2 NORTH SEA HERRING
2.10 Short Term Projection by Area and Fleet
Short term projections have been done as last year. There have been no changes in the basis of input parameters, but details are outlined below for completeness.
Fleet Definitions
The fleet definitions are the same as last year with fleets D and E still combined (called D in this report, but D&E in last year’s report), because there are no separate quotas for the two fleets. The fleet definitions are:
North Sea
Fleet A: Directed herring fisheries with purse seiners and trawlers Fleet B: All other vessels where herring is taken as by-catch Division IIIa
Fleet C: Directed herring fisheries with purse seiners and trawlers Fleet D: By-catches of herring caught in the small-mesh fisheries Input Data for Short Term Projections
All the input data for the short term projections are summarised in Table 2.10.1.
The starting point for the projection is the stock of North Sea autumn-spawners in the North Sea and Division IIIa combined at 1 January 2001. The ICA estimates of all age groups from 0–9+ are used (Table 2.8.12).
Catches by fleet in reference year: 2000 data from input files Table 2.2.6.
Stock Numbers:
For 2000 the total stock number was taken from ICA (Population Abundance year 2000, Table 2.8.12).
For 2001 the total stock number was taken from ICA (Population Abundance year 2001, Table 2.8.12).
For 2002 0-ringer the stock number was set to 44 000 million as used in the past four years. This value is very close to the estimate of 42 100 million obtained from the Beverton-Holt stock-recruit relationship in ICES 1998 C (Study Group on the stock-recruitment relationship in North Sea Herring), at an SSB of around 900 thousand tonnes.
Fishing Mortalities: fishing mortalities for age classes 2 and older are taken from Table 2.8.11 for 2000. Fishing mortalities for 0 and 1 ringers are calculated (see below).
Mean Weights at age in the stock: the averages of the last 2 years’ mean weights (1999 and 2000) were used (Table 2.8.5). Note that weights used in the assessment are already smoothed.
Maturity at age: The average maturity at age for 1999 and 2000 was used (Table 2.8.7)
Mean weights in the catch by fleet: A weighted mean of the last two years was taken i.e., 1999 and 2000 (Table 2.2.6), except for fleet D where the weights in 1999 were exceptionally low.
Proportion of M and F before spawning: Unchanged from last year at 0.67.
Proportions North Sea autumn spawners in the North Sea and Div. IIIa in 2001–2002 (Split factors)
Projections for North Sea herring were carried out by fleet and area. The proportion of 0- and 1-ringers that occur in Division IIIa is likely to vary between years depending on the size of the year class. The procedure for splitting is as last year, and the results are shown below.
The split factor used for the short term predictions distinguishes the proportions of North Sea autumn spawners being present in the North Sea and Division IIIa. Some of the split factors are directly estimated from surveys, other values are estimated from a general linear model (GLM) which relates the proportion of 1-ringers in Division IIIa to the MIK index of 0-ringers. This is discussed in detail below.
In general the split-factor is estimated from proportions of the IBTS 1-ringers in the North Sea and in Div. IIIa, and not from the 0-ringers. It is then assumed that the split-factor that applies to a year class as 1-ringers, also applied to that same year class as 0-ringers. The assumption is that the spatial distribution occurs as 0-ringers. 1-ringers remain in the area where they ended up as 0-ringers, and only migrate back to the North Sea from Division IIIa as 2-ringers. This assumption and the origin of the split-factors used in the short-term predictions are illustrated in the text table below.
Year 0-ringer distribution 1-ringer distribution
2000 (last yr in ICA) This split-factor (0-ringers in 2000) is equal to the split-factor of IBTS 1-ringers in 2001
This split-factor (1-ringers in 2000) is obtained from the proportions estimated for the 1-ringers in the IBTS in 2000
2001 (Assessment )
This split-factor is equal to the regressed 1-ringer distribution of 2001, i.e., obtained from the MIK value for 2001 (yr class 2000) and the GLM
This split-factor is obtained from the proportions estimated for the 1-ringers in the IBTS in 2001
2002 This split-factor is equal to that of 1-ringers in 2003, i.e., estimated by taking the average MIK index for the year classes 1981 to 1999 and the GLM to predict the split.
This split-factor is obtained from the MIK value for 2001(yr class 2000), and a general linear model (GLM) to predict the split.
This split-factor (1-ringers in 2003) is estimated by taking the average MIK index for the yr classes 1981-2000 and the GLM to predict the split-factor.
Summary of Proportions North Sea autumn spawners in the North Sea used in projections:
0-ringers 1-ringers 2000 0.547 0.654 2001 0.58 0.547 2002 0.67 0.58
The value of 1-ringers in 2002 and 0-ringers in 2001 (0.58) was determined by a general linear model between the MIK index and the IBTS 1-ringer proportion in Division IIIa (see comments below). The MIK index of 0-ringers in 2001 is 214.8 which predicts a proportion of 0.42 in Division IIIa (1-0.42=0.58 in the North Sea).
The value of 0-ringers in 2002 (and 1-ringers in 2003, which is not used) of 0.67 was estimated from the general linear model (identity link) and an average MIK index over 1981−2000 (141.5), which gives an estimated proportion of 0.33 in Division IIIa.
Comments on the General Linear Model
Table 2.10.2 shows the observed values and the two models: one with Gamma errors and an inverse link function, and one with Gamma errors and an identity link. The details of these models are discussed in O’Brien and Darby (1997, Working Document to HAWG) and Basson (1997, and 1998 Working Documents to HAWG). The analysis was done in Splus, and summary results are given in Table 2.10.3 for completeness. Results are not very different from those presented last year. For the range of MIK-observations, the two models lead to reasonably similar estimates of the proportion in Division IIIa. Both models are, however, likely to break down when used for prediction with an MIK index that lies outside the range of observed values. Problems are likely to be particularly acute if the predicted value is close to 0 or 1. The MIK index for 2001 is reasonably high (214.8), but not outside the range previously observed. The standard errors of the predicted values based on this MIK index are therefore high compared to predictions based on the mean MIK index (Table 2.10.2). The predicted values from the two models are also very similar. In the absence of any knowledge of a mechanistic relationship, the WG again used the linear model for prediction purposes. Model choice does not make a big difference to the predicted values this year.
Method for the short-term projections
The same spreadsheet used last year was used again, and the procedure is again described for completeness. The process is in two steps. The first is to compute local partial fishing mortalities for each fleet, corresponding to the stock in the area where the fleet operates. This is done using stock numbers and fleet wise catches the last assessment year, which is used as reference year. The next step is to project the stock forwards, starting with the stock numbers at the start of the first prediction year taken from the assessments, and applying the local fishing mortalities, each raised by an F-factor. Catches by fleet, the ensuing overall fishing mortality, and the SSB are computed and presented.
The area-specific stock numbers and fishing mortalities apply only to 0- and 1- ringers. Older fish are treated as one uniform stock, and can be found both in the North Sea and in IIIa.
The computation of local partial fishing mortalities in the reference year is done as follows:
• The initial stock number at age N0(a) is divided between the areas according to the assumed split factors.
• Stock numbers N1(a) at the end of the year are computed in each area j using Pope’s approximation:
N1j(a) = N0j(a)*exp(-M(a)) - Cj(a)*exp(-M(a)/2) where Cj(a) is the total catch at age in the area.
• Total local mortality Zj(a) is computed as log(N0j(a)/N1j(a)) and the total fishing mortality as Fj(a) = Zj(a)-M(a).
• Fleet wise partial F’s are obtained by dividing the total area F proportional to the catches
• For ages 2 and older, the total F according to the input is divided between the fleets proportional to the catches.
In the prediction itself, the local fleet wise partial F’s are manipulated by F-factors, which apply to all ages, i.e., the fishing pattern is kept. The process is as follows:
• The initial stock number at age N0(a) is divided between the areas according to the assumed split factors.
• The local (area j) partial F’s, as adjusted by the f-factors are used to compute the catches at age by fleet using Cj(a) = N0j(a)*(1-exp(-Z(j(a)))/Zj(a).
• Stock numbers N1(a) at the end of the year for the whole stock are computed in each area j using Pope’s approximation:
N1(a) = N0(a)*exp(-M(a)) - C(a)*exp(-M(a)/2) where C(a) is the total catch at age by all fleets.
• Total mortality Z (a) for the whole stock is computed as log(N0 (a)/N1(a)) and the total fishing mortality as F(a) = Z(a)-M(a).
• Yield is obtained by multiplying catches at age with fleet-specific weights at age.
SSB is obtained by first computing the stock numbers at spawning time as Nsp(a) = exp(-Z(a)*prop), where prop is the proportion of the mortality before spawning. These stock numbers are multiplied with weight at age in the stock, and summed over all ages.
stock. Therefore, the catches by the fleets in Division IIIa and in Subarea IV are not independent of each other. As a consequence, there are multiple solutions as to the share between the fleets even when fishing mortalities for juveniles (as F0-1) and adults (as F2–6) are specified. In order to get a unique solution, additional constraints in terms of catch ratios between fleets have to be specified. This must be done individually for each scenario. The 'Solver' facility in Excel is then used for finding the solution.
Prediction for 2001 and management option tables for 2002 Assumptions and Predictions for 2001
As in recent years, there have been some overshoot of the overall TAC for North Sea autumn spawners. A catch constraint, based on TACs and recent observed overshoots of the set TACs, was therefore used for projections in 2001.
Two kinds of information are needed to calculate the fleet specific catch constraints, the fraction of the TACs in Division IIIa which is assumed to represent autumn spawners, and the expected deviation from the TACs for each fleet.
We assumed that the proportion of autumn spawners in the TAC for fleets C and D would be similar to proportions observed in recent catches. The rounded, average proportion based on catches in 1999–2000 are 0.41 for fleet C and 0.72 for fleet D. The years 1999 – 2000 were used because the same regulations applied in those years as in 2001.
Furthermore, in recent years, the catches by the A fleet have been above the TAC, while they has been below the TAC or bycatch ceiling for the other fleets. Given that there are no changes in regulations which may change the way in which the fleets operate, the mean deviation in 1999 and 2000 was used for 2001. Thus, a 19% overshoot of the TAC was assumed for the A fleet in the North Sea, while the B fleet was assumed to take 49% of the bycatch ceiling in the North Sea, the C fleet 85% of the North Sea autumn spawner part of the TAC in Division IIIa, and the D fleet 76% of the North Sea autumn spawner part of the bycatch ceiling in Division IIIa. The low catch for fleet C is thought to be partly due to area misreporting, which contributes to the overshoot for fleet A. The resulting expected catches used as catch constraints for 2001 are shown in Table 2.10.4, which also includes the source of the data input to this calculation.
The overall overshoot is only about 7%, but it has an impact in the individual catches by fleet because it is not evenly distributed across fleets.
Management Option Tables for 2002
Table 2.10.5 gives management options for 2002. The upper table is based on TACs with overshoot in 2001. The lower table is based on F status quo = F2000. The method for estimating the expected catches by fleet was described above.
As noted above, in addition to constraints on fishing mortalities, some constraints in terms of relative catches between fleets are required to ensure that a unique solution for F-factors by fleet are obtained. The constraint used in the present examples is to keep the ratio of the catches by fleets A and C, and between fleets B and D constant, as noted in Table 2.10.5. It should be noted, however, that other ways of specifying the share of the outtake between fleets are also possible.
Since the adult fishing mortality in recent years has been considerably higher than assumed, a run with status quo F = F2000 for all years, including the intermediate year 2001 was included (Sc. VII). Likewise, a run was made with a fishing mortality in 2002 equal to that corresponding to the TAC constraint in 2001 (Sc. I). Furthermore, runs were made with catches in 2002 equal to either the assumed catches in 2001 (Sc. II), or to the adopted TACs for 2001 (Sc.
III). Scenarios with fishing mortalities at the levels adopted for SSB above and below 1.3 million tonnes (Sc. IV – VI) are also included. An overview of the scenarios considered is given in the text table below.
Scenario Assumption for
II Catches as estimated in
2001 none
Maintain catch ratios for fleets
All scenarios indicate a rapid increase in spawning biomass and in yield. This is caused mainly by the 1998 year class, which is believed to be strong. The following year classes are also believed to be relatively strong, and contribute further to the expected increase in SSB and yield.
The WG is concerned about the tendency of over-estimating projected SSB (see Figure 2.12.1). As noted in Section 2.8, this is usually because of downward revisions of the stock sizes in recent years in subsequent assessments. This issue is of particular relevance this year given (a) the high estimates of the year classes from 1998 and onwards, and (b) given that current estimated SSB is below Blim Taking the uncertainty estimated by ICA forwards, the range (5-percentile to 95 percentile) for SSB estimated by the ICP medium term prediction is 768 – 1634 thousand tonnes for 2001 and there is about 8% probability that it still will be below Blim = 800 000 tonnes. For comparison, the probability that SSB was below Blim in 2000 was 54%. The medium term prediction with STPR (see Section 2.11) indicates an even wider range (Figure 2.11.1).
Comments on the short-term projections
The need to revise the software for the short term predictions, and to evaluate the usefulness of the split of the stock of young herring was recognised in last years report. A study group has been established and has set up a work plan as described in Section 1.8.