Modelling selectivity as a random walk process for the offshore trawl fleet for M. paradoxus

In the current South African hake Reference Set of assessments, commercial fishing selectivity is assumed to be constant over fixed, pre-defined periods. In the case of the offshore trawl fleet, the three periods of fixed and changing selectivity (pre-1977, 1977-1984, and post-1992) have been selected to take account of the changes in the selectivity likely due to the phasing out of the (illegal) use of net liners to enhance catch rates. For the longline fleet, three periods have also been selected (pre-1999, 2000 2005, and post-2005). These have been chosen by examining the residual patterns of the fit to the catch-at length data for that fleet.

In this analysis, the selectivity of M. paradoxus by the offshore trawl fleet (the largest component of the catches) is modelled instead as a random-walk process (similar to the approach in SAM) to allow it to vary more freely over time (see Appendix A for details). Catch-at-length data for the offshore trawl fleet are currently available for the period 1981-2012 (with a gap over 2000-2004) for the west coast, and over 1975-1996 for the south coast. The random walk process is therefore estimated only for those periods for which data are available; for the remainder of the assessment period, averages are used (see Table A.1). The reason why a random walk process cannot be readily estimated for both M. paradoxus and M. capensis is that the data available are not disaggregated by species. The exercise here is intended as a simple first cut to examine the potential of such a model for selectivity.