Space-time modelling of blue ling for fisheries stock management

Fishery catch data offer a rich potential source of information for management, if modelling can separate out the effects of fishing effort, species behaviour and population abundance. Here, we model catch data from the blue ling fishery off the northwest coast of Scotland, using generalised additive mixed models with a space time interaction represented via a novel tensor product of a soap film smooth of space with a penalized regression spline of time. The use of soap film smoothers avoids imposing correspondences between spatially adjacent areas that are in fact separated by the stock boundary. The comparison of the performance of the soap film smooth for spacetime with that of a thin plate regression spline based on root mean squared prediction errors and k-means cross-validation suggests that in this application, the former is better overall and in particular for modelling local changes. Further, a model with continuous space-year interaction performed better compared with one with an additive space-year effect. After model selection, checking and validation, there is evidence for increasing blue ling abundance from 20002010 in some spatial locations. Copyright (c) 2013 John Wiley & Sons, Ltd.