Simulated data sets Extracted from:

The data sets shared a common time period of 30 years and age range from 0 to 16 years. The data were provided to the analysts as data files for recorded catch at age, weight at age, fraction mature at age, two surveys covering different age ranges 1, 2, and 5—16. These three different data sets were generated, one without any noise (data set 1), one with noise both in survey data and commercial catches (data set 2) and one in which the selection pattern of surveys and catches varied over time over the last 10 years, along with noise in the survey and catch data (data set 3). Thus, data sets 1-3 provided an increasing complexity of challenge to the models, and data set 3 was considered to be similar to a number of real world applications, including those faced by the Working group.

The underlying stock model was made close to the dynamics of the Norwegian spring spawning herring, and had the following characteristics: Simulated recruitments were drawn from a multinomial distribution, with different mean-variance characteristics for “good” vs. “poor-average” year classes. The probability for “good” recruitment was 1 in 8, and in the case of good recruitment the recruitment was drawn at random with a uniform probability between 50 and 100 units. In cases of poor to average recruitment, the recruitment was drawn at random with a uniform probability between 1 and 10 units. The instantaneous coefficient of natural mortality (M) is set to 0.15 for all age groups, which is input as a given (not estimated) by the assessment programs.

In data sets 2 and 3 the catch is generated with an assumed sampling error. The error in catches was generated from the true catch data using a gamma distribution with the CV of 0.3 with a probability of 0.9 and the CV of 0.9 with a probability of 0.1. One survey for the adult stock (age 5-16) and one survey for the juvenile stock (age 1-2) were simulated. For the adult stock survey, the following model for the selection-at-age parameters for the survey was applied: (1.0 – exp (-(age – 5))), age <= – exp (0.072 (age – 10)), age > 5 It was noted that one of the problems connected to the assessment of Norwegian spring spawning herring was whether this stock is separable. Recruitment of large year classes from the Barents Sea to the fishery in the Norwegian Sea may generate non-separability due to the fishing fleet operating on different age components of the stock. The Norwegian fleet operates along the Norwegian coast, thus largely missing newly recruited year classes, while vessels from other countries operate in the Norwegian Sea. This effect was incorporated in data set 3.

Recruitment in numbers was interpolated linearly from 1.0 when the change starts to 0.0 at the end of the period. The effect was a gradual remove of the downward part of the selection for older fish. The survey data were generated using an expected value of the true stock values multiplied by the above selection. For survey 2 a flat selection pattern was used. For data sets 2 and 3 a gamma distribution with a CV of 0.2 was used to generate noise in the survey data. Also, a year effect was added by drawing a random number uniform in (0.7,1.3) that was applied to all age groups in each survey. The year effects in each survey were independent. Additionally, the age distribution was multiplied by a normalized age distribution obtained by drawing from the multinomial distribution with N = 1000 and expected values equal to the original normalized age distribution. The rationale for this is that the relative uncertainty tends to be larger for weak year classes where the determination of age-disaggregated abundance relies on only a few scales or otoliths. This created not only additional variance, but also a bias that was nonlinearly dependent on abundance.

In simulations the underlying stock was started with a uniform age structure and run over 30 years to yield an age structure complying with the chosen recruitment model. During the subsequent 30-year data generation period, first the two survey numbers at age were generated. The stock was simulated forward by using the modelled catch selection, (i.e. the catches were assumed to taken gradually during the year). The plus group was updated by adding the oldest true age group and the stock was reduced by natural mortality and fishing mortality. In order to generate a number of outliers, with a probability of 0.1 the standard deviation of perceived catches and surveys were multiplied by 3. All the above mentioned details were not reported to the working group members before the assessment.