An approach to weighting the various Operating Models in a Reference Set in inverse relation to the similarity of their results

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How to weight results from different OMs in getting a “best” representation across their differing results is a problem not only in fisheries but also in Climate Change. We attempt here to borrow an approach from the latter field and compare it to the conventional likelihood (or AIC) basis sometimes used in fisheries, which gives higher weights to models in a Reference Set (RS) that fit the data better. In contrast, a major problem perceived in Climate Change analyses, when averaging over an ensemble of models, is how to avoid “bias” through including too many models which scarcely differ amongst each other – one therefore downweights models on the basis of “nearness” of their results to each other. Here we apply a multi-dimensional scaling (MDS) approach which has been applied for weighting different Climate Change models to the RS developed for selecting the current OMP used to recommend TACs for the South African hake fishery. It is found that the MDS and AIC weights are very different, which begs the question of how then to “average” across these two distinct bases for model preference to perhaps obtain some combined weight. It was nevertheless found that in all the cases considered, the weighted RS provided a higher spawning biomass projection for M. paradoxus than the equally weighted RS used to select the current hake OMP in 2014. This suggests that, had some unequal weighting approach been used in 2014, it might have led to a slightly less conservative OMP, which allowed for greater catches to be taken, being selected.