Single and multispecies reference points for Baltic fish stocks

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1 ICES Journal of Marine Science, 56: Article No. jmsc , available online at on Single and multispecies reference points for Baltic fish stocks H. Gislason Gislason, H Single and multispecies reference points for Baltic fish stocks. ICES Journal of Marine Science, 56: Single and multispecies models are used to examine the effect of species interaction on biological reference points for cod, herring, and sprat in the Baltic. The results demonstrate that reference points are different in single and multispecies contexts. Reference points for fishing mortality based on single-species yield and SSB calculations are difficult to use when natural mortality depends on the absolute abundance of the predators and their alternative prey. Reference points based on maximizing total yield from the system may lead to impractical results when species interact. Multispecies predictions suggest that the cod stock in the Baltic should be reduced to a very low level of biomass in order to benefit from the higher productivity of herring and sprat, its major prey. Such a result stresses the need for incorporating socio-economic considerations in the definition of target reference points. Management advice based on biomass reference points will also differ. In the single species situation the combinations of cod and pelagic fishing effort for which the equilibrium spawningstock biomass of the three species is above the biomass reference points forms a rectangular area. When biological interaction is taken into account the limits of this area becomes curved. Reference limits for forage fish cannot be defined without considering changes in the biomass of their natural predators. Likewise, reference limits for predators cannot be defined without considering changes in the biomass of their prey International Council for the Exploration of the Sea Key words: multispecies models, biological reference points, species interaction. Received 26 October 1998; accepted 12 May H. Gislason: University of Copenhagen, c/o Danish Institute for Fisheries Research, Charlottenlund Castle, DK2920 Charlottenlund, Denmark. Tel: ; fax: ; hg@dfu.min.dk Introduction The call to develop a precautionary approach to fisheries management has recently renewed the debate about the definition and estimation of biological reference points (e.g. Smith et al., 1993; Caddy and Mahon, 1995; FAO, 1995; Rosenberg and Restrepo, 1995; ICES, 1997c). Biological reference points are used as benchmarks to characterize the state of a stock or fishery. They are commonly divided into target and limit reference points. Target reference points represent a desired level of fishing mortality or biomass, while limit reference points are used to define either an upper bound to the fishing mortality or a lower bound to the biomass. Biological reference points are often derived from models where the yield from the fishery and the biomass of the exploited stock is related to fishing mortality (Caddy and Mahon, 1995). It is common practice to use single-species models where each species is considered in isolation from the rest of the ecosystem. Little effort has so far been spent on examining how reference points might be defined and used in a multispecies context. However, species interactions are likely to have direct effects on biological reference points (Brander, 1988; ICES, 1997d). Failure to account for these may lead to undesirable outcomes, such as overexploitation and stock collapses, even if the probability of such outcomes appears to be negligible in a single species analysis. Not accounting for species interactions may be just as problematic as neglecting uncertainty in the basic assessment data in the overall management plan (ICES, 1997d). Previous analyses of multispecies and multifleet fisheries models have shown that the maximum overall benefit to society cannot be estimated without considering the relative value of the different species caught and the costs associated with their capture (May et al., 1979; Flaaten, 1988). In fisheries where the economic benefit to society is the overriding management concern, it has been proposed to use the maximum of the long-term resource rent, defined as the gross catch value minus /99/ $30.00/ International Council for the Exploration of the Sea

2 572 H. Gislason the harvest costs, as the main economic management objective (Flaaten, 1998). The fish community in the Baltic Sea is relatively simple and dominated by cod, herring, and sprat (Elmgren, 1984). These species are the primary targets for the commercial fishery and the interactions among them are well studied (Sparholt, 1994). Single and multispecies model are used to estimate and compare a few of the commonly used reference points for cod, herring, and sprat in the central Baltic. The models are initially used to assess the historic stock size and fishing mortality of the three species. Based on these assessments long-term equilibrium predictions of yield, biomass, value, and resource rent are made at various fishing mortalities. food available. In years with less food available growth will be slower. Weight at age of cod is thus described by: where Avail(a,y): is the amount of food available to cod age group a in year y; w (a,y) is the average weight of cod age group a in year y; and: The model framework The models consist of a single-species VPA (Gulland, 1965; Megrey, 1989), a MultiSpecies VPA (MSVPA) (Gislason and Helgason, 1985; Sparre 1991; Magnusson, 1995), and an extended MultiSpecies VPA (MSGVPA), in which cod growth and maturity are modelled as a function of available food. All three models were used in both retrospective and predictive modes and operated with an annual timestep. In the predictive mode an average of the fishing mortalities over a recent number of years was used to predict long-term equilibrium yields and biomasses in the status quo situation. Separate effort multipliers were used to change the status quo fishing mortalities generated by the two major fisheries: the cod fishery and the pelagic fishery for herring and sprat. An index of total catch value was calculated by multiplying the catch of each species by its relative first-hand price. An index of costs was generated by assuming that the fisheries presently are in bionomic equilibrium where costs and catch value balance (Clark, 1985), and that costs were directly proportional to effort. Resource rent was estimated by subtracting costs from the value of the catch. Recruitment was predicted from a Ricker stock and recruitment relationship (Ricker, 1954): where w obs (a,y) is the average observed weight at age of cod age group a in year y; and ny is the number of years over which the calculations are performed. Food consumption is calculated by assuming constant conversion efficiency at age: where R(a,y) is the per capita food consumption of cod age group a in year y; and CE(a) is the conversion efficiency; i.e. the proportion of the total food intake that is converted to somatic growth for cod age group a. In a model where growth and food intake depend on the amount of available food, it is inconsistent to assume that the biomass of other food is constant and does not respond to changes in predation. The model was therefore extended by a simple description of the dynamics of other food in which the biomass of other food was made a function of the predator s intake. The total intake of other food of type b, is calculated by the model from: N (0,y)=R1 SSB(y)exp[ R2 SSB(y)] (1) where R1 and R2 are species-specific constants determined from the recruitment and SSB estimated in the retrospective part of the models. In the MSGVPA, cod growth depends on the amount of available food. Weight-at-age is assumed to equal weight-at-age in the cohort during the preceding year plus a growth term. The growth term depends on whether the amount of available food in a particular year is above or below the average. Growth will be faster than average in years where there is more than average where Suit(a,b) is the suitability of other food of type b to predation by cod age group a; Nz (a,y) is the average number of fish alive in age group a during year y; and Bz(b,y) is the average biomass of other food of type b in year y. The average biomass of other food of type b was assumed to decline exponentially as a function of the amount eaten: Bz(b,y)=exp[K(b) L(b)Cons(*,b,y)] (7)

3 Baltic fish stocks 573 where Bz(b,y) is the average biomass of other food of type b in year y; K(b) is a constant expressing the log of the biomass of other food type b when predation is zero, corresponding to the unexploited biomass in a surplus production model; and L(b) is a constant expressing the amount of change in log biomass of other food per unit of predator consumption. Finally, the forecasting part of the model was extended to take changes in maturity at age of cod into account by introducing a sigmoid relationship between the proportion mature and body weight: PM(a,y)={1 exp[ PM1*w (a,y)]} PM2 (8) where PM1 and PM2 are constants determined by non-linear regression of proportion mature vs. observed weights at age. Saduria and other invertebrates. First, it was assumed that other food of age 4+ cod contained only Saduria. Secondly, for ages 1 3, it was assumed that Saduria constituted the same proportion of the diet as for older cod and that the remainder of the other food category consisted of other invertebrates. In the MSVPA, the biomass of Saduria was set to 4 million tons and the total amount of other invertebrates to 10 million tons. In the MSGVPA, these biomasses were used to calculate K(b). Alternative biologically plausible values for the biomass of other invertebrates and Saduria produced virtually identical results in both the MSVPA and MSGVPA, confirming the insensitivity of the models to the input biomass of other food (Finn et al., 1991). The observed weights-at-age for the 0-group and for all age groups in were used as the starting values in the growth model incorporated in the MSGVPA. Input data The three models were used to analyse a single set of assessment data from the central Baltic, which cover the period from to Catch-at-age, terminal fishing mortalities, proportion mature-at-age, single-species total natural mortality, and weight-at-age for herring and sprat were taken from ICES (1997a). For cod, quarterly weight-at-age and stomach contents data for 1991 were obtained from the revised set of input data generated by ICES (1997b). 1 The quarterly values were averaged for each year to produce annual mean weights-at-age and annual stomach content at age. Residual natural mortality, M1(s), was set to 0.2 for all three species, the same value as used in ICES (1997b). Food conversion efficiencies for different age groups of cod were taken from ICES (1992). An index of firsthand value was derived by assuming that cod was 10 times as valuable as herring and sprat. This estimate reflects the relative price in Denmark and Sweden, two of the major fishing nations (Directorate of Fisheries, 1997; OECD, 1997). In the stomach content database, all food items except cod, herring, and sprat are lumped together in one category of other food. However, the species composition of this category is not the same for large and small cod. For cod >50 cm (age group 4+) it consists almost exclusively of a large isopod, Saduria entomon, while for smaller cod other invertebrates are also included (Sparholt, 1994). Initial attempts to model cod growth with only one category of other food proved unable to describe the changes in the growth of older cod, and it was therefore decided to split other food into 1 The database is currently being revised, but the most recent version of the data was kindly made available by Stefan Neuenfeldt (pers. comm.). Parameter estimation Annual fishing mortalities were estimated by Newton iteration in all three models. Average suitability coefficients in the two multispecies versions were estimated from all available stomach content data in an iterative procedure as explained in Magnusson (1995). The parameters, L(b), used to describe the change in the biomass of invertebrates and Saduria in the MSGVPA were estimated by minimizing the sum of squares of deviation between observed and estimated weight-at-age in the model. The Ricker stock recruitment relationship was fitted separately for each model. Because of changes in environmental conditions, cod recruitment success has changed considerably over the years (Sparholt, 1996). The number of recruits produced per SSB drop in the middle of the 1980s (Sparholt, 1995). In order not to generate too optimistic predictions only data from the low recruitment period from 1986 to 1995 were used. The right hand downward sloping side of the Ricker curve is often attributed to cannibalism (Hilborn and Walters, 1992). In the multispecies models, cannibalism is already dealt with, and, in accordance with Sparholt (1995, 1996), a linear rather than a dome-shaped stock recruitment relationship for cod was therefore assumed by setting the parameter R2 to zero. For herring and sprat, the data contained little information about the shape of the stock recruitment curve. Initial parameter estimates resulted in recruitment maxima far outside the observations and produced unlikely predictions of virgin stock biomass. The parameters were therefore selected so that the maximum of the stock recruitment curve corresponded to the point defined by the average SSB and average recruitment over the period from to 1995.

4 574 H. Gislason (a) SSB, tons ( 10 3 ) Recruitment at age 0 ( 10 3 ) Recruitment at age 0 ( 10 3 ) Av. F(4 7) SSB (b) SSB, tons ( 10 3 ) Recruitment at age 0 ( 10 3 ) Recruitment at age 0 ( 10 3 ) Av. F(3 6) SSB 2000 Figure 1. (a) and (b).

5 Baltic fish stocks (c) 0.70 SSB, tons ( 10 3 ) Recruitment at age 0 ( 10 3 ) Recruitment at age 0 ( 10 3 ) Av. F(3 7) SSB VPA MSVPA MSGVPA VPA MSVPA MSGVPA Figure 1. (c). Figure 1. Spawning-Stock Biomass (SSB), average fishing mortality (F), recruitment, and SSB recruitment relationship estimated by single-species VPA, MSVPA, and MSGVPA. (a) cod, (b) herring, (c) sprat The non-linear regression used to estimate the parameters in the equation describing the proportion mature-at-age explained 99% of the variance in the data. The status quo fishing mortality used in the prediction was calculated by rescaling the average exploitation patterns to the fishing mortality in 1996, the last year of the retrospective analysis. Basic output The spawning-stock sizes, average fishing mortalities, recruitment estimates, and stock recruitment relationships produced by the three models are compared in Figure 1. The models produce almost identical estimates of spawning-stock biomass, but recruitment differs. Prior to 1990, recruitment is generally estimated to have been at a higher level in the multispecies models than in the single species VPA. The estimated fishing mortalities are similar, except for sprat, where fishing mortality is estimated to be lower prior to 1986 in the multispecies models. The total predation estimated by the two multispecies models is shown in Figure 2. The estimated consumption of cod, herring, and sprat is of the same magnitude in both models, but is less variable in the MSGVPA than in the MSVPA. The predicted weight at age of cod in the MSGVPA is compared to the observed in Figure 3 for cod age groups 1 5. For ages 1 3 the predicted weight at age is close to the observed, but they deviate for ages 4 and 5, particularly in the most recent years. In addition, the discrepancy between the patterns for ages 4 and 5 in suggests that there may be problems with the weight-atage data. Correlations between observed and predicted weight-at-age were significant for all ages (Fig. 4). However, with the exception of age group 3, the predicted weight-at-age in general changed less than the observed. The status quo fishing mortality for cod, herring, and sprat is given in Table 1 together with the corresponding spawning-stock biomasses and virgin SSB s estimated from each model. Note that for herring and sprat the status quo SSB s are larger than the virgin SSB s in both multispecies models.

6 576 H. Gislason Tons ( 10 3 ) Tons ( 10 3 ) (a) (b) Selection of reference points Year Cod Herring Sprat Figure 2. Total consumption of cod, herring, and sprat estimated by (a) MSVPA and (b) MSGVPA. ICES (1997c) contains a list of commonly used reference points. Many of these are derived by using single-species SSB per recruit calculations to estimate the fishing mortality corresponding to a specific replacement line in a plot of SSB vs. recruitment (e.g. F low,f med,f high, F crash, and F loss ). It is not straightforward to estimate these reference points in a multispecies context, because natural mortality, and hence also SSB per recruit, changes as a function of the absolute abundance of the predators and their prey (Gislason, 1991, 1993). A particular replacement line is a function of both fishing and predation mortality and these may vary independently. Therefore, only target reference points based on predictions of yield (F 0.1,F MSY ), value, and resource rent were considered together with limit reference points based on predictions of virgin SSB or on precautionary SBB, B pa,asdefined by ICES (1997c, 1998). Weight (kg) Results 1987 Year 1992 Age 5 Age 4 Age 3 Age 2 Age 1 Figure 3. Observed weight-at-age (filled symbols) of cod ages 1 5 compared to estimated weight-at-age from MSGVPA (open symbols). Figure 5a shows how F MSY for cod depends on the relative fishing effort in the pelagic fishery. In the single-species model, where natural mortality and growth are constant, F MSY is constant. In the two multispecies models, F MSY depends on the amount of pelagic fishing effort, because cod cannibalism increases as the pelagic fishery reduces the biomass of herring and sprat. An increase in the fishing mortality of cod will counteract the increase in cannibalism by reducing the biomass of older cod. F MSY is higher in MSGVPA than in MSVPA. In MSGVPA, a higher fishing mortality and lower stock size will be counteracted by increases in cod growth. The effort in the pelagic fishery that will generate the maximum catch of herring and sprat combined is likewise a function of cod effort (Fig. 5b). If the biomass of cod is high (low cod fishing mortality), predation mortality is high. With a high predation mortality, fishing mortality has to be reduced in order to avoid recruitment overfishing. Except for herring and sprat at low cod fishing mortality, the single-species model produces lower F MSY values than the two multispecies models. The F 0.1 curves follow the same pattern as the F MSY curves (Fig. 5c and d). Again the two multispecies models generate higher F 0.1 values than the singlespecies model, and both for cod and for herring and sprat combined, F 0.1 increases as a function of the fishing effort in the alternative fishery. Therefore, if there are strong species interactions, it is impossible to derive a single fixed value for F MSY for any species, without

7 Baltic fish stocks 577 Estimated weight-at-age R 2 = 0.70 Age R 2 = 0.42 Age 4 Estimated weight-at-age R 2 = 0.79 Age R 2 = 0.27 Age Estimated weight-at-age R 2 = Age R 2 = 0.17 Age Observed weight-at-age Observed weight-at-age Figure 4. Estimated vs. observed weight-at-age for cod ages 1 6. Table 1. Estimates of status quo fishing mortality (year 1 ), SSB, and virgin SSB ( 10 3 tons) produced by the three models. Status quo F Status quo SSB Virgin SSB Cod age 4 7 Herring age 3 6 Sprat age 3 7 Cod Herring Sprat Cod Herring Sprat VPA MSVPA MSGVPA conditioning this value on the stock size of its predators and/or prey. An alternative would be to define F MSY as the effort combination that generates the maximum total yield from the system. In the single-species situation the result is trivial: The maximum yield is generated by keeping fishing mortality at F MSY in each of the fisheries, i.e. by decreasing cod effort by 30% and increasing pelagic effort by 26%. In the multispecies situation, both models show that cod should be fished down to the lowest biomass possible in order to benefit from the higher productivity of its prey. Because cod is more valuable than herring and sprat these results make little sense in a management context. The value surfaces are shown in Figure 6 and the effort multipliers for which the maximum overall value is

8 578 H. Gislason Relative cod effort (a) Relative pelagic effort (b) Relative cod effort Relative pelagic effort (c) Relative pelagic effort Relative pelagic effort Relative cod effort 3 (d) Relative cod effort VPA MSVPA MSGVPA Figure 5. Relative effort corresponding to F MSY (a) or F 0.1 (c) in the cod fishery vs. relative effort in the fishery for pelagic species, and relative effort corresponding to F MSY (b)orf 0.1 (d) in the pelagic fishery vs. relative effortinthecodfishery. obtained are given in Table 2a. The single-species results are again trivial. As before, the maximum value is generated at the single-species F MSY by reducing cod effort by 30% and increasing pelagic effort by 26%. In the MSVPA, cod effort should be increased by 15% and pelagic effort by 63% to generate the maximum value. The MSGVPA predicts that cod effort should be increased by 86% and pelagic effort by 82% to reach the maximum. The differences between the two latter models is again due to compensatory changes in weight- and maturity-at-age, making the cod stock more resilient to exploitation in MSGVPA than in MSVPA. Estimating F 0.1, the fishing mortality where the slope of the value surface is a tenth of the slope at the origin, is not straightforward. The slope at the origin is a function of both cod and pelagic fishing mortality. Various fixed relationships between cod and pelagic effort factors were therefore explored. For each fixed relationship, the slope at the origin was determined and the point where the slope of the value surface was 10% of the slope at the origin identified (Fig. 7). In all three models the F 0.1 contour bends backward at low cod effort. The highest values of F 0.1 are generated by the MSGVPA, whereas the single-species model produced, in general, the lowest. However, there is no simple relationship between the fishing mortalities generated by the two fisheries and the overall F 0.1. Thus, in a multispecies context it appears difficult to use the overall F 0.1 as a target reference point. The effort combinations that would generate the maximum resource rent are given in Table 2b. For cod the three models produce similar results. Cod fishing mortality should be approximately halved to generate the maximum resource rent. For the pelagic fishery the answers depend on the model. In the multispecies models, fishing mortality should be reduced to 10% or less of the present level, while in the single-species model fishing mortality should be halved. The difference between single and multispecies results is once again caused by the indirect effect of herring and sprat biomass on cod cannibalism. The three models were also used to investigate limit reference points based on total spawning-stock biomass. The equilibrium SSB for cod, herring, and sprat were predicted for various combinations of cod and pelagic effort. These predictions were compared to the biomass reference points by plotting the effort combinations that would lead to stock sizes below or above a particular reference point in a surface plot (Fig. 8). Two different reference points were considered. The fishing mortality where SSB fell below 50% of the virgin SSB (Fig. 8a c), and the precautionary biomass reference point, B pa (Fig. 8d f) adopted by ICES (1998). The target reference

9 Baltic fish stocks 579 (a) Cod effort Table 2. Effort multipliers for which the highest value of the total landings (a) and the highest resource rent (b) of the Baltic fishery is obtained. Cod is assumed to be 10 times more valuable than herring and sprat, and costs in (b) to be directly proportional to effort (total value in arbitrary units). (a) Fishery VPA MSVPA MSGVPA Cod Herring and sprat Total value (b) Fishery VPA MSVPA MSGVPA 6.0 (b) Cod Herring and sprat Total value Cod effort Cod effort 2.0 VPA MSVPA MSGVPA (c) Pelagic effort Figure 7. Isolines of F 0.1 estimated by single-species predictions, MSVPA, and MSGVPA. F 0.1 estimated as the effort combination where the slope of the relative value of the total catch is one-tenth of the slope at the origin Pelagic effort Cod effort points corresponding to maximum catch value and resource rent are also included in the figure. In the single species case, the combination of efforts where all three species are above 50% of their virgin SSB is rectangular (Fig. 8a). For a cod effort above half the present, the cod stock will be below 50% of its virgin biomass. For herring and sprat, an increase in effort above the present will produce a SSB below B 50%.In MSVPA, the cod effort influences the borderline where Figure 6. Relative total value of catch for different combinations of effort in the pelagic and cod fishery. Cod assumed to be 10 times as valuable as herring and sprat. (a) Single-species predictions, (b) MSVPA, (c) MSGVPA.

10 580 H. Gislason Figure 8. Effort combinations for which the predicted SSB is above either 50% of the virgin SSB (a,b,c) or above Bpa (d,e,f) shown together with the effort combinations corresponding to the current fishing mortality, maximum overall value of catch, and maximum net revenue. Bpa equal to 240,, and 275 thousand tons for cod, herring, and sprat, respectively (ICES 1998). (a), (d) Single-species predictions, (b), (e) MSVPA, (c), (f) MSGVPA.

11 Baltic fish stocks 581 the pelagic species drop below 50% of their virgin level. If cod effort is high, the cod stock and the predation mortality it generates on herring and sprat are both reduced. In this situation, sprat and herring can sustain higher fishing mortalities before their biomasses fall below the limit. If pelagic effort is high, cannibalism of cod increases, and the stock is no longer able to sustain high effort. The same applies to the MSGVPA, except that cod in general is able to sustain higher effort, due to the compensatory changes in growth and maturity at low cod biomass caused by increases in the available food for cod. In single species VPA and MSVPA, the cod stock is predicted to be below 50% of its virgin biomass at the present effort. In MSGVPA, present fishing is predicted to lead to a spawning stock that is slightly less than 50% of the virgin. The effort combination producing maximum resource rent lies in the area where all three species are above 50% of their virgin SSB. The picture changes somewhat if the precautionary biomass, B pa, is used as the reference point (Fig. 8d f). Single-species VPA indicates that the present fishing effort is likely to result in a SSB for cod and herring below B pa, while the predicted SSB for sprat is above B pa. In MSVPA predictions cod is below B pa, but herring and sprat are above. Finally, the MSGVPA predicts that all three species would be above B pa at current effort. The effort combination producing maximum value is once more outside the sustainable area where the SSB of all three species are above B pa. The effort combination producing maximum resource rent is within the sustainable area in all three models. Discussion The results clearly show how single-species reference points are affected by species interaction. Instead of being point estimates, they are turned into reference curves or surfaces, when two or more fisheries and species are considered. Furthermore, the single-species estimates do not always fall on the curves generated by the multispecies models. Compared to the single-species predictions, both multispecies models predict that higher efforts than the present are needed to achieve MSY in the two fisheries. The differences between multispecies and single-species predictions raise questions about the utility of single-species reference points in situations where species interactions are important. In multispecies assessments it is potentially misleading to consider each fishery in isolation. Even though curves of cod F MSY vs. pelagic effort can be constructed for the Baltic, they are of limited use because they do not simultaneously reflect how changes in predation on herring and sprat will affect the yield from the pelagic fishery. In the multispecies situation maximization of total yield by weight points to a strategy where the predators are fished down to the lowest biomass possible in order to benefit from the larger productive capacity of their prey. In a management context this result makes little sense. Cod is more valuable than herring and sprat and it seems more sensible to use the total catch value of the combined fishery rather than the yield in the search for the optimum. However, this requires that estimates of the relative value of the different species are available. In this paper it was, for simplicity, assumed that 1 kg of cod was 10 times more valuable than 1 kg of herring and sprat, and that discount rates were zero. Clearly a much more detailed analysis of the socio-economics of the various fisheries is necessary. Without such an analysis useful target reference points cannot be derived. When total catch value is considered, the single species model predicts that cod effort should be reduced by 30% and that pelagic effort should be increased by 26%, while both multispecies models suggest that effort should be increased. In the MSGVPA the maximum is found at a combination of cod and pelagic fishing efforts corresponding to a 86% increase of the fishery for cod and an 82% increase in the fishery for herring and sprat. This suggests that F MSY could be a dangerous reference point to use in a multispecies context. For all three species it lies beyond the range of historical observations where uncertainty about the stock dynamics may lead to an unacceptable high risk of stock collapses. Estimates of effort combinations corresponding to F 0.1 can be derived from the slope of the overall value surface. However, it is difficult to derive a single value that can be used as an overall reference point. For this reason tentative estimates of costs were used to calculate the combination of effort that would produce the maximum resource rent. Surprisingly, for cod all models produced similar results, suggesting that cod effort should be reduced by 50 60%. Although this reference point for cod appears to be robust to the choice of model, this is not the case for the pelagic fishery, where the maximum resource rent was obtained at a much lower level of effort in the multispecies than in the single-species case. However, more information on the economics of the fisheries would be required before a maximum resource rent approach could be considered acceptable for management. The position of the present situation in relation to the biomass reference limits differs between the three models. The multispecies models allow a higher effort in the pelagic fishery at high levels of cod effort than the single-species model. At low levels of cod effort the multispecies models predict that the pelagic fishery should be reduced or even closed to keep the pelagic species above the limits. For cod, the multispecies models predict that fishing should be reduced at high levels of pelagic effort, while at low levels of pelagic effort cod effort can be higher than in the

12 582 H. Gislason single-species case. This is most pronounced in the MSGVPA where growth increases with increases in available food. These results show that it is impossible to define a safe level of biomass without taking changes in species interactions into account. Reference limits for forage fish cannot be defined without considering changes in the biomass of their natural predators. Likewise, reference limits for predators cannot be defined without considering changes in the biomass of their prey. The results also point to the importance of structural uncertainty in the model formulation. Alternative models could have been used. For instance, Rijnsdorp (1993), suggested that maturity-at-age depends not only on weight-at-age, but also on the age of the fish and its previous growth history. However, insufficient data were available to warrant a more complicated model than the simple relationship between maturity and weight-at-age used here. Also the recruitment model could have been expanded. The use of a simple Ricker relationship allows extrapolations outside the range of observed values and does not reflect the large uncertainty about the form of the relationship, particularly at low spawning-stock size. Large residuals are obtained when the models are fitted to the historic data. Sparholt (1996) incorporated sprat and herring predation on cod eggs and larvae in the stock recruitment relationship, effectively producing yet another feedback loop not considered here. Additional uncertainty about the future development of the environment in the Baltic might be added (Kuikka et al., 1999). Clearly all uncertainties will have to be taken into account before the models might be considered operational for management purposes. Besides the need to provide a relative value to the landings of different species and fleets, one of the main impediments for using multispecies models is the difficulty of illustrating the present situation in relation to the reference points in an easy comprehensible way, when more than two species and fisheries are considered. The Baltic is relatively easy in this respect, but in more complicated systems, like the North Sea, the multidimensionality of biological and technical interactions makes this a challenging task. Acknowledgements I would like to thank the members of the ICES Multispecies Assessment Working Group for valuable comments and discussions. Its chairman, Jake Rice, provided useful comments and suggestions on an earlier draft of this paper. References Brander, K Multispecies fisheries of the Irish Sea. In Fish Population Dynamics: the implications for management, 2nd ed, Ed. by J. A. Gulland. John Wiley & Sons, Ltd, UK. Caddy, J. 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