Emmi Nieminen Marko Lindroos & Outi Heikinheimo. Optimal bioeconomic multispecies fisheries management: A Baltic Sea case study

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1 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

2 Optimal bioeconomic multispecies fisheries management: A Baltic Sea case study Nieminen, E. 1, Lindroos, M. 1 & Heikinheimo, O 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

3 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

4 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

5 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

6 (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 (Western Baltic cod) and subdivisions (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

7 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 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 ) 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

8 3 Population dynamics model We simulate the population dynamics for each species in age groups as a N ( t) N ( t 1e ) a a 1 Z 1( t 1) (1) where N a-1 (t-1) is the number of individuals in age group a-1 at time t-1, and Z a-1 (t-1) is the total mortality of the cohort (Hilborn & Walters 1992). The total age-specific mortality Z a-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 M a-1 (t-1): Z ( t 1) F( t 1) M ( t 1) a 1 a 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: a SSB() t N () t e MO WA (3) a F() t M () t a a a where () a() N() F t M t ate is the stock size of age group a at the time of spawning, MO a is the proportion of mature individuals in age group a, and WA a 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

9 The recruitment function for herring and sprat is modelled by using Ricker s formation as in ICES (2005) and Heikinheimo (2010): Rt () SSBte () 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): Rt () SSBte () SSB( t) ( E E ) (5) where, and are recruitment parameters. The difference E 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 , and we use this value for the case of good environmental conditions. Based on a bad salinity period in , we use a value of 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

10 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 Ft () H t N t 1 e () () ( ) * ( )*( F t M a t a a ) F() t Ma() t (6) and the annual total harvest in biomass H() t WAaHa() t (7) a (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

11 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 n Ca( Nh s( t)) P () t ( N ( t)) ( D ) a n n h s h s (8) where C 2 a is the maximum herring and sprat consumption in numbers by cod in age group a. In other words, C a is the number of prey individuals eaten in one year when the abundance of the clupeids was at a maximum level. The values for C a are derived according to the results of SGMAB (Study Group on Multispecies Assessment in the Baltic) key run. D 3 h+s 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 D h+s, but it considered only the cod stock in ICES subdivisions We use a value of 325,000 million for the whole Baltic Sea. 2 C a =[ ]. 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

12 N h+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 P h, a ( t) N h N ( t) P ( t) h a (9) ( t) wn s ( t) P s, a ( t) N wn s ( t) P ( t) wn ( t) s a (10) s ( t) where P h,a (t) is the number of herring eaten by one cod in age group a in one year t, and P s,a (t) is the number of sprat eaten by one cod in age group a in one year t. N h (t) and N s (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 M2 () t h 8 a 1 N () t P () t ca, ha, N () t h (11) M2 () t s 8 a 1 N () t P () t ca, sa, N () t s (12) where N c,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*M2 h. 11

13 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

14 C () t c c c Ht () Bt () 2 (13) where C c (t) are the total costs of cod harvesting in one year t, c c 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 ) We use the cost parameter according to Kronbak and Lindroos (2007), where c c 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 Ct () cet () (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: Fh() t Fs() t Fh() t Ch s( t) Xcf ( 1 Xc ) d (15) q q f d 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 c f is 644 /effort day for fodder herring and sprat, and c d 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

15 they also have higher fuel costs. In addition, food vessels have higher quality demands related to hygienic requirements. (Kulmala et al ) Catchability coefficient q is divided in Kulmala (2004) into several classes between different vessel segments, and we combine these coefficients so that q is for human consumption herring and 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: X 4 8 H () t H () t ha, sa, a 2 a H () t H () t ha, sa, a 2 a 2 (16) 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

16 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 from ICES (2009) and the simulation period is 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: max 50 Pc() t Ph() t Ps() t Cc() t Ch s() t t 1 (17) ( 1 r) t=1 15

17 This objective function consists of revenues and costs of harvesting. P c (t), P h (t) and P s (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). C c and C h+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. 1) Cod recruitment parameter under good/bad environmental conditions. Cod Herring Sprat a Age range Recruitment function parameter e 5 Recruitment function parameter * *10-6 Recruitment function parameter Recruitment function parameter 0.8/ ) - - c c, c f, c d Cost parameter /3227 2) 644 q f, q d Catchability coefficient - 4.7*10-6 /4.3*10-5 2) 4.7*10-6 p Price of fish ( /kg) /0.2 2) ) Cost parameter, catchability coefficient and price of fodder herring/human consumption herring. 16

18 Table 2. Initial values of population dynamics of cod. Age Population Mean Maturity Natural group size ('000) weight (kg) proportion mortality a N c,a (1) WA c,a MO c,a 1) M c,a /0.7/ /0.3/ /0.2/ /0.2/ /0.2/ /0.2/ /0.2/ /0.2/0.2 1) 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 Population size ('000) Mean weight (kg) a N h,a (1) 2) WA h,a Maturity proportion MO h,a Natural mortality /0.04/ /0.04/ /0.04/ /0.04/ /0.04/ /0.04/ /0.04/ ) Mean weight in the herring spawning stock (age groups 2-8) with cod stock sizes of < 1,000 million / 1,000-1,500 million / > 1,500 million individuals M1 h,a Table 4. Initial values of population dynamics of sprat. Age Population Mean Maturity Natural group size ('000) weight (kg) proportion mortality a N s,a (1) WA s,a MO s,a M1 s,a

19 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

20 Fig. 4. The net present values under different scenarios with 2 % discount rate 4. 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. N c N h N s SSB c SSB h SSB s F c F h F s H c H h H s NPV Scenario Scenario Scenario Scenario 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 , and they are based on ICES (2009) concerning the whole Baltic Sea. 4 Time period 1-50 refers to years

21 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 quo 5. 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 Catch Net present value 1,800 million 5 We define status quo as the present situation, i.e. the first period. 20

22 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

23 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

24 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 (%). Cod Herring Sprat Fishing mortality Stock size in numbers Spawning stock biomass Catches Net present value 5,300 million 23

25 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

26 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 (%). Cod Herring Sprat Fishing mortality Stock size in numbers Spawning stock biomass Catch 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

27 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 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

28 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 (%). Cod Herring Sprat Fishing mortality Stock size in numbers Spawning stock biomass Catch Net present value 15,400 million 27

29 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

30 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

31 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) and net present values (NPV) compared to Scenario 2 (%). Economic parameters Change in parameter H c H h H s N c N h N s F c F h F s NPV c c +50 % c f +50 % & c d +50 % p c +25 % p h +25 % p s +25 % r = D +25 % C +25 % Biological parameters c +10 % c +10 % c +10 % h +10 % h +10% s +10 % s +10 %

32 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 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

33 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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