ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on April 21, 2008
ICES Journal of Marine Science: Journal du Conseil 2008 65(6):822-831; doi:10.1093/icesjms/fsn057
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Modelling combined harvest and effort regulations: the case of the Dutch beam trawl fishery for plaice and sole in the North Sea
Institute of Food and Resource Economics, University of Copenhagen, Rolighedsvej 25, 1958 Frederiksberg C, Denmark
Correspondence to A. Hoff: tel: +45 35 336896; fax: +45 35 336801; e-mail: ah{at}foi.dk
Hoff, A. and Frost, H. 2008. Modelling combined harvest and effort regulations: the case of the Dutch beam trawl fishery for plaice and sole in the North Sea. – ICES Journal of Marine Science, 65: 822–831.Currently, several European fishing fleets are regulated through a combination of harvest and effort control. The two regulation schemes are interrelated, i.e. a given quota limit will necessarily determine the effort used, and vice versa. It is important to acknowledge this causality when assessing combined effort and harvest regulation systems. A bioeconomic feedback model is presented that takes into account the causality between effort and harvest control by switching back and forth between the two, depending on which is the binding rule. The model consists of a biological and an economic operation module, the former simulating stock assessment and quota establishment, and the latter simulating the economic fleet dynamics. When harvest control is binding, catch is evaluated using the biological projection formula, whereas the economics-based Cobb–Douglas production function is used when effort is binding. The method is applied to the Dutch beam trawl fishery for plaice and sole in the North Sea.
Keywords: bioeconomic feedback model, effort control, fleet dynamics, FLR, harvest control
Received 14 September 2007; accepted 7 March 2008; advance access publication 21 April 2008.
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Introduction |
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 Top Introduction The Dutch beam trawl...The modelDataSimulation resultsSensitivity analysisDiscussionAppendixReferences |
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Theoretical economic contributions to fisheries management seek optimal solutions in terms of allocation of production factors (Bjørndal and Brasão, 2006). In practice, however, optimal solutions are seldom pursued in pure form, as indicated in the resource management regulation of the Common Fisheries Policy in Europe (EC, 2002). With the introduction of the 2002 reform of the CFP, effort restrictions were given stronger weight alongside quota control and limited entry to the fisheries in the form of capacity restrictions (fishing licenses). There are two key reasons to consider effort restrictions parallel with quota control. First, with the massive overcapacity of the European fishing fleet, quotas do not seem able to limit the quantity of fish being caught, because too many vessels are chasing too few fish. Moreover, it is legal and mandatory to discard undersized fish and over-quota catches within the EU, which leads to catches above the TAC for many species, in particular, those that are already heavily exploited. Within the general EU regulation, quotas are not transferable, although some member states apply such a system (OECD, 2005). By introducing effort restrictions at an EU level, in the form of a limited transferable number of sea days, individual vessels may be forced to catch less than their full harvest capacity within a given period (Shepherd, 2003). Transferable sea days encourage fishers to transfer sea days to more profitable vessels, and to lay up or sell less profitable ones (Cambell and Lindner, 1990). The second reason to include effort restrictions is that most fleets harvest several species, each equipped with individual quotas which are often exhausted at different rates (Jákupsstovu et al., 2007). By introducing control of sea days alongside quotas, it is assumed that overexploitation of some species is to some degree prevented, at the expense, however, of underexploiting other species. There is therefore a need for modelling and analytical approaches acknowledge that there are different routes to optimal solutions, and that these routes require investigation. Our purpose here, therefore, is to investigate the impact of combined restrictions (quotas and effort) on stock recovery and fleet economics, and to a less extent the effect of tradable sea days.
We present a bioeconomic simulation model developed with the aim of assessing the economic and biological effects of recovery plans under the new CFP, taking into account the causal relationship between quota restrictions set by the recovery scheme and the additional limitations on sea days. The model has a biological and an economic operation module, the former simulating the development of the fish populations in question and the establishment of quotas each year, and the latter simulating the economic dynamics of the fleet, i.e. fleet catches and earnings, fleet effort, and capital investment/disinvestment. Given the mixed nature of the management scheme considered here, the model can switch between harvest and effort restrictions. This switching mechanism is an improvement of existing bioeconomic models of fisheries, which usually consider either harvest or effort control (Ulrich et al., 2002).
We apply our model to the Dutch beam trawl fishery for plaice (Pleuronectes platessa) and sole (Solea solea) in the North Sea. The fishery in the North Sea yields annual catches of 
18 000 t of sole and 72 000 t of plaice (EC, 2005a), and the sale of the same two species yields 
160 million and 140 million, respectively. Plaice and sole are caught in the North Sea by Danish, German, Belgian, English, and Dutch vessels. According to the International Council for the Exploration of the Sea (ICES), the plaice stock in the North Sea in 2006 is at risk of reduced reproductive capacity (ICES, 2006a). The sole stock is also at risk of reduced reproductive capacity, and is moreover at risk of being harvested unsustainably. As such, it has been proposed by ICES and by the Scientific, Technical, and Economic Committee for Fisheries in the EU (STECF) that measures be taken to establish a multi-annual plan for management of the stocks of plaice and sole in the North Sea (EC, 2007). Such a plan was finally agreed in June 2007, and its objectives are (i) to bring the plaice and sole stocks in the North Sea within safe biological limits (i.e. to bring the spawning-stock biomasses, SSBs, of the two stocks above the precautionary limits of 230 000 t for plaice and 35 000 t for sole), and (ii) to ensure that the two stocks are in future harvested based on maximum sustainable yield and under sustainable economic, environmental, and social conditions. An account of the steps leading up to the plan is given by Curtis et al. (2007). The recovery plan, which consists of combined quota and effort regulations, is simulated here using a bioeconomic model.
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The Dutch beam trawl fleet |
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In 2004, the Dutch beam trawl fleet consisted of 171 vessels <24 m and 131 vessels >24 m. Both fleets operated at small economic losses in the period 2002–2004, indicating overcapacity and declining stocks. The smaller beam trawlers target cod (Gadus morhua), plaice, and sole, and in terms of landings value, plaice and sole constitute 34%, shrimp 44%, and other fish, in particular flatfish, 17%. The balance of 5% of value is cod. The larger beam trawlers target plaice and sole, which together constitute 80% of their total landings value, the balance being contributed mainly by other flatfish (AER, 2005).
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The model |
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The model is based on an earlier multifleet multispecies model (Hoff and Frost, 2006, 2007). It is a dynamic feedback model with annual time-steps. It switches between quota and effort restrictions on the fleet, depending on which control is binding. The number of vessels Vy,b in year y in fleet b based on previous years’ profit is:
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| (1) |
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Vbmin and Vbmax are the minimum and maximum numbers of vessels allowed in fleet b, and 
y,b is the average profit over ub + 1 years discounted over 
years; it is used for evaluating capacity change. The parameters 
b and ob are the prices per unit capacity of investments or disinvestments; Ib+ and Ib– the shares of, respectively, positive and negative profits used for investment/disinvestment in capacity; wb the lag in the investment decision, i.e. the number of years from decision to invest/disinvest until the change is actually put into force; Py,b the net profit; 
the interest rate; and the expected lifetime of a vessel. It is assumed that there is no decommissioning of vessels. In Equation (1), it is assumed that changes in capacity are determined by the opportunity cost of capital including an option for asymmetry in entry and exit. The price of a vessel b transforms pecuniary capital into physical capital, and the reciprocal of b includes a fisher’s perception of opportunity costs (Bjørndal and Conrad, 1987).
Based on estimated stock Ns,a,y-1 and observed catches cs,a,y-1 (both in numbers) for species s of age a in year y – 1, the resulting fishing mortality rate Fs,a,y-1 for species s at age a in year y – 1 is estimated by solving the following cohort catch equation for F:
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| (2) |
Here, Ms,a is the natural mortality rate of species s at age a. Equation (2) can be solved numerically by most mathematical/statistical software packages.
Next, the stock is projected 1 year forward:
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| (3) |
The number of recruits Ns,1,y depends on the stock–recruitment (S–R) relationship; here, a Ricker function and constant recruitment are used.
The TACs for plaice and sole in year y are set according to the multi-annual recovery plan for plaice and sole mentioned above (EC, 2007). For both species, the plan states that the TAC of species s in a given year should be the maximum of (i) the TAC that will result in a 10% decrease in the fishing mortality rate relative to the previous year, and (ii) the TAC that will result in a fishing mortality rate of around 
s for ages 2–6 of the stock (s = 0.3 for plaice, and s = 0.2 for sole). Moreover, if the TAC for year y determined by these rules is 15% above or below the TAC of the previous year, the TAC must be set equal to 1.15 or 0.85 times the TAC in the previous year, respectively. In addition to this quota regulation, the plaice and sole fishery are subject to effort limitations. The estimated fishing mortality rate of year y–1 [Equation (2)] is thus scaled into two proposed fishing mortality rates for year y using rules (i) and (ii):
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| (4) |
A tilde over a parameter in this equation and subsequently indicates that it is a proposed and not a realized value. Rule (ii) has been translated into meaning the TAC that will result in a fishing mortality rate 
s for all ages 2–6 of the stock. This has been done for modelling purposes, but also on the assumption that it will generally be difficult to implement a fishing mortality rate of exactly s for ages 2–6, even given very selective gear.
The proposed fishing mortalities are then used to evaluate a total catch proposal 
s,y (in weight):
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| (5) |
s,a,y,(I) the proposed catch weight in year y for species s at age a, evaluated with the fishing mortality given by scenario I.
As the catch is the sum of landings and discards (a large quantity of especially juvenile plaice are discarded, whereas there is almost no discarding of sole in the North Sea), the landings are assumed to be equal to the proposed TAC, 
s,y. It is assumed that the landings fraction is constant across years for each age class. Hence, the proposed catches are scaled up to obtain the proposed TAC, s,y:
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The quota of species s for fleet b, qb,s,y, is set using Qs,y, the country share 
, and the fleet share 
:
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is constant throughout the simulation period, but the fleet shares are based on fleet catches in the previous year.
The effort (number of sea days) needed per vessel in fleet b to catch species s is
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| (8) |
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| (9) |
a ws,a Ns,a,y is the stock biomass. This cpue relationship assumes that landings are determined by the conventional economic Cobb–Douglas production function (Conrad and Clark, 1994 ch.2), cf. Appendix. β and 
are functions of the parameters of this Cobb–Douglas function.
Equation (8) gives the number of sea days necessary for a vessel in fleet b to catch its full quota of each species s. The fisher’s choice of effort 
b,y can be either (i) the minimum of the two efforts, (ii) the maximum of the two efforts, or (iii) a third effort, e.g. from a profit-maximizing perspective. The actual number of sea days used in year y by a vessel in fleet b is further determined by the effort limit 
b,y, set by the regulation
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| (10) |
b,y is not set strictly according to the recovery plan for plaice and sole (EC, 2007), where it is stated that "Each year, the Council shall decide (...) on an adjustment to the maximum level of fishing effort available for fleets where either or both plaice and sole comprise an important part of the landings (...)". Not knowing the actual rule by which this annual effort has been set, it has been decided to follow the sea-days regulation set in EC (2005b) in connection with recovery plans for cod, inter alia, in the North Sea.
The actual landings of species s corresponding to the effort given by Equation (10) are determined by using the cpue relationship [Equation (9)], but see also Equation (A2) in the Appendix:
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| (11) |
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| (12) |
Figure 1 shows the steps of the biological operations model. Given the observed landings of the two species taken by the fleet [Equation (11)], it is straightforward to evaluate the total landings revenue Rb,y, the fixed and variable costs and profit of each fleet in year y. The revenue of fleet b is
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s the price flexibility rate, and 
b the fraction which the catch value of plaice and sole constitutes of the total catch value.
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The fixed costs (Kb,y) and variable costs (Gb,y) in year y are
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| (15) |
The model is implemented in FLR (Fisheries Laboratory in R; Kell et al., 2007), which is a collection of tools in R for the construction of bioeconomic simulation models of fisheries and ecological systems (http://flr-project.org/doku.phphttp://flr-project.org/doku.php).
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Data |
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The start year in the simulation is set to 2004, because economic data from 2005 on are not at present reliable. It is assumed that the plaice and sole recovery plan started in 2005, although in reality the starting year is 2008. Each simulation is run for 30 years to give a complete picture of the stock recovery/development and the progress of fleet dynamics towards equilibrium. The stocks of plaice and sole are initialized in 2004 using cohort and catch data from ICES (2006b). Natural mortalities and the maturity rates of the stocks are constant throughout the simulation period, and equal to the values in ICES (2006b).
The fitted Ricker S–R functions (non-linear least-squares fits) provided poor descriptions of the historical SSB (S) and recruitment (R) variations for plaice and sole (Figure 2, Table 1). Therefore, two S–R scenarios were run, one in which the estimated Ricker functions were used, and one where constant recruitment, equal to the average values based on the historical data, is used (see Table 1).
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, for plaice and sole in the North Sea.The Dutch beam trawl fleet operating in the North Sea in 2004 was initialized using data from AER (2005); see summary in Table 2. Note that the initial (observed) number of sea days for beam trawlers >24 m exceeds the maximum allowed number of sea days used in the regulation. It was therefore assumed that the effort regulation was first put into force in the year following the initiation year (2004), for which observed values were used for all variables. The maximum allowed number of sea days for each fleet given in Table 2 was set according to the regulation specified in EC (2005b).
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The price flexibility
in the price function is based on work by the working group of the flatfish recovery plan (SEC, 2006). The group estimated price flexibilities for sole and plaice as 0.37 and 0.16, respectively, using a model for the North Sea only. We selected 0.2, to include a modest price effect. If price flexibility is 0, no price effect is assumed, and usage of high price flexibilities will fully dissipate the economic impact of changes in landings, e.g. a flexibility rate of 1 will mean that gross revenue is constant.
The parameter values of the Cobb–Douglas function are based on Danielsson et al. (1997) and Eide et al. (2003), who estimated increasing returns to scale for cod caught by bottom trawls at β = 0.7 and = 1, and β = 0.34 and = 0.8, respectively. For northern hake, Garza-Gil et al. (2003) estimated almost constant returns to scale, i.e. β+ = 0.9. For bottom trawls, these analyses showed that changes in catches were more sensitive to changes in sea days than changes in stock abundance. Hence, our estimates of β = 0.8 and = 1 place more importance on stock effects than may be realistic.
A discount rate at of 5% was used. From a fisher’s perspective, this is too low (Hillis and Whelan, 1992; Harrison et al., 2002). From the perspective of society, it tends to be too high (HM Treasury, 2003). The effect of an increase in the discount rate is that investments and disinvestments will be lower at a given profit, leading to less fluctuation in the capital stock over time.
Finally, the Dutch share (relative stability) of the total EU North Sea plaice TAC is set at 38.45% and for sole at 75.23% [SEC (2004) 1710]. Relative stability coefficients are not published, but originate in a Council Resolution in 1976.
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Simulation results |
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Three scenarios were simulated with the model described above. In scenario "Min", the effort chosen by the vessels is set to the number of sea days necessary to take the most restrictive of the quotas of the two species. In scenario "Max", the selected effort is set to the sea days necessary to exhaust both quotas, and in scenario "Optim", the average number of sea days per vessel is set to the number maximizing the average vessel (and therefore fleet) profit. In all three scenarios, the possibility exists that the chosen number of sea days will be above the effort limitation set by the recovery plan, which would then be the limiting factor for the catches [Equation (10)]. Each effort scenario was run using the estimated Ricker S–R relationships, and with constant recruitment.
For plaice, the stock was slightly below the precautionary S level (Spa) in the initiation year (2004), then recovered to above Spa in 3 years in all scenarios (Figure 3a). The development of the plaice stock above Spa followed two patterns, depending on the selected S–R relationship, whereas the chosen effort allocation rule (maximum, minimum, or optimal effort) had little impact. With constant recruitment, S levelled out at 900 000 t within 12–20 years (depending on the effort scenario). If the value of the constant recruitment was increased, the equilibrium value attained by S also increased (see sensitivity analysis below). When the Ricker S–R function was used, the stock started oscillating around 600 000 t after 10–20 years. These oscillations were caused by passing from one side of the maximum of the Ricker curve to the other side. Above 350 000 t, the S–R relationship is on the decreasing (right) part of the curve, implying that increasing S leads to decreasing R, creating decreasing cohorts which will decrease S in the long term. When S decreases, therefore, R will also increase, so creating increasing cohorts, etc. For plaice, it can be concluded that although the stock was said to be at risk of reduced reproductive capacity, it seemed that the stock could fairly quickly be brought above safe biological limits given an appropriate recovery scheme.
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For sole the pattern was different (Figure 3b). The sole stock was almost half the precautionary limit in the start year, and it took around 4 years to reach Spa for all scenarios except when the Ricker S–R was assumed in combination with the maximum effort scenario, in which case it took 14 years for the stock to reach Spa. When constant recruitment was assumed, the sole stock increased to an equilibrium value (within 10 years), but contrary to plaice, this equilibrium value for sole varied significantly, with the effort scenario being highest for the minimum effort scenario, lowest for the maximum effort scenario, and in between these two when the effort optimizing the annual profit was used. When the Ricker S–R was used, the sole S increased at a slower rate, because R increased only slowly with S (left part of the Ricker curve for sole in Figure 2).
Comparison of the simulated developments of the plaice and sole stocks indicated that it was the sole quota which was limiting, because the development of the sole stock depended heavily on the effort used, less effort being needed to take the sole quota than the plaice quota.
Figure 4 demonstrates fleet profits for each effort scenario. First, the initial profits for both fleets were negative, indicating that the fleets operated at excess resource utilization in the start year (2004). The profits then increased to positive values within 2–4 years and stayed positive in most scenarios, except for the small beam trawlers in the maximum effort scenario, for which the profit was about zero when constant recruitment was assumed (Figure 4a) and oscillated around zero when the Ricker S–R was assumed (Figure 4b). Although the annual profits for the optimal effort scenarios were the highest at the beginning of the simulation period, the profits for the minimum effort scenario were highest at the end for both fleets with both recruitment scenarios. This may at first glance seem strange, but it must be remembered that the different effort scenarios lead to different development trends for the stock, effort, and fleet capacity, and thus to different developments in landings values and costs. Seeing, for example, that especially the development of the sole stock depends significantly on the effort, and that this stock increased the most when minimum effort was chosen each year, this indicates that although it may seem optimal for the fishers to maximize profit each year in the short term, it is actually more economically optimal in the long term to comply with the limiting quota of the two species.
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The effort of the large beam trawlers in the start year was higher than the effort limit of 156 sea days put into force by the management programme in the second year of the model (Figure 5). The effort of both fleets decreased during the first simulation year, indicating excess use of resources over what was needed to take the quotas in the start year. For both S–R scenarios, limit effort of 156 sea days was only reached in the maximum effort scenario. The maximum effort was always connected to the plaice quota, so plaice will therefore not always be fully exploited because of the effort regulation. In the two other effort scenarios, the effort limit was not reached. When constant recruitment was assumed (Figure 5a), the effort maximizing the annual profit (Optim Effort) lay between the minimum and maximum effort measures for both fleets, whereas the optimizing effort was outside this range when the Ricker S–R was assumed (Figure 5b). The effort optimizing the economic situation (maximizing annual profit) for the fishery did not match the effort needed to take any of the quotas in both S–R scenarios. Therefore, the quotas set based on biological considerations will seldom be economically optimal for the fishery in the short term (
5–10 years). In the long term, however, the minimum effort choice may be economically optimal, as shown above. Finally, in Figure 5, the efforts of both fleets have a nadir at around 2013 independent of the effort scenario and S–R assumption. This is caused by a combination of decreasing quotas while stocks increase and hence an increasing cpue in the same period.
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The development in fleet capacity, measured as number of vessels in each fleet, followed the development in profit as expected [cf. Equation (1); Figure 6]. Therefore, fleet capacity decreased at the beginning of the simulation period for all scenarios as a consequence of the initial negative profit, and increased later to the maximum allowed capacity for most scenarios following the positive profit trends. The only exception was the maximum effort scenario in the Ricker S–R case (Figure 6b), where the capacity of the small beam trawlers oscillated because of the oscillations of profit below zero.
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Sensitivity analysis |
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TopIntroductionThe Dutch beam trawl...The modelDataSimulation resultsSensitivity analysisDiscussionAppendixReferences |
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Sensitivity analyses were performed for recruitment, variable and fixed fleet costs, depreciation, and the scaling parameters β and
in the cpue relationship. Percentage deviation from the base case (i.e. the simulations discussed above) of profits and SSB after 30 years obtained by varying the parameters were evaluated. Table 3 lists the results of the analyses. Positive percentages means that the value when varying the parameter is higher than the base case value, and vice versa.
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Constant recruitment (R) was set to the 25% and 75% quartiles of the average historical recruitment data for plaice and sole (Table 1). Profit and SSB values after 30 years are very sensitive to the values of R, and both increase with increasing R. Notably, the profit of small beam trawlers varies by >700% from the base case in the maximum scenario (note, however, that the profit of the small beam trawlers is close to zero in the maximum scenario under constant R and that percentage deviations may therefore seem large), and the SSB of sole by >80% in the maximum scenario after 30 years.
Variable costs (G) in year 1 were set to 0.5x and 2x the base-case values. The profits after 30 years are very sensitive to the variation in G, especially for the small beam trawlers, where a profit deviation of >1000% is observed in the maximum scenario. For SSB (S), that of sole is rather sensitive to the value of G (with a variation of up to 72%), especially when it is increased above the base case value, whereas that of plaice is almost unaffected.
Fixed costs (K) in year 1 were set to 0.5x and 2x the base-case values. The same pattern is seen as for the variation of variable costs, i.e. that profits of both fleet segments (especially the small beam trawlers) and the SSB of sole are highly sensitive to variation in K.
The discount rate was set to 0.1 and 0.15 (compared with the base-case value of 0.05). Neither fleet profits nor species SSBs after 30 years showed any variation as a function of discount rate. The results are therefore not included in Table 3.
The cpue (U) scaling factor was set to 0.01 and 9, and the biomass (U) scaling factor to 0.1 and 1. In both cases, the profits of both fleets after 30 years and the sole SSBs were very sensitive to the variations in these parameters, but the plaice stock was sensitive to a lesser degree. The profit of particularly the small beam trawlers varied extensively when the parameters were changed.
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Discussion |
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TopIntroductionThe Dutch beam trawl...The modelDataSimulation resultsSensitivity analysisDiscussionAppendixReferences |
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We have presented a bioeconomic model to assess the impact of the proposed recovery schemes for plaice and sole in the North Sea (EC, 2007) on capital dynamics in the Dutch beam trawl fleet, for which this mixed fishery has great importance. An empirical analysis of capital dynamics within fisheries can be found in Bjørndal and Conrad (1987), apart from which there is little empirical information about investments within fisheries.
The new recovery plan for the two species includes quota and effort control, and the model is a step forward compared with existing bioeconomic models such as the EIAA model [SEC (2004) 1710], in the sense that our model takes both types of control into account. Few models covering this area have been published. However, one model can be used for comparative purposes, that of Ulrich et al. (2002). In that study, analyses were performed for the Dutch beam trawl fishery using a bioeconomic model that differs from ours in three areas mainly. First, although capacity in terms of number of vessels is kept constant in the analyses of Ulrich et al. (2002), the capacity in our model is subject to change by the use of an entry/exit (investment) function. Second, effort in terms of sea days is a linear function of fishing mortality rate applying catchability coefficients in the Ulrich et al. (2002) model, but this is not the case in our model. Our model applies a non-linear production function describing the relationship between landings and effort that implicitly implies a non-linear relationship between effort and the rate of fishing mortality. Third, whereas the Ulrich et al. (2002) model works under only one harvest control rule at a time, our model is subjected to two simultaneous harvest control rules at a time, each binding at different points in time for the fleet segments in our analysis.
The inclusion of these extensions in our model compared with that of the Ulrich et al. (2002) model leads to faster recovery of the fish stocks, increased vessel profit, more fluctuations in sea days, and a significant instant reduction in capacity over around 4 years, followed by an increase in capacity to a level close to the initial state after four more years.
Our model was run for six scenarios, two S–R assumptions (constant recruitment, and Ricker S–R function), and three fisher behaviour scenarios regarding their choice of effort, i.e. selecting the maximum or the minimum of the effort necessary to catch the quotas of plaice and sole, respectively, or choosing the effort that maximizes their annual profit. Sensitivity analyses were run to test the influence of the choice of initiation parameters on model results.
The simulations indicated that if fishers comply with the additional effort regulation, the plaice and sole stocks will increase to above their precautionary limits within 3–4 years of initiation of the recovery programme. This quick recovery may seem surprising, but the plaice and sole stocks were actually not that much below the precautionary limits in the start year, and because the model assumes full compliance with the effort limitation set by the recovery scheme, it should be expected that the stocks would increase fairly quickly. This even happens when fishers choose to exceed the sole quota and to try to fish their full plaice quota, because in this case the effort restriction will be limiting for the final catches. The only exception to this was that the sole stock increased fairly slowly (reaching the precautionary limit after 12 years) when fishers chose maximum effort (i.e. violating the sole stock), and when a Ricker S–R relationship was assumed. The implications of this last result are that the new recovery scheme may in fact not be efficient when the aim is to build the sole stocks, because it is straightforward to assume that fishers will usually keep fishing until the last quota (in this case plaice) has been filled, although quotas of other species might be exceeded, and that the S–R relationship is not constant but varying. Therefore, the results indicate that it might be worthwhile considering tightening the management of plaice and sole in the North Sea even further (e.g. by lowering the quotas and the effort limits) if the primary aim is to bring the sole stock back above its precautionary limit soon.
The simulations also showed that although it might seem obvious from a fisher’s perspective to choose the effort that optimizes profit each year, this might not be an optimal behaviour in the long term (20 years), because the profit obtained in the case where fishers comply with both quotas (so choosing the minimum effort) will in the long term increase to above the level of profit obtained when the fisher tries to optimize his annual short-term profit. The reason for this seeming paradox is of course that the stocks are allowed to increase at a faster speed when the fishery complies with all quotas, in the long term leading to higher catches and values. This result is interesting from a management perspective because it indicates that it is important to find a way to inform fishers of the long-term effects of their short-term behaviour.
Finally, our model simulations indicated that the effort limitation put into place in the recovery scheme only actively limits the fishing effort when fishers choose to exceed one (or more) quotas and to continue fishing until all quotas have been filled. In that case, the effort limitation puts an upper bound on their catches in the case when they then choose to comply with this controlling factor (which is assumed in the model simulations). As such, the effort limitation might be useful as an extra controlling factor in management plans.
The results of our model simulations do not take into account possible effort creep. Effort creep allows fishers to take higher catches without deploying additional effort, so makes it easier to take the full quotas of all species, even within the effort limitation set by the management scheme. Seeing that the model in its present form is fairly complex, we have chosen to ignore this aspect in our present context, but exploring the effects of effort creep will be a natural step to include in our future work with the model. Likewise, the catch value fractions are assumed constant in the simulations, an assumption made because of a lack of information about effort allocation on the species. This assumption is questionable, however, particularly for shrimp, which may be caught totally or partly independent of sole and plaice by beam trawlers <24 m long. Alternatively, species other than sole and plaice could be kept constant. Finally, the sensitivity analyses show that the results of the simulations are highly sensitive to the choice of the initial parameters entered into the model. It is therefore important to select reliable values of these parameters before running the model, i.e. to perform a thorough preliminary analysis of the state of the problem being considered.
The model is a true, integrated, bioeconomic model, because the final catches of the two species each year depend on fisher behaviour and economics. Simpler biological models including economics first evaluate the stock development independent of the fleet dynamics, and second evaluate various economic indicators at the end of each year as a function of the biological catches, but without these economic factors feeding back into the biological development in the next year [SEC (2004) 1710]. We believe that to obtain a more reliable assessment of management measures, the feedback must work in both directions, i.e. it must take into account the fact that the stock development influences the fleet economy, but also that the fleet economy will also influence stock development.
This said, it must also be emphasized that the model is of course a simplification of the real dynamics between fish biology, management plans, and economics, and that there is still room to improve the model to get more tractable impact assessments. It has for instance been made clear during the simulations that the model is highly sensitive to the parameter values input, so effort needs to be put into calibrating this and other models correctly.
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Appendix |
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TopIntroductionThe Dutch beam trawl...The modelDataSimulation resultsSensitivity analysisDiscussionAppendixReferences |
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Relationship between catch per unit effort and the landings production function
The catch per unit effort (cpue) formula given in Equation (9) is directly related to the assumption that the landings are given by the conventional economic Cobb–Douglas production function (Conrad and Clark, 1994 ch.2; Danielsson, et al., 1997; Eide et al., 2003; Garza-Gil et al., 2003), depending on the SSB and the effort. Equation (9) states that
|
| (A1) |
When the landings are evaluated using the economics-based Cobb–Douglas production function (Eb,y being the total effort used by fleet b in year y):
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| (A2) |
Fl,s and 
b,s, b,s:
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| (A3) |
The standard formula for cpue is
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| (A4) |
|
| (A5) |
b,s > 0 when b,s < 1, i.e. that decreasing returns to scale in the effort imply that the cpue decreases with increasing landings, and vice versa. |
Acknowledgements |
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The work presented here was performed under the EU 6th framework programme EFIMAS (Operational Evaluation Tools for Fisheries Management Options). We thank two anonymous referees whose comments on the submitted draft proved most useful. Funding to pay the Open Access publication charges for this article was provided by the Institute of Food and Resource Economics, University of Copenhagen.
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References |
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