ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on May 30, 2008
ICES Journal of Marine Science: Journal du Conseil 2008 65(7):1203-1215; doi:10.1093/icesjms/fsn088
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Effort allocation and marine protected areas: is the North Sea Plaice Box a management compromise?
Institute of Food and Resource Economics, University of Copenhagen, Rolighedsvej 25, 1958 Frederiksberg C, Denmark
Correspondence to J. Kjærsgaard: tel: +45 3528 6881; fax: +45 3528 6801; e-mail: jk{at}foi.dk
Kjærsgaard, J., and Frost, H. 2008. Effort allocation and marine protected areas: is the North Sea Plaice Box a management compromise? – ICES Journal of Marine Science, 65: 1203–1215.A complex bioeconomic model is used to study the economic and biological consequences of establishing a marine protected area (MPA). The model is a multispecies age-structured bioeconomic model that treats days at sea and number of vessels, for different fleets fishing inside and outside the protected area, as endogenous variables. A simulation applies an adaptive investment rule that determines fleet size from year to year, and an optimization procedure provides a benchmark for a profit-maximizing solution over time. In contrast to most conventional studies on MPAs, fishing within the protected area is possible. Moreover, the stock is not divided between inside and outside the protected area, although the abundance of different age classes in each area differs. Therefore, the economic and biological impacts of fishing inside or outside are different. The North Sea flatfish fishery is used as a case study, so the analysis is particularly relevant because North Sea flatfish regulation is currently under revision.
Keywords: bioeconomic model, marine protected area, North Sea Plaice Box
Received 16 July 2007; accepted 12 April 2008; advance access publication 30 May 2008.
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Introduction |
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Restricting access to fishing areas as a management tool has received some interest in recent years. The rationale for establishing a marine protected area (MPA) can be concerns about the state of threatened fish stocks, a wish to protect the seabed, or to allow for alternative uses of the area (e.g. ecotourism rather than fishing). In other words, it would allow a more-sustainable exploitation of the resources in future. The general effectiveness of a protected area is, however, not established. An interesting discussion on the prospects for protected areas as a management tool can be found in Hilborn et al. (2004). Success depends on the implementation, the enforcement, and the biological (or ecological) conditions specific to the case considered.
Our purpose here is to present an integrated bioeconomic framework that can pursue the trade-offs between different objectives related to instituting an MPA. It is likely that there are different stakeholders with conflicting objectives concerning the fishery. This would influence the formulation of the regulation and eventually the biological and economic repercussions. Motives for creating a protected area can include the aim of achieving sustainable stock levels, for instance related to the precautionary principle. At the same time, concerns about ensuring the short-term existence for fishers in different fleet segments and nations may play a role. Generally, any fishery regulation has to balance multiple different interests concerning the optimal exploitation of the resources, interests accounting for biological and (socio-) economic concerns. Here, we investigate the consequences for objectives related to profits, stock levels, and distribution of income.
To investigate the interplay between these objectives, a bioeconomic model is developed, one that links a multispecies age-structured biological module with a multifleet, multinational production module. The model is a dynamic numerical allocation model. It can perform both optimizations and feedback simulations to determine fishing effort for different fleet segments, and the resulting interaction between biological and economic parameters. The model is novel in the way it combines biology and economics more extensively than experienced thus far. A model comparable with ours in terms of effort reallocation, but with less complexity, is that of Bjørndal and Brasão (2006); it is a model that addresses highly migratory species rather than MPAs. Our model is data-intensive, and some parameters are associated with uncertainty because of a lack of information.
Several publications exist covering the bioeconomics of MPAs. They have very little empirical foundation in terms of the economic component (see Grafton et al., 2005, for a review of the literature of MPAs). The biological contributions are comprehensive, e.g. Pastoors et al. (2000), Rijnsdorp et al. (2001), and Marchal et al. (2002). A number of papers cover analytical long-term equilibrium models and consider a closed area combined with different assumptions about such a management regime on the outside, e.g. open access and optimal harvest, maximizing net present value (NPV) of future catches (Hannesson, 1998; Conrad, 1999; Armstrong and Skonhoft, 2006). Such analyses are well suited to demonstrating how different management parameters and conditions interact with the economics and biology of a system. The model developed here is more in line with the detailed applied models presented by Holland and Brazee (1996), Holland (2003), and Smith and Wilen (2003). A model on swordfish (Xiphias gladius) constructed by Lee et al. (2000), like ours, is constructed in GAMS (Brooke et al., 1988), and applies a profit-maximizing procedure similar to ours. Those listed are all age-structured models. Effort is fixed in Holland and Brazee (1996), or effort is disaggregated as a control variable. Lee et al. (2000) do not address MPAs, and there is no entry/exit of capital in their model. Our model also includes competing fleets. Moreover, because of the age structure of the fish stock component, individual stocks (e.g. plaice, Pleuronectes platessa) are not modelled independently inside and outside the potential MPA. However, the young age groups live mainly inside the protected area (space 1), and the older age groups mainly outside (space 2). This element is modelled in such a way that because the young age groups mainly live inside space 1, they are exploited by certain fleets (catch compositions with a large share of young age classes), whereas the older age groups living mainly outside space 1 are exploited primarily by other fleets, with different fishing mortality rates. The movement from young to old age groups over time represents the movement from space 1 to space 2.
In 1989, a protected area, which became known as the North Sea Plaice Box, was instituted within the North Sea. Its primary purpose was to protect spawning grounds and to ensure sustainable stock levels of plaice. We use this example of the North Sea Plaice Box as our case study. Beam trawlers of >300 hp, or 221 kW, were excluded from fishing in the box. Initially, they were only excluded for two quarters of the year, but from 1995 they were excluded year-round (European Community, 1998). Other vessels could still operate within the box. As a result, aggregated effort in the box decreased, but discarding of undersized plaice in the fishery (observed up to 90% by number) is still a concern, and there has been no improvement in stock status since the plaice box was established. Some believe the plaice box to be a management compromise, where the continued activity inside the box by vessels of <300 hp jeopardizes the success of the whole MPA.
We believe that our model can provide a lot of information for managers, in this case in the European Commission, related to different management schemes. The empirical analysis we present is particularly relevant because the management of the North Sea flatfish fishery currently attracts much interest.
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The North Sea Plaice Box |
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The North Sea flatfish fishery, targeting plaice and sole (Solea solea), is conducted primarily by Dutch, British, and Danish vessels, with small catches also by vessels from Germany, Belgium, and a few other nations. The production capacity of North Sea flatfish fleets is documented by Lindebo (2005), who concludes that the fishery was overcapitalized in 1998, such that the same catch could have been taken then by 77% of the fleet. This suggests that a reallocation of fixed inputs would improve the overall economic performance. The results from our analysis confirm this situation in a dynamic framework.
The most recent assessment of the ecological effects of the plaice box is found in Grift et al. (2004). Based on that report, it is not possible to conclude whether or not the box has been a success. Part of the problem is that no measure was specified, or monitored, for this purpose. Moreover, the state of the plaice stock worsened significantly just before the implementation of the box. Time-series of spawning-stock biomass (SSB), catch, landings, and discards of plaice are shown in Figure 1a. The plaice stock started to decline in 1987, and the catch, discards, and landings followed shortly after. Catch relative to SSB in a given year is depiced in Figure 1b for plaice and sole, respectively. There is no convincing indication that the catch relative to SSB has been reduced, but the increasing trends before 1989 are less distinct in the years that followed. The stock of sole expanded in the early 1990s, but dropped again to its previous level from 1996. Changes in growth rates, spatial distribution, temperature, and in still high rates of discarding are believed to have had an effect on the development of stocks and recruitment (Grift et al., 2004). The scattergrams in Figure 2a and b compare the recruitment with SSB for plaice and sole (data from 1957 to 2004). There does not seem to be a sound basis for considering a functional link. The introduction of the plaice box did reduce fishing effort within the MPA. After 1995, when beam trawlers >300 hp were excluded from the box, the effort (in hp-days at sea) was reduced to 23% of the pre-box level (Grift et al., 2004).
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In our analysis, the plaice box is evaluated bioeconomically, and different scenarios reflect alternative management initiatives. The purpose is to generate knowledge of optimal exploitation of resources—given the relevant political, economic, and biological interests. The question is whether this compromise regulation actually improved the situation, and if the exclusive objective of establishing the plaice box had been to improve the state of the stocks allowing for more-sustainable exploitation of the resource, should the protected area have been closed for fishing completely?
We use our model to assess the consequences if (i) there had been no box, (ii) if fishing in the box had been entirely prohibited, (iii) if capital inputs were reduced in equal proportions across all segments (i.e. effectuating a capacity policy where the numbers of vessels in all segments are reduced), and (iv) if maximizing long-term profits had been the main concern of the managers.
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Conceptual framework |
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There are three key features of the framework introduced here. There is no formal subdivision of the stocks considered between inside and outside the MPA. Differences in catch compositions inside and outside space 1 are provided by information on discards and landings, which also describe how the availability of different age classes to a given gear varies inside and outside the protected area (see Appendix). Fleet segments are characterized by size and gear and whether they catch fish inside or outside the box. If they fish inside the box, a higher fraction of the catch consists of young age classes because the availability of younger age classes is greater inside the box than outside (and vice versa). Most fish of the younger age classes are within the boundaries of the MPA, whereas older age classes are more dispersed. Figure 3 shows the abundance of juvenile plaice in the North Sea and the extent of the plaice box; juvenile plaice are abundant near the Danish west coast of Jutland, within the boundaries of the box.
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The stocks are exploited by several different fleet segments, each with different impacts on the stocks. The different types of vessel have different catch compositions (catch-at-age), resulting in different rates of discarding. It is assumed that the dominant share of discarded fish does not survive (Kaiser and Spencer, 1995; Suuronen, 2005). Vessels are characterized by physical measures (size and type of gear employed) and where they operate.
Fishing within the protected area is allowed, although in most other MPAs it is prohibited. Our model has a more continuous framework so that the consequences of different degrees of fishing activity (including no activity) in the protected area can be assessed. This formulation is convenient when the spatial distribution of fish of different age classes differ, as is true for North Sea plaice. The age classes are not divided between inside and outside the protected area, but it is the catch compositions of different fleet segments that drive the model. Given that we look at the effects of management options on the total stock, we do not need to make explicit assumptions about the proportion of fish in space 1. In other words, given that annual catch-at-age data are available, it is not necessary to model how many fish remain inside or outside the protected area. Instead, our model only needs to account for the reduction in the total population attributable to catches taken inside or outside the MPA by the different fleet segments.
When juvenile flatfish grow larger, they migrate further from the coast, i.e. older age classes are more dispersed. Often the relative stock densities combined with a migration rate have been used to model such inter-area flows in bioeconomics (e.g. Holland and Brazee, 1996; Hannesson, 1998). Here, though, we do not need to make assumptions about migration, because only one area is assumed for the population. Instead, the model uses appropriately adjusted selectivities to simulate the availability of fish to a given fleet. When making a distinction between fleets operating inside and outside the protected area and between different gear types, our analysis becomes an effort-control issue.
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Multifleet, multispecies, age-structured bioeconomic model |
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Here, we present our generic framework. The model treats fleet size and effort as endogenous variables determined either by running a simulation or an optimization procedure (Frost and Kjærsgaard, 2003, provide a review of numerical allocation models applied in fisheries). In the simulation procedure, the number of vessels and their activity levels are determined within each period. Expectations about the future are based on the results of preceding years, and fisher behaviour is based on a "local" adjustment of fixed capital and days at sea. The optimization procedure reveals the overall best (profit-maximizing) allocation of activity across time and fleet segments. A diagram illustrating the mechanisms of our model is given in Figure 4. The behaviour is modelled by selecting days at sea and an investment strategy. The activity of vessels induces costs. Given the stock levels and vessel activity, a corresponding amount of fish is caught, some of which is discarded. The catches influence the stock biomass of the subsequent period, and the profits determine the investments (or disinvestments).
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The model has a high level of detail, but it can be explained by only a few equations. The following indices are employed: t = 0, ... ,T; c = 1, ... ,C; s = 1, ... , S; and fs = 1, ... ,FS, where t = time, c = cohort (age class) s = species, and fs = fleet segment.
Catches and landings
The catch number by fleet segment fs of species s, cohort c, in period t, is calculated as a share of the total catch, i.e.:
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is the aggregated rate of fishing mortality for all fleet segments.
Accounting for discards, the number of fish landed by fleet segment fs of species s, cohort c, in period t, is
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| (2) |
dcs1 is the share of the catch of species s and cohort c that is discarded.
Profits
The profit in fleet segment fs at time t is given as revenue less variable and fixed costs:
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The parameters wcs, ps, VCt,fs, and FCt,fs specify landings weight in kilogrammes, prices per kg, variable cost per unit of effort (day at sea), and fixed costs per vessel, respectively. NDt,fs is the number of days at sea for the whole fleet segment in period t, and NVt,fs is the number of vessels. Total profit at time t is determined by summing the profits of all fleet segments.
The choices of days at sea (effort) influence the rates of fishing mortality. The following relationship is used:
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| (4) |
describes the degree to which a change in effort is mirrored in the fishing mortality. Often the link between sea days and fishing mortality is assumed to be linear. The EIAA model, which is used in the annual assessments of economic consequences from the advice on next year's European Union (EU) quotas (SEC, 2004), however, also applies a non-linear relationship (depending on prices and biomasses). On the other hand, for most analytical models, a Schaefer model is used, and the link between sea days and fishing mortality is embodied in the harvest function, assuming that the harvest is equal to the growth of the stock (see Eide et al., 2003, for detail of bioeconomic production functions).
Optimization
Given an objective or a range of objectives, NV and ND are selected to achieve an optimal solution. Different scenarios can be formulated in terms of both restrictions and objectives. The objectives could relate to overall profit, total stock size, fleet segment profit, and income distribution, and structural and technical restrictions may be imposed.
Simulation
An empirical analysis of capital dynamics within fisheries can be found in Bjørndal and Conrad (1987). Those authors investigated the statistical fit of different capital adjustment functions. For our purpose, it is assumed that investment decisions are determined by expectations about possible future earnings. As an indicator of possible future (lifetime) earnings, profits in the previous t* years are considered. In this case, NV and ND are calculated for every period based on economic performance in the previous years and subject to previous biological conditions of the stocks. Further, partial adjustment is assumed, i.e. only part of the profit is invested (as in Jørgensen and Jensen, 1999). The following simple capital adjustment function is applied (a similar approach can be found in Hoff and Frost, 2006):
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Ifs–/VfsOUT, then asymmetry in the investment/disinvestment incentives exist (entry is easier than exit). The term 
is the average profit in the preceding t* years, r is the discount rate, and (1–(1+r)–LTfs)/r is the capitalization factor discounting future profits, where LT is the investment horizon. The type of capital adjustment function above is flexible, for example, by applying different time horizons and interest rates, and introducing decommissioning grants or restrictions related to regulation (such as that newcomers may have to buy tonnage, increasing the price). The current setup ensures that for open access to a fishery, the fleets adapt until profits are dissipated as expected. Apart from Bjørndal and Conrad (1987) and Jensen (1990), there is little empirical information on investments within fisheries.
In the simulation, the change in the average number of sea days per vessel ND/NV for fleet segment fs is related to the state of the stocks. The average number of days in period t is multiplied by a coefficient (describing the change in earning possibilities) to estimate the average number of days in period t+1. The adjustment coefficient includes changes in the biomass for the different species, weighted individually for the different fleet segments according to their relative share of (the total fleet segment) catch value.
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| (6) |
denotes the stock biomass of species s at time t. The scalar 0 
1 is a stock–effort flexibility parameter (if = 0, then the average number of days at sea per vessel remains constant). NDfsmax specifies the maximum number of days allowed at sea per vessel in segment fs. The rationale behind Equation (6) is that if fishers can make more money per day, then they would elect to fish for more days. It is unlikely that the change in days per vessel is entirely flexible with respect to changes in potential earnings, i.e. that there is a one-to-one connection. Therefore, the flexibility rate can ensure a more conservative estimate. Different restrictions on the allowable number of vessels and days at sea can be applied to investigate relevant scenarios. Moreover, in both the optimization and simulation procedure, quotas can be imposed, for example, to ensure that myopic behaviour does not immediately drive the stock to zero.
Population dynamics
Developments in the number of fish in different cohorts (age classes) is calculated by a population model (decay function; see Hilborn and Walters, 1992, p. 71), e.g. the number of fish of species s at time t+1 in cohort c+1 is
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| (7) |
The parenthesis (1 – dcs
s) accounts for the possibility that when fish are discarded, a portion (0 s 1) survives.
Recruitment (Nt,1s) in a stock is often related to the stock of mature fish, i.e. SSB, which is given by 
, 0 
cs 1 being a maturity index. Beverton–Holt and Ricker are two commonly used functional forms linking recruitment to SSB. The former assumes that recruitment increases towards an asymptote as SSB increases, and the latter implies that recruitment falls for high values of SSB (Hilborn and Walters, 1992, Chapter 7). If no link can be established between recruitment and SSB, constant recruitment may be the most reasonable assumption.
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Data and conditioning |
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The present application includes two species (plaice and sole), and ten fleet segments from four countries. The most important fleet segments in term of landings of plaice and sole since the establishment of the plaice box have been included. These are displayed in Table 1 with respect to nationality, hp class, gear type, and location. The share of fishing mortality allocated to non-included vessels is assumed to remain at the 1990 level. The starting point of the model is 1990, 1 year after the plaice box was introduced. The reason for not starting in 1989 is that data on landings and effort are not available for that year for all relevant fleet segments.
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Age-structured models describe the stock dynamics for plaice and sole, as explained in the model section, with 1990 as the initial year. As mentioned above, there is no clear relationship between SSB and recruitment, so it is assumed that recruitment is constant and equal to the average for the period 1990–2004 for both stocks (plaice 983 590 thousand and sole 126 421 thousand). Revenue from other species is included at a constant level per day at sea, i.e. the share of revenue not originating from landings of plaice and sole. This assumption implies that if the effort is increased, revenue from other species increases. This is a reasonable assumption, because it is effort rather than catches of individual species that is controlled.
The main data sources used to parameterize the model are:
- plaice box evaluation, after Grift et al. (2004);
- landings, effort, and discard data, after Grift et al. (2004);
- assessment of demersal stocks in the North Sea (stocks, recruitment, discard, fishing mortality rates), after ICES (2005);
- discard sampling of the Dutch beam trawl fleet in 2004, after van Keeken and Pastoors (2005);
- costs, from the Danish Institute of Food and Resource Economics and from EU Concerted Action data (AER, 2005);
- prices, from average registered landings in Denmark, 2001–2003 (Danish Fisheries Directorate);
- discard data for Danish fisheries, after Anon. (2006).
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Unfortunately, information about discards at a fleet segment level and catch-at-age is incomplete, and has to be approximated. The available data on discards are used to determine the overall discard shares for the different fleet segments, then to calculate catch-at-age and initial fleet-segment rates of fishing mortality. The overall discard rate is determined by the fishing mortalities and the rates of discarding-at-age. Discarding- and weight-at-age may vary over time, though for plaice the variation is limited so we considered it reasonable to apply constant values. Constant values are also applied for sole although information about discarding-at-age is sparse. The main reason for discarding in the flatfish fishery is the undersized fish that are caught, and because size-at-age is not thought to have changed noticeably over time, we believe that applying constant values is appropriate.
Because information on costs back to 1990 is incomplete, an approximation is applied. Average costs from 2001 to 2003 are adjusted by the observed revenue per day in the catch and landing dataset relative to revenue per day in the cost dataset. To ensure commensurability, average 2001–2003 prices have been applied.
The investment horizon applied (LT) was set arbitrarily to 20 years, corresponding to a 5% linear depreciation, in line with Davidse et al. (1993) and Jørgensen and Jensen (1999), who applied a rate of 4%. Discounting implies that taking into account a longer horizon would not have a great effect on the results. Moreover, fishers would be anticipated to consider a shorter time horizon. Information regarding the values of VIN is constructed from ships' brokers' sales lists. The fixed prices represent average prices in the relevant fleet segment, including fishing rights. VOUT is assumed to be 20% above VIN. This asymmetry (VOUT > VIN) is applied to achieve a system with a greater incentive to enter than to leave a fishery. From the perspective of opportunity cost, this could represent a situation with limited alternative ways of making a living, a situation often facing fishers. The partial adjustment previously mentioned is modelled by fixing I+, I– at 15%. The implication of these assumptions is that the greater the asymmetry, the less the variation in fish stock abundance and fleet capital. Profit over time will be less than for symmetry. If the partial adjustment increases, the variation of the stock abundance and the fleet capital will increase, and vice versa.
The effort–fishing mortality flexibility rate is fixed at 0.75. The stock–effort flexibility rate , equal to 0.5, is applied to reflect the influence changes in average days at sea per vessel has on changes in fish stocks. Applying < 1 implies that changes in biomass are not linearly reflected in the number of sea days, i.e. that adjusting fishing intensity is not entirely flexible. Finally, it is not considered likely that the average number of days at sea within the different fleet segments is unbounded. Therefore, only a 20% increase is permitted, or 250 days at the most.
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Results |
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The results are evaluated in terms of overall profit, allocation of effort across fleet segments, and stock profiles measured in terms of SSB. The model can produce a comprehensive quantity of output. Annual stock levels are calculated by age class, and profit and activity by fleet segment and year. The results describe the isolated effects related to the flatfish fishery in the North Sea, depending on how the activity is allocated. The consequences for the stocks need to be considered in light of the current management plans. In 1999, the EU and Norway agreed a long-term management plan for plaice, in accordance with the precautionary approach (Bpa). The reference point above which SSB should remain (Bpa) was 300 000 t. This level was reapplied in subsequent years up to 2005, when it was lowered to 230 000 t. In 2005, Bpa for sole was 35 000 t.
Our results focus on the consequences for the plaice stock, consequences for the stock of sole generally following the same pattern. However, the SSB for sole does not fall below Bpa for any scenario. To evaluate different management (effort control) options related to the flatfish fishery and the establishment of the plaice box, the following scenarios are considered:
- Actual;
- Open access;
- Maximize profit;
- Complete closure:
- Free entry (entry to the fishery outside the box is allowed),
- No entry (entry to the fishery outside the box is prohibited);
- Free entry (entry to the fishery outside the box is allowed),
- Reduce capital input:
- Maintain 1990 level,
- 90% of 1990 level,
- 80% of 1990 level.
- Maintain 1990 level,
1. Actual
This scenario is calculated based on observations of landings and stock sizes. True landings and effort data are combined with cost data to calculate the economic performance of the vessels. The number of vessels in a given year is determined by dividing the total number of days at sea by the average number of days at sea per vessel in the cost data. Hence, it is assumed that the number of sea days per vessel is constant, so fixed costs may be over- or underestimated. As the calculation is based on observed data, it only covers the period 1990–2003. The other scenarios were run for twice as long (until 2020), and the assumptions about selectivity, etc. are carried forward. This means that the model is initialized (in 1990), and the catches and discards are calculated from year to year according to the equations outlined above.
2. Open access
In this case, the simulation model is used to evaluate the consequences if there is unlimited entry to the fishery both inside and outside the box, i.e. NVfsmax in Equation (5) is set to infinity. Beam trawlers >300 hp are not restricted, i.e. all fleet segments can operate from 1990 on. This situation gives a likely indication of what would have been the consequences if the fishery had been left to itself, with no effort control.
3. Maximize profit
This scenario applies an optimization procedure in which the number of vessels and the number of sea days per vessel that maximizes profit are estimated. That implies that the total discounted future profit from all segments is maximized, and effort is allocated to vessels in the most economically efficient manner. A 30-year period from 1990 is considered. In this case, though, no account is taken of the distribution of income. The objective function, which is maximized, is
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3% can be found in HM Treasury (2003), and Hillis and Whelan (1992) state that the discount rate of fishers may be as high as >20%. This scenario, as the open access one, provides two points of reference, but the profit-maximizing situation is opposite to the open access situation (where profits are exhausted).
4. Complete closure
This scenario investigates whether the desired stock improvements could have been achieved if fishing in the plaice box had been prohibited for all fleet segments, not only for vessels with >300 hp. The vessels that used to fish within the box are forced to fish outside the box (modelled as entry to the fleets fishing outside the box) or to stop fishing entirely if the profit is too low. There is an obvious conflict between this scenario on the one hand, and ensuring equal distribution of income and the continued existence of smaller vessels on the other, but it is interesting to determine whether the stock levels would improve. Two situations are considered: first, it is assumed that entry to the fishery outside the box is allowed [scenario 4(i)], and second, entry to the fishery outside the box is prohibited [scenario 4(ii)].
5. Reduce capital input
Here, we investigate the consequences if the numbers of vessels are reduced in equal proportion across all fleet segments, i.e. the total fishing pressure is decreased. Initially, a simulation is performed where the number of vessels is fixed at the 1990 level, but subsequently, the number is reduced instantly to 90% and 80% of the 1990 level. The consequent reduction in fishing mortality influences the stock sizes and overall profit.
Scenario outputs
For all these scenarios, projections of the aggregated profits and the stock abundances of plaice (SSB) are depicted in Figure 5. The profit-maximizing solution (scenario 3) suggests that both profits and stocks can be improved substantially if there are no bounds on the allocation of effort. The suggested strategy resembles pulse-fishing, which switches between phases of intensive and minimal fishing, the latter while stocks rebuild. The level of improvement in this case will depend on the effects such an exploitation pattern have on recruitment. The results also suggest that an initial 3-year closure is needed before fishing should be permitted. This implies that the long-term profit-maximizing fishing pattern requires high initial financial loss and considerable compromise in income stability. However, the fluctuations in profit seem to stabilize over time. This pattern is mirrored by evaluating the SSB of plaice. It appears to stabilize at 800 000 t, i.e. about twice the level in 1990.
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As would be expected, in the simulation of open access (scenario 2), the fishery is overcapitalized to the extent that potential profits are totally eliminated. The long-term SSB of plaice declines from 1990, but it is above the actual situation in 2003, and Bpa.
The complete closure simulations (scenario 4) describe the situation where fishing inside the plaice box is entirely prohibited from 1990 on. In the free entry case [scenario 4(i)], entry to the fishery outside the box is allowed, whereas in the no entry case [scenario 4(ii)] there can be no new entrants. Allowing new entrants results in the same situation as the open access fishery above. Profit is eventually exhausted. Moreover, the stock of plaice approaches the same level as for the open access situation. If no new entrants are allowed to the fishery outside the box, the fishery is profitable and the SSB stabilizes at 95% of its initial level. In other words, even if fishing in the box is prohibited, profit is exhausted and the stock approaches that at the open access level if fishing is not constrained outside the box. This suggests that the fishery inside the box is perhaps of less importance, i.e. that prohibiting fishing inside the box is not alone sufficient to improve the overall profitability of the fishery and the state of the stock.
This is investigated further by the reduced capital simulations (scenario 5) where the level of capital input (across all segments) is considered. First, when the number of vessels is fixed to the number observed in 1990 [scenario 5(i)], the SSB approaches a level corresponding of 314 000 t (77% of the initial level), which is higher than Bpa, but the profit is negative. Compared with the results with complete closure of the box and no entry [scenario 4(ii)], it appears that allowing fishing inside the box undermines the overall profit and reduces the long-term SSB (from 95% to 77% of the initial level). The fishery inside the box is therefore not irrelevant. Further, when the number of vessels in all fleet segments was reduced to 90% and 80% of the initial number in 1990 [scenarios 5(ii) and 5(iii)], the results indicate improvements in long-term profit and stock levels relative to those achieved when the number of vessels is fixed at the number in 1990 (Figure 5). However, both profit and stock levels remain below their corresponding values in 1990. Reducing the number of vessels to 80% of the 1990 level results in approximately the same level of profit as for the case with no fishing in the box and no entry outside, but the stock level is lower. For both scenarios, however, the SSB is above Bpa, indicating that both cases are sustainable but that the income is distributed differently over fleet segments.
The results in Figure 5 rely on different structures of the fishing fleet, and the detailed consequences of distribution of effort are hidden. To demonstrate the calculated long-term consequences within individual fleet segments for selected scenarios, the number of vessels in 2015 is considered (Table 4). The exact numbers should be interpreted with caution; it is rather the changes from the initial level that are of interest (changes are denoted by 
%), because they represent the change in catching capacity. Exact numbers in 2015 may present a biased picture, because technology is fixed to the 1990 level, so disregarding technological developments. For example, with an annual technological enhancement of 3%, the numbers in 2015 should be corrected (multiplied) by a factor of 1.03–25 = 0.48.
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For the profit-maximizing scenario, only 33 vessels are active in 2015. This number is radically lower (93%) than the starting point because the fishery is in a phase with low fishing intensity caused by the cyclical development induced by the investment behaviour that implies changes in the number of vessels. The number fluctuates, and 3 years earlier there were 188 vessels. Allocation of effort among fleet segments is, however, more or less fixed. The fishery is prosecuted mainly outside the box by large beam trawlers >300 hp from the Netherlands (NL) and the United Kingdom (UK). In reality, it is not likely that fixed capital fluctuates to this extent. Nonetheless, the profit-maximizing situation provides a benchmark. It indicates that there are significant potential overall gains to be made in terms of long-term profit by allowing the stock to grow and to leave the fishery to a reduced number of large beam trawlers operating outside the box. The fishery would be concentrated in fewer vessels, but short-term losses are unavoidable. The potential overall profit would not benefit all fleet segments. It compromises the continued existence of fleet segments fishing inside the box. Therefore, leaving the fishery to large beam trawlers fishing outside the box is not a clear-cut first and best solution, unless the opportunity costs, i.e. alternative employment for labour and capital of the various fleet segments, have been investigated.
In the open access simulation (scenario 2), the total number of vessels operating increases by 51%, and all fleet segments remain represented. Notable is that the number of large UK beam trawlers fishing outside the box increases. In contrast, it appears that the numbers of NL beam trawlers, fishing both inside and outside the box, are reduced. These vessels are characterized by being very dependent on the plaice fishery. Therefore, as the stock decreases and the number of other vessels increases, NL beam trawlers cannot remain profitable and are forced out of the fishery. It appears too that the open access long-term stock level is higher than the actual 2003 level. This is because the number of plaice-targeting vessels is reduced. Note that the results rely on the assumption that the catch value per day of other species is constant, giving vessels less dependent on plaice and sole an advantage. Therefore, the possibilities for expansion of some fleet segments may be slightly optimistic.
Complete closure with no entry [scenario 4(ii)] excludes all fishing activities within the box, but besides a reduction in NL beam trawlers <300 hp, all vessels remain active outside the box. Finally, reducing capital input by 20% [scenario 5(iii)] maintains activity across all fleet segments. In this case, the overall profit in the long term is positive. However, the profit is negative for NL beam trawlers, except for those >300 hp operating outside the box. Segments with negative long-term profit do not in reality remain active.
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Sensitivity analysis and robustness |
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The North Sea flatfish fishery is not a closed one. Effort allocation to fishing vessels has been limited through regulation of other species and bearing in mind the principle of relative stability in quota shares between EU member states. However, it is possible to legitimate assumptions by investigating sensitivity with respect to parameter values. Moreover, it seems sensible that the starting point of the model should depict the actual initial situation. This can be evaluated by comparing the open access simulation with the actual situation in 1990. It appears that the simulation gives a reasonable approximation, minor discrepancies being explained by, for instance, applying average recruitment over the period 1990–2004 instead of actual recruitment level in 1990.
Biological parameters
Assumptions about recruitment and discard rates by age class are basic for managing stocks and earnings. The model was conditioned (sometimes also referred to as calibrated or initialized) with constant recruitment (averages from 1990 to 2004; ICES, 2005) because no relationship between recruitment and SSB could be established. The standard deviation (s.d.) around the observed recruitment values is, though, high. Therefore, simulations were performed with stochastic variation in the recruitment. A normal distribution with mean and s.d. based on data from 1990 to 2004 was applied (for plaice mean = 983 590 and s.d. = 475 007, for sole mean = 126 421 and s.d. = 88 751, in thousands). When this variation is included in the model, the general trends depicted in Figure 5 remain, but as would be expected, the pattern is noisier (less smooth).
Economic parameters
The applied values of parameters listed in Table 3 influence the projection and distribution of effort among the different fleet segments in the feedback simulation module. For example, experimenting with the values for IIN/VIN and IOUT/VOUT shows that small changes do not change the general solution. However, considerably larger values, i.e. where a greater share of the profit is invested and disinvested, will intensify the fluctuations so that equilibrium states are reached further out into the future. Changing the relative values among fleet segments influences the relative distribution of effort, as would be expected.
Cost and catch composition (species and cohorts) are crucial to the economic performance of different fleet segments. Therefore, the analysis would have gained from applying real costs from 1990 rather than approximate values. However, the relative economic performances among fleet segments are believed not to change significantly over time. Such values are important in projecting the allocation of effort. The inclusion of technological development could play a role in the model, but this has not been accounted for in the present analysis.
Optimization
The time horizon of 30 years was selected to study whether the system converges towards equilibrium, although in real world fisheries management, the planning horizon is usually not as long. On the other hand, applying a shorter time horizon would provide a less reliable picture; there would be an incentive to (over)fish the stock soon because there would be no concern about the fishery in the long term. Optimizations with different discount rates have been performed. If, for example, the discount rate is doubled, the same pattern is achieved as for the low discount rate, but the fishing pressure in the early years is intensified at the expense of later years. The reason for this is that fishers value immediate profit more than profit earned in the distant future. If the discount rate is zero, the result is pulse-fishing, with intervals of approximately 7 years (from peak to peak on the profit curve). Solving non-linear optimization problems generally only guarantees a local optimum. Applying a broad range of starting values for the endogenous variables in the optimization did not, however, change the optimal solution, indicating that the optimum value we found is stable.
In general, both the optimization and simulation demonstrate stable results. This does not mean that the parameters do not influence the results, but rather that the results are reasonably reliable, because small changes in parameter values do not cause drastic changes to the results.
Finally, it is clear that uncertainties about the parameters, fluctuations in the stocks, and exogenous factors such as water temperature may also influence the system. It is, however, beyond the scope of this work to investigate this issue further. The primary aim has been to isolate management repercussions related to the allocation of effort. For such a purpose, it can actually be an advantage to consider other factors equal, because the effects caused by management are not blurred by uncontrollable environmental variables (see Sethi et al., 2005).
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Concluding remarks |
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Before an MPA is established, it is important that managers state their objectives clearly and specify relevant indicators to measure the success of the regulation, as well as how it should be monitored. The plaice box is a good example of how a regulation balances different interests. The objectives of establishing the plaice box included a wish to protect juveniles and to improve stocks, but also to maintain activity within the different fleet segments (in this case representing different nations). In biologically evaluating the plaice box, no clear conclusions were drawn, and an indicator of success was requested (Grift et al., 2004).
Our analysis has considered different management schemes and prospects for the flatfish fishery in the North Sea. The starting point is 1990, i.e. 1 year after the plaice box was established, so the alternative solutions can be evaluated in light of the actual development. The results indicate that a necessary condition for achieving a profitable fishery with biomasses above the reference point (Bpa) is to reduce the fishing pressure from that in 1990. A reduction in the number of vessels is unavoidable; continuing with the number of vessels in 1990 would not be profitable. Open access would result in zero profit and exclude many of the Dutch beam trawlers. In other words, if the box is not established, other management initiatives have to be put into effect to control the exploitation of the stocks, to ensure profitability and sustainability of stocks.
If the main concern of managers is to maximize overall profit, the flatfish fishery should be conducted by a limited number of large beam trawlers fishing outside the plaice box. The large beam trawlers are specialized in the flatfish fishery and dependent on the stock being healthy to operate profitably. In this case, continued activity within most fleet segments (and nations) would be sacrificed. If access to the plaice box had been banned, the model suggests that the existing number of vessels in 1990 fishing outside the box could be profitable and that the stocks would be above Bpa. This would not have been possible if fishing in the box was permitted. Finally, sustainable stock levels could be attained by reducing the number of vessels in all fleet segments. Overall profit would be positive, but Dutch beam trawlers, except those >300 hp fishing outside the box, would not be profitable and would have to leave the fishery.
The presence of trade-offs between profits, stocks, and distributions of income are evident. It is a challenge to managers, in this case the EU, to account for the different interests of producers and governments. Achieving sustainable stock levels and positive profits from a fishery will jeopardize the continued participation in the fishery of some fleet segments. It seems clear from our analysis that the plaice box, as instituted, is not a success. Had access to the box been prohibited, two out of three possible aims might have been achieved. However, there are different national interests, and some are in conflict with banning fishing inside the box. Perhaps this situation could be accommodated by allowing tradability of quotas between nations. Large beam trawlers operating outside the box are identified as potentially the most profitable, so they would have an incentive to accumulate quotas. Gathering quotas on these vessels would approach the profit-maximizing scenario, which also results in the healthiest stock levels.
We believe that our model can contribute with new and valuable information to management trade-offs between biology, economics, and income distribution related to MPAs. There is potential, however, for further development of the model and additional analyses. Price and cost functions could be made more complex, and analyses of discards and selectivity could be performed. Reducing discarding, including outside the box, could have positive effects on the system, biologically and economically. Also, optimizations with different formulations of objectives and constraints could provide more information about the trade-offs associated with the allocation of effort. In terms of the simulation, experiments with different variations of the capital investment function could be interesting. For instance, investment functions could be formulated to take into account trends in economic performance and stock levels, so that increasing levels of both in preceding years would imply increasing incentives to invest.
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Appendix: further issues related to parameterizing the model |
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 TopIntroductionThe North Sea Plaice...Conceptual frameworkMultifleet, multispecies, age...Data and conditioningResultsSensitivity analysis and...Concluding remarks Appendix: further issues related... References |
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This Appendix is intended to clarify how crucial parameters have been determined and basic assumptions made about the input used by the model. Not all the information we need has been easily attainable, so approximate measures have sometimes had to be taken.
Discards-at-age
ICES (2005) provides both landings- and catch-at-age for plaice, and based on this information, the average discard rate by age can be calculated. The average 1989–1994 level has been applied in the model. Based on Table 3.3.9 of van Keeken and Pastoors (2005), data on discards-at-age for sole can be obtained. Information regarding (total) discards for the different fleet segments was obtained as listed below:
- plaice box evaluation (Grift et al., 2004);
- discarding in Danish fisheries, Working Paper from The Danish Ministry of Food, Agriculture and fisheries (Anon., 2006);
- discard sampling of the Dutch beam trawl fleet in 2004 (van Keeken and Pastoors, 2005).
Catch-at-age and rates of fishing mortality for different fleet segments (initial)
The catch composition of a given fleet segment with respect to fish age is determined based on total discards for that segment compared with the total discards and the catch composition for all segments. Consider this example (Figure A1). Assume that the discard rate of fleet segment X is above the aggregated (average) discard rate. Then the catch composition of vessels from that fleet segment is determined by shifting the composition curve to the left, because discard rates are higher for younger fish (and vice versa if the level is below the aggregated level). The shift mirrors the difference in discard rate between that of fleet segment X and the aggregated discard rate.
The catch composition is used to calculate the share of catch-at-age for different fleet segments. This share is multiplied by the total fishing mortality to obtain the fishing mortality per fleet-segment-at-age, i.e. the initial fishing mortality for fleet segment 
of cohort c, species s, is given by
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| (A1) |
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Costs and prices
Cost from 2001 to 2003 is applied. The cost components are fuel, other running costs, employment, and fixed costs. Fuel and other running costs are measured in thousand euros per day, employment as a share of revenue, and fixed costs in thousand euros per year. To avoid incompatibility, the average sales prices from 2001 to 2003 are employed. Costs are adjusted by the observed revenue per day in the catch-and-landings dataset (for 1990–1994) relative to the revenue per day in the cost dataset (for 2001–2003). In other words, the model operates with fixed (2001–2003) prices.
In calculating the actual performance, there is a break in the data before and after 1995, notably for Dutch beam trawlers <300 hp. Therefore, in this case, a distinction is made between costs in the two periods 1990–1994 and 1995–2003.
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Acknowledgements |
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Researchers from the Fisheries Economics and Management Division at the Institute of Food and Resource Economics, Denmark, and Niels Vestergaard, University of Southern Denmark, have contributed to this work with valuable comments and suggestions. Their help is gratefully acknowledged. The comments and suggestions of two anonymous referees and the editor are also greatly appreciated. Remaining errors, however, should be attributed solely to the authors.
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