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ICES Journal of Marine Science, 60: 709–720. 2003 doi:10.1016/S1054–3139(03)00042-0 Using AMOEBAs to display multispecies, multifleet fisheries advice Jeremy S. Collie, Henrik Gislason, and Morten Vinther Collie, J. S., Gislason, H., and Vinther, M. 2003. Using AMOEBAs to display multispecies, multifleet fisheries advice. – ICES Journal of Marine Science, 60: 709–720. In multispecies fish communities, predation levels change dynamically in response to changes in the abundance of predator and prey species, as influenced by the fisheries that exploit them. In addition to community-level metrics, it remains necessary to track the abundance of each species relative to its biological reference point. In situations with many interacting species, exploited by multiple fishing fleets, it can be complicated to illustrate how the effort of each fleet will affect the abundance of each species. We have adapted the AMOEBA approach to graph the reference levels of multiple interacting species exploited by multiple fleets. This method is illustrated with 10 species and eight fishing fleets in the North Sea. We fit a relatively simple response-surface model to the predictions of a fully age-structured multispecies model. The response-surface model links the AMOEBA for fishing effort to separate AMOEBAs for spawning stock biomass, fishing mortality, and yield. Ordination is used to give the shape of the AMOEBAs functional meaning by relating fish species to the fleets that catch them. The aim is to present the results of dynamic multispecies models in a format that can be readily understood by decision makers. Interactive versions of the AMOEBAs can be used to identify desirable combinations of effort levels and to test the compatibility of the set of single-species biological reference points. Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved. Keywords: ecological indicators, fisheries management, multispecies models, North Sea. Received 14 March 2002; accepted 5 March 2003. J. S. Collie: University of Rhode Island, Graduate School of Oceanography, Narragansett, RI 02882, USA. H. Gislason: University of Copenhagen, c/o Danish Institute for Fisheries Research, Charlottenlund Castle, 2920 Charlottenlund, Denmark; tel.: þ45 3396 3361; fax: þ45 3396 3333; e-mail: [email protected]. M. Vinther: Danish Institute for Fisheries Research, Charlottenlund Castle, 2920 Charlottenlund, Denmark; tel.: þ45 3396 3353; fax: þ45 3396 3333; e-mail: [email protected]. Correspondence to J. S. Collie; tel.: þ1 401 874 6859; fax: þ1 401 874 6240; e-mail: [email protected]. Introduction There is widespread acceptance that an ecosystem perspective is needed to manage marine fisheries but much less practical experience on how to do so. It is now recognized that ecosystems themselves cannot be managed; it is the human users of ecosystems that must be regulated (Bax et al., 1999). In marine fisheries, two approaches have emerged for incorporating ecosystem considerations into management decisions (Murawski, 2000). One is to use the metrics of community ecology, such as species diversity and size spectra, as indicators of ecosystem status, ecosystem health, and ecosystem services (Rice, 2000). The other approach is to incorporate additional ecosystem constraints into traditional management decisions. With respect to the first approach, criteria to aid in the selection of ecosystem objectives and their associated metrics 1054–3139/03/080709þ12 $30.00 have been put forward by the ICES Working Group on Ecosystem Effects of Fishing Activities (ICES, 2001, 2002a). Although rapid progress is being made, there is presently little theoretical understanding of how many of the proposed metrics respond to changes in harvesting, and what the desirable level of the metrics should be. For many important ecosystem properties, scientific understanding of the link between human impacts and ecosystem response is insufficient, and considerable effort is therefore needed before the approach can be fully implemented (ICES, 2002a). Although the concept of ecosystem health seems an intuitive analogy with the human body, it breaks down on closer examination because ecosystems can exist in multiple states, in all of which basic ecological functions are maintained (Hall, 1999). The second approach is to define reference levels for taxa other than the targets of the directed fishery. These ecosystem constraints have been considered as additional levers to Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved. 710 J. S. Collie et al. nudge the management process toward meeting ecosystem, or at least community-level objectives (Bax et al., 1999). Another way to view these constraints is as additional dimensions or objectives to be satisfied in fishery management plans. Examples of ecosystem constraints are limits on the take of marine mammals in fisheries, catch limits on forage fish to preserve their predators, and area closures to protect structural epifauna. Progress can be expected with both approaches, but in the short-term it is more pragmatic to incorporate ecosystem considerations as additional constraints to existing fishery management plans (Murawski, 2000). Adding ecosystem constraints is likely to increase the complexity of the advice and may therefore increase the difficulties of reaching consensus if trade-offs cannot be presented to stakeholders and managers in an easily comprehensible way. Among the most important ecosystem processes in marine fish communities are trophic interactions among the fish species. There is empirical evidence that the mortality rate of prey species depends on predator abundance and, conversely, that predator growth rates depend on prey abundance (Collie, 2001). Competition is implied by many ecological models but is certainly more difficult to demonstrate than predation, and is also less likely to be structuring highly interconnected marine food webs. There is a strong parallel between the two approaches to incorporating ecosystem considerations and the types of multispecies models used for each approach. Models of the entire ecosystem (e.g. network models, dynamic ecosystem models) should lend themselves to the derivation of ecosystem metrics (Hollowed et al., 2000). On the other hand, community-level models of interacting species are more useful for adding ecosystem constraints to the single-species models that are widely used in fisheries management. A second dichotomy is whether the multispecies model is age structured or just tracks the total abundance or biomass of each species (Hollowed et al., 2000); age-structured models are most widely used in the management of temperate marine fish. When does multispecies advice matter in fisheries management? In the short term, the feeding requirements of predators must be considered when setting annual harvest quotas for forage fish species (e.g. capelin off Norway). In the medium term, biological reference points may need to be adjusted to account for variable predation rates on prey species and variable growth rates of predators (Collie and Gislason, 2001). Long-term management strategies need to account for the implicit trade-offs in prey and predator yields (May et al., 1979). In boreal ecosystems with a small number of interacting species, it may be straightforward to condition the reference levels of a target species on the abundances of interacting species (Livingston and Tjelmeland, 2000). In temperate ecosystems with a large number of fish species, the increased dimensionality necessitates different approaches. The North Sea is a good example of such an ecosystem. It harbours an intensive multispecies and multifleet fishery using a variety of gears. Demersal fisheries for human consumption catch a mixture of roundfish species, such as cod, haddock, whiting, and saithe, that are piscivorous to some extent, or target flatfish species such as sole and plaice, often with a bycatch of roundfish species. Pelagic fisheries for human consumption are directed at species such as herring and mackerel, while the industrial fishery targets forage species, such as sandeel, Norway pout, and sprat, and uses them for production of fishmeal and fish oil. Due to excessive levels of fishing mortality many of the demersal stocks are at present considered to be outside safe biological limits (ICES, 2002b). The European Common Fisheries Policy has multiple objectives (Halliday and Pinhorn, 1996). In the short term these are: (a) to ensure the continuity of each stock as a commercially viable resource; (b) to decrease the fishing effort on overexploited stocks in order to ensure yields that are stable from year to year; and (c) to ensure the highest possible catch from stocks, consistent with (a) and (b) and taking into account the relationships among stocks. ICES has established precautionary biomass (Bpa) and fishing mortality (Fpa) levels for each stock to meet objectives (a) and (b). These precautionary targets are intended to maintain each stock at a productive level and to provide a high probability of avoiding stock collapse. Objective (c) implies that fishery yields should be maximized, subject to the biological constraints and multispecies interactions. The North Sea fisheries have for many years been managed with a system of quotas or total allowable catches (TACs). Particularly for the species caught in the mixed demersal fisheries, this system has failed to produce the intended reductions in fishing mortality. There are several reasons for this failure, one of which is that the TACs often have been set independently for each species. This has contributed to extensive discarding and to little or no reduction in overall fishing mortality despite reductions in landings. As concluded by Holden (1994), the TAC system is a fundamentally flawed system for managing the mixed demersal fisheries in the North Sea. Due to technical interactions, fishing mortality cannot be regulated independently for each species. In addition there are important biological interactions taking place and these interactions need to be taken into account in the medium and longterm projections used for formulating rebuilding strategies (ICES, 1997). Age-structured multispecies and multifleet models (e.g. MSFOR) have thus been developed. Such models can be used to investigate the consequences of different fishing mortalities while accounting for interactions among fishing fleets and between the predators and prey (Pope, 1991). Although the models have now been available for more than a decade they have not been used routinely in fisheries management, partly because of their intensive data and computing requirements, but mainly because the increased complexity of multispecies models is thought to hinder decision making (Brugge and Holden, 1991). In an attempt to Using AMOEBAs to display multispecies, multifleet fisheries advice construct a simpler multispecies model, Pope (1989) proposed fitting a simpler response-surface model to the results of the more complicated multispecies model, and then using the response-surface model to investigate alternative levels of fishing effort. The ICES Multispecies Assessment Working Group (MSAWG) used a multispecies Schaefer or Fox model fit to the projections of the MSFOR model (ICES, 1992). This approach greatly simplifies the multispecies model, but leaves the problem of visualizing the results in as many dimensions as there are interacting species and fishing fleets. Joint levels of F0.1 and Fmsy for interacting fishing fleets can be calculated (Pope, 1989) but such communitywide indices do not ensure that reference levels for individual species will be met. Pope (1997) emphasized that ‘‘whatever model of complex, multispecies, multifleet, multiarea fisheries is adopted, it will be of little use in the real world unless its results can be presented to the managers in as clear and as unambiguous fashion as possible’’. The results of multispecies models can be presented with decision tables or radar plots. AMOEBAs are extensions of radar plots that can be useful for visualizing multidimensional situations in which several constraints must be met simultaneously (Laane and Peters, 1993). Pioneered in the Netherlands in the context of water quality objectives, AMOEBA is the Dutch acronym for ‘‘a general method of ecosystem description and assessment’’ (Ten Brink et al., 1991). The AMOEBA approach has been applied to shellfish restoration in North Carolina (Wefering et al., 2000) and has also been proposed for displaying ecological quality objectives in the North Sea (Lanters et al., 1999). In this paper we show how AMOEBAs can be used to visualize the results of multispecies models applied to the North Sea fish community. We extend the AMOEBA concept by giving the shape of the AMOEBAs functional meaning and by making them change dynamically in response to changing effort levels. In creating the AMOEBA plots we followed Tufte’s (1983) principles of graphic excellence. According to Tufte, graphic displays should: show the data in a way that makes large data sets coherent; induce the viewer to think about the substance rather than about the methodology; present many numbers in a small space; encourage the eye to compare the different pieces of data; and serve a reasonably clear purpose. The ultimate objective of this work is to present the results of multispecies fishery models in a format that can be readily understood and used by decision makers. Methods In this paper we analyzed the multispecies, multifleet fishery of the North Sea. Multispecies VPA and projections 711 were made using the 4M program (Vinther et al., 2001). The 4M (Multi-species, Multi-Fleet and Multi-Area Model) package is a newer and extended implementation of the MSVPA/MSFOR programs previously used by the ICES MSAWG. The forecasts were based on an MSVPA run similar to the so-called ‘‘key-run’’ made at the last MSAWG Meeting (ICES, 1997). This MSVPA included data for 10 VPA species (Table 1) for the period 1974–1995 such that 1996 became the first projection year. Recruitment in the projections was assumed to follow a Ricker stock-recruitment relation fitted to the MSVPA output for all VPA species except North Sea mackerel. An arithmetic mean of the estimated recruits in 1986–1995 was used for mackerel because the stock-recruitment relation was indeterminate. Abundance of species without analytical assessment (‘‘other predators’’) was kept constant at the 1995 level in the projections. Fishing mortalities (F) estimated for 1995 by the MSVPA were used as base line or status-quo levels in the projections. These F values were partitioned to partial F by fleet according to catch numbers given by the STCF database (Anon., 1991; Lewy et al., 1992), which includes detailed catch information for 56 national fleets fishing in the North Sea in 1991. These 56 fleets were aggregated into eight new fleets defined by the gear used or target species; ‘‘other gears’’ include national fleets that did not fit the grouping. Average partial Fs over the age range used by ICES in the calculation of reference F values are presented in Table 2. The exploitation patterns of the fishing fleets and the stock sizes of each species have changed considerably since 1991, Table 1. Species included in multispecies assessment. Size or age groups VPA species Cod Haddock Whiting Saithe Mackerel (North Sea stock) Herring Norway pout Sandeel Plaice Sole Other predators (abundance Grey gurnards Western stock mackerel Raja radiata Grey seals Sea birds Other species Predator/ prey Abbreviation for figures 0–11þ 0–11þ 0–10þ 0–15þ 0–15þ Yes/Yes Yes/Yes Yes/Yes Yes/(Yes) Yes/(Yes) COD HAD WHG POK MAC 0–9þ 0–3þ 0–6þ 0–15þ 0–15þ No/Yes No/Yes No/Yes No/(Yes) No/(Yes) HER NOP SAN PLE SOL given as input) 0–3 Yes/No 0–1 Yes/No 0–3 Yes/No 1 Yes/No 1 Yes/No 1 Yes/No Prey (Yes) indicates very low predation mortality. 712 J. S. Collie et al. Table 2. Average fishing mortality by fleet and species as used in the status-quo projection. Also listed are the precautionary reference levels for fishing mortality (Fpa) and SSB (Bpa) from ICES (2002b). For herring and mackerel only, the status-quo SSB levels were used as proxies for Bpa because these two stocks have components that are not resident in the North Sea. A plus sign (þ) indicates fishing mortality <0.01 and a minus sign () indicates a species not caught by that gear. Species Fleet Cod Haddock Whiting Saithe Plaice Sole Herring Mackerel Sandeel Norway pout Beam trawl Fixed gear Industrial (small meshed trawl) Pelagic (purse seine and trawl) Saithe (trawl) Seine net Trawl Other gears All fleets Precautionary F level Precautionary biomass level (kt) 0.03 0.10 0.02 þ þ 0.01 0.01 þ 0.04 þ þ 0.05 0.35 0.02 þ 0.35 0.02 þ þ þ 0.05 þ þ 0.02 0.36 0.36 þ þ þ þ þ 0.47 0.10 þ þ 0.01 0.21 0.28 0.16 0.81 0.65 150 0.01 0.30 0.35 0.05 0.73 0.70 140 þ 0.16 0.27 0.01 0.49 0.65 315 0.09 0.01 0.16 0.11 0.42 0.40 200 þ 0.05 0.05 0.07 0.55 0.30 300 þ 0.03 0.11 0.51 0.40 35 þ þ 0.11 0.20 0.83 0.25 311a þ þ 0.01 þ 0.12 0.17 86a þ 0.01 0.36 0.59 600 þ þ 0.36 0.84 150 a Status-quo SSB used as a proxy for Bpa. such that each fleet probably accounts for a different percentage of the total catch of each species than in 1991. Therefore the status-quo exploitation patterns would need to be updated before the results of projecting different management options could be used for actual management decisions. Fishing mortality was assumed to be proportional to fishing effort. Different fishing efforts could then be modelled as multiples of the status-quo levels. Projections of yield and spawning stock biomass (SSB) were made for the statusquo F, and with changes in F of 10, 25, and 50% both for all fleets combined, and by individual fleet. Each projection was run for 50 years to a (near) equilibrium state. The 4M model explicitly differentiates between retained and discarded catch. The multispecies production model was fit to the retained catch (yield) only. In this manner discarding is accounted for implicitly but is not tracked separately with the production model. Response-surface models were fit to the projections in which fishing effort for each fleet was increased by 10% in turn. The projections with other levels of fishing effort were used to compare the predictions of the simple response-surface model with those of the age-structured 4M model. The response-surface model is a generalization of the system of equations examined by Larkin (1966). Specifically, it is a multispecies production model of the Schaefer form: X dSSBs SSBs qg eg SSBs ¼ rs SSBs 1 dt as g ð1Þ where SSBs is the SSB of species s, q is a catchability coefficient, and eg is fishing effort in fleet g. The equilibrium SSB is: SSBs ¼ as X bgs eg ð2Þ g where as is the SSB of species s in the absence of fishing and parameter bgs ¼ qg as =rs measures the reduction of SSBs per unit of fishing effort in fleet g. For convenience, fishing effort (eg) was scaled to equal one in a reference year (1995). For each species, SSB was predicted with the 4M model for the status-quo effort level and a 10% increase in the effort of each fleet in turn. With m fishing fleets and n species, these calculations can be expressed in matrix notation as: S¼EA ð3Þ where S is an (m þ 1) n matrix of SSB values, E is an (m þ 1) (m þ 1) effort-change matrix, and A is the (m þ 1) n matrix of parameter estimates, with one column for each species. Matrix E represents the changes in effort levels, with 1.1 on the diagonal, except for the first element which is 1.0, corresponding to the a parameters. This system of equations was solved by inverting the effort-change matrix, E. Separate equations were used to predict equilibrium SSB or yield in weight. Equilibrium yield is the product of equilibrium biomass and fishing mortality. Equations analogous to Equations (2) and (3) can be written to predict the equilibrium yield of a given fleet, f: Yfs ¼ afs ef X bfgs ef eg g Dividing by ef, yield per unit effort, YPUE is: ð4Þ Using AMOEBAs to display multispecies, multifleet fisheries advice YPUEfs ¼ afs X ð5Þ bfgs eg g Here afs is the unfished YPUE of species s in fleet f and bfgs measures the reduction in YPUE per unit of fishing effort. In matrix notation, Uf ¼ E Pf ð6Þ where Uf is an (m þ 1) n matrix of YPUE values and E is the same effort-change matrix. The (m þ 1) n matrix of parameter estimates, Pf, can be estimated from the inverse of E, and once obtained it can be used to predict yield for different levels of fishing effort. A separate yield model was estimated for each fishing fleet. Fishing mortality rates corresponding to different combinations of fishing effort were calculated as: Fs ¼ X eg F1995 gs ð7Þ g where the partial fishing mortalities in 1995 were taken from Table 2. AMOEBA plots were used to display changes in SSB, yield, and fishing mortality resulting from changes in fishing effort and the resultant changes in species interactions. Angles for plotting the AMOEBAs were calculated with principal components analysis (PCA) of the table of yields by species and fleets, projected with status-quo effort levels. The PCA was calculated from the correlation matrix so that species and fleets with high yields would not dominate the principal components (PCs). We plotted the first two PCs using polar coordinates. The PCA loadings gave the angles for the fishing fleets and the PCA scores gave the corresponding angles for the fish species. The AMOEBAs were then used to investigate the consequences of different combinations of fishing effort. Effort levels corresponding to the multispecies maximum sustainable yield (MSY) can be found by maximizing the yield of each fleet as defined in Equation (4). Let Yf ¼ X af ¼ Yfs g X afs s bfg ¼ X bfgs ð8Þ s be the aggregate values for fleet f summed over species. Then aggregate yield can be expressed as Yf ¼ af ef X bfg ef eg ð9Þ g The partial derivative of yield with respect to effort in fleet f is: X qYf ¼ af bfg eg 2bff ef qef g6¼f ð10Þ The multispecies MSY is obtained when these partial derivatives are set to zero for all fleets simultaneously (Pope, 1989). Let B be the m m matrix with 2bff on the 713 main diagonal and bfg in the remainder. In vector notation, MSY is obtained when a ¼ B Emsy ð11Þ and the vector Emsy can be obtained from the inverse of B. Though easy to calculate, Emsy, is not a very useful reference point because it ignores the costs inherent in increasing fishing effort. Fishing costs are unknown, but their effect can be approximated by assuming that at status-quo effort levels, fishing costs equal the revenue or yield (Pope, 1997; Gislason, 1999). Most of the commercially important fish stocks in the North Sea suffer from overfishing and the majority of stocks are currently below the precautionary spawning biomass limits defined by ICES (ICES, 2002b). The North Sea fisheries are operating at a level exceeding that necessary to produce the maximum return both in tons caught and economic value. Although the situation differs from fleet to fleet and good economic data are lacking, the financial returns from fisheries are in many cases modest despite considerable subsidies. Financial returns fluctuate from year to year and in some cases costs and capital depreciation exceed revenues (European Commission, 2001). It is therefore not unreasonable to assume that the North Sea fisheries by and large are close to the level of effort corresponding to the bionomic equilibrium of the Gordon–Schaefer bio-economic fisheries model. This level is defined as the level of effort where opportunity costs would equal revenues in an equilibrium situation (Clark, 1985). Opportunity costs include costs due to fuel, gear and supplies, interest and depreciation on capital, as well as wages of skipper and crew. Assuming that each fleet is at the bionomic equilibrium, fishing costs equals revenue and the effort levels for maximum economic yield (Emey) can be calculated from: a Ysq ¼ B Emey ð12Þ where Ysq is the vector of status-quo yields for each fleet. Further constraints on the effort levels may be required to ensure that the SSBs of all species are above the precautionary levels (Bpa) and that the fishing mortality rates are below Fpa. Bounded nonlinear optimization was used to identify a set of effort levels to maximize yield while ensuring SSB Bpa and F Fpa for all species. Results The predictions of equilibrium SSB and yield made with the multispecies production model agree well with those of the 4M model for either a 50% increase or decrease in effort for all fleets (Figure 1). The differences between models are insubstantial (the points are largely superimposed) compared with the differences between the effort scenarios. With 50% effort the SSB of most species would be higher except for haddock, mackerel, Norway pout, and whiting (Figure 1a). For these species, an increase in predation mortality appears to compensate for the decrease in fishing mortality. With 714 J. S. Collie et al. Figure 1. Predictions of the 4M model and the multispecies production model with 50% reduction or 50% increase in effort in all fishing fleets. The species abbreviations are defined in Table 1 and the fleet abbreviations are defined in Table 4. þ50% fishing effort, the multispecies production model predicts the elimination of cod and herring, whereas the 4M model predicts small, but positive, SSB. With decreased fishing effort, yields of cod and herring were higher due to an increase in abundance (Figure 1b). Yields of haddock, Norway pout, sandeel, and whiting were lower, due to increased predation and lower fishing effort. With increased fishing effort, yield in the industrial fleet was lower, due to less sandeel while yield in the pelagic fleet was higher, reflecting the increase in herring (Figure 1c). In these validation runs, the multispecies production model was used to predict conditions other than the data that were used to estimate the model parameters (þ10% effort). This close agreement indicates that the simpler response-surface model captures the main dynamics of the fishery and can be used to investigate different effort combinations, within a range of 50% around the status-quo levels. The multispecies projections incorporate both technical and biological interactions (Table 3). Technical interactions occur because most fishing gears catch more than one species. Beam trawls catch sole and plaice and thus the SSB of both species would increase with a decrease in effort in the beam trawl fleet. Biological interactions occur because of predation among the modelled species. For example a decrease in seine effort would lead to an increase in the SSB of the predator cod but would decrease herring SSB because of increased predation. These species interactions can be plotted in three dimensions for a single species and pairs of fleets. Haddock SSB would increase with decreased effort in the trawl fishery and decrease with decreased effort in the industrial fishery due to increased abundance of the predators cod, whiting, and saithe (Figure 2). In this example, there was also close agreement between projections made with the multispecies production model and with the 4M model; the maximum difference between the two response surfaces was 6% (Figure 2). Ordination was used to project the entire table of fleetby-species interactions in two dimensions. The first two Using AMOEBAs to display multispecies, multifleet fisheries advice 715 Table 3. Percent change in SSB of each species resulting from a 25% decrease in fishing effort of each fleet in turn, as estimated with the 4M model. Negative values result from increases in predator populations. Listed at the bottom are the scores of the first two PCs of the PCA of yields by species and fleet projected with status-quo effort levels. Species Fleet Cod Haddock Whiting Beam trawl Fixed gear Industrial (small meshed trawl) Pelagic (purse seine and trawl) Saithe (trawl) Seine net Trawl Other gears 2.89 5.81 4.47 0.77 0.62 2.12 0.71 Principal component 1 scores Principal component 2 scores Saithe Plaice Sole Herring 0.14 0.74 3.48 0.05 0.13 4.15 19.80 0.61 0.05 25.41 1.30 0.04 0.39 0.10 17.85 0.12 0.23 0.01 0.01 0.00 0.97 13.24 20.93 13.82 0.25 5.36 3.57 0.01 0.10 0.20 0.23 1.39 6.45 1.34 12.03 8.17 0.08 2.46 3.02 4.12 1.81 1.34 2.00 1.45 0.12 0.73 1.71 0.23 1.00 0.85 PCs accounted for 28 and 26% of the variance; the third and forth components explained only 15 and 13%. The species and fleets are well separated in two dimensions, expect whiting, which had low scores for PC1 and PC2 (Table 3), possibly because of its important role as both predator and prey species. Cod and haddock had similar scores for the first two PCs (Table 3), but different scores for PC3. Likewise sole, mackerel, and Norway pout clustered on the first two PCs and separated on the third, as they are caught by different fleets. With respect to fleets, some pairs had similar loadings for the first two PCs (Table 4) and different loadings for PC3 (fixed and seine) or PC4 (trawl and saithe; pelagic and other). Thus the PCA provides a useful ordination of species and fleets but there is additional variation not explained by the first two PCs. Mackerel Sandeel Norway pout 0.00 0.00 1.91 0.14 0.22 12.90 0.03 0.40 7.84 14.99 12.73 0.37 0.13 0.01 0.06 1.86 8.48 0.12 3.34 0.30 15.83 0.03 0.00 1.47 0.02 0.02 0.21 0.02 0.64 0.21 2.30 2.18 0.90 1.21 0.33 1.36 3.87 1.17 0.11 2.18 0.80 1.42 0.08 In the AMOEBA plots, the directions of the fleet vectors correspond to the directions of the species caught by that fishing gear (Figure 3). It can easily be seen that sandeel is caught by the industrial fishery and that sole and plaice are caught with beam trawls. The orientation of these arrows makes it easier to see which species will be affected by changes in fishing effort of particular fishing fleets. The flatfish vectors are in the upper left quadrant, the roundfish in the upper right, and the pelagic species are scattered in the other quadrants. It should be stressed that the PCA was used only to aid in displaying the results of the multispecies model and in no way influences the multispecies projections. The angles derived from the PCA provide a more informative grouping of fleets and species in two dimensions than could be achieved in a one-dimensional Table 4. Reference levels of fishing effort identified with the multispecies Schaefer model. Also listed are the loadings for the first two PCs of the PCA of yields by species and fleet projected with status-quo effort levels. Fleet Figure 2. Response-surface model for haddock SSB as a function of fishing effort in the trawl and industrial fleets. Fishing effort is expressed relative to 1 for the status quo and effort in the remaining six fishing fleets was fixed at 1. The flat plane corresponds to SSB predicted with the multispecies production model; the broken lines indicate the curved surface predicted by 4M model for effort levels at the edges of the plane. Beam trawl Fixed gear Industrial (small meshed trawl) Pelagic (purse seine and trawl) Saithe (trawl) Seine net Trawl Other gears a Effort relative to status quo Abbreviations for plotting Emsy Emey Epa PCA loadings PC1 PC2 0.98 0.53 0.55 0.2a 2.08 0.73 1.77 0.51 0.22 btr fix ind 0.176 0.159 0.255 0.254 0.320 0.235 0.81 0.82 0.21 pel 0.187 0.619 3.02 2.39 1.42 1.11 sth sei trl oth 0.287 0.008 0.407 0.376 0.642 0.063 0.327 0.572 0.96 0.71 0.86 0.86 0.54 0.56 0.24 0.54 Constrained to prevent a negative estimate. 716 J. S. Collie et al. Figure 3. AMOEBA plots with status-quo effort levels. In each AMOEBA the circle represents the reference level and the arrows are the levels predicted with the multispecies model. Effort and landings are plotted relative to the status quo. Fishing mortality is plotted relative to Fpa and SSB is plotted relative to Bpa. Species abbreviations are given in Table 1 and fleet abbreviations in Table 4. plot or table, or by regular spacing of the vectors around the circle. Beyond their utility as a plotting device, the angles derived from PCA are not important to the projection; in fact some of the angles were jittered slightly to avoid overlapping the vectors. The vector lengths indicate the magnitude of each quantity relative to its status-quo or reference level. These quantities were calculated with the multispecies production model, independently of the PCA. With status-quo effort levels, plaice, whiting, and cod SSB would all be below their precautionary biomass (Bpa) levels, and plaice, sole, cod, saithe, and herring fishing mortality would exceed the precautionary (Fpa) levels (Figure 3). The MSY effort levels were much higher than status quo for several of the fleets (Table 4), but yields in the industrial, seine, and saithe fleets would increase only slightly. At Emsy, SSB would be below Bpa for all species except sole, mackerel, Norway pout, and sandeel, and fishing mortality would exceed Fpa for all species except mackerel and Norway pout. Effort levels for maximum economic yield (Emey) were all less than the status quo except for the fixed gear (Table 4). Fixed gear has a very different exploitation pattern than trawl and seine nets. The mean age of cod, plaice, and sole in fixed gear is at least 1 year older than the other gear types. Effort reduction in the other fleets would increase the fixed gear yield because fixed gear targets older fish. For the remaining fleets Emey was less than one because fishing costs would exceed revenues at higher effort levels. At Emey cod SSB would be below Bpa and fishing mortality would exceed Fpa for plaice, cod, and herring (Figure 4), but all the other biological constraints would be met. With bounded nonlinear optimization, a combination of effort levels was identified that would satisfy all the biological constraints while maximizing yield (Epa, Table 4). This combination required substantial reduction in the industrial, pelagic, and trawl fleets in order to raise cod SSB above Bpa and to decrease fishing mortality on cod and herring (Figure 5). At these precautionary effort levels, the Using AMOEBAs to display multispecies, multifleet fisheries advice 717 Figure 4. AMOEBA plots with effort levels for MEY. The features of the AMOEBAs are explained in the caption to Figure 3. roundfish would be at or near their Bpa levels, while the other species would be well above Bpa. The shapes of the AMOEBAs represent the composition of the fishery and the fish community. Compared with the status quo (Figure 3), the precautionary effort levels would reduce the industrial and pelagic fleets and shift the fish community toward the prey species, especially sandeel and herring (Figure 5). The area of the AMOEBA, relative to its area at the reference levels, could be considered for use as a community-level index. Likewise, the volume of the AMOEBA could be calculated to capture more of the variance in species catch by fleet. However, such a summary index is much less informative than looking at the actual AMOEBA. Discussion We have shown how AMOEBAs can be constructed and used to display the main interactions in a multispecies, multifleet fishery on a single page. These plots sufficiently capture the trade-offs in multiple fishery objectives. The biological objectives require satisfying the Bpa and Fpa constraints for each species. Our results indicate that these constraints can be jointly met even when predator–prey interactions are included. For the prey species, the benefits of decreased fishing mortality appear to outweigh the increased predation mortality that occurs with increased predator abundance. At the precautionary effort levels (Table 4) the SSB of all species would be higher than the status-quo levels. This result differs from earlier MSFOR projections in which the result of increased mesh size in the roundfish fleet was to decrease the yields of the prey species because of increased predation (Pope, 1991). The earlier MSFOR projections did not include stock-recruitment relationships, but assumed constant recruitment, and thus decoupled recruitment from fishing mortality. In the 4M model, recruitment of the prey species increases with lower fishing mortality and higher SSB. However, the stock-recruitment relationships remain uncertain because they were fit to short time series of variable data. The 718 J. S. Collie et al. Figure 5. AMOEBA plots with precautionary effort levels. The features of the AMOEBAs are explained in the caption to Figure 3. incorporation of the stock-recruitment relationships also tends to cause oscillations in the projected abundances. Economic objectives operate at the fleet level. We used the yield in weight of each fleet as a surrogate for economic performance. It would be preferable to express yield in monetary units to account for price differences among species. However, we lacked price data that were appropriately averaged over time, subfleets, and size of fish. Therefore, in our estimate of MEY we implicitly assumed that the value per weight of each fleet’s catch would remain constant with different effort levels. Pope (1997) also found that attaining MEY would require reducing effort in the roundfish and industrial fleets, with the other fleets kept near their status-quo levels. Social objectives are usually expressed at a finer level of geographic detail (e.g. fishing ports) than the main fleets in our model. One approach would be to include an AMOEBA for social objectives (e.g. employment) and to assume that ports with similar gears would be similarly affected by effort changes (Pope, 1997). However, if there are substantial national differences, even within the main gear groups, a two-tiered approach may be required. A coarser management model with aggregated fishing fleets would operate at the international level. The output from this model would then be made available to national groups to make second-stage models at further levels of disaggregation (Pope, 1997). In this study, we used a multispecies Schaefer model to describe the North Sea multispecies fishery. It was at first surprising that a simple production model could match the 4M model predictions so closely. However, the multispecies Schaefer model was fit to the 4M projections, and the simpler model appears to capture the main interactions. In this manner, simplified management advice can be given without further need for a more detailed biological model. The multispecies Schaefer model was very convenient for this application because the projections can be made almost instantly, which facilitates an interactive computer model. The model projections should be most reliable close to the status-quo effort levels; the MSAWG cautioned against extrapolating beyond a range of one half or twice the status-quo effort (ICES, 1992). We found very close agreement between the model predictions within a range of 50% of status-quo effort levels for all fleets. At þ50% effort the model projections began to diverge because the multispecies production model predicted extinction of cod Using AMOEBAs to display multispecies, multifleet fisheries advice and herring, whereas the 4M model predicted that both species would persist at low levels. The essential features of this display are that the AMOEBAs are linked with a multispecies model and that projections can be made simply by altering effort levels. Alternative model formulations could be used and/or extensions made to the present model. One approach would be to use the 4M model to make all the projections, without fitting the simpler production model. However, detailed accounting of age structure may be unnecessary unless changes in mesh size are investigated or there is a large price differential with size of fish. In this study the biological interactions appeared to be secondary to the direct fishery effects on each species. However, we may have down-played the biological interactions by ignoring variations in the predation mortality inflicted by the ‘‘other predators’’ in Table 1. Also, we did not consider the potential bottom-up effects of the prey species on the growth rates of their predators. Prey-dependent growth has been incorporated in other multispecies models (e.g. Gislason, 1999) but is thought to be less important in the North Sea because of a large variety of alternative prey species. An alternative approach is to fit the multispecies production model directly to catch and abundance data without accounting for age structure (e.g. Collie and DeLong, 1999). Preliminary attempts to fit a multispecies production model to North Sea data have not been successful even though the species were grouped into three larger functional units and MSVPA derived biomasses and catches were used as input. As concluded by Sullivan (1991) the number of parameters in multispecies production models is so large that very long data series often are needed to fit even the simplest multispecies system. Parameter estimation may be facilitated by introducing auxiliary data on fishing effort, recruitment indices, mean weight of fish in the stock, growth parameters, residual natural mortality, and food composition. Such an approach was followed by Horbowy (1996), who derived a multispecies production model for Baltic cod, herring, and sprat from the age-structured multispecies model of Andersen and Ursin (1977) and obtained biomass estimates consistent with results from age-structured models. The multispecies Schaefer model was fit to equilibrium conditions and therefore did not consider the time dynamics of moving from the status quo to the desired situation. These equilibrium solutions give useful targets relative to present conditions, but in practice it would be useful to have AMOEBAs for 1–5 year projections as well. It would also be useful to incorporate stochasticity, especially to account for uncertainty in the stock-recruitment relationships. If a stochastic multispecies model was used, the arrowheads in each AMOEBA could be replaced with error bars. Uncertainty in the ordination could be represented with wedges in place of the arrows. The bio-economic objectives could also be extended, for example by including effort–cost relationships and price elasticity; such extensions would give a higher value to reducing fishing effort. Social 719 objectives could also be represented with AMOEBAs but the challenge is that, to be included, they must be quantified (Pope, 1997). While all these extensions are technically feasible, additions to the AMOEBA plots should only be made if they serve a reasonably clear purpose. The combinations of effort levels in Table 4 were meant more for illustration than for prognostication. The partial fishing mortalities were based on 1991 values (Table 2); fishing patterns have almost certainly changed since then. Before making actual projections, the status-quo effort levels would need to be updated from 1995 to present. Nevertheless, several general conclusions can be made regarding multispecies biological reference points. Joint levels of F0.1 and Fmsy can be calculated with the methods of linear algebra, but they are of limited usefulness because of the tendency for extremely high or low values for some fleets. Reference levels based on MEY appear to be more useful because they prevent extreme effort levels and because of the explicit link to bioeconomics. In the Baltic Sea, multispecies reference points based on MEY were also more sensible than the joint F0.1 and Fmsy levels (Gislason, 1999). A priority should be to incorporate more realistic cost functions. Our results suggest that it is possible to satisfy the Bpa and Fpa levels of all species but that substantial reductions in fishing effort of some fleets would be necessary. Relative to the status quo, there would also be foregone yield, although this loss would at least be partially compensated by increased catch per unit effort. In reality, we should not rely on projections with effort levels less than one half the status quo because they imply levels of stock abundance far different than those used to fit the models. Fishing effort is more likely to be reduced in a step-wise fashion, with multispecies models refit at each step. The AMOEBA plots are very useful for displaying the trade-offs among biological, economic, and social objectives. It is unlikely that any ‘‘optimal’’ effort combination will be chosen. More realistically, solutions will be sought that maximize the objectives while violating as few constraints as possible (Pope, 1997). The advantage of the AMOEBA approach is that these trade-offs can be viewed explicitly. We have also developed an interactive version of the program in which the effort levels can be changed in the graphical interface. In summary, we have demonstrated a method for the clear and concise presentation of advice for a multispecies, multifleet fishery. Incorporation of biological interactions does require a multispecies model, but the presentation of advice is no more complex than that required for the technological interactions among fishing fleets. Acknowledgements We thank Allison DeLong, Terry Quinn, Marie-Joëlle Rochet, and Stephen Hall for helpful comments on earlier drafts of this paper. The research was funded by the European Commission (Project QLK5-CT1999-01609) and the Danish Ministry of Food, Agriculture and Fisheries. 720 J. S. Collie et al. 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