3
Scenario 3
5.5
49
10
1.0
0.9
0.04
0.59
0.24
0.47
570
200
11
12.1
Scenario 4
5.5
51
48
1.4
1.0
0.2
0.42
0.03
0.01
570
40
0.8
15.4
N=stock size in numbers (thousands of millions), SSB=spawning stock size (millions in tonnes), F=fishing
mortality rate, H=catch (thousands of tonnes), NPV=net present value (billion €).
Bad environmental conditions
We used the fishing mortalities 0.59 for cod, 0.24 for herring, and 0.47 for sprat as current
mortalities. These mortalities are averages from years 2006-2008, and they are based on ICES
(2009) concerning the whole Baltic Sea.
4
Time period 1-50 refers to years 2009-2058.
19
If the current situation continues, the cod stock size in numbers will decrease slightly in the
simulation period (Table 7 and Fig. 5). Even if the stock size decreases, the catch and
spawning stock biomass stabilize soon to their steady states, which are higher than in status
quo5. This is due to a positive change in the age structure which leads to a stock with older
and weightier individuals.
Herring and sprat stock sizes in numbers of individuals decrease as well in the simulation
period. The herring stock size decreases about 12 % and the sprat stock 7 %. At the same time
the spawning stock biomasses decrease even more. These are due to the older cod individuals
in the sea that consume more their prey species, and also to the high fishing mortalities. Due
to the lower herring and sprat stocks also the catches decrease.
The net present value in the simulation period in Scenario 1 is 1,800 million €.
Table 7. The difference between the average steady state of Scenario 1 and status quo (%).
Cod
Herring
Sprat
Stock size in numbers
Spawning stock biomass
-3
22
-12
-17
-7
-23
Catch
17
-13
-16
Net present value
5
1,800 million €
We define status quo as the present situation, i.e. the first period.
20
Fig. 5. Catches, spawning stock biomasses, population sizes and predation mortalities with
current fishing mortalities in Scenario 1 (note the different scales in y-axis).
The current harvesting of cod, herring and sprat in the Baltic Sea may not be at the most
profitable level, and thus we optimize the fishing mortalities for maximizing the economic
profits in the simulation period.
The initial estimate of the fishing mortality for each species under bad environmental
conditions (Scenario 2) is 0.15, and in the second period the mortality starts evolving towards
the optimum (Fig. 6). In this case the harvesting of cod and herring result pulse fishing, in
which the harvesting in some period occurs at a high level and in the next period the
harvesting might be even zero. In spite of pulse fishing, we calculated average fishing
mortalities for each species in order to conduct comparisons between scenarios. The optimal
fishing mortality of cod increases after a couple of years of lower harvesting period. The
21
optimal average fishing mortality is about 0.28 before the mortality becomes more unstable
when the simulation period approaches its end. The optimal fishing mortalities of herring and
sprat are 0.21 and 0.05 respectively.
Fig. 6. Optimal fishing mortalities under bad environmental conditions.
We can compare these mortalities to the current situation in Scenario 1, and the results are
clear: cod mortality should decrease from 0.59 to 0.28, herring from 0.24 to 0.21, and sprat
from 0.47 to 0.05 to be the economic optimum. This states that the less valuable species, i.e.
sprat, should be harvested much less when the abundance of its predator species increases
significantly and affects negatively on its prey species. In addition, it is more profitable to
harvest cod, which is the most valuable of these three species. The cod stock would recover
due to the lower fishing mortality, and even if the fishing mortality was lower than before, the
stock increases and the lower fishing mortality may yield higher catches in the long run. The
optimal level of the fishing mortality of cod is almost the same as the target fishing mortality
level advised by ICES for the cod stock in subdivisions 25-32, which is 0.3 (ICES 2010b).
The lower fishing mortalities of cod and herring yield higher stock sizes and catches (Table 8
and Fig. 7). Spawning stock biomasses of cod and herring increase even more than the stock
22
sizes in numbers. This is due to a positive change in the age structures and also an increase in
the mean weight of the herring spawning stock.
Even if the fishing mortality and catches of sprat decrease significantly, the sprat stock
increases more moderately. This is due to the increased cod stock that now regulates the sprat
stock through predation. The predation does not affect the herring stock as strongly because
cod prefers sprat as food. The sprat stock size is affected by two mortalities that have opposite
effects: the lower fishing mortality rate affects positively the abundance of sprat, but at the
same time the increased cod stock affects negatively the sprat stock. In the optimal fishery the
fishing pressure changes more towards herring and cod, which are more valuable species.
The net present value in Scenario 2 is 5,300 million €. This is almost three times higher than
in Scenario 1. Thus, by fishing mortality optimizing the profits in the 50 years simulation
period can be multiplied. This is very remarkable, and the result indicates that the current
situation is not the most profitable at all.
Table 8. The difference between the average steady state of Scenario 2 and status quo (%).
Fishing mortality
Stock size in numbers
Spawning stock biomass
Catches
Net present value
Cod
Herring
Sprat
-53
110
280
114
-12
1
50
40
-88
16
11
-84
5,300 million €
23
Fig. 7. The optimal catches, spawning stock biomasses, population sizes and predation
mortalities in Scenario 2 (note the different scales in y-axis).
Good environmental conditions
The situation would be quite different, if the environmental conditions improved and more
salinity flowed to the Baltic Sea (Table 9 and Fig. 8). The cod stock would increase almost
seven times compared to status quo. This has major effects on the herring and sprat stock
sizes, and they decrease due to the increased predation mortality. The effect is even more
significant for sprat because cod prefers sprat as food. The spawning stock biomass of herring
decreases more moderately than its stock size due to the assumption that the mean weight in
the herring spawning stock biomass benefits from the decreased sprat stock size.
Now the fishery yields discounted profits of 12,000 million € in the simulation period. This is
almost seven times higher than in Scenario 1, and over two times higher than in Scenario 2.
24
Thus, good environmental conditions can yield very high profits due to the increased cod
stock. Still, it must be noted that these conditions cannot be guaranteed, and thus the higher
profits are uncertain. In addition, climate change seems to have a negative influence on the
salinity level due to increased rainfall (HELCOM 2007) and thus bad environmental
conditions may be prevailing in the future too.
Table 9. The difference between the average steady state of Scenario 3 and status quo (%).
Fishing mortality
Cod
0
Herring
0
Sprat
0
Stock size in numbers
Spawning stock biomass
Catch
680
690
650
-35
-10
-8
-95
-97
-97
Net present value
12,000 million €
Fig. 8. Catches, spawning stock biomasses, population sizes and predation mortalities with
current fishing mortalities in Scenario 3 (note the different scales in y-axis).
25
Next we optimize the fishing mortalities under good environmental conditions. Due to the
higher cod recruitment success, cod can be harvested substantially more, and the optimal
fishing mortality is even 0.42 (Fig. 9). Still this mortality rate is lower than the current one
which is 0.59. Even if the environmental conditions improved, the current fishing mortality
level of cod would be too high and it should be lower to be the economic optimum. Under
good environmental conditions the abundance of cod is so high that there exists less herring
and sprat to harvest due to high predation mortality by cod. Thus, the fishing mortalities of
herring and sprat are very low.
Fig. 9. Optimal fishing mortalities under good environmental conditions.
Herring and sprat are not that profitable to harvest anymore due to their low abundance (Table
10 and Fig. 10). Under these circumstances the higher cod stock feeds especially sprat so
strongly that sprat stock size in numbers decreases 77 % from the current situation, and SSB
even more. This occurs despite the fishing mortality of sprat decreases 99 %. The herring and
sprat stocks increase in Scenario 4 compared to Scenario 3. In Scenario 3 both the fishing
pressures and the predation mortalities towards these species are very high. After optimizing
the mortalities the stocks increase compared to Scenario 3 although the predation is still very
high.
26
The cod stocks in numbers are about the same size in Scenarios 3 and 4. The stocks do not
exceed this maximal limit due to very high cannibalism towards young cod individuals at
these high cod densities, and thus the cannibalism regulates the cod stock. Although the stock
sizes are almost the same in numbers, the spawning stock biomass in the optimizing Scenario
4 is much higher than in Scenario 3. This is again due to a positive change in cod stock’s age
structure resulting from lower F. The stock consists now of older individuals which are larger
and thus more valuable for harvesting. Also the catches are again almost the same in
Scenarios 3 and 4, but still the net present value is higher in Scenario 4 due to larger
individuals. Thus, the revenues gained from the cod harvesting increase, and at the same time
the harvesting costs decrease because they are inversely dependent on the stock biomass. The
higher net present value in Scenario 4 may also be due to the lower harvesting of less valuable
species sprat and herring.
The net present value is even higher in Scenario 4 than in Scenario 3.
Table 10. The difference between the average steady state of Scenario 4 and status quo (%).
Fishing mortality
Cod
-28
Herring
-86
Sprat
-99
Stock size in numbers
Spawning stock biomass
380
950
-32
-4
-77
-84
Catch
650
-84
-100
Net present value
15,400 million €
27
Fig. 10. The optimal catches, spawning stock biomasses, population sizes and predation
mortalities in Scenario 4 (note the different scales in y-axis).
When comparing these scenarios we must remember, that due to the current progress of
climate change, the bad environmental conditions for cod recruitment will probably be
dominant in the future, and the high abundance of sprat is expected to continue (ICES 2008a;
Heikinheimo 2010). Thus, we can assume that Scenario 2 is our optimal situation in the future,
and for gaining greater net present value the fishing mortality of cod must be much lower than
today.
Sensitivity analysis
We conduct a sensitivity analysis for all important parameters for assessing the robustness of
the model. The most significant effects occur when parameters related to cod are changed.
When the cost parameter of cod increases 50 %, and it is more expensive to harvest cod, the
28
cod catch and the net present value both decrease 10 % (Table 11). An increase in the cod
fishing cost parameter has also influence on the herring and sprat fisheries. The fishing
mortality of sprat decreases 25 % and catch 23 % due to the increased cod stock. Instead, the
fishing mortality of herring increases 16 % and the catch 13 %. The cost increase concerning
herring and sprat is conducted at the same time for both species because they are harvested at
the same time by the same vessels. A 50 % increase in these parameters results in significant
decrease in the herring fishery, and now it is more profitable to harvest cod.
When the cod price is increased by 25 %, the optimal fishing mortality of cod increases 7 %
and the net present value even 30 %. Also the sprat harvesting increases significantly due to
the increased cod harvesting that leaves more sprat into sea. An increase in the price of
herring and sprat does not have such a significant effect on the net present value, but still
there are changes in the catches and population sizes.
The higher the discount rate is, the more the present situation is valued, and the future profits
are more neglected. The used discount factor in all previous cases has been 2 %. When the
rate is increased to 4 %, the total net present value will decrease 33 %. The fishing mortality
of herring decreases quite remarkably, cod decreases more moderately, and sprat even
increases.
A 25 % increase in parameter D affects as 5 % increase in NPV. A growth in D means that
there are more herring and sprat in the sea, and thus their catches increase remarkably. An
increase in parameter C, the maximum consumption one cod can eat herring and sprat in one
year, has the opposite effect: when this parameter is increased by 25 %, the herring stock
decreases 9 % and the sprat stock even 15 %. Likewise, the herring catch decreases 23 % and
29
the sprat catch 21 %. The net present value reduces 5 % due to the increased consumption of
cod.
The recruitment parameters are quite sensitive. If
c
parameter in the cod recruitment function
is increased by 10 %, it will increase the cod stock very significantly, and that has a negative
effect on the herring and sprat stock sizes. Total NPV will increase even 82 %. Other
recruitment parameters than the cod recruitment parameter
c
have smaller effects on the total
net present value, but still they have effects on the population sizes and catches.
Table 11. Changes in the average steady state catches (H), numbers of individuals (N), fishing mortalities (F)
Biological parameters
Economic parameters
and net present values (NPV) compared to Scenario 2 (%).
Change in parameter
cc +50 %
Hc
-10
Hh
13
Hs
-23
Nc
3
Nh
-3
Ns
5
Fc
-16
Fh
16
Fs
-25
NPV
-10
cf +50 % & cd +50 %
10
-24
58
0
5
-2
24
-26
76
-5
pc +25 %
7
3
28
-1
-5
1
9
11
35
30
ph +25 %
7
13
28
-1
-5
2
5
16
35
7
ps +25 %
-5
3
43
1
-1
-5
-5
2
70
2
r = 0.04
-6
-7
-6
1
7
-1
-2
-9
3
-33
D +25 %
-1
23
136
-2
1
5
22
17
127
5
C +25 %
-2
-23
-21
-1
-9
-15
-14
-14
4
-5
107
-68
-89
132
-23
-55
8
-60
-66
82
c +10
%
c
+10 %
-7
4
15
-6
0
0
-12
-1
28
1
c
+10 %
3
-7
70
0
2
2
16
6
58
0
h
+10 %
-4
19
39
-1
6
0
5
23
45
3
h
+10%
-5
-6
9
2
-9
3
-3
-3
8
-1
s
+10 %
-6
10
28
2
0
19
-10
-3
11
2
s
+10 %
3
-4
10
0
-6
-12
17
18
-4
0
30
7 Discussion and conclusions
According to our results it is important to take the species interactions into account in
modelling. Especially cod and sprat affect a lot each other, and their biological interactions
should not be omitted. The fishery of cod, herring and sprat in the Baltic Sea is at present
profitable, but the profits could be much higher by optimizing the fishing mortalities. Under
current environmental conditions the profits would be maximized if the fishing mortalities of
each species were lower: the fishing mortality of cod should decrease from 0.59 to 0.28,
herring from 0.24 to 0.21, and sprat from 0.47 to 0.05. These mortalities yield almost three
times higher total profits in the simulation period than would be gained with the current
fishing mortalities.
Under both scenarios under good environmental conditions the net present value would be
about eight times higher than would be gained under bad conditions with the current fishing
mortalities. The improved environmental conditions would affect positively the cod
abundance. The increased cod stock would furthermore affect the herring and sprat stocks
negatively and their harvesting would almost disappear. The optimal fishing mortality rates
under good environmental conditions would decrease from 0.59 to 0.42 for cod, from 0.24 to
0.03 for herring, and from 0.47 to 0.01 for sprat.
Our model is somewhat simplified but still it proves that at present cod is harvested at a too
high level. If the current bad environmental conditions were dominant in the future too, which
is quite likely due to the ongoing climate change, the fishing mortality of cod should be much
smaller than today. When the fishing mortality of cod is lower, the stock would recover and it
can yield higher catches and profits in the future. If the environmental conditions improved,
the cod stock would recover even with current fishing mortalities.
31
We considered that some model extensions could be carried out in the future research. Our
model does not take into account the relationship between the cod stock and the abundance of
its food. This means that when the abundance of the prey species is lower, cod does not have
as much to eat anymore and that should affect the abundance of the cod stock negatively. If
we had assumed that the amount of herring and sprat affects the amount of cod, the results
could have been different. We could also have included the interaction of sprat feeding on cod
eggs into the model. The cod cannibalism has been taken into account simply by higher
natural mortality when the abundance of the cod stock is at a high level. This could have been
taken into consideration also through a predation function towards young cod individuals that
are the target of cannibalism.
The results especially under good environmental conditions may not be totally realistic due to
the constant price. Instead we could have used a price function that varies according to the
amount of harvests or some other reasons. Due to the constant price, the harvesting of herring
and sprat nearly ceases under good environmental conditions. In reality, the prices would rise
when the abundance of herring and sprat decreases (i.e. harvests decrease), and thus it would
be profitable to harvest them again.
In the future it might be important to include also uncertainty into the model. We did not take
this into account, and all the parameters are certain and fixed. According to our sensitivity
analysis stochasticity might be important, especially in the recruitment parameter values and
other parameters related to cod. In addition, we used the same optimal fishing mortality for all
age groups that are harvested. One extension in the model could be that the optimal fishing
mortality varies according to age groups.
32
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Timo Sipiläinen & Subal Kumbhakar (2010). Effects of direct payments on farm performance: The case
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