year class
2.6 Assessment of North Sea herring
2.6.1 Data exploration and preliminary modelling
2.6.1.1 Choice and properties of indices for North Sea herring
Acoustic, Bottom trawl, MIK and Larvae surveys are available for the assessment of herring. The surveys and the years for which they are available are given in Table 2.6.1.1. A series of basic analyses have been conducted to check the basic utility of the surveys available.
Table 2.6.1.2 provides an indication of the survey self consistency with the correlation coefficient between estimates of the same cohort at successive rings in successive years. This indicates that the most self-consistent estimates come from the acoustic survey for most rings, the IBTS 1st quarter survey provides reliable estimates of 0-, 1-, and 2-ring herring.
The 3rd quarter IBTS seems to provide more repeatable estimates at older rings, but the correlation is much poorer than for the young fish in the 1st quarter IBTS and for the acoustic survey.
Table 2.6.1.3 shows the agreement between the different indices in the same year. The 1st and 3rd quarter IBTS surveys indicate good agreement for the 0-ring herring, and the 1st quarter IBTS and acoustic survey show agreement on 1-ring.
However, in general the different surveys seem to contain different information at older rings.
Table 2.6.1.4 shows the agreement between the surveys and the assessment, using the assessment method and weighting factors from the 2002 HAWG. The MLAI, Acoustic and IBTS 1st Quarter indices are used in the assessment, the IBTS 3rd Quarter is not currently used. The correlation values will be affected by the influence of the surveys on the assessment though in all cases the majority of the assessment data comes from the converged VPA. The best agreement occurs for MIK (shown as 0-ring IBTS 1Q), 1-rings from the IBTS 1st quarter, 2-8 with the Acoustic survey and the SSB with the Larvae survey. For the IBTS 3rd Quarter only 0-ring herring seems to be correlated to the VPA results.
Table 2.6.1.5 shows the sampling error by ring by survey. These estimates are obtained from bootstrap resampling for numbers at ring for each survey area, assuming identically independently distributed observations, correcting in all cases for spatial autocorrelation using geostatistical methods (ICES CM 2001/ACFM:22). Sampling error is lowest for the Acoustic survey at 3- and 4-ring and the MIK survey (IBTS 1Q 0-ring). The sampling error is higher but still reasonable for the IBTS 1st Quarter 1-ring, the Acoustic 2-ring and 5-8-ring and the MLAI SSB index. The IBTS 3rd Quarter index and the IBTS 1st Quarter 3-5-ring index has relatively high sampling errors. A similar pattern can be seen for the CV in Table 2.6.1.6.
In conclusion the analysis of variance and correlation indicates that the MLAI provides a good SSB index, the acoustic survey provides good information from 1-8-ring and the IBTS 1st Quarter from 0- & 1-ring. The IBTS 1st Quarter 2-5-ring is useful but noisy, as is the IBTS 3rd Quarter 0-ring index although the latter is still considered too noisy to be included in the assessment. The IBTS 3rd Quarter 1-5 index is not consistent.
All these surveys took time to establish and reach a common operating procedure and a relatively constant area so that subsequent small deviations of area coverage etc. would be acceptable. The issue of which time period should be used
has not been examined in detail recently. However, most recently the time period for the acoustic survey was reviewed within the assessment WG report 1996 (ICES CM1996/ Assess:10).
On occasion single values from surveys may look as if they should be discarded or down-weighted. For example, examination of the 2-ring from IBTS 1st Quarter in 1988 suggests that it is an outlier in the series. There could be arguments to remove this value. However, in reviewing the data series we can more easily make these judgements in retrospect. It is more difficult when the ‘outlier’ is in the terminal year and therefore more difficult to carry out in practice. In any case with a small number of observations on each year class there will almost always be by chance one year class where most of the observations are low (or high), balanced by one or two high (or low) values. One way to examine these issues is to look at statistical properties of the index and to see if an observation appears to be unusual.
Mean variance plots for each of the indices are given in Figure 2.6.1.1.
These graphs show no obvious outliers, suggesting that the statistical properties are reasonably consistent and that
‘outliers’ are really part of the properties of each index. Thus at least for making judgements about weighting factors it is necessary to include all the data. We have to accept that if an index is capable of having an unusual high catchability in one year it may do so again. The WG is generally not in favour of picking out observations simply because they look odd. As a process it is arbitrary and may eventually result in bias. For example the IBTS 2-ring index in 1988 appears high in retrospect and for some reason either in 1988 the catchability did increase or for some other reason this cohort was underestimated on other occasions. However, if we have no basis for judging which of these two alternatives happened, assuming the former could be wrong. Thus, no individual data points have been excluded in the assessment.
2.6.1.2 Selection of weighting of indices in the assessment of North Sea herring
The HAWG in 2002 moved from arbitrary index weighting used for the previous 6 years (1996-2001) to a more objective method. ACFM set up the study group SGEHAP (ICES CM 2001/ACFM:22) with one of its objectives to try to rationalise the survey index weighting in the assessment. SGEHAP produced a final report in October 2001 which provides a full description of the conclusions and supporting arguments, the main issues are summarised here:
SGEHAP investigated the selection of index weighting through two main approaches:
• Sampling variance derived from survey variance.
• Structural variance from residuals between indices and assessment.
The method for estimating survey variance is described in detail in the SGEHAP report. Inverse variance weights were calculated for each index by ring. Where ring-disaggregated indices are provided and correlation between measurement error by ring was observed, the weighting factors at ring were rescaled to a level that reflected the amount of independent information. This was based on the perception that if the error in estimating each ring was independent then the full weight would be required. If the error was completely correlated the appropriate weight would be the weight of a ring spread equally amongst all the rings. The weighting values are given in Table 2.6.1.7. The weighting values for structural error were derived from the residuals between the surveys and the assessment. This method is similar in concept to the index weighting method used in XSA. In ICA index weighting may be adaptively changed to minimise the overall sum of squares in the maximum likelihood function. The sampling error is ignored and only structural error is included, the method incorporates no prior assumption about the relative merits of the sources of data.
In the SGEHAP study the structural differences were examined in two ways, first by using the ICA adaptive method of weighting for all the bootstrapped datasets. Secondly by obtaining a single set of adaptive weights from the WG data series and using these as fixed values. The ‘structural’ weights for the indices are shown along with the inverse variance weights Table 2.6.1.7.
The HAWG in 2002 extended the review to look in more detail at retrospective patterns. In particular the weighting for 0- and 1-ringer in fitting a separable model to catch. The fishery for North Sea herring has been managed by two TACs, for adults and juveniles (0- & 1-ringers). Over recent years the TAC for juveniles has not been set with reference to the observed fluctuation in juvenile abundance but has been linked to the adult TAC. While it might be correct under these circumstances to apply a separable constraint to the adults, it would be inappropriate to include the juveniles so the influence of 0- and 1-ring catches is down-weighted. On this basis the WG in 2002 selected index weighting which both minimised the variability in the assessment output but also reduced the retrospective revision of management parameters (F, SSB and recruitment). However, they could not find a method that minimised the revision of all of these parameters but selected the one that performed best for two out of three. This was done by down-weighting the influence of catch of 0- and 1-ringers in the assessment.
A number of points can be drawn from Table 2.6.1.7:-
• The MIK index is given much more weight in the inverse variance method
• The structural method gives three times the weight to the acoustic index relative to the IBTS survey
• The inverse variance method reduces the influence of the acoustic index, giving twice the weight to the acoustic index relative to the IBTS index
• The structural error method gives relatively higher weights at older ages contrasting with the inverse variance method giving decreasing weights with age.
Both ‘fixed’ structural weights and fully adaptive weighting was tested and found to give higher variance in all management parameters than the inverse variance weights. However, the differences in index weighting were noted and explored further in SGEHAP and two additional weighting methods were tested:
1) Using the mean of both methods. Conceptually the idea was that such weighting would provide a compromise between sampling and structural sources of error, and thus might be expected to give a more optimum overall method.
2) Specifically reducing the weight on the MIK. This reflected the idea that although the survey is rather precise it might be given incorrectly large weight. There were concerns that the assumed constant natural mortality throughout the year might be unreasonable, and in reality natural mortality might be more variable, due for example to seasonal fluctuations in predation on 0 group, i.e. the demands of the model might create problems.
However, the conclusions from investigations were that the inverse variance method outperformed both these options.
In conclusion: while the WG has not considered all possible weighting (by estimating weights through some objective function), it has made an extensive review covering both inverse variance and structural errors, and it considered that the inverse variance method provided the better method. The weights also express the WG view that the young herring are best estimated with MIK and IBTS surveys, and the older herring are best evaluated through the acoustic survey.
2.6.1.3 Period of separable constraint
The ICA model includes the assumption of the exploitation pattern being constant over a number of years. The changes in the regulations in 1996 have affected the various components of the fishery differently. The TACs for the human consumption fleet in the North Sea and Division IIIa were reduced to 50 %. By-catch ceilings for the small-meshed fleets were implemented corresponding to a reduction in fishing mortality of 75 % compared to 1995. These fleets exploit juvenile herring as by-catch. As a result a single separability assumption is likely to be violated if it extends further back in time than 1997.
At recent meetings of this WG, the separable period has been split up into two different periods: 1992-1996 and 1997 onwards. In the WG 2001 it was considered that the number of years after the change in selection was long enough to use only a single separable period of four years. In this WG, as in 2002, a selection period of 5 years was used.
Exploration of a 6-year period showed no important differences in the model fit.
2.6.1.4 Comparison of assessment model
ICA has been used for at least the last eight years for the assessment of North Sea herring. It was felt that after the findings of the recent WGMG (ICES CM2003/D:03), the performance of ICA should be compared with another regularly used assessment model, XSA. Concern at WGMG was raised about the instability in the selection patterns at older ages impacting on the earlier part of the time-series. The approach used was to choose XSA settings that reflect as many of the assumptions of the ICA model of North Sea herring. The shrinkage of F was set very low and for the retrospective run a shifting tuning window was used (different from the single XSA analysis which used the whole series). The model settings are given in Table 2.6.1.8 and the summary of the results in Table 2.6.1.9. It is clear that XSA gives very similar results to ICA.
XSA is very sensitive to the number of ages used for F shrinkage. In the present study the use of only the oldest true age (8-ring) gave a SSB of 1,570,000 t. Dependency on the actual level of shrinkage, compared to number of ages used was much smaller. The XSA assessment is very consistent with the ICA assessment (Figure 2.6.1.2). However, the retrospective bias in XSA is slightly smaller even with the use of a tuning window of 8 years which contributes to instability because of the limited number of years used for the catchability regressions (Figure 2.6.1.3). When using high shrinkage (=0.5) the retrospective bias was much smaller (~0.05) on both F and SSB. As both ICA and XSA gave
very similar perceptions of the state of the stock, the Working Group felt that the use of the ICA model was still appropriate. Continuing its use also maintains consistency with assessments in previous years.
2.6.1.5 Conclusions on the use of data in the NS assessment
The final choice of indices by year is given in Table 2.6.2.1. This choice was made on the basis of correlation and variance analysis and on data exploration carried out during the two previous Working Groups. The SGEHAP study group looked extensively at the issue of weighting and has selected values based on a full and careful study treating each index in a consistent manner. The WG has considered this with careful attention to retrospective patterns and come to the conclusion that the inverse variance weights were a good choice. The 0-1-ring catches were down-weighted because they are taken by a separate fleet that works independently of those exploiting older fish, but with a TAC which changes in a similar manner. These juvenile catches are probably a poorer indicator of juvenile abundance than the surveys. A down-weighting of these values seems to improve the analytic retrospective performance of the assessment (ICES 2002/ACFM:12)
2.6.2 The stock assessment 2.6.2.1 Model used
Assessment of the stock was carried out by fitting the integrated catch-at-age model (ICA) including a separable constraint over a five-year period as explained above (Patterson, 1998, Needle 2000), see Section 1.6 and the quality handbook.
2.6.2.2 Results
The ICA output is presented in Tables 2.6.2.2 and 2.6.2.3, with model fit and parameter estimates in Table 2.6.2.4, and in Figures 2.6.2.1 - 2.6.2.6. The standard graphical output of ICA is not shown. Rather a small program was written that could plot the result for each variable on the same page, so that comparisons can be made between indices. This was also motivated by technical difficulties with output from the ICAVIEW program. Uncertainty analysis of the final assessment is presented in Figure 2.6.2.7, although this only reflects the uncertainty in fitting the model and does not include uncertainty in the model specification. Estimates of fishing mortality at 2-6 ringer in 2002 vary between 0.21 and 0.28 (25 and 75 percentile respectively) and SSB in 2002 between 1.44 and 1.75 million tonnes. There appears to be a relatively good agreement between the point estimates of the final assessment and the median values of the Monte Carlo evaluations. Long-term trends in yield, fishing mortality, spawning stock biomass and recruitment are given in Figure 2.6.2.8.
The spawning stock at spawning time 2002 is estimated at approximately 1.6 million tonnes. Around 41% of the estimated SSB in 2002 consists of the 1998 year class (see Section 2.10). However, as noted last year, the 2000 year class is also estimated to be very strong. The current estimate of the 2000 year class as 1-ring fish is the third highest since 1960, so in the near future the stock is expected to increase further. The year classes 1998 and 2000 are now estimated as respectively 70.0 and 84.6 billion fish and are expected to contribute to a further increase of the spawning stock. The first estimate of the 2002 year class is 20.0 billion, which is based on the MIK index only.
Fishing mortality on 2-6 ringer herring in 2002 is estimated at around 0.24, and on 0-1-ringer herring at 0.04.
Analytic retrospective analysis of the assessment (Figure 2.6.2.9) shows a strong bias over the last 5 years (-0.3 in F2-6) but little variation in that bias (0.15 in F2-6, estimation method described in 1.6.3). Bias in the recruitment estimates is lower. The retrospective selection patterns show a marked change in 2001 (Figure 2.6.2.10), this is probably due to separable period moving back into the time of the change in the catching behaviour and management of the fishery in 1996. The issue of the retrospective bias is discussed in Section 2.10.5.
2.7 Short-term projection by fleets