A Simple Age- and Growth-Dependent Sequential Selectivity Function for Trawls - An Additional Module for the Eco²-Model.

The selectivity properties of trawls are traditionally given as a function of fish length. This saves time during selectivity trials at sea and enables rapid calculation of the selectivity properties of the trawls. The tedious age readings are not necessary. If we assume a constant Fulton’s condition factor of fish then the length-based selectivity properties for the specie under consideration are an exclusive characteristic of the used trawl described by the parameters length-selection factor, range-selection factor and mesh opening. The length-based selectivity function is independent of the growth rates of fish. This, however, is a disadvantage when it comes to exploitation models. The length based results can not immediately be used in management models. It is important also to know when growth rates change, for example, by changing forage availability. Fast-growing fish in good years is accessible earlier to fishery than slow-growing fish in starvation periods. An equation describing the selectivity properties of trawls as a function of time is needed. This can easily be accomplished by inserting the fish length as a time-dependent function. However, age-dependent selectivity functions are difficult to handle within the derivation of stock equations. They inflate the results and prevent partly closed analytical solutions. The goal here is not exciting new biological knowledge, but a new simple mathematical function which describes the retention probability of trawls with sufficient accuracy while allowing sequential calculations in a simple manner. An example illustrates at the end of the manuscript in an exemplary fashion how an overfished (food in abundance – constant growth) and an underutilized fish stock (limited food – low growth rate) responds on changes in recruitment which causes variable nutritional requirements.