Introduction

BORMICON (BOReal MIgration and CONsumption model) is a simulation model and estimation model developed at the Marine Research institute. It is described in [1]. The model is designed as multispecies - multiarea model but can also be used as a single species model.

The main characteristics that distinguish the model from most stock assessment model is that the model stores number and mean weight of fish in each age and length group , not only in each age group. This means that growth has to be modelled. It is done by calculating the mean growth for each length group according to some growth equation, for example von Bertalanfy's equation. The next step is then to spread the growth. Then certain proportion of the fishes do not grow, some proportion grows one length group, some proportion two length groups, etc. The proportions are selected so the following 3 equations are satisfied.

$$\sum{p_i} = 1$$

$$\sum{ip_i} = \mu$$

$$\sum{i(p_i-\mu)^2} = \sigma^2$$

Here $\mu$ is the calculated mean growth and $\sigma^2$ the variance in growth, calculated from $\sigma^2 = K_0+K_1\mu$. K₀ and K₁are constants that are pre specified or estimated and control the spreading of the length distribution.

Often all three of the equations can not be solved exactly. Then the first equation is solved exactly and much more weight put on approximating the second equation than the third one. In summary this means that priority is put on not loosing fish (or gaining), then to get the mean growth (in length) correct and last to get the dispersion correct.

All fleets (predators) in the model have length based selection pattern. This means that fleets can select the largest individuals of each age group and therefore, affect mean weight at age.

The model does not use catch in number directly as input data, but rather length distributions, otholith samples and other data used to calculate catch in numbers. An objective function is then used to minimize the discrepancy between the model output and those data. This means that the model can use data that are not sampled regularly enough to calculate annual catch in number.

In the runs presented here two types of fleets are used.

1.

The total amount caught by the fleet is specified and distributed on different length groups according to abundance and the selection pattern. The same proportion is caught of each age group in a length group.

2.

The proportion caught (approximately fishing mortality when short timesteps are used) is specified. This proportion is then multiplied by the selection pattern so it is only for the length groups that are fully recruited that this proportion is caught. When fishing mortality is mentioned in this article it often refers to this proportion.

Fleets with total amount caught specified are used for the past but fleets with proportion caught specified are used in future simulations.

In the paper here the model is used to examine 4 stocks.

• Plaice
• Redfish
• Wolffish
• Haddock

The formulation used is a relatively simple one. It's main characteristics are.

• One area
• Two fleets catching each species, a commercial fleet and a survey. Selection patterns of both fleets are described by a logit function, whose parameters are estimated
• Growth is described by the von Bertalanffy's function.

Data used in the objective function to be minimized are.

• Length distributions from commercial catch and survey
• Age length keys p(a/L) from commerical catch and survey
• Length disaggregated survey indices (most often in 5cm length groups)
• Mean length at age from survey, and commercial catches
• Understocking (Not enough biomass exists to cover the catch)

The total objective function to be minimized is a weighted sum of the different components. Selection of the weights is more or less ad hoc and can affect the final results greatly.

Estimated data were.

• Initial number in each age group
• Recruitment each year
• Parameters in the growth equation
• Selection patterns of commercial fleet and survey. Two parameters for each fleet

The estimation can at times be tricky as some of the parameters are strongly correlated. Fixing some parameters temporarily and relaxing them later can help in the estimation process.

When the estimation is finished the following things are examined.

• Development of catchable biomass the next years using some different catch options
• Yield per recruit is calculated based on the estimated growth parameters and selection pattern of the commercial fleet. This differs from traditional yield per recruit as the catch affects mean weigth at age, due to length based selection
• F_0.1 is calculated from the Y/R curve and development of catch and catchable biomass is calculated based on F_0.1.

The amount of available data varies greatly for the species investigated here. Most data are availvable for haddock where extensive otholith and length sampling has been done for decades. XSA has been used for haddock in recent year. The only goal of including haddock here is to see what the model does with a stock where a comparison is available. It must though be born in mind that even if the model performs well on haddock it does not nessecarily mean that is performs well on those stocks where much less data exist.