ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on November 1, 2007
ICES Journal of Marine Science: Journal du Conseil 2007 64(9):1641-1649; doi:10.1093/icesjms/fsm155
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Precisely wrong or vaguely right: simulations of noisy discard data and trends in fishing effort being included in the stock assessment of North Sea plaice
Wageningen-IMARES, PO Box 68, 1970 AB IJmuiden, The Netherlands
Correspondence to M. Dickey-Collas: tel: +31 255 564646; fax: +31 255 564644; e-mail: mark.dickeycollas{at}wur.nl.
Dickey-Collas, M., Pastoors, M. A, and van Keeken, O. A. 2007. Precisely wrong or vaguely right: simulations of noisy discard data and trends in fishing effort being included in the stock assessment of North Sea plaice. – ICES Journal of Marine Science, 64: 000–000.ICES stock assessments of North Sea plaice are routinely carried out with eXtended Survivors Analysis (XSA), based on landings and survey data. Recently, the assessments included data on discarded young fish, sampled with high variance. Fishing effort has been declining since the mid-1990s, so conditioning the estimated fishing mortality (F) on the recent past could introduce bias into the perceived stock size. Simulated populations with North Sea plaice-like characteristics are used to explore the dependence of the perceived stock dynamics on the inclusion of discards data at different sampling noise, using the same methods and XSA settings as ICES. The sensitivities of the results were tested against different trends in fishing effort and recruitment, and different scenarios for "shrinkage" (i.e. the way in which the past is used to estimate the most recent fishing mortality). Within the bounds of the simulation assumptions, the perception of population trends from an XSA stock assessment can be biased when there are trends in fishing effort: decreasing effort leads to underestimating SSB and overestimating F. When discards are not included, bias in SSB is greatest when effort decreases, and bias in F is greatest when effort increases. Bias in SSB and F were removed by including discard data, but at substantial loss of precision. If effort shows a clear trend and discards are substantial and estimated noisily, the recent trend in the target population may be hard to track with an XSA-type assessment methodology.
Keywords: bias, discarding, Pleuronectes platessa, simulated population, stock assessment, variance, XSA
Received 21 November 2006; accepted 1 October 2007; advance access publication 1 January 2007.
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Introduction |
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 Top Introduction Material and methodsResultsDiscussionReferences |
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North Sea plaice (Pleuronectes platessa) is mainly exploited by a beam trawl fleet that targets both sole (Solea solea) and plaice (Daan, 1997; Piet and Rice, 2004). The legal minimum mesh size in the fleet is heavily geared towards catching the slimmer sole, which leads to substantial discarding of plaice (Van Beek et al., 1990). The differing catching potential of each species with differing relative total allowable catches (TACs), which cannot be accounted for in the management system based on single-species TACs and fixed national quota shares, also leads to increased discarding of young plaice (Daan, 1997; Kraak et al., 2004). This practice of discarding is legal within the EU. However, concern has been raised about the impact of not incorporating discards as a source of mortality on the quality of stock assessments and their associated management advice (ICES, 1986; Alverson et al., 1994; Casey, 1996; Dingsor, 2001; Borges et al., 2005).
The annual numbers of young plaice discarded by the North Sea beam trawl fleet varies greatly between years (Van Beek, 1998) and the time-series of empirical estimates of discarding is patchy (ICES, 2005). For the most recent years (1999–2005), shipboard observer estimates of the numbers-at-age discarded may be raised to the total fleet by the ratio of sampled effort to total fleet effort, but for the period before 1999, reconstructions of annual discards using modelled estimates of growth, spatial distribution, and (mesh and sorting) selectivity ogives have been made (Van Keeken et al., 2003; ICES, 2005; also see recommendation in ICES, 1986). From 2004 on, these discard estimates have been included in the stock assessment of North Sea plaice and in the catch predictions (ICES, 2005). However, it is not clear how the inclusion of noisy estimates of discarding has affected the stock assessment (ICES, 2006a).
Compared with port samples of landings, samples of discarded fish are few. This is due to the necessity of using onboard observers to estimate discards (Stratoudakis et al., 1998; Tamsett et al., 1999; Allen et al., 2002). As a consequence, estimates of discards are less precise than estimates of landings (Stratoudakis et al., 1999; Cotter et al., 2002; Rochet et al., 2002; Punt et al., 2006), although bias can of course arise also from trends in the misreporting of catch. This has opened up a debate as to the usefulness of including discard estimates in the assessment (Cotter et al., 2004; ICES, 2004; STECF, 2005). This debate has centred on "bias vs. precision": excluding discards obviously introduces bias, whereas including discards could increase variance and decrease precision. If the bias was consistent (e.g. similar proportions of discards by year), the interpretation of trends would be easier than when noisy discard estimates are added to remove the bias (ICES, 1986), because the signal would be lost in the noise.
The beam trawl fleets fishing for flatfish in the North Sea have shown a substantial decrease in number of fishing days since 1995 (ICES, 2006a). The eXtended Survivors Analysis (XSA) model used to assess the North Sea plaice stock (Darby and Flatman, 1994; Shepherd, 1999) has conservative features: the survivor population is partly driven by the mean fishing mortality of the recent past (ICES, 1983, 1987), which has became known as the "shrinkage" option. Shrinkage in XSA is aimed at balancing bias and precision: including shrinkage may introduce bias, whereas excluding it may increase the variance. The use of XSA has been criticized precisely for its over-reliance on the shrinkage option. However, these criticisms are largely anecdotal and virtually no study has investigated and documented the influence of conservative measures such as shrinkage. Cotter et al. (2004) raised concerns about using XSA when catch-at-age data for landings and discards were combined, because such datasets are often not collected independently or raised.
We address some of these issues by evaluating the quality of XSA assessment of North Sea plaice using catch data that include or exclude discard data. We do not consider the pertinence of input data and assessment method to the overall management of the stock (Kell et al., 1999; Ulrich et al., 2002; Kraak et al., 2004), but only how trends in effort and the quality of discard estimates affect our ability to assess the state of a stock. This analysis cannot be carried out on real data, because the underlying dynamics of the one and only realization represented by the available data remain unknown (Rosenberg and Restrepo, 1994). Therefore, simulations are based on an operating model representing the true dynamics and allowing observations to be generated, which are then used in an XSA to evaluate the perceived dynamics (NRC, 1998; Restrepo, 1998; Mohn, 1999; ICES, 2003, 2004).
Instead of using the same model to create and assess the population, the true population was constructed by a separable model, and XSA was used for the assessment. This should introduce more noise into the assessment and enhance the realism of the simulations, because assumptions within any assessment model are unlikely to match completely the processes governing the true population. A range of different scenarios for increasing and decreasing trends in fishing effort, different trends in recruitment, and different noise associated with discard sampling was tested by assessing the simulated observations with both high and low shrinkage in XSA. Bias in and precision of the perceived populations were quantified, and the results are reviewed in light of the current stock assessment for North Sea plaice.
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Material and methods |
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TopIntroductionMaterial and methodsResultsDiscussionReferences |
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A plaice-like population was generated using the methodology of Hjorleifsson as applied in the ICES Workshop on Advanced Fish stock Assessment Techniques (ICES, 2006b). The model consists of four components: a population dynamics model, a fleet dynamics model, an observation error model, and an assessment model. We used periodic functions to generate different types of trends in the simulated populations because we found that periodic functions can mimic almost any pattern that we wished to explore. The simulator is written in Microsoft Excel (ICES, 2006b) and extended with a dynamic link library implementation of XSA (Shepherd, 1999; Kell et al., 2005).
Population dynamics model
Recruitment at age 1 (R) at the beginning of each year (y) is modelled using a periodic function (Figure 1):
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the mean (assumed) recruitment, P the length of the periodic function, Yshift a shift factor that determines the start of the periodic function relative to the start of the time-series, and 
r is a normally distributed number with a mean of zero and a standard deviation of 
R. The exponential transforms the normal distributed random numbers to lognormal distributed random numbers. We use R as coefficient of variation (CV) when dealing with lognormal distributions, and the CV on recruitment that was generated in the simulations was arbitrarily set at 0.4. This was based on visual inspection of the interannual variance in recruitment. However, from post-simulations, it was apparent that the observed CV in the ICES stock assessment of North Sea plaice is 0.53, which means that the variance in the recruitment has been underestimated in the simulations. The simulated population exhibited less variability than the North Sea plaice in reality, so the simulations are probably "better" behaved than the true system.
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Population numbers-at-age (Na; a > age at recruitment) in the start year (y = 1) were derived from the recruitment in the start year using the standard exponential decay function
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Fleet dynamics model
Selectivity of the fishery by age and year (Sa,y) was modelled by using a double half-Gaussian function (Figure 2).
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The year trend in F of the fully selected age group was modelled using the periodic function
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is the mean (assumed) fishing mortality, and Fa,y is determined by a separable model:
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Catches were generated using the standard Baranov equation:
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Observation model
The observed catches-at-age are modelled as:
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Ca is an age-specific error term.
Unaccounted removals (i.e. discards) are approximated by a proportion (fa,y) of the catch at each age and in each year not accounted for in the observed catch matrix. The final catch generated for the stock assessment is:
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The relationship between population numbers-at-age and survey abundance-at-age (U) was modelled as:
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Ua is the age-specific error term for the index estimation. The catchability qa,y is the product of a catchability by year (qy), representing the catchability of the fully selected age group, and a catchability by age (qa), equivalent to the selection pattern of the fishery. A dome-shaped selection pattern was used in the simulations, similar to the observed mean F-at-age in the ICES assessment (ICES, 2005). The simulations used two simulated calibration series (Figure 3), one reflecting a commercial fishery with relatively high selection on the older ages, the other reflecting a research survey predominantly aimed at younger fish.
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Assessment model
All simulations were carried out with XSA in an implementation available for Microsoft Excel (Kell et al., 1999, 2006). The settings were the same as used by the ICES assessment working group (ICES, 2005; Tables 1
–3).
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Scenarios
In the scenarios, we investigated different combinations of the following variables and processes:
- increasing or decreasing fishing effort during the final years. Of these, the simulations of decreasing effort are considered to reflect the recent trend in the fishery, but the overall test is to investigate the sensitivity of the assessment results to non-stationary effort;
- inclusion or exclusion of discard data;
- observing discards with different observation errors (using CVs of 0.2 and 0.5 to mimic precise and imprecise observations; actual values were loosely derived from previous studies on market sampling and discards; see Kell et al., 2003);
- increasing or decreasing recruitment during the final years. Of these, the simulations of decreasing recruitment are considered to reflect the recent trend in the North Sea plaice stock;
- using high or low shrinkage in the XSA model.
For each scenario, 100 Monte Carlo iterations were carried out over a 25-year period. In each iterations, random numbers were drawn and used in the appropriate process formulations and observation errors. The results of the iterations were summarized for a number of key performance statistics and retained for further analysis. The bias in the assessments was approximated using the relative difference between the observed and the true indicators of spawning-stock biomass (SSB), mean F (ages 2–6), and R in the final year:
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The distance between the 5th and 95th percentiles of the estimated biases was taken as a proxy for the confidence interval (CI) in the final year:
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Results |
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When simulated populations were generated without noise, the assessment model was able to capture their dynamics. This indicates that the model was correctly configured. Changing the trend in fishing effort, both the shrinkage used in estimating terminal F and the inclusion of discards (with varying noise in the signal) had an impact on the bias and/or precision of XSA (Figures 4 and 5). In contrast, simulations in which the recruitment trend was changed had no impact on the bias or the precision and will not be discussed further.
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The inclusion of discards in the assessment reduced the bias in the estimated SSB while only marginally increasing the CI. Excluding discards had more effect on the bias in F when effort was increasing and on SSB when effort was decreasing (Figure 5, see the discussion later). Discarding was the only factor to impact on the estimates of recruitment. Not only was the bias reduced and the CI increased by including discards (Figure 5), but the interannual changes in the deviation from the true recruitment between years increased greatly (Figures 4 and 6). There is also a difference in the bias under low shrinkage conditions with decreasing effort, resulting in a positive bias in F, but increasing effort resulted in no bias in F. The reason for the difference in bias between increasing effort and decreasing effort at low shrinkage is unclear. This may be due to the disproportionate relationship between numbers and fishing mortality in the convergence properties of virtual population analysis (VPA). At high F (increased effort), there is rapid convergence and a rapidly diminishing error, whereas at low F, there is slower convergence. Hence, bias is noticeable at low effort levels but reduced at higher effort levels. It is unclear if this result is specific to XSA or common to other VPA-based methods.
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The choice of whether to use low or high shrinkage also had an impact. High shrinkage increased systematic bias in SSB but lowered the noise (Figure 5). Interestingly, high shrinkage increased the bias in F when fishing effort was increasing, an output that did not occur under low shrinkage. Shrinkage itself did not affect bias or precision in recruitment in any clear manner.
The changes in trends in fishing effort are crucial when considering the impact of including discards or shrinkage in XSA. When effort is declining, XSA tends to underestimate SSB, and when effort is increasing, XSA tends to overestimate SSB (Figure 5). Using a lower shrinkage alleviates the bias except when discards are not included, and reducing effort leads to a substantial underestimation of SSB. The bias in F is generally opposite to the bias in SSB. However, when effort is decreasing, the overestimation of F appears to be largely independent of the shrinkage applied. Application of a weak shrinkage (2.0) generally reduces the bias in the assessment. The "cost" of the low shrinkage in terms of greater variance was mainly observed in estimated F, and to a lesser extent in estimated recruitment.
When effort was increasing, the inclusion of precise discard data gave greater bias and higher variance than when using precise discard data (Figure 5, bottom right). This may be explained partly from the time-series of bias in recruitment under the two different assumptions. The use of precise discard data results in relatively narrow CIs over the time-series, but the uncertainty increases in the final year. When the noisy discard data are used, the model cannot fit the recruitment data, which results in large CIs that appear to narrow in the most recent year. It is unclear what the driving mechanism is for this process.
Combining all these observations suggests that the bias by not including discards in estimating SSB is greatest when effort is decreasing and greatest in estimating F when effort is increasing (Figure 5). When noisy discard estimates are included in the stock assessment, the bias in estimated recruitment disappears, but at the cost of very high variance around the estimates. The use of shrinkage in XSA does not necessarily result in greater bias in F, because it is dependent on the recent trends in fishing effort. The overall perception of population trends from an XSA stock assessment appears to be influenced by recent trends in fishing effort.
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Discussion |
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Our overall conclusion is that the perception of population trends from XSA can be biased considerably when fishing effort is following either an increasing or a decreasing trajectory. There is interaction between trends in effort and whether or not discards are included in the assessment process: when discards are not included, bias in SSB is greatest when effort is decreasing, and bias in F is greatest when effort is increasing (Figure 5). The bias can be negated to a large extent by including discard data, but when these data are noisy, the bias disappears at the cost of very high variance around the estimates.
Bias can be introduced into a stock assessment in other ways, including the misreporting of catches, changes in selection of both the fishery and the survey, changes in distribution of the fishery, and stock size influences on catchability. Here, we concentrated on discard practices and effort trends as two of the perceived main issues in the North Sea plaice fishery, but linkages with other potential causes of bias have not been addressed and may well impact our findings.
Some of the results obtained from this simulation appear to support the tacit knowledge of assessment working groups within ICES. Working groups often claim that assessments perform worse when there are substantial changes in a fishery (ICES, 1986, 1995). XSA is expected to perform better under such conditions than a separable model, as long as the catch-at-age data are robust. However, the specific bias caused by XSA observed here has not been described in the literature, although Cotter et al. (2004) were explicitly critical of the reweighting algorithms in XSA and argued for simpler methods, in the direction of "indicators" rather than "assessments" (Kelly and Codling, 2006). Our results imply that even with low shrinkage, XSA is conservative in estimating both F and SSB, although the magnitude of the effect depends on the recent trend in fishing effort.
Yin and Sampson (2004) investigated the role of different potential sources of errors in stock assessment and found that length of the time-series, sample sizes for age compositions, variability in survey biomass, and fishing effort were the most influential factors for their statistical catch-at-age model. Following their arguments and those of ICES (1986), adding noisy discard data will affect the assessment by increasing the variance in the catch-at-age matrix of younger fish. This idea is supported by our results, because the recruitment estimates had the largest CI in the final year and showed greatest interannual variability. Jonsson and Hjörleifsson (2000) evaluated all ICES stock assessments and found substantial bias in 20% of the cases examined for F, 30% for SSB, and 40% for R. Furthermore, the CVs they found were larger than assumed by ICES working groups when they defined reference points (ICES, 1998). Incorporating poorly estimated discard data could increase further the uncertainties of the assessments, but with lower bias.
All the results of a simulation study obviously depend on the assumptions made. Our simulations intended to mimic the stock dynamics of North Sea plaice, a stock for which discarding of undersized fish is a major issue. In an attempt to facilitate understanding, variability in discarding (caused by growth and distribution change) as assumed by the reconstruction of the time-series used in the current assessment of North Sea plaice (Van Keeken et al., 2003; ICES, 2005) has not been included. The basis for the parameter estimates in the operating model was provided by ICES (2005). The noise used in generating observations from the operating model were loosely based on O'Brien et al. (2001) and Kell et al. (2003), who looked at the quality of the market sampling and research vessel surveys for demersal species in the North Sea. However, knowledge of the CVs on our observations in general may be more uncertain that the quality of the observations themselves. As a result of the methods used and sampling intensity, discard estimates are thought to be less precise than landings data (Stratoudakis et al., 1999; Cotter et al., 2002; Rochet et al., 2002). The assumptions commonly used for estimating annual discards (e.g. that discards are proportional to catch or effort) have been contested (Rochet and Trenkel, 2005). We have bracketed the uncertainty in the observation process of discards by using either a CV of 0.2 (relatively precise estimates) or 0.5 (noisy estimates), but published records that suggest that either of these two values is a more likely value for North Sea plaice do not exist.
Instead of using the noisy discards estimates directly in an assessment method, an alternative would be to estimate the discards in the assessment method and to use the observed discard proportions as sources of validation. Punt et al. (2006) applied this approach to the assessments for two stocks off southeastern Australia, and found that including discard data in the assessments led to a reduction in uncertainty.
The XSA calibration against independent fleet information is a key process in deriving the final year estimates of stock abundance and F (see development of the method in ICES, 1981, 1983). We did not investigate the sensitivity in the choice between the commercial and research survey calibration series applied, but it could be conjectured that the inclusion of a non-biased commercial series of catch per unit effort (cpue) might have stabilized the estimates of SSB and F because of sample information on the older ages. The current practice in the assessment working group has been to reject commercial cpue series and to base the calibration on research vessel surveys characterized by a relatively low selectivity on the older ages. This might induce another bias.
The calibration series were generated assuming no trend in catchability, so imply a linear relationship between fishing effort and fishing mortality. Worries about changes in catchability were the initial drivers that led to the stiff function that developed into shrinkage (ICES, 1981, 1983). In practice, however, there are clear indications that catchability in commercial fleets increases over time through improvements in gear and propulsion and other equipment (Marchal et al., 2003; Rijnsdorp et al., 2006), and catchability may also depend on stock size. The implications of changes in catchability on the perception of stock size were not investigated here, but it would be expected that they would also have a substantial effect on stock perceptions.
The use of a dome-shaped selection pattern, as used in the stock assessment, may well have influenced our findings. Assessment results appear to be sensitive to the choice of the q plateau under the dome-shaped selection assumption. Therefore, any study, which explores these ideas further should consider a simulation that uses a sigmoid selection pattern too. Although this is not used in the current stock assessment or this study, it may provide valuable insight to the bias in XSA under simulated conditions.
Although our analysis concentrated on the sensitivity of XSA, potential consequences for management can be considered. The traditional method for providing short-term catch advice in ICES, based on a recent stock assessment and last year's survey data, is built on the premise that the most recent assessment is also the most accurate. However, the simulations show that there is no axiomatic coupling between the most recent assessment and the most accurate population estimates. Reliable estimates of recruitment are considered essential for making short-term forecasts for heavily exploited species. Our results suggest that recruitment estimates may be easily either seriously biased (when discards are not taken into account) or highly uncertain (when noisy discard estimates are included). Under such conditions, reliable forecasts of absolute catch relative to equally uncertain reference point forecasts are virtually impossible to make, particularly when the bias depends on recent developments in the fishery. The critical question is whether fish stocks can be managed in the short term with these implied values of noise and bias, if the assessment cannot take into account the consequences of recent management measures?
Hilborn (2003) argued that fisheries science has to move away from producing short-term tactical advice on catch quota based on annual assessments towards simple harvest control rules that have been tested for robustness in simulation experiments (Butterworth and Punt, 1999; Kell et al., 1999; Punt et al., 2002a, b, c; Peterman, 2004). However, it is important that such simulations take into account potential biases in the fishery system and the sometimes non-intuitive linkages between different parts of the system. Simplistically, in simulations of management systems based on catch-at-age models, one must be aware of unexpected interactions between bias, precision, and recent trends in fishing effort.
If the results of XSA serve as the basis for short-term fisheries management advice, should confidence in that advice be lessened because of the results reported here? If effort shows a clear trend and discards are substantial, and noisily estimated, confidence in the predictions should probably be less. Under such conditions, the recent signal from the target population may be hard to track with this type of assessment methodology.
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Acknowledgements |
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Our study was funded by the Dutch Ministry of Agriculture, Nature Conservation, and Food Quality (LNV) within the "F-project", which aims to improve the scientific basis for stock assessments of North Sea plaice and sole. We thank Einar Hjörleifsson and Dankert Skagen for allowing us to make extensive use of their Excel population simulator developed for their advanced course in stock assessment, as well as for their valuable comments on the draft manuscript. We also thank Laurie Kell for making his Dynamic Link Library implementation of the XSA available. Niels Daan, J-J Maguire, Rob Scott, and an anonymous referee also gave valuable advice on the manuscript.
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References |
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