Comparing conceptual frameworks for a fish community MSY (FCMSY) using management strategy evaluation—an example from the North Sea

Abstract

Maximum sustainable yield (MSY) is a well-established concept that is mandated by legislation, and has a clear theoretical meaning in terms of a single stock. However, its definition is problematic in a multispecies setting, which makes it more difficult to apply the MSY principle. In this study of the North Sea fish community, we consider several possible MSY candidates, and evaluate them in terms of their ability to produce optimum long-term yield whilst avoiding unacceptable risk of stock impairment. We perform this evaluation with an ensemble of size-structured models using a management strategy evaluation approach, in which harvest control rules (HCRs) are used to determine levels of fishing as a function of the proposed MSY target and stock status, taking account of recruitment and model parameter uncertainties. We find that HCRs of the type considered here are always useful in the scenarios we tested, as they reduce overfishing risk much more than average long-term yield. This is independent of the precise form of the HCR, so it is more important to implement one rigorously than obsess over the rule details. For a lax definition of overfishing, which accepts relatively severe stock depletion (B < 10% B₀), and using HCRs, risks are “low” across all strategies, and the Nash equilibrium is the best performing MSY approach considered here. For more stringent definitions of “at risk” (e.g. likelihood of B < 20% of B₀), the application of HCRs can allow a range of alternative formulations of MSY. Thus, the definition of MSY may be sensitive to judgements about acceptable levels of risk, and consistent application of a sensible management framework may be more important than developing the best possible theoretical definition of MSY.

fish community, harvest control rule, management strategy evaluation, MSY, multispecies model, North Sea, risk, trade-off, uncertainty

Introduction

Managing fish stocks in accordance with obtaining Maximum Sustainable Yield or MSY (Mesnil, 2012) has been widely advocated by international bodies, including the Food and Agriculture Organisation or FAO (1966), the International Whaling Commission or IWC (Allan and Kirkwood, 1988; the United Nations, UN, 2002). It is also enshrined as an objective in the 1982 UN Convention on the Law of the Sea (UNCLOS), where it is the only reference point specifically referred to (Caddy, 1999). MSY is an intuitive concept, which aims for the maximum return that is sustainable in the long-term, and hence does not undermine the ability for future generations to achieve the same rewards as those available now. It is also relatively straightforward to define for a single stock (Schaefer, 1954). However, it is much more problematic for a multispecies community (Guillen et al., 2013), where it is not in general possible to maximize the yield of all stocks simultaneously (FAO, 2001), whilst maximizing the total yield may place the most vulnerable stocks at unacceptable risk. We need a conceptual framework for a fish community MSY (FCMSY) that allows for the necessity to trade-off stock yields against each other without generating unacceptable levels of risk across the community.

In this study, we consider some possible definitions of FCMSY, and we evaluate the outcomes of managing to them in terms of overall levels of risk and reward across the fish community. This is done by carrying out a management strategy evaluation or MSE (Sainsbury et al., 2000; Punt et al., 2016) within a multispecies and mixed fisheries framework. For each characterization of FCMSY, we frame harvest control rules (HCRs—Kvamsdal et al., 2016), which are then used to manage towards the MSY objective, and we evaluate the long-term outcomes as a function of expected gross economic yields [catch × gross revenue per unit catch, and hence different from maximum economic yield (MEY—Hoshino et al., 2018), which would additionally involve discounting the revenues and subtracting the costs of fishing], and the risks of stock depletion summed across the multispecies community. In so doing we can address the following three questions, (i) of the alternatives considered, what is the best definition of a multispecies MSY in terms of expected outcomes, (ii) does the use of HCRs reduce differences in the performance of alternative definitions of MSY by lowering both fishing mortality and risks whenever stock status deteriorates, and (iii) how sensitive are performance statistics to the form of the HCR and the choice of MSY_trigger?

Material and methods

We investigated the outcomes of managing to different FCMSY definitions using a modified version of the length-based multispecies model developed by Hall et al. (2006) and subsequently modified by Rochet et al. (2011) and Thorpe et al. (2015). This North Sea LeMans model is used as the operating model for the MSE and has been described in detail in Thorpe et al. (2015, 2016, 2017), so here we just summarize the main features briefly. A total of 21 fish species is represented in 32 equal length classes of 5 cm. These are common across stocks and span the full range of sizes in the fish community. Thus, the longest fish, cod, may be present in all length classes, whereas smaller species such as sprat may only be present in, say, five. Individuals progress through length classes as they grow and mature at a threshold length at maturity. Reproduction is described with a hockey-stick spawner–recruit relationship (Barrowman and Myers, 2000), which determines the number of recruits entering the smallest size class as a function of the biomass of mature individuals. Species’ dynamics are linked via predation mortality (M2), which is an emergent property depending upon predator and prey abundance as determined by a diet matrix and the preferred predator/prey weight ratio. Individuals are also susceptible to residual natural mortality (M1) and fishing mortality (F). Parameterization and validation of the model are described in Thorpe et al. (2015).

The consequences of parameter uncertainty were assessed by developing 78 125 models [five variants for each of seven key parameters covering (i) diet matrix, (ii) predator size-preference, (iii) non-predation natural mortality, (iv) spawner–recruit initial steepness, (v) efficiency of growth, (vi) asymptotic length, and (vii) maximum recruitment], with parameters drawn from ranges that spanned literature estimates. Details of the parameter choices and their underlying rationale can be found in Thorpe et al. (2015). Models in the unfiltered ensemble were screened against stock assessment estimates of SSB to identify plausible models. The screening criteria were (i) all species should persist in the absence of fishing, and (ii) the mean predicted SSB of assessed species after 30 years simulated fishing at average 1990–2010 rates (ICES, 2012), should be within a factor of two of the SSB estimated in ICES (2012). Stochastic recruitment around the deterministic hockey-stick spawner–recruit relationship was simulated using a lognormal distribution scaled so as to both preserve mean recruitment levels and reproduce variability of similar magnitude to that found in the ICES stock–recruit database (see Thorpe et al., 2017). Each parameter combination was tested three times, and accepted if all three simulations were plausible, giving rise to a filtered ensemble (FE) of 63 members—see Thorpe et al. (2015) for a description of the parameter screening process, and Thorpe et al. (2017) for details of the stochastic recruitment. We used a factor of two because biomass estimates from assessments are uncertain, and because a range of processes including environmental factors influence abundance in the real world. However, a previous analysis suggests that changing this factor, which affects the FE size, has only modest impacts on predictions made by the FE for FE sizes between 50 and 1000 (Thorpe et al., 2015).

In Thorpe et al. (2017), we assumed constant fishing mortality in accordance with management targeting a specific point within the pretty good yield ranges (Hilborn, 2010; Rindorf et al., 2017a, b), with the resulting yields and risks being long-term averages. In practice, however, a target fishing mortality would also depend on the stock abundances, and would be reduced if the stock status was outside safe biological limit (ICES, 2016a). In the current study, we take account of this by performing an MSE (Kell et al., 2007; ICES, 2013; Punt et al., 2016; Mackinson et al., 2018), using pre-agreed sets of rules, which determine the level of fishing mortality to apply across the community for any particular year, given estimates of the stock abundances at that time. Here, following Mackinson et al. (2018), we use HCRs of hockey stick form (Figure 1, Table 1), designed to deliver MSY during times of high stock abundance, with pre-specified reductions if stock abundance falls below a certain limit (equivalent to MSY B_trigger in standard ICES terminology; ICES, 2016a). Limits for management action (reducing F or closing the fishery) were set with reference to the estimated stock abundance as a fraction of the unfished abundance (B₀).

Figure 1.

Schematic of the harvest control rule (HCR) showing the relationship between the imposed fishing mortality and the stock status expressed as a fraction of the unfished biomass. (a) Illustrates the case where fishing mortality is fixed irrespective of stock status, (b) where mortality is linearly reduced with estimated biomass below B_trigger (standard ICES approach), and (c) which follows (b) except that a fishery closure is implemented when stock biomass below B_lim, albeit with a low level of residual fishing (F_min) even after the fishery is closed. These scenarios are inspired by the study of Mackinson et al. (2018) where a similar treatment is used. We also examined the “protective” and “precautionary” cases of Mackinson et al. (2018), but they made only a modest impact and are not considered further in this study.

Table 1.

Scenarios for the management strategy evaluation.

Scenario	Risk threshold	Harvest control rule (see Figure 1)	Btrigger
1	0.10	FIXED	NONE
2	0.15	FIXED	NONE
3	0.20	FIXED	NONE
4	0.10	ICES	0.30
5	0.15	ICES	0.30
6	0.20	ICES	0.30
7	0.10	Realistic	0.30
8	0.15	Realistic	0.30
9	0.20	Realistic	0.30
10	0.10	ICES	0.40
11	0.20	ICES	0.40

Risk thresholds and B_trigger are expressed as fractions of the virgin biomass B₀.

Within the MSE framework, stock status was determined annually, taking the modelled SSB and applying normally distributed observation error from the last-but-one year; fishing mortality for the following year was then assigned using the agreed HCR, and applied subject to a normally distributed error term to reflect uncertainty in implementation of an agreed FCMSY target. The two-year lag reflects time delays associated with the current assessment framework. The impact of the HCR is expected to be a function of the HCR form (1, 2, or 3) in Figure 1, the reference points for reducing fishing (B_trigger) and for closing the fishery (B_lim), and the degree of uncertainty involved in specifying B and implementing F. A variety of these choices was tested as shown in Table 1. In a real-world example, these choices would typically emerge from stakeholder discussion and depend upon stakeholder priorities. Thus, if MSC certification was very important, the result might be a more restrictive HCR than those considered here. Uncertainties in B and F were assumed to be log-normally distributed with standard deviations of 50 and 30%, respectively, with the uncertainty in B including measurement uncertainty for both the current and reference levels of each stock, but the process could be readily adapted to consider other levels of uncertainty.

We evaluated five different sets of estimates of F corresponding with FCMSY, as per Table 2. The first is based on single species assessments from the year 2012 and is described in detail in Thorpe et al. (2015). Although based upon 5-year-old assessments, this gives an indication of possible changes in the level of performance through time when compared with the other candidates for FCMSY. The second is the 21-stock stochastic Nash equilibrium (NE) determined in Thorpe et al. (2017). Nash equilibria could potentially be used to advantage as definitions of FCMSY (Farcas and Rossberg, 2016; Norrstrom et al., 2017). At the NE, long-term average yield for all 21 stocks combined cannot be improved by changing fishing on any particular stock in isolation, so it can be thought of as an MSY proxy that might emerge if each stock, managed independently, sought to maximize its own yield. The last three estimates are based on targeting the top, middle, and bottom of the current (as of 2017) ICES “pretty good yield” ranges with fishing being limited when the first choke stock is reached (corresponding with the “no discarding” scenarios in Mackinson et al., 2018 and assuming adherence to the landings obligation—which requires that all catches be landed and counted against the TAC for the relevant stock). Estimates for seven of the stocks are taken directly from ICES reports (see Table 3); estimates for the remainder are generated from mixed fishery interactions, given four fleets (beam, otter, industrial, pelagic) with catchabilities as defined in Thorpe et al. (2016). The estimates are generated as follows: for the central estimate M-PGY we assumed (i) maximization of F across the 21 stocks subject to; (ii) none of the seven stocks for which ranges are provided can be fished above the middle of their ranges, and (iii) the effort of the fleets expressed relative to their 1990–2010 average level of effort is not allowed to diverge beyond a factor of three (representing the impact of political constraints associated with the doctrine of relative stability). U-PGY was taken to be 1.37 x M-PGY, and L-PGY was taken to be 0.68 x M-PGY, to reflect the average spreads across the published range estimates. (As a sensitivity study we also constructed U-PGY and L-PGY in the same manner as M-PGY—this led to compressed ranges due to choking by haddock and/or whiting, which have narrow PGY ranges, but the general pattern of results was very similar.)

Table 2.

Target fishing mortalities for model stocks.

Stock	COD	DAB	GUG	HAD	HER	HOM	LEM	MAC	MON	NOP	PLA	PLE	POD	POK	RJN	RJR	SAN	SPR	SOL	WHG	WIT
2012 Single species FMSY (ICES, 2012c;Thorpe et al., 2015)	0.19	0.41	0.25	0.30	0.25	0.50	0.33	0.32	0.10	0.35	0.60	0.25	0.72	0.30	0.11	0.15	0.35	1.30	0.22	0.21	0.27
Nash equilibrium (Thorpe et al., 2017)	0.20	0.52	0.42	0.38	0.46	0.52	0.45	0.42	0.21	0.61	0.49	0.18	0.56	0.28	0.14	0.29	0.46	0.65	0.37	0.39	0.34
U-PGY	0.46	0.24	0.26	0.19	0.39	0.73	0.24	0.77	0.26	0.59	0.24	0.30	0.26	0.49	0.24	0.24	0.71	1.33	0.37	0.15	0.24
M-PGY	0.31	0.17	0.19	0.19	0.33	0.53	0.17	0.56	0.19	0.43	0.17	0.21	0.19	0.36	0.17	0.17	0.51	0.96	0.20	0.14	0.17
L-PGY	0.20	0.12	0.13	0.17	0.24	0.37	0.12	0.39	0.13	0.30	0.12	0.15	0.13	0.21	0.12	0.12	0.36	0.67	0.11	0.14	0.12

The basis for the single species estimates is explained in Thorpe et al. (2015), and the 21-stock Nash equilibrium is calculated in Thorpe et al. (2017). The PGY range mortalities, U-PGY, M-PGY, and L-PGY, are calculated as follows: (i) ICES PGY range advice is directly applied where available, (ii) the central range estimate (M-PGY) is determined from the simple 4-fleet fishery (beam, otter, industrial, and pelagic) of Thorpe et al. (2016) by maximizing F subject to the constraints that the values in Table 3 are not exceeded, and the relative effort of the least and most active fleets does not diverge by a factor of >3 from 1990 to 2010 average values. U-PGY for the stocks that lack range advice is calculated by multiplying M-PGY by 1.37, and L-PGY is taken as U-PGY/2, reflecting the average spread of the seven published ranges.

Following Thorpe et al. (2015), we group stocks for which there is no assessment together with the assessed stock or stocks, which is or are deemed to be most similar in order to estimate the appropriate F for that stock. PLA, DAB, LEM, WIT, RJR, RJN, are grouped with plaice (PLE). POD, GUG, and MON are grouped with COD, HAD, and WHG (details in Thorpe et al., 2015), leading to some F estimates being common to >1 stock. The stocks are mainly in the North Sea (ICES Subarea 4); however, if the assessment unit includes ICES Division 3a, it is 4 and 3a, and if the stock is more widely ranging, values have been imputed for the portion of it in the North Sea.

Table 3.

Pretty good yield ranges based upon ICES advice for the North Sea.

Stock	COD	DAB	GUG	HAD	HER	HOM	LEM	MAC	MON	NOP	PLA	PLE	POD	POK	RJN	RJR	SAN	SPR	SOL	WHG	WIT
ICES range advice
FUPPER	0.46			0.194	0.39							0.30		0.49					0.37	0.15
MFMSY	0.31			0.194	0.33							0.21		0.36					0.20	0.14
FLOWER	0.198			0.167	0.24							0.146		0.21					0.113	0.14
REF	1			2	3							4		5					6	7

These form the basis for the modelled scenarios U-PGY, M-PGY, and L-PGY shown in Table 2. Stocks without an entry are indirectly constrained by the stocks for which there are PGY ranges through mixed fisheries interactions with the seven directly constrained stocks.

REF: 1-ICES (2017a), 2-ICES (2017b), 3-ICES(2016b), 4-ICES (2017c), 5-ICES(2015a), 6-ICES(2015b), 7-ICES (2017d).

We ran the MSE simulations for 50 years and defined management outcomes in terms of an average of the last 30 years of the simulation. We focused on the expected outcomes for risk and reward, and present results showing the gross economic yield (expected catch × value), and risk of stock depletion adjusted to reflect the need to avoid concentrating risk on a few stocks in the community to an unacceptable degree. The way in which we define and evaluate the risks and rewards associated with each FCMSY approach is detailed in Appendix A. By defining a community risk in the manner described we can be sure it meets the ICES definition of precautionary (i.e. if any single stock has a high chance of depletion, the community risk will also be high, irrespective of the risks to the other twenty stocks). We defined stocks to be depleted when their biomass was below a certain fraction of the estimated unfished biomass (B₀). In previous work we have defined a stock to be at risk when its biomass falls below 10% of B₀ (Thorpe et al., 2016, 2017), but other definitions have been suggested (Smith et al., 2009) so we also consider 15 and 20% of B₀. Results were expressed as the ensemble mean (across 63 ensemble members). Each calculation was repeated 100 times to take account of stochastic recruitment variation (Thorpe et al., 2017).

Results

Figure 2a–c shows expected outcomes in the absence of a HCR, where a constant F is applied, irrespective of stock status (HCR1 in Figure 1), where stocks are assumed depleted if (i) B < 0.1 B₀, (ii) B < 0.15 B₀, and (iii) B < 0.2 B₀. Each outcome is expressed relative to that based on the ICES single species stock assessments for 2012 (which would lie at the origin). In each plot, outcomes in the bottom right quadrant are better than for ICES (2012) (lower risk and higher yield); outcomes in the top left are clearly worse (higher risk and lower reward), whilst those in the other quadrants might be better or worse depending upon societal risk appetite. Relative to the ICES (2012) FCMSY approach, the NE (gold) is clearly superior for all risk thresholds, though its degree of superiority decreases as the risk threshold increases. The middle of the PGY ranges is similar to ICES (2012), whist targeting the upper part of the PGY ranges is an inferior approach, consistent with Thorpe et al. (2017). Targeting the lowest part of the PGY ranges (green) involves a clear trade-off, with the lowest yield, but is the safest approach, and would be the optimal choice for a very risk-averse society. Thus, the optimum approach will be either green or gold, depending upon risk appetite. However, 10% of virgin biomass is quite a severe level of depletion, and other risk thresholds have been suggested (Smith et al., 2009). Choosing a 15 or 20% threshold leads to higher risks of depletion for all scenarios and hence greater differences between them (Figure 2b and c), but does not change the nature of the trade-offs.

Figure 2.

Expected outcomes in terms of expected gross economic yield (MGBP = million £) and community-wide risk of stock depletion. Each outcome is expressed as a difference from the ICES (2012) FCMSY approach (which by definition therefore lies at the origin). Outcomes lying in the bottom right are better (lower risk, higher reward) and in the top left are worse (higher risk, lower reward). The left three plots are for constant F (HCR1 in Figure 1) with stocks considered depleted when biomass falls to (a) <10% of B₀, (b) <15% of B₀, and (c) <20% of B₀ (Scenarios 1, 2, and 3, respectively, in Table 1). The right three plots are for HCR2 (Figure 1), with stocks considered depleted when biomass falls to (d) <10% of B₀, (e) <15% of B₀, and (f) <20% of B₀ (Scenarios 4, 5, and 6, respectively, in Table 1). Gold represents FCMSY based upon the 21-stock Nash equilibrium, and pink, blue, and green FCMSY based upon targeting the top, middle, and bottom of the PGY ranges, respectively for 2017. The coloured squares represent a smallest region of the risk-reward space, which is centred on the mean and covers 50% of the instances. The fishing mortalities applied in each scenario are presented in Figure 1 and Table 1.

In practice, however, fishing mortality would not remain constant irrespective of stock status, but would be reduced if stock abundance fell below a pre-specified point, MSY B_trigger in ICES terminology (see Figure 1). Figure 2d–f shows the outcomes that might be expected if fishing mortality is cut during episodes of poor stock status by adopting a standard ICES-style HCR (HCR2 in Figure 1). This HCR results in reduced F and catch when the estimated stock biomass falls below 30% of virgin biomass (B₀—the stock biomass when there is no fishing on any stock). We chose B_trigger to be 30% because this is below the central estimates of B_MSY for all stocks (Thorpe et al., 2015—their Figure 2b), and should only result in reduced fishing once a stock has clearly fallen below its B_MSY. The main impact of implementing HCR2 is to reduce risk across the strategies (and hence the difference between ICES, 2012 and the other options), whilst having only a slight impact on yield. Thus, the right-hand plots all shift towards the central line on the risk (y) axis, whilst there is little movement on the reward (x) axis. The broad picture, in which the Nash is better, the bottom of the PGY ranges safer, the centre of the PGY ranges similar, and the top of the PGY ranges worse is unchanged. However, for a lax definition of “at risk” (B < 10% B₀, Figure 2a and d), all the options are now so safe that the low PGY-range loses its selling point—there is no need in this case to have the additional safety of fishing at the bottom of the ranges if a HCR is being applied. For a strict definition of “at risk” (B < 20% B₀, Figure 2c and f), the Nash loses its advantage over ICES (2012) in terms of risk, whilst remaining much higher yielding, and arguably better since ∼25% of the outcomes are in the lower right quadrant, and none is in the top left.

In addition to comparing strategies (Figure 2), we also looked at the impact of different HCRs on each FCMSY approach. Figure 3 shows the change in expected risks and gross returns for each approach as a result of fishing in accordance with HCR2 (HCR2–HCR1, Figure 3a–c), and further limiting fishing using HCR3 (HCR3–HCR2, Figure 3d–f). HCR2 represents a standard ICES-type HCR where fishing is reduced linearly once biomass falls below B_trigger, and HCR3 a modified rule in which fishing is further limited if biomass falls below B_lim. The clear message from Figure 3 is that application of an HCR is beneficial irrespective of the approach chosen, because risks are reduced significantly (outcomes shifted downwards) whilst rewards are little affected (average outcomes do not shift left or right). The benefits of the HCR increase for more stringent definitions of at risk, for B < 0.15 B₀ (Figure 3b and e), and particularly for B < 0.2 B₀ (Figure 3c and f). The impact of adopting a more protective HCR (in this case moving from HCR2 to HCR3) is to reduce risk and slightly reduce returns for all strategies for achieving FCMSY. However, because the decrease in risk is relatively greater than the decrease in returns, HCR3 performs better than HCR2 for all strategies (shown by the higher number of instances in the bottom right than the top left quadrants). Nevertheless, the benefits of moving from HCR2 to HCR3 are smaller than the benefits of moving from the fixed-F HCR1 to HCR2. Following Mackinson et al. (2018) we also considered two further HCRs (their “protective” and “precautionary” options), but they were not materially different from HCR3.

We also considered the impact of increasing B_trigger from 0.3 B₀ to 0.4 B₀ for “at risk” definitions of B < 10% and B < 20% of B₀ (Figure 4). This would be expected to reduce risk by cutting fishing at higher levels of biomass, but would also be expected to reduce long term yield, because B_MSY for some stocks may be close to or even below B_trigger. We find that the impacts are small for “at risk” = 10% B₀, but for “at risk” = 20% B₀, risks and yields both tend to decrease, as expected. Again, the reduction in risk appears larger than that of yield, and it could be argued that the more cautious definition of B_trigger is beneficial in these circumstances (instances in the bottom right quadrant are much more numerous than those in the top left). For the 0.1 B₀ threshold the ICES HCR is effective at reducing risk to low levels for all FCMSY strategies for both values of B_trigger. In this case, the loss of yield by choosing a higher value for B_trigger is not really justified because risk was already low. For the 0.2 B₀ threshold, the reduction in risk is somewhat larger, and increasing B_trigger more justifiable for providing some additional safety at a cost of modest yield foregone, but in both cases the impacts are modest.

Figure 3.

Change in expected risk and reward as a result of modified fishing in accordance with an ICES-type HCR (HCR2) vs. fixed F (HCR1) (a–c), and in terms of HCR3 (realistic fishery closure) vs. HCR2, the standard ICES-type HCR (d–f). Results are shown in terms of changes in gross economic yield (million £) and the fish community risk index for “at risk” definitions of (a) and (c) B < 0.1 B₀, (b) and (d) B < 0.15 B₀, and (c) and (f) B < 0.2 B₀, respectively. Black represents FCMSY based upon ICES (2012) assessments, gold FCMSY based upon the 21-stock Nash equilibrium, and pink, blue, and green FCMSY are based upon targeting the top, middle, and bottom of the PGY ranges for 2017.

Figure 4.

Impact of changing the definition of B_trigger on expected risk and reward outcomes. Outcomes are expressed as changes in risk and reward when B_trigger is increased from 0.3 to 0.4 for (a) “at risk” where B < 0.1 B₀ (Scenario 10—Scenario 4) and (b) “at risk” where B < 0.2 B₀ (Scenario 11—Scenario 6).

Discussion

Optimum sustainable fisheries management involves extracting the maximum long-term yield from the community without leading to societally unacceptable changes in the stock structure. Presentation of outcomes in terms of risk and reward (following Thorpe et al., 2016, 2017) is a good way of doing this, because it captures the essence of the trade-offs involved, assuming that we can characterize the overall risk to community stocks such that it is a proxy for societal acceptance of biological risks associated with the choice of fishing strategies. For this reason, we use an adjusted risk metric, which penalizes loading the risk disproportionately on a small subset of the stocks, reflecting the believe that society wishes to preserve all stocks and would disfavour approaches that willingly sacrificed stocks to maximize yield in a multispecies fishery.

MSY is an intuitive concept, which is mandated by legislation, but in the context of multispecies fish communities, it is hard to define. A pragmatic definition is that any fishing approach, which achieves near optimum levels of yield for acceptable risk in the long term is consistent with FCMSY, the community MSY. In this study we have evaluated five potential candidates, one based on the 2012 ICES single species assessments (Thorpe et al., 2015), one based on a 21-stock NE (Thorpe et al., 2017), and thee based upon targeting the top, middle, and bottom of the ICES PGY ranges. In the absence of an HCR (assuming constant fishing mortality irrespective of stock status) we found that the highest yield was achieved by the NE, and the lowest risk by the lower PGY ranges, and that either might be the optimum approach, depending upon the decision-maker’s risk appetite. The other three approaches were inferior to the NE, resulting in lower yield and equivalent or higher risk. We found this to be the case for all definitions of “at risk” considered here. We find that differences in outcomes associated with choice of FCMSY approach outweigh differences within the same approach due to stochastic recruitment uncertainty (there is a clear separation of colours in Figure 2), so our conclusion is robust to this uncertainty source.

In practice, fishing would not be constant, but would be reduced when stock status declined, and we modelled this by performing a MSE on the five candidate FCMSY approaches, using three different HCRs (Mackinson et al., 2018 and Figure 1), assuming that all catch was landed (no discarding) and normally distributed uncertainty in F of 30% and in B of 50%. We found that applying any of the HCRs was always beneficial because they reduced risk much more than yield for all definitions of “at risk.” This is because the yield lost in the short term by limiting fishing when stock status deteriorates is mostly recovered later when the stock improves as a result. For an “at risk” definition of B < 0.1 B₀, risks were reduced so much that the Nash became the single optimum approach (application of an HCR removes the need to also fish at the bottom of the PGY ranges). For an “at risk” definition of B < 0.15 B₀, application of an HCR improved outcomes (lower risk for similar reward) across the board, but does not alter the relative balance between the approaches—either the Nash or lower PGY ranges are best, depending upon risk appetite. In the case where “at risk” means B < 0.2 B₀, again the HCR improves outcomes across the board, but the benefits for the Nash are less than for the other scenarios, such that the relative balance between the approaches is altered. Now either the lower and middle PGY ranges, ICES (2012), or the Nash might be the best choice, depending on whether risk appetite is low, medium, or high. The upper PGY approach remains a poor choice, however. Whilst we have used a risk threshold common to all stocks (as e.g.Smith et al., 2009; Worm et al., 2009), it would be possible to adapt the threshold to the perceived resilience of the stock (e.g. B < 0.1 B₀ for “resilient” stocks and B < 0.2 B₀ for “sensitive” stocks).

We also compared the performance of HCR2 representing the basic concept that F is reduced as stock status declines, and HCR3, representing the effect of additional steps to limit fishing if a stock is in poor shape. We find that for all definitions of “at risk” and FCMSY, HCR3 results in reduced risk but has little impact on yield. In all cases, the number of instances where HCR3 performance is superior (lower risk, higher return) is much higher than the opposite outcome (higher risk, lower return), so in the long run HCR3 is likely to perform better than HCR2. The inference is that steps to limit or close a fishery when stock status is very poor are beneficial in the long run. It should be noted though that the difference between HCR2 and HCR3 (or another variant) are much less than the difference between HCR2 and the fixed-F HCR1, so the key benefit is obtained by decreasing fishing mortality once stock status deteriorates, consistent with the ICES advice and use of MSY B_trigger.

Our results reflect the model framework used, and thus come with the caveats discussed previously (Thorpe et al., 2015, 2016, 2017). Thus, the uncertainty estimates are likely to be too low, as they do not reflect structural uncertainty (see e.g. Spence et al., 2018). One key assumption is that of food-independent growth. Whilst this may be a reasonable simplification for the North Sea, it would be instructive to compare it with alternative model frameworks that do not make this assumption (Blanchard et al., 2014; Spence et al., 2016). Centre points of the F-ranges for the stocks where there are no published estimates were calculated on the basis of the 4-fleet structure (beam, otter, industrial, pelagic fleets) of Thorpe et al. (2016), assuming (i) F across all stocks is maximized, (ii) choking at the top, middle, and bottom of the ranges, and (iii) assuming a maximum change in relative effort between the fleets of three compared with the 1990–2010 period. The 4-fleet structure generates simplified technical interactions, so it may be worth repeating the study with more realistic fleet segments. We also assume a constant environment, whereas in practice overall productivity, and hence “MSY” changes with time (Larkin, 1977; Capuzzo et al., 2018). In addition to this assumption, we have further assumed that it is possible to determine the appropriate virgin or unfished biomass B₀, associated with the assumed constant environment. Whilst this is reasonable for ecosystems with a short history of fishing, for others such as the North Sea that have long been subject to exploitation, this assumption is more problematic. We have made the assumption because it provides a clear baseline for stock abundance independent of our thinking on what constitutes FCMSY (and hence BMSY-based proxies), but the methods could easily be adapted for other methods of determining stock reference points.

We have assumed in our evaluation, that the key risk of interest to society can be captured by our risk of stock depletion, and the key reward is the gross expected revenue, whereas communities may have other priorities such as sustainable sources of income (even if lower), levels of profitability in the fishery, jobs provided, or preservation of a way of life. Nevertheless, the methods used here could be applied to other relevant metrics, provided they can be identified and quantified in some way, and it illustrates the trade-offs that are often involved in fisheries management.

We have also assumed stochastic (white-noise) recruitment about a mean dependent on spawning stock biomass (SSB), so there is no serial correlation in the recruitment variability beyond that caused by autocorrelation in SSB. In reality, if the recruitment variability was partly forced by environmental processes, there would probably be some additional autocorrelation, which would tend to reduce the performance of the HCRs below what is simulated here.

We have further assumed a stock–recruit relation of the hockey-stick form. If instead a Ricker form of the curve had been assumed (density-dependent decreases in recruitment at high stock size), this would have led to lower estimates of virgin biomass and hence improved stock status (lower risk estimates), tending to offset the previous assumption to a degree, but the study could readily be repeated with both recruitment assumptions relaxed.

In this study, we have used an ensemble of multispecies models with stochastic recruitment to evaluate the long-term outcomes of fishing to alternative formulations of multispecies MSY in terms of risk and reward. We consider the impact of a variety of HCRs, and assumptions concerning the point at which a stock would be considered “at risk.” We find that (i) the FCMSY based on the NE gives the highest yields and is always a competitive approach, although a very risk-averse society might choose to fish in the lower part of the PGY ranges instead, (ii) HCRs of the type considered here are always useful, as they reduce risk much more than yield, and (iii) the difference between HCR2 and HCR3 is significantly less than the difference between either of them and HCR1, so it is seems to be more important to rigorously implement a HCR that reduces fishing as stock status deteriorates rather than obsess over the precise details of such a rule.

For a lax definition of at risk (B < 10% B₀), and using HCRs, risks are low across all strategies, and the NE is the best performing MSY approach considered here. For more stringent definitions of “at risk” (e.g. B < 20% of B₀), the application of HCRs can allow a range of alternative formulations of MSY to produce acceptable outcomes in terms of risk and reward. Thus, the definition of MSY may be sensitive to judgements about acceptable levels of risk, and consistent application of a sensible management framework may be more important than developing the best possible theoretical definition of MSY.

Acknowledgements

This study has been funded by Defra, with a contribution from the EU H2020 project “PANDORA.” Supercomputing support has been provided by HPC at the UEA. We would like to thank the assistant editor Jan-Jaap Poos and two anonymous referees for their helpful comments, which we feel have greatly improved the presentation of the work. This work has also benefitted from discussions at the ICES Working Group on Multispecies Assessment Methods (WGSAM), currently co-chaired by Sarah Gaichas (USA) and Alex Kempf (Germany).

APPENDIX A: Characterization of the management outcomes in terms of risk and reward

Outcomes of the management strategy evaluation were characterized in a two-dimensional space of risk and reward (see also Thorpe et al., 2016, 2017). The justification for this choice is that it captures the essential tension in management between maximizing yield (reward) and preventing long-term degradation of stock structure (biological risk).

In this study, we evaluate risk and reward over the long term (last 30 years of a 50-year simulation) assuming a constant environment. We use a FE of 63 model variants (as in Thorpe et al., 2017). The reward is expressed as gross economic yield (in millions of £per year), and is simply the catch tonnage × price per tonne (Thorpe et al., 2017) summed across the 21 stocks in the model, and averaged across the 63 model variants and the last 30 years of the simulation.

In the case of risk, a simple average of the number of times the stock biomass is deemed to be “at risk” (B < 0.1 B₀ or B < 0.2 B₀) will not suffice. If an average were used across our community of 21 stocks, it would be possible to deplete one stock with 100% probability whilst the overall risk across the community might remain compliant with the precautionary principle (<5%) if there was very little risk to any of the other 20 stocks. This scenario might seem extreme, but would be possible with a highly species-selective pelagic fishery, and would of course not be acceptable. So, we need a risk metric which:

• A) Increases with the overall risk to stocks across the community.

• B) Defaults to the individual risk to a stock in the case where all stocks are subject to the same risk, and

• C) Heavily penalises outcomes where the risk is loaded disproportionately onto a small number of stocks.

• D) Has a value between 0 (no risk to any stock) and 1 (all stocks at certain risk of depletion).

Here, we use a simple community risk metric (CR), which has these properties and is related to the individual risk of depletion (e.g. B < 0.1 B₀ or B < 0.2 B₀) of stock i (R_i) as follows:

$$CR=\frac{{{\displaystyle \sum }}_{i=1}^n(R_i\text{*}{i}^{-t})}{{{\displaystyle \sum }}_{i=1}^n{i}^{-t}}$$

where n is the number of stocks in the community, t is the tolerance of risk concentration (societal appetite for tolerating higher risk to an individual stock), and R_i varies between 0 (no risk of stock depletion) and 1 (100% probability of stock depletion) for stock i of n, sorted in order of decreasing risk, R₁ > R₂ > R₃ … > R_n.Table A1 shows the behaviour of this metric for a few simple examples, illustrating that it has the required properties. In the limit that the risk tolerance is spread evenly across the community (t = 0) the community risk defaults to the mean risk (first scenario). In the limit there is no tolerance of risk concentration and we consider the community risk as equivalent to the most endangered stock (t = inf), the community risk defaults to 1 if a single stock is depleted with certainty, even though the risk level might be precautionary if were averaged across all stocks (an extreme case of this is the second scenario). In other cases, the community risk will always be higher than the mean risk, lower than the highest individual risk, and increase with unevenness of risk loading across the community. In this way it penalizes outcomes that focus the risk on a small number of stocks. In our study, we have set t = 1, but other values could be chosen depending on the willingness of the decision-maker to accept concentration of risk.

Table A1.

Comparison of the community risk CR with the mean risk to stocks for some simple examples, colour coded by ensemble mean risk measure (green = precautionary, light orange >0.05–0.10, dark orange >0.10–0.20, and red >0.20).

	Scenario risk profile for a hypothetical 21-stock fish community
	5% risk of depletion across the community All stocks R = 0.05	One stock depleted, others untouched. One stock has R = 1.0 All other stocks R = 0	5 stocks have R = 0.2 17 stocks have R = 0	10 stocks have R = 0.1 11 stocks have R = 0
Mean risk to stocks	0.050	0.048	0.048	0.048
t = 1: this study	0.050	0.270	0.125	0.085
t = inf: defaults to highest risk	0.050	1.000	0.200	0.100
t = 0: defaults to mean risk	0.050	0.048	0.048	0.048

The risk of depletion for each stock is then calculated by averaging across each of the 63 model variants and 30-year time-period, before being combined into a community risk metric using the above formula. So, for each ensemble member we calculate a risk to each stock by taking the total fraction of time that the stock biomass lies below the “at risk” threshold during the last 30 years of the simulation. Then for each stock we average the risk across the 63 ensemble members to produce an ensemble mean risk per stock. Finally, a community risk metric is assembled from the 21 risks to individual stocks.

For each FCMSY approach, the impact of stochastic recruitment (see Thorpe et al., 2017 for details of implementation in the model framework) is assessed by performing 100 calculations (100 instances of 63 model variants, each evaluated for 30 years), and each calculation is plotted separately in the figures. Therefore, the spread of points of the same colour illustrates the variability of outcomes across an approach due to stochastic recruitment, the differences between colour groups illustrates the effect of choosing a different FCMSY approach.