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Case study 9: Approach 1: Evaluation of different cod stock assessment models

Data and parameters

Stock data

Stock assessment data were taken from Baltic Fisheries Assessment Working Group, WGBFAS (ICES, 2006). Growth in future was assumed as average of observed values (data from WGBFAS). Analyses conducted so far did not indicate large changes in cod growth or density dependent effects.

Fleet data

Data on catch volume and catch at age in numbers (total and by fleets) were taken from WGBFAS (ICES, 2006).


Two approaches in modelling were undertaken. In first (Approach A) the models were fitted to observed data for Baltic cod stock and fishery and used for prediction. In second (Approach B)the models were fitted to generated stock dynamics, where different aspects of cod biology and exploitations were simulated, aspects no covered (or partly covered) by applied assessment models. In addition, in that approach the effect of bias in age reading on XSA estimates was analysed.

FLR: Packages used are FLCore Ver 1.4-4, FLXSA, FLSR, FLBRP, FLAssess

Data inputs are modelled by the FLCore classes FLStock, FLIndices, FLBiol, which contain all the input data required for and the outputs from the conditioning.

Approach A

The age independent models were used for stock assessment and the management advice. It were used both the stock-production (e.g. Schaefer 1954, Pella and Tomlinson 1969) and difference models with explicit recruitment sub-model (e.g. Horbowy 1992). The models were fitted to observed catches and/or survey indices of stock size with effort and (in case of difference models) recruitment indices. The fishing effort was standardised based on catch and effort data from major countries catching cod.

FLR (Operating Model)

The model is based on the approach of Horbowy (2005) developed to overcome problems resulting from changing gear and survey design. It is the age-structured assessment model which fits model estimates of total mortality (Z) to survey estimates of Z. In 2001 new standard gear was introduced in cod bottom trawl survey. To make use of both old series of survey data (till 2001) and new data (since 2001) the calibration experiments were conducted and old survey data were recalculated into new units. Many calibration experiments were conducted and advanced statistical methods were used to derive correction factors to old data.

However, it were still some doubts if observed signal in the survey data was result of stock increase or effect of new gear and especially change of survey design – this created some controversy when parameterizing XSA during WGBFAS meeting in 2004 (ICES, 2004). Two option for the XSA parameterization were presented: one used 0.5 as SE of the F-shrinkage mean while the other used 0.75. Obviously, the option with higher SE of the shrinkage mean resulted in assessment incorporating more signal from the survey than the option with SE of 0.5. As this signal shows increase in stock size in recent years the SSB estimated by XSA incorporating 0.75 as SE of the F-shrinkage mean showed more optimistic view of the stock size in recent years than the 0.5 option. However, the question arises if the signal is true. The answer to this question can not be only based on the XSA diagnostic: the options with released shrinkage will usually give better diagnostics in terms of correlations and residuals as shrinkage introduces some bias into the assessment. As developed method (Horbowy, 2005) fits model estimates of Z to its survey estimates, it works on relative scale and avoids problems with gear change (especially, if survey estimates of Z, referring to year when gear was changed, were excluded or downweighted). In the developed model the recalculation of the old survey data into new units is not needed.

Conditioning of Operating Model

The operating model was conditioned on survey data and catch at age data. The approach of Horbowy (2005) was used.

Approach B

The goal of this analysis is to investigate the models performance using Operating Models. Thus, cod stock with specific dynamics and harvest rules will be generated for series of years, next the data from generated stock needed for assessment will be sampled, and assessment with Schaefer/difference models performed. Finally, obtained results will be compared with generated values to see how well the models approximate stock, given imposed aspects of the generated stock.

The Operating Model consists of three parts:

  • 1st, historical part provides conditioning of the model by fitting it to survey observations from 1980-2004,
  • in 2nd, future part of the model, cod stock/fisheries with specific aspects is generated for 2005-2024, using values estimated in historical part, including stock numbers for 2005 as starting point of simulation,
  • in 3rd part the values generated in 2nd part are sampled for catch at age and survey at age, and next the Schaefer and difference models are used to re-estimate stock dynamics on the basis of sampled values.

The 3rd part was repeated usually 200 times to produce Monte Carlo replicates for each assumed values of CV for catch at age sampling and survey indices at age samples. In addition to difference and production models, for comparison of estimation abilities of the models, the XSA was also used in the 3rd part to estimate stock size. As the age reading of Baltic cod is problematic and there are large inconsistencies in aging from different countries, the options were provided where sampled age was biased, to see how much it influences the stock and mortality estimates. The conditioning of the model was based on approach of Horbowy (2005)(see Approach A).

In the 2nd part of the model the following options were included in simulations:

  1. initial stock numbers (2005) estimated in conditioning part of the Operating Model,
  2. stock-recruitment relation from FLR, the hockey-stick model was selected, but it is possible to use other models as well (e.g. Ricker, Beverton & Holt); the model parameters (including CV for error) were estimated in conditioning part of the Operating Model,
  3. two gears: trawl and gill-net which may differ both in catchability and selectivity,
  4. stock assessment with Schaefer (1954) or difference model (Horbowy, 1992), in addition assessment with XSA,
  5. management with two options:
    • F-status quo
    • Harvest Control Rule (HCR) in which
             F = Flow for SSB<Blim,
             F = Fpa for SSB>Bpa
             F lineary decreases from Fpa to Flow for  Blim < SSB < Bpa

The weight at age, maturities, and natural mortality were kept constant and equal to average from values used in historical part of the Operating Model. The variability into the generated values was introduced by adding random log-normal error to initial stock numbers and to recruitment resulting from hockey-stick sub-model.

The weight at age, maturities, and natural mortality were kept constant and equal to average from values used in historical part of the Operating Model. The variability into the generated values was introduced by adding random log-normal error to initial stock numbers and to recruitment resulting from hockey-stick sub-model.

In 3rd part of the Operating Model data from generated stock and fishery (survey cpue, catch, fishing effort, catch at age data) were drawn at random to be used in assessment of stock size with Schaefer, difference, or XSA model. Drawing was simulated by adding to generated value random log-normal error with the SE in catch and effort ranging from 0.1 to 0.3 with step 0.1, and with survey SE varying from 0.15 to 0.45 with step 0.15. Next, assessment were performed using Schaefer model, difference model, and XSA. Assessment results (biomass, fishing mortalities, stock size at age in case of XSA) were compared with generated values. The following scenarios in generated values (2nd part of Operating Model) were considered:

  1. Basic: hockey stick Stock-Recruitment and constant selectivity.
  2. Basic & and high change in recruitment in 6th and 7th simulation year; recruitment resulting from S-R function was increased by 100% and 50%, respectively. The aim of this scenario was to simulate improvement in environment condition for cod reproduction.
  3. Basic & and high change in selectivity to simulate change in gears and mesh size in cod fishery (introduction of Bacoma window and T90 trawls). In 10th simulation year selectivity changed at age 2, 3, 4 from 0.12, 0.50, 0.94 to 0.21, 0,65, 1.08, respectively.
  4. Basic & included systematic error in age reading, e.g. 50% at given age is read correctly while 50% is over-aged by 1 year. Two options were considered: over-aging (i.e. reader gives for some fish age older than true age) and under-aging (i.e. reader gives for some fish age younger than true one). It was assumed that mis-aging is by 1 year only.
Historical Estimates of Time Series

Stock numbers at age are estimated with Horbowy (2005) model.

Biological Parameters

Growth (weight at age in catch and stock) and maturity were taken from WGBFAS data.

Stock Recruitment Relationships

Stock and recruitment model was assumed as hockey-stick (double linear, segmented regression), with inclussion of environmental eefects. The recruitment sub-models were fitted to recruitment numbers and stock size estimated within Horbowy (2005) approach.

Fisheries & Fleets

In this simplified approach differences in fleets are not taken into account.


No economic model was applied as in this approach neither age structure no fleets are relevant. Thus economic model would mainly lead to recalculation of catches from volume units into money units.

Reference Points

BRPs developed within ICES (established in 1998) were used. In April - May 2008 these biomass reference points are considered not valid, following ICES findings. Now new biomass points were proposed so far.

Observation Error Model

Error in catch volume and/or survey estimates of stock size was taken into account.

Management Procedure

Two management alternatives were considered. One was a F-status quo approach, second was Harvest Control Rukle (HCR) in which

     F = Flow for SSB<Blim,
     F = Fpa for SSB>Bpa
     F lineary decreases from Fpa to Flow for  Blim < SSB < Bpa


Approach A

Analyses with production/difference models

The derived effort indices correspond well to estimates of fishing mortality from XSA (ca. 90% of variance explained).

The estimates of cod biomass with Schaefer (1954) stock-production model and difference model (Horbowy, 1992) show similar trends and values as estimates from the XSA, applied in ICES assessment. However, these models basing on commercial effort data produce higher biomasses in recent years than the XSA, which may be related to severe underreporting of Baltic cod catches. The MSY from Schaefer model is 230,000 tons and related F is 0.38, comparing to recent years F of above 1.0. The Fox (1970) model fits badly producing strong effects in residuals. The Pella & Tomlinson (1969) model was tried for range of assumed shape (n) parameters (there is not enough information in the data to fit all parameters simultaneously). The best fit was obtained for n=0.8, but estimates of MSY and carrying capacity were unrealistic. Results obtained so far are summarised in Horbowy (2006)

Retrospective patterns are most consistent for difference model. In case of Schaefer model retrospective estimates of biomass are consistent in recent years and diverge very much for 1980s. Retrospective predictions of biomass and catches are shown in Fig. 1. For the 1998-2001 the biomass predicted by the models was closer to biomass observed (estimates from most recent assessment) than the biomass predicted by ICES.

Schafer model predictions of catches were most divergent from observed catches, especially for 1997-1998. Predictions by difference models and ICES predictions deviated similarly from observed catches. The table below presents mean relative difference between predicted and observed biomass and catches for both models and ICES predictions.

Schaefer Difference ICES
catches 0.61 0.27 0.37
biomass 0.56 0.51 0.78

The analysis shows that retrospective predictions by Schaefer and difference models of status quo biomass and catches deviate less (or similarly) from the observed catches and biomass than (as) the ICES predictions based on XSA.

Biological Operating model fit

Conducted analysis indicates that developed biological operating model produces similar estimates of stock size and fishing mortality as ICES estimates with XSA using shrinkage SE of 0.5. However, these estimates differ substantially from XSE with shrinkage SE of 0.75.Results obtained so far with OM are presented partly in .ppt file

Approach B

Results are presented in terms of median of estimated variables (SSB, average fishing mortality F-bar, stock numbers and fishing mortality at age in terminal year). The medians are compared with generated values.

Scenario 1

The difference model performed quite well and average relative difference between generated SSB and biomass estimated by the model was 4% and 21%, respectively for exploitation strategies with Fsq and HCR defined in methods section. The Schaefer model reproduced generated values less precise, relative error with respect to generated values were 33% and 28% for Fsq and HCR, respectively (Fig. 1 and 2).

Scenario 2

The disturbance in recruitment in 6th and 7th simulation year did not effect much difference model – its errors with respect to generated values were on average 6% and 9% for Fsq and HCR exploitation, respectively. In case of Schaefer model the error reached to 33% and 29% for considered exploitations, respectively (Fig. 1 & 2). Better behavior of the difference model could be expected as in this approach recruitment is explicitly simulated which is not the case for the Schaefer model.

Scenario 3

The simulated change in selectivity in 10th year affected both models, but the negative effect was stronger on Schaefer model results. Errors of SSB for difference model were 16 and 20% for Fsq and HCR, respectively. For Schaefer model these errors reached 32 and 26%, respectively (Fig. 1 & 2).

Scenario 4

The bias in age reading had different effects on XSA results, depending if bias in catch at age was similar to that in survey at age. Different variables estimated with XSA were differently effected. The lowest was impact on SSB as bias in catch at age implicated also opposite bias in weight at age and these two effects cancelled to large extent, especially when bias in catch at age was the same as bias in survey indices at age. Then error in SSB was 2-3% and it increased to 15-20% when bias in survey at age was smaller than bias in catch at age (Fig. 3). Error in fishing mortality Fbar was higher than that of SSB and it varied mainly from 5 to 10% (Fig. 4). The most effected by error were stock numbers and fishing mortality in terminal year (Fig. 5 and 6). For terminal stock numbers bias ranged from 10-15% for ages 2-3 till up to 150% for ages 6-8. Terminal F was biased by -60 to 20% and higher was bias at younger ages. The bias in terminal numbers and F is serious problem as these values are basis for ICES short-term projection. Basic conclusion from this analysis is that with biased age reading we are able to provide relatively good estimates of historical stock biomass and to lower extent F, but terminal stock size and fishing mortality are very seriously biased.

Conclusions from simulations results

  1. Production/difference models
  • Difference model performed much better that Schafer model
  • For difference model disturbance in recruitment did not create major errors while change in selectivity produced bias in biomass estimates
  • For Schaefer model in all scenarios huge deviations from generated values were observed
  1. XSA and aging bias
  • When catch at age and survey at age bias were the same, estimates of SSB differed very little from generated values. This error was somewhat higher in case of historical fishing mortality, and increased when catch at age and survey at age bias were very different.
  • The age bias had very big effect on stock and F estimates in terminal year.


Horbowy, J. 2005. Cod assessment model with tuning to survey estimates of total mortality. Working paper to the WGBFAS, Hamburg, 12-21 April, 2005

Horbowy, J. 2006. Management of the eastern Baltic cod with stock-production or difference models. Poster to ICES Symposjum on evaluation of management strategies. SFMS 44, Dublin 2006

Horbowy, J. 2007. Two models of cod management – is complex model better ? (in Polish). Conference on Mathematical models: explanation o rover-simplification of ecology. University of Toruń, Toruń, Poland

Kronbak, L., Lindroos M. 2006. An Enforcemen-Coalition Model:Fishermen and Authorities Forming Coalitions. Environmental and Resource Economics, 35: 169-194.

Pietikäinen, L. 2005. Cod fishery of the European Union and Russia at the Baltic Sea - a game theoretic analysis. Department of Economics and Management, Working Papers no 30, University of Helsinki

Links to Other Work

This work has been done in collaboration with work conducted in relation to the ICES Baltic Assessment Working Group, ICES WGBFAS.


Fox, W.W. 1970. An exponential surplus yield modelf or optimizing exploited fish populations. Trans. Am. Fish. Soc., 99:80-88

Horbowy, J. 1992. The differential alternative to the Deriso difference production model. ICES J. mar. Sci. 49:167-174

ICES. 1994. Report of the Workshop on Baltic Cod Age Reading. ICES CM 1994/J:5

ICES. 1999. Report of the Study Group on Baltic Cod Age Reading. ICES CM 1999/H:Baltic Committee

ICES. 2006. Report of the Study Group on Aging issues of Baltic Cod. ICES CM 2006/BCC:08

Pella, J.J., Tomlinson, P.K. 1969. A generalized stock production model. Bull. Inter-Am. Trop. Tuna Comm. 13:419-496

Schaefer, M.B. 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bull. Inter-Am. Trop. Tuna Comm., 1:25-56

Shepherd J.G. 1999. Extended survivors analysis: An improved method for the analysis of catch-at-age data and abundance indices. ICES J. mar. Sci., 56: 584-591


This work has been done in collaboration with work conducted in relation to the ICES Baltic Assessment Working Group, ICES WGBFAS.

EFIMAS Contribution to the work

The far major part of the work has been done under the EU-FP6-EFIMAS Project.

Participants: Jan Horbowy (SFI), Magdalena Podolska (SFI), Ryszard Grzebielec (SFI), Krzysztof Radtke (SFI)


Notes: See text from Meeting Minutes WP4 from EFIMAS Maastricht Meetings, September 2006.

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