Static versus dynamic model for forecasting salmon pre-fishery abundance of the River Bush: a Bayesian comparison

When catch levels are to be set annually in order to maintain escapement above a pre-determined threshold, a forecast of abundance is needed prior to fishery opening (pre-fishery abundance, PFA). In Atlantic salmon (Salmo salar), a simple approach for forecasting PFA is to use a measure of abundance of the stock available at the time the catch advice is elaborated (e.g. smolt counts) and, combined with knowledge about survival, derive an estimate of PFA. Adopting a Bayesian setting, we compare a static (i.e. time invariant) versus a dynamic model in a simple real-world case based on the River Bush (Northern Ireland, UK) data. The static model is a standard regression type model, i.e. the parameters associated to predictors are assumed fixed over time, whereas the more flexible dynamic modelling allows parameters to vary over time. We put forward an application-oriented approach for the comparison of models in relation to their management advice objectives, with cross-validation techniques being used to assess the quality of PFA forecasts. The flexibility of the dynamic model reveals advantages at a price, in terms of precision. Dynamic modelling appears as a valuable option for salmon PFA forecast which should be considered more systematically.