Spatial age-length key modelling using continuation ratio logits

Many fish stock assessments are based on numbers at age from research sampling programmes and samples from commercial catches. However, only a small fraction of the catch is typically analyzed for age as this is a costly and time-consuming process. Larger samples of the length distribution and a so-called age-length key (ALK) is then used to obtain the age distribution. Regional differences in ALKs are not uncommon, but stratification is often problematic due to a small number of samples. Here, we combine generalized additive modelling with continuation ratio logits to model the probability of age given length and spatial coordinates to overcome these issues. The method is applied to data gathered on North Sea haddock (Melanogrammus aeglefinus), cod (Gadus morhua), whiting (Merlangius merlangus) and herring (Clupea harengus) and its implications for a simple age-based survey index of abundance are examined. The spatial varying ALK outperforms simpler approaches with respect to AIC and BIC, and the survey indices created using the spatial varying ALK displays better internal and external consistency indicating improved precision.