ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on April 30, 2007
ICES Journal of Marine Science: Journal du Conseil 2007 64(4):679-685; doi:10.1093/icesjms/fsm048
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Management implications and options for a stock with unstable or uncertain dynamics: west of Scotland herring
FRS Marine Laboratory Aberdeen, PO Box 101, Victoria Road, Aberdeen AB11 9DB, Scotland, UK
Correspondence to E. J. Simmonds: tel:+44 1224 295366; fax:+44 1224 295511; e-mail: j.simmonds{at}marlab.ac.uk
Simmonds, E. J., and Keltz, S. 2007. Management implications and options for a stock with unstable or uncertain dynamics: west of Scotland herring. – ICES Journal of Marine Science, 64: 679–685.An evaluation of the stock-recruitment relationship for west of Scotland herring indicates that the models fitting the data from different periods deviate substantially. The different perceptions of the population dynamics processes emerging from these relationships lead to a range of potential scenarios for future development of the stock. Optimized strategic choices vary between exploitation at fishing mortality (F) of 0.25 and 0.45, with substantial differences in long-term yield depending primarily on the validity of the underlying stock–recruitment relationship. A detailed evaluation of the consequences for management in the short, medium and long term is presented. The uncertainty in stock dynamics and the strategic options are discussed along with the consequences for potential yield caused by the choice between management options. The study includes an evaluation showing that it may take at least ten years of exploitation at reduced yield before the current uncertainties about stock productivity might be resolved.
Keywords: herring, management strategies, stock–recruit relationship
Received 30 June 2006; accepted 27 February 2007; advance access publication 30 April 2007.
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Introduction |
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 Top Introduction Operating model and HCRResults and discussionConclusionsReferences |
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The World Summit on Sustainable Development (WSSD, 2002) stated in paragraph 31a of its implementation section that there would be a "commitment to restoring [fish] stocks to levels that can produce maximum sustainable yields (MSY) by 2015". The European Commission (CEC, 2006) expressed the view that "in the long term, [fish] stock size depends on recruitment and natural and fishing mortality rates. ... FMSY is the fishing mortality rate that will, on average, result in a stock size that produces the MSY. FMSY is a more achievable measure than the stock size that produces MSY, because it is less dependent on the marine environment and ecosystem effects and is a potentially manageable quantity", so supporting a shift from the policy statement of WSSD of a biomass-based management target to a fishery-based target. This would of course require that FMSY can be estimated. In the case of west of Scotland (VIa north) herring (Clupea harengus), there is some uncertainty as to what constitutes FMSY, because the recent extension backwards (1957–1975) of the time-series (ICES, 2005b) indicated unusually good recruitment during this period relative to the later period.
Using the assessment data in ICES (2005b), the medium-term management options developed here follow the structure contained in ICES (2006). We concentrate on appropriate management options for medium-term exploitation, and consider the implications of changes in the productivity of the stock, or more explicitly the possible range of stock–recruitment relationships and their influence on management choices.
The stock is currently managed through a total allowable catch (TAC). TAC management, backed up with proper enforcement, is generally considered appropriate for herring stocks (Simmonds, 2007). However, area misreporting is a major problem for the VIa stock (ICES, 2006). Discarding in the targeted herring fishery is low, but some discarding of herring may occur in the mackerel (Scomber scombrus) fishery in the same area and there may be some highgrading in the freezer trawler fleets.
No explicit management objectives have been formulated for the stock, but the objectives implied from the CEC (2006) policy document are to obtain maximum stable yield within a precautionary approach. The operational objective underlying the ICES (2005c) Advice is to keep the stock above the limit reference point for spawning-stock biomass (Blim), which has been estimated as 50 000 t. However, this figure is based on an analysis of the data from 1976 to 2001, before the longer time-series became available.
A harvest control rule (HCR) with a fishing mortality (F) target, and restrictions on year-on-year changes in TAC, would therefore be an appropriate choice for consideration. The current assessment (ICES, 2005b) provides a reasonable basis for evaluating such a HCR. Figure 1 illustrates the stock history: spawning-stock biomass was depleted in the 1970s and has not recovered to former levels, and neither has recruitment (R).
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The major consideration for stochastic simulation is the choice of an appropriate stock–recruit relationship (B/R; B refers here to spawning-stock biomass), because the one observed in recent years may be different from that fitted to the full time-series. The higher B observed in the 1960s suggests that there may be potential for a larger spawning-stock biomass than currently observed. Although the possibility of recovery towards a higher B has to be accounted for, an explicit B target may not be appropriate, because it may well be unachievable. An alternative might be to set a long-term target for F, which would allow expansion of the stock if productivity increased. In addition to a long-term target F, TAC advice should remain based on currently observed R and annual growth, in case this is all that can be achieved if current lower R is attributable to environmental influences rather than to reduced B.
To evaluate the possibilities for management, Monte Carlo methods have been used with a range of HCR based on target Fs.
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Operating model and HCR |
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TopIntroductionOperating model and HCRResults and discussionConclusionsReferences |
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The simulation was carried out using STPR3 and S3S (Skagen, 2004, in STECF, 2004) and the methods used in ICES (2005a). The basic equations of the operating model can be expressed as a Leslie matrix (Leslie, 1945, 1948):
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) is derived from a fixed age-based natural mortality (Ma), and fishing mortality (Fa, y) is derived from a HCR implemented using projected Fy estimated from values of Fy – 2 and spawning-stock biomass (By) by projection, and implementation error 
(C) in the catch for the intermediate year:
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| (2) |
Growth and maturity data refer to observed weights-at-age and fraction mature-at-age from annual acoustic surveys of the area conducted since 1991. Stochastic variation is introduced by randomly selecting data from a single year, so taking account of the range of observed variability and the correlation between weight and fraction mature, but ignoring potential cohort-related effects. All values of M, weight, and maturity, and the average selection pattern for the past three years were taken from ICES (2005b).
The HCR chosen consists of three states: (i) depleted state with fixed F1 
F2 (some intermediate F value) for B < Blim of 50 000 t; (ii) intermediate state with a fixed F2 for Blim < B < Btrigger; and (iii) sustainable state with fixed F3 for B > Btrigger (B refers to the TAC year).
Recruitment of herring (Figure 1), R = N0 (first row in the Leslie matrix), may depend on many environmental factors (e.g. temperature—Fiksen and Slotte, 2002; food supply—De Silva, 1973; Möllmann et al., 2004; weather—Williams and Quinn, 2000) as well as stock size (Goodwin et al., 2006). Although significant for some stocks (e.g. Baltic cod, Gadus morhua; Sparholt, 1996), these factors generally explain only a few percentage points of the variability. A major source of uncertainty is the different range in both R and B estimated before and after the collapse (Figure 1). This could have had various causes: reproductive potential was reduced; even the relatively low F (0.35) in recent years (Figure 1) was too high to allow recovery; during the collapse an important component of the stock was removed, changing its dynamics; the closure of 50% of the spawning grounds (nominally in force since the 1970s) may have caused excess pressure on the remaining 50%, resulting in suboptimal recruitment; natural mortality is higher now than it used to be [Hammond and Harris (2006) estimated that consumption of VIa herring by seals increased roughly from 2 700 t to 12 200 t from 1985 to 2002, but suggested that seal consumption might have been even lower during the 1960s]; and there may also be errors in the estimated catch-at-age array over the period. More important, in simulating future R, any environmental factors would have to be predicted before their effects could be taken into account. Because no such model is available for the area, future variability is modelled as the historical B-dependence observed in the B/R relationship, in combination with a stochastic function to simulate the effects of all other factors.
The B/R data for the periods 1957–1974 and 1975–2000, with three fitted relationships (Figure 2), do not show major differences in perception of mean R during the past and recent period, which could be accounted for by the change in B. However, the differences between the estimated relationships are considerable, depending on whether they are calculated based on the entire time-series or just on the recent period. Based on the Akaike Information Criteria (AIC) corrected for the number of observations, among various models (cf. Needle, 2002) tested, the Shepherd (1982) model (S model, first formulated in Maynard Smith and Slatkin, 1973) fitted best for both periods, implying that three parameters are helpful in functionally describing the observed stock–recruitment data. Also, the pattern of residuals around the S model was perhaps slightly "better behaved" than for the other models, but the differences were small and provide little support for choosing one above the other. However, one advantage of the third parameter is that it allows the flexibility to fit both density-dependent and depensatory models. Both S and Change-point (CP) models were fitted to the 1975–2000 data (Sshort, CPshort), but only the S model was used for the entire time-series (Slong).
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In fitting B/R models and choosing between them, attention needs to be given to the criteria used. The B and R data are both derived from a single model, and B values will inevitably be autocorrelated because estimates for adjacent years consist largely of the same cohorts with constant relative strengths.
Considering the independence of errors in their estimation, B and R use data from different but overlapping years, but always from different cohorts. Although there may be some interaction because of fitting selectivity functions, the interdependence of errors is limited. Therefore, although there may be autocorrelation in B, this is not the issue when choosing between relationships, but only the correlation in the errors in estimating R and B for the same year would matter.
In choosing between B/R models (provided the residuals of the parameters are not significantly correlated, as is the case here), the AIC criteria provide the appropriate measure for comparing models, once the assumption of an underlying relationship is accepted. Moreover, the regression method assumes that B is estimated without error, and that the R estimates are dominated by process variability, not measurement error. As B is derived from several cohorts, and taken only from the converged part of the virtual population analysis, this is a reasonable assumption.
Using a bootstrap method to estimate the precision of the parameters, there was no overlap in the estimated values of the exponent. This technique, which assumes independence of B/R pairs, cannot be used to derive significance, because B values are not independent. Nevertheless, the complete lack of overlap strongly suggests that effectively different dynamics operated during the later period compared with what might be deduced for the entire period.
The evidence for two periods is supported using the method of Gilbert (1997), who used a positive median value of 
R/B to evaluate the hypothesis of a B/R paradigm. This herring stock has a median value of 6, with 60% of R/B > 0, which strongly supports the existence of such a relationship. However, carrying out the analysis on the earlier and later period separately, the median values for 1957–1974 and 1975–2000 were 13 and 1.5, respectively. This suggests a much stronger B/R relationship during the earlier period than during the later one, and reinforces the need to consider the CPshort model (see below), which infers greater independence of B/R for the later period. Finally if we consider potential R as the sequence of deviations from the B/R relationship, there is some evidence of a change in potential R from the earlier period to the later one. Using the definition of productivity from Dutil and Brander (2003), taking the stochastic component of R from the fit to Slong, and applying this time-series around a time-invariant mean R, along with biological data from the assessment (ICES, 2006), there is indication of a shift in productivity from 1974 to 2000. This is primarily because the largest residuals responsible for the largest R in the earlier period are not seen in the later period.
A mechanistic problem arises with concluding that the S model reflects the recent time-series correctly, because this implies a declining R at mid-range B when we know from the longer time-series that R increased at higher B. Using a CP model (Needle, 2002) does not have this implication, although it has little underlying biological functionality. This model may be preferable because R does not decrease at higher B, and may therefore be regarded as a compromise option between Sshort and Slong. To test the importance of depensatory behaviour implied by this model choice, both S and CP models were fitted to the 1975–2000 data and these were used in management exploration, along with the S model from the entire time-series.
The point in time to separate the two periods, in order to fit the different models, cannot be determined definitively and is to some extent arbitrary. Delaying the start point in the choice of years for the truncated period does not make much difference to the models, the later period always giving a preference for depensatory models. The stochastic component of R (the deviations from the models that can differ among models) can be seen in the close match of the three simulated and observed cumulative probability density functions (Figure 3).
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Uncertainty in the assessment and decision-making processes in the simulation are represented as general error levels in measurement and implementation. However, not all elements for management are fully included. For example, the direction and magnitude of implementation error is modelled independently from the management decision, whereas in the real world this may not be the case.
Assessment as a source of observation error is implemented as a s.d. of 30% and a bias of +10%, as observed in a retrospective analysis of the assessments. These values are slightly larger than indicated by the quality control sheets for the stock over the period 1995–2003 (ICES, 2005b). The poor quality (high uncertainty) of the assessment is caused by low levels of sampling of the catch and the availability of only a single 20-d survey for tuning.
No systematic implementation error is included in the simulation. Recent history (15 y) provides no evidence of catches exceeding quota. Rather, quota appears to have been systematically underutilized because catches taken elsewhere are reported as coming from VIa (N). To represent some implementation error, a 10% s.d. is applied to the actual catch. This may slightly exceed observed variability, but can at least reflect some area misreporting.
An extensive range of HCR parameter options was tested. For each test, 1000 stock trajectories were determined assuming one of the selected B/R relationships with appropriate stochasticity. For each set of simulations, the mean yield, 95% on yield, the annual change in yield, and the risk of B falling below Blim at least once in the period were estimated. This was done for an extensive range of HCR parameters (Btrigger, F1, F2, and F3) to explore the range of options fully.
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Results and discussion |
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TopIntroductionOperating model and HCRResults and discussionConclusionsReferences |
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Each set of 1000 simulations provides one point estimate of the (most probable) median yield, and these point estimates were plotted against the long-term target F3 (values of the other parameters may change, giving different mean yields at the same F3). Figure 4a, c, and e show all median medium-term (after 10 y) yield for different F3 values at their associated risk levels for the three B/R relationships. Risk is defined as the probability of B falling below Blim (50 000 t) at least once in ten years. For each value of F3, a range of Btrigger, F1, F2, and the constraint on year-on-year change in TAC were tested, fully exploring yield and risk under a wide range of HCR options. This can lead to similar yields at the same F3, but with different risks attributable to the other parameters in the HCR. Therefore, to show only those risks considered precautionary, the selection for risks < 5 % are shown in Figure 4b, d, and f. Therefore, the maximum median medium-term yields against F3 for strategies that are precautionary are obtained as the upper limit of points in these graphs. The results for the two B/R models fitted to the truncated series (Sshort and CPshort) are similar, showing peaks in yield of 45 000 t at around F3 = 0.5 (Figure 4d and f). Greater yields at much lower values of F3 were obtained for Slong (Figure 4b). These results are for unconstrained year-on-year change in TAC. If a 15% limit of change is introduced, the optimal yields and Fs for the short B/R models would be a little lower, at 40 000 t and F = 0.45. For the selection of an appropriate FMSY for managing the stock, the sensitivity of the simulations to the B/R relationship is a critical aspect. The difference in the slope at the origin between Sshort and Slong is close to a factor of four. Although such a difference is substantial, it is within the range of values for different populations of the same species given by Myers et al. (1999).
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Although there may be differences in yield because of the fine detail of the HCR (illustrated by the range of medium-term yields shown at any single value of F3), the overriding differences are caused by the choice of the period over which the B/R relationship is assumed and the subsequent choice of target F. Although Sshort and CPshort suggest a median MSY of around 45 000 t per year at F3 = 0.5, the gains in moving to an F above 0.4 are small. Increasing F above 0.4 increases the risk of B falling below Blim above the 5% level.
Using Slong would imply that greater yields are possible by exploiting the stock at a lower rate and allowing spawning-stock biomass to rise to a more productive state. With this model, F3 = 0.35 gives a stable catch, whereas higher F3 values may cause a small decline (Figure 5a). A long-term target of about 0.25 should be low enough to allow increases in stock size (Figure 5a) and deliver greater yields in the medium term. Using Sshort, F3 = 0.25 would give a lower sustainable median yield of about 38 000 t.
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Conclusions |
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TopIntroductionOperating model and HCRResults and discussionConclusionsReferences |
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Although there is no definitive assurance of any regime shift during the period 1957–2000, there is strong evidence of change. The key issue for providing advice is not whether there has been a real shift, but rather to accept that, for whatever reason, there have been long periods characterized by sufficiently different stock–recruitment relationships to result in markedly different long-term advice. Ignoring this evidence for change may give a misleadingly optimistic prognosis. Should management choose the objective of a stock increase and a strategy that has a fair probability for the stock to expand to the levels observed in the 1970s, a target F of 0.25 would be recommended. If for biological reasons not yet understood, expansion of the stock is currently not possible, this choice would reduce the yield by about 12% in the long-term relative to the maximum medium yield achievable. At current prices for herring, such a reduction would sacrifice revenue of
1.5 million per year at first-sale value. Viewed from a purely economic perspective, this loss of revenue might be justified to give longer-term benefits, but such benefits cannot be guaranteed. Currently, we have no basis for knowing whether the recent low levels of recruitment reflect a lower productivity of the stock or represent a population dynamics response to current exploitation rates, which if reduced would allow expansion. The implication is that management strategies allowing for stock expansion carry the risk of reduced yield for no benefit. Before choosing a policy that allows stock expansion, it is worth examining the period that would be required for different exploitation strategies to determine with reasonable probability that there has been a shift in productivity. If the stock is exploited at F3 = 0.25, then after ten years, some 30% of the plausible outcomes overlap (Figure 5). This implies a 70% probability of being able to differentiate between which of the shorter- or longer-term stock–recruitment relationships was more appropriate. At higher target F, the overlap of plausible outcomes would increase, and the inability to distinguish between them would be greater. At F3 = 0.35, the two regimes may be effectively indistinguishable. Therefore, if the lower exploitation regime is chosen and successfully implemented, managers must be prepared to wait for at least ten years before there is a high probability of determining whether the objective of stock increase is realistic.
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References |
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TopIntroductionOperating model and HCRResults and discussionConclusionsReferences |
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